Finite Group Databasebeta

← C3×#62945 #10681552

Subgroups — C3×#62945 #10681552

Order 768.

6478 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3563C214yesmaximal, complemented
2C3×#3563C218yesmaximal, complemented
3C3×#3555C214yesmaximal, complemented
4C3×#3552C218yesmaximal, complemented
5C3×#3544C214yesmaximal, complemented
6C3×#3538C218yesmaximal, complemented
7C3×#3520C214yesmaximal, complemented
8C3×#3515C214yesmaximal, complemented
9C3×#3503C212yesmaximal, complemented
10C3×#3503C214yesmaximal, complemented
11C3×#3502C211yesmaximal, characteristic, complemented
12C3×#3495C214yesmaximal, complemented
13C3×#3492C212yesmaximal, complemented
14C3×#3475C212yesmaximal, complemented
15C2×C3×#554C211yesmaximal, characteristic, complemented
16C3×#3461C211yesmaximal, characteristic, complemented
17C2×C3×#544C212yesmaximal, complemented
18#62945C311yesmaximal, characteristic, direct product factor, Sylow
19C3×#564C2218yescomplemented
20C3×#563C22116yescomplemented
21C3×#563C22116yescomplemented
22C3×#563C2218yescomplemented
23C3×Q82C2214yescomplemented
24C3×Q82C2214yescomplemented
25C3×#557C2214yescomplemented
26C3×#557C2218yescomplemented
27C3×#557C2218yescomplemented
28C3×#557C2214yescomplemented
29C3×#556C2212yes—
30C3×#556C2214yes—
31C3×#556C2218yescomplemented
32C3×#555C2212yes—
33C3×#554C2214yes—
34C3×#554C2214yes—
35C3×#554C2218yes—
36C3×#554C2212yes—
37C3×#554C2218yes—
38C3×#554C2218yescomplemented
39C3×#554C2218yescomplemented
40C3×#554C2214yescomplemented
41C3×#553C2214yes—
42C3×#553C2218yescomplemented
43C3×#552C2214yes—
44C3×#552C2214yes—
45C3×#552C22116yes—
46C3×#552C2218yes—
47C3×#552C2218yescomplemented
48C3×#552C2218yescomplemented
49C3×#552C2218yescomplemented
50C3×#552C22116yescomplemented
51C3×#552C2218yescomplemented
52C3×#551C2218yes—
53C3×#551C22116yes—
54C3×D4×Q8C2214yes—
55C3×D4×Q8C2218yes—
56C3×D4×Q8C22116yescomplemented
57C3×D4×Q8C2214yescomplemented
58C3×#548C2218yes—
59C3×#547C2212yes—
60C3×#547C2214yes—
61C3×#547C2214yes—
62C3×#547C2218yescomplemented
63C3×#546C2214yes—
64C3×#544C2211yescharacteristic
65C3×#544C2212yes—
66C3×#544C2214yes—
67C3×#544C2218yes—
68C3×#544C2214yes—
69C3×#544C2218yescomplemented
70C3×#544C2218yescomplemented
71C3×#544C22116yescomplemented
72C3×#544C2218yescomplemented
73C3×#544C2218yescomplemented
74C3×#542C2218yes—
75C3×#542C2214yescomplemented
76C3×#542C2218yescomplemented
77C3×#541C2214yescomplemented
78C3×#541C2218yescomplemented
79C3×#541C2218yescomplemented
80C3×#541C22116yescomplemented
81C3×#541C22116yescomplemented
82C3×#539C2214yes—
83C3×#539C2218yes—
84C3×#539C22116yes—
85C3×#539C22116yescomplemented
86C3×#537C2211yescharacteristic
87C3×#536C2212yes—
88C3×#536C22116yescomplemented
89C3×#533C2212yes—
90C3×#533C2214yes—
91C3×#533C2214yescomplemented
92C3×#533C2218yescomplemented
93C3×#533C2214yescomplemented
94C2×C3×C4⋊Q8C2211yescharacteristic
95C2×C3×C4⋊Q8C2218yescomplemented
96C2×C3×C4⋊Q8C2214yescomplemented
97C3×#529C2214yes—
98C3×#529C2214yes—
99C3×#529C2218yes—
100C3×#529C2214yescomplemented
101C3×#529C2218yescomplemented
102C2×C3×#125C2212yes—
103C2×C3×#125C2218yescomplemented
104C3×#525C2214yes—
105C3×#525C2218yes—
106C2×C3×C22⋊Q8C2218yes—
107C2×C3×C22⋊Q8C2212yes—
108C2×C3×C22⋊Q8C2214yes—
109C3×#520C2214yes—
110C3×#520C2218yes—
111C3×#519C2212yes—
112C3×C4×#41C2212yes—
113C3×C4×#41C2214yes—
114C2×C3×C4×Q8C2211yescharacteristic
115C2×C3×C4×D4C2211yescharacteristic
116C2×C3×C4×D4C2212yes—
117C2×C3×#117C2214yes—
118C22×C3×C4⋊C4C2212yes—
119#3563C2×C314yescomplemented
120#3563C2×C318yescomplemented
121#3555C2×C314yescomplemented
122#3552C2×C318yescomplemented
123#3544C2×C314yescomplemented
124#3538C2×C318yescomplemented
125#3520C2×C314yescomplemented
126#3515C2×C314yescomplemented
127#3503C2×C312yescomplemented
128#3503C2×C314yescomplemented
129#3502C2×C311yescharacteristic, complemented
130#3495C2×C314yescomplemented
131#3492C2×C312yescomplemented
132#3475C2×C312yescomplemented
133C2×#554C2×C311yescharacteristic, complemented
134#3461C2×C311yescharacteristic, complemented
135C2×#544C2×C312yescomplemented
136C2×C3×#41C2312yes—
137C2×C3×#41C2314yes—
138C2×C3×#41C2318yes—
139C22×C3×Q8C2311yescharacteristic
140C22×C3×Q8C2312yes—
141C22×C3×Q8C2318yes—
142C22×C3×Q8C2318yes—
143C22×C3×D4C2311yescharacteristic
144C23×C3×C4C2312yes—
145C23×C3×C4C2314yes—
146C3×C4⋊Q8C2312yes—
147C3×C4⋊Q8C2314yes—
148C3×C4⋊Q8C23116yes—
149C3×C4⋊Q8C23116yes—
150C3×C4⋊Q8C2314yes—
151C3×C4⋊Q8C2318yes—
152C3×C4⋊Q8C2318yes—
153C3×C4⋊Q8C2318yes—
154C3×C4⋊Q8C23116yes—
155C3×C4⋊Q8C2318yes—
156C3×C4⋊Q8C2314yes—
157C3×C4⋊Q8C2314yes—
158C3×C4⋊Q8C2318yes—
159C3×C4⋊Q8C23116yes—
160C3×C4⋊Q8C2312yes—
161C3×C4⋊Q8C2314yes—
162C3×C4⋊Q8C2314yes—
163C3×#126C2318yes—
164C3×#126C2318yes—
165C3×#126C2318yes—
166C3×#126C2318yes—
167C3×#126C23116yes—
168C3×#126C23116yes—
169C3×#126C23116yes—
170C3×#126C23116yes—
171C3×#126C23116yes—
172C3×#126C2318yes—
173C3×#125C2318yes—
174C3×#125C23116yes—
175C3×#125C2318yes—
176C3×#125C23116yes—
177C3×#125C23116yes—
178C3×#125C23116yes—
179C3×#125C2318yes—
180C3×#125C2314yes—
181C3×#125C23116yes—
182C3×#125C23116yes—
183C3×#125C23116yes—
184C3×#125C2318yes—
185C3×#125C2314yes—
186C3×#125C2318yes—
187C3×#125C23116yes—
188C3×#125C2318yes—
189C3×#125C2318yes—
190C3×#125C2314yes—
191C3×#125C2314yes—
192C3×#125C2318yes—
193C3×#124C2318yes—
194C3×#124C2314yes—
195C3×#124C23116yes—
196C3×#124C2314yes—
197C3×#124C2314yes—
198C3×#123C23116yes—
199C3×#123C2318yes—
200C3×#123C23116yes—
201C3×#123C23116yes—
202C3×#123C2318yes—
203C3×#123C2318yes—
204C3×#123C2318yes—
205C3×#123C2318yes—
206C3×#123C2318yes—
207C3×#123C23116yes—
208C3×C22⋊Q8C23116yes—
209C3×C22⋊Q8C2318yes—
210C3×C22⋊Q8C2318yes—
211C3×C22⋊Q8C2318yes—
212C3×C22⋊Q8C2318yes—
213C3×C22⋊Q8C23116yes—
214C3×C22⋊Q8C23116yes—
215C3×C22⋊Q8C23116yes—
216C3×C22⋊Q8C23116yes—
217C3×C22⋊Q8C2314yes—
218C3×C22⋊Q8C2318yes—
219C3×C22⋊Q8C2318yes—
220C3×C22⋊Q8C23116yes—
221C3×C22⋊Q8C23116yes—
222C3×C22⋊Q8C2318yes—
223C3×C22⋊Q8C23116yes—
224C3×C22⋊Q8C2314yes—
225C3×C22⋊Q8C2314yes—
226C3×C22⋊Q8C2318yes—
227C3×C22⋊Q8C2314yes—
228C3×C22⋊Q8C2318yes—
229C3×C22⋊Q8C2314yes—
230C3×C22⋊Q8C2314yes—
231C3×C22⋊Q8C2314yes—
232C3×C22⋊Q8C2314yes—
233C3×C22⋊Q8C2314yes—
234C3×C22⋊Q8C23116yes—
235C3×C22⋊Q8C2318yes—
236C3×#121C2314yes—
237C3×#121C2314yes—
238C3×#121C2318yes—
239C3×#121C2314yes—
240C3×#121C2318yes—
241C3×#121C2314yes—
242C3×#121C2314yes—
243C3×#120C2318yes—
244C3×C4×Q8C2314yes—
245C3×C4×Q8C2312yes—
246C3×C4×Q8C2314yes—
247C3×C4×Q8C2318yes—
248C3×C4×Q8C2318yes—
249C3×C4×Q8C2318yes—
250C3×C4×Q8C2318yes—
251C3×C4×Q8C2314yes—
252C3×C4×Q8C2312yes—
253C3×C4×Q8C2314yes—
254C3×C4×Q8C2318yes—
255C3×C4×Q8C2314yes—
256C3×C4×Q8C2314yes—
257C3×C4×Q8C2318yes—
258C3×C4×Q8C2318yes—
259C3×C4×Q8C23116yes—
260C3×C4×D4C2312yes—
261C3×C4×D4C2314yes—
262C3×C4×D4C2314yes—
263C3×C4×D4C2312yes—
264C3×C4×D4C2318yes—
265C3×C4×D4C2314yes—
266C3×C4×D4C2314yes—
267C3×C4×D4C2318yes—
268C3×C4×D4C2314yes—
269C3×C4×D4C2312yes—
270C3×C4×D4C2314yes—
271C3×C4×D4C2318yes—
272C3×C4×D4C2312yes—
273C3×C4×D4C23116yes—
274C3×C4×D4C23116yes—
275C3×C4×D4C23116yes—
276C3×C4×D4C2318yes—
277C3×C4×D4C2318yes—
278C3×C4×D4C2314yes—
279C3×#117C2312yes—
280C3×#117C2314yes—
281C3×#117C2318yes—
282C3×#117C2318yes—
283C3×#117C2314yes—
284C3×#117C2314yes—
285C3×#117C2314yes—
286C3×#117C2318yes—
287C3×#117C2314yes—
288C3×#117C2318yes—
289C3×#117C2318yes—
290C3×#117C23116yes—
291C3×#117C2318yes—
292C3×#117C2318yes—
293C3×#117C23116yes—
294C2×C3×C4⋊C4C2311yescharacteristic
295C2×C3×C4⋊C4C2312yes—
296C2×C3×C4⋊C4C2314yes—
297C2×C3×C4⋊C4C2318yes—
298C2×C3×C4⋊C4C2318yes—
299C2×C3×C4⋊C4C2314yes—
300C2×C3×C4⋊C4C2314yes—
301C2×C3×C4⋊C4C2311yescharacteristic
302C2×C3×C4⋊C4C2312yes—
303C2×C3×C4⋊C4C2312yes—
304C2×C3×C4⋊C4C23116yes—
305C2×C3×C4⋊C4C2318yes—
306C2×C3×C4⋊C4C2318yes—
307C2×C3×C4⋊C4C2314yes—
308C2×C3×C4⋊C4C2318yes—
309C2×C3×C22⋊C4C2318yes—
310C2×C3×C22⋊C4C2314yes—
311C2×C3×C22⋊C4C2312yes—
312C2×C3×C42C2318yes—
313C2×C3×C42C2311yescharacteristic
314C2×C3×C42C2312yes—
315C2×C3×C42C2314yes—
316#564C22×C318yescomplemented
317#563C22×C3116yescomplemented
318#563C22×C3116yescomplemented
319#563C22×C318yescomplemented
320Q82C22×C314yescomplemented
321Q82C22×C314yescomplemented
322#557C22×C314yescomplemented
323#557C22×C318yescomplemented
324#557C22×C318yescomplemented
325#557C22×C314yescomplemented
326#556C22×C312yes—
327#556C22×C314yes—
328#556C22×C318yescomplemented
329#555C22×C312yes—
330#554C22×C314yes—
331#554C22×C314yes—
332#554C22×C318yes—
333#554C22×C312yes—
334#554C22×C318yes—
335#554C22×C318yescomplemented
336#554C22×C318yescomplemented
337#554C22×C314yescomplemented
338#553C22×C314yes—
339#553C22×C318yescomplemented
340#552C22×C314yes—
341#552C22×C314yes—
342#552C22×C3116yes—
343#552C22×C318yes—
344#552C22×C318yescomplemented
345#552C22×C318yescomplemented
346#552C22×C318yescomplemented
347#552C22×C3116yescomplemented
348#552C22×C318yescomplemented
349#551C22×C318yes—
350#551C22×C3116yes—
351D4×Q8C22×C314yes—
352D4×Q8C22×C318yes—
353D4×Q8C22×C3116yescomplemented
354D4×Q8C22×C314yescomplemented
355#548C22×C318yes—
356#547C22×C312yes—
357#547C22×C314yes—
358#547C22×C314yes—
359#547C22×C318yescomplemented
360#546C22×C314yes—
361#544C22×C311yescharacteristic
362#544C22×C312yes—
363#544C22×C314yes—
364#544C22×C318yes—
365#544C22×C314yes—
366#544C22×C318yescomplemented
367#544C22×C318yescomplemented
368#544C22×C3116yescomplemented
369#544C22×C318yescomplemented
370#544C22×C318yescomplemented
371#542C22×C318yes—
372#542C22×C314yescomplemented
373#542C22×C318yescomplemented
374#541C22×C314yescomplemented
375#541C22×C318yescomplemented
376#541C22×C318yescomplemented
377#541C22×C3116yescomplemented
378#541C22×C3116yescomplemented
379#539C22×C314yes—
380#539C22×C318yes—
381#539C22×C3116yes—
382#539C22×C3116yescomplemented
383#537C22×C311yescharacteristic
384#536C22×C312yes—
385#536C22×C3116yescomplemented
386#533C22×C312yes—
387#533C22×C314yes—
388#533C22×C314yescomplemented
389#533C22×C318yescomplemented
390#533C22×C314yescomplemented
391C2×C4⋊Q8C22×C311yescharacteristic
392C2×C4⋊Q8C22×C318yescomplemented
393C2×C4⋊Q8C22×C314yescomplemented
394#529C22×C314yes—
395#529C22×C314yes—
396#529C22×C318yes—
397#529C22×C314yescomplemented
398#529C22×C318yescomplemented
399C2×#125C22×C312yes—
400C2×#125C22×C318yescomplemented
401#525C22×C314yes—
402#525C22×C318yes—
403C2×C22⋊Q8C22×C318yes—
404C2×C22⋊Q8C22×C312yes—
405C2×C22⋊Q8C22×C314yes—
406#520C22×C314yes—
407#520C22×C318yes—
408#519C22×C312yes—
409C4×#41C22×C312yes—
410C4×#41C22×C314yes—
411C2×C4×Q8C22×C311yescharacteristic
412C2×C4×D4C22×C311yescharacteristic
413C2×C4×D4C22×C312yes—
414C2×#117C22×C314yes—
415C22×C4⋊C4C22×C312yes—
416C24×C3C2412yes—
417C3×#41—216no—
418C3×#41—28no—
419C3×#41—88no—
420C2×C3×Q8—24no—
421C2×C3×Q8—82no—
422C2×C3×Q8—88no—
423C2×C3×Q8—88no—
424C2×C3×Q8C2414yes—
425C2×C3×Q8C2412yes—
426C2×C3×Q8C2414yes—
427C2×C3×Q8C2418yes—
428C2×C3×Q8C2414yes—
429C2×C3×Q8C24116yes—
430C2×C3×Q8C2418yes—
431C2×C3×Q8C2414yes—
432C2×C3×D4—24no—
433C2×C3×D4C2414yes—
434C2×C3×D4C2418yes—
435C2×C3×D4C2412yes—
436C2×C3×D4C2412yes—
437C2×C3×D4C2411yescharacteristic
438C2×C3×D4C2418yes—
439C2×C3×D4C2414yes—
440C2×C3×D4C2411yescharacteristic
441C22×C3×C4—28no—
442C22×C3×C4—84no—
443C22×C3×C4C2411yescharacteristic
444C22×C3×C4C2414yes—
445C22×C3×C4C2412yes—
446C22×C3×C4C2418yes—
447C22×C3×C4C2414yes—
448C22×C3×C4C2414yes—
449C22×C3×C4C2412yes—
450C22×C3×C4C2414yes—
451C22×C3×C4C2411yescharacteristic
452C22×C3×C4C2418yes—
453C22×C3×C4C2412yes—
454C22×C3×C4C2414yes—
455C22×C3×C4C2414yes—
456C22×C3×C4C2418yes—
457C22×C3×C4C24116yes—
458C22×C3×C4C2418yes—
459C22×C3×C4C2411yescharacteristic
460C3×C4⋊C4C2414yes—
461C3×C4⋊C4C2418yes—
462C3×C4⋊C4C2414yes—
463C3×C4⋊C4C2414yes—
464C3×C4⋊C4C24116yes—
465C3×C4⋊C4C2412yes—
466C3×C4⋊C4C2412yes—
467C3×C4⋊C4C2414yes—
468C3×C4⋊C4C2418yes—
469C3×C4⋊C4C24116yes—
470C3×C4⋊C4C2414yes—
471C3×C4⋊C4C2414yes—
472C3×C4⋊C4C2412yes—
473C3×C4⋊C4C2418yes—
474C3×C4⋊C4C2418yes—
475C3×C4⋊C4C2418yes—
476C3×C4⋊C4C24116yes—
477C3×C4⋊C4C24116yes—
478C3×C4⋊C4C2414yes—
479C3×C4⋊C4C2412yes—
480C3×C4⋊C4C24116yes—
481C3×C4⋊C4C24116yes—
482C3×C4⋊C4C24116yes—
483C3×C4⋊C4C2418yes—
484C3×C4⋊C4C2418yes—
485C3×C4⋊C4C2414yes—
486C3×C4⋊C4C2414yes—
487C3×C4⋊C4C2418yes—
488C3×C4⋊C4C2418yes—
489C3×C4⋊C4C2414yes—
490C3×C4⋊C4C2418yes—
491C3×C4⋊C4C2418yes—
492C3×C4⋊C4C2418yes—
493C3×C4⋊C4C2418yes—
494C3×C4⋊C4C2418yes—
495C3×C4⋊C4C2414yes—
496C3×C22⋊C4C2414yes—
497C3×C22⋊C4C2418yes—
498C3×C22⋊C4C2418yes—
499C3×C22⋊C4C2414yes—
500C3×C22⋊C4C2418yes—
501C3×C22⋊C4C2418yes—
502C3×C22⋊C4C2418yes—
503C3×C22⋊C4C2414yes—
504C3×C22⋊C4C2418yes—
505C3×C22⋊C4C2418yes—
506C3×C22⋊C4C2418yes—
507C3×C22⋊C4C2418yes—
508C3×C22⋊C4C2418yes—
509C3×C22⋊C4C2414yes—
510C3×C22⋊C4C24116yes—
511C3×C22⋊C4C2418yes—
512C3×C22⋊C4C2414yes—
513C3×C22⋊C4C2418yes—
514C3×C42C2414yes—
515C3×C42C2412yes—
516C3×C42C2418yes—
517C3×C42C2414yes—
518C3×C42C2418yes—
519C3×C42C2412yes—
520C3×C42C2414yes—
521C3×C42C2418yes—
522C3×C42C2414yes—
523C3×C42C2414yes—
524C3×C42C24116yes—
525C3×C42C24116yes—
526C2×#41C23×C312yes—
527C2×#41C23×C314yes—
528C2×#41C23×C318yes—
529C22×Q8C23×C311yescharacteristic
530C22×Q8C23×C312yes—
531C22×Q8C23×C318yes—
532C22×Q8C23×C318yes—
533C22×D4C23×C311yescharacteristic
534C23×C4C23×C312yes—
535C23×C4C23×C314yes—
536C4⋊Q8C23×C314yes—
537C4⋊Q8C23×C314yes—
538C4⋊Q8C23×C312yes—
539C4⋊Q8C23×C314yes—
540C4⋊Q8C23×C318yes—
541C4⋊Q8C23×C3116yes—
542C4⋊Q8C23×C318yes—
543C4⋊Q8C23×C318yes—
544C4⋊Q8C23×C318yes—
545C4⋊Q8C23×C3116yes—
546C4⋊Q8C23×C318yes—
547C4⋊Q8C23×C312yes—
548C4⋊Q8C23×C314yes—
549C4⋊Q8C23×C314yes—
550C4⋊Q8C23×C314yes—
551C4⋊Q8C23×C3116yes—
552C4⋊Q8C23×C3116yes—
553#126C23×C318yes—
554#126C23×C318yes—
555#126C23×C318yes—
556#126C23×C318yes—
557#126C23×C318yes—
558#126C23×C3116yes—
559#126C23×C3116yes—
560#126C23×C3116yes—
561#126C23×C3116yes—
562#126C23×C3116yes—
563#125C23×C318yes—
564#125C23×C318yes—
565#125C23×C314yes—
566#125C23×C318yes—
567#125C23×C3116yes—
568#125C23×C318yes—
569#125C23×C3116yes—
570#125C23×C318yes—
571#125C23×C318yes—
572#125C23×C314yes—
573#125C23×C314yes—
574#125C23×C318yes—
575#125C23×C314yes—
576#125C23×C318yes—
577#125C23×C3116yes—
578#125C23×C3116yes—
579#125C23×C3116yes—
580#125C23×C3116yes—
581#125C23×C3116yes—
582#125C23×C3116yes—
583#124C23×C318yes—
584#124C23×C314yes—
585#124C23×C314yes—
586#124C23×C314yes—
587#124C23×C3116yes—
588#123C23×C318yes—
589#123C23×C3116yes—
590#123C23×C318yes—
591#123C23×C318yes—
592#123C23×C318yes—
593#123C23×C318yes—
594#123C23×C318yes—
595#123C23×C3116yes—
596#123C23×C3116yes—
597#123C23×C3116yes—
598C22⋊Q8C23×C314yes—
599C22⋊Q8C23×C318yes—
600C22⋊Q8C23×C318yes—
601C22⋊Q8C23×C3116yes—
602C22⋊Q8C23×C3116yes—
603C22⋊Q8C23×C3116yes—
604C22⋊Q8C23×C318yes—
605C22⋊Q8C23×C3116yes—
606C22⋊Q8C23×C318yes—
607C22⋊Q8C23×C318yes—
608C22⋊Q8C23×C314yes—
609C22⋊Q8C23×C314yes—
610C22⋊Q8C23×C318yes—
611C22⋊Q8C23×C314yes—
612C22⋊Q8C23×C318yes—
613C22⋊Q8C23×C314yes—
614C22⋊Q8C23×C314yes—
615C22⋊Q8C23×C314yes—
616C22⋊Q8C23×C314yes—
617C22⋊Q8C23×C314yes—
618C22⋊Q8C23×C318yes—
619C22⋊Q8C23×C3116yes—
620C22⋊Q8C23×C318yes—
621C22⋊Q8C23×C318yes—
622C22⋊Q8C23×C3116yes—
623C22⋊Q8C23×C3116yes—
624C22⋊Q8C23×C3116yes—
625C22⋊Q8C23×C3116yes—
626#121C23×C314yes—
627#121C23×C314yes—
628#121C23×C318yes—
629#121C23×C314yes—
630#121C23×C318yes—
631#121C23×C314yes—
632#121C23×C314yes—
633#120C23×C318yes—
634C4×Q8C23×C314yes—
635C4×Q8C23×C314yes—
636C4×Q8C23×C314yes—
637C4×Q8C23×C312yes—
638C4×Q8C23×C312yes—
639C4×Q8C23×C314yes—
640C4×Q8C23×C318yes—
641C4×Q8C23×C318yes—
642C4×Q8C23×C318yes—
643C4×Q8C23×C318yes—
644C4×Q8C23×C318yes—
645C4×Q8C23×C314yes—
646C4×Q8C23×C314yes—
647C4×Q8C23×C318yes—
648C4×Q8C23×C318yes—
649C4×Q8C23×C3116yes—
650C4×D4C23×C312yes—
651C4×D4C23×C314yes—
652C4×D4C23×C314yes—
653C4×D4C23×C312yes—
654C4×D4C23×C318yes—
655C4×D4C23×C314yes—
656C4×D4C23×C314yes—
657C4×D4C23×C318yes—
658C4×D4C23×C314yes—
659C4×D4C23×C312yes—
660C4×D4C23×C314yes—
661C4×D4C23×C318yes—
662C4×D4C23×C312yes—
663C4×D4C23×C3116yes—
664C4×D4C23×C3116yes—
665C4×D4C23×C3116yes—
666C4×D4C23×C318yes—
667C4×D4C23×C318yes—
668C4×D4C23×C314yes—
669#117C23×C312yes—
670#117C23×C314yes—
671#117C23×C318yes—
672#117C23×C318yes—
673#117C23×C314yes—
674#117C23×C314yes—
675#117C23×C314yes—
676#117C23×C318yes—
677#117C23×C314yes—
678#117C23×C318yes—
679#117C23×C318yes—
680#117C23×C3116yes—
681#117C23×C318yes—
682#117C23×C318yes—
683#117C23×C3116yes—
684C2×C4⋊C4C23×C311yescharacteristic
685C2×C4⋊C4C23×C312yes—
686C2×C4⋊C4C23×C314yes—
687C2×C4⋊C4C23×C318yes—
688C2×C4⋊C4C23×C318yes—
689C2×C4⋊C4C23×C314yes—
690C2×C4⋊C4C23×C314yes—
691C2×C4⋊C4C23×C311yescharacteristic
692C2×C4⋊C4C23×C312yes—
693C2×C4⋊C4C23×C312yes—
694C2×C4⋊C4C23×C3116yes—
695C2×C4⋊C4C23×C318yes—
696C2×C4⋊C4C23×C318yes—
697C2×C4⋊C4C23×C314yes—
698C2×C4⋊C4C23×C318yes—
699C2×C22⋊C4C23×C318yes—
700C2×C22⋊C4C23×C314yes—
701C2×C22⋊C4C23×C312yes—
702C2×C42C23×C318yes—
703C2×C42C23×C311yescharacteristic
704C2×C42C23×C312yes—
705C2×C42C23×C314yes—
706C23×C3—24no—
707C23×C3—24no—
708C23×C3—42no—
709C23×C3C2512yes—
710C23×C3C2514yes—
711C23×C3C2511yescharacteristic
712C23×C3C2512yes—
713C3×Q8—28no—
714C3×Q8—24no—
715C3×Q8—28no—
716C3×Q8—44no—
717C3×Q8—48no—
718C3×Q8—416no—
719C3×Q8—44no—
720C3×Q8—48no—
721C3×D4—24no—
722C3×D4—28no—
723C3×D4—216no—
724C3×D4—22no—
725C3×D4—24no—
726C3×D4—44no—
727C3×D4—48no—
728C3×D42−1+414yes—
729C2×C3×C4—24no—
730C2×C3×C4—24no—
731C2×C3×C4—216no—
732C2×C3×C4—28no—
733C2×C3×C4—28no—
734C2×C3×C4—22no—
735C2×C3×C4—28no—
736C2×C3×C4—28no—
737C2×C3×C4—42no—
738C2×C3×C4—48no—
739C2×C3×C4—44no—
740C2×C3×C4—48no—
741C2×C3×C4—48no—
742C2×C3×C4—41no—
743C2×C3×C4—44no—
744C2×C3×C4—416no—
745C2×C3×C42−1+414yes—
746C2×C3×C4C2514yes—
747C2×C3×C4C2518yes—
748C2×C3×C4C2514yes—
749C2×C3×C4C2511yescharacteristic
750C2×C3×C4C2514yes—
751C2×C3×C4C2514yes—
752C2×C3×C4C2514yes—
753C2×C3×C4C2512yes—
754C2×C3×C4C2518yes—
755C2×C3×C4C2518yes—
756C2×C3×C4C2514yes—
757C2×C3×C4C2511yescharacteristic
758C2×C3×C4C2512yes—
759C24C24×C312yes—
760#41—216no—
761#41—28no—
762#41—88no—
763C2×Q8—24no—
764C2×Q8—82no—
765C2×Q8—88no—
766C2×Q8—88no—
767C2×Q8C24×C314yes—
768C2×Q8C24×C312yes—
769C2×Q8C24×C314yes—
770C2×Q8C24×C318yes—
771C2×Q8C24×C314yes—
772C2×Q8C24×C3116yes—
773C2×Q8C24×C318yes—
774C2×Q8C24×C314yes—
775C2×D4—24no—
776C2×D4C24×C314yes—
777C2×D4C24×C318yes—
778C2×D4C24×C312yes—
779C2×D4C24×C312yes—
780C2×D4C24×C311yescharacteristic
781C2×D4C24×C318yes—
782C2×D4C24×C314yes—
783C2×D4C24×C311yescharacteristic
784C22×C4—28no—
785C22×C4—84no—
786C22×C4C24×C311yescharacteristic
787C22×C4C24×C314yes—
788C22×C4C24×C312yes—
789C22×C4C24×C318yes—
790C22×C4C24×C314yes—
791C22×C4C24×C314yes—
792C22×C4C24×C312yes—
793C22×C4C24×C314yes—
794C22×C4C24×C311yescharacteristic
795C22×C4C24×C318yes—
796C22×C4C24×C312yes—
797C22×C4C24×C314yes—
798C22×C4C24×C314yes—
799C22×C4C24×C318yes—
800C22×C4C24×C3116yes—
801C22×C4C24×C318yes—
802C22×C4C24×C311yescharacteristic
803C4⋊C4C24×C314yes—
804C4⋊C4C24×C318yes—
805C4⋊C4C24×C314yes—
806C4⋊C4C24×C314yes—
807C4⋊C4C24×C3116yes—
808C4⋊C4C24×C312yes—
809C4⋊C4C24×C312yes—
810C4⋊C4C24×C314yes—
811C4⋊C4C24×C318yes—
812C4⋊C4C24×C3116yes—
813C4⋊C4C24×C314yes—
814C4⋊C4C24×C314yes—
815C4⋊C4C24×C312yes—
816C4⋊C4C24×C318yes—
817C4⋊C4C24×C318yes—
818C4⋊C4C24×C318yes—
819C4⋊C4C24×C3116yes—
820C4⋊C4C24×C3116yes—
821C4⋊C4C24×C314yes—
822C4⋊C4C24×C312yes—
823C4⋊C4C24×C3116yes—
824C4⋊C4C24×C3116yes—
825C4⋊C4C24×C3116yes—
826C4⋊C4C24×C318yes—
827C4⋊C4C24×C318yes—
828C4⋊C4C24×C314yes—
829C4⋊C4C24×C314yes—
830C4⋊C4C24×C318yes—
831C4⋊C4C24×C318yes—
832C4⋊C4C24×C314yes—
833C4⋊C4C24×C318yes—
834C4⋊C4C24×C318yes—
835C4⋊C4C24×C318yes—
836C4⋊C4C24×C318yes—
837C4⋊C4C24×C318yes—
838C4⋊C4C24×C314yes—
839C22⋊C4C24×C314yes—
840C22⋊C4C24×C318yes—
841C22⋊C4C24×C318yes—
842C22⋊C4C24×C314yes—
843C22⋊C4C24×C318yes—
844C22⋊C4C24×C318yes—
845C22⋊C4C24×C318yes—
846C22⋊C4C24×C314yes—
847C22⋊C4C24×C318yes—
848C22⋊C4C24×C318yes—
849C22⋊C4C24×C318yes—
850C22⋊C4C24×C318yes—
851C22⋊C4C24×C318yes—
852C22⋊C4C24×C314yes—
853C22⋊C4C24×C3116yes—
854C22⋊C4C24×C318yes—
855C22⋊C4C24×C314yes—
856C22⋊C4C24×C318yes—
857C42C24×C314yes—
858C42C24×C312yes—
859C42C24×C318yes—
860C42C24×C314yes—
861C42C24×C318yes—
862C42C24×C312yes—
863C42C24×C314yes—
864C42C24×C318yes—
865C42C24×C314yes—
866C42C24×C314yes—
867C42C24×C3116yes—
868C42C24×C3116yes—
869C22×C3—22no—
870C22×C3—21no—
871C22×C3—22no—
872C22×C3—21no—
873C22×C3—22no—
874C22×C3—24no—
875C22×C3—24no—
876C22×C3—22no—
877C22×C3—24no—
878C22×C3—22no—
879C22×C3—48no—
880C22×C3C2×2−1+412yes—
881C22×C3C2×2−1+414yes—
882C22×C3C2611yescharacteristic
883C3×C4—24no—
884C3×C4—24no—
885C3×C4—21no—
886C3×C4—28no—
887C3×C4—24no—
888C3×C4—24no—
889C3×C4—24no—
890C3×C4—28no—
891C3×C4—28no—
892C3×C4—24no—
893C3×C4—22no—
894C3×C4C2×2−1+414yes—
895C3×C4C2×2−1+412yes—
896C23—24no—
897C23—24no—
898C23—42no—
899C23C25×C312yes—
900C23C25×C314yes—
901C23C25×C311yescharacteristic
902C23C25×C312yes—
903Q8—28no—
904Q8—24no—
905Q8—28no—
906Q8—44no—
907Q8—48no—
908Q8—416no—
909Q8—44no—
910Q8—48no—
911D4—24no—
912D4—28no—
913D4—216no—
914D4—22no—
915D4—24no—
916D4—44no—
917D4—48no—
918D4C3×2−1+414yes—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—216no—
922C2×C4—28no—
923C2×C4—28no—
924C2×C4—22no—
925C2×C4—28no—
926C2×C4—28no—
927C2×C4—42no—
928C2×C4—48no—
929C2×C4—44no—
930C2×C4—48no—
931C2×C4—48no—
932C2×C4—41no—
933C2×C4—44no—
934C2×C4—416no—
935C2×C4C3×2−1+414yes—
936C2×C4C25×C314yes—
937C2×C4C25×C318yes—
938C2×C4C25×C314yes—
939C2×C4C25×C311yescharacteristic
940C2×C4C25×C314yes—
941C2×C4C25×C314yes—
942C2×C4C25×C314yes—
943C2×C4C25×C312yes—
944C2×C4C25×C318yes—
945C2×C4C25×C318yes—
946C2×C4C25×C314yes—
947C2×C4C25×C311yescharacteristic
948C2×C4C25×C312yes—
949C2×C3—22no—
950C2×C3—24no—
951C2×C3—44no—
952C2×C3—42no—
953C2×C3C22×2−1+411yescharacteristic
954C2×C3C22×2−1+411yescharacteristic
955C2×C3H(7,𝔽2)11yescharacteristic
956C22—22no—
957C22—21no—
958C22—22no—
959C22—21no—
960C22—22no—
961C22—24no—
962C22—24no—
963C22—22no—
964C22—24no—
965C22—22no—
966C22—48no—
967C22C2×C3×2−1+412yes—
968C22C2×C3×2−1+414yes—
969C22C26×C311yescharacteristic
970C4—24no—
971C4—24no—
972C4—21no—
973C4—28no—
974C4—24no—
975C4—24no—
976C4—24no—
977C4—28no—
978C4—28no—
979C4—24no—
980C4—22no—
981C4C2×C3×2−1+414yes—
982C4C2×C3×2−1+412yes—
983C3#6294511yescharacteristic, direct product factor, Sylow
984C2—22no—
985C2—24no—
986C2—42no—
987C2—44no—
988C2C22×C3×2−1+411yescharacteristic
989C2C22×C3×2−1+411yescharacteristic
990C2C3×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×#3563C2semidirect
2. C3×#3563C2semidirect
3. C3×#3555C2semidirect
4. C3×#3552C2semidirect
5. C3×#3544C2semidirect
6. C3×#3538C2semidirect
7. C3×#3520C2semidirect
8. C3×#3515C2semidirect
9. C3×#3503C2semidirect
10. C3×#3503C2semidirect
11. C3×#3502C2semidirect
12. C3×#3495C2semidirect
13. C3×#3492C2semidirect
14. C3×#3475C2semidirect
15. C2×C3×#554C2semidirect
16. C3×#3461C2semidirect
17. C2×C3×#544C2semidirect
18. #62945C3direct (N × H)
19. C3×#564C22semidirect
20. C3×#563C22semidirect
21. C3×#563C22semidirect
22. C3×#563C22semidirect
23. C3×Q82C22semidirect
24. C3×Q82C22semidirect
25. C3×#557C22semidirect
26. C3×#557C22semidirect
27. C3×#557C22semidirect
28. C3×#557C22semidirect
31. C3×#556C22semidirect
38. C3×#554C22semidirect
39. C3×#554C22semidirect
40. C3×#554C22semidirect
42. C3×#553C22semidirect
47. C3×#552C22semidirect
48. C3×#552C22semidirect
49. C3×#552C22semidirect
50. C3×#552C22semidirect
51. C3×#552C22semidirect
56. C3×D4×Q8C22semidirect
57. C3×D4×Q8C22semidirect
62. C3×#547C22semidirect
69. C3×#544C22semidirect
70. C3×#544C22semidirect
71. C3×#544C22semidirect
72. C3×#544C22semidirect
73. C3×#544C22semidirect
75. C3×#542C22semidirect
76. C3×#542C22semidirect
77. C3×#541C22semidirect
78. C3×#541C22semidirect
79. C3×#541C22semidirect
80. C3×#541C22semidirect
81. C3×#541C22semidirect
85. C3×#539C22semidirect
88. C3×#536C22semidirect
91. C3×#533C22semidirect
92. C3×#533C22semidirect
93. C3×#533C22semidirect
95. C2×C3×C4⋊Q8C22semidirect
96. C2×C3×C4⋊Q8C22semidirect
100. C3×#529C22semidirect
101. C3×#529C22semidirect
103. C2×C3×#125C22semidirect
119. #3563C2×C3semidirect
120. #3563C2×C3semidirect
121. #3555C2×C3semidirect
122. #3552C2×C3semidirect
123. #3544C2×C3semidirect
124. #3538C2×C3semidirect
125. #3520C2×C3semidirect
126. #3515C2×C3semidirect
127. #3503C2×C3semidirect
128. #3503C2×C3semidirect
129. #3502C2×C3semidirect
130. #3495C2×C3semidirect
131. #3492C2×C3semidirect
132. #3475C2×C3semidirect
133. C2×#554C2×C3semidirect
134. #3461C2×C3semidirect
135. C2×#544C2×C3semidirect
316. #564C22×C3semidirect
317. #563C22×C3semidirect
318. #563C22×C3semidirect
319. #563C22×C3semidirect
320. Q82C22×C3semidirect
321. Q82C22×C3semidirect
322. #557C22×C3semidirect
323. #557C22×C3semidirect
324. #557C22×C3semidirect
325. #557C22×C3semidirect
328. #556C22×C3semidirect
335. #554C22×C3semidirect
336. #554C22×C3semidirect
337. #554C22×C3semidirect
339. #553C22×C3semidirect
344. #552C22×C3semidirect
345. #552C22×C3semidirect
346. #552C22×C3semidirect
347. #552C22×C3semidirect
348. #552C22×C3semidirect
353. D4×Q8C22×C3semidirect
354. D4×Q8C22×C3semidirect
359. #547C22×C3semidirect
366. #544C22×C3semidirect
367. #544C22×C3semidirect
368. #544C22×C3semidirect
369. #544C22×C3semidirect
370. #544C22×C3semidirect
372. #542C22×C3semidirect
373. #542C22×C3semidirect
374. #541C22×C3semidirect
375. #541C22×C3semidirect
376. #541C22×C3semidirect
377. #541C22×C3semidirect
378. #541C22×C3semidirect
382. #539C22×C3semidirect
385. #536C22×C3semidirect
388. #533C22×C3semidirect
389. #533C22×C3semidirect
390. #533C22×C3semidirect
392. C2×C4⋊Q8C22×C3semidirect
393. C2×C4⋊Q8C22×C3semidirect
397. #529C22×C3semidirect
398. #529C22×C3semidirect
400. C2×#125C22×C3semidirect
983. C3#62945direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#35632
C3×#35552
C3×#35522
C3×#35442
C3×#35382
C3×#35202
C3×#35152
C3×#35032
C3×#35022
C3×#34952
C3×#34922
C3×#34752
C2×C3×#5542
C3×#34612
C2×C3×#5442
#629453