Finite Group Databasebeta

← C3×#62983 #10681590

Subgroups — C3×#62983 #10681590

Order 768.

8054 conjugacy classes of subgroups.

The subgroup lattice has 1118 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3519C218yesmaximal, complemented
2C3×#3519C214yesmaximal, complemented
3C3×#3514C214yesmaximal, complemented
4C3×#3513C218yesmaximal, complemented
5C3×#3508C212yesmaximal, complemented
6C3×#3505C214yesmaximal, complemented
7C3×#3501C211yesmaximal, characteristic, complemented
8C3×#3494C214yesmaximal, complemented
9C3×#3490C218yesmaximal, complemented
10C3×#3484C212yesmaximal, complemented
11C3×#3481C214yesmaximal, complemented
12C3×#3475C212yesmaximal, complemented
13C3×D4×#41C214yesmaximal, complemented
14C2×C3×#546C214yesmaximal, complemented
15C2×C3×D42C211yesmaximal, characteristic, complemented
16C3×C4×H(5,𝔽2)C211yesmaximal, characteristic, complemented
17C2×C3×#518C212yesmaximal, complemented
18#62983C311yesmaximal, characteristic, direct product factor, Sylow
19C2×C3×H(5,𝔽2)C2211yescharacteristic
20C22×C3×#41C2214yescomplemented
21C23×C3×D4C2212yes—
22C23×C3×D4C2212yescomplemented
23C3×#559C2214yescomplemented
24C3×#559C2214yescomplemented
25C3×#556C2212yescomplemented
26C3×#555C2212yescomplemented
27C3×#555C2218yescomplemented
28C3×#554C2212yescomplemented
29C3×#554C2214yescomplemented
30C3×#554C2218yescomplemented
31C3×#553C2214yescomplemented
32C3×#553C2218yescomplemented
33C3×#553C2218yescomplemented
34C3×#553C2218yescomplemented
35C3×#553C22116yescomplemented
36C3×#552C2214yescomplemented
37C3×#552C2214yescomplemented
38C3×#551C2218yescomplemented
39C3×#551C22116yescomplemented
40C3×#551C22116yescomplemented
41C3×#551C22116yescomplemented
42C3×#550C2214yescomplemented
43C3×#550C2214yescomplemented
44C3×D4×Q8C2214yescomplemented
45C3×#548C2218yescomplemented
46C3×#547C2212yescomplemented
47C3×#547C2218yescomplemented
48C3×#546C2214yescomplemented
49C3×#546C22116yescomplemented
50C3×#546C2218yescomplemented
51C3×#546C2218yescomplemented
52C3×#546C2218yescomplemented
53C3×#546C2218yescomplemented
54C3×#546C2218yescomplemented
55C3×#546C22116yescomplemented
56C3×#546C22116yescomplemented
57C3×#546C22116yescomplemented
58C3×#546C2218yescomplemented
59C3×D42C2214yescomplemented
60C3×D42C2218yescomplemented
61C3×D42C2214yescomplemented
62C3×D42C2218yescomplemented
63C3×D42C2218yescomplemented
64C3×#544C2212yescomplemented
65C3×#543C2214yescomplemented
66C3×#542C2218yescomplemented
67C3×#540C2218yescomplemented
68C3×#540C2218yescomplemented
69C3×#539C2218yescomplemented
70C3×#538C22116yescomplemented
71C3×#538C22116yescomplemented
72C3×#538C2218yescomplemented
73C3×#535C2214yescomplemented
74C3×#534C2218yescomplemented
75C3×#533C2212yescomplemented
76C3×#532C2218yescomplemented
77C3×#532C2214yescomplemented
78C3×#532C2214yescomplemented
79C2×C3×#127C2211yescharacteristic, complemented
80C3×#529C2218yescomplemented
81C3×#529C2214yescomplemented
82C3×#529C2218yescomplemented
83C3×#529C2218yescomplemented
84C2×C3×#124C2214yescomplemented
85C3×#525C2214yescomplemented
86C3×#525C22116yescomplemented
87C3×#525C22116yescomplemented
88C3×#525C2218yescomplemented
89C2×C3×#123C2218yescomplemented
90C2×C3×C22⋊Q8C2214yescomplemented
91C2×C3×#121C2212yescomplemented
92C2×C3×#121C2212yescomplemented
93C2×C3×#121C2214yescomplemented
94C2×C3×#121C2218yescomplemented
95C2×C3×#120C2214yescomplemented
96C2×C3×#120C2218yescomplemented
97C3×#520C2212yescomplemented
98C3×#520C2214yescomplemented
99C3×#518C2211yescharacteristic
100C3×#518C2212yes—
101C3×#518C2218yescomplemented
102C3×#518C2214yescomplemented
103C3×#518C2214yescomplemented
104C3×#518C2218yescomplemented
105C3×#518C2218yescomplemented
106C3×#518C2214yescomplemented
107C3×C4×#41C2212yescomplemented
108C3×C4×#41C2214yescomplemented
109C3×C4×#41C2214yescomplemented
110C2×C3×C4×D4C2211yescharacteristic
111C2×C3×C4×D4C2211yescharacteristic, complemented
112C2×C3×C4×D4C2214yescomplemented
113C2×C3×C4×D4C2218yescomplemented
114C2×C3×C4×D4C2218yescomplemented
115C2×C3×C4×D4C2214yescomplemented
116C2×C3×C4×D4C2214yescomplemented
117C2×C3×#117C2214yescomplemented
118C22×C3×C22⋊C4C2218yescomplemented
119#3519C2×C318yescomplemented
120#3519C2×C314yescomplemented
121#3514C2×C314yescomplemented
122#3513C2×C318yescomplemented
123#3508C2×C312yescomplemented
124#3505C2×C314yescomplemented
125#3501C2×C311yescharacteristic, complemented
126#3494C2×C314yescomplemented
127#3490C2×C318yescomplemented
128#3484C2×C312yescomplemented
129#3481C2×C314yescomplemented
130#3475C2×C312yescomplemented
131D4×#41C2×C314yescomplemented
132C2×#546C2×C314yescomplemented
133C2×D42C2×C311yescharacteristic, complemented
134C4×H(5,𝔽2)C2×C311yescharacteristic, complemented
135C2×#518C2×C312yescomplemented
136C25×C3C2314yes—
137C3×H(5,𝔽2)—28no—
138C2×C3×#41—416no—
139C2×C3×#41C2314yes—
140C2×C3×#41C2312yes—
141C2×C3×#41C2314yes—
142C2×C3×#41C23116yescomplemented
143C2×C3×#41C2318yescomplemented
144C2×C3×#41C2318yescomplemented
145C22×C3×Q8C2314yescomplemented
146C22×C3×D4—216no—
147C22×C3×D4—48no—
148C22×C3×D4C2318yes—
149C22×C3×D4C2314yes—
150C22×C3×D4C2312yes—
151C22×C3×D4C2318yes—
152C22×C3×D4C2311yescharacteristic
153C22×C3×D4C2314yes—
154C22×C3×D4C2314yes—
155C22×C3×D4C2314yes—
156C22×C3×D4C2314yes—
157C22×C3×D4C2318yes—
158C22×C3×D4C2314yes—
159C22×C3×D4C2312yes—
160C22×C3×D4C2312yes—
161C22×C3×D4C2311yescharacteristic
162C22×C3×D4C2318yescomplemented
163C22×C3×D4C2318yescomplemented
164C23×C3×C4C2312yes—
165C23×C3×C4C2312yes—
166C23×C3×C4C2318yescomplemented
167C23×C3×C4C2314yescomplemented
168C23×C3×C4C2318yescomplemented
169C3×C4⋊Q8C2312yescomplemented
170C3×C4⋊Q8C2312yescomplemented
171C3×C4⋊Q8C2318yescomplemented
172C3×#127C2314yes—
173C3×#127C2314yes—
174C3×#127C2318yescomplemented
175C3×#126C2318yescomplemented
176C3×#126C2318yescomplemented
177C3×#126C2318yescomplemented
178C3×#126C23116yescomplemented
179C3×#126C23116yescomplemented
180C3×#125C2314yescomplemented
181C3×#125C2318yescomplemented
182C3×#125C2318yescomplemented
183C3×#125C2314yescomplemented
184C3×#124C2314yes—
185C3×#124C2318yescomplemented
186C3×#124C2318yescomplemented
187C3×#124C2318yescomplemented
188C3×#124C23116yescomplemented
189C3×#124C2318yescomplemented
190C3×#124C23116yescomplemented
191C3×#123C2318yes—
192C3×#123C2318yes—
193C3×#123C23116yescomplemented
194C3×#123C23116yescomplemented
195C3×#123C23116yescomplemented
196C3×#123C23116yescomplemented
197C3×#123C2318yescomplemented
198C3×#123C23116yescomplemented
199C3×#123C23116yescomplemented
200C3×#123C23116yescomplemented
201C3×#123C2318yescomplemented
202C3×C22⋊Q8C2314yes—
203C3×C22⋊Q8C2318yes—
204C3×C22⋊Q8C2314yes—
205C3×C22⋊Q8C2318yescomplemented
206C3×C22⋊Q8C2318yescomplemented
207C3×C22⋊Q8C2314yescomplemented
208C3×C22⋊Q8C2318yescomplemented
209C3×C22⋊Q8C2314yescomplemented
210C3×C22⋊Q8C23116yescomplemented
211C3×C22⋊Q8C23116yescomplemented
212C3×C22⋊Q8C23116yescomplemented
213C3×C22⋊Q8C2314yescomplemented
214C3×#121C2318yes—
215C3×#121C2314yes—
216C3×#121C2318yes—
217C3×#121C2318yes—
218C3×#121C2318yes—
219C3×#121C2318yes—
220C3×#121C23116yescomplemented
221C3×#121C2318yescomplemented
222C3×#121C23116yescomplemented
223C3×#121C23116yescomplemented
224C3×#121C23116yescomplemented
225C3×#121C2314yescomplemented
226C3×#121C23116yescomplemented
227C3×#121C23116yescomplemented
228C3×#121C23116yescomplemented
229C3×#121C2314yescomplemented
230C3×#121C2318yescomplemented
231C3×#121C2318yescomplemented
232C3×#121C2318yescomplemented
233C3×#120C2318yes—
234C3×#120C23116yes—
235C3×#120C23116yes—
236C3×#120C23116yes—
237C3×#120C23116yescomplemented
238C3×#120C23116yescomplemented
239C3×#120C23116yescomplemented
240C3×C4×Q8C2312yescomplemented
241C3×C4×Q8C2312yescomplemented
242C3×C4×Q8C2314yescomplemented
243C3×C4×Q8C2314yescomplemented
244C3×C4×Q8C2314yescomplemented
245C3×C4×Q8C2314yescomplemented
246C3×C4×D4C2314yes—
247C3×C4×D4C2314yes—
248C3×C4×D4C2314yes—
249C3×C4×D4C2314yes—
250C3×C4×D4C2314yes—
251C3×C4×D4C2314yes—
252C3×C4×D4C2312yes—
253C3×C4×D4C2318yes—
254C3×C4×D4C2318yes—
255C3×C4×D4C2318yes—
256C3×C4×D4C2314yes—
257C3×C4×D4C2312yes—
258C3×C4×D4C2314yes—
259C3×C4×D4C2318yescomplemented
260C3×C4×D4C2318yescomplemented
261C3×C4×D4C2318yescomplemented
262C3×C4×D4C2318yescomplemented
263C3×C4×D4C2318yescomplemented
264C3×C4×D4C2312yescomplemented
265C3×C4×D4C23116yescomplemented
266C3×C4×D4C23116yescomplemented
267C3×C4×D4C2318yescomplemented
268C3×C4×D4C2318yescomplemented
269C3×C4×D4C23116yescomplemented
270C3×C4×D4C23116yescomplemented
271C3×C4×D4C2318yescomplemented
272C3×C4×D4C2314yescomplemented
273C3×C4×D4C2318yescomplemented
274C3×C4×D4C23116yescomplemented
275C3×C4×D4C2318yescomplemented
276C3×C4×D4C2312yescomplemented
277C3×C4×D4C2318yescomplemented
278C3×C4×D4C2318yescomplemented
279C3×C4×D4C23116yescomplemented
280C3×C4×D4C2318yescomplemented
281C3×#117C2312yes—
282C3×#117C2314yes—
283C3×#117C2318yes—
284C3×#117C2318yescomplemented
285C3×#117C2314yescomplemented
286C3×#117C2314yescomplemented
287C3×#117C2314yescomplemented
288C3×#117C2318yescomplemented
289C3×#117C2314yescomplemented
290C3×#117C2318yescomplemented
291C3×#117C2314yescomplemented
292C3×#117C23116yescomplemented
293C2×C3×C4⋊C4C2311yescharacteristic
294C2×C3×C4⋊C4C2311yescharacteristic
295C2×C3×C4⋊C4C2314yescomplemented
296C2×C3×C4⋊C4C2314yescomplemented
297C2×C3×C4⋊C4C2314yescomplemented
298C2×C3×C4⋊C4C2314yescomplemented
299C2×C3×C4⋊C4C2314yescomplemented
300C2×C3×C4⋊C4C2318yescomplemented
301C2×C3×C22⋊C4C2318yes—
302C2×C3×C22⋊C4C2314yes—
303C2×C3×C22⋊C4C2318yes—
304C2×C3×C22⋊C4C23116yes—
305C2×C3×C22⋊C4C2312yes—
306C2×C3×C22⋊C4C2312yes—
307C2×C3×C22⋊C4C2314yes—
308C2×C3×C22⋊C4C23116yescomplemented
309C2×C3×C22⋊C4C2318yescomplemented
310C2×C3×C22⋊C4C2318yescomplemented
311C2×C3×C22⋊C4C23116yescomplemented
312C2×C3×C22⋊C4C2314yescomplemented
313C2×C3×C22⋊C4C2318yescomplemented
314C2×C3×C22⋊C4C2318yescomplemented
315C2×C3×C22⋊C4C2318yescomplemented
316C2×C3×C42C2311yescharacteristic
317C2×C3×C42C2318yescomplemented
318C2×C3×C42C2314yescomplemented
319C2×C3×C42C2314yescomplemented
320C2×H(5,𝔽2)C22×C311yescharacteristic
321C22×#41C22×C314yescomplemented
322C23×D4C22×C312yes—
323C23×D4C22×C312yescomplemented
324#559C22×C314yescomplemented
325#559C22×C314yescomplemented
326#556C22×C312yescomplemented
327#555C22×C312yescomplemented
328#555C22×C318yescomplemented
329#554C22×C312yescomplemented
330#554C22×C314yescomplemented
331#554C22×C318yescomplemented
332#553C22×C314yescomplemented
333#553C22×C318yescomplemented
334#553C22×C318yescomplemented
335#553C22×C318yescomplemented
336#553C22×C3116yescomplemented
337#552C22×C314yescomplemented
338#552C22×C314yescomplemented
339#551C22×C318yescomplemented
340#551C22×C3116yescomplemented
341#551C22×C3116yescomplemented
342#551C22×C3116yescomplemented
343#550C22×C314yescomplemented
344#550C22×C314yescomplemented
345D4×Q8C22×C314yescomplemented
346#548C22×C318yescomplemented
347#547C22×C312yescomplemented
348#547C22×C318yescomplemented
349#546C22×C314yescomplemented
350#546C22×C3116yescomplemented
351#546C22×C318yescomplemented
352#546C22×C318yescomplemented
353#546C22×C318yescomplemented
354#546C22×C318yescomplemented
355#546C22×C318yescomplemented
356#546C22×C3116yescomplemented
357#546C22×C3116yescomplemented
358#546C22×C3116yescomplemented
359#546C22×C318yescomplemented
360D42C22×C314yescomplemented
361D42C22×C318yescomplemented
362D42C22×C314yescomplemented
363D42C22×C318yescomplemented
364D42C22×C318yescomplemented
365#544C22×C312yescomplemented
366#543C22×C314yescomplemented
367#542C22×C318yescomplemented
368#540C22×C318yescomplemented
369#540C22×C318yescomplemented
370#539C22×C318yescomplemented
371#538C22×C3116yescomplemented
372#538C22×C3116yescomplemented
373#538C22×C318yescomplemented
374#535C22×C314yescomplemented
375#534C22×C318yescomplemented
376#533C22×C312yescomplemented
377#532C22×C318yescomplemented
378#532C22×C314yescomplemented
379#532C22×C314yescomplemented
380C2×#127C22×C311yescharacteristic, complemented
381#529C22×C318yescomplemented
382#529C22×C314yescomplemented
383#529C22×C318yescomplemented
384#529C22×C318yescomplemented
385C2×#124C22×C314yescomplemented
386#525C22×C314yescomplemented
387#525C22×C3116yescomplemented
388#525C22×C3116yescomplemented
389#525C22×C318yescomplemented
390C2×#123C22×C318yescomplemented
391C2×C22⋊Q8C22×C314yescomplemented
392C2×#121C22×C312yescomplemented
393C2×#121C22×C312yescomplemented
394C2×#121C22×C314yescomplemented
395C2×#121C22×C318yescomplemented
396C2×#120C22×C314yescomplemented
397C2×#120C22×C318yescomplemented
398#520C22×C312yescomplemented
399#520C22×C314yescomplemented
400#518C22×C311yescharacteristic
401#518C22×C312yes—
402#518C22×C318yescomplemented
403#518C22×C314yescomplemented
404#518C22×C314yescomplemented
405#518C22×C318yescomplemented
406#518C22×C318yescomplemented
407#518C22×C314yescomplemented
408C4×#41C22×C312yescomplemented
409C4×#41C22×C314yescomplemented
410C4×#41C22×C314yescomplemented
411C2×C4×D4C22×C311yescharacteristic
412C2×C4×D4C22×C311yescharacteristic, complemented
413C2×C4×D4C22×C314yescomplemented
414C2×C4×D4C22×C318yescomplemented
415C2×C4×D4C22×C318yescomplemented
416C2×C4×D4C22×C314yescomplemented
417C2×C4×D4C22×C314yescomplemented
418C2×#117C22×C314yescomplemented
419C22×C22⋊C4C22×C318yescomplemented
420C24×C3—216no—
421C24×C3—48no—
422C24×C3—84no—
423C24×C3C2412yes—
424C24×C3C2418yes—
425C24×C3C2414yes—
426C24×C3C2418yes—
427C24×C3C2414yes—
428C24×C3C2412yes—
429C3×#41—216no—
430C3×#41—216no—
431C3×#41—28no—
432C3×#41—432no—
433C3×#41—416no—
434C3×#41—88no—
435C2×C3×Q8—48no—
436C2×C3×Q8C2412yes—
437C2×C3×Q8C2414yes—
438C2×C3×Q8C2414yes—
439C2×C3×Q8C2418yes—
440C2×C3×D4—216no—
441C2×C3×D4—216no—
442C2×C3×D4—232no—
443C2×C3×D4—232no—
444C2×C3×D4—216no—
445C2×C3×D4—24no—
446C2×C3×D4—216no—
447C2×C3×D4—28no—
448C2×C3×D4—44no—
449C2×C3×D4—48no—
450C2×C3×D4—416no—
451C2×C3×D4—48no—
452C2×C3×D4—416no—
453C2×C3×D4—82no—
454C2×C3×D4—88no—
455C2×C3×D4#4118yescomplemented
456C2×C3×D4C2414yes—
457C2×C3×D4C2412yes—
458C2×C3×D4C2411yescharacteristic
459C2×C3×D4C24116yes—
460C2×C3×D4C2418yes—
461C2×C3×D4C2418yes—
462C2×C3×D4C2412yes—
463C2×C3×D4C2418yes—
464C2×C3×D4C2418yes—
465C2×C3×D4C2414yes—
466C2×C3×D4C2418yes—
467C2×C3×D4C2418yes—
468C2×C3×D4C24116yes—
469C2×C3×D4C2418yes—
470C2×C3×D4C24116yes—
471C2×C3×D4C2414yes—
472C2×C3×D4C2414yes—
473C2×C3×D4C2411yescharacteristic
474C22×C3×C4—28no—
475C22×C3×C4—44no—
476C22×C3×C4—48no—
477C22×C3×C4—416no—
478C22×C3×C4—88no—
479C22×C3×C4C2411yescharacteristic
480C22×C3×C4C2414yes—
481C22×C3×C4C2418yes—
482C22×C3×C4C2414yes—
483C22×C3×C4C2414yes—
484C22×C3×C4C2414yes—
485C22×C3×C4C2414yes—
486C22×C3×C4C2412yes—
487C22×C3×C4C2414yes—
488C22×C3×C4C2411yescharacteristic
489C22×C3×C4C2414yes—
490C22×C3×C4C2418yes—
491C22×C3×C4C2414yes—
492C22×C3×C4C2412yes—
493C22×C3×C4C2418yes—
494C22×C3×C4C2414yes—
495C22×C3×C4C2418yes—
496C22×C3×C4C24116yes—
497C22×C3×C4C24116yes—
498C22×C3×C4C2414yes—
499C22×C3×C4C2418yes—
500C22×C3×C4C2411yescharacteristic
501C3×C4⋊C4C2414yes—
502C3×C4⋊C4C2412yes—
503C3×C4⋊C4C2412yes—
504C3×C4⋊C4C2412yes—
505C3×C4⋊C4C2412yes—
506C3×C4⋊C4C2414yes—
507C3×C4⋊C4C2418yes—
508C3×C4⋊C4C2414yes—
509C3×C4⋊C4C2418yes—
510C3×C4⋊C4C2414yes—
511C3×C4⋊C4C2414yes—
512C3×C4⋊C4C2418yes—
513C3×C4⋊C4C2418yes—
514C3×C4⋊C4C24116yes—
515C3×C4⋊C4C2418yes—
516C3×C4⋊C4C2414yes—
517C3×C4⋊C4C2418yes—
518C3×C4⋊C4C2418yes—
519C3×C4⋊C4C2418yes—
520C3×C4⋊C4C2414yes—
521C3×C22⋊C4C2414yes—
522C3×C22⋊C4C2418yes—
523C3×C22⋊C4C2418yes—
524C3×C22⋊C4C2418yes—
525C3×C22⋊C4C2418yes—
526C3×C22⋊C4C24116yes—
527C3×C22⋊C4C24116yes—
528C3×C22⋊C4C24116yes—
529C3×C22⋊C4C2418yes—
530C3×C22⋊C4C2414yes—
531C3×C22⋊C4C24116yes—
532C3×C22⋊C4C2414yes—
533C3×C22⋊C4C2418yes—
534C3×C22⋊C4C2414yes—
535C3×C22⋊C4C2418yes—
536C3×C22⋊C4C2414yes—
537C3×C22⋊C4C2418yes—
538C3×C22⋊C4C24116yes—
539C3×C22⋊C4C24116yes—
540C3×C22⋊C4C2418yes—
541C3×C22⋊C4C2418yes—
542C3×C42C2412yes—
543C3×C42C2412yes—
544C3×C42C2414yes—
545C3×C42C2414yes—
546C3×C42C2418yes—
547C3×C42C2418yes—
548C3×C42C2418yes—
549C3×C42C2418yes—
550C3×C42C2414yes—
551C25C23×C314yes—
552H(5,𝔽2)—28no—
553C2×#41—416no—
554C2×#41C23×C312yes—
555C2×#41C23×C314yes—
556C2×#41C23×C314yes—
557C2×#41C23×C3116yescomplemented
558C2×#41C23×C318yescomplemented
559C2×#41C23×C318yescomplemented
560C22×Q8C23×C314yescomplemented
561C22×D4—216no—
562C22×D4—48no—
563C22×D4C23×C318yes—
564C22×D4C23×C314yes—
565C22×D4C23×C314yes—
566C22×D4C23×C314yes—
567C22×D4C23×C311yescharacteristic
568C22×D4C23×C314yes—
569C22×D4C23×C312yes—
570C22×D4C23×C318yes—
571C22×D4C23×C314yes—
572C22×D4C23×C318yes—
573C22×D4C23×C314yes—
574C22×D4C23×C312yes—
575C22×D4C23×C312yes—
576C22×D4C23×C311yescharacteristic
577C22×D4C23×C318yescomplemented
578C22×D4C23×C318yescomplemented
579C23×C4C23×C312yes—
580C23×C4C23×C312yes—
581C23×C4C23×C318yescomplemented
582C23×C4C23×C314yescomplemented
583C23×C4C23×C318yescomplemented
584C4⋊Q8C23×C312yescomplemented
585C4⋊Q8C23×C312yescomplemented
586C4⋊Q8C23×C318yescomplemented
587#127C23×C314yes—
588#127C23×C314yes—
589#127C23×C318yescomplemented
590#126C23×C318yescomplemented
591#126C23×C318yescomplemented
592#126C23×C318yescomplemented
593#126C23×C3116yescomplemented
594#126C23×C3116yescomplemented
595#125C23×C314yescomplemented
596#125C23×C318yescomplemented
597#125C23×C318yescomplemented
598#125C23×C314yescomplemented
599#124C23×C314yes—
600#124C23×C318yescomplemented
601#124C23×C3116yescomplemented
602#124C23×C318yescomplemented
603#124C23×C318yescomplemented
604#124C23×C3116yescomplemented
605#124C23×C318yescomplemented
606#123C23×C318yes—
607#123C23×C318yes—
608#123C23×C3116yescomplemented
609#123C23×C3116yescomplemented
610#123C23×C3116yescomplemented
611#123C23×C318yescomplemented
612#123C23×C3116yescomplemented
613#123C23×C3116yescomplemented
614#123C23×C3116yescomplemented
615#123C23×C3116yescomplemented
616#123C23×C318yescomplemented
617C22⋊Q8C23×C314yes—
618C22⋊Q8C23×C318yes—
619C22⋊Q8C23×C314yes—
620C22⋊Q8C23×C318yescomplemented
621C22⋊Q8C23×C318yescomplemented
622C22⋊Q8C23×C314yescomplemented
623C22⋊Q8C23×C318yescomplemented
624C22⋊Q8C23×C314yescomplemented
625C22⋊Q8C23×C3116yescomplemented
626C22⋊Q8C23×C3116yescomplemented
627C22⋊Q8C23×C3116yescomplemented
628C22⋊Q8C23×C314yescomplemented
629#121C23×C318yes—
630#121C23×C314yes—
631#121C23×C318yes—
632#121C23×C318yes—
633#121C23×C318yes—
634#121C23×C318yes—
635#121C23×C3116yescomplemented
636#121C23×C318yescomplemented
637#121C23×C3116yescomplemented
638#121C23×C3116yescomplemented
639#121C23×C3116yescomplemented
640#121C23×C314yescomplemented
641#121C23×C3116yescomplemented
642#121C23×C3116yescomplemented
643#121C23×C3116yescomplemented
644#121C23×C314yescomplemented
645#121C23×C318yescomplemented
646#121C23×C318yescomplemented
647#121C23×C318yescomplemented
648#120C23×C318yes—
649#120C23×C3116yes—
650#120C23×C3116yes—
651#120C23×C3116yes—
652#120C23×C3116yescomplemented
653#120C23×C3116yescomplemented
654#120C23×C3116yescomplemented
655C4×Q8C23×C312yescomplemented
656C4×Q8C23×C314yescomplemented
657C4×Q8C23×C312yescomplemented
658C4×Q8C23×C314yescomplemented
659C4×Q8C23×C314yescomplemented
660C4×Q8C23×C314yescomplemented
661C4×D4C23×C314yes—
662C4×D4C23×C314yes—
663C4×D4C23×C314yes—
664C4×D4C23×C314yes—
665C4×D4C23×C314yes—
666C4×D4C23×C314yes—
667C4×D4C23×C312yes—
668C4×D4C23×C318yes—
669C4×D4C23×C318yes—
670C4×D4C23×C318yes—
671C4×D4C23×C314yes—
672C4×D4C23×C312yes—
673C4×D4C23×C314yes—
674C4×D4C23×C318yescomplemented
675C4×D4C23×C312yescomplemented
676C4×D4C23×C3116yescomplemented
677C4×D4C23×C3116yescomplemented
678C4×D4C23×C318yescomplemented
679C4×D4C23×C318yescomplemented
680C4×D4C23×C3116yescomplemented
681C4×D4C23×C3116yescomplemented
682C4×D4C23×C318yescomplemented
683C4×D4C23×C318yescomplemented
684C4×D4C23×C318yescomplemented
685C4×D4C23×C314yescomplemented
686C4×D4C23×C318yescomplemented
687C4×D4C23×C3116yescomplemented
688C4×D4C23×C318yescomplemented
689C4×D4C23×C318yescomplemented
690C4×D4C23×C312yescomplemented
691C4×D4C23×C318yescomplemented
692C4×D4C23×C318yescomplemented
693C4×D4C23×C318yescomplemented
694C4×D4C23×C3116yescomplemented
695C4×D4C23×C318yescomplemented
696#117C23×C312yes—
697#117C23×C314yes—
698#117C23×C318yes—
699#117C23×C318yescomplemented
700#117C23×C314yescomplemented
701#117C23×C314yescomplemented
702#117C23×C314yescomplemented
703#117C23×C318yescomplemented
704#117C23×C314yescomplemented
705#117C23×C318yescomplemented
706#117C23×C314yescomplemented
707#117C23×C3116yescomplemented
708C2×C4⋊C4C23×C311yescharacteristic
709C2×C4⋊C4C23×C311yescharacteristic
710C2×C4⋊C4C23×C314yescomplemented
711C2×C4⋊C4C23×C314yescomplemented
712C2×C4⋊C4C23×C314yescomplemented
713C2×C4⋊C4C23×C314yescomplemented
714C2×C4⋊C4C23×C314yescomplemented
715C2×C4⋊C4C23×C318yescomplemented
716C2×C22⋊C4C23×C318yes—
717C2×C22⋊C4C23×C314yes—
718C2×C22⋊C4C23×C318yes—
719C2×C22⋊C4C23×C3116yes—
720C2×C22⋊C4C23×C312yes—
721C2×C22⋊C4C23×C312yes—
722C2×C22⋊C4C23×C314yes—
723C2×C22⋊C4C23×C3116yescomplemented
724C2×C22⋊C4C23×C318yescomplemented
725C2×C22⋊C4C23×C318yescomplemented
726C2×C22⋊C4C23×C3116yescomplemented
727C2×C22⋊C4C23×C314yescomplemented
728C2×C22⋊C4C23×C318yescomplemented
729C2×C22⋊C4C23×C318yescomplemented
730C2×C22⋊C4C23×C318yescomplemented
731C2×C42C23×C311yescharacteristic
732C2×C42C23×C318yescomplemented
733C2×C42C23×C314yescomplemented
734C2×C42C23×C314yescomplemented
735C23×C3—24no—
736C23×C3—216no—
737C23×C3—216no—
738C23×C3—24no—
739C23×C3—28no—
740C23×C3—216no—
741C23×C3—28no—
742C23×C3—42no—
743C23×C3—48no—
744C23×C3—42no—
745C23×C3—42no—
746C23×C3—44no—
747C23×C3—48no—
748C23×C3—44no—
749C23×C3—44no—
750C23×C3—48no—
751C23×C3—44no—
752C23×C3—832no—
753C23×C3C2×#4118yescomplemented
754C23×C3C2512yes—
755C23×C3C2518yes—
756C23×C3C2514yes—
757C23×C3C2511yescharacteristic
758C23×C3C2514yes—
759C23×C3C2512yes—
760C3×Q8—24no—
761C3×Q8—28no—
762C3×Q8—48no—
763C3×Q8—44no—
764C3×D4—232no—
765C3×D4—28no—
766C3×D4—216no—
767C3×D4—24no—
768C3×D4—216no—
769C3×D4—216no—
770C3×D4—216no—
771C3×D4—24no—
772C3×D4—22no—
773C3×D4—28no—
774C3×D4—44no—
775C3×D4—48no—
776C3×D4—416no—
777C3×D4—48no—
778C3×D4—416no—
779C3×D4—48no—
780C3×D4C2×#41116yescomplemented
781C3×D4H(5,𝔽2)14yescomplemented
782C2×C3×C4—24no—
783C2×C3×C4—28no—
784C2×C3×C4—216no—
785C2×C3×C4—28no—
786C2×C3×C4—28no—
787C2×C3×C4—28no—
788C2×C3×C4—22no—
789C2×C3×C4—28no—
790C2×C3×C4—28no—
791C2×C3×C4—44no—
792C2×C3×C4—44no—
793C2×C3×C4—42no—
794C2×C3×C4—48no—
795C2×C3×C4—48no—
796C2×C3×C4—416no—
797C2×C3×C4—44no—
798C2×C3×C4—48no—
799C2×C3×C4—48no—
800C2×C3×C4—416no—
801C2×C3×C4—41no—
802C2×C3×C4—44no—
803C2×C3×C4C2×#4114yescomplemented
804C2×C3×C4C2514yes—
805C2×C3×C4C2514yes—
806C2×C3×C4C2514yes—
807C2×C3×C4C2512yes—
808C2×C3×C4C2514yes—
809C2×C3×C4C2518yes—
810C2×C3×C4C2518yes—
811C2×C3×C4C2514yes—
812C2×C3×C4C2511yescharacteristic
813C2×C3×C4C2512yes—
814C2×C3×C4C2511yescharacteristic
815C24—216no—
816C24—48no—
817C24—84no—
818C24C24×C312yes—
819C24C24×C318yes—
820C24C24×C314yes—
821C24C24×C318yes—
822C24C24×C314yes—
823C24C24×C312yes—
824#41—216no—
825#41—216no—
826#41—28no—
827#41—432no—
828#41—416no—
829#41—88no—
830C2×Q8—48no—
831C2×Q8C24×C312yes—
832C2×Q8C24×C314yes—
833C2×Q8C24×C314yes—
834C2×Q8C24×C318yes—
835C2×D4—216no—
836C2×D4—216no—
837C2×D4—232no—
838C2×D4—232no—
839C2×D4—216no—
840C2×D4—24no—
841C2×D4—216no—
842C2×D4—28no—
843C2×D4—44no—
844C2×D4—48no—
845C2×D4—416no—
846C2×D4—48no—
847C2×D4—416no—
848C2×D4—82no—
849C2×D4—88no—
850C2×D4C3×#4118yescomplemented
851C2×D4C24×C314yes—
852C2×D4C24×C312yes—
853C2×D4C24×C311yescharacteristic
854C2×D4C24×C3116yes—
855C2×D4C24×C318yes—
856C2×D4C24×C318yes—
857C2×D4C24×C312yes—
858C2×D4C24×C318yes—
859C2×D4C24×C318yes—
860C2×D4C24×C314yes—
861C2×D4C24×C318yes—
862C2×D4C24×C318yes—
863C2×D4C24×C3116yes—
864C2×D4C24×C318yes—
865C2×D4C24×C3116yes—
866C2×D4C24×C314yes—
867C2×D4C24×C314yes—
868C2×D4C24×C311yescharacteristic
869C22×C4—28no—
870C22×C4—44no—
871C22×C4—48no—
872C22×C4—416no—
873C22×C4—88no—
874C22×C4C24×C311yescharacteristic
875C22×C4C24×C314yes—
876C22×C4C24×C318yes—
877C22×C4C24×C314yes—
878C22×C4C24×C314yes—
879C22×C4C24×C314yes—
880C22×C4C24×C314yes—
881C22×C4C24×C312yes—
882C22×C4C24×C314yes—
883C22×C4C24×C311yescharacteristic
884C22×C4C24×C314yes—
885C22×C4C24×C318yes—
886C22×C4C24×C314yes—
887C22×C4C24×C312yes—
888C22×C4C24×C318yes—
889C22×C4C24×C314yes—
890C22×C4C24×C318yes—
891C22×C4C24×C3116yes—
892C22×C4C24×C3116yes—
893C22×C4C24×C314yes—
894C22×C4C24×C318yes—
895C22×C4C24×C311yescharacteristic
896C4⋊C4C24×C314yes—
897C4⋊C4C24×C312yes—
898C4⋊C4C24×C312yes—
899C4⋊C4C24×C312yes—
900C4⋊C4C24×C312yes—
901C4⋊C4C24×C314yes—
902C4⋊C4C24×C318yes—
903C4⋊C4C24×C314yes—
904C4⋊C4C24×C318yes—
905C4⋊C4C24×C314yes—
906C4⋊C4C24×C314yes—
907C4⋊C4C24×C318yes—
908C4⋊C4C24×C318yes—
909C4⋊C4C24×C3116yes—
910C4⋊C4C24×C318yes—
911C4⋊C4C24×C314yes—
912C4⋊C4C24×C318yes—
913C4⋊C4C24×C318yes—
914C4⋊C4C24×C318yes—
915C4⋊C4C24×C314yes—
916C22⋊C4C24×C314yes—
917C22⋊C4C24×C318yes—
918C22⋊C4C24×C318yes—
919C22⋊C4C24×C318yes—
920C22⋊C4C24×C318yes—
921C22⋊C4C24×C3116yes—
922C22⋊C4C24×C3116yes—
923C22⋊C4C24×C3116yes—
924C22⋊C4C24×C318yes—
925C22⋊C4C24×C314yes—
926C22⋊C4C24×C3116yes—
927C22⋊C4C24×C314yes—
928C22⋊C4C24×C318yes—
929C22⋊C4C24×C314yes—
930C22⋊C4C24×C318yes—
931C22⋊C4C24×C314yes—
932C22⋊C4C24×C318yes—
933C22⋊C4C24×C3116yes—
934C22⋊C4C24×C3116yes—
935C22⋊C4C24×C318yes—
936C22⋊C4C24×C318yes—
937C42C24×C312yes—
938C42C24×C312yes—
939C42C24×C314yes—
940C42C24×C314yes—
941C42C24×C318yes—
942C42C24×C318yes—
943C42C24×C318yes—
944C42C24×C318yes—
945C42C24×C314yes—
946C22×C3—22no—
947C22×C3—24no—
948C22×C3—21no—
949C22×C3—22no—
950C22×C3—24no—
951C22×C3—21no—
952C22×C3—22no—
953C22×C3—24no—
954C22×C3—28no—
955C22×C3—24no—
956C22×C3—28no—
957C22×C3—22no—
958C22×C3—28no—
959C22×C3—24no—
960C22×C3—22no—
961C22×C3—48no—
962C22×C3—432no—
963C22×C3—48no—
964C22×C3—88no—
965C22×C3—88no—
966C22×C3—816no—
967C22×C3C22×#4112yes—
968C22×C3C22×#4118yes—
969C22×C3C2×H(5,𝔽2)14yes—
970C22×C3C2611yescharacteristic
971C3×C4—24no—
972C3×C4—24no—
973C3×C4—24no—
974C3×C4—21no—
975C3×C4—24no—
976C3×C4—28no—
977C3×C4—24no—
978C3×C4—28no—
979C3×C4—22no—
980C3×C4C22×#4114yes—
981C3×C4C2×H(5,𝔽2)12yes—
982C23—24no—
983C23—216no—
984C23—216no—
985C23—24no—
986C23—28no—
987C23—216no—
988C23—28no—
989C23—42no—
990C23—48no—
991C23—42no—
992C23—42no—
993C23—44no—
994C23—48no—
995C23—44no—
996C23—44no—
997C23—48no—
998C23—44no—
999C23—832no—
1000C23C2×C3×#4118yescomplemented
1001C23C25×C312yes—
1002C23C25×C318yes—
1003C23C25×C314yes—
1004C23C25×C311yescharacteristic
1005C23C25×C314yes—
1006C23C25×C312yes—
1007Q8—24no—
1008Q8—28no—
1009Q8—48no—
1010Q8—44no—
1011D4—232no—
1012D4—28no—
1013D4—216no—
1014D4—24no—
1015D4—216no—
1016D4—216no—
1017D4—216no—
1018D4—24no—
1019D4—22no—
1020D4—28no—
1021D4—44no—
1022D4—48no—
1023D4—416no—
1024D4—48no—
1025D4—416no—
1026D4—48no—
1027D4C2×C3×#41116yescomplemented
1028D4C3×H(5,𝔽2)14yescomplemented
1029C2×C4—24no—
1030C2×C4—28no—
1031C2×C4—216no—
1032C2×C4—28no—
1033C2×C4—28no—
1034C2×C4—28no—
1035C2×C4—22no—
1036C2×C4—28no—
1037C2×C4—28no—
1038C2×C4—44no—
1039C2×C4—44no—
1040C2×C4—42no—
1041C2×C4—48no—
1042C2×C4—48no—
1043C2×C4—416no—
1044C2×C4—44no—
1045C2×C4—48no—
1046C2×C4—48no—
1047C2×C4—416no—
1048C2×C4—41no—
1049C2×C4—44no—
1050C2×C4C2×C3×#4114yescomplemented
1051C2×C4C25×C314yes—
1052C2×C4C25×C314yes—
1053C2×C4C25×C314yes—
1054C2×C4C25×C312yes—
1055C2×C4C25×C314yes—
1056C2×C4C25×C318yes—
1057C2×C4C25×C318yes—
1058C2×C4C25×C314yes—
1059C2×C4C25×C311yescharacteristic
1060C2×C4C25×C312yes—
1061C2×C4C25×C311yescharacteristic
1062C2×C3—24no—
1063C2×C3—22no—
1064C2×C3—28no—
1065C2×C3—48no—
1066C2×C3—42no—
1067C2×C3—44no—
1068C2×C3C23×#4111yescharacteristic
1069C2×C3C22×H(5,𝔽2)11yescharacteristic
1070C2×C3H(7,𝔽2)11yescharacteristic
1071C22—22no—
1072C22—24no—
1073C22—21no—
1074C22—22no—
1075C22—24no—
1076C22—21no—
1077C22—22no—
1078C22—24no—
1079C22—28no—
1080C22—24no—
1081C22—28no—
1082C22—22no—
1083C22—28no—
1084C22—24no—
1085C22—22no—
1086C22—48no—
1087C22—48no—
1088C22—432no—
1089C22—88no—
1090C22—816no—
1091C22—88no—
1092C22C22×C3×#4112yes—
1093C22C22×C3×#4118yes—
1094C22C2×C3×H(5,𝔽2)14yes—
1095C22C26×C311yescharacteristic
1096C4—24no—
1097C4—24no—
1098C4—24no—
1099C4—21no—
1100C4—24no—
1101C4—28no—
1102C4—24no—
1103C4—28no—
1104C4—22no—
1105C4C22×C3×#4114yes—
1106C4C2×C3×H(5,𝔽2)12yes—
1107C3#6298311yescharacteristic, direct product factor, Sylow
1108C2—24no—
1109C2—22no—
1110C2—28no—
1111C2—42no—
1112C2—48no—
1113C2—44no—
1114C2C23×C3×#4111yescharacteristic
1115C2C22×C3×H(5,𝔽2)11yescharacteristic
1116C2C3×H(7,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C3C26
commutator, Frattini, cosocleC22C26×C3
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C3 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×#3519C2semidirect
2. C3×#3519C2semidirect
3. C3×#3514C2semidirect
4. C3×#3513C2semidirect
5. C3×#3508C2semidirect
6. C3×#3505C2semidirect
7. C3×#3501C2semidirect
8. C3×#3494C2semidirect
9. C3×#3490C2semidirect
10. C3×#3484C2semidirect
11. C3×#3481C2semidirect
12. C3×#3475C2semidirect
13. C3×D4×#41C2semidirect
14. C2×C3×#546C2semidirect
15. C2×C3×D42C2semidirect
16. C3×C4×H(5,𝔽2)C2semidirect
17. C2×C3×#518C2semidirect
18. #62983C3direct (N × H)
20. C22×C3×#41C22semidirect
22. C23×C3×D4C22semidirect
23. C3×#559C22semidirect
24. C3×#559C22semidirect
25. C3×#556C22semidirect
26. C3×#555C22semidirect
27. C3×#555C22semidirect
28. C3×#554C22semidirect
29. C3×#554C22semidirect
30. C3×#554C22semidirect
31. C3×#553C22semidirect
32. C3×#553C22semidirect
33. C3×#553C22semidirect
34. C3×#553C22semidirect
35. C3×#553C22semidirect
36. C3×#552C22semidirect
37. C3×#552C22semidirect
38. C3×#551C22semidirect
39. C3×#551C22semidirect
40. C3×#551C22semidirect
41. C3×#551C22semidirect
42. C3×#550C22semidirect
43. C3×#550C22semidirect
44. C3×D4×Q8C22semidirect
45. C3×#548C22semidirect
46. C3×#547C22semidirect
47. C3×#547C22semidirect
48. C3×#546C22semidirect
49. C3×#546C22semidirect
50. C3×#546C22semidirect
51. C3×#546C22semidirect
52. C3×#546C22semidirect
53. C3×#546C22semidirect
54. C3×#546C22semidirect
55. C3×#546C22semidirect
56. C3×#546C22semidirect
57. C3×#546C22semidirect
58. C3×#546C22semidirect
59. C3×D42C22semidirect
60. C3×D42C22semidirect
61. C3×D42C22semidirect
62. C3×D42C22semidirect
63. C3×D42C22semidirect
64. C3×#544C22semidirect
65. C3×#543C22semidirect
66. C3×#542C22semidirect
67. C3×#540C22semidirect
68. C3×#540C22semidirect
69. C3×#539C22semidirect
70. C3×#538C22semidirect
71. C3×#538C22semidirect
72. C3×#538C22semidirect
73. C3×#535C22semidirect
74. C3×#534C22semidirect
75. C3×#533C22semidirect
76. C3×#532C22semidirect
77. C3×#532C22semidirect
78. C3×#532C22semidirect
79. C2×C3×#127C22semidirect
80. C3×#529C22semidirect
81. C3×#529C22semidirect
82. C3×#529C22semidirect
83. C3×#529C22semidirect
84. C2×C3×#124C22semidirect
85. C3×#525C22semidirect
86. C3×#525C22semidirect
87. C3×#525C22semidirect
88. C3×#525C22semidirect
89. C2×C3×#123C22semidirect
90. C2×C3×C22⋊Q8C22semidirect
91. C2×C3×#121C22semidirect
92. C2×C3×#121C22semidirect
93. C2×C3×#121C22semidirect
94. C2×C3×#121C22semidirect
95. C2×C3×#120C22semidirect
96. C2×C3×#120C22semidirect
97. C3×#520C22semidirect
98. C3×#520C22semidirect
101. C3×#518C22semidirect
102. C3×#518C22semidirect
103. C3×#518C22semidirect
104. C3×#518C22semidirect
105. C3×#518C22semidirect
106. C3×#518C22semidirect
107. C3×C4×#41C22semidirect
108. C3×C4×#41C22semidirect
109. C3×C4×#41C22semidirect
111. C2×C3×C4×D4C22semidirect
112. C2×C3×C4×D4C22semidirect
113. C2×C3×C4×D4C22semidirect
114. C2×C3×C4×D4C22semidirect
115. C2×C3×C4×D4C22semidirect
116. C2×C3×C4×D4C22semidirect
117. C2×C3×#117C22semidirect
118. C22×C3×C22⋊C4C22semidirect
119. #3519C2×C3semidirect
120. #3519C2×C3semidirect
121. #3514C2×C3semidirect
122. #3513C2×C3semidirect
123. #3508C2×C3semidirect
124. #3505C2×C3semidirect
125. #3501C2×C3semidirect
126. #3494C2×C3semidirect
127. #3490C2×C3semidirect
128. #3484C2×C3semidirect
129. #3481C2×C3semidirect
130. #3475C2×C3semidirect
131. D4×#41C2×C3semidirect
132. C2×#546C2×C3semidirect
133. C2×D42C2×C3semidirect
134. C4×H(5,𝔽2)C2×C3semidirect
135. C2×#518C2×C3semidirect
142. C2×C3×#41C23semidirect
143. C2×C3×#41C23semidirect
144. C2×C3×#41C23semidirect
145. C22×C3×Q8C23semidirect
162. C22×C3×D4C23semidirect
163. C22×C3×D4C23semidirect
166. C23×C3×C4C23semidirect
167. C23×C3×C4C23semidirect
168. C23×C3×C4C23semidirect
169. C3×C4⋊Q8C23semidirect
170. C3×C4⋊Q8C23semidirect
171. C3×C4⋊Q8C23semidirect
174. C3×#127C23semidirect
175. C3×#126C23semidirect
176. C3×#126C23semidirect
177. C3×#126C23semidirect
178. C3×#126C23semidirect
179. C3×#126C23semidirect
180. C3×#125C23semidirect
181. C3×#125C23semidirect
182. C3×#125C23semidirect
183. C3×#125C23semidirect
185. C3×#124C23semidirect
186. C3×#124C23semidirect
187. C3×#124C23semidirect
188. C3×#124C23semidirect
189. C3×#124C23semidirect
190. C3×#124C23semidirect
193. C3×#123C23semidirect
194. C3×#123C23semidirect
195. C3×#123C23semidirect
196. C3×#123C23semidirect
197. C3×#123C23semidirect
198. C3×#123C23semidirect
199. C3×#123C23semidirect
200. C3×#123C23semidirect
201. C3×#123C23semidirect
205. C3×C22⋊Q8C23semidirect
206. C3×C22⋊Q8C23semidirect
207. C3×C22⋊Q8C23semidirect
208. C3×C22⋊Q8C23semidirect
209. C3×C22⋊Q8C23semidirect
210. C3×C22⋊Q8C23semidirect
211. C3×C22⋊Q8C23semidirect
212. C3×C22⋊Q8C23semidirect
213. C3×C22⋊Q8C23semidirect
220. C3×#121C23semidirect
221. C3×#121C23semidirect
222. C3×#121C23semidirect
223. C3×#121C23semidirect
224. C3×#121C23semidirect
225. C3×#121C23semidirect
226. C3×#121C23semidirect
227. C3×#121C23semidirect
228. C3×#121C23semidirect
229. C3×#121C23semidirect
230. C3×#121C23semidirect
231. C3×#121C23semidirect
232. C3×#121C23semidirect
237. C3×#120C23semidirect
238. C3×#120C23semidirect
239. C3×#120C23semidirect
240. C3×C4×Q8C23semidirect
241. C3×C4×Q8C23semidirect
242. C3×C4×Q8C23semidirect
243. C3×C4×Q8C23semidirect
244. C3×C4×Q8C23semidirect
245. C3×C4×Q8C23semidirect
259. C3×C4×D4C23semidirect
260. C3×C4×D4C23semidirect
261. C3×C4×D4C23semidirect
262. C3×C4×D4C23semidirect
263. C3×C4×D4C23semidirect
264. C3×C4×D4C23semidirect
265. C3×C4×D4C23semidirect
266. C3×C4×D4C23semidirect
267. C3×C4×D4C23semidirect
268. C3×C4×D4C23semidirect
269. C3×C4×D4C23semidirect
270. C3×C4×D4C23semidirect
271. C3×C4×D4C23semidirect
272. C3×C4×D4C23semidirect
273. C3×C4×D4C23semidirect
274. C3×C4×D4C23semidirect
275. C3×C4×D4C23semidirect
276. C3×C4×D4C23semidirect
277. C3×C4×D4C23semidirect
278. C3×C4×D4C23semidirect
279. C3×C4×D4C23semidirect
280. C3×C4×D4C23semidirect
284. C3×#117C23semidirect
285. C3×#117C23semidirect
286. C3×#117C23semidirect
287. C3×#117C23semidirect
288. C3×#117C23semidirect
289. C3×#117C23semidirect
290. C3×#117C23semidirect
291. C3×#117C23semidirect
292. C3×#117C23semidirect
295. C2×C3×C4⋊C4C23semidirect
296. C2×C3×C4⋊C4C23semidirect
297. C2×C3×C4⋊C4C23semidirect
298. C2×C3×C4⋊C4C23semidirect
299. C2×C3×C4⋊C4C23semidirect
300. C2×C3×C4⋊C4C23semidirect
308. C2×C3×C22⋊C4C23semidirect
309. C2×C3×C22⋊C4C23semidirect
310. C2×C3×C22⋊C4C23semidirect
311. C2×C3×C22⋊C4C23semidirect
312. C2×C3×C22⋊C4C23semidirect
313. C2×C3×C22⋊C4C23semidirect
314. C2×C3×C22⋊C4C23semidirect
315. C2×C3×C22⋊C4C23semidirect
317. C2×C3×C42C23semidirect
318. C2×C3×C42C23semidirect
319. C2×C3×C42C23semidirect
321. C22×#41C22×C3semidirect
323. C23×D4C22×C3semidirect
324. #559C22×C3semidirect
325. #559C22×C3semidirect
326. #556C22×C3semidirect
327. #555C22×C3semidirect
328. #555C22×C3semidirect
329. #554C22×C3semidirect
330. #554C22×C3semidirect
331. #554C22×C3semidirect
332. #553C22×C3semidirect
333. #553C22×C3semidirect
334. #553C22×C3semidirect
335. #553C22×C3semidirect
336. #553C22×C3semidirect
337. #552C22×C3semidirect
338. #552C22×C3semidirect
339. #551C22×C3semidirect
340. #551C22×C3semidirect
341. #551C22×C3semidirect
342. #551C22×C3semidirect
343. #550C22×C3semidirect
344. #550C22×C3semidirect
345. D4×Q8C22×C3semidirect
346. #548C22×C3semidirect
347. #547C22×C3semidirect
348. #547C22×C3semidirect
349. #546C22×C3semidirect
350. #546C22×C3semidirect
351. #546C22×C3semidirect
352. #546C22×C3semidirect
353. #546C22×C3semidirect
354. #546C22×C3semidirect
355. #546C22×C3semidirect
356. #546C22×C3semidirect
357. #546C22×C3semidirect
358. #546C22×C3semidirect
359. #546C22×C3semidirect
360. D42C22×C3semidirect
361. D42C22×C3semidirect
362. D42C22×C3semidirect
363. D42C22×C3semidirect
364. D42C22×C3semidirect
365. #544C22×C3semidirect
366. #543C22×C3semidirect
367. #542C22×C3semidirect
368. #540C22×C3semidirect
369. #540C22×C3semidirect
370. #539C22×C3semidirect
371. #538C22×C3semidirect
372. #538C22×C3semidirect
373. #538C22×C3semidirect
374. #535C22×C3semidirect
375. #534C22×C3semidirect
376. #533C22×C3semidirect
377. #532C22×C3semidirect
378. #532C22×C3semidirect
379. #532C22×C3semidirect
380. C2×#127C22×C3semidirect
381. #529C22×C3semidirect
382. #529C22×C3semidirect
383. #529C22×C3semidirect
384. #529C22×C3semidirect
385. C2×#124C22×C3semidirect
386. #525C22×C3semidirect
387. #525C22×C3semidirect
388. #525C22×C3semidirect
389. #525C22×C3semidirect
390. C2×#123C22×C3semidirect
391. C2×C22⋊Q8C22×C3semidirect
392. C2×#121C22×C3semidirect
393. C2×#121C22×C3semidirect
394. C2×#121C22×C3semidirect
395. C2×#121C22×C3semidirect
396. C2×#120C22×C3semidirect
397. C2×#120C22×C3semidirect
398. #520C22×C3semidirect
399. #520C22×C3semidirect
402. #518C22×C3semidirect
403. #518C22×C3semidirect
404. #518C22×C3semidirect
405. #518C22×C3semidirect
406. #518C22×C3semidirect
407. #518C22×C3semidirect
408. C4×#41C22×C3semidirect
409. C4×#41C22×C3semidirect
410. C4×#41C22×C3semidirect
412. C2×C4×D4C22×C3semidirect
413. C2×C4×D4C22×C3semidirect
414. C2×C4×D4C22×C3semidirect
415. C2×C4×D4C22×C3semidirect
416. C2×C4×D4C22×C3semidirect
417. C2×C4×D4C22×C3semidirect
418. C2×#117C22×C3semidirect
419. C22×C22⋊C4C22×C3semidirect
455. C2×C3×D4#41semidirect
557. C2×#41C23×C3semidirect
558. C2×#41C23×C3semidirect
559. C2×#41C23×C3semidirect
560. C22×Q8C23×C3semidirect
577. C22×D4C23×C3semidirect
578. C22×D4C23×C3semidirect
581. C23×C4C23×C3semidirect
582. C23×C4C23×C3semidirect
583. C23×C4C23×C3semidirect
584. C4⋊Q8C23×C3semidirect
585. C4⋊Q8C23×C3semidirect
586. C4⋊Q8C23×C3semidirect
589. #127C23×C3semidirect
590. #126C23×C3semidirect
591. #126C23×C3semidirect
592. #126C23×C3semidirect
593. #126C23×C3semidirect
594. #126C23×C3semidirect
595. #125C23×C3semidirect
596. #125C23×C3semidirect
597. #125C23×C3semidirect
598. #125C23×C3semidirect
600. #124C23×C3semidirect
601. #124C23×C3semidirect
602. #124C23×C3semidirect
603. #124C23×C3semidirect
604. #124C23×C3semidirect
605. #124C23×C3semidirect
608. #123C23×C3semidirect
609. #123C23×C3semidirect
610. #123C23×C3semidirect
611. #123C23×C3semidirect
612. #123C23×C3semidirect
613. #123C23×C3semidirect
614. #123C23×C3semidirect
615. #123C23×C3semidirect
616. #123C23×C3semidirect
620. C22⋊Q8C23×C3semidirect
621. C22⋊Q8C23×C3semidirect
622. C22⋊Q8C23×C3semidirect
623. C22⋊Q8C23×C3semidirect
624. C22⋊Q8C23×C3semidirect
625. C22⋊Q8C23×C3semidirect
626. C22⋊Q8C23×C3semidirect
627. C22⋊Q8C23×C3semidirect
628. C22⋊Q8C23×C3semidirect
635. #121C23×C3semidirect
636. #121C23×C3semidirect
637. #121C23×C3semidirect
638. #121C23×C3semidirect
639. #121C23×C3semidirect
640. #121C23×C3semidirect
641. #121C23×C3semidirect
642. #121C23×C3semidirect
643. #121C23×C3semidirect
644. #121C23×C3semidirect
645. #121C23×C3semidirect
646. #121C23×C3semidirect
647. #121C23×C3semidirect
652. #120C23×C3semidirect
653. #120C23×C3semidirect
654. #120C23×C3semidirect
655. C4×Q8C23×C3semidirect
656. C4×Q8C23×C3semidirect
657. C4×Q8C23×C3semidirect
658. C4×Q8C23×C3semidirect
659. C4×Q8C23×C3semidirect
660. C4×Q8C23×C3semidirect
674. C4×D4C23×C3semidirect
675. C4×D4C23×C3semidirect
676. C4×D4C23×C3semidirect
677. C4×D4C23×C3semidirect
678. C4×D4C23×C3semidirect
679. C4×D4C23×C3semidirect
680. C4×D4C23×C3semidirect
681. C4×D4C23×C3semidirect
682. C4×D4C23×C3semidirect
683. C4×D4C23×C3semidirect
684. C4×D4C23×C3semidirect
685. C4×D4C23×C3semidirect
686. C4×D4C23×C3semidirect
687. C4×D4C23×C3semidirect
688. C4×D4C23×C3semidirect
689. C4×D4C23×C3semidirect
690. C4×D4C23×C3semidirect
691. C4×D4C23×C3semidirect
692. C4×D4C23×C3semidirect
693. C4×D4C23×C3semidirect
694. C4×D4C23×C3semidirect
695. C4×D4C23×C3semidirect
699. #117C23×C3semidirect
700. #117C23×C3semidirect
701. #117C23×C3semidirect
702. #117C23×C3semidirect
703. #117C23×C3semidirect
704. #117C23×C3semidirect
705. #117C23×C3semidirect
706. #117C23×C3semidirect
707. #117C23×C3semidirect
710. C2×C4⋊C4C23×C3semidirect
711. C2×C4⋊C4C23×C3semidirect
712. C2×C4⋊C4C23×C3semidirect
713. C2×C4⋊C4C23×C3semidirect
714. C2×C4⋊C4C23×C3semidirect
715. C2×C4⋊C4C23×C3semidirect
723. C2×C22⋊C4C23×C3semidirect
724. C2×C22⋊C4C23×C3semidirect
725. C2×C22⋊C4C23×C3semidirect
726. C2×C22⋊C4C23×C3semidirect
727. C2×C22⋊C4C23×C3semidirect
728. C2×C22⋊C4C23×C3semidirect
729. C2×C22⋊C4C23×C3semidirect
730. C2×C22⋊C4C23×C3semidirect
732. C2×C42C23×C3semidirect
733. C2×C42C23×C3semidirect
734. C2×C42C23×C3semidirect
753. C23×C3C2×#41semidirect
780. C3×D4C2×#41semidirect
781. C3×D4H(5,𝔽2)semidirect
803. C2×C3×C4C2×#41semidirect
850. C2×D4C3×#41semidirect
1000. C23C2×C3×#41semidirect
1027. D4C2×C3×#41semidirect
1028. D4C3×H(5,𝔽2)semidirect
1050. C2×C4C2×C3×#41semidirect
1107. C3#62983direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×#35192
C3×#35142
C3×#35132
C3×#35082
C3×#35052
C3×#35012
C3×#34942
C3×#34902
C3×#34842
C3×#34812
C3×#34752
C3×D4×#412
C2×C3×#5462
C2×C3×D422
C3×C4×H(5,𝔽2)2
C2×C3×#5182
#629833