Finite Group Databasebeta

← #11807558

Subgroups — #11807558

Order 1152.

1247 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63897C211yesmaximal, characteristic
2#10592364C211yesmaximal, characteristic
3C3×#4655C211yesmaximal, characteristic, complemented
4C3×#4649C211yesmaximal, characteristic, complemented
5#10591320C211yesmaximal, characteristic
6C4×#3722C211yesmaximal, characteristic, complemented
7#10591262C211yesmaximal, characteristic, complemented
8#10591260C211yesmaximal, characteristic, complemented
9#10591258C211yesmaximal, characteristic, complemented
10#10591258C211yesmaximal, characteristic, complemented
11Dic3×Dic3⋊C4C211yesmaximal, characteristic, complemented
12#10591233C211yesmaximal, characteristic, complemented
13#10591233C211yesmaximal, characteristic, complemented
14#10591194C211yesmaximal, characteristic, complemented
15#10591194C211yesmaximal, characteristic, complemented
16#74975—31nomaximal
17#73667—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×#624C2211yescharacteristic
21C2×#3752C2211yescharacteristic
22C2×#3752C2211yescharacteristic
23C2×#3752C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×Dic3⋊C4C2211yescharacteristic
26C2×C3×Dic3⋊C4C2211yescharacteristic
27C2×C3×Dic3⋊C4C2211yescharacteristic
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×Dic3⋊Dic3C2211yescharacteristic
33C2×#3722C2211yescharacteristic
34C2×#3722C2211yescharacteristic
35C2×#3722C2211yescharacteristic
36C2×#3722C2211yescharacteristic
37C2×#3722C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×Dic32C2211yescharacteristic
41C2×Dic32C2211yescharacteristic
42C2×Dic32C2211yescharacteristic
43#63897C418yescomplemented
44C32×#95C2211yescharacteristic
45#63658C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×#894—31no—
55C2×#894—31no—
56C3×#387—31no—
57C3×C4×C4⋊C4—31no—
58#4990—31no—
59#4990—31no—
60#4988—31no—
61#4980—31no—
62#4978—31no—
63Dic3×C4⋊C4—31no—
64#4940—31no—
65#4940—31no—
66#4939—31no—
67C4×(C2×D3)⋊C4—31no—
68C4×(C2×D3)⋊C4—31no—
69C4×(C2×D3)⋊C4—31no—
70C4×(C2×D3)⋊C4—31no—
71C4×Dic3⋊C4—31no—
72#4670—31no—
73#4670—31no—
74#4669—31no—
75#4669—31no—
76#4666—31no—
77#4666—31no—
78#4666—31no—
79#4666—31no—
80#4665—31no—
81#4665—31no—
82#4665—61no—
83#4655D311yescharacteristic, complemented
84#4649D311yescharacteristic, complemented
85C23×C3⋊D3C2311yescharacteristic
86C23×C3⋊D3C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C2×C4⋊(C3⋊D3)—41no—
93C2×C4⋊(C3⋊D3)—41no—
94C2×C4⋊(C3⋊D3)C2×C414yes—
95C2×C4×C3⋊D3—22no—
96C2×C4×C3⋊D3—22no—
97C2×C4×C3⋊D3—41no—
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C2×#624—41no—
107C2×#624—41no—
108C2×#624C2×C414yescomplemented
109#3752—22no—
110#3752—22no—
111#3752—41no—
112C3×C4⋊Dic3—41no—
113C3×Dic3⋊C4—22no—
114C3×Dic3⋊C4C2×C414yescomplemented
115C3×Dic3⋊C4C2×C414yescomplemented
116C3×C4×Dic3—22no—
117C3×C4×Dic3—41no—
118C3×C4×Dic3—41no—
119C3×C4×Dic3—41no—
120Dic3⋊Dic3—22no—
121#3722—22no—
122#3722—22no—
123#3722—22no—
124#3722—22no—
125#3722C2×C414yes—
126#3722C2×C414yes—
127#3722C2×C414yescomplemented
128Dic32—22no—
129Dic32—41no—
130Dic32—41no—
131#2374—91noSylow
132C22×D12—31no—
133C22×D12—31no—
134C22×D12—61no—
135C22×C4×D3—31no—
136C22×C4×D3—31no—
137C22×C4×D3—31no—
138C22×C4×D3—31no—
139C22×C4×D3—61no—
140C2×C3×C4⋊C4—31no—
141C2×C3×C4⋊C4—31no—
142C2×C3×C4⋊C4—31no—
143C2×C3×C4⋊C4—31no—
144C2×C3×C42—31no—
145C2×C3×C42—31no—
146C2×C3×C42—31no—
147C2×C3×C42—31no—
148C2×(C2×D3)⋊C4—31no—
149C2×(C2×D3)⋊C4—31no—
150C2×(C2×D3)⋊C4—31no—
151C2×(C2×D3)⋊C4—31no—
152C2×(C2×D3)⋊C4—31no—
153C2×(C2×D3)⋊C4—31no—
154C2×(C2×D3)⋊C4—31no—
155C2×(C2×D3)⋊C4—31no—
156C2×(C2×D3)⋊C4—31no—
157C2×(C2×D3)⋊C4—31no—
158C2×(C2×D3)⋊C4—31no—
159C2×(C2×D3)⋊C4—31no—
160C2×(C2×D3)⋊C4—31no—
161C2×(C2×D3)⋊C4—31no—
162C2×(C2×D3)⋊C4—31no—
163C2×(C2×D3)⋊C4—31no—
164C2×(C2×D3)⋊C4—31no—
165C2×(C2×D3)⋊C4—31no—
166C2×(C2×D3)⋊C4—31no—
167C2×(C2×D3)⋊C4—31no—
168C2×(C2×D3)⋊C4—61no—
169C2×(C2×D3)⋊C4—61no—
170C2×(C2×D3)⋊C4—61no—
171C2×C4⋊Dic3—31no—
172C2×C4⋊Dic3C2×D311yescharacteristic
173C2×Dic3⋊C4—31no—
174C2×Dic3⋊C4C2×D311yescharacteristic
175C2×Dic3⋊C4C2×D311yescharacteristic
176C2×Dic3⋊C4C2×D311yescharacteristic
177C2×C4×Dic3—31no—
178C2×C4×Dic3—31no—
179C2×C4×Dic3—31no—
180C2×C4×Dic3—31no—
181C2×C4×Dic3—31no—
182C2×C4×Dic3—31no—
183C2×C4×Dic3C2×D311yescharacteristic
184C2×C4×Dic3C2×D311yescharacteristic
185C2×C4×Dic3C2×D311yescharacteristic
186C2×C4×Dic3C2×D311yescharacteristic
187#894—38no—
188#894—38no—
189C3×#95—21no—
190C3×#95—31no—
191C3×#95—31no—
192C3×#95—31no—
193C3×#95—31no—
194C3×#95C2×D311yescharacteristic
195C3×#95C2×D311yescharacteristic
196C3⋊#95—31no—
197C3⋊#95—31no—
198C3⋊#95—31no—
199C3⋊#95—31no—
200C3⋊#95—31no—
201C3⋊#95—31no—
202C3⋊#95—31no—
203C3⋊#95—31no—
204C3⋊#95—31no—
205C3⋊#95—31no—
206C3⋊#95—61no—
207C3⋊#95C2×D311yescharacteristic
208C3⋊#95C2×D311yescharacteristic
209C3⋊#95C2×D311yescharacteristic
210C3⋊#95C2×D311yescharacteristic
211C23×C32C2411yescharacteristic
212C22×C3⋊D3—21no—
213C22×C3⋊D3—21no—
214C22×C3⋊D3—21no—
215C22×C3⋊D3—21no—
216C22×C3⋊D3—21no—
217C22×C3⋊D3—21no—
218C22×C3⋊D3—21no—
219C22×C3⋊D3—21no—
220C22×C3⋊D3—21no—
221C22×C3⋊D3—21no—
222C22×C3⋊D3—21no—
223C22×C3⋊D3—21no—
224C22×C3⋊D3C22×C412yes—
225C22×C3⋊D3C22×C412yes—
226C2×C32×C4—21no—
227C2×C32×C4—21no—
228C2×C32×C4—21no—
229C2×C32×C4—21no—
230C2×C32×C4—21no—
231C2×C32×C4—21no—
232C2×C32×C4—21no—
233C2×C32×C4C22×C412yes—
234C2×C32×C4#4112yes—
235C2×C3⋊Dic3—21no—
236C2×C3⋊Dic3—21no—
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3#4112yes—
241C4⋊(C3⋊D3)—44no—
242C4×C3⋊D3—44no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3C22×C412yes—
262C2×C3×Dic3C22×C412yes—
263C2×C3×Dic3C22×C412yes—
264C2×C3×Dic3C22×C412yes—
265C2×C3×Dic3#4112yes—
266C2×C3×Dic3#4112yes—
267#624—44no—
268C2×#123—91no—
269#390—91no—
270#388—91no—
271#388—91no—
272#388—91no—
273#388—91no—
274#387—31no—
275#387—91no—
276#386—91no—
277C4×C4⋊C4—31no—
278C4×C4⋊C4—91no—
279C4×C22⋊C4—91no—
280C4×C22⋊C4—91no—
281C4×C22⋊C4—91no—
282C4×C22⋊C4—91no—
283C23×D3—31no—
284C23×D3—31no—
285C23×D3—31no—
286C23×D3—31no—
287C23×D3—61no—
288C23×D3—61no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—31no—
293C22×C3×C4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4C22×D311yescharacteristic
301C22×C3×C4C22×D311yescharacteristic
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C22×Dic3—31no—
307C22×Dic3—31no—
308C22×Dic3—31no—
309C22×Dic3—31no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3C22×D311yescharacteristic
313C22×Dic3C22×D311yescharacteristic
314C22×Dic3C22×D311yescharacteristic
315C22×Dic3C22×D311yescharacteristic
316C22×Dic3C22×D311yescharacteristic
317C22×Dic3C22×D311yescharacteristic
318C22×Dic3C22×D311yescharacteristic
319C22×Dic3C22×D311yescharacteristic
320C2×D12—34no—
321C2×D12—34no—
322C2×D12—64no—
323C2×D12—121no—
324C2×D12—121no—
325C2×D12—121no—
326C2×D12—121no—
327C2×D12—122no—
328C2×D12—122no—
329C2×C4×D3—34no—
330C2×C4×D3—34no—
331C2×C4×D3—62no—
332C2×C4×D3—62no—
333C2×C4×D3—62no—
334C2×C4×D3—62no—
335C2×C4×D3—122no—
336C2×C4×D3—122no—
337C2×C4×D3—121no—
338C2×C4×D3—121no—
339C2×C4×D3—121no—
340C2×C4×D3—121no—
341C2×C4×D3—121no—
342C2×C4×D3—121no—
343C2×C4×D3—122no—
344C3×C4⋊C4—34no—
345C3×C4⋊C4—34no—
346C3×C4⋊C4—62no—
347C3×C4⋊C4—121no—
348C3×C42—62no—
349C3×C42—121no—
350C3×C42—121no—
351C3×C42—121no—
352(C2×D3)⋊C4—34no—
353(C2×D3)⋊C4—34no—
354(C2×D3)⋊C4—34no—
355(C2×D3)⋊C4—34no—
356(C2×D3)⋊C4—34no—
357(C2×D3)⋊C4—34no—
358(C2×D3)⋊C4—62no—
359(C2×D3)⋊C4—62no—
360(C2×D3)⋊C4—62no—
361(C2×D3)⋊C4—62no—
362(C2×D3)⋊C4—62no—
363(C2×D3)⋊C4—62no—
364(C2×D3)⋊C4—62no—
365(C2×D3)⋊C4—62no—
366(C2×D3)⋊C4—62no—
367(C2×D3)⋊C4—62no—
368(C2×D3)⋊C4—62no—
369(C2×D3)⋊C4—62no—
370(C2×D3)⋊C4—122no—
371(C2×D3)⋊C4—122no—
372(C2×D3)⋊C4—121no—
373(C2×D3)⋊C4—121no—
374(C2×D3)⋊C4—122no—
375C4⋊Dic3—41no—
376C4⋊Dic3—62no—
377Dic3⋊C4—22no—
378Dic3⋊C4—62no—
379Dic3⋊C4C4×D314yescomplemented
380Dic3⋊C4C4×D314yescomplemented
381C4×Dic3—22no—
382C4×Dic3—41no—
383C4×Dic3—41no—
384C4×Dic3—41no—
385C4×Dic3—62no—
386C4×Dic3—62no—
387C4×Dic3—121no—
388C4×Dic3—121no—
389C4×Dic3—121no—
390C4×Dic3—121no—
391C22×C32C23×C411yescharacteristic
392C22×C32C2×#4111yescharacteristic
393C22×C32C2×#4111yescharacteristic
394C22×C32C2×#4111yescharacteristic
395C22×C32C2×#4111yescharacteristic
396C22×C32H(5,𝔽2)11yescharacteristic
397C22×C32H(5,𝔽2)11yescharacteristic
398C2×C3⋊D3—22no—
399C2×C3⋊D3—22no—
400C2×C3⋊D3—22no—
401C2×C3⋊D3—22no—
402C2×C3⋊D3—22no—
403C2×C3⋊D3—22no—
404C2×C3⋊D3—41no—
405C2×C3⋊D3—41no—
406C2×C3⋊D3—41no—
407C2×C3⋊D3—41no—
408C2×C3⋊D3—41no—
409C2×C3⋊D3—41no—
410C2×C3⋊D3—41no—
411C2×C3⋊D3—41no—
412C32×C4—22no—
413C32×C4—22no—
414C32×C4—41no—
415C3⋊Dic3—22no—
416C3⋊Dic3—41no—
417C3×Dic3—22no—
418C3×Dic3—22no—
419C3×Dic3—22no—
420C3×Dic3—22no—
421C3×Dic3—22no—
422C3×Dic3—22no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C22×D4—91no—
426C23×C4—91no—
427C23×C4—91no—
428#123—98no—
429C2×C4⋊C4—31no—
430C2×C4⋊C4—31no—
431C2×C4⋊C4—31no—
432C2×C4⋊C4—31no—
433C2×C4⋊C4—91no—
434C2×C22⋊C4—91no—
435C2×C22⋊C4—91no—
436C2×C22⋊C4—91no—
437C2×C22⋊C4—91no—
438C2×C22⋊C4—91no—
439C2×C22⋊C4—91no—
440C2×C22⋊C4—91no—
441C2×C22⋊C4—91no—
442C2×C22⋊C4—91no—
443C2×C22⋊C4—91no—
444C2×C42—31no—
445C2×C42—31no—
446C2×C42—31no—
447C2×C42—31no—
448C2×C42—91no—
449C2×C42—91no—
450C2×C42—91no—
451#95—31no—
452#95—31no—
453#95—31no—
454#95—31no—
455#95—91no—
456#95—91no—
457#95—91no—
458#95—91no—
459#95—91no—
460#95D3211yescharacteristic
461C23×C3—21no—
462C23×C3C23×D311yescharacteristic
463C23×C3C23×D311yescharacteristic
464C22×D3—32no—
465C22×D3—32no—
466C22×D3—32no—
467C22×D3—32no—
468C22×D3—62no—
469C22×D3—62no—
470C22×D3—62no—
471C22×D3—62no—
472C22×D3—61no—
473C22×D3—61no—
474C22×D3—61no—
475C22×D3—61no—
476C22×D3—61no—
477C22×D3—61no—
478C22×D3—61no—
479C22×D3—61no—
480C22×D3—61no—
481C22×D3—61no—
482C22×D3—61no—
483C22×D3—61no—
484C22×D3—61no—
485C22×D3—61no—
486C22×D3—61no—
487C22×D3—61no—
488C22×D3—61no—
489C22×D3—61no—
490C22×D3—61no—
491C22×D3—61no—
492C22×D3—61no—
493C22×D3—61no—
494C22×D3—61no—
495C22×D3—61no—
496C22×D3—121no—
497C22×D3—121no—
498C22×D3—121no—
499C22×D3—121no—
500C22×D3—121no—
501C22×D3—121no—
502C22×D3—121no—
503C22×D3—121no—
504C22×D3—121no—
505C22×D3—121no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—22no—
521C2×C3×C4—22no—
522C2×C3×C4—32no—
523C2×C3×C4—32no—
524C2×C3×C4—32no—
525C2×C3×C4—32no—
526C2×C3×C4—32no—
527C2×C3×C4—32no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4C2×C4×D312yes—
554C2×C3×C4C2×C4×D312yes—
555C2×C3×C4#23512yes—
556C2×C3×C4#23912yes—
557C2×Dic3—21no—
558C2×Dic3—21no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—21no—
568C2×Dic3—21no—
569C2×Dic3—21no—
570C2×Dic3—21no—
571C2×Dic3—21no—
572C2×Dic3—21no—
573C2×Dic3—21no—
574C2×Dic3—21no—
575C2×Dic3—32no—
576C2×Dic3—32no—
577C2×Dic3—62no—
578C2×Dic3—61no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—61no—
588C2×Dic3—121no—
589C2×Dic3—121no—
590C2×Dic3—121no—
591C2×Dic3—121no—
592C2×Dic3—121no—
593C2×Dic3C2×C4×D312yes—
594C2×Dic3C2×C4×D312yes—
595C2×Dic3C2×C4×D312yes—
596C2×Dic3C2×C4×D312yes—
597C2×Dic3#23512yes—
598C2×Dic3#23912yes—
599D12—124no—
600D12—124no—
601D12—128no—
602C4×D3—124no—
603C4×D3—124no—
604C4×D3—124no—
605C4×D3—124no—
606C4×D3—128no—
607C2×C32C4×#4111yescharacteristic
608C2×C32C4×#4111yescharacteristic
609C2×C32#51811yescharacteristic
610C2×C32#55111yescharacteristic
611C2×C32#55311yescharacteristic
612C2×C32#55311yescharacteristic
613C2×C32#55911yescharacteristic
614C3⋊D3—42no—
615C3⋊D3—42no—
616C24—91no—
617C24—91no—
618C2×D4—94no—
619C2×D4—361no—
620C2×D4—361no—
621C22×C4—31no—
622C22×C4—31no—
623C22×C4—31no—
624C22×C4—31no—
625C22×C4—31no—
626C22×C4—31no—
627C22×C4—31no—
628C22×C4—31no—
629C22×C4—94no—
630C22×C4—91no—
631C22×C4—91no—
632C22×C4—182no—
633C22×C4—182no—
634C22×C4—361no—
635C22×C4—361no—
636C22×C4—361no—
637C22×C4C2×D3211yescharacteristic
638C22×C4C2×D3211yescharacteristic
639C22×C4C2×D3211yescharacteristic
640C4⋊C4—34no—
641C4⋊C4—34no—
642C4⋊C4—62no—
643C4⋊C4—121no—
644C4⋊C4—182no—
645C22⋊C4—94no—
646C22⋊C4—94no—
647C22⋊C4—94no—
648C22⋊C4—182no—
649C22⋊C4—182no—
650C22⋊C4—182no—
651C22⋊C4—182no—
652C22⋊C4—182no—
653C22⋊C4—182no—
654C22⋊C4—361no—
655C42—62no—
656C42—121no—
657C42—121no—
658C42—121no—
659C42—182no—
660C42—361no—
661C42—361no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3C22×C4×D311yescharacteristic
670C22×C3C22×C4×D311yescharacteristic
671C22×C3C2×#23511yescharacteristic
672C22×C3C2×#23511yescharacteristic
673C22×C3#100411yescharacteristic
674C22×C3#100411yescharacteristic
675C22×C3C2×#23911yescharacteristic
676C22×C3C2×#23911yescharacteristic
677C22×C3D3×#4111yescharacteristic
678C22×C3D3×#4111yescharacteristic
679C22×C3D3×#4111yescharacteristic
680C22×C3D3×#4111yescharacteristic
681C22×C3#100911yescharacteristic
682C22×C3#100911yescharacteristic
683C2×D3—64no—
684C2×D3—62no—
685C2×D3—62no—
686C2×D3—62no—
687C2×D3—62no—
688C2×D3—62no—
689C2×D3—62no—
690C2×D3—62no—
691C2×D3—62no—
692C2×D3—62no—
693C2×D3—62no—
694C2×D3—62no—
695C2×D3—62no—
696C2×D3—122no—
697C2×D3—122no—
698C2×D3—122no—
699C2×D3—122no—
700C2×D3—122no—
701C2×D3—122no—
702C2×D3—122no—
703C2×D3—122no—
704C2×D3—122no—
705C2×D3—121no—
706C2×D3—121no—
707C2×D3—121no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—121no—
711C2×D3—121no—
712C2×D3—121no—
713C2×D3—121no—
714C2×D3—121no—
715C2×D3—121no—
716C2×D3—121no—
717C2×D3—121no—
718C2×D3—121no—
719C2×D3—121no—
720C2×D3—121no—
721C2×D3—241no—
722C2×D3—241no—
723C2×D3—241no—
724C2×D3—241no—
725C3×C4—22no—
726C3×C4—22no—
727C3×C4—22no—
728C3×C4—22no—
729C3×C4—42no—
730C3×C4—42no—
731C3×C4—41no—
732C3×C4—41no—
733C3×C4—62no—
734C3×C4—62no—
735C3×C4—62no—
736C3×C4—62no—
737C3×C4—62no—
738C3×C4—62no—
739C3×C4—81no—
740C3×C4—121no—
741C3×C4—121no—
742Dic3—22no—
743Dic3—22no—
744Dic3—22no—
745Dic3—22no—
746Dic3—22no—
747Dic3—22no—
748Dic3—41no—
749Dic3—41no—
750Dic3—62no—
751Dic3—62no—
752Dic3—122no—
753Dic3—121no—
754Dic3—121no—
755Dic3—241no—
756C32#237411yescharacteristic, complemented, Sylow
757C23—92no—
758C23—92no—
759C23—181no—
760C23—181no—
761C23—181no—
762C23—181no—
763C23—181no—
764C23—181no—
765C23—181no—
766C23—181no—
767C23—181no—
768C23—181no—
769C23—181no—
770C23—181no—
771C23C22×D3211yescharacteristic
772D4—364no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—32no—
781C2×C4—32no—
782C2×C4—32no—
783C2×C4—32no—
784C2×C4—32no—
785C2×C4—32no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—61no—
790C2×C4—61no—
791C2×C4—61no—
792C2×C4—61no—
793C2×C4—61no—
794C2×C4—61no—
795C2×C4—61no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—92no—
805C2×C4—181no—
806C2×C4—181no—
807C2×C4—181no—
808C2×C4—181no—
809C2×C4—181no—
810C2×C4—364no—
811C2×C4—364no—
812C2×C4#379912yes—
813C2×C4C4×D3212yes—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—21no—
819C2×C3—21no—
820C2×C3—21no—
821C2×C3C4×#23511yescharacteristic
822C2×C3#551411yescharacteristic
823C2×C3#552211yescharacteristic
824C2×C3#552711yescharacteristic
825C2×C3#554011yescharacteristic
826C2×C3#554511yescharacteristic
827C2×C3#554511yescharacteristic
828C2×C3C4×#23911yescharacteristic
829C2×C3C4×#23911yescharacteristic
830C2×C3#558511yescharacteristic
831C2×C3#563711yescharacteristic
832C2×C3#566411yescharacteristic
833C2×C3#569511yescharacteristic
834C2×C3#570911yescharacteristic
835D3—124no—
836D3—122no—
837D3—122no—
838D3—122no—
839D3—122no—
840D3—242no—
841C22—182no—
842C22—182no—
843C22—182no—
844C22—182no—
845C22—182no—
846C22—182no—
847C22—361no—
848C22—361no—
849C22—361no—
850C22—361no—
851C22—361no—
852C22—361no—
853C22—361no—
854C22—361no—
855C22C2×#379911yescharacteristic
856C22C2×C4×D3211yescharacteristic
857C22D3×#23511yescharacteristic
858C22#6431211yescharacteristic
859C22#6431411yescharacteristic
860C22#6431411yescharacteristic
861C22D3×#23911yescharacteristic
862C4—22no—
863C4—22no—
864C4—41no—
865C4—62no—
866C4—62no—
867C4—62no—
868C4—62no—
869C4—62no—
870C4—62no—
871C4—121no—
872C4—121no—
873C4—182no—
874C4—361no—
875C3—21no—
876C3#7366711yescharacteristic, complemented
877C3#7497511yescharacteristic, complemented
878C2—362no—
879C2—362no—
880C2C4×#379911yescharacteristic
881C2#1059409711yescharacteristic
882C2#1059416611yescharacteristic
883C2#1059425611yescharacteristic
884C2#1059436211yescharacteristic
885C2#1059454911yescharacteristic
886C2#1059456211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenter#95D32
hypocenterC32#2374
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
3. C3×#4655C2semidirect
4. C3×#4649C2semidirect
6. C4×#3722C2semidirect
7. #10591262C2semidirect
8. #10591260C2semidirect
9. #10591258C2semidirect
10. #10591258C2semidirect
11. Dic3×Dic3⋊C4C2semidirect
12. #10591233C2semidirect
13. #10591233C2semidirect
14. #10591194C2semidirect
15. #10591194C2semidirect
43. #63897C4semidirect
83. #4655D3semidirect
84. #4649D3semidirect
108. C2×#624C2×C4semidirect
114. C3×Dic3⋊C4C2×C4semidirect
115. C3×Dic3⋊C4C2×C4semidirect
127. #3722C2×C4semidirect
379. Dic3⋊C4C4×D3semidirect
380. Dic3⋊C4C4×D3semidirect
756. C32#2374semidirect
876. C3#73667semidirect
877. C3#74975semidirect

Maximal subgroups

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

subgroupindex
C2×#638972
#105923642
C3×#46552
C3×#46492
#105913202
C4×#37222
#105912622
#105912602
#105912582
Dic3×Dic3⋊C42
#105912332
#105911942
#749753
#736673