Finite Group Databasebeta

← C3×#62929 #10681536

Subgroups — C3×#62929 #10681536

Order 768.

6566 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3565C218yesmaximal, complemented
2C3×#3561C218yesmaximal, complemented
3C3×#3547C218yesmaximal, complemented
4C3×#3547C214yesmaximal, complemented
5C3×#3544C214yesmaximal, complemented
6C3×#3536C214yesmaximal, complemented
7C3×#3518C214yesmaximal, complemented
8C3×#3511C214yesmaximal, complemented
9C3×#3503C212yesmaximal, complemented
10C3×#3501C211yesmaximal, characteristic, complemented
11C3×#3495C214yesmaximal, complemented
12C3×#3494C214yesmaximal, complemented
13C3×#3493C212yesmaximal, complemented
14C3×#3475C212yesmaximal, complemented
15C2×C3×#555C211yesmaximal, characteristic, complemented
16C3×#3460C211yesmaximal, characteristic, complemented
17C3×#3458C212yesmaximal, complemented
18#62929C311yesmaximal, characteristic, direct product factor, Sylow
19C3×#563C22116yescomplemented
20C3×#562C22116yescomplemented
21C3×#562C22116yescomplemented
22C3×Q82C2214yescomplemented
23C3×#557C2214yescomplemented
24C3×#556C2212yescomplemented
25C3×#556C2218yescomplemented
26C3×#556C2218yescomplemented
27C3×#556C22116yescomplemented
28C3×#555C2214yes—
29C3×#555C2214yes—
30C3×#555C2218yes—
31C3×#555C2212yescomplemented
32C3×#555C2218yescomplemented
33C3×#555C2218yescomplemented
34C3×#554C2218yes—
35C3×#554C2212yescomplemented
36C3×#554C2214yescomplemented
37C3×#554C2218yescomplemented
38C3×#554C2214yescomplemented
39C3×#553C2214yescomplemented
40C3×#553C2218yescomplemented
41C3×#553C2218yescomplemented
42C3×#553C2218yescomplemented
43C3×#552C2214yes—
44C3×#552C2214yescomplemented
45C3×#552C2218yescomplemented
46C3×#552C2218yescomplemented
47C3×#552C22116yescomplemented
48C3×#551C2218yes—
49C3×#551C22116yes—
50C3×D4×Q8C2218yes—
51C3×D4×Q8C2214yescomplemented
52C3×D4×Q8C2214yescomplemented
53C3×#548C22116yescomplemented
54C3×#548C2218yescomplemented
55C3×#547C2212yescomplemented
56C3×#547C2218yescomplemented
57C3×#547C2218yescomplemented
58C3×#546C2214yes—
59C3×#546C22116yes—
60C3×#544C2211yescharacteristic
61C3×#544C2212yes—
62C3×#544C2214yes—
63C3×#544C2218yescomplemented
64C3×#544C2218yescomplemented
65C3×#544C2214yescomplemented
66C3×#544C2218yescomplemented
67C3×#543C2218yes—
68C3×#543C2214yes—
69C3×#542C2214yescomplemented
70C3×#542C2218yescomplemented
71C3×#542C2218yescomplemented
72C3×#542C22116yescomplemented
73C3×#542C2218yescomplemented
74C3×#542C22116yescomplemented
75C3×#542C22116yescomplemented
76C3×#541C2218yescomplemented
77C3×#540C2214yescomplemented
78C3×#540C2218yescomplemented
79C3×#539C2218yescomplemented
80C3×#538C2214yes—
81C3×#538C2218yes—
82C3×#537C2211yescharacteristic
83C3×#537C2218yescomplemented
84C3×#537C2218yescomplemented
85C3×#536C2214yescomplemented
86C3×#536C22116yescomplemented
87C3×#535C2212yes—
88C3×#533C2218yes—
89C3×#533C2212yes—
90C3×#533C2218yescomplemented
91C3×#533C2218yescomplemented
92C3×#533C2214yescomplemented
93C3×#532C2214yescomplemented
94C3×#532C2218yescomplemented
95C2×C3×C4⋊Q8C2211yescharacteristic
96C2×C3×C4⋊Q8C2214yescomplemented
97C3×#529C2218yes—
98C3×#529C2214yescomplemented
99C3×#529C2214yescomplemented
100C3×#529C2218yescomplemented
101C3×#529C2218yescomplemented
102C2×C3×#124C2214yes—
103C3×#525C2214yes—
104C3×#525C2214yes—
105C2×C3×C22⋊Q8C2214yes—
106C2×C3×#121C2212yes—
107C2×C3×#121C2212yes—
108C3×#520C2214yes—
109C3×#520C2214yescomplemented
110C3×#519C2214yescomplemented
111C3×#518C2212yes—
112C3×C4×#41C2212yes—
113C3×C4×#41C2214yescomplemented
114C2×C3×C4×D4C2211yescharacteristic
115C2×C3×C4×D4C2211yescharacteristic
116C2×C3×#117C2212yes—
117C2×C3×#117C2214yes—
118C2×C3×#117C2212yes—
119#3565C2×C318yescomplemented
120#3561C2×C318yescomplemented
121#3547C2×C314yescomplemented
122#3547C2×C318yescomplemented
123#3544C2×C314yescomplemented
124#3536C2×C314yescomplemented
125#3518C2×C314yescomplemented
126#3511C2×C314yescomplemented
127#3503C2×C312yescomplemented
128#3501C2×C311yescharacteristic, complemented
129#3495C2×C314yescomplemented
130#3494C2×C314yescomplemented
131#3493C2×C312yescomplemented
132#3475C2×C312yescomplemented
133C2×#555C2×C311yescharacteristic, complemented
134#3460C2×C311yescharacteristic, complemented
135#3458C2×C312yescomplemented
136C2×C3×#41C2312yes—
137C2×C3×#41C2314yes—
138C2×C3×#41C2314yes—
139C2×C3×#41C23116yes—
140C22×C3×Q8C2314yes—
141C22×C3×Q8C2312yes—
142C22×C3×Q8C2318yes—
143C22×C3×D4C2311yescharacteristic
144C22×C3×D4C2311yescharacteristic
145C22×C3×D4C2314yes—
146C23×C3×C4C2312yes—
147C23×C3×C4C2312yes—
148C3×C4⋊Q8C23116yes—
149C3×C4⋊Q8C2314yes—
150C3×C4⋊Q8C2318yes—
151C3×C4⋊Q8C2318yes—
152C3×C4⋊Q8C2318yes—
153C3×C4⋊Q8C2314yes—
154C3×C4⋊Q8C2312yes—
155C3×C4⋊Q8C2318yes—
156C3×C4⋊Q8C2314yes—
157C3×C4⋊Q8C2312yes—
158C3×C4⋊Q8C2318yes—
159C3×C4⋊Q8C2318yes—
160C3×C4⋊Q8C2318yes—
161C3×#127C2314yes—
162C3×#126C2318yes—
163C3×#126C2318yes—
164C3×#126C23116yes—
165C3×#126C23116yes—
166C3×#126C23116yes—
167C3×#126C23116yes—
168C3×#126C2318yes—
169C3×#126C2318yes—
170C3×#125C23116yes—
171C3×#125C23116yes—
172C3×#125C2318yes—
173C3×#125C2314yes—
174C3×#125C2318yes—
175C3×#125C2318yes—
176C3×#125C2314yes—
177C3×#125C2314yes—
178C3×#125C2318yes—
179C3×#125C2318yes—
180C3×#124C2318yes—
181C3×#124C23116yes—
182C3×#124C23116yes—
183C3×#124C23116yes—
184C3×#124C23116yes—
185C3×#124C2314yes—
186C3×#124C2314yes—
187C3×#124C2318yes—
188C3×#124C2318yes—
189C3×#124C23116yes—
190C3×#123C2318yes—
191C3×#123C2318yes—
192C3×#123C2318yes—
193C3×#123C2318yes—
194C3×#123C23116yes—
195C3×#123C23116yes—
196C3×#123C23116yes—
197C3×#123C23116yes—
198C3×#123C23116yes—
199C3×#123C2318yes—
200C3×#123C2318yes—
201C3×C22⋊Q8C2318yes—
202C3×C22⋊Q8C2318yes—
203C3×C22⋊Q8C23116yes—
204C3×C22⋊Q8C23116yes—
205C3×C22⋊Q8C23116yes—
206C3×C22⋊Q8C23116yes—
207C3×C22⋊Q8C23116yes—
208C3×C22⋊Q8C2318yes—
209C3×C22⋊Q8C23116yes—
210C3×C22⋊Q8C23116yes—
211C3×C22⋊Q8C2314yes—
212C3×C22⋊Q8C2318yes—
213C3×C22⋊Q8C2318yes—
214C3×C22⋊Q8C2314yes—
215C3×C22⋊Q8C2314yes—
216C3×C22⋊Q8C2314yes—
217C3×C22⋊Q8C2314yes—
218C3×C22⋊Q8C2314yes—
219C3×C22⋊Q8C2314yes—
220C3×C22⋊Q8C2314yes—
221C3×C22⋊Q8C23116yes—
222C3×C22⋊Q8C23116yes—
223C3×C22⋊Q8C2318yes—
224C3×C22⋊Q8C23116yes—
225C3×#121C2318yes—
226C3×#121C2318yes—
227C3×#121C23116yes—
228C3×#121C2318yes—
229C3×#121C23116yes—
230C3×#121C23116yes—
231C3×#121C23116yes—
232C3×#121C2318yes—
233C3×#121C2318yes—
234C3×#121C2318yes—
235C3×#121C2314yes—
236C3×#121C2314yes—
237C3×#121C2314yes—
238C3×#121C2314yes—
239C3×#121C2314yes—
240C3×#121C2314yes—
241C3×#121C2314yes—
242C3×#121C2314yes—
243C3×#120C2318yes—
244C3×#120C2318yes—
245C3×C4×Q8C2312yes—
246C3×C4×Q8C2314yes—
247C3×C4×Q8C2318yes—
248C3×C4×Q8C2318yes—
249C3×C4×Q8C2312yes—
250C3×C4×Q8C2314yes—
251C3×C4×Q8C2318yes—
252C3×C4×Q8C2318yes—
253C3×C4×Q8C2318yes—
254C3×C4×Q8C2314yes—
255C3×C4×Q8C23116yes—
256C3×C4×Q8C2318yes—
257C3×C4×D4C2312yes—
258C3×C4×D4C2312yes—
259C3×C4×D4C2314yes—
260C3×C4×D4C2314yes—
261C3×C4×D4C2314yes—
262C3×C4×D4C2314yes—
263C3×C4×D4C2312yes—
264C3×C4×D4C2314yes—
265C3×C4×D4C2312yes—
266C3×C4×D4C2318yes—
267C3×C4×D4C2314yes—
268C3×C4×D4C2318yes—
269C3×C4×D4C2318yes—
270C3×C4×D4C2318yes—
271C3×C4×D4C23116yes—
272C3×C4×D4C2318yes—
273C3×C4×D4C2318yes—
274C3×C4×D4C23116yes—
275C3×C4×D4C2318yes—
276C3×C4×D4C2318yes—
277C3×C4×D4C23116yes—
278C3×#117C2312yes—
279C3×#117C2314yes—
280C3×#117C2314yes—
281C3×#117C2318yes—
282C3×#117C2318yes—
283C3×#117C2314yes—
284C3×#117C2318yes—
285C3×#117C2314yes—
286C3×#117C2314yes—
287C3×#117C2318yes—
288C3×#117C2318yes—
289C3×#117C2314yes—
290C3×#117C2314yes—
291C3×#117C2318yes—
292C3×#117C2314yes—
293C3×#117C23116yes—
294C3×#117C2318yes—
295C3×#117C23116yes—
296C2×C3×C4⋊C4C2311yescharacteristic
297C2×C3×C4⋊C4C2311yescharacteristic
298C2×C3×C4⋊C4C2312yes—
299C2×C3×C4⋊C4C2312yes—
300C2×C3×C4⋊C4C2314yes—
301C2×C3×C4⋊C4C2314yes—
302C2×C3×C4⋊C4C2318yes—
303C2×C3×C4⋊C4C2314yes—
304C2×C3×C4⋊C4C2318yes—
305C2×C3×C4⋊C4C2318yes—
306C2×C3×C22⋊C4C2314yes—
307C2×C3×C22⋊C4C2314yes—
308C2×C3×C22⋊C4C2318yes—
309C2×C3×C22⋊C4C2312yes—
310C2×C3×C22⋊C4C2312yes—
311C2×C3×C22⋊C4C2318yes—
312C2×C3×C42C2314yes—
313C2×C3×C42C2318yes—
314C2×C3×C42C2311yescharacteristic
315C2×C3×C42C2314yes—
316#563C22×C3116yescomplemented
317#562C22×C3116yescomplemented
318#562C22×C3116yescomplemented
319Q82C22×C314yescomplemented
320#557C22×C314yescomplemented
321#556C22×C312yescomplemented
322#556C22×C318yescomplemented
323#556C22×C318yescomplemented
324#556C22×C3116yescomplemented
325#555C22×C314yes—
326#555C22×C314yes—
327#555C22×C318yes—
328#555C22×C312yescomplemented
329#555C22×C318yescomplemented
330#555C22×C318yescomplemented
331#554C22×C318yes—
332#554C22×C312yescomplemented
333#554C22×C314yescomplemented
334#554C22×C318yescomplemented
335#554C22×C314yescomplemented
336#553C22×C314yescomplemented
337#553C22×C318yescomplemented
338#553C22×C318yescomplemented
339#553C22×C318yescomplemented
340#552C22×C314yes—
341#552C22×C314yescomplemented
342#552C22×C318yescomplemented
343#552C22×C318yescomplemented
344#552C22×C3116yescomplemented
345#551C22×C318yes—
346#551C22×C3116yes—
347D4×Q8C22×C318yes—
348D4×Q8C22×C314yescomplemented
349D4×Q8C22×C314yescomplemented
350#548C22×C3116yescomplemented
351#548C22×C318yescomplemented
352#547C22×C312yescomplemented
353#547C22×C318yescomplemented
354#547C22×C318yescomplemented
355#546C22×C314yes—
356#546C22×C3116yes—
357#544C22×C311yescharacteristic
358#544C22×C312yes—
359#544C22×C314yes—
360#544C22×C318yescomplemented
361#544C22×C318yescomplemented
362#544C22×C314yescomplemented
363#544C22×C318yescomplemented
364#543C22×C318yes—
365#543C22×C314yes—
366#542C22×C314yescomplemented
367#542C22×C318yescomplemented
368#542C22×C318yescomplemented
369#542C22×C3116yescomplemented
370#542C22×C318yescomplemented
371#542C22×C3116yescomplemented
372#542C22×C3116yescomplemented
373#541C22×C318yescomplemented
374#540C22×C314yescomplemented
375#540C22×C318yescomplemented
376#539C22×C318yescomplemented
377#538C22×C314yes—
378#538C22×C318yes—
379#537C22×C311yescharacteristic
380#537C22×C318yescomplemented
381#537C22×C318yescomplemented
382#536C22×C314yescomplemented
383#536C22×C3116yescomplemented
384#535C22×C312yes—
385#533C22×C318yes—
386#533C22×C312yes—
387#533C22×C318yescomplemented
388#533C22×C318yescomplemented
389#533C22×C314yescomplemented
390#532C22×C314yescomplemented
391#532C22×C318yescomplemented
392C2×C4⋊Q8C22×C311yescharacteristic
393C2×C4⋊Q8C22×C314yescomplemented
394#529C22×C318yes—
395#529C22×C314yescomplemented
396#529C22×C314yescomplemented
397#529C22×C318yescomplemented
398#529C22×C318yescomplemented
399C2×#124C22×C314yes—
400#525C22×C314yes—
401#525C22×C314yes—
402C2×C22⋊Q8C22×C314yes—
403C2×#121C22×C312yes—
404C2×#121C22×C312yes—
405#520C22×C314yes—
406#520C22×C314yescomplemented
407#519C22×C314yescomplemented
408#518C22×C312yes—
409C4×#41C22×C312yes—
410C4×#41C22×C314yescomplemented
411C2×C4×D4C22×C311yescharacteristic
412C2×C4×D4C22×C311yescharacteristic
413C2×#117C22×C312yes—
414C2×#117C22×C314yes—
415C2×#117C22×C312yes—
416C24×C3C2412yes—
417C24×C3C2412yes—
418C3×#41—28no—
419C3×#41—48no—
420C3×#41—48no—
421C3×#41—816no—
422C2×C3×Q8—48no—
423C2×C3×Q8—82no—
424C2×C3×Q8—88no—
425C2×C3×Q8C2412yes—
426C2×C3×Q8C2414yes—
427C2×C3×Q8C2418yes—
428C2×C3×Q8C2414yes—
429C2×C3×Q8C2414yes—
430C2×C3×Q8C24116yes—
431C2×C3×Q8C2418yes—
432C2×C3×D4—24no—
433C2×C3×D4—42no—
434C2×C3×D4—84no—
435C2×C3×D4C2414yes—
436C2×C3×D4C2414yes—
437C2×C3×D4C2412yes—
438C2×C3×D4C2412yes—
439C2×C3×D4C2418yes—
440C2×C3×D4C2418yes—
441C2×C3×D4C2414yes—
442C2×C3×D4C2412yes—
443C2×C3×D4C2418yes—
444C2×C3×D4C2418yes—
445C2×C3×D4C24116yes—
446C22×C3×C4—28no—
447C22×C3×C4—44no—
448C22×C3×C4C2412yes—
449C22×C3×C4C2414yes—
450C22×C3×C4C2411yescharacteristic
451C22×C3×C4C2414yes—
452C22×C3×C4C2414yes—
453C22×C3×C4C2414yes—
454C22×C3×C4C2414yes—
455C22×C3×C4C2412yes—
456C22×C3×C4C2411yescharacteristic
457C22×C3×C4C2414yes—
458C22×C3×C4C2418yes—
459C22×C3×C4C2418yes—
460C22×C3×C4C2414yes—
461C22×C3×C4C2418yes—
462C22×C3×C4C2418yes—
463C22×C3×C4C2414yes—
464C22×C3×C4C24116yes—
465C22×C3×C4C2411yescharacteristic
466C3×C4⋊C4C2414yes—
467C3×C4⋊C4C2414yes—
468C3×C4⋊C4C2414yes—
469C3×C4⋊C4C2412yes—
470C3×C4⋊C4C2418yes—
471C3×C4⋊C4C2412yes—
472C3×C4⋊C4C2418yes—
473C3×C4⋊C4C2411yescharacteristic
474C3×C4⋊C4C2414yes—
475C3×C4⋊C4C2414yes—
476C3×C4⋊C4C2411yescharacteristic
477C3×C4⋊C4C2412yes—
478C3×C4⋊C4C2414yes—
479C3×C4⋊C4C2418yes—
480C3×C4⋊C4C2418yes—
481C3×C4⋊C4C24116yes—
482C3×C4⋊C4C24116yes—
483C3×C4⋊C4C2418yes—
484C3×C4⋊C4C24116yes—
485C3×C4⋊C4C2418yes—
486C3×C4⋊C4C2418yes—
487C3×C4⋊C4C2418yes—
488C3×C4⋊C4C2414yes—
489C3×C4⋊C4C2414yes—
490C3×C4⋊C4C2414yes—
491C3×C4⋊C4C24116yes—
492C3×C4⋊C4C2414yes—
493C3×C4⋊C4C2418yes—
494C3×C4⋊C4C24116yes—
495C3×C4⋊C4C2414yes—
496C3×C22⋊C4C2418yes—
497C3×C22⋊C4C2414yes—
498C3×C22⋊C4C2418yes—
499C3×C22⋊C4C2414yes—
500C3×C22⋊C4C2418yes—
501C3×C22⋊C4C24116yes—
502C3×C22⋊C4C2418yes—
503C3×C22⋊C4C2418yes—
504C3×C22⋊C4C24116yes—
505C3×C22⋊C4C2418yes—
506C3×C22⋊C4C2414yes—
507C3×C22⋊C4C2418yes—
508C3×C22⋊C4C2418yes—
509C3×C22⋊C4C2418yes—
510C3×C22⋊C4C2418yes—
511C3×C22⋊C4C2418yes—
512C3×C22⋊C4C2414yes—
513C3×C22⋊C4C24116yes—
514C3×C22⋊C4C2414yes—
515C3×C22⋊C4C2418yes—
516C3×C22⋊C4C2418yes—
517C3×C42C2414yes—
518C3×C42C2412yes—
519C3×C42C2418yes—
520C3×C42C2418yes—
521C3×C42C2418yes—
522C3×C42C2418yes—
523C3×C42C2412yes—
524C3×C42C2418yes—
525C3×C42C2414yes—
526C3×C42C2414yes—
527C3×C42C24116yes—
528C2×#41C23×C312yes—
529C2×#41C23×C314yes—
530C2×#41C23×C314yes—
531C2×#41C23×C3116yes—
532C22×Q8C23×C314yes—
533C22×Q8C23×C312yes—
534C22×Q8C23×C318yes—
535C22×D4C23×C311yescharacteristic
536C22×D4C23×C311yescharacteristic
537C22×D4C23×C314yes—
538C23×C4C23×C312yes—
539C23×C4C23×C312yes—
540C4⋊Q8C23×C314yes—
541C4⋊Q8C23×C314yes—
542C4⋊Q8C23×C312yes—
543C4⋊Q8C23×C318yes—
544C4⋊Q8C23×C318yes—
545C4⋊Q8C23×C318yes—
546C4⋊Q8C23×C314yes—
547C4⋊Q8C23×C312yes—
548C4⋊Q8C23×C318yes—
549C4⋊Q8C23×C318yes—
550C4⋊Q8C23×C318yes—
551C4⋊Q8C23×C318yes—
552C4⋊Q8C23×C3116yes—
553#127C23×C314yes—
554#126C23×C3116yes—
555#126C23×C318yes—
556#126C23×C3116yes—
557#126C23×C318yes—
558#126C23×C318yes—
559#126C23×C318yes—
560#126C23×C3116yes—
561#126C23×C3116yes—
562#125C23×C318yes—
563#125C23×C314yes—
564#125C23×C318yes—
565#125C23×C318yes—
566#125C23×C314yes—
567#125C23×C3116yes—
568#125C23×C314yes—
569#125C23×C318yes—
570#125C23×C318yes—
571#125C23×C3116yes—
572#124C23×C3116yes—
573#124C23×C3116yes—
574#124C23×C318yes—
575#124C23×C314yes—
576#124C23×C314yes—
577#124C23×C318yes—
578#124C23×C318yes—
579#124C23×C3116yes—
580#124C23×C3116yes—
581#124C23×C3116yes—
582#123C23×C318yes—
583#123C23×C318yes—
584#123C23×C318yes—
585#123C23×C318yes—
586#123C23×C318yes—
587#123C23×C3116yes—
588#123C23×C318yes—
589#123C23×C3116yes—
590#123C23×C3116yes—
591#123C23×C3116yes—
592#123C23×C3116yes—
593C22⋊Q8C23×C314yes—
594C22⋊Q8C23×C318yes—
595C22⋊Q8C23×C318yes—
596C22⋊Q8C23×C318yes—
597C22⋊Q8C23×C314yes—
598C22⋊Q8C23×C314yes—
599C22⋊Q8C23×C314yes—
600C22⋊Q8C23×C314yes—
601C22⋊Q8C23×C314yes—
602C22⋊Q8C23×C318yes—
603C22⋊Q8C23×C314yes—
604C22⋊Q8C23×C314yes—
605C22⋊Q8C23×C3116yes—
606C22⋊Q8C23×C3116yes—
607C22⋊Q8C23×C318yes—
608C22⋊Q8C23×C3116yes—
609C22⋊Q8C23×C318yes—
610C22⋊Q8C23×C3116yes—
611C22⋊Q8C23×C3116yes—
612C22⋊Q8C23×C3116yes—
613C22⋊Q8C23×C3116yes—
614C22⋊Q8C23×C3116yes—
615C22⋊Q8C23×C3116yes—
616C22⋊Q8C23×C3116yes—
617#121C23×C318yes—
618#121C23×C318yes—
619#121C23×C318yes—
620#121C23×C318yes—
621#121C23×C314yes—
622#121C23×C314yes—
623#121C23×C314yes—
624#121C23×C314yes—
625#121C23×C314yes—
626#121C23×C314yes—
627#121C23×C318yes—
628#121C23×C314yes—
629#121C23×C314yes—
630#121C23×C3116yes—
631#121C23×C318yes—
632#121C23×C3116yes—
633#121C23×C3116yes—
634#121C23×C3116yes—
635#120C23×C318yes—
636#120C23×C318yes—
637C4×Q8C23×C312yes—
638C4×Q8C23×C312yes—
639C4×Q8C23×C314yes—
640C4×Q8C23×C314yes—
641C4×Q8C23×C318yes—
642C4×Q8C23×C318yes—
643C4×Q8C23×C318yes—
644C4×Q8C23×C318yes—
645C4×Q8C23×C318yes—
646C4×Q8C23×C314yes—
647C4×Q8C23×C3116yes—
648C4×Q8C23×C318yes—
649C4×D4C23×C312yes—
650C4×D4C23×C312yes—
651C4×D4C23×C314yes—
652C4×D4C23×C314yes—
653C4×D4C23×C314yes—
654C4×D4C23×C314yes—
655C4×D4C23×C312yes—
656C4×D4C23×C314yes—
657C4×D4C23×C312yes—
658C4×D4C23×C318yes—
659C4×D4C23×C314yes—
660C4×D4C23×C318yes—
661C4×D4C23×C318yes—
662C4×D4C23×C318yes—
663C4×D4C23×C3116yes—
664C4×D4C23×C318yes—
665C4×D4C23×C318yes—
666C4×D4C23×C3116yes—
667C4×D4C23×C318yes—
668C4×D4C23×C318yes—
669C4×D4C23×C3116yes—
670#117C23×C312yes—
671#117C23×C314yes—
672#117C23×C314yes—
673#117C23×C318yes—
674#117C23×C318yes—
675#117C23×C314yes—
676#117C23×C318yes—
677#117C23×C314yes—
678#117C23×C314yes—
679#117C23×C318yes—
680#117C23×C318yes—
681#117C23×C314yes—
682#117C23×C314yes—
683#117C23×C318yes—
684#117C23×C314yes—
685#117C23×C3116yes—
686#117C23×C318yes—
687#117C23×C3116yes—
688C2×C4⋊C4C23×C311yescharacteristic
689C2×C4⋊C4C23×C311yescharacteristic
690C2×C4⋊C4C23×C312yes—
691C2×C4⋊C4C23×C312yes—
692C2×C4⋊C4C23×C314yes—
693C2×C4⋊C4C23×C314yes—
694C2×C4⋊C4C23×C318yes—
695C2×C4⋊C4C23×C314yes—
696C2×C4⋊C4C23×C318yes—
697C2×C4⋊C4C23×C318yes—
698C2×C22⋊C4C23×C314yes—
699C2×C22⋊C4C23×C314yes—
700C2×C22⋊C4C23×C318yes—
701C2×C22⋊C4C23×C312yes—
702C2×C22⋊C4C23×C312yes—
703C2×C22⋊C4C23×C318yes—
704C2×C42C23×C314yes—
705C2×C42C23×C318yes—
706C2×C42C23×C311yescharacteristic
707C2×C42C23×C314yes—
708C23×C3—24no—
709C23×C3—24no—
710C23×C3—42no—
711C23×C3—42no—
712C23×C3—42no—
713C23×C3—42no—
714C23×C3C2514yes—
715C23×C3C2514yes—
716C23×C3C2514yes—
717C23×C3C2511yescharacteristic
718C3×Q8—24no—
719C3×Q8—28no—
720C3×Q8—48no—
721C3×Q8—44no—
722C3×Q8—48no—
723C3×Q8—416no—
724C3×Q8—44no—
725C3×D4—28no—
726C3×D4—28no—
727C3×D4—24no—
728C3×D4—24no—
729C3×D4—42no—
730C3×D4—416no—
731C3×D4—48no—
732C3×D4—44no—
733C3×D4—48no—
734C3×D4—48no—
735C3×D4—48no—
736C2×C3×C4—24no—
737C2×C3×C4—28no—
738C2×C3×C4—28no—
739C2×C3×C4—28no—
740C2×C3×C4—22no—
741C2×C3×C4—28no—
742C2×C3×C4—28no—
743C2×C3×C4—44no—
744C2×C3×C4—42no—
745C2×C3×C4—44no—
746C2×C3×C4—48no—
747C2×C3×C4—44no—
748C2×C3×C4—41no—
749C2×C3×C4—416no—
750C2×C3×C4—48no—
751C2×C3×C4—48no—
752C2×C3×C4—48no—
753C2×C3×C42−1+414yes—
754C2×C3×C4C2512yes—
755C2×C3×C4C2514yes—
756C2×C3×C4C2512yes—
757C2×C3×C4C2512yes—
758C2×C3×C4C2514yes—
759C2×C3×C4C2518yes—
760C2×C3×C4C2514yes—
761C2×C3×C4C2514yes—
762C2×C3×C4C2518yes—
763C2×C3×C4C2518yes—
764C2×C3×C4C2511yescharacteristic
765C2×C3×C4C2512yes—
766C2×C3×C4C2511yescharacteristic
767C24C24×C312yes—
768C24C24×C312yes—
769#41—28no—
770#41—48no—
771#41—48no—
772#41—816no—
773C2×Q8—48no—
774C2×Q8—82no—
775C2×Q8—88no—
776C2×Q8C24×C312yes—
777C2×Q8C24×C314yes—
778C2×Q8C24×C318yes—
779C2×Q8C24×C314yes—
780C2×Q8C24×C314yes—
781C2×Q8C24×C3116yes—
782C2×Q8C24×C318yes—
783C2×D4—24no—
784C2×D4—42no—
785C2×D4—84no—
786C2×D4C24×C314yes—
787C2×D4C24×C314yes—
788C2×D4C24×C312yes—
789C2×D4C24×C312yes—
790C2×D4C24×C318yes—
791C2×D4C24×C318yes—
792C2×D4C24×C314yes—
793C2×D4C24×C312yes—
794C2×D4C24×C318yes—
795C2×D4C24×C318yes—
796C2×D4C24×C3116yes—
797C22×C4—28no—
798C22×C4—44no—
799C22×C4C24×C312yes—
800C22×C4C24×C314yes—
801C22×C4C24×C311yescharacteristic
802C22×C4C24×C314yes—
803C22×C4C24×C314yes—
804C22×C4C24×C314yes—
805C22×C4C24×C314yes—
806C22×C4C24×C312yes—
807C22×C4C24×C311yescharacteristic
808C22×C4C24×C314yes—
809C22×C4C24×C318yes—
810C22×C4C24×C318yes—
811C22×C4C24×C314yes—
812C22×C4C24×C318yes—
813C22×C4C24×C318yes—
814C22×C4C24×C314yes—
815C22×C4C24×C3116yes—
816C22×C4C24×C311yescharacteristic
817C4⋊C4C24×C314yes—
818C4⋊C4C24×C314yes—
819C4⋊C4C24×C314yes—
820C4⋊C4C24×C312yes—
821C4⋊C4C24×C318yes—
822C4⋊C4C24×C312yes—
823C4⋊C4C24×C318yes—
824C4⋊C4C24×C311yescharacteristic
825C4⋊C4C24×C314yes—
826C4⋊C4C24×C314yes—
827C4⋊C4C24×C311yescharacteristic
828C4⋊C4C24×C312yes—
829C4⋊C4C24×C314yes—
830C4⋊C4C24×C318yes—
831C4⋊C4C24×C318yes—
832C4⋊C4C24×C3116yes—
833C4⋊C4C24×C3116yes—
834C4⋊C4C24×C318yes—
835C4⋊C4C24×C3116yes—
836C4⋊C4C24×C318yes—
837C4⋊C4C24×C318yes—
838C4⋊C4C24×C318yes—
839C4⋊C4C24×C314yes—
840C4⋊C4C24×C314yes—
841C4⋊C4C24×C314yes—
842C4⋊C4C24×C3116yes—
843C4⋊C4C24×C314yes—
844C4⋊C4C24×C318yes—
845C4⋊C4C24×C3116yes—
846C4⋊C4C24×C314yes—
847C22⋊C4C24×C318yes—
848C22⋊C4C24×C314yes—
849C22⋊C4C24×C318yes—
850C22⋊C4C24×C314yes—
851C22⋊C4C24×C318yes—
852C22⋊C4C24×C3116yes—
853C22⋊C4C24×C318yes—
854C22⋊C4C24×C318yes—
855C22⋊C4C24×C3116yes—
856C22⋊C4C24×C318yes—
857C22⋊C4C24×C314yes—
858C22⋊C4C24×C318yes—
859C22⋊C4C24×C318yes—
860C22⋊C4C24×C318yes—
861C22⋊C4C24×C318yes—
862C22⋊C4C24×C318yes—
863C22⋊C4C24×C314yes—
864C22⋊C4C24×C3116yes—
865C22⋊C4C24×C314yes—
866C22⋊C4C24×C318yes—
867C22⋊C4C24×C318yes—
868C42C24×C314yes—
869C42C24×C312yes—
870C42C24×C318yes—
871C42C24×C318yes—
872C42C24×C318yes—
873C42C24×C318yes—
874C42C24×C312yes—
875C42C24×C318yes—
876C42C24×C314yes—
877C42C24×C314yes—
878C42C24×C3116yes—
879C22×C3—21no—
880C22×C3—21no—
881C22×C3—24no—
882C22×C3—24no—
883C22×C3—24no—
884C22×C3—24no—
885C22×C3—24no—
886C22×C3—24no—
887C22×C3—24no—
888C22×C3—24no—
889C22×C3—24no—
890C22×C3—84no—
891C22×C3—84no—
892C22×C3C2×2−1+412yes—
893C22×C3C2611yescharacteristic
894C3×C4—22no—
895C3×C4—22no—
896C3×C4—24no—
897C3×C4—21no—
898C3×C4—24no—
899C3×C4—24no—
900C3×C4—28no—
901C3×C4—28no—
902C3×C4—28no—
903C3×C4—24no—
904C3×C4—22no—
905C3×C4C2×2−1+414yes—
906C3×C4#58512yes—
907C23—24no—
908C23—24no—
909C23—42no—
910C23—42no—
911C23—42no—
912C23—42no—
913C23C25×C314yes—
914C23C25×C314yes—
915C23C25×C314yes—
916C23C25×C311yescharacteristic
917Q8—24no—
918Q8—28no—
919Q8—48no—
920Q8—44no—
921Q8—48no—
922Q8—416no—
923Q8—44no—
924D4—28no—
925D4—28no—
926D4—24no—
927D4—24no—
928D4—42no—
929D4—416no—
930D4—48no—
931D4—44no—
932D4—48no—
933D4—48no—
934D4—48no—
935C2×C4—24no—
936C2×C4—28no—
937C2×C4—28no—
938C2×C4—28no—
939C2×C4—22no—
940C2×C4—28no—
941C2×C4—28no—
942C2×C4—44no—
943C2×C4—42no—
944C2×C4—44no—
945C2×C4—48no—
946C2×C4—44no—
947C2×C4—41no—
948C2×C4—416no—
949C2×C4—48no—
950C2×C4—48no—
951C2×C4—48no—
952C2×C4C3×2−1+414yes—
953C2×C4C25×C312yes—
954C2×C4C25×C314yes—
955C2×C4C25×C312yes—
956C2×C4C25×C312yes—
957C2×C4C25×C314yes—
958C2×C4C25×C318yes—
959C2×C4C25×C314yes—
960C2×C4C25×C314yes—
961C2×C4C25×C318yes—
962C2×C4C25×C318yes—
963C2×C4C25×C311yescharacteristic
964C2×C4C25×C312yes—
965C2×C4C25×C311yescharacteristic
966C2×C3—22no—
967C2×C3—44no—
968C2×C3—44no—
969C2×C3—44no—
970C2×C3C22×2−1+411yescharacteristic
971C2×C3C2×#58511yescharacteristic
972C2×C3H(7,𝔽2)11yescharacteristic
973C22—21no—
974C22—21no—
975C22—24no—
976C22—24no—
977C22—24no—
978C22—24no—
979C22—24no—
980C22—24no—
981C22—24no—
982C22—24no—
983C22—24no—
984C22—84no—
985C22—84no—
986C22C2×C3×2−1+412yes—
987C22C26×C311yescharacteristic
988C4—22no—
989C4—22no—
990C4—24no—
991C4—21no—
992C4—24no—
993C4—24no—
994C4—28no—
995C4—28no—
996C4—28no—
997C4—24no—
998C4—22no—
999C4C2×C3×2−1+414yes—
1000C4C3×#58512yes—
1001C3#6292911yescharacteristic, direct product factor, Sylow
1002C2—22no—
1003C2—44no—
1004C2—44no—
1005C2—44no—
1006C2C22×C3×2−1+411yescharacteristic
1007C2C2×C3×#58511yescharacteristic
1008C2C3×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×#3565C2semidirect
2. C3×#3561C2semidirect
3. C3×#3547C2semidirect
4. C3×#3547C2semidirect
5. C3×#3544C2semidirect
6. C3×#3536C2semidirect
7. C3×#3518C2semidirect
8. C3×#3511C2semidirect
9. C3×#3503C2semidirect
10. C3×#3501C2semidirect
11. C3×#3495C2semidirect
12. C3×#3494C2semidirect
13. C3×#3493C2semidirect
14. C3×#3475C2semidirect
15. C2×C3×#555C2semidirect
16. C3×#3460C2semidirect
17. C3×#3458C2semidirect
18. #62929C3direct (N × H)
19. C3×#563C22semidirect
20. C3×#562C22semidirect
21. C3×#562C22semidirect
22. C3×Q82C22semidirect
23. C3×#557C22semidirect
24. C3×#556C22semidirect
25. C3×#556C22semidirect
26. C3×#556C22semidirect
27. C3×#556C22semidirect
31. C3×#555C22semidirect
32. C3×#555C22semidirect
33. C3×#555C22semidirect
35. C3×#554C22semidirect
36. C3×#554C22semidirect
37. C3×#554C22semidirect
38. C3×#554C22semidirect
39. C3×#553C22semidirect
40. C3×#553C22semidirect
41. C3×#553C22semidirect
42. C3×#553C22semidirect
44. C3×#552C22semidirect
45. C3×#552C22semidirect
46. C3×#552C22semidirect
47. C3×#552C22semidirect
51. C3×D4×Q8C22semidirect
52. C3×D4×Q8C22semidirect
53. C3×#548C22semidirect
54. C3×#548C22semidirect
55. C3×#547C22semidirect
56. C3×#547C22semidirect
57. C3×#547C22semidirect
63. C3×#544C22semidirect
64. C3×#544C22semidirect
65. C3×#544C22semidirect
66. C3×#544C22semidirect
69. C3×#542C22semidirect
70. C3×#542C22semidirect
71. C3×#542C22semidirect
72. C3×#542C22semidirect
73. C3×#542C22semidirect
74. C3×#542C22semidirect
75. C3×#542C22semidirect
76. C3×#541C22semidirect
77. C3×#540C22semidirect
78. C3×#540C22semidirect
79. C3×#539C22semidirect
83. C3×#537C22semidirect
84. C3×#537C22semidirect
85. C3×#536C22semidirect
86. C3×#536C22semidirect
90. C3×#533C22semidirect
91. C3×#533C22semidirect
92. C3×#533C22semidirect
93. C3×#532C22semidirect
94. C3×#532C22semidirect
96. C2×C3×C4⋊Q8C22semidirect
98. C3×#529C22semidirect
99. C3×#529C22semidirect
100. C3×#529C22semidirect
101. C3×#529C22semidirect
109. C3×#520C22semidirect
110. C3×#519C22semidirect
113. C3×C4×#41C22semidirect
119. #3565C2×C3semidirect
120. #3561C2×C3semidirect
121. #3547C2×C3semidirect
122. #3547C2×C3semidirect
123. #3544C2×C3semidirect
124. #3536C2×C3semidirect
125. #3518C2×C3semidirect
126. #3511C2×C3semidirect
127. #3503C2×C3semidirect
128. #3501C2×C3semidirect
129. #3495C2×C3semidirect
130. #3494C2×C3semidirect
131. #3493C2×C3semidirect
132. #3475C2×C3semidirect
133. C2×#555C2×C3semidirect
134. #3460C2×C3semidirect
135. #3458C2×C3semidirect
316. #563C22×C3semidirect
317. #562C22×C3semidirect
318. #562C22×C3semidirect
319. Q82C22×C3semidirect
320. #557C22×C3semidirect
321. #556C22×C3semidirect
322. #556C22×C3semidirect
323. #556C22×C3semidirect
324. #556C22×C3semidirect
328. #555C22×C3semidirect
329. #555C22×C3semidirect
330. #555C22×C3semidirect
332. #554C22×C3semidirect
333. #554C22×C3semidirect
334. #554C22×C3semidirect
335. #554C22×C3semidirect
336. #553C22×C3semidirect
337. #553C22×C3semidirect
338. #553C22×C3semidirect
339. #553C22×C3semidirect
341. #552C22×C3semidirect
342. #552C22×C3semidirect
343. #552C22×C3semidirect
344. #552C22×C3semidirect
348. D4×Q8C22×C3semidirect
349. D4×Q8C22×C3semidirect
350. #548C22×C3semidirect
351. #548C22×C3semidirect
352. #547C22×C3semidirect
353. #547C22×C3semidirect
354. #547C22×C3semidirect
360. #544C22×C3semidirect
361. #544C22×C3semidirect
362. #544C22×C3semidirect
363. #544C22×C3semidirect
366. #542C22×C3semidirect
367. #542C22×C3semidirect
368. #542C22×C3semidirect
369. #542C22×C3semidirect
370. #542C22×C3semidirect
371. #542C22×C3semidirect
372. #542C22×C3semidirect
373. #541C22×C3semidirect
374. #540C22×C3semidirect
375. #540C22×C3semidirect
376. #539C22×C3semidirect
380. #537C22×C3semidirect
381. #537C22×C3semidirect
382. #536C22×C3semidirect
383. #536C22×C3semidirect
387. #533C22×C3semidirect
388. #533C22×C3semidirect
389. #533C22×C3semidirect
390. #532C22×C3semidirect
391. #532C22×C3semidirect
393. C2×C4⋊Q8C22×C3semidirect
395. #529C22×C3semidirect
396. #529C22×C3semidirect
397. #529C22×C3semidirect
398. #529C22×C3semidirect
406. #520C22×C3semidirect
407. #519C22×C3semidirect
410. C4×#41C22×C3semidirect
1001. C3#62929direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#35652
C3×#35612
C3×#35472
C3×#35442
C3×#35362
C3×#35182
C3×#35112
C3×#35032
C3×#35012
C3×#34952
C3×#34942
C3×#34932
C3×#34752
C2×C3×#5552
C3×#34602
C3×#34582
#629293