Finite Group Databasebeta

← #11807917

Subgroups — #11807917

Order 1152.

1133 conjugacy classes of subgroups.

The subgroup lattice has 865 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63913C211yesmaximal, characteristic
2#10592345C211yesmaximal, characteristic, complemented
3C3×#4669C211yesmaximal, characteristic, complemented
4C3×#4668C211yesmaximal, characteristic, complemented
5#10591381C211yesmaximal, characteristic
6#10591377C211yesmaximal, characteristic, complemented
7#10591372C211yesmaximal, characteristic, complemented
8#10591363C211yesmaximal, characteristic
9#10591305C211yesmaximal, characteristic, complemented
10#10591287C211yesmaximal, characteristic, complemented
11#10591283C211yesmaximal, characteristic, complemented
12#10591278C211yesmaximal, characteristic, complemented
13#10591245C211yesmaximal, characteristic, complemented
14#10591245C211yesmaximal, characteristic, complemented
15#10591213C211yesmaximal, characteristic, complemented
16#75493—31nomaximal
17#74402—31nomaximal
18C22×#634C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×#625C2211yescharacteristic
21C22×D3×Dic3C2211yescharacteristic
22C2×#3750C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C3×(C2×D3)⋊C4C2211yescharacteristic
25C2×C3×(C2×D3)⋊C4C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×Dic3⋊Dic3C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×(C2×D3)⋊Dic3C2211yescharacteristic
36C2×(C2×D3)⋊Dic3C2211yescharacteristic
37C2×(C2×D3)⋊Dic3C2211yescharacteristic
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×Dic32C2211yescharacteristic
41#63913C418yescomplemented
42C32×#95C2211yescharacteristic
43#63658C2211yescharacteristic
44#63658C2211yescharacteristic
45#63658C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×#885—31no—
55C2×#885—31no—
56C3×#388—31no—
57C3×#385—31no—
58#5213—31no—
59#5210—31no—
60#4990—31no—
61#4989—31no—
62#4989—31no—
63#4977—31no—
64#4977—31no—
65#4973—31no—
66#4958—31no—
67#4956—31no—
68#4956—31no—
69#4951—31no—
70#4950—31no—
71#4946—31no—
72#4945—31no—
73#4944—31no—
74#4940—31no—
75#4929—31no—
76#4670—31no—
77#4669D311yescharacteristic, complemented
78#4668—31no—
79#4668D311yescharacteristic, complemented
80#4650—31no—
81#4650—31no—
82#4646—31no—
83#4646—31no—
84#4646—61no—
85C23×C3×D3C2311yescharacteristic
86C23×C3×D3C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C2×#634—41no—
95C2×#634—41no—
96C2×#634C2×C414yescomplemented
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C2×C3×C4×D3—41no—
104C2×C3×C4×D3—41no—
105C2×C3×C4×D3—41no—
106C2×#625—41no—
107C2×#625—41no—
108C2×#625C2×C414yes—
109C2×D3×Dic3—41no—
110C2×D3×Dic3—41no—
111C2×D3×Dic3—41no—
112#3750—41no—
113C4×C3⋊Dic3—41no—
114C3×(C2×D3)⋊C4—41no—
115C3×(C2×D3)⋊C4—41no—
116C3×(C2×D3)⋊C4—41no—
117C3×(C2×D3)⋊C4C2×C414yescomplemented
118C3×(C2×D3)⋊C4C2×C414yescomplemented
119C3×C4⋊Dic3—41no—
120C3×Dic3⋊C4—41no—
121C3×Dic3⋊C4—41no—
122C3×C4×Dic3—41no—
123Dic3⋊Dic3—41no—
124Dic3⋊Dic3—41no—
125(C2×D3)⋊Dic3—41no—
126(C2×D3)⋊Dic3—41no—
127(C2×D3)⋊Dic3—41no—
128(C2×D3)⋊Dic3C2×C414yescomplemented
129(C2×D3)⋊Dic3C2×C414yescomplemented
130Dic32C2×C414yescomplemented
131#2379—91noSylow
132C23×C3×C4—31no—
133C22×#67—31no—
134C22×#67—31no—
135C23×Dic3—31no—
136C22×C4×D3—31no—
137C22×C4×D3C2×D311yescharacteristic
138C22×Dic6—31no—
139C22×Dic6—31no—
140C22×Dic6—61no—
141C2×C3×C4⋊C4—31no—
142C2×C3×C4⋊C4—31no—
143C2×C3×C4⋊C4—31no—
144C2×C3×C22⋊C4—31no—
145C2×C3×C22⋊C4—31no—
146C2×C3×C22⋊C4—31no—
147C2×C3×C22⋊C4—31no—
148C2×C3×C22⋊C4—31no—
149C2×C3×C42—31no—
150C2×#217—31no—
151C2×#217—31no—
152C2×#217—31no—
153C2×#217—31no—
154C2×#217—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)⋊C4C2×D311yescharacteristic
161C2×(C2×D3)⋊C4C2×D311yescharacteristic
162C2×(C2×D3)⋊C4C2×D311yescharacteristic
163C2×(C2×D3)⋊C4C2×D311yescharacteristic
164C2×(C2×D3)⋊C4C2×D311yescharacteristic
165C2×C4⋊Dic3—31no—
166C2×C4⋊Dic3—31no—
167C2×C4⋊Dic3C2×D311yescharacteristic
168C2×Dic3⋊C4—31no—
169C2×Dic3⋊C4—31no—
170C2×Dic3⋊C4—31no—
171C2×Dic3⋊C4—31no—
172C2×Dic3⋊C4—61no—
173C2×Dic3⋊C4C2×D311yescharacteristic
174C2×Dic3⋊C4C2×D311yescharacteristic
175C2×C4×Dic3—31no—
176C2×C4×Dic3—31no—
177C2×C4×Dic3—31no—
178C2×C4×Dic3—31no—
179C2×C4×Dic3—61no—
180C2×C4×Dic3C2×D311yescharacteristic
181#885—38no—
182#885—38no—
183C3×#95—21no—
184C3×#95—31no—
185C3×#95—31no—
186C3×#95C2×D311yescharacteristic
187C3×#95C2×D311yescharacteristic
188C3⋊#95—31no—
189C3⋊#95—31no—
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—31no—
205C3⋊#95—31no—
206C3⋊#95—61no—
207C3⋊#95—61no—
208C3⋊#95—61no—
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×C4—21no—
234C2×C32×C4C22×C412yes—
235C2×C3⋊Dic3—21no—
236C2×C3⋊Dic3—21no—
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3—21no—
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3C22×C412yes—
246C2×C3⋊Dic3C22×C412yes—
247#634—44no—
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×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3C22×C412yes—
265C2×C3×Dic3C22×C412yes—
266C3×C4×D3—44no—
267#625—44no—
268D3×Dic3—44no—
269C2×#124—91no—
270#391—91no—
271#391—91no—
272#388—31no—
273#388—91no—
274#388—91no—
275#388—91no—
276#386—91no—
277#386—91no—
278#385—31no—
279#385—91no—
280#385—91no—
281#385—91no—
282#382—91no—
283#382—91no—
284C24×C3—31no—
285C24×C3—31no—
286C23×D3C22×D311yescharacteristic
287C23×D3C22×D311yescharacteristic
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—31no—
292C22×C3×C4—31no—
293C22×C3×C4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—121no—
298C22×C3×C4—121no—
299C22×C3×C4—121no—
300C22×C3×C4C22×D311yescharacteristic
301C22×C3×C4C22×D311yescharacteristic
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C2×#67—34no—
307C2×#67—34no—
308C2×#67—121no—
309C2×#67—121no—
310C2×#67—121no—
311C2×#67—121no—
312C22×Dic3—31no—
313C22×Dic3—31no—
314C22×Dic3—31no—
315C22×Dic3—31no—
316C22×Dic3—31no—
317C22×Dic3—31no—
318C22×Dic3—31no—
319C22×Dic3—31no—
320C22×Dic3—61no—
321C22×Dic3—61no—
322C22×Dic3—61no—
323C22×Dic3—61no—
324C22×Dic3—121no—
325C22×Dic3—121no—
326C22×Dic3—121no—
327C22×Dic3C22×D311yescharacteristic
328C22×Dic3C22×D311yescharacteristic
329C22×Dic3C22×D311yescharacteristic
330C22×Dic3C22×D311yescharacteristic
331C22×Dic3C22×D311yescharacteristic
332C22×Dic3C22×D311yescharacteristic
333C2×C4×D3—41no—
334C2×C4×D3—41no—
335C2×C4×D3—41no—
336C2×C4×D3—121no—
337C2×C4×D3—121no—
338C2×C4×D3—121no—
339C2×Dic6—34no—
340C2×Dic6—34no—
341C2×Dic6—64no—
342C2×Dic6—121no—
343C2×Dic6—121no—
344C2×Dic6—121no—
345C2×Dic6—121no—
346C2×Dic6—122no—
347C2×Dic6—122no—
348C3×C4⋊C4—121no—
349C3×C4⋊C4—121no—
350C3×C4⋊C4—121no—
351C3×C22⋊C4—34no—
352C3×C22⋊C4—34no—
353C3×C22⋊C4—121no—
354C3×C22⋊C4—121no—
355C3×C22⋊C4—121no—
356C3×C42—121no—
357#217—34no—
358#217—34no—
359#217—121no—
360#217—121no—
361#217—121no—
362(C2×D3)⋊C4—34no—
363(C2×D3)⋊C4—34no—
364(C2×D3)⋊C4—41no—
365(C2×D3)⋊C4—41no—
366(C2×D3)⋊C4—41no—
367(C2×D3)⋊C4—121no—
368(C2×D3)⋊C4—121no—
369(C2×D3)⋊C4—121no—
370(C2×D3)⋊C4C4×D314yescomplemented
371(C2×D3)⋊C4C4×D314yescomplemented
372C4⋊Dic3—41no—
373C4⋊Dic3—121no—
374C4⋊Dic3—121no—
375Dic3⋊C4—41no—
376Dic3⋊C4—41no—
377Dic3⋊C4—121no—
378Dic3⋊C4—121no—
379Dic3⋊C4—121no—
380Dic3⋊C4—121no—
381Dic3⋊C4—122no—
382C4×Dic3—34no—
383C4×Dic3—34no—
384C4×Dic3—41no—
385C4×Dic3—121no—
386C4×Dic3—121no—
387C4×Dic3—122no—
388C22×C32C23×C411yescharacteristic
389C22×C32H(5,𝔽2)11yescharacteristic
390C22×C32H(5,𝔽2)11yescharacteristic
391C22×C32H(5,𝔽2)11yescharacteristic
392C22×C32H(5,𝔽2)11yescharacteristic
393C22×C322−1+411yescharacteristic
394C22×C322−1+411yescharacteristic
395C2×C3×D3—22no—
396C2×C3×D3—22no—
397C2×C3×D3—22no—
398C2×C3×D3—22no—
399C2×C3×D3—22no—
400C2×C3×D3—22no—
401C2×C3×D3—41no—
402C2×C3×D3—41no—
403C2×C3×D3—41no—
404C2×C3×D3—41no—
405C2×C3×D3—41no—
406C2×C3×D3—41no—
407C2×C3×D3—41no—
408C2×C3×D3—41no—
409C32×C4—22no—
410C32×C4—41no—
411C32×C4—41no—
412C3⋊Dic3—22no—
413C3⋊Dic3—22no—
414C3⋊Dic3—41no—
415C3⋊Dic3—41no—
416C3×Dic3—22no—
417C3×Dic3—22no—
418C3×Dic3—41no—
419C3×Dic3—41no—
420C3×Dic3—41no—
421C3×Dic3—41no—
422C22×Q8—91no—
423C22×D4—91no—
424C23×C4—31no—
425C23×C4—91no—
426#124—98no—
427C2×C4⋊C4—31no—
428C2×C4⋊C4—31no—
429C2×C4⋊C4—31no—
430C2×C4⋊C4—91no—
431C2×C4⋊C4—91no—
432C2×C4⋊C4—91no—
433C2×C22⋊C4—31no—
434C2×C22⋊C4—31no—
435C2×C22⋊C4—31no—
436C2×C22⋊C4—31no—
437C2×C22⋊C4—31no—
438C2×C22⋊C4—91no—
439C2×C22⋊C4—91no—
440C2×C22⋊C4—91no—
441C2×C22⋊C4—91no—
442C2×C22⋊C4—91no—
443C2×C42—31no—
444C2×C42—91no—
445C2×C42—91no—
446#95—31no—
447#95—31no—
448#95—91no—
449#95—91no—
450#95—91no—
451#95—91no—
452#95—91no—
453#95—91no—
454#95—91no—
455#95—91no—
456#95—91no—
457#95D3211yescharacteristic
458C23×C3—21no—
459C23×C3—32no—
460C23×C3—32no—
461C23×C3—61no—
462C23×C3—61no—
463C23×C3—61no—
464C23×C3—61no—
465C23×C3—61no—
466C23×C3—61no—
467C23×C3—61no—
468C23×C3—61no—
469C23×C3—61no—
470C23×C3—61no—
471C23×C3—61no—
472C23×C3—61no—
473C23×C3C23×D311yescharacteristic
474C23×C3C23×D311yescharacteristic
475C22×D3—21no—
476C22×D3—21no—
477C22×D3—21no—
478C22×D3—21no—
479C22×D3—21no—
480C22×D3—21no—
481C22×D3—21no—
482C22×D3—21no—
483C22×D3—21no—
484C22×D3—21no—
485C22×D3—21no—
486C22×D3—21no—
487C22×D3C2×C4×D312yes—
488C22×D3C2×C4×D312yes—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—22no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—22no—
507C2×C3×C4—32no—
508C2×C3×C4—32no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—124no—
533C2×C3×C4C2×C4×D312yes—
534C2×C3×C4C2×C4×D312yes—
535#67—124no—
536#67—124no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—32no—
554C2×Dic3—32no—
555C2×Dic3—32no—
556C2×Dic3—32no—
557C2×Dic3—62no—
558C2×Dic3—62no—
559C2×Dic3—62no—
560C2×Dic3—62no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—61no—
569C2×Dic3—62no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—61no—
573C2×Dic3—61no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—61no—
577C2×Dic3—61no—
578C2×Dic3—61no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—121no—
583C2×Dic3—121no—
584C2×Dic3—121no—
585C2×Dic3—121no—
586C2×Dic3—121no—
587C2×Dic3—121no—
588C2×Dic3—121no—
589C2×Dic3—124no—
590C2×Dic3C2×C4×D312yes—
591C2×Dic3C2×C4×D312yes—
592C4×D3—44no—
593C4×D3—124no—
594Dic6—124no—
595Dic6—124no—
596Dic6—128no—
597C2×C32#51811yescharacteristic
598C2×C32#52011yescharacteristic
599C2×C32#52011yescharacteristic
600C2×C32H(3,𝔽4)11yescharacteristic
601C2×C32#56211yescharacteristic
602C2×C32#56211yescharacteristic
603C2×C32#56311yescharacteristic
604C3×D3—42no—
605C3×D3—42no—
606C24—31no—
607C24—31no—
608C2×Q8—94no—
609C2×Q8—361no—
610C2×Q8—361no—
611C2×D4—94no—
612C2×D4—361no—
613C2×D4—361no—
614C22×C4—31no—
615C22×C4—31no—
616C22×C4—31no—
617C22×C4—31no—
618C22×C4—31no—
619C22×C4—31no—
620C22×C4—91no—
621C22×C4—91no—
622C22×C4—91no—
623C22×C4—91no—
624C22×C4—121no—
625C22×C4—121no—
626C22×C4—121no—
627C22×C4—361no—
628C22×C4—361no—
629C22×C4—361no—
630C22×C4C2×D3211yescharacteristic
631C22×C4C2×D3211yescharacteristic
632C22×C4C2×D3211yescharacteristic
633C4⋊C4—121no—
634C4⋊C4—121no—
635C4⋊C4—121no—
636C4⋊C4—361no—
637C4⋊C4—361no—
638C4⋊C4—361no—
639C22⋊C4—34no—
640C22⋊C4—34no—
641C22⋊C4—94no—
642C22⋊C4—94no—
643C22⋊C4—121no—
644C22⋊C4—121no—
645C22⋊C4—121no—
646C22⋊C4—361no—
647C22⋊C4—361no—
648C22⋊C4—361no—
649C42—94no—
650C42—121no—
651C42—361no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—62no—
660C22×C3—62no—
661C22×C3—62no—
662C22×C3—62no—
663C22×C3—62no—
664C22×C3—62no—
665C22×C3—121no—
666C22×C3—121no—
667C22×C3—121no—
668C22×C3—121no—
669C22×C3—121no—
670C22×C3—121no—
671C22×C3—121no—
672C22×C3—121no—
673C22×C3C22×C4×D311yescharacteristic
674C22×C3C22×C4×D311yescharacteristic
675C22×C3#100411yescharacteristic
676C22×C3#100411yescharacteristic
677C22×C3#100411yescharacteristic
678C22×C3#100411yescharacteristic
679C22×C3#100411yescharacteristic
680C22×C3#100711yescharacteristic
681C22×C3#100911yescharacteristic
682C22×C3#100911yescharacteristic
683C22×C3#100911yescharacteristic
684C22×C3#101011yescharacteristic
685C22×C3#101011yescharacteristic
686C22×C3#101011yescharacteristic
687C2×D3—22no—
688C2×D3—22no—
689C2×D3—22no—
690C2×D3—22no—
691C2×D3—22no—
692C2×D3—22no—
693C2×D3—41no—
694C2×D3—41no—
695C2×D3—41no—
696C2×D3—41no—
697C2×D3—41no—
698C2×D3—41no—
699C2×D3—41no—
700C2×D3—41no—
701C3×C4—22no—
702C3×C4—22no—
703C3×C4—42no—
704C3×C4—42no—
705C3×C4—41no—
706C3×C4—41no—
707C3×C4—41no—
708C3×C4—41no—
709C3×C4—62no—
710C3×C4—62no—
711C3×C4—81no—
712C3×C4—121no—
713C3×C4—121no—
714C3×C4—121no—
715C3×C4—121no—
716Dic3—22no—
717Dic3—22no—
718Dic3—41no—
719Dic3—41no—
720Dic3—41no—
721Dic3—41no—
722Dic3—64no—
723Dic3—62no—
724Dic3—62no—
725Dic3—62no—
726Dic3—62no—
727Dic3—122no—
728Dic3—122no—
729Dic3—121no—
730Dic3—121no—
731Dic3—121no—
732Dic3—121no—
733Dic3—241no—
734C32#237911yescharacteristic, complemented, Sylow
735C23—32no—
736C23—32no—
737C23—61no—
738C23—61no—
739C23—61no—
740C23—61no—
741C23—61no—
742C23—61no—
743C23—61no—
744C23—61no—
745C23—61no—
746C23—61no—
747C23—61no—
748C23—61no—
749C23C22×D3211yescharacteristic
750Q8—364no—
751D4—364no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—32no—
761C2×C4—32no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—92no—
779C2×C4—92no—
780C2×C4—124no—
781C2×C4—181no—
782C2×C4—181no—
783C2×C4—181no—
784C2×C4—181no—
785C2×C4—181no—
786C2×C4—181no—
787C2×C4—181no—
788C2×C4—181no—
789C2×C4—181no—
790C2×C4—181no—
791C2×C4—364no—
792C2×C4C4×D3212yes—
793C2×C3—21no—
794C2×C3—21no—
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—122no—
801C2×C3—122no—
802C2×C3#550411yescharacteristic
803C2×C3#552311yescharacteristic
804C2×C3#554511yescharacteristic
805C2×C3#554511yescharacteristic
806C2×C3#554611yescharacteristic
807C2×C3#554611yescharacteristic
808C2×C3#559411yescharacteristic
809C2×C3#562111yescharacteristic
810C2×C3#564611yescharacteristic
811C2×C3#564711yescharacteristic
812C2×C3#566711yescharacteristic
813C2×C3#566711yescharacteristic
814C2×C3#568311yescharacteristic
815C2×C3#571211yescharacteristic
816D3—42no—
817D3—42no—
818C22—62no—
819C22—62no—
820C22—62no—
821C22—62no—
822C22—62no—
823C22—62no—
824C22—121no—
825C22—121no—
826C22—121no—
827C22—121no—
828C22—121no—
829C22—121no—
830C22—121no—
831C22—121no—
832C22#6429811yescharacteristic
833C22C2×C4×D3211yescharacteristic
834C22#6430711yescharacteristic
835C22#6431311yescharacteristic
836C22#6431411yescharacteristic
837C22#6431411yescharacteristic
838C22#6431511yescharacteristic
839C4—22no—
840C4—41no—
841C4—41no—
842C4—62no—
843C4—62no—
844C4—121no—
845C4—121no—
846C4—121no—
847C4—121no—
848C4—182no—
849C4—182no—
850C4—361no—
851C4—361no—
852C3—21no—
853C3#7440211yescharacteristic, complemented
854C3#7549311yescharacteristic, complemented
855C2—122no—
856C2—122no—
857C2#1059388711yescharacteristic
858C2#1059423911yescharacteristic
859C2#1059425611yescharacteristic
860C2#1059430911yescharacteristic
861C2#1059435911yescharacteristic
862C2#1059458511yescharacteristic
863C2#1059459111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC22×#625C22
hypercenter#95D32
hypocenterC32#2379
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. #10592345C2semidirect
3. C3×#4669C2semidirect
4. C3×#4668C2semidirect
6. #10591377C2semidirect
7. #10591372C2semidirect
9. #10591305C2semidirect
10. #10591287C2semidirect
11. #10591283C2semidirect
12. #10591278C2semidirect
13. #10591245C2semidirect
14. #10591245C2semidirect
15. #10591213C2semidirect
41. #63913C4semidirect
77. #4669D3semidirect
79. #4668D3semidirect
96. C2×#634C2×C4semidirect
117. C3×(C2×D3)⋊C4C2×C4semidirect
118. C3×(C2×D3)⋊C4C2×C4semidirect
128. (C2×D3)⋊Dic3C2×C4semidirect
129. (C2×D3)⋊Dic3C2×C4semidirect
130. Dic32C2×C4semidirect
370. (C2×D3)⋊C4C4×D3semidirect
371. (C2×D3)⋊C4C4×D3semidirect
734. C32#2379semidirect
853. C3#74402semidirect
854. C3#75493semidirect

Maximal subgroups

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

subgroupindex
C2×#639132
#105923452
C3×#46692
C3×#46682
#105913812
#105913772
#105913722
#105913632
#105913052
#105912872
#105912832
#105912782
#105912452
#105912132
#754933
#744023