Finite Group Databasebeta

← C3×#62915 #10681522

Subgroups — C3×#62915 #10681522

Order 768.

6986 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3559C218yesmaximal, complemented
2C3×#3552C214yesmaximal, complemented
3C3×#3547C214yesmaximal, complemented
4C3×#3544C218yesmaximal, complemented
5C3×#3538C214yesmaximal, complemented
6C3×#3535C218yesmaximal, complemented
7C3×#3515C214yesmaximal, complemented
8C3×#3503C212yesmaximal, complemented
9C3×#3501C211yesmaximal, characteristic, complemented
10C3×#3499C214yesmaximal, complemented
11C3×#3494C214yesmaximal, complemented
12C3×#3492C212yesmaximal, complemented
13C3×#3489C214yesmaximal, complemented
14C3×#3475C212yesmaximal, complemented
15C2×C3×#547C211yesmaximal, characteristic, complemented
16C3×#3460C211yesmaximal, characteristic, complemented
17C2×C3×#544C212yesmaximal, complemented
18#62915C311yesmaximal, characteristic, direct product factor, Sylow
19C2×C3×2−1+4C2214yescomplemented
20C22×C3×#41C2212yes—
21C3×#563C22116yescomplemented
22C3×#563C22116yescomplemented
23C3×#562C22116yescomplemented
24C3×Q82C2214yescomplemented
25C3×#557C2214yescomplemented
26C3×#556C2212yescomplemented
27C3×#555C2212yescomplemented
28C3×#555C2218yescomplemented
29C3×#554C2218yes—
30C3×#554C2212yescomplemented
31C3×#554C2218yescomplemented
32C3×#554C2214yescomplemented
33C3×#554C2218yescomplemented
34C3×#554C2214yescomplemented
35C3×#553C2214yescomplemented
36C3×#553C2218yescomplemented
37C3×#553C2218yescomplemented
38C3×#553C2218yescomplemented
39C3×#552C2214yes—
40C3×#552C2214yescomplemented
41C3×#552C2218yescomplemented
42C3×#552C22116yescomplemented
43C3×#552C2218yescomplemented
44C3×#551C2218yes—
45C3×#551C22116yes—
46C3×D4×Q8C2218yes—
47C3×D4×Q8C2214yescomplemented
48C3×D4×Q8C2214yescomplemented
49C3×D4×Q8C2218yescomplemented
50C3×#548C2218yescomplemented
51C3×#547C2214yes—
52C3×#547C2218yes—
53C3×#547C2214yes—
54C3×#547C2212yescomplemented
55C3×#547C2218yescomplemented
56C3×#547C22116yescomplemented
57C3×#547C2218yescomplemented
58C3×#547C2218yescomplemented
59C3×#547C22116yescomplemented
60C3×#546C2214yes—
61C3×#546C22116yes—
62C3×#544C2211yescharacteristic
63C3×#544C2212yes—
64C3×#544C2214yes—
65C3×#544C2218yes—
66C3×#544C2218yescomplemented
67C3×#544C2218yescomplemented
68C3×#544C2218yescomplemented
69C3×#544C2218yescomplemented
70C3×#543C2214yes—
71C3×#542C2214yescomplemented
72C3×#542C2218yescomplemented
73C3×#542C22116yescomplemented
74C3×#541C2218yescomplemented
75C3×#540C2214yescomplemented
76C3×#540C2218yescomplemented
77C3×#539C2218yes—
78C3×#539C22116yescomplemented
79C3×#539C22116yescomplemented
80C3×#539C2218yescomplemented
81C3×#538C2214yes—
82C3×#537C2211yescharacteristic
83C3×#537C2214yescomplemented
84C3×#537C2218yescomplemented
85C3×#536C2218yescomplemented
86C3×#536C2214yescomplemented
87C3×#536C22116yescomplemented
88C3×#536C2218yescomplemented
89C3×#535C2212yes—
90C3×#533C2212yes—
91C3×#533C2214yescomplemented
92C3×#532C2214yescomplemented
93C3×#532C2218yescomplemented
94C2×C3×C4⋊Q8C2211yescharacteristic
95C2×C3×C4⋊Q8C2218yescomplemented
96C2×C3×C4⋊Q8C2214yescomplemented
97C3×#529C2214yescomplemented
98C3×#529C2218yescomplemented
99C3×#529C2214yescomplemented
100C3×#529C2218yescomplemented
101C2×C3×#125C2218yescomplemented
102C3×#525C2214yes—
103C3×#525C2214yes—
104C3×#525C2218yes—
105C2×C3×#123C2214yes—
106C2×C3×C22⋊Q8C2218yes—
107C2×C3×C22⋊Q8C2212yes—
108C2×C3×C22⋊Q8C2214yes—
109C2×C3×#121C2212yes—
110C3×#520C2214yes—
111C3×#520C2214yescomplemented
112C3×#518C2212yes—
113C3×C4×#41C2212yes—
114C3×C4×#41C2214yescomplemented
115C2×C3×C4×D4C2211yescharacteristic
116C2×C3×C4×D4C2211yescharacteristic
117C2×C3×#117C2214yes—
118C22×C3×C4⋊C4C2212yes—
119#3559C2×C318yescomplemented
120#3552C2×C314yescomplemented
121#3547C2×C314yescomplemented
122#3544C2×C318yescomplemented
123#3538C2×C314yescomplemented
124#3535C2×C318yescomplemented
125#3515C2×C314yescomplemented
126#3503C2×C312yescomplemented
127#3501C2×C311yescharacteristic, complemented
128#3499C2×C314yescomplemented
129#3494C2×C314yescomplemented
130#3492C2×C312yescomplemented
131#3489C2×C314yescomplemented
132#3475C2×C312yescomplemented
133C2×#547C2×C311yescharacteristic, complemented
134#3460C2×C311yescharacteristic, complemented
135C2×#544C2×C312yescomplemented
136C3×2−1+4—416no—
137C2×C3×#41—48no—
138C2×C3×#41C2314yes—
139C2×C3×#41C2314yes—
140C2×C3×#41C2312yes—
141C2×C3×#41C2318yes—
142C2×C3×#41C2314yes—
143C2×C3×#41C2314yes—
144C2×C3×#41C2318yes—
145C2×C3×#41C23116yes—
146C22×C3×Q8C2312yes—
147C22×C3×Q8C2318yes—
148C22×C3×Q8C2314yes—
149C22×C3×Q8C2318yes—
150C22×C3×D4C2311yescharacteristic
151C22×C3×D4C2311yescharacteristic
152C22×C3×D4C2314yes—
153C23×C3×C4C2312yes—
154C23×C3×C4C2314yes—
155C23×C3×C4C2312yes—
156C3×C4⋊Q8C2318yes—
157C3×C4⋊Q8C23116yes—
158C3×C4⋊Q8C2314yes—
159C3×C4⋊Q8C2318yes—
160C3×C4⋊Q8C23116yes—
161C3×C4⋊Q8C2314yes—
162C3×C4⋊Q8C2314yes—
163C3×C4⋊Q8C2318yes—
164C3×C4⋊Q8C2312yes—
165C3×C4⋊Q8C23116yes—
166C3×C4⋊Q8C2318yes—
167C3×C4⋊Q8C2318yes—
168C3×C4⋊Q8C2312yes—
169C3×#127C2314yes—
170C3×#126C2318yes—
171C3×#126C2318yes—
172C3×#126C2318yes—
173C3×#126C23116yes—
174C3×#126C2318yes—
175C3×#126C23116yes—
176C3×#126C23116yes—
177C3×#125C23116yes—
178C3×#125C2318yes—
179C3×#125C23116yes—
180C3×#125C23116yes—
181C3×#125C2314yes—
182C3×#125C2318yes—
183C3×#125C23116yes—
184C3×#125C2318yes—
185C3×#125C2318yes—
186C3×#125C2314yes—
187C3×#125C2314yes—
188C3×#124C2318yes—
189C3×#124C23116yes—
190C3×#124C23116yes—
191C3×#124C2314yes—
192C3×#124C2314yes—
193C3×#124C2318yes—
194C3×#123C2318yes—
195C3×#123C23116yes—
196C3×#123C23116yes—
197C3×#123C23116yes—
198C3×#123C2318yes—
199C3×#123C23116yes—
200C3×#123C23116yes—
201C3×#123C23116yes—
202C3×#123C23116yes—
203C3×#123C2318yes—
204C3×#123C2318yes—
205C3×#123C23116yes—
206C3×#123C2318yes—
207C3×#123C2318yes—
208C3×C22⋊Q8C2318yes—
209C3×C22⋊Q8C23116yes—
210C3×C22⋊Q8C23116yes—
211C3×C22⋊Q8C23116yes—
212C3×C22⋊Q8C2318yes—
213C3×C22⋊Q8C2318yes—
214C3×C22⋊Q8C2318yes—
215C3×C22⋊Q8C23116yes—
216C3×C22⋊Q8C23116yes—
217C3×C22⋊Q8C23116yes—
218C3×C22⋊Q8C23116yes—
219C3×C22⋊Q8C2314yes—
220C3×C22⋊Q8C2318yes—
221C3×C22⋊Q8C2314yes—
222C3×C22⋊Q8C2318yes—
223C3×C22⋊Q8C2318yes—
224C3×C22⋊Q8C2318yes—
225C3×C22⋊Q8C2318yes—
226C3×C22⋊Q8C23116yes—
227C3×C22⋊Q8C2314yes—
228C3×C22⋊Q8C2314yes—
229C3×C22⋊Q8C2314yes—
230C3×C22⋊Q8C2314yes—
231C3×C22⋊Q8C2314yes—
232C3×C22⋊Q8C2318yes—
233C3×C22⋊Q8C2314yes—
234C3×C22⋊Q8C2318yes—
235C3×#121C2318yes—
236C3×#121C2318yes—
237C3×#121C23116yes—
238C3×#121C23116yes—
239C3×#121C2318yes—
240C3×#121C2318yes—
241C3×#121C2314yes—
242C3×#121C2314yes—
243C3×#121C2314yes—
244C3×#121C2314yes—
245C3×#121C2314yes—
246C3×#121C2318yes—
247C3×#121C2314yes—
248C3×#121C2314yes—
249C3×#121C2314yes—
250C3×#121C23116yes—
251C3×#120C2318yes—
252C3×#120C2318yes—
253C3×C4×Q8C2312yes—
254C3×C4×Q8C2318yes—
255C3×C4×Q8C2314yes—
256C3×C4×Q8C2318yes—
257C3×C4×Q8C2312yes—
258C3×C4×Q8C2314yes—
259C3×C4×Q8C2314yes—
260C3×C4×Q8C2318yes—
261C3×C4×D4C2312yes—
262C3×C4×D4C2314yes—
263C3×C4×D4C2312yes—
264C3×C4×D4C2314yes—
265C3×C4×D4C2314yes—
266C3×C4×D4C2314yes—
267C3×C4×D4C2312yes—
268C3×C4×D4C2314yes—
269C3×C4×D4C2312yes—
270C3×C4×D4C2314yes—
271C3×C4×D4C2318yes—
272C3×C4×D4C2318yes—
273C3×C4×D4C2318yes—
274C3×C4×D4C2318yes—
275C3×C4×D4C23116yes—
276C3×C4×D4C2318yes—
277C3×C4×D4C23116yes—
278C3×C4×D4C2318yes—
279C3×C4×D4C2318yes—
280C3×C4×D4C23116yes—
281C3×C4×D4C23116yes—
282C3×#117C2312yes—
283C3×#117C2314yes—
284C3×#117C2318yes—
285C3×#117C2318yes—
286C3×#117C2314yes—
287C3×#117C2314yes—
288C3×#117C2314yes—
289C3×#117C2318yes—
290C3×#117C2314yes—
291C3×#117C2318yes—
292C3×#117C2314yes—
293C3×#117C2318yes—
294C3×#117C23116yes—
295C2×C3×C4⋊C4C2311yescharacteristic
296C2×C3×C4⋊C4C2312yes—
297C2×C3×C4⋊C4C2314yes—
298C2×C3×C4⋊C4C2318yes—
299C2×C3×C4⋊C4C2318yes—
300C2×C3×C4⋊C4C2314yes—
301C2×C3×C4⋊C4C2314yes—
302C2×C3×C4⋊C4C2311yescharacteristic
303C2×C3×C4⋊C4C2318yes—
304C2×C3×C4⋊C4C2318yes—
305C2×C3×C4⋊C4C2314yes—
306C2×C3×C4⋊C4C23116yes—
307C2×C3×C4⋊C4C2318yes—
308C2×C3×C4⋊C4C2312yes—
309C2×C3×C4⋊C4C2318yes—
310C2×C3×C22⋊C4C2318yes—
311C2×C3×C22⋊C4C2312yes—
312C2×C3×C22⋊C4C2312yes—
313C2×C3×C22⋊C4C2318yes—
314C2×C3×C22⋊C4C2314yes—
315C2×C3×C42C2318yes—
316C2×C3×C42C2311yescharacteristic
317C2×C3×C42C2314yes—
318C2×2−1+4C22×C314yescomplemented
319C22×#41C22×C312yes—
320#563C22×C3116yescomplemented
321#563C22×C3116yescomplemented
322#562C22×C3116yescomplemented
323Q82C22×C314yescomplemented
324#557C22×C314yescomplemented
325#556C22×C312yescomplemented
326#555C22×C312yescomplemented
327#555C22×C318yescomplemented
328#554C22×C318yes—
329#554C22×C312yescomplemented
330#554C22×C318yescomplemented
331#554C22×C314yescomplemented
332#554C22×C318yescomplemented
333#554C22×C314yescomplemented
334#553C22×C314yescomplemented
335#553C22×C318yescomplemented
336#553C22×C318yescomplemented
337#553C22×C318yescomplemented
338#552C22×C314yes—
339#552C22×C314yescomplemented
340#552C22×C318yescomplemented
341#552C22×C3116yescomplemented
342#552C22×C318yescomplemented
343#551C22×C318yes—
344#551C22×C3116yes—
345D4×Q8C22×C318yes—
346D4×Q8C22×C314yescomplemented
347D4×Q8C22×C314yescomplemented
348D4×Q8C22×C318yescomplemented
349#548C22×C318yescomplemented
350#547C22×C314yes—
351#547C22×C318yes—
352#547C22×C314yes—
353#547C22×C312yescomplemented
354#547C22×C318yescomplemented
355#547C22×C3116yescomplemented
356#547C22×C318yescomplemented
357#547C22×C318yescomplemented
358#547C22×C3116yescomplemented
359#546C22×C314yes—
360#546C22×C3116yes—
361#544C22×C311yescharacteristic
362#544C22×C312yes—
363#544C22×C314yes—
364#544C22×C318yes—
365#544C22×C318yescomplemented
366#544C22×C318yescomplemented
367#544C22×C318yescomplemented
368#544C22×C318yescomplemented
369#543C22×C314yes—
370#542C22×C314yescomplemented
371#542C22×C318yescomplemented
372#542C22×C3116yescomplemented
373#541C22×C318yescomplemented
374#540C22×C314yescomplemented
375#540C22×C318yescomplemented
376#539C22×C318yes—
377#539C22×C3116yescomplemented
378#539C22×C3116yescomplemented
379#539C22×C318yescomplemented
380#538C22×C314yes—
381#537C22×C311yescharacteristic
382#537C22×C314yescomplemented
383#537C22×C318yescomplemented
384#536C22×C318yescomplemented
385#536C22×C314yescomplemented
386#536C22×C3116yescomplemented
387#536C22×C318yescomplemented
388#535C22×C312yes—
389#533C22×C312yes—
390#533C22×C314yescomplemented
391#532C22×C314yescomplemented
392#532C22×C318yescomplemented
393C2×C4⋊Q8C22×C311yescharacteristic
394C2×C4⋊Q8C22×C318yescomplemented
395C2×C4⋊Q8C22×C314yescomplemented
396#529C22×C314yescomplemented
397#529C22×C318yescomplemented
398#529C22×C314yescomplemented
399#529C22×C318yescomplemented
400C2×#125C22×C318yescomplemented
401#525C22×C314yes—
402#525C22×C314yes—
403#525C22×C318yes—
404C2×#123C22×C314yes—
405C2×C22⋊Q8C22×C318yes—
406C2×C22⋊Q8C22×C312yes—
407C2×C22⋊Q8C22×C314yes—
408C2×#121C22×C312yes—
409#520C22×C314yes—
410#520C22×C314yescomplemented
411#518C22×C312yes—
412C4×#41C22×C312yes—
413C4×#41C22×C314yescomplemented
414C2×C4×D4C22×C311yescharacteristic
415C2×C4×D4C22×C311yescharacteristic
416C2×#117C22×C314yes—
417C22×C4⋊C4C22×C312yes—
418C24×C3C2412yes—
419C24×C3C2412yes—
420C3×#41—216no—
421C3×#41—216no—
422C3×#41—28no—
423C3×#41—48no—
424C3×#41—416no—
425C3×#41—416no—
426C3×#41—432no—
427C3×#41—48no—
428C2×C3×Q8—416no—
429C2×C3×Q8—44no—
430C2×C3×Q8—48no—
431C2×C3×Q8—416no—
432C2×C3×Q8C2412yes—
433C2×C3×Q8C2414yes—
434C2×C3×Q8C2414yes—
435C2×C3×Q8C2414yes—
436C2×C3×Q8C2418yes—
437C2×C3×Q8C2414yes—
438C2×C3×Q8C2414yes—
439C2×C3×Q8C24116yes—
440C2×C3×D4—24no—
441C2×C3×D4—24no—
442C2×C3×D4—48no—
443C2×C3×D4C2414yes—
444C2×C3×D4C2414yes—
445C2×C3×D4C2412yes—
446C2×C3×D4C2418yes—
447C2×C3×D4C2412yes—
448C2×C3×D4C2418yes—
449C2×C3×D4C2411yescharacteristic
450C2×C3×D4C2418yes—
451C2×C3×D4C2418yes—
452C2×C3×D4C2418yes—
453C2×C3×D4C2414yes—
454C2×C3×D4C2418yes—
455C2×C3×D4C2411yescharacteristic
456C22×C3×C4—28no—
457C22×C3×C4—44no—
458C22×C3×C4—48no—
459C22×C3×C4C2414yes—
460C22×C3×C4C2418yes—
461C22×C3×C4C2414yes—
462C22×C3×C4C2411yescharacteristic
463C22×C3×C4C2414yes—
464C22×C3×C4C2412yes—
465C22×C3×C4C2418yes—
466C22×C3×C4C2414yes—
467C22×C3×C4C2414yes—
468C22×C3×C4C2411yescharacteristic
469C22×C3×C4C2418yes—
470C22×C3×C4C2414yes—
471C22×C3×C4C2414yes—
472C22×C3×C4C2412yes—
473C22×C3×C4C2418yes—
474C22×C3×C4C2418yes—
475C22×C3×C4C24116yes—
476C22×C3×C4C2418yes—
477C22×C3×C4C2414yes—
478C22×C3×C4C2411yescharacteristic
479C3×C4⋊C4C2414yes—
480C3×C4⋊C4C2418yes—
481C3×C4⋊C4C2414yes—
482C3×C4⋊C4C24116yes—
483C3×C4⋊C4C2412yes—
484C3×C4⋊C4C2412yes—
485C3×C4⋊C4C2414yes—
486C3×C4⋊C4C2418yes—
487C3×C4⋊C4C2414yes—
488C3×C4⋊C4C2418yes—
489C3×C4⋊C4C24116yes—
490C3×C4⋊C4C24116yes—
491C3×C4⋊C4C2418yes—
492C3×C4⋊C4C2414yes—
493C3×C4⋊C4C2418yes—
494C3×C4⋊C4C2414yes—
495C3×C4⋊C4C2412yes—
496C3×C4⋊C4C2418yes—
497C3×C4⋊C4C2418yes—
498C3×C4⋊C4C24116yes—
499C3×C4⋊C4C2412yes—
500C3×C4⋊C4C24116yes—
501C3×C4⋊C4C24116yes—
502C3×C4⋊C4C2414yes—
503C3×C4⋊C4C2418yes—
504C3×C4⋊C4C2418yes—
505C3×C4⋊C4C2418yes—
506C3×C4⋊C4C2414yes—
507C3×C4⋊C4C2414yes—
508C3×C22⋊C4C2418yes—
509C3×C22⋊C4C2414yes—
510C3×C22⋊C4C2414yes—
511C3×C22⋊C4C2418yes—
512C3×C22⋊C4C2418yes—
513C3×C22⋊C4C24116yes—
514C3×C22⋊C4C24116yes—
515C3×C22⋊C4C2418yes—
516C3×C22⋊C4C2414yes—
517C3×C22⋊C4C2418yes—
518C3×C22⋊C4C2418yes—
519C3×C22⋊C4C2418yes—
520C3×C22⋊C4C2414yes—
521C3×C22⋊C4C24116yes—
522C3×C22⋊C4C2414yes—
523C3×C22⋊C4C2418yes—
524C3×C22⋊C4C2418yes—
525C3×C22⋊C4C2418yes—
526C3×C22⋊C4C2418yes—
527C3×C42C2414yes—
528C3×C42C2412yes—
529C3×C42C2418yes—
530C3×C42C2412yes—
531C3×C42C2418yes—
532C3×C42C2414yes—
533C3×C42C2418yes—
534C3×C42C2414yes—
535C3×C42C24116yes—
5362−1+4—416no—
537C2×#41—48no—
538C2×#41C23×C312yes—
539C2×#41C23×C314yes—
540C2×#41C23×C314yes—
541C2×#41C23×C314yes—
542C2×#41C23×C318yes—
543C2×#41C23×C3116yes—
544C2×#41C23×C318yes—
545C2×#41C23×C314yes—
546C22×Q8C23×C312yes—
547C22×Q8C23×C318yes—
548C22×Q8C23×C314yes—
549C22×Q8C23×C318yes—
550C22×D4C23×C311yescharacteristic
551C22×D4C23×C311yescharacteristic
552C22×D4C23×C314yes—
553C23×C4C23×C312yes—
554C23×C4C23×C314yes—
555C23×C4C23×C312yes—
556C4⋊Q8C23×C314yes—
557C4⋊Q8C23×C314yes—
558C4⋊Q8C23×C314yes—
559C4⋊Q8C23×C318yes—
560C4⋊Q8C23×C312yes—
561C4⋊Q8C23×C3116yes—
562C4⋊Q8C23×C318yes—
563C4⋊Q8C23×C318yes—
564C4⋊Q8C23×C318yes—
565C4⋊Q8C23×C318yes—
566C4⋊Q8C23×C3116yes—
567C4⋊Q8C23×C312yes—
568C4⋊Q8C23×C3116yes—
569#127C23×C314yes—
570#126C23×C318yes—
571#126C23×C318yes—
572#126C23×C318yes—
573#126C23×C3116yes—
574#126C23×C318yes—
575#126C23×C3116yes—
576#126C23×C3116yes—
577#125C23×C314yes—
578#125C23×C318yes—
579#125C23×C3116yes—
580#125C23×C3116yes—
581#125C23×C318yes—
582#125C23×C318yes—
583#125C23×C314yes—
584#125C23×C318yes—
585#125C23×C314yes—
586#125C23×C3116yes—
587#125C23×C3116yes—
588#124C23×C314yes—
589#124C23×C314yes—
590#124C23×C318yes—
591#124C23×C318yes—
592#124C23×C3116yes—
593#124C23×C3116yes—
594#123C23×C3116yes—
595#123C23×C3116yes—
596#123C23×C3116yes—
597#123C23×C318yes—
598#123C23×C318yes—
599#123C23×C318yes—
600#123C23×C3116yes—
601#123C23×C318yes—
602#123C23×C318yes—
603#123C23×C318yes—
604#123C23×C3116yes—
605#123C23×C3116yes—
606#123C23×C3116yes—
607#123C23×C3116yes—
608C22⋊Q8C23×C314yes—
609C22⋊Q8C23×C318yes—
610C22⋊Q8C23×C314yes—
611C22⋊Q8C23×C318yes—
612C22⋊Q8C23×C318yes—
613C22⋊Q8C23×C318yes—
614C22⋊Q8C23×C318yes—
615C22⋊Q8C23×C318yes—
616C22⋊Q8C23×C318yes—
617C22⋊Q8C23×C3116yes—
618C22⋊Q8C23×C3116yes—
619C22⋊Q8C23×C314yes—
620C22⋊Q8C23×C314yes—
621C22⋊Q8C23×C318yes—
622C22⋊Q8C23×C314yes—
623C22⋊Q8C23×C314yes—
624C22⋊Q8C23×C314yes—
625C22⋊Q8C23×C318yes—
626C22⋊Q8C23×C314yes—
627C22⋊Q8C23×C318yes—
628C22⋊Q8C23×C318yes—
629C22⋊Q8C23×C3116yes—
630C22⋊Q8C23×C3116yes—
631C22⋊Q8C23×C3116yes—
632C22⋊Q8C23×C3116yes—
633C22⋊Q8C23×C3116yes—
634C22⋊Q8C23×C3116yes—
635#121C23×C318yes—
636#121C23×C318yes—
637#121C23×C314yes—
638#121C23×C314yes—
639#121C23×C314yes—
640#121C23×C318yes—
641#121C23×C314yes—
642#121C23×C314yes—
643#121C23×C318yes—
644#121C23×C314yes—
645#121C23×C314yes—
646#121C23×C314yes—
647#121C23×C3116yes—
648#121C23×C318yes—
649#121C23×C3116yes—
650#121C23×C3116yes—
651#120C23×C318yes—
652#120C23×C318yes—
653C4×Q8C23×C312yes—
654C4×Q8C23×C312yes—
655C4×Q8C23×C314yes—
656C4×Q8C23×C314yes—
657C4×Q8C23×C318yes—
658C4×Q8C23×C318yes—
659C4×Q8C23×C314yes—
660C4×Q8C23×C318yes—
661C4×D4C23×C312yes—
662C4×D4C23×C314yes—
663C4×D4C23×C312yes—
664C4×D4C23×C314yes—
665C4×D4C23×C314yes—
666C4×D4C23×C314yes—
667C4×D4C23×C312yes—
668C4×D4C23×C314yes—
669C4×D4C23×C312yes—
670C4×D4C23×C314yes—
671C4×D4C23×C318yes—
672C4×D4C23×C318yes—
673C4×D4C23×C318yes—
674C4×D4C23×C318yes—
675C4×D4C23×C3116yes—
676C4×D4C23×C318yes—
677C4×D4C23×C3116yes—
678C4×D4C23×C318yes—
679C4×D4C23×C318yes—
680C4×D4C23×C3116yes—
681C4×D4C23×C3116yes—
682#117C23×C312yes—
683#117C23×C314yes—
684#117C23×C318yes—
685#117C23×C318yes—
686#117C23×C314yes—
687#117C23×C314yes—
688#117C23×C314yes—
689#117C23×C318yes—
690#117C23×C314yes—
691#117C23×C318yes—
692#117C23×C314yes—
693#117C23×C318yes—
694#117C23×C3116yes—
695C2×C4⋊C4C23×C311yescharacteristic
696C2×C4⋊C4C23×C312yes—
697C2×C4⋊C4C23×C314yes—
698C2×C4⋊C4C23×C318yes—
699C2×C4⋊C4C23×C318yes—
700C2×C4⋊C4C23×C314yes—
701C2×C4⋊C4C23×C314yes—
702C2×C4⋊C4C23×C311yescharacteristic
703C2×C4⋊C4C23×C318yes—
704C2×C4⋊C4C23×C318yes—
705C2×C4⋊C4C23×C314yes—
706C2×C4⋊C4C23×C3116yes—
707C2×C4⋊C4C23×C318yes—
708C2×C4⋊C4C23×C312yes—
709C2×C4⋊C4C23×C318yes—
710C2×C22⋊C4C23×C318yes—
711C2×C22⋊C4C23×C312yes—
712C2×C22⋊C4C23×C312yes—
713C2×C22⋊C4C23×C318yes—
714C2×C22⋊C4C23×C314yes—
715C2×C42C23×C318yes—
716C2×C42C23×C311yescharacteristic
717C2×C42C23×C314yes—
718C23×C3—24no—
719C23×C3—24no—
720C23×C3—24no—
721C23×C3—42no—
722C23×C3—42no—
723C23×C3—42no—
724C23×C3C2514yes—
725C23×C3C2512yes—
726C23×C3C2514yes—
727C23×C3C2512yes—
728C23×C3C2511yescharacteristic
729C3×Q8—28no—
730C3×Q8—28no—
731C3×Q8—24no—
732C3×Q8—44no—
733C3×Q8—48no—
734C3×Q8—416no—
735C3×Q8—44no—
736C3×Q8—44no—
737C3×D4—24no—
738C3×D4—216no—
739C3×D4—216no—
740C3×D4—28no—
741C3×D4—22no—
742C3×D4—28no—
743C3×D4—24no—
744C3×D4—48no—
745C3×D4—48no—
746C3×D4—48no—
747C3×D4—44no—
748C3×D4—48no—
749C3×D4H(5,𝔽2)14yes—
750C2×C3×C4—216no—
751C2×C3×C4—216no—
752C2×C3×C4—24no—
753C2×C3×C4—22no—
754C2×C3×C4—28no—
755C2×C3×C4—28no—
756C2×C3×C4—28no—
757C2×C3×C4—28no—
758C2×C3×C4—28no—
759C2×C3×C4—42no—
760C2×C3×C4—44no—
761C2×C3×C4—44no—
762C2×C3×C4—48no—
763C2×C3×C4—48no—
764C2×C3×C4—44no—
765C2×C3×C4—48no—
766C2×C3×C4—41no—
767C2×C3×C4—416no—
768C2×C3×C4—48no—
769C2×C3×C42−1+414yescomplemented
770C2×C3×C4C2514yes—
771C2×C3×C4C2514yes—
772C2×C3×C4C2512yes—
773C2×C3×C4C2518yes—
774C2×C3×C4C2514yes—
775C2×C3×C4C2514yes—
776C2×C3×C4C2518yes—
777C2×C3×C4C2511yescharacteristic
778C2×C3×C4C2518yes—
779C2×C3×C4C2514yes—
780C2×C3×C4C2511yescharacteristic
781C2×C3×C4C2512yes—
782C24C24×C312yes—
783C24C24×C312yes—
784#41—216no—
785#41—216no—
786#41—28no—
787#41—48no—
788#41—416no—
789#41—416no—
790#41—432no—
791#41—48no—
792C2×Q8—416no—
793C2×Q8—44no—
794C2×Q8—48no—
795C2×Q8—416no—
796C2×Q8C24×C312yes—
797C2×Q8C24×C314yes—
798C2×Q8C24×C314yes—
799C2×Q8C24×C314yes—
800C2×Q8C24×C318yes—
801C2×Q8C24×C314yes—
802C2×Q8C24×C314yes—
803C2×Q8C24×C3116yes—
804C2×D4—24no—
805C2×D4—24no—
806C2×D4—48no—
807C2×D4C24×C314yes—
808C2×D4C24×C314yes—
809C2×D4C24×C312yes—
810C2×D4C24×C318yes—
811C2×D4C24×C312yes—
812C2×D4C24×C318yes—
813C2×D4C24×C311yescharacteristic
814C2×D4C24×C318yes—
815C2×D4C24×C318yes—
816C2×D4C24×C318yes—
817C2×D4C24×C314yes—
818C2×D4C24×C318yes—
819C2×D4C24×C311yescharacteristic
820C22×C4—28no—
821C22×C4—44no—
822C22×C4—48no—
823C22×C4C24×C314yes—
824C22×C4C24×C318yes—
825C22×C4C24×C314yes—
826C22×C4C24×C311yescharacteristic
827C22×C4C24×C314yes—
828C22×C4C24×C312yes—
829C22×C4C24×C318yes—
830C22×C4C24×C314yes—
831C22×C4C24×C314yes—
832C22×C4C24×C311yescharacteristic
833C22×C4C24×C318yes—
834C22×C4C24×C314yes—
835C22×C4C24×C314yes—
836C22×C4C24×C312yes—
837C22×C4C24×C318yes—
838C22×C4C24×C318yes—
839C22×C4C24×C3116yes—
840C22×C4C24×C318yes—
841C22×C4C24×C314yes—
842C22×C4C24×C311yescharacteristic
843C4⋊C4C24×C314yes—
844C4⋊C4C24×C318yes—
845C4⋊C4C24×C314yes—
846C4⋊C4C24×C3116yes—
847C4⋊C4C24×C312yes—
848C4⋊C4C24×C312yes—
849C4⋊C4C24×C314yes—
850C4⋊C4C24×C318yes—
851C4⋊C4C24×C314yes—
852C4⋊C4C24×C318yes—
853C4⋊C4C24×C3116yes—
854C4⋊C4C24×C3116yes—
855C4⋊C4C24×C318yes—
856C4⋊C4C24×C314yes—
857C4⋊C4C24×C318yes—
858C4⋊C4C24×C314yes—
859C4⋊C4C24×C312yes—
860C4⋊C4C24×C318yes—
861C4⋊C4C24×C318yes—
862C4⋊C4C24×C3116yes—
863C4⋊C4C24×C312yes—
864C4⋊C4C24×C3116yes—
865C4⋊C4C24×C3116yes—
866C4⋊C4C24×C314yes—
867C4⋊C4C24×C318yes—
868C4⋊C4C24×C318yes—
869C4⋊C4C24×C318yes—
870C4⋊C4C24×C314yes—
871C4⋊C4C24×C314yes—
872C22⋊C4C24×C318yes—
873C22⋊C4C24×C314yes—
874C22⋊C4C24×C314yes—
875C22⋊C4C24×C318yes—
876C22⋊C4C24×C318yes—
877C22⋊C4C24×C3116yes—
878C22⋊C4C24×C3116yes—
879C22⋊C4C24×C318yes—
880C22⋊C4C24×C314yes—
881C22⋊C4C24×C318yes—
882C22⋊C4C24×C318yes—
883C22⋊C4C24×C318yes—
884C22⋊C4C24×C314yes—
885C22⋊C4C24×C3116yes—
886C22⋊C4C24×C314yes—
887C22⋊C4C24×C318yes—
888C22⋊C4C24×C318yes—
889C22⋊C4C24×C318yes—
890C22⋊C4C24×C318yes—
891C42C24×C314yes—
892C42C24×C312yes—
893C42C24×C318yes—
894C42C24×C312yes—
895C42C24×C318yes—
896C42C24×C314yes—
897C42C24×C318yes—
898C42C24×C314yes—
899C42C24×C3116yes—
900C22×C3—21no—
901C22×C3—22no—
902C22×C3—22no—
903C22×C3—21no—
904C22×C3—24no—
905C22×C3—24no—
906C22×C3—22no—
907C22×C3—22no—
908C22×C3—24no—
909C22×C3—24no—
910C22×C3—24no—
911C22×C3—24no—
912C22×C3—22no—
913C22×C3—48no—
914C22×C3—84no—
915C22×C3C2×H(5,𝔽2)14yes—
916C22×C3C2×2−1+412yes—
917C22×C3C2611yescharacteristic
918C3×C4—24no—
919C3×C4—24no—
920C3×C4—21no—
921C3×C4—28no—
922C3×C4—28no—
923C3×C4—24no—
924C3×C4—24no—
925C3×C4—24no—
926C3×C4—28no—
927C3×C4—22no—
928C3×C4C2×H(5,𝔽2)12yes—
929C3×C4C2×2−1+414yes—
930C23—24no—
931C23—24no—
932C23—24no—
933C23—42no—
934C23—42no—
935C23—42no—
936C23C25×C314yes—
937C23C25×C312yes—
938C23C25×C314yes—
939C23C25×C312yes—
940C23C25×C311yescharacteristic
941Q8—28no—
942Q8—28no—
943Q8—24no—
944Q8—44no—
945Q8—48no—
946Q8—416no—
947Q8—44no—
948Q8—44no—
949D4—24no—
950D4—216no—
951D4—216no—
952D4—28no—
953D4—22no—
954D4—28no—
955D4—24no—
956D4—48no—
957D4—44no—
958D4—48no—
959D4—48no—
960D4—48no—
961D4C3×H(5,𝔽2)14yes—
962C2×C4—216no—
963C2×C4—216no—
964C2×C4—24no—
965C2×C4—22no—
966C2×C4—28no—
967C2×C4—28no—
968C2×C4—28no—
969C2×C4—28no—
970C2×C4—28no—
971C2×C4—42no—
972C2×C4—44no—
973C2×C4—44no—
974C2×C4—48no—
975C2×C4—416no—
976C2×C4—48no—
977C2×C4—48no—
978C2×C4—44no—
979C2×C4—48no—
980C2×C4—41no—
981C2×C4C3×2−1+414yescomplemented
982C2×C4C25×C314yes—
983C2×C4C25×C314yes—
984C2×C4C25×C312yes—
985C2×C4C25×C318yes—
986C2×C4C25×C314yes—
987C2×C4C25×C314yes—
988C2×C4C25×C318yes—
989C2×C4C25×C311yescharacteristic
990C2×C4C25×C318yes—
991C2×C4C25×C314yes—
992C2×C4C25×C311yescharacteristic
993C2×C4C25×C312yes—
994C2×C3—22no—
995C2×C3—24no—
996C2×C3—44no—
997C2×C3—42no—
998C2×C3—44no—
999C2×C3C22×H(5,𝔽2)11yescharacteristic
1000C2×C3C22×2−1+411yescharacteristic
1001C2×C32−1+611yescharacteristic
1002C22—21no—
1003C22—22no—
1004C22—22no—
1005C22—21no—
1006C22—24no—
1007C22—24no—
1008C22—22no—
1009C22—22no—
1010C22—24no—
1011C22—24no—
1012C22—24no—
1013C22—24no—
1014C22—22no—
1015C22—48no—
1016C22—84no—
1017C22C2×C3×H(5,𝔽2)14yes—
1018C22C2×C3×2−1+412yes—
1019C22C26×C311yescharacteristic
1020C4—24no—
1021C4—24no—
1022C4—21no—
1023C4—28no—
1024C4—28no—
1025C4—24no—
1026C4—24no—
1027C4—24no—
1028C4—28no—
1029C4—22no—
1030C4C2×C3×H(5,𝔽2)12yes—
1031C4C2×C3×2−1+414yes—
1032C3#6291511yescharacteristic, direct product factor, Sylow
1033C2—22no—
1034C2—24no—
1035C2—42no—
1036C2—44no—
1037C2—44no—
1038C2C22×C3×H(5,𝔽2)11yescharacteristic
1039C2C22×C3×2−1+411yescharacteristic
1040C2C3×2−1+611yescharacteristic
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×#3559C2semidirect
2. C3×#3552C2semidirect
3. C3×#3547C2semidirect
4. C3×#3544C2semidirect
5. C3×#3538C2semidirect
6. C3×#3535C2semidirect
7. C3×#3515C2semidirect
8. C3×#3503C2semidirect
9. C3×#3501C2semidirect
10. C3×#3499C2semidirect
11. C3×#3494C2semidirect
12. C3×#3492C2semidirect
13. C3×#3489C2semidirect
14. C3×#3475C2semidirect
15. C2×C3×#547C2semidirect
16. C3×#3460C2semidirect
17. C2×C3×#544C2semidirect
18. #62915C3direct (N × H)
19. C2×C3×2−1+4C22semidirect
21. C3×#563C22semidirect
22. C3×#563C22semidirect
23. C3×#562C22semidirect
24. C3×Q82C22semidirect
25. C3×#557C22semidirect
26. C3×#556C22semidirect
27. C3×#555C22semidirect
28. C3×#555C22semidirect
30. C3×#554C22semidirect
31. C3×#554C22semidirect
32. C3×#554C22semidirect
33. C3×#554C22semidirect
34. C3×#554C22semidirect
35. C3×#553C22semidirect
36. C3×#553C22semidirect
37. C3×#553C22semidirect
38. C3×#553C22semidirect
40. C3×#552C22semidirect
41. C3×#552C22semidirect
42. C3×#552C22semidirect
43. C3×#552C22semidirect
47. C3×D4×Q8C22semidirect
48. C3×D4×Q8C22semidirect
49. C3×D4×Q8C22semidirect
50. C3×#548C22semidirect
54. C3×#547C22semidirect
55. C3×#547C22semidirect
56. C3×#547C22semidirect
57. C3×#547C22semidirect
58. C3×#547C22semidirect
59. C3×#547C22semidirect
66. C3×#544C22semidirect
67. C3×#544C22semidirect
68. C3×#544C22semidirect
69. C3×#544C22semidirect
71. C3×#542C22semidirect
72. C3×#542C22semidirect
73. C3×#542C22semidirect
74. C3×#541C22semidirect
75. C3×#540C22semidirect
76. C3×#540C22semidirect
78. C3×#539C22semidirect
79. C3×#539C22semidirect
80. C3×#539C22semidirect
83. C3×#537C22semidirect
84. C3×#537C22semidirect
85. C3×#536C22semidirect
86. C3×#536C22semidirect
87. C3×#536C22semidirect
88. C3×#536C22semidirect
91. C3×#533C22semidirect
92. C3×#532C22semidirect
93. C3×#532C22semidirect
95. C2×C3×C4⋊Q8C22semidirect
96. C2×C3×C4⋊Q8C22semidirect
97. C3×#529C22semidirect
98. C3×#529C22semidirect
99. C3×#529C22semidirect
100. C3×#529C22semidirect
101. C2×C3×#125C22semidirect
111. C3×#520C22semidirect
114. C3×C4×#41C22semidirect
119. #3559C2×C3semidirect
120. #3552C2×C3semidirect
121. #3547C2×C3semidirect
122. #3544C2×C3semidirect
123. #3538C2×C3semidirect
124. #3535C2×C3semidirect
125. #3515C2×C3semidirect
126. #3503C2×C3semidirect
127. #3501C2×C3semidirect
128. #3499C2×C3semidirect
129. #3494C2×C3semidirect
130. #3492C2×C3semidirect
131. #3489C2×C3semidirect
132. #3475C2×C3semidirect
133. C2×#547C2×C3semidirect
134. #3460C2×C3semidirect
135. C2×#544C2×C3semidirect
318. C2×2−1+4C22×C3semidirect
320. #563C22×C3semidirect
321. #563C22×C3semidirect
322. #562C22×C3semidirect
323. Q82C22×C3semidirect
324. #557C22×C3semidirect
325. #556C22×C3semidirect
326. #555C22×C3semidirect
327. #555C22×C3semidirect
329. #554C22×C3semidirect
330. #554C22×C3semidirect
331. #554C22×C3semidirect
332. #554C22×C3semidirect
333. #554C22×C3semidirect
334. #553C22×C3semidirect
335. #553C22×C3semidirect
336. #553C22×C3semidirect
337. #553C22×C3semidirect
339. #552C22×C3semidirect
340. #552C22×C3semidirect
341. #552C22×C3semidirect
342. #552C22×C3semidirect
346. D4×Q8C22×C3semidirect
347. D4×Q8C22×C3semidirect
348. D4×Q8C22×C3semidirect
349. #548C22×C3semidirect
353. #547C22×C3semidirect
354. #547C22×C3semidirect
355. #547C22×C3semidirect
356. #547C22×C3semidirect
357. #547C22×C3semidirect
358. #547C22×C3semidirect
365. #544C22×C3semidirect
366. #544C22×C3semidirect
367. #544C22×C3semidirect
368. #544C22×C3semidirect
370. #542C22×C3semidirect
371. #542C22×C3semidirect
372. #542C22×C3semidirect
373. #541C22×C3semidirect
374. #540C22×C3semidirect
375. #540C22×C3semidirect
377. #539C22×C3semidirect
378. #539C22×C3semidirect
379. #539C22×C3semidirect
382. #537C22×C3semidirect
383. #537C22×C3semidirect
384. #536C22×C3semidirect
385. #536C22×C3semidirect
386. #536C22×C3semidirect
387. #536C22×C3semidirect
390. #533C22×C3semidirect
391. #532C22×C3semidirect
392. #532C22×C3semidirect
394. C2×C4⋊Q8C22×C3semidirect
395. C2×C4⋊Q8C22×C3semidirect
396. #529C22×C3semidirect
397. #529C22×C3semidirect
398. #529C22×C3semidirect
399. #529C22×C3semidirect
400. C2×#125C22×C3semidirect
410. #520C22×C3semidirect
413. C4×#41C22×C3semidirect
769. C2×C3×C42−1+4semidirect
981. C2×C4C3×2−1+4semidirect
1032. C3#62915direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#35592
C3×#35522
C3×#35472
C3×#35442
C3×#35382
C3×#35352
C3×#35152
C3×#35032
C3×#35012
C3×#34992
C3×#34942
C3×#34922
C3×#34892
C3×#34752
C2×C3×#5472
C3×#34602
C2×C3×#5442
#629153