Finite Group Databasebeta

← #11805794

Subgroups — #11805794

Order 1152.

1319 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63894C211yesmaximal, characteristic
2#10592364C211yesmaximal, characteristic
3C3×#4654C211yesmaximal, characteristic, complemented
4C3×#4648C211yesmaximal, characteristic, complemented
5#10591380C211yesmaximal, characteristic
6#10591371C211yesmaximal, characteristic, complemented
7#10591370C211yesmaximal, characteristic, complemented
8#10591367C211yesmaximal, characteristic, complemented
9#10591289C211yesmaximal, characteristic, complemented
10C4×#3722C211yesmaximal, characteristic, complemented
11#10591270C211yesmaximal, characteristic, complemented
12#10591233C211yesmaximal, characteristic, complemented
13#10591233C211yesmaximal, characteristic, complemented
14#10591223C211yesmaximal, characteristic, complemented
15#10591194C211yesmaximal, characteristic, complemented
16#75306—31nomaximal
17#73417—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×#624C2211yescharacteristic
21C22×#624C2211yescharacteristic
22C22×#624C2211yescharacteristic
23C2×#3752C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
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×Dic32C2211yescharacteristic
39#63894C418yescomplemented
40C32×#95C2211yescharacteristic
41#63658C2211yescharacteristic
42C3×C3⋊#95C2211yescharacteristic
43C3×C3⋊#95C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×#893—31no—
55C2×C4×D12—31no—
56C3×#387—31no—
57C3×#376—31no—
58#4990—31no—
59#4987—31no—
60#4980—31no—
61#4940—31no—
62#4940—31no—
63C4×(C2×D3)⋊C4—31no—
64C4×(C2×D3)⋊C4—31no—
65C4×(C2×D3)⋊C4—31no—
66C4×(C2×D3)⋊C4—31no—
67#4937—31no—
68#4670—31no—
69#4667—31no—
70#4666—31no—
71#4666—31no—
72#4665—31no—
73#4665—31no—
74#4665—31no—
75#4665—31no—
76#4665—61no—
77#4664—31no—
78#4664—31no—
79D3×#95—31no—
80D3×#95—31no—
81#4654—31no—
82#4654D311yescharacteristic, complemented
83#4651—31no—
84#4648D311yescharacteristic, 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)—22no—
93C2×C4⋊(C3⋊D3)—22no—
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—22no—
107C2×#624—22no—
108C2×#624—41no—
109C2×#624—41no—
110C2×#624—41no—
111C2×#624—41no—
112C2×#624—41no—
113C2×#624C2×C414yes—
114C2×#624C2×C414yescomplemented
115#3752—22no—
116#3752—22no—
117#3752—41no—
118C3×C4⋊Dic3C2×C414yescomplemented
119C3×Dic3⋊C4—41no—
120C3×C4×Dic3—22no—
121C3×C4×Dic3—22no—
122C3×C4×Dic3—41no—
123C3×C4×Dic3C2×C414yescomplemented
124Dic3⋊Dic3—41no—
125#3722—22no—
126#3722—22no—
127#3722—41no—
128#3722C2×C414yes—
129#3722C2×C414yescomplemented
130Dic32—41no—
131#2353—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—31no—
140C22×C4×D3—31no—
141C22×C4×D3—31no—
142C22×C4×D3—31no—
143C22×C4×D3—61no—
144C2×C3×C4⋊C4—31no—
145C2×C3×C4⋊C4—31no—
146C2×C3×C42—31no—
147C2×C3×C42—31no—
148C2×C3×C42—31no—
149C2×C3×C42—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—61no—
167C2×(C2×D3)⋊C4—61no—
168C2×(C2×D3)⋊C4—61no—
169C2×C4⋊Dic3—31no—
170C2×C4⋊Dic3C2×D311yescharacteristic
171C2×Dic3⋊C4—31no—
172C2×Dic3⋊C4C2×D311yescharacteristic
173C2×C4×Dic3—31no—
174C2×C4×Dic3—31no—
175C2×C4×Dic3C2×D311yescharacteristic
176C2×C4×Dic3C2×D311yescharacteristic
177C2×C4×Dic3C2×D311yescharacteristic
178C2×C4×Dic3C2×D311yescharacteristic
179#893—38no—
180C4×D12—38no—
181C3×#95—21no—
182C3×#95—31no—
183C3×#95—31no—
184C3×#95—31no—
185C3×#95—31no—
186C3×#95—31no—
187C3×#95—31no—
188C3×#95C2×D311yescharacteristic
189C3×#95C2×D311yescharacteristic
190C3⋊#95—31no—
191C3⋊#95—31no—
192C3⋊#95—31no—
193C3⋊#95—31no—
194C3⋊#95—31no—
195C3⋊#95—31no—
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—61no—
205C3⋊#95C2×D311yescharacteristic
206C3⋊#95C2×D311yescharacteristic
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⋊D3C22×C412yes—
223C22×C3⋊D3C22×C412yes—
224C22×C3⋊D3#4112yes—
225C22×C3⋊D3#4112yes—
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—21no—
241C4⋊(C3⋊D3)—28no—
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×Dic3—21no—
262C2×C3×Dic3C22×C412yes—
263C2×C3×Dic3C22×C412yes—
264C2×C3×Dic3C22×C412yes—
265C2×C3×Dic3C22×C412yes—
266C2×C3×Dic3#4112yes—
267#624—44no—
268#624—44no—
269#624—44no—
270C2×C4×D4—91no—
271#388—91no—
272#388—91no—
273#387—31no—
274#387—91no—
275#386—91no—
276#386—91no—
277#383—91no—
278#381—91no—
279#380—91no—
280C4×C22⋊C4—91no—
281C4×C22⋊C4—91no—
282C4×C22⋊C4—91no—
283#376—31no—
284C2×#95—91no—
285C23×D3—31no—
286C23×D3—31no—
287C23×D3—31no—
288C23×D3—31no—
289C23×D3—61no—
290C23×D3—61no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
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×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C22×D311yescharacteristic
308C22×Dic3—31no—
309C22×Dic3—31no—
310C22×Dic3—31no—
311C22×Dic3—31no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314C22×Dic3C22×D311yescharacteristic
315C22×Dic3C22×D311yescharacteristic
316C22×Dic3C22×D311yescharacteristic
317C22×Dic3C22×D311yescharacteristic
318C22×Dic3C22×D311yescharacteristic
319C22×Dic3C22×D311yescharacteristic
320C22×Dic3C22×D311yescharacteristic
321C22×Dic3C22×D311yescharacteristic
322C2×D12—34no—
323C2×D12—34no—
324C2×D12—64no—
325C2×D12—62no—
326C2×D12—62no—
327C2×D12—62no—
328C2×D12—62no—
329C2×D12—122no—
330C2×D12—122no—
331C2×C4×D3—34no—
332C2×C4×D3—34no—
333C2×C4×D3—34no—
334C2×C4×D3—34no—
335C2×C4×D3—62no—
336C2×C4×D3—62no—
337C2×C4×D3—62no—
338C2×C4×D3—62no—
339C2×C4×D3—62no—
340C2×C4×D3—62no—
341C2×C4×D3—62no—
342C2×C4×D3—62no—
343C2×C4×D3—122no—
344C2×C4×D3—122no—
345C2×C4×D3—121no—
346C2×C4×D3—121no—
347C2×C4×D3—121no—
348C2×C4×D3—121no—
349C2×C4×D3—121no—
350C2×C4×D3—121no—
351C2×C4×D3—121no—
352C2×C4×D3—121no—
353C2×C4×D3—121no—
354C2×C4×D3—121no—
355C2×C4×D3—121no—
356C2×C4×D3—121no—
357C2×C4×D3—122no—
358C3×C4⋊C4—34no—
359C3×C4⋊C4—121no—
360C3×C42—34no—
361C3×C42—62no—
362C3×C42—62no—
363C3×C42—121no—
364(C2×D3)⋊C4—34no—
365(C2×D3)⋊C4—34no—
366(C2×D3)⋊C4—34no—
367(C2×D3)⋊C4—34no—
368(C2×D3)⋊C4—62no—
369(C2×D3)⋊C4—62no—
370(C2×D3)⋊C4—62no—
371(C2×D3)⋊C4—62no—
372(C2×D3)⋊C4—62no—
373(C2×D3)⋊C4—62no—
374(C2×D3)⋊C4—62no—
375(C2×D3)⋊C4—62no—
376(C2×D3)⋊C4—122no—
377(C2×D3)⋊C4—122no—
378(C2×D3)⋊C4—121no—
379(C2×D3)⋊C4—121no—
380(C2×D3)⋊C4—121no—
381(C2×D3)⋊C4—121no—
382(C2×D3)⋊C4—122no—
383C4⋊Dic3—121no—
384C4⋊Dic3C4×D314yescomplemented
385Dic3⋊C4—41no—
386Dic3⋊C4—121no—
387C4×Dic3—22no—
388C4×Dic3—22no—
389C4×Dic3—41no—
390C4×Dic3—121no—
391C4×Dic3—121no—
392C4×Dic3C4×D314yescomplemented
393C22×C32C23×C411yescharacteristic
394C22×C32C2×#4111yescharacteristic
395C22×C32C2×#4111yescharacteristic
396C22×C32C2×#4111yescharacteristic
397C22×C32C2×#4111yescharacteristic
398C22×C32H(5,𝔽2)11yescharacteristic
399C22×C32H(5,𝔽2)11yescharacteristic
400C2×C3⋊D3—22no—
401C2×C3⋊D3—22no—
402C2×C3⋊D3—22no—
403C2×C3⋊D3—22no—
404C2×C3⋊D3—22no—
405C2×C3⋊D3—22no—
406C2×C3⋊D3—22no—
407C2×C3⋊D3—22no—
408C2×C3⋊D3—22no—
409C2×C3⋊D3—41no—
410C2×C3⋊D3—41no—
411C2×C3⋊D3—41no—
412C2×C3⋊D3—41no—
413C2×C3⋊D3#11714yes—
414C32×C4—22no—
415C32×C4—22no—
416C32×C4—41no—
417C3⋊Dic3—41no—
418C3⋊Dic3—41no—
419C3×Dic3—22no—
420C3×Dic3—22no—
421C3×Dic3—22no—
422C3×Dic3—22no—
423C3×Dic3—22no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C22×D4—91no—
428C23×C4—91no—
429C23×C4—91no—
430C23×C4—91no—
431C23×C4—91no—
432C4×D4—98no—
433C2×C4⋊C4—31no—
434C2×C4⋊C4—31no—
435C2×C4⋊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—
449#95—31no—
450#95—31no—
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#95—91no—
461#95—91no—
462#95D3211yescharacteristic
463C23×C3—21no—
464C23×C3C23×D311yescharacteristic
465C23×C3C23×D311yescharacteristic
466C22×D3—32no—
467C22×D3—32no—
468C22×D3—32no—
469C22×D3—32no—
470C22×D3—32no—
471C22×D3—32no—
472C22×D3—32no—
473C22×D3—32no—
474C22×D3—62no—
475C22×D3—62no—
476C22×D3—62no—
477C22×D3—62no—
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—61no—
497C22×D3—61no—
498C22×D3—121no—
499C22×D3—121no—
500C22×D3—121no—
501C22×D3—121no—
502C22×D3—121no—
503C22×D3—121no—
504C22×D3—121no—
505C22×D3—121no—
506C22×D3—121no—
507C22×D3—121no—
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—21no—
521C2×C3×C4—21no—
522C2×C3×C4—22no—
523C2×C3×C4—22no—
524C2×C3×C4—32no—
525C2×C3×C4—32no—
526C2×C3×C4—32no—
527C2×C3×C4—32no—
528C2×C3×C4—32no—
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—41no—
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×C4—61no—
554C2×C3×C4—61no—
555C2×C3×C4C2×C4×D312yes—
556C2×C3×C4C2×C4×D312yes—
557C2×C3×C4#23512yes—
558C2×C3×C4#23912yes—
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—21no—
576C2×Dic3—21no—
577C2×Dic3—21no—
578C2×Dic3—62no—
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—61no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—121no—
592C2×Dic3—121no—
593C2×Dic3—121no—
594C2×Dic3—121no—
595C2×Dic3—121no—
596C2×Dic3C2×C4×D312yes—
597C2×Dic3C2×C4×D312yes—
598C2×Dic3C2×C4×D312yes—
599C2×Dic3C2×C4×D312yes—
600C2×Dic3#23512yes—
601D12—68no—
602D12—68no—
603D12—128no—
604C4×D3—124no—
605C4×D3—124no—
606C4×D3—124no—
607C4×D3—124no—
608C4×D3—124no—
609C4×D3—124no—
610C4×D3—124no—
611C4×D3—124no—
612C4×D3—128no—
613C2×C32C2×#11711yescharacteristic
614C2×C32C4×#4111yescharacteristic
615C2×C32#51811yescharacteristic
616C2×C32#55111yescharacteristic
617C2×C32#55111yescharacteristic
618C2×C32#55311yescharacteristic
619C2×C32#55311yescharacteristic
620C3⋊D3—24no—
621C3⋊D3—42no—
622C24—91no—
623C24—91no—
624C2×D4—94no—
625C2×D4—182no—
626C2×D4—182no—
627C22×C4—31no—
628C22×C4—31no—
629C22×C4—31no—
630C22×C4—31no—
631C22×C4—31no—
632C22×C4—31no—
633C22×C4—31no—
634C22×C4—31no—
635C22×C4—94no—
636C22×C4—94no—
637C22×C4—91no—
638C22×C4—91no—
639C22×C4—182no—
640C22×C4—182no—
641C22×C4—182no—
642C22×C4—182no—
643C22×C4—361no—
644C22×C4—361no—
645C22×C4—361no—
646C22×C4—361no—
647C22×C4—361no—
648C22×C4—361no—
649C22×C4C2×D3211yescharacteristic
650C22×C4C2×D3211yescharacteristic
651C22×C4C2×D3211yescharacteristic
652C4⋊C4—34no—
653C4⋊C4—121no—
654C4⋊C4—361no—
655C22⋊C4—94no—
656C22⋊C4—94no—
657C22⋊C4—182no—
658C22⋊C4—182no—
659C22⋊C4—182no—
660C22⋊C4—182no—
661C22⋊C4—361no—
662C22⋊C4—361no—
663C42—34no—
664C42—62no—
665C42—62no—
666C42—121no—
667C42—361no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3C22×C4×D311yescharacteristic
676C22×C3C22×C4×D311yescharacteristic
677C22×C3C2×#23511yescharacteristic
678C22×C3C2×#23511yescharacteristic
679C22×C3#100411yescharacteristic
680C22×C3C2×#23911yescharacteristic
681C22×C3D3×#4111yescharacteristic
682C22×C3D3×#4111yescharacteristic
683C22×C3D3×#4111yescharacteristic
684C22×C3D3×#4111yescharacteristic
685C22×C3D3×#4111yescharacteristic
686C22×C3#100911yescharacteristic
687C22×C3#100911yescharacteristic
688C22×C3#100911yescharacteristic
689C2×D3—34no—
690C2×D3—34no—
691C2×D3—64no—
692C2×D3—62no—
693C2×D3—62no—
694C2×D3—62no—
695C2×D3—62no—
696C2×D3—62no—
697C2×D3—62no—
698C2×D3—62no—
699C2×D3—62no—
700C2×D3—62no—
701C2×D3—62no—
702C2×D3—62no—
703C2×D3—62no—
704C2×D3—62no—
705C2×D3—62no—
706C2×D3—62no—
707C2×D3—62no—
708C2×D3—62no—
709C2×D3—62no—
710C2×D3—122no—
711C2×D3—122no—
712C2×D3—122no—
713C2×D3—122no—
714C2×D3—122no—
715C2×D3—122no—
716C2×D3—122no—
717C2×D3—122no—
718C2×D3—122no—
719C2×D3—121no—
720C2×D3—121no—
721C2×D3—121no—
722C2×D3—121no—
723C2×D3—121no—
724C2×D3—121no—
725C2×D3—121no—
726C2×D3—121no—
727C2×D3—241no—
728C2×D3—241no—
729C2×D3—241no—
730C2×D3—241no—
731C3×C4—22no—
732C3×C4—22no—
733C3×C4—22no—
734C3×C4—22no—
735C3×C4—42no—
736C3×C4—42no—
737C3×C4—41no—
738C3×C4—41no—
739C3×C4—62no—
740C3×C4—62no—
741C3×C4—62no—
742C3×C4—62no—
743C3×C4—62no—
744C3×C4—81no—
745C3×C4—121no—
746C3×C4—121no—
747C3×C4—121no—
748Dic3—22no—
749Dic3—22no—
750Dic3—22no—
751Dic3—22no—
752Dic3—22no—
753Dic3—41no—
754Dic3—41no—
755Dic3—41no—
756Dic3—122no—
757Dic3—121no—
758Dic3—121no—
759Dic3—121no—
760Dic3—121no—
761Dic3—241no—
762C32#235311yescharacteristic, complemented, Sylow
763C23—92no—
764C23—92no—
765C23—92no—
766C23—92no—
767C23—181no—
768C23—181no—
769C23—181no—
770C23—181no—
771C23—181no—
772C23—181no—
773C23—181no—
774C23—181no—
775C23—181no—
776C23—181no—
777C23C22×D3211yescharacteristic
778D4—188no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—32no—
787C2×C4—32no—
788C2×C4—32no—
789C2×C4—32no—
790C2×C4—32no—
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—61no—
805C2×C4—61no—
806C2×C4—61no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—181no—
811C2×C4—181no—
812C2×C4—181no—
813C2×C4—181no—
814C2×C4—181no—
815C2×C4—181no—
816C2×C4—364no—
817C2×C4—364no—
818C2×C4—364no—
819C2×C4—364no—
820C2×C4#379912yes—
821C2×C4C4×D3212yes—
822C2×C3—21no—
823C2×C3—21no—
824C2×C3—21no—
825C2×C3—21no—
826C2×C3—21no—
827C2×C3—21no—
828C2×C3—21no—
829C2×C3C4×#23511yescharacteristic
830C2×C3D3×#11711yescharacteristic
831C2×C3D3×#11711yescharacteristic
832C2×C3#552111yescharacteristic
833C2×C3#552711yescharacteristic
834C2×C3#552711yescharacteristic
835C2×C3#553011yescharacteristic
836C2×C3#553011yescharacteristic
837C2×C3#554511yescharacteristic
838C2×C3C4×#23911yescharacteristic
839C2×C3#563711yescharacteristic
840C2×C3#566111yescharacteristic
841C2×C3#569511yescharacteristic
842C2×C3#570511yescharacteristic
843D3—64no—
844D3—64no—
845D3—124no—
846D3—122no—
847D3—122no—
848D3—242no—
849C22—94no—
850C22—182no—
851C22—182no—
852C22—182no—
853C22—182no—
854C22—182no—
855C22—182no—
856C22—182no—
857C22—182no—
858C22—182no—
859C22—361no—
860C22—361no—
861C22—361no—
862C22—361no—
863C22C2×#379911yescharacteristic
864C22C2×C4×D3211yescharacteristic
865C22D3×#23511yescharacteristic
866C22#6431211yescharacteristic
867C22#6431211yescharacteristic
868C22#6431411yescharacteristic
869C22#6432011yescharacteristic
870C4—22no—
871C4—22no—
872C4—41no—
873C4—62no—
874C4—62no—
875C4—62no—
876C4—62no—
877C4—62no—
878C4—121no—
879C4—121no—
880C4—121no—
881C4—361no—
882C4—361no—
883C3—21no—
884C3#7341711yescharacteristic, complemented
885C3#7530611yescharacteristic, complemented
886C2—184no—
887C2—362no—
888C2C4×#379911yescharacteristic
889C2#1059405211yescharacteristic
890C2#1059416611yescharacteristic
891C2#1059420411yescharacteristic
892C2#1059457811yescharacteristic
893C2#1059460411yescharacteristic
894C2#1059464311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenter#95D32
hypocenterC32#2353
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
3. C3×#4654C2semidirect
4. C3×#4648C2semidirect
6. #10591371C2semidirect
7. #10591370C2semidirect
8. #10591367C2semidirect
9. #10591289C2semidirect
10. C4×#3722C2semidirect
11. #10591270C2semidirect
12. #10591233C2semidirect
13. #10591233C2semidirect
14. #10591223C2semidirect
15. #10591194C2semidirect
39. #63894C4semidirect
82. #4654D3semidirect
84. #4648D3semidirect
114. C2×#624C2×C4semidirect
118. C3×C4⋊Dic3C2×C4semidirect
123. C3×C4×Dic3C2×C4semidirect
129. #3722C2×C4semidirect
384. C4⋊Dic3C4×D3semidirect
392. C4×Dic3C4×D3semidirect
762. C32#2353semidirect
884. C3#73417semidirect
885. C3#75306semidirect

Maximal subgroups

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

subgroupindex
C2×#638942
#105923642
C3×#46542
C3×#46482
#105913802
#105913712
#105913702
#105913672
#105912892
C4×#37222
#105912702
#105912332
#105912232
#105911942
#753063
#734173