Finite Group Databasebeta

← C3×#62932 #10681539

Subgroups — C3×#62932 #10681539

Order 768.

6354 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3564C218yesmaximal, complemented
2C3×#3557C218yesmaximal, complemented
3C3×#3555C214yesmaximal, complemented
4C3×#3555C218yesmaximal, complemented
5C3×#3550C214yesmaximal, complemented
6C3×#3538C214yesmaximal, complemented
7C3×#3523C214yesmaximal, complemented
8C3×#3510C214yesmaximal, complemented
9C3×#3509C212yesmaximal, complemented
10C3×#3507C214yesmaximal, complemented
11C3×#3502C212yesmaximal, complemented
12C3×#3501C211yesmaximal, characteristic, complemented
13C3×#3495C214yesmaximal, complemented
14C3×Q8×#41C212yesmaximal, complemented
15C2×C3×#556C211yesmaximal, characteristic, complemented
16C3×#3461C212yesmaximal, complemented
17C3×#3460C211yesmaximal, characteristic
18#62932C311yesmaximal, characteristic, direct product factor, Sylow
19C3×#563C22116yescomplemented
20C3×#563C22116yescomplemented
21C3×#563C22116yescomplemented
22C3×#559C2218yes—
23C3×#559C2218yes—
24C3×Q82C2212yescomplemented
25C3×Q82C2218yescomplemented
26C3×#557C2212yescomplemented
27C3×#557C2214yescomplemented
28C3×#557C2218yescomplemented
29C3×#557C2218yescomplemented
30C3×#557C2218yescomplemented
31C3×#557C2214yescomplemented
32C3×#557C2214yescomplemented
33C3×#556C2214yes—
34C3×#556C2214yes—
35C3×#556C2218yes—
36C3×#556C2218yes—
37C3×#556C2218yes—
38C3×#556C2218yescomplemented
39C3×#556C2214yescomplemented
40C3×#556C22116yescomplemented
41C3×#556C2214yescomplemented
42C3×#554C2214yes—
43C3×#554C2218yes—
44C3×#554C2214yes—
45C3×#554C2218yes—
46C3×#554C2212yescomplemented
47C3×#554C2214yescomplemented
48C3×#552C2218yes—
49C3×#552C2218yes—
50C3×#552C2218yescomplemented
51C3×#552C22116yescomplemented
52C3×#552C2218yescomplemented
53C3×#552C22116yescomplemented
54C3×#551C22116yes—
55C3×#551C22116yes—
56C3×D4×Q8C2214yes—
57C3×D4×Q8C2214yes—
58C3×D4×Q8C2212yescomplemented
59C3×D4×Q8C2218yescomplemented
60C3×#544C2211yescharacteristic
61C3×#544C2212yes—
62C3×#544C2218yes—
63C3×#544C2214yescomplemented
64C3×#544C2218yescomplemented
65C3×#543C2214yes—
66C3×#542C2214yes—
67C3×#542C2218yes—
68C3×#542C2218yes—
69C3×#542C2218yescomplemented
70C3×#542C2218yescomplemented
71C3×#542C22116yescomplemented
72C3×#541C2218yescomplemented
73C3×#541C2218yescomplemented
74C3×#541C2218yescomplemented
75C3×#541C2218yescomplemented
76C3×#541C22116yescomplemented
77C3×#541C22116yescomplemented
78C3×#540C2214yes—
79C3×#539C2218yes—
80C3×#539C22116yescomplemented
81C3×#539C2218yescomplemented
82C3×#538C2214yes—
83C3×#537C2211yescharacteristic
84C3×#536C2214yes—
85C3×#536C2214yescomplemented
86C3×#536C2218yescomplemented
87C3×#535C2212yes—
88C3×#533C2212yes—
89C3×#533C2214yes—
90C3×#533C2218yes—
91C3×#533C2218yescomplemented
92C3×#533C2214yescomplemented
93C3×#533C2218yescomplemented
94C3×#533C2214yescomplemented
95C3×#533C2214yescomplemented
96C3×#532C2214yes—
97C2×C3×C4⋊Q8C2211yescharacteristic
98C3×#529C2214yes—
99C3×#529C2218yes—
100C3×#529C2218yes—
101C3×#529C2218yes—
102C3×#529C2218yescomplemented
103C2×C3×#126C2214yes—
104C2×C3×#124C2212yes—
105C3×#525C2214yes—
106C2×C3×C22⋊Q8C2212yes—
107C2×C3×C22⋊Q8C2214yes—
108C3×#520C2214yescomplemented
109C3×#519C2214yes—
110C3×#519C2214yescomplemented
111C3×#518C2212yes—
112C3×C4×#41C2212yes—
113C3×C4×#41C2214yes—
114C2×C3×C4×Q8C2212yes—
115C2×C3×C4×Q8C2211yescharacteristic
116C2×C3×C4×Q8C2214yescomplemented
117C2×C3×C4×D4C2211yescharacteristic
118C2×C3×#117C2212yes—
119#3564C2×C318yescomplemented
120#3557C2×C318yescomplemented
121#3555C2×C314yescomplemented
122#3555C2×C318yescomplemented
123#3550C2×C314yescomplemented
124#3538C2×C314yescomplemented
125#3523C2×C314yescomplemented
126#3510C2×C314yescomplemented
127#3509C2×C312yescomplemented
128#3507C2×C314yescomplemented
129#3502C2×C312yescomplemented
130#3501C2×C311yescharacteristic, complemented
131#3495C2×C314yescomplemented
132Q8×#41C2×C312yescomplemented
133C2×#556C2×C311yescharacteristic, complemented
134#3461C2×C312yescomplemented
135#3460C2×C311yescharacteristic
136C2×C3×#41C2312yes—
137C2×C3×#41C2314yes—
138C22×C3×Q8C2312yes—
139C22×C3×Q8C2311yescharacteristic
140C22×C3×Q8C2314yes—
141C22×C3×Q8C2314yes—
142C22×C3×D4C2311yescharacteristic
143C23×C3×C4C2312yes—
144C3×C4⋊Q8C2318yes—
145C3×C4⋊Q8C2314yes—
146C3×C4⋊Q8C2314yes—
147C3×C4⋊Q8C2318yes—
148C3×C4⋊Q8C23116yes—
149C3×C4⋊Q8C23116yes—
150C3×C4⋊Q8C2312yes—
151C3×C4⋊Q8C2314yes—
152C3×C4⋊Q8C2318yes—
153C3×C4⋊Q8C2314yes—
154C3×C4⋊Q8C2318yes—
155C3×C4⋊Q8C2318yes—
156C3×C4⋊Q8C2314yes—
157C3×C4⋊Q8C2314yes—
158C3×C4⋊Q8C2312yes—
159C3×C4⋊Q8C2318yes—
160C3×C4⋊Q8C2314yes—
161C3×#127C2314yes—
162C3×#126C23116yes—
163C3×#126C23116yes—
164C3×#126C23116yes—
165C3×#126C23116yes—
166C3×#126C23116yes—
167C3×#126C23116yes—
168C3×#126C23116yes—
169C3×#126C23116yes—
170C3×#126C23116yes—
171C3×#126C2318yes—
172C3×#126C23116yes—
173C3×#125C2318yes—
174C3×#125C2318yes—
175C3×#125C23116yes—
176C3×#125C23116yes—
177C3×#125C23116yes—
178C3×#125C23116yes—
179C3×#125C2314yes—
180C3×#125C2314yes—
181C3×#125C2314yes—
182C3×#125C2318yes—
183C3×#125C2318yes—
184C3×#125C23116yes—
185C3×#125C2314yes—
186C3×#125C23116yes—
187C3×#125C2318yes—
188C3×#125C2318yes—
189C3×#125C2318yes—
190C3×#124C2318yes—
191C3×#124C23116yes—
192C3×#124C23116yes—
193C3×#124C2318yes—
194C3×#124C2318yes—
195C3×#124C2318yes—
196C3×#124C2314yes—
197C3×#124C2318yes—
198C3×#123C23116yes—
199C3×#123C23116yes—
200C3×#123C23116yes—
201C3×#123C23116yes—
202C3×#123C2318yes—
203C3×#123C2318yes—
204C3×#123C23116yes—
205C3×#123C23116yes—
206C3×C22⋊Q8C2318yes—
207C3×C22⋊Q8C2318yes—
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⋊Q8C2318yes—
221C3×C22⋊Q8C2314yes—
222C3×C22⋊Q8C2314yes—
223C3×C22⋊Q8C2318yes—
224C3×C22⋊Q8C2318yes—
225C3×C22⋊Q8C2314yes—
226C3×C22⋊Q8C2318yes—
227C3×C22⋊Q8C2314yes—
228C3×C22⋊Q8C2318yes—
229C3×C22⋊Q8C2314yes—
230C3×C22⋊Q8C2318yes—
231C3×C22⋊Q8C2314yes—
232C3×C22⋊Q8C2318yes—
233C3×C22⋊Q8C2318yes—
234C3×#121C2314yes—
235C3×#121C2314yes—
236C3×#121C2314yes—
237C3×#121C2314yes—
238C3×#121C2314yes—
239C3×#121C2318yes—
240C3×#120C2318yes—
241C3×C4×Q8C2318yes—
242C3×C4×Q8C2318yes—
243C3×C4×Q8C2312yes—
244C3×C4×Q8C2318yes—
245C3×C4×Q8C2314yes—
246C3×C4×Q8C2312yes—
247C3×C4×Q8C2314yes—
248C3×C4×Q8C2318yes—
249C3×C4×Q8C23116yes—
250C3×C4×Q8C2318yes—
251C3×C4×Q8C2318yes—
252C3×C4×Q8C2312yes—
253C3×C4×Q8C2318yes—
254C3×C4×Q8C2314yes—
255C3×C4×Q8C2314yes—
256C3×C4×Q8C2314yes—
257C3×C4×Q8C2318yes—
258C3×C4×Q8C2314yes—
259C3×C4×Q8C2312yes—
260C3×C4×Q8C2318yes—
261C3×C4×Q8C2318yes—
262C3×C4×Q8C2318yes—
263C3×C4×Q8C2318yes—
264C3×C4×Q8C2318yes—
265C3×C4×Q8C2314yes—
266C3×C4×Q8C2318yes—
267C3×C4×D4C2314yes—
268C3×C4×D4C2314yes—
269C3×C4×D4C2318yes—
270C3×C4×D4C2318yes—
271C3×C4×D4C23116yes—
272C3×C4×D4C23116yes—
273C3×C4×D4C2314yes—
274C3×C4×D4C2314yes—
275C3×C4×D4C2314yes—
276C3×C4×D4C2318yes—
277C3×C4×D4C2312yes—
278C3×C4×D4C2314yes—
279C3×C4×D4C2318yes—
280C3×C4×D4C2312yes—
281C3×C4×D4C2318yes—
282C3×C4×D4C2318yes—
283C3×#117C2314yes—
284C3×#117C2314yes—
285C3×#117C2318yes—
286C3×#117C2314yes—
287C3×#117C2312yes—
288C3×#117C2314yes—
289C3×#117C2318yes—
290C3×#117C23116yes—
291C3×#117C2314yes—
292C3×#117C23116yes—
293C3×#117C2318yes—
294C3×#117C23116yes—
295C3×#117C23116yes—
296C3×#117C2318yes—
297C2×C3×C4⋊C4C2311yescharacteristic
298C2×C3×C4⋊C4C2312yes—
299C2×C3×C4⋊C4C2311yescharacteristic
300C2×C3×C4⋊C4C2314yes—
301C2×C3×C4⋊C4C2312yes—
302C2×C3×C4⋊C4C2314yes—
303C2×C3×C4⋊C4C2318yes—
304C2×C3×C4⋊C4C2314yes—
305C2×C3×C4⋊C4C2318yes—
306C2×C3×C4⋊C4C2312yes—
307C2×C3×C22⋊C4C2314yes—
308C2×C3×C22⋊C4C2312yes—
309C2×C3×C22⋊C4C2318yes—
310C2×C3×C22⋊C4C2314yes—
311C2×C3×C42C2314yes—
312C2×C3×C42C2311yescharacteristic
313C2×C3×C42C2312yes—
314C2×C3×C42C2318yes—
315C2×C3×C42C2314yes—
316#563C22×C3116yescomplemented
317#563C22×C3116yescomplemented
318#563C22×C3116yescomplemented
319#559C22×C318yes—
320#559C22×C318yes—
321Q82C22×C312yescomplemented
322Q82C22×C318yescomplemented
323#557C22×C312yescomplemented
324#557C22×C314yescomplemented
325#557C22×C318yescomplemented
326#557C22×C318yescomplemented
327#557C22×C318yescomplemented
328#557C22×C314yescomplemented
329#557C22×C314yescomplemented
330#556C22×C314yes—
331#556C22×C314yes—
332#556C22×C318yes—
333#556C22×C318yes—
334#556C22×C318yes—
335#556C22×C318yescomplemented
336#556C22×C314yescomplemented
337#556C22×C3116yescomplemented
338#556C22×C314yescomplemented
339#554C22×C314yes—
340#554C22×C318yes—
341#554C22×C314yes—
342#554C22×C318yes—
343#554C22×C312yescomplemented
344#554C22×C314yescomplemented
345#552C22×C318yes—
346#552C22×C318yes—
347#552C22×C318yescomplemented
348#552C22×C3116yescomplemented
349#552C22×C318yescomplemented
350#552C22×C3116yescomplemented
351#551C22×C3116yes—
352#551C22×C3116yes—
353D4×Q8C22×C314yes—
354D4×Q8C22×C314yes—
355D4×Q8C22×C312yescomplemented
356D4×Q8C22×C318yescomplemented
357#544C22×C311yescharacteristic
358#544C22×C312yes—
359#544C22×C318yes—
360#544C22×C314yescomplemented
361#544C22×C318yescomplemented
362#543C22×C314yes—
363#542C22×C314yes—
364#542C22×C318yes—
365#542C22×C318yes—
366#542C22×C318yescomplemented
367#542C22×C318yescomplemented
368#542C22×C3116yescomplemented
369#541C22×C318yescomplemented
370#541C22×C318yescomplemented
371#541C22×C318yescomplemented
372#541C22×C318yescomplemented
373#541C22×C3116yescomplemented
374#541C22×C3116yescomplemented
375#540C22×C314yes—
376#539C22×C318yes—
377#539C22×C3116yescomplemented
378#539C22×C318yescomplemented
379#538C22×C314yes—
380#537C22×C311yescharacteristic
381#536C22×C314yes—
382#536C22×C314yescomplemented
383#536C22×C318yescomplemented
384#535C22×C312yes—
385#533C22×C312yes—
386#533C22×C314yes—
387#533C22×C318yes—
388#533C22×C318yescomplemented
389#533C22×C314yescomplemented
390#533C22×C318yescomplemented
391#533C22×C314yescomplemented
392#533C22×C314yescomplemented
393#532C22×C314yes—
394C2×C4⋊Q8C22×C311yescharacteristic
395#529C22×C314yes—
396#529C22×C318yes—
397#529C22×C318yes—
398#529C22×C318yes—
399#529C22×C318yescomplemented
400C2×#126C22×C314yes—
401C2×#124C22×C312yes—
402#525C22×C314yes—
403C2×C22⋊Q8C22×C312yes—
404C2×C22⋊Q8C22×C314yes—
405#520C22×C314yescomplemented
406#519C22×C314yes—
407#519C22×C314yescomplemented
408#518C22×C312yes—
409C4×#41C22×C312yes—
410C4×#41C22×C314yes—
411C2×C4×Q8C22×C312yes—
412C2×C4×Q8C22×C311yescharacteristic
413C2×C4×Q8C22×C314yescomplemented
414C2×C4×D4C22×C311yescharacteristic
415C2×#117C22×C312yes—
416C24×C3C2412yes—
417C3×#41—28no—
418C3×#41—48no—
419C2×C3×Q8—28no—
420C2×C3×Q8—42no—
421C2×C3×Q8—48no—
422C2×C3×Q8—48no—
423C2×C3×Q8C2418yes—
424C2×C3×Q8C2412yes—
425C2×C3×Q8C2412yes—
426C2×C3×Q8C2414yes—
427C2×C3×Q8C2414yes—
428C2×C3×Q8C2418yes—
429C2×C3×Q8C2412yes—
430C2×C3×Q8C2418yes—
431C2×C3×Q8C2418yes—
432C2×C3×Q8C2414yes—
433C2×C3×D4—24no—
434C2×C3×D4C2414yes—
435C2×C3×D4C2414yes—
436C2×C3×D4C2412yes—
437C2×C3×D4C2418yes—
438C2×C3×D4C2418yes—
439C2×C3×D4C2414yes—
440C22×C3×C4—44no—
441C22×C3×C4C2414yes—
442C22×C3×C4C2414yes—
443C22×C3×C4C2411yescharacteristic
444C22×C3×C4C2414yes—
445C22×C3×C4C2414yes—
446C22×C3×C4C2412yes—
447C22×C3×C4C2412yes—
448C22×C3×C4C2411yescharacteristic
449C22×C3×C4C2412yes—
450C22×C3×C4C2418yes—
451C22×C3×C4C2414yes—
452C22×C3×C4C2418yes—
453C22×C3×C4C2418yes—
454C22×C3×C4C2418yes—
455C22×C3×C4C2414yes—
456C22×C3×C4C2411yescharacteristic
457C3×C4⋊C4C2411yescharacteristic
458C3×C4⋊C4C2414yes—
459C3×C4⋊C4C2414yes—
460C3×C4⋊C4C2418yes—
461C3×C4⋊C4C2412yes—
462C3×C4⋊C4C2414yes—
463C3×C4⋊C4C2411yescharacteristic
464C3×C4⋊C4C2418yes—
465C3×C4⋊C4C2414yes—
466C3×C4⋊C4C24116yes—
467C3×C4⋊C4C2418yes—
468C3×C4⋊C4C2414yes—
469C3×C4⋊C4C2418yes—
470C3×C4⋊C4C2418yes—
471C3×C4⋊C4C2418yes—
472C3×C4⋊C4C2414yes—
473C3×C4⋊C4C24116yes—
474C3×C4⋊C4C2418yes—
475C3×C4⋊C4C2414yes—
476C3×C4⋊C4C2418yes—
477C3×C4⋊C4C24116yes—
478C3×C4⋊C4C2414yes—
479C3×C4⋊C4C2414yes—
480C3×C4⋊C4C2412yes—
481C3×C4⋊C4C2412yes—
482C3×C4⋊C4C2418yes—
483C3×C4⋊C4C2414yes—
484C3×C4⋊C4C2418yes—
485C3×C4⋊C4C2414yes—
486C3×C4⋊C4C2414yes—
487C3×C4⋊C4C2414yes—
488C3×C4⋊C4C24116yes—
489C3×C4⋊C4C24116yes—
490C3×C4⋊C4C24116yes—
491C3×C4⋊C4C2418yes—
492C3×C4⋊C4C2418yes—
493C3×C4⋊C4C2418yes—
494C3×C22⋊C4C2418yes—
495C3×C22⋊C4C2418yes—
496C3×C22⋊C4C2418yes—
497C3×C22⋊C4C24116yes—
498C3×C22⋊C4C2418yes—
499C3×C22⋊C4C24116yes—
500C3×C22⋊C4C2414yes—
501C3×C22⋊C4C2418yes—
502C3×C22⋊C4C2418yes—
503C3×C22⋊C4C2418yes—
504C3×C22⋊C4C24116yes—
505C3×C22⋊C4C2414yes—
506C3×C22⋊C4C2414yes—
507C3×C22⋊C4C2418yes—
508C3×C22⋊C4C2418yes—
509C3×C22⋊C4C24116yes—
510C3×C42C2412yes—
511C3×C42C2414yes—
512C3×C42C2418yes—
513C3×C42C2418yes—
514C3×C42C2414yes—
515C3×C42C2412yes—
516C3×C42C2418yes—
517C3×C42C2414yes—
518C3×C42C2418yes—
519C3×C42C2414yes—
520C3×C42C2418yes—
521C3×C42C2414yes—
522C3×C42C24116yes—
523C3×C42C24116yes—
524C2×#41C23×C312yes—
525C2×#41C23×C314yes—
526C22×Q8C23×C312yes—
527C22×Q8C23×C311yescharacteristic
528C22×Q8C23×C314yes—
529C22×Q8C23×C314yes—
530C22×D4C23×C311yescharacteristic
531C23×C4C23×C312yes—
532C4⋊Q8C23×C314yes—
533C4⋊Q8C23×C314yes—
534C4⋊Q8C23×C314yes—
535C4⋊Q8C23×C312yes—
536C4⋊Q8C23×C312yes—
537C4⋊Q8C23×C318yes—
538C4⋊Q8C23×C314yes—
539C4⋊Q8C23×C314yes—
540C4⋊Q8C23×C318yes—
541C4⋊Q8C23×C318yes—
542C4⋊Q8C23×C314yes—
543C4⋊Q8C23×C318yes—
544C4⋊Q8C23×C318yes—
545C4⋊Q8C23×C318yes—
546C4⋊Q8C23×C314yes—
547C4⋊Q8C23×C3116yes—
548C4⋊Q8C23×C3116yes—
549#127C23×C314yes—
550#126C23×C3116yes—
551#126C23×C3116yes—
552#126C23×C318yes—
553#126C23×C3116yes—
554#126C23×C3116yes—
555#126C23×C3116yes—
556#126C23×C3116yes—
557#126C23×C3116yes—
558#126C23×C3116yes—
559#126C23×C3116yes—
560#126C23×C3116yes—
561#125C23×C314yes—
562#125C23×C314yes—
563#125C23×C314yes—
564#125C23×C318yes—
565#125C23×C318yes—
566#125C23×C3116yes—
567#125C23×C314yes—
568#125C23×C3116yes—
569#125C23×C318yes—
570#125C23×C318yes—
571#125C23×C318yes—
572#125C23×C318yes—
573#125C23×C318yes—
574#125C23×C3116yes—
575#125C23×C3116yes—
576#125C23×C3116yes—
577#125C23×C3116yes—
578#124C23×C318yes—
579#124C23×C318yes—
580#124C23×C314yes—
581#124C23×C318yes—
582#124C23×C318yes—
583#124C23×C318yes—
584#124C23×C3116yes—
585#124C23×C3116yes—
586#123C23×C318yes—
587#123C23×C3116yes—
588#123C23×C3116yes—
589#123C23×C318yes—
590#123C23×C3116yes—
591#123C23×C3116yes—
592#123C23×C3116yes—
593#123C23×C3116yes—
594C22⋊Q8C23×C314yes—
595C22⋊Q8C23×C318yes—
596C22⋊Q8C23×C318yes—
597C22⋊Q8C23×C318yes—
598C22⋊Q8C23×C318yes—
599C22⋊Q8C23×C318yes—
600C22⋊Q8C23×C314yes—
601C22⋊Q8C23×C314yes—
602C22⋊Q8C23×C318yes—
603C22⋊Q8C23×C318yes—
604C22⋊Q8C23×C314yes—
605C22⋊Q8C23×C318yes—
606C22⋊Q8C23×C314yes—
607C22⋊Q8C23×C318yes—
608C22⋊Q8C23×C314yes—
609C22⋊Q8C23×C318yes—
610C22⋊Q8C23×C314yes—
611C22⋊Q8C23×C3116yes—
612C22⋊Q8C23×C318yes—
613C22⋊Q8C23×C318yes—
614C22⋊Q8C23×C318yes—
615C22⋊Q8C23×C318yes—
616C22⋊Q8C23×C318yes—
617C22⋊Q8C23×C318yes—
618C22⋊Q8C23×C3116yes—
619C22⋊Q8C23×C3116yes—
620C22⋊Q8C23×C3116yes—
621C22⋊Q8C23×C3116yes—
622#121C23×C314yes—
623#121C23×C314yes—
624#121C23×C314yes—
625#121C23×C314yes—
626#121C23×C314yes—
627#121C23×C318yes—
628#120C23×C318yes—
629C4×Q8C23×C312yes—
630C4×Q8C23×C318yes—
631C4×Q8C23×C312yes—
632C4×Q8C23×C314yes—
633C4×Q8C23×C318yes—
634C4×Q8C23×C314yes—
635C4×Q8C23×C314yes—
636C4×Q8C23×C318yes—
637C4×Q8C23×C314yes—
638C4×Q8C23×C318yes—
639C4×Q8C23×C312yes—
640C4×Q8C23×C314yes—
641C4×Q8C23×C314yes—
642C4×Q8C23×C312yes—
643C4×Q8C23×C318yes—
644C4×Q8C23×C318yes—
645C4×Q8C23×C318yes—
646C4×Q8C23×C318yes—
647C4×Q8C23×C318yes—
648C4×Q8C23×C318yes—
649C4×Q8C23×C318yes—
650C4×Q8C23×C318yes—
651C4×Q8C23×C314yes—
652C4×Q8C23×C318yes—
653C4×Q8C23×C3116yes—
654C4×Q8C23×C318yes—
655C4×D4C23×C314yes—
656C4×D4C23×C314yes—
657C4×D4C23×C314yes—
658C4×D4C23×C318yes—
659C4×D4C23×C314yes—
660C4×D4C23×C312yes—
661C4×D4C23×C314yes—
662C4×D4C23×C318yes—
663C4×D4C23×C312yes—
664C4×D4C23×C314yes—
665C4×D4C23×C318yes—
666C4×D4C23×C318yes—
667C4×D4C23×C318yes—
668C4×D4C23×C3116yes—
669C4×D4C23×C318yes—
670C4×D4C23×C3116yes—
671#117C23×C314yes—
672#117C23×C314yes—
673#117C23×C318yes—
674#117C23×C314yes—
675#117C23×C312yes—
676#117C23×C314yes—
677#117C23×C318yes—
678#117C23×C3116yes—
679#117C23×C314yes—
680#117C23×C3116yes—
681#117C23×C318yes—
682#117C23×C3116yes—
683#117C23×C3116yes—
684#117C23×C318yes—
685C2×C4⋊C4C23×C311yescharacteristic
686C2×C4⋊C4C23×C312yes—
687C2×C4⋊C4C23×C311yescharacteristic
688C2×C4⋊C4C23×C314yes—
689C2×C4⋊C4C23×C312yes—
690C2×C4⋊C4C23×C314yes—
691C2×C4⋊C4C23×C318yes—
692C2×C4⋊C4C23×C314yes—
693C2×C4⋊C4C23×C318yes—
694C2×C4⋊C4C23×C312yes—
695C2×C22⋊C4C23×C314yes—
696C2×C22⋊C4C23×C312yes—
697C2×C22⋊C4C23×C318yes—
698C2×C22⋊C4C23×C314yes—
699C2×C42C23×C314yes—
700C2×C42C23×C311yescharacteristic
701C2×C42C23×C312yes—
702C2×C42C23×C318yes—
703C2×C42C23×C314yes—
704C23×C3—24no—
705C23×C3—42no—
706C23×C3—42no—
707C23×C3C2514yes—
708C23×C3C2514yes—
709C23×C3C2511yescharacteristic
710C3×Q8—216no—
711C3×Q8—24no—
712C3×Q8—24no—
713C3×Q8—28no—
714C3×Q8—42no—
715C3×Q8—48no—
716C3×Q8—48no—
717C3×Q8—44no—
718C3×Q8—48no—
719C3×Q8—44no—
720C3×D4—28no—
721C3×D4—28no—
722C3×D4—24no—
723C3×D4—48no—
724C3×D4—44no—
725C3×D4—48no—
726C2×C3×C4—28no—
727C2×C3×C4—28no—
728C2×C3×C4—22no—
729C2×C3×C4—28no—
730C2×C3×C4—28no—
731C2×C3×C4—44no—
732C2×C3×C4—42no—
733C2×C3×C4—48no—
734C2×C3×C4—42no—
735C2×C3×C4—41no—
736C2×C3×C4—48no—
737C2×C3×C4—44no—
738C2×C3×C4—42no—
739C2×C3×C4—48no—
740C2×C3×C4—48no—
741C2×C3×C42−1+414yes—
742C2×C3×C4C2512yes—
743C2×C3×C4C2518yes—
744C2×C3×C4C2512yes—
745C2×C3×C4C2514yes—
746C2×C3×C4C2514yes—
747C2×C3×C4C2514yes—
748C2×C3×C4C2512yes—
749C2×C3×C4C2518yes—
750C2×C3×C4C2514yes—
751C2×C3×C4C2518yes—
752C2×C3×C4C2514yes—
753C2×C3×C4C2511yescharacteristic
754C2×C3×C4C2512yes—
755C2×C3×C4C2511yescharacteristic
756C24C24×C312yes—
757#41—28no—
758#41—48no—
759C2×Q8—28no—
760C2×Q8—42no—
761C2×Q8—48no—
762C2×Q8—48no—
763C2×Q8C24×C318yes—
764C2×Q8C24×C312yes—
765C2×Q8C24×C312yes—
766C2×Q8C24×C314yes—
767C2×Q8C24×C314yes—
768C2×Q8C24×C318yes—
769C2×Q8C24×C312yes—
770C2×Q8C24×C318yes—
771C2×Q8C24×C318yes—
772C2×Q8C24×C314yes—
773C2×D4—24no—
774C2×D4C24×C314yes—
775C2×D4C24×C314yes—
776C2×D4C24×C312yes—
777C2×D4C24×C318yes—
778C2×D4C24×C318yes—
779C2×D4C24×C314yes—
780C22×C4—44no—
781C22×C4C24×C314yes—
782C22×C4C24×C314yes—
783C22×C4C24×C311yescharacteristic
784C22×C4C24×C314yes—
785C22×C4C24×C314yes—
786C22×C4C24×C312yes—
787C22×C4C24×C312yes—
788C22×C4C24×C311yescharacteristic
789C22×C4C24×C312yes—
790C22×C4C24×C318yes—
791C22×C4C24×C314yes—
792C22×C4C24×C318yes—
793C22×C4C24×C318yes—
794C22×C4C24×C318yes—
795C22×C4C24×C314yes—
796C22×C4C24×C311yescharacteristic
797C4⋊C4C24×C311yescharacteristic
798C4⋊C4C24×C314yes—
799C4⋊C4C24×C314yes—
800C4⋊C4C24×C318yes—
801C4⋊C4C24×C312yes—
802C4⋊C4C24×C314yes—
803C4⋊C4C24×C311yescharacteristic
804C4⋊C4C24×C318yes—
805C4⋊C4C24×C314yes—
806C4⋊C4C24×C3116yes—
807C4⋊C4C24×C318yes—
808C4⋊C4C24×C314yes—
809C4⋊C4C24×C318yes—
810C4⋊C4C24×C318yes—
811C4⋊C4C24×C318yes—
812C4⋊C4C24×C314yes—
813C4⋊C4C24×C3116yes—
814C4⋊C4C24×C318yes—
815C4⋊C4C24×C314yes—
816C4⋊C4C24×C318yes—
817C4⋊C4C24×C3116yes—
818C4⋊C4C24×C314yes—
819C4⋊C4C24×C314yes—
820C4⋊C4C24×C312yes—
821C4⋊C4C24×C312yes—
822C4⋊C4C24×C318yes—
823C4⋊C4C24×C314yes—
824C4⋊C4C24×C318yes—
825C4⋊C4C24×C314yes—
826C4⋊C4C24×C314yes—
827C4⋊C4C24×C314yes—
828C4⋊C4C24×C3116yes—
829C4⋊C4C24×C3116yes—
830C4⋊C4C24×C3116yes—
831C4⋊C4C24×C318yes—
832C4⋊C4C24×C318yes—
833C4⋊C4C24×C318yes—
834C22⋊C4C24×C318yes—
835C22⋊C4C24×C318yes—
836C22⋊C4C24×C318yes—
837C22⋊C4C24×C3116yes—
838C22⋊C4C24×C318yes—
839C22⋊C4C24×C3116yes—
840C22⋊C4C24×C314yes—
841C22⋊C4C24×C318yes—
842C22⋊C4C24×C318yes—
843C22⋊C4C24×C318yes—
844C22⋊C4C24×C3116yes—
845C22⋊C4C24×C314yes—
846C22⋊C4C24×C314yes—
847C22⋊C4C24×C318yes—
848C22⋊C4C24×C318yes—
849C22⋊C4C24×C3116yes—
850C42C24×C312yes—
851C42C24×C314yes—
852C42C24×C318yes—
853C42C24×C318yes—
854C42C24×C314yes—
855C42C24×C312yes—
856C42C24×C318yes—
857C42C24×C314yes—
858C42C24×C318yes—
859C42C24×C314yes—
860C42C24×C318yes—
861C42C24×C314yes—
862C42C24×C3116yes—
863C42C24×C3116yes—
864C22×C3—21no—
865C22×C3—21no—
866C22×C3—24no—
867C22×C3—24no—
868C22×C3—24no—
869C22×C3—24no—
870C22×C3—24no—
871C22×C3—24no—
872C22×C3—84no—
873C22×C3C2×2−1+412yes—
874C22×C3C2611yescharacteristic
875C3×C4—24no—
876C3×C4—28no—
877C3×C4—21no—
878C3×C4—24no—
879C3×C4—24no—
880C3×C4—24no—
881C3×C4—28no—
882C3×C4—22no—
883C3×C4—28no—
884C3×C4—22no—
885C3×C4—24no—
886C3×C4—22no—
887C3×C4C2×2−1+414yes—
888C3×C4#58512yes—
889C23—24no—
890C23—42no—
891C23—42no—
892C23C25×C314yes—
893C23C25×C314yes—
894C23C25×C311yescharacteristic
895Q8—216no—
896Q8—24no—
897Q8—24no—
898Q8—28no—
899Q8—42no—
900Q8—48no—
901Q8—48no—
902Q8—44no—
903Q8—44no—
904Q8—48no—
905D4—28no—
906D4—28no—
907D4—24no—
908D4—44no—
909D4—48no—
910D4—48no—
911C2×C4—28no—
912C2×C4—28no—
913C2×C4—22no—
914C2×C4—28no—
915C2×C4—28no—
916C2×C4—44no—
917C2×C4—42no—
918C2×C4—42no—
919C2×C4—48no—
920C2×C4—48no—
921C2×C4—48no—
922C2×C4—42no—
923C2×C4—41no—
924C2×C4—48no—
925C2×C4—44no—
926C2×C4C3×2−1+414yes—
927C2×C4C25×C312yes—
928C2×C4C25×C318yes—
929C2×C4C25×C312yes—
930C2×C4C25×C314yes—
931C2×C4C25×C314yes—
932C2×C4C25×C314yes—
933C2×C4C25×C312yes—
934C2×C4C25×C318yes—
935C2×C4C25×C314yes—
936C2×C4C25×C318yes—
937C2×C4C25×C314yes—
938C2×C4C25×C311yescharacteristic
939C2×C4C25×C312yes—
940C2×C4C25×C311yescharacteristic
941C2×C3—22no—
942C2×C3—44no—
943C2×C3—44no—
944C2×C3C22×2−1+411yescharacteristic
945C2×C3C2×#58511yescharacteristic
946C2×C32−1+611yescharacteristic
947C22—21no—
948C22—21no—
949C22—24no—
950C22—24no—
951C22—24no—
952C22—24no—
953C22—24no—
954C22—24no—
955C22—84no—
956C22C2×C3×2−1+412yes—
957C22C26×C311yescharacteristic
958C4—24no—
959C4—28no—
960C4—21no—
961C4—24no—
962C4—24no—
963C4—24no—
964C4—28no—
965C4—22no—
966C4—28no—
967C4—22no—
968C4—24no—
969C4—22no—
970C4C2×C3×2−1+414yes—
971C4C3×#58512yes—
972C3#6293211yescharacteristic, direct product factor, Sylow
973C2—22no—
974C2—44no—
975C2—44no—
976C2C22×C3×2−1+411yescharacteristic
977C2C2×C3×#58511yescharacteristic
978C2C3×2−1+611yescharacteristic
subgroupG/H
center, socleC22×C3C26
commutator, Frattini, cosocleC22C26×C3
prime radicalC3×#3460C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#3564C2semidirect
2. C3×#3557C2semidirect
3. C3×#3555C2semidirect
4. C3×#3555C2semidirect
5. C3×#3550C2semidirect
6. C3×#3538C2semidirect
7. C3×#3523C2semidirect
8. C3×#3510C2semidirect
9. C3×#3509C2semidirect
10. C3×#3507C2semidirect
11. C3×#3502C2semidirect
12. C3×#3501C2semidirect
13. C3×#3495C2semidirect
14. C3×Q8×#41C2semidirect
15. C2×C3×#556C2semidirect
16. C3×#3461C2semidirect
18. #62932C3direct (N × H)
19. C3×#563C22semidirect
20. C3×#563C22semidirect
21. C3×#563C22semidirect
24. C3×Q82C22semidirect
25. C3×Q82C22semidirect
26. C3×#557C22semidirect
27. C3×#557C22semidirect
28. C3×#557C22semidirect
29. C3×#557C22semidirect
30. C3×#557C22semidirect
31. C3×#557C22semidirect
32. C3×#557C22semidirect
38. C3×#556C22semidirect
39. C3×#556C22semidirect
40. C3×#556C22semidirect
41. C3×#556C22semidirect
46. C3×#554C22semidirect
47. C3×#554C22semidirect
50. C3×#552C22semidirect
51. C3×#552C22semidirect
52. C3×#552C22semidirect
53. C3×#552C22semidirect
58. C3×D4×Q8C22semidirect
59. C3×D4×Q8C22semidirect
63. C3×#544C22semidirect
64. C3×#544C22semidirect
69. C3×#542C22semidirect
70. C3×#542C22semidirect
71. C3×#542C22semidirect
72. C3×#541C22semidirect
73. C3×#541C22semidirect
74. C3×#541C22semidirect
75. C3×#541C22semidirect
76. C3×#541C22semidirect
77. C3×#541C22semidirect
80. C3×#539C22semidirect
81. C3×#539C22semidirect
85. C3×#536C22semidirect
86. C3×#536C22semidirect
91. C3×#533C22semidirect
92. C3×#533C22semidirect
93. C3×#533C22semidirect
94. C3×#533C22semidirect
95. C3×#533C22semidirect
102. C3×#529C22semidirect
108. C3×#520C22semidirect
110. C3×#519C22semidirect
116. C2×C3×C4×Q8C22semidirect
119. #3564C2×C3semidirect
120. #3557C2×C3semidirect
121. #3555C2×C3semidirect
122. #3555C2×C3semidirect
123. #3550C2×C3semidirect
124. #3538C2×C3semidirect
125. #3523C2×C3semidirect
126. #3510C2×C3semidirect
127. #3509C2×C3semidirect
128. #3507C2×C3semidirect
129. #3502C2×C3semidirect
130. #3501C2×C3semidirect
131. #3495C2×C3semidirect
132. Q8×#41C2×C3semidirect
133. C2×#556C2×C3semidirect
134. #3461C2×C3semidirect
316. #563C22×C3semidirect
317. #563C22×C3semidirect
318. #563C22×C3semidirect
321. Q82C22×C3semidirect
322. Q82C22×C3semidirect
323. #557C22×C3semidirect
324. #557C22×C3semidirect
325. #557C22×C3semidirect
326. #557C22×C3semidirect
327. #557C22×C3semidirect
328. #557C22×C3semidirect
329. #557C22×C3semidirect
335. #556C22×C3semidirect
336. #556C22×C3semidirect
337. #556C22×C3semidirect
338. #556C22×C3semidirect
343. #554C22×C3semidirect
344. #554C22×C3semidirect
347. #552C22×C3semidirect
348. #552C22×C3semidirect
349. #552C22×C3semidirect
350. #552C22×C3semidirect
355. D4×Q8C22×C3semidirect
356. D4×Q8C22×C3semidirect
360. #544C22×C3semidirect
361. #544C22×C3semidirect
366. #542C22×C3semidirect
367. #542C22×C3semidirect
368. #542C22×C3semidirect
369. #541C22×C3semidirect
370. #541C22×C3semidirect
371. #541C22×C3semidirect
372. #541C22×C3semidirect
373. #541C22×C3semidirect
374. #541C22×C3semidirect
377. #539C22×C3semidirect
378. #539C22×C3semidirect
382. #536C22×C3semidirect
383. #536C22×C3semidirect
388. #533C22×C3semidirect
389. #533C22×C3semidirect
390. #533C22×C3semidirect
391. #533C22×C3semidirect
392. #533C22×C3semidirect
399. #529C22×C3semidirect
405. #520C22×C3semidirect
407. #519C22×C3semidirect
413. C2×C4×Q8C22×C3semidirect
972. C3#62932direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#35642
C3×#35572
C3×#35552
C3×#35502
C3×#35382
C3×#35232
C3×#35102
C3×#35092
C3×#35072
C3×#35022
C3×#35012
C3×#34952
C3×Q8×#412
C2×C3×#5562
C3×#34612
C3×#34602
#629323