Finite Group Databasebeta

← C3×#62959 #10681566

Subgroups — C3×#62959 #10681566

Order 768.

6354 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3565C218yesmaximal, complemented
2C3×#3564C218yesmaximal, complemented
3C3×#3561C214yesmaximal, complemented
4C3×#3555C218yesmaximal, complemented
5C3×#3555C214yesmaximal, complemented
6C3×#3552C214yesmaximal, complemented
7C3×#3523C214yesmaximal, complemented
8C3×#3518C214yesmaximal, complemented
9C3×#3509C214yesmaximal, complemented
10C3×#3503C212yesmaximal, complemented
11C3×#3502C211yesmaximal, characteristic, complemented
12C3×#3495C214yesmaximal, complemented
13C3×#3493C212yesmaximal, complemented
14C3×#3475C212yesmaximal, complemented
15C2×C3×#556C211yesmaximal, characteristic, complemented
16C3×#3461C211yesmaximal, characteristic, complemented
17C3×#3458C212yesmaximal, complemented
18#62959C311yesmaximal, characteristic, direct product factor, Sylow
19C3×#563C2218yes—
20C3×#563C22116yescomplemented
21C3×#563C22116yescomplemented
22C3×#562C2218yes—
23C3×Q82C2214yescomplemented
24C3×Q82C2214yescomplemented
25C3×#557C2214yescomplemented
26C3×#557C2218yescomplemented
27C3×#557C2214yescomplemented
28C3×#557C2214yescomplemented
29C3×#557C2214yescomplemented
30C3×#557C2218yescomplemented
31C3×#556C2214yes—
32C3×#556C2214yes—
33C3×#556C2218yes—
34C3×#556C2212yes—
35C3×#556C2218yes—
36C3×#556C2218yescomplemented
37C3×#556C2218yescomplemented
38C3×#556C2214yescomplemented
39C3×#556C22116yescomplemented
40C3×#556C2218yescomplemented
41C3×#555C2212yes—
42C3×#555C2218yescomplemented
43C3×#554C2212yes—
44C3×#554C2218yes—
45C3×#554C2218yescomplemented
46C3×#554C2214yescomplemented
47C3×#553C2214yes—
48C3×#553C2218yescomplemented
49C3×#552C2214yes—
50C3×#552C2214yes—
51C3×#552C22116yes—
52C3×#552C2218yescomplemented
53C3×#552C2218yescomplemented
54C3×#552C2218yescomplemented
55C3×#552C22116yescomplemented
56C3×#551C2218yes—
57C3×#551C22116yes—
58C3×D4×Q8C2218yes—
59C3×D4×Q8C2214yescomplemented
60C3×D4×Q8C2214yescomplemented
61C3×#548C2218yes—
62C3×#547C2212yes—
63C3×#546C2214yes—
64C3×#544C2211yescharacteristic
65C3×#544C2212yes—
66C3×#544C2214yes—
67C3×#544C2214yes—
68C3×#544C2218yescomplemented
69C3×#544C2218yescomplemented
70C3×#544C2218yescomplemented
71C3×#543C2218yes—
72C3×#542C2218yes—
73C3×#542C22116yes—
74C3×#542C2214yescomplemented
75C3×#542C2218yescomplemented
76C3×#542C22116yescomplemented
77C3×#541C2214yescomplemented
78C3×#541C2218yescomplemented
79C3×#541C22116yescomplemented
80C3×#541C2218yescomplemented
81C3×#541C22116yescomplemented
82C3×#541C22116yescomplemented
83C3×#539C2214yes—
84C3×#539C22116yescomplemented
85C3×#538C2218yes—
86C3×#537C2211yescharacteristic
87C3×#536C2212yes—
88C3×#536C2218yes—
89C3×#533C2218yes—
90C3×#533C2212yes—
91C3×#533C2214yes—
92C3×#533C2218yescomplemented
93C3×#533C2218yescomplemented
94C3×#533C2214yescomplemented
95C3×#533C2218yescomplemented
96C3×#533C2214yescomplemented
97C2×C3×C4⋊Q8C2211yescharacteristic
98C2×C3×C4⋊Q8C2214yescomplemented
99C3×#529C2214yes—
100C3×#529C2214yes—
101C3×#529C2218yes—
102C3×#529C2218yes—
103C3×#529C2214yescomplemented
104C3×#529C2218yescomplemented
105C2×C3×#126C2214yes—
106C2×C3×#124C2212yes—
107C3×#525C2214yes—
108C2×C3×C22⋊Q8C2212yes—
109C3×#520C2214yes—
110C3×#519C2212yes—
111C3×#519C2218yescomplemented
112C3×C4×#41C2212yes—
113C3×C4×#41C2214yes—
114C2×C3×C4×Q8C2211yescharacteristic
115C2×C3×C4×Q8C2212yes—
116C2×C3×C4×D4C2211yescharacteristic
117C2×C3×#117C2212yes—
118C2×C3×#117C2214yes—
119#3565C2×C318yescomplemented
120#3564C2×C318yescomplemented
121#3561C2×C314yescomplemented
122#3555C2×C318yescomplemented
123#3555C2×C314yescomplemented
124#3552C2×C314yescomplemented
125#3523C2×C314yescomplemented
126#3518C2×C314yescomplemented
127#3509C2×C314yescomplemented
128#3503C2×C312yescomplemented
129#3502C2×C311yescharacteristic, complemented
130#3495C2×C314yescomplemented
131#3493C2×C312yescomplemented
132#3475C2×C312yescomplemented
133C2×#556C2×C311yescharacteristic, complemented
134#3461C2×C311yescharacteristic, complemented
135#3458C2×C312yescomplemented
136C2×C3×#41C2312yes—
137C2×C3×#41C2314yes—
138C22×C3×Q8C2311yescharacteristic
139C22×C3×Q8C2312yes—
140C22×C3×Q8C2318yes—
141C22×C3×D4C2311yescharacteristic
142C23×C3×C4C2312yes—
143C3×C4⋊Q8C2312yes—
144C3×C4⋊Q8C2314yes—
145C3×C4⋊Q8C23116yes—
146C3×C4⋊Q8C2318yes—
147C3×C4⋊Q8C23116yes—
148C3×C4⋊Q8C2314yes—
149C3×C4⋊Q8C2318yes—
150C3×C4⋊Q8C2318yes—
151C3×C4⋊Q8C2318yes—
152C3×C4⋊Q8C2318yes—
153C3×C4⋊Q8C2314yes—
154C3×C4⋊Q8C2312yes—
155C3×C4⋊Q8C2318yes—
156C3×C4⋊Q8C2318yes—
157C3×C4⋊Q8C2314yes—
158C3×C4⋊Q8C2314yes—
159C3×C4⋊Q8C2314yes—
160C3×#126C23116yes—
161C3×#126C23116yes—
162C3×#126C23116yes—
163C3×#126C2318yes—
164C3×#126C23116yes—
165C3×#126C2318yes—
166C3×#126C23116yes—
167C3×#126C23116yes—
168C3×#126C23116yes—
169C3×#126C2318yes—
170C3×#126C2318yes—
171C3×#126C2318yes—
172C3×#126C23116yes—
173C3×#125C2318yes—
174C3×#125C2314yes—
175C3×#125C23116yes—
176C3×#125C23116yes—
177C3×#125C23116yes—
178C3×#125C23116yes—
179C3×#125C2318yes—
180C3×#125C2314yes—
181C3×#125C2318yes—
182C3×#125C2314yes—
183C3×#125C2318yes—
184C3×#125C23116yes—
185C3×#125C2314yes—
186C3×#125C2318yes—
187C3×#125C23116yes—
188C3×#125C2318yes—
189C3×#125C2318yes—
190C3×#124C2314yes—
191C3×#124C2318yes—
192C3×#124C23116yes—
193C3×#124C23116yes—
194C3×#124C2318yes—
195C3×#124C2314yes—
196C3×#124C2318yes—
197C3×#124C2318yes—
198C3×#124C2314yes—
199C3×#123C23116yes—
200C3×#123C23116yes—
201C3×#123C2318yes—
202C3×#123C2318yes—
203C3×#123C2318yes—
204C3×#123C23116yes—
205C3×#123C2318yes—
206C3×#123C2318yes—
207C3×#123C2318yes—
208C3×C22⋊Q8C23116yes—
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⋊Q8C2318yes—
218C3×C22⋊Q8C2318yes—
219C3×C22⋊Q8C2314yes—
220C3×C22⋊Q8C2314yes—
221C3×C22⋊Q8C2318yes—
222C3×C22⋊Q8C2314yes—
223C3×C22⋊Q8C2314yes—
224C3×C22⋊Q8C2314yes—
225C3×C22⋊Q8C2314yes—
226C3×C22⋊Q8C23116yes—
227C3×C22⋊Q8C2314yes—
228C3×C22⋊Q8C23116yes—
229C3×C22⋊Q8C2314yes—
230C3×C22⋊Q8C2314yes—
231C3×C22⋊Q8C23116yes—
232C3×C22⋊Q8C2318yes—
233C3×#121C2318yes—
234C3×#121C23116yes—
235C3×#121C2314yes—
236C3×#121C2314yes—
237C3×#121C2314yes—
238C3×#121C2314yes—
239C3×#121C2314yes—
240C3×#120C2318yes—
241C3×C4×Q8C2312yes—
242C3×C4×Q8C2314yes—
243C3×C4×Q8C2314yes—
244C3×C4×Q8C2318yes—
245C3×C4×Q8C2318yes—
246C3×C4×Q8C2318yes—
247C3×C4×Q8C2314yes—
248C3×C4×Q8C2318yes—
249C3×C4×Q8C2314yes—
250C3×C4×Q8C2314yes—
251C3×C4×Q8C2318yes—
252C3×C4×Q8C2314yes—
253C3×C4×Q8C2314yes—
254C3×C4×Q8C2312yes—
255C3×C4×Q8C2318yes—
256C3×C4×Q8C23116yes—
257C3×C4×Q8C23116yes—
258C3×C4×Q8C2318yes—
259C3×C4×Q8C2314yes—
260C3×C4×Q8C2318yes—
261C3×C4×Q8C2318yes—
262C3×C4×Q8C2318yes—
263C3×C4×Q8C2318yes—
264C3×C4×D4C2312yes—
265C3×C4×D4C2312yes—
266C3×C4×D4C2314yes—
267C3×C4×D4C2318yes—
268C3×C4×D4C2314yes—
269C3×C4×D4C2312yes—
270C3×C4×D4C2314yes—
271C3×C4×D4C2314yes—
272C3×C4×D4C2318yes—
273C3×C4×D4C2312yes—
274C3×C4×D4C23116yes—
275C3×C4×D4C2318yes—
276C3×C4×D4C2318yes—
277C3×C4×D4C2314yes—
278C3×C4×D4C2318yes—
279C3×C4×D4C23116yes—
280C3×#117C2312yes—
281C3×#117C2314yes—
282C3×#117C2318yes—
283C3×#117C2318yes—
284C3×#117C2314yes—
285C3×#117C2314yes—
286C3×#117C2318yes—
287C3×#117C2318yes—
288C3×#117C2314yes—
289C3×#117C2314yes—
290C3×#117C2318yes—
291C3×#117C2318yes—
292C3×#117C2318yes—
293C3×#117C23116yes—
294C3×#117C23116yes—
295C3×#117C2318yes—
296C3×#117C23116yes—
297C2×C3×C4⋊C4C2311yescharacteristic
298C2×C3×C4⋊C4C2312yes—
299C2×C3×C4⋊C4C2314yes—
300C2×C3×C4⋊C4C2314yes—
301C2×C3×C4⋊C4C2311yescharacteristic
302C2×C3×C4⋊C4C2314yes—
303C2×C3×C4⋊C4C2312yes—
304C2×C3×C4⋊C4C2318yes—
305C2×C3×C4⋊C4C2312yes—
306C2×C3×C4⋊C4C2318yes—
307C2×C3×C22⋊C4C2314yes—
308C2×C3×C22⋊C4C2318yes—
309C2×C3×C22⋊C4C2312yes—
310C2×C3×C22⋊C4C2314yes—
311C2×C3×C42C2314yes—
312C2×C3×C42C2318yes—
313C2×C3×C42C2311yescharacteristic
314C2×C3×C42C2312yes—
315C2×C3×C42C2314yes—
316#563C22×C318yes—
317#563C22×C3116yescomplemented
318#563C22×C3116yescomplemented
319#562C22×C318yes—
320Q82C22×C314yescomplemented
321Q82C22×C314yescomplemented
322#557C22×C314yescomplemented
323#557C22×C318yescomplemented
324#557C22×C314yescomplemented
325#557C22×C314yescomplemented
326#557C22×C314yescomplemented
327#557C22×C318yescomplemented
328#556C22×C314yes—
329#556C22×C314yes—
330#556C22×C318yes—
331#556C22×C312yes—
332#556C22×C318yes—
333#556C22×C318yescomplemented
334#556C22×C318yescomplemented
335#556C22×C314yescomplemented
336#556C22×C3116yescomplemented
337#556C22×C318yescomplemented
338#555C22×C312yes—
339#555C22×C318yescomplemented
340#554C22×C312yes—
341#554C22×C318yes—
342#554C22×C318yescomplemented
343#554C22×C314yescomplemented
344#553C22×C314yes—
345#553C22×C318yescomplemented
346#552C22×C314yes—
347#552C22×C314yes—
348#552C22×C3116yes—
349#552C22×C318yescomplemented
350#552C22×C318yescomplemented
351#552C22×C318yescomplemented
352#552C22×C3116yescomplemented
353#551C22×C318yes—
354#551C22×C3116yes—
355D4×Q8C22×C318yes—
356D4×Q8C22×C314yescomplemented
357D4×Q8C22×C314yescomplemented
358#548C22×C318yes—
359#547C22×C312yes—
360#546C22×C314yes—
361#544C22×C311yescharacteristic
362#544C22×C312yes—
363#544C22×C314yes—
364#544C22×C314yes—
365#544C22×C318yescomplemented
366#544C22×C318yescomplemented
367#544C22×C318yescomplemented
368#543C22×C318yes—
369#542C22×C318yes—
370#542C22×C3116yes—
371#542C22×C314yescomplemented
372#542C22×C318yescomplemented
373#542C22×C3116yescomplemented
374#541C22×C314yescomplemented
375#541C22×C318yescomplemented
376#541C22×C3116yescomplemented
377#541C22×C318yescomplemented
378#541C22×C3116yescomplemented
379#541C22×C3116yescomplemented
380#539C22×C314yes—
381#539C22×C3116yescomplemented
382#538C22×C318yes—
383#537C22×C311yescharacteristic
384#536C22×C312yes—
385#536C22×C318yes—
386#533C22×C318yes—
387#533C22×C312yes—
388#533C22×C314yes—
389#533C22×C318yescomplemented
390#533C22×C318yescomplemented
391#533C22×C314yescomplemented
392#533C22×C318yescomplemented
393#533C22×C314yescomplemented
394C2×C4⋊Q8C22×C311yescharacteristic
395C2×C4⋊Q8C22×C314yescomplemented
396#529C22×C314yes—
397#529C22×C314yes—
398#529C22×C318yes—
399#529C22×C318yes—
400#529C22×C314yescomplemented
401#529C22×C318yescomplemented
402C2×#126C22×C314yes—
403C2×#124C22×C312yes—
404#525C22×C314yes—
405C2×C22⋊Q8C22×C312yes—
406#520C22×C314yes—
407#519C22×C312yes—
408#519C22×C318yescomplemented
409C4×#41C22×C312yes—
410C4×#41C22×C314yes—
411C2×C4×Q8C22×C311yescharacteristic
412C2×C4×Q8C22×C312yes—
413C2×C4×D4C22×C311yescharacteristic
414C2×#117C22×C312yes—
415C2×#117C22×C314yes—
416C24×C3C2412yes—
417C3×#41—28no—
418C3×#41—48no—
419C2×C3×Q8—24no—
420C2×C3×Q8—44no—
421C2×C3×Q8—416no—
422C2×C3×Q8C2414yes—
423C2×C3×Q8C2412yes—
424C2×C3×Q8C2414yes—
425C2×C3×Q8C2414yes—
426C2×C3×Q8C2414yes—
427C2×C3×Q8C2414yes—
428C2×C3×Q8C2418yes—
429C2×C3×Q8C24116yes—
430C2×C3×Q8C2414yes—
431C2×C3×D4—42no—
432C2×C3×D4C2414yes—
433C2×C3×D4C2412yes—
434C2×C3×D4C2412yes—
435C2×C3×D4C2418yes—
436C2×C3×D4C2414yes—
437C2×C3×D4C2418yes—
438C2×C3×D4C2412yes—
439C22×C3×C4—28no—
440C22×C3×C4C2411yescharacteristic
441C22×C3×C4C2412yes—
442C22×C3×C4C2414yes—
443C22×C3×C4C2412yes—
444C22×C3×C4C2414yes—
445C22×C3×C4C2414yes—
446C22×C3×C4C2414yes—
447C22×C3×C4C2412yes—
448C22×C3×C4C2411yescharacteristic
449C22×C3×C4C2414yes—
450C22×C3×C4C2418yes—
451C22×C3×C4C2418yes—
452C22×C3×C4C2414yes—
453C22×C3×C4C24116yes—
454C22×C3×C4C2411yescharacteristic
455C3×C4⋊C4C2414yes—
456C3×C4⋊C4C2412yes—
457C3×C4⋊C4C2418yes—
458C3×C4⋊C4C2412yes—
459C3×C4⋊C4C2418yes—
460C3×C4⋊C4C2414yes—
461C3×C4⋊C4C2411yescharacteristic
462C3×C4⋊C4C2414yes—
463C3×C4⋊C4C2414yes—
464C3×C4⋊C4C2418yes—
465C3×C4⋊C4C2418yes—
466C3×C4⋊C4C2418yes—
467C3×C4⋊C4C24116yes—
468C3×C4⋊C4C2411yescharacteristic
469C3×C4⋊C4C2412yes—
470C3×C4⋊C4C24116yes—
471C3×C4⋊C4C2418yes—
472C3×C4⋊C4C2418yes—
473C3×C4⋊C4C2418yes—
474C3×C4⋊C4C2418yes—
475C3×C4⋊C4C2414yes—
476C3×C4⋊C4C2414yes—
477C3×C4⋊C4C2418yes—
478C3×C4⋊C4C2414yes—
479C3×C4⋊C4C24116yes—
480C3×C4⋊C4C2418yes—
481C3×C4⋊C4C24116yes—
482C3×C4⋊C4C2418yes—
483C3×C4⋊C4C2418yes—
484C3×C4⋊C4C2418yes—
485C3×C4⋊C4C2414yes—
486C3×C4⋊C4C24116yes—
487C3×C4⋊C4C2418yes—
488C3×C4⋊C4C2418yes—
489C3×C4⋊C4C2418yes—
490C3×C4⋊C4C2414yes—
491C3×C22⋊C4C2414yes—
492C3×C22⋊C4C2418yes—
493C3×C22⋊C4C2414yes—
494C3×C22⋊C4C2418yes—
495C3×C22⋊C4C24116yes—
496C3×C22⋊C4C2418yes—
497C3×C22⋊C4C24116yes—
498C3×C22⋊C4C2414yes—
499C3×C22⋊C4C2418yes—
500C3×C22⋊C4C2418yes—
501C3×C22⋊C4C2418yes—
502C3×C22⋊C4C2418yes—
503C3×C22⋊C4C2418yes—
504C3×C22⋊C4C2414yes—
505C3×C22⋊C4C24116yes—
506C3×C22⋊C4C2414yes—
507C3×C22⋊C4C2418yes—
508C3×C22⋊C4C2418yes—
509C3×C42C2414yes—
510C3×C42C2412yes—
511C3×C42C2418yes—
512C3×C42C2418yes—
513C3×C42C2418yes—
514C3×C42C2418yes—
515C3×C42C2412yes—
516C3×C42C2414yes—
517C3×C42C2414yes—
518C3×C42C2414yes—
519C3×C42C2418yes—
520C3×C42C2414yes—
521C3×C42C24116yes—
522C3×C42C24116yes—
523C2×#41C23×C312yes—
524C2×#41C23×C314yes—
525C22×Q8C23×C311yescharacteristic
526C22×Q8C23×C312yes—
527C22×Q8C23×C318yes—
528C22×D4C23×C311yescharacteristic
529C23×C4C23×C312yes—
530C4⋊Q8C23×C314yes—
531C4⋊Q8C23×C314yes—
532C4⋊Q8C23×C312yes—
533C4⋊Q8C23×C318yes—
534C4⋊Q8C23×C318yes—
535C4⋊Q8C23×C318yes—
536C4⋊Q8C23×C312yes—
537C4⋊Q8C23×C314yes—
538C4⋊Q8C23×C314yes—
539C4⋊Q8C23×C318yes—
540C4⋊Q8C23×C318yes—
541C4⋊Q8C23×C314yes—
542C4⋊Q8C23×C314yes—
543C4⋊Q8C23×C318yes—
544C4⋊Q8C23×C318yes—
545C4⋊Q8C23×C3116yes—
546C4⋊Q8C23×C3116yes—
547#126C23×C3116yes—
548#126C23×C3116yes—
549#126C23×C318yes—
550#126C23×C318yes—
551#126C23×C318yes—
552#126C23×C318yes—
553#126C23×C3116yes—
554#126C23×C318yes—
555#126C23×C3116yes—
556#126C23×C3116yes—
557#126C23×C3116yes—
558#126C23×C3116yes—
559#126C23×C3116yes—
560#125C23×C318yes—
561#125C23×C314yes—
562#125C23×C318yes—
563#125C23×C314yes—
564#125C23×C314yes—
565#125C23×C318yes—
566#125C23×C3116yes—
567#125C23×C318yes—
568#125C23×C314yes—
569#125C23×C318yes—
570#125C23×C3116yes—
571#125C23×C318yes—
572#125C23×C318yes—
573#125C23×C3116yes—
574#125C23×C3116yes—
575#125C23×C3116yes—
576#125C23×C3116yes—
577#124C23×C318yes—
578#124C23×C318yes—
579#124C23×C314yes—
580#124C23×C318yes—
581#124C23×C318yes—
582#124C23×C314yes—
583#124C23×C314yes—
584#124C23×C3116yes—
585#124C23×C3116yes—
586#123C23×C318yes—
587#123C23×C318yes—
588#123C23×C318yes—
589#123C23×C318yes—
590#123C23×C318yes—
591#123C23×C318yes—
592#123C23×C3116yes—
593#123C23×C3116yes—
594#123C23×C3116yes—
595C22⋊Q8C23×C318yes—
596C22⋊Q8C23×C318yes—
597C22⋊Q8C23×C314yes—
598C22⋊Q8C23×C314yes—
599C22⋊Q8C23×C318yes—
600C22⋊Q8C23×C314yes—
601C22⋊Q8C23×C314yes—
602C22⋊Q8C23×C318yes—
603C22⋊Q8C23×C314yes—
604C22⋊Q8C23×C314yes—
605C22⋊Q8C23×C3116yes—
606C22⋊Q8C23×C314yes—
607C22⋊Q8C23×C3116yes—
608C22⋊Q8C23×C3116yes—
609C22⋊Q8C23×C314yes—
610C22⋊Q8C23×C314yes—
611C22⋊Q8C23×C318yes—
612C22⋊Q8C23×C3116yes—
613C22⋊Q8C23×C318yes—
614C22⋊Q8C23×C318yes—
615C22⋊Q8C23×C3116yes—
616C22⋊Q8C23×C3116yes—
617C22⋊Q8C23×C3116yes—
618C22⋊Q8C23×C3116yes—
619C22⋊Q8C23×C3116yes—
620#121C23×C314yes—
621#121C23×C314yes—
622#121C23×C314yes—
623#121C23×C314yes—
624#121C23×C318yes—
625#121C23×C314yes—
626#121C23×C3116yes—
627#120C23×C318yes—
628C4×Q8C23×C314yes—
629C4×Q8C23×C314yes—
630C4×Q8C23×C314yes—
631C4×Q8C23×C318yes—
632C4×Q8C23×C314yes—
633C4×Q8C23×C314yes—
634C4×Q8C23×C314yes—
635C4×Q8C23×C312yes—
636C4×Q8C23×C312yes—
637C4×Q8C23×C318yes—
638C4×Q8C23×C318yes—
639C4×Q8C23×C3116yes—
640C4×Q8C23×C318yes—
641C4×Q8C23×C3116yes—
642C4×Q8C23×C318yes—
643C4×Q8C23×C318yes—
644C4×Q8C23×C314yes—
645C4×Q8C23×C314yes—
646C4×Q8C23×C318yes—
647C4×Q8C23×C318yes—
648C4×Q8C23×C318yes—
649C4×Q8C23×C318yes—
650C4×Q8C23×C318yes—
651C4×D4C23×C312yes—
652C4×D4C23×C312yes—
653C4×D4C23×C314yes—
654C4×D4C23×C318yes—
655C4×D4C23×C314yes—
656C4×D4C23×C312yes—
657C4×D4C23×C314yes—
658C4×D4C23×C314yes—
659C4×D4C23×C318yes—
660C4×D4C23×C312yes—
661C4×D4C23×C3116yes—
662C4×D4C23×C318yes—
663C4×D4C23×C318yes—
664C4×D4C23×C314yes—
665C4×D4C23×C318yes—
666C4×D4C23×C3116yes—
667#117C23×C312yes—
668#117C23×C314yes—
669#117C23×C318yes—
670#117C23×C318yes—
671#117C23×C314yes—
672#117C23×C314yes—
673#117C23×C318yes—
674#117C23×C318yes—
675#117C23×C314yes—
676#117C23×C314yes—
677#117C23×C318yes—
678#117C23×C318yes—
679#117C23×C318yes—
680#117C23×C3116yes—
681#117C23×C3116yes—
682#117C23×C318yes—
683#117C23×C3116yes—
684C2×C4⋊C4C23×C311yescharacteristic
685C2×C4⋊C4C23×C312yes—
686C2×C4⋊C4C23×C314yes—
687C2×C4⋊C4C23×C314yes—
688C2×C4⋊C4C23×C311yescharacteristic
689C2×C4⋊C4C23×C314yes—
690C2×C4⋊C4C23×C312yes—
691C2×C4⋊C4C23×C318yes—
692C2×C4⋊C4C23×C312yes—
693C2×C4⋊C4C23×C318yes—
694C2×C22⋊C4C23×C314yes—
695C2×C22⋊C4C23×C318yes—
696C2×C22⋊C4C23×C312yes—
697C2×C22⋊C4C23×C314yes—
698C2×C42C23×C314yes—
699C2×C42C23×C318yes—
700C2×C42C23×C311yescharacteristic
701C2×C42C23×C312yes—
702C2×C42C23×C314yes—
703C23×C3—24no—
704C23×C3—42no—
705C23×C3—42no—
706C23×C3C2514yes—
707C23×C3C2514yes—
708C23×C3C2511yescharacteristic
709C3×Q8—28no—
710C3×Q8—24no—
711C3×Q8—28no—
712C3×Q8—28no—
713C3×Q8—416no—
714C3×Q8—44no—
715C3×Q8—44no—
716C3×Q8—44no—
717C3×Q8—48no—
718C3×D4—28no—
719C3×D4—24no—
720C3×D4—24no—
721C3×D4—42no—
722C3×D4—48no—
723C3×D4—44no—
724C3×D4—48no—
725C2×C3×C4—24no—
726C2×C3×C4—24no—
727C2×C3×C4—28no—
728C2×C3×C4—28no—
729C2×C3×C4—28no—
730C2×C3×C4—22no—
731C2×C3×C4—28no—
732C2×C3×C4—41no—
733C2×C3×C4—44no—
734C2×C3×C4—48no—
735C2×C3×C4—42no—
736C2×C3×C4—416no—
737C2×C3×C4—44no—
738C2×C3×C4—48no—
739C2×C3×C42−1+414yes—
740C2×C3×C4C2512yes—
741C2×C3×C4C2514yes—
742C2×C3×C4C2514yes—
743C2×C3×C4C2514yes—
744C2×C3×C4C2518yes—
745C2×C3×C4C2511yescharacteristic
746C2×C3×C4C2512yes—
747C2×C3×C4C2514yes—
748C2×C3×C4C2512yes—
749C2×C3×C4C2514yes—
750C2×C3×C4C2518yes—
751C2×C3×C4C2518yes—
752C2×C3×C4C2512yes—
753C2×C3×C4C2511yescharacteristic
754C24C24×C312yes—
755#41—28no—
756#41—48no—
757C2×Q8—24no—
758C2×Q8—44no—
759C2×Q8—416no—
760C2×Q8C24×C314yes—
761C2×Q8C24×C312yes—
762C2×Q8C24×C314yes—
763C2×Q8C24×C314yes—
764C2×Q8C24×C314yes—
765C2×Q8C24×C314yes—
766C2×Q8C24×C318yes—
767C2×Q8C24×C3116yes—
768C2×Q8C24×C314yes—
769C2×D4—42no—
770C2×D4C24×C314yes—
771C2×D4C24×C312yes—
772C2×D4C24×C312yes—
773C2×D4C24×C318yes—
774C2×D4C24×C314yes—
775C2×D4C24×C318yes—
776C2×D4C24×C312yes—
777C22×C4—28no—
778C22×C4C24×C311yescharacteristic
779C22×C4C24×C312yes—
780C22×C4C24×C314yes—
781C22×C4C24×C312yes—
782C22×C4C24×C314yes—
783C22×C4C24×C314yes—
784C22×C4C24×C314yes—
785C22×C4C24×C312yes—
786C22×C4C24×C311yescharacteristic
787C22×C4C24×C314yes—
788C22×C4C24×C318yes—
789C22×C4C24×C318yes—
790C22×C4C24×C314yes—
791C22×C4C24×C3116yes—
792C22×C4C24×C311yescharacteristic
793C4⋊C4C24×C314yes—
794C4⋊C4C24×C312yes—
795C4⋊C4C24×C318yes—
796C4⋊C4C24×C312yes—
797C4⋊C4C24×C318yes—
798C4⋊C4C24×C314yes—
799C4⋊C4C24×C311yescharacteristic
800C4⋊C4C24×C314yes—
801C4⋊C4C24×C314yes—
802C4⋊C4C24×C318yes—
803C4⋊C4C24×C318yes—
804C4⋊C4C24×C318yes—
805C4⋊C4C24×C3116yes—
806C4⋊C4C24×C311yescharacteristic
807C4⋊C4C24×C312yes—
808C4⋊C4C24×C3116yes—
809C4⋊C4C24×C318yes—
810C4⋊C4C24×C318yes—
811C4⋊C4C24×C318yes—
812C4⋊C4C24×C318yes—
813C4⋊C4C24×C314yes—
814C4⋊C4C24×C314yes—
815C4⋊C4C24×C318yes—
816C4⋊C4C24×C314yes—
817C4⋊C4C24×C3116yes—
818C4⋊C4C24×C318yes—
819C4⋊C4C24×C3116yes—
820C4⋊C4C24×C318yes—
821C4⋊C4C24×C318yes—
822C4⋊C4C24×C318yes—
823C4⋊C4C24×C314yes—
824C4⋊C4C24×C3116yes—
825C4⋊C4C24×C318yes—
826C4⋊C4C24×C318yes—
827C4⋊C4C24×C318yes—
828C4⋊C4C24×C314yes—
829C22⋊C4C24×C314yes—
830C22⋊C4C24×C318yes—
831C22⋊C4C24×C314yes—
832C22⋊C4C24×C318yes—
833C22⋊C4C24×C3116yes—
834C22⋊C4C24×C318yes—
835C22⋊C4C24×C3116yes—
836C22⋊C4C24×C314yes—
837C22⋊C4C24×C318yes—
838C22⋊C4C24×C318yes—
839C22⋊C4C24×C318yes—
840C22⋊C4C24×C318yes—
841C22⋊C4C24×C318yes—
842C22⋊C4C24×C314yes—
843C22⋊C4C24×C3116yes—
844C22⋊C4C24×C314yes—
845C22⋊C4C24×C318yes—
846C22⋊C4C24×C318yes—
847C42C24×C314yes—
848C42C24×C312yes—
849C42C24×C318yes—
850C42C24×C318yes—
851C42C24×C318yes—
852C42C24×C318yes—
853C42C24×C312yes—
854C42C24×C314yes—
855C42C24×C314yes—
856C42C24×C314yes—
857C42C24×C318yes—
858C42C24×C314yes—
859C42C24×C3116yes—
860C42C24×C3116yes—
861C22×C3—21no—
862C22×C3—21no—
863C22×C3—24no—
864C22×C3—24no—
865C22×C3—24no—
866C22×C3—24no—
867C22×C3—24no—
868C22×C3—24no—
869C22×C3—84no—
870C22×C3C2×2−1+412yes—
871C22×C3C2611yescharacteristic
872C3×C4—22no—
873C3×C4—22no—
874C3×C4—24no—
875C3×C4—24no—
876C3×C4—24no—
877C3×C4—21no—
878C3×C4—28no—
879C3×C4—28no—
880C3×C4—22no—
881C3×C4—24no—
882C3×C4—28no—
883C3×C4—24no—
884C3×C4C2×2−1+414yes—
885C3×C4#58512yes—
886C23—24no—
887C23—42no—
888C23—42no—
889C23C25×C314yes—
890C23C25×C314yes—
891C23C25×C311yescharacteristic
892Q8—28no—
893Q8—24no—
894Q8—28no—
895Q8—28no—
896Q8—416no—
897Q8—44no—
898Q8—44no—
899Q8—44no—
900Q8—48no—
901D4—28no—
902D4—24no—
903D4—24no—
904D4—42no—
905D4—48no—
906D4—48no—
907D4—44no—
908C2×C4—24no—
909C2×C4—24no—
910C2×C4—28no—
911C2×C4—28no—
912C2×C4—28no—
913C2×C4—22no—
914C2×C4—28no—
915C2×C4—416no—
916C2×C4—44no—
917C2×C4—48no—
918C2×C4—41no—
919C2×C4—44no—
920C2×C4—48no—
921C2×C4—42no—
922C2×C4C3×2−1+414yes—
923C2×C4C25×C312yes—
924C2×C4C25×C314yes—
925C2×C4C25×C314yes—
926C2×C4C25×C314yes—
927C2×C4C25×C318yes—
928C2×C4C25×C311yescharacteristic
929C2×C4C25×C312yes—
930C2×C4C25×C314yes—
931C2×C4C25×C312yes—
932C2×C4C25×C314yes—
933C2×C4C25×C318yes—
934C2×C4C25×C318yes—
935C2×C4C25×C312yes—
936C2×C4C25×C311yescharacteristic
937C2×C3—22no—
938C2×C3—44no—
939C2×C3—44no—
940C2×C3C22×2−1+411yescharacteristic
941C2×C3C2×#58511yescharacteristic
942C2×C32−1+611yescharacteristic
943C22—21no—
944C22—21no—
945C22—24no—
946C22—24no—
947C22—24no—
948C22—24no—
949C22—24no—
950C22—24no—
951C22—84no—
952C22C2×C3×2−1+412yes—
953C22C26×C311yescharacteristic
954C4—22no—
955C4—22no—
956C4—24no—
957C4—24no—
958C4—24no—
959C4—21no—
960C4—28no—
961C4—28no—
962C4—22no—
963C4—24no—
964C4—28no—
965C4—24no—
966C4C2×C3×2−1+414yes—
967C4C3×#58512yes—
968C3#6295911yescharacteristic, direct product factor, Sylow
969C2—22no—
970C2—44no—
971C2—44no—
972C2C22×C3×2−1+411yescharacteristic
973C2C2×C3×#58511yescharacteristic
974C2C3×2−1+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×#3565C2semidirect
2. C3×#3564C2semidirect
3. C3×#3561C2semidirect
4. C3×#3555C2semidirect
5. C3×#3555C2semidirect
6. C3×#3552C2semidirect
7. C3×#3523C2semidirect
8. C3×#3518C2semidirect
9. C3×#3509C2semidirect
10. C3×#3503C2semidirect
11. C3×#3502C2semidirect
12. C3×#3495C2semidirect
13. C3×#3493C2semidirect
14. C3×#3475C2semidirect
15. C2×C3×#556C2semidirect
16. C3×#3461C2semidirect
17. C3×#3458C2semidirect
18. #62959C3direct (N × H)
20. C3×#563C22semidirect
21. C3×#563C22semidirect
23. C3×Q82C22semidirect
24. C3×Q82C22semidirect
25. C3×#557C22semidirect
26. C3×#557C22semidirect
27. C3×#557C22semidirect
28. C3×#557C22semidirect
29. C3×#557C22semidirect
30. C3×#557C22semidirect
36. C3×#556C22semidirect
37. C3×#556C22semidirect
38. C3×#556C22semidirect
39. C3×#556C22semidirect
40. C3×#556C22semidirect
42. C3×#555C22semidirect
45. C3×#554C22semidirect
46. C3×#554C22semidirect
48. C3×#553C22semidirect
52. C3×#552C22semidirect
53. C3×#552C22semidirect
54. C3×#552C22semidirect
55. C3×#552C22semidirect
59. C3×D4×Q8C22semidirect
60. C3×D4×Q8C22semidirect
68. C3×#544C22semidirect
69. C3×#544C22semidirect
70. C3×#544C22semidirect
74. C3×#542C22semidirect
75. C3×#542C22semidirect
76. C3×#542C22semidirect
77. C3×#541C22semidirect
78. C3×#541C22semidirect
79. C3×#541C22semidirect
80. C3×#541C22semidirect
81. C3×#541C22semidirect
82. C3×#541C22semidirect
84. C3×#539C22semidirect
92. C3×#533C22semidirect
93. C3×#533C22semidirect
94. C3×#533C22semidirect
95. C3×#533C22semidirect
96. C3×#533C22semidirect
98. C2×C3×C4⋊Q8C22semidirect
103. C3×#529C22semidirect
104. C3×#529C22semidirect
111. C3×#519C22semidirect
119. #3565C2×C3semidirect
120. #3564C2×C3semidirect
121. #3561C2×C3semidirect
122. #3555C2×C3semidirect
123. #3555C2×C3semidirect
124. #3552C2×C3semidirect
125. #3523C2×C3semidirect
126. #3518C2×C3semidirect
127. #3509C2×C3semidirect
128. #3503C2×C3semidirect
129. #3502C2×C3semidirect
130. #3495C2×C3semidirect
131. #3493C2×C3semidirect
132. #3475C2×C3semidirect
133. C2×#556C2×C3semidirect
134. #3461C2×C3semidirect
135. #3458C2×C3semidirect
317. #563C22×C3semidirect
318. #563C22×C3semidirect
320. Q82C22×C3semidirect
321. Q82C22×C3semidirect
322. #557C22×C3semidirect
323. #557C22×C3semidirect
324. #557C22×C3semidirect
325. #557C22×C3semidirect
326. #557C22×C3semidirect
327. #557C22×C3semidirect
333. #556C22×C3semidirect
334. #556C22×C3semidirect
335. #556C22×C3semidirect
336. #556C22×C3semidirect
337. #556C22×C3semidirect
339. #555C22×C3semidirect
342. #554C22×C3semidirect
343. #554C22×C3semidirect
345. #553C22×C3semidirect
349. #552C22×C3semidirect
350. #552C22×C3semidirect
351. #552C22×C3semidirect
352. #552C22×C3semidirect
356. D4×Q8C22×C3semidirect
357. D4×Q8C22×C3semidirect
365. #544C22×C3semidirect
366. #544C22×C3semidirect
367. #544C22×C3semidirect
371. #542C22×C3semidirect
372. #542C22×C3semidirect
373. #542C22×C3semidirect
374. #541C22×C3semidirect
375. #541C22×C3semidirect
376. #541C22×C3semidirect
377. #541C22×C3semidirect
378. #541C22×C3semidirect
379. #541C22×C3semidirect
381. #539C22×C3semidirect
389. #533C22×C3semidirect
390. #533C22×C3semidirect
391. #533C22×C3semidirect
392. #533C22×C3semidirect
393. #533C22×C3semidirect
395. C2×C4⋊Q8C22×C3semidirect
400. #529C22×C3semidirect
401. #529C22×C3semidirect
408. #519C22×C3semidirect
968. C3#62959direct (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×#35642
C3×#35612
C3×#35552
C3×#35522
C3×#35232
C3×#35182
C3×#35092
C3×#35032
C3×#35022
C3×#34952
C3×#34932
C3×#34752
C2×C3×#5562
C3×#34612
C3×#34582
#629593