Finite Group Databasebeta

← #11807556

Subgroups — #11807556

Order 1152.

1201 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63884C211yesmaximal, characteristic
2#10592348C211yesmaximal, characteristic, complemented
3C3×#4665C211yesmaximal, characteristic
4C3×#4655C211yesmaximal, characteristic, complemented
5#10591368C211yesmaximal, characteristic, complemented
6Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7#10591323C211yesmaximal, characteristic
8#10591287C211yesmaximal, characteristic, complemented
9#10591287C211yesmaximal, characteristic, complemented
10#10591281C211yesmaximal, characteristic, complemented
11#10591281C211yesmaximal, characteristic, complemented
12C4×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
13#10591263C211yesmaximal, characteristic, complemented
14#10591241C211yesmaximal, characteristic, complemented
15#10591237C211yesmaximal, characteristic, complemented
16#74975—31nomaximal
17#74681—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×D3×Dic3C2211yescharacteristic
21C2×#3750C2211yescharacteristic
22C2×#3750C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
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×C4×Dic3C2211yescharacteristic
32C2×Dic3⋊Dic3C2211yescharacteristic
33C2×(C2×D3)⋊Dic3C2211yescharacteristic
34C2×(C2×D3)⋊Dic3C2211yescharacteristic
35C2×(C2×D3)⋊Dic3C2211yescharacteristic
36C2×(C2×D3)⋊Dic3C2211yescharacteristic
37C2×(C2×D3)⋊Dic3C2211yescharacteristic
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×Dic32C2211yescharacteristic
41C2×Dic32C2211yescharacteristic
42C2×Dic32C2211yescharacteristic
43#63884C418yescomplemented
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×#935—31no—
55C2×#894—31no—
56C3×#387—31no—
57C3×#386—31no—
58#5221—31no—
59C4×#217—31no—
60C4×#217—31no—
61#4988—31no—
62#4978—31no—
63Dic3×C4⋊C4—31no—
64#4944—31no—
65#4944—31no—
66#4944—31no—
67#4944—31no—
68Dic3×C22⋊C4—31no—
69Dic3×C22⋊C4—31no—
70C4×(C2×D3)⋊C4—31no—
71C4×(C2×D3)⋊C4—31no—
72#4670—31no—
73#4670—31no—
74#4669—31no—
75#4669—31no—
76#4666—31no—
77#4666—31no—
78#4665D311yescharacteristic
79#4655—31no—
80#4655D311yescharacteristic, complemented
81#4649—31no—
82#4649—31no—
83#4649—31no—
84#4649—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
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C2×C3×D12—41no—
101C2×C3×D12—41no—
102C2×C3×D12C2×C414yes—
103C2×C3×C4×D3—22no—
104C2×C3×C4×D3—22no—
105C2×C3×C4×D3—41no—
106C2×D3×Dic3—41no—
107C2×D3×Dic3—41no—
108C2×D3×Dic3C2×C414yescomplemented
109#3750—22no—
110#3750C2×C414yescomplemented
111C4×C3⋊Dic3—22no—
112C4×C3⋊Dic3—41no—
113C4×C3⋊Dic3—41no—
114C3×(C2×D3)⋊C4—22no—
115C3×(C2×D3)⋊C4—22no—
116C3×(C2×D3)⋊C4—41no—
117C3×C4⋊Dic3—41no—
118C3×Dic3⋊C4C2×C414yescomplemented
119C3×C4×Dic3—41no—
120Dic3⋊Dic3—22no—
121(C2×D3)⋊Dic3—22no—
122(C2×D3)⋊Dic3—22no—
123(C2×D3)⋊Dic3—22no—
124(C2×D3)⋊Dic3—22no—
125(C2×D3)⋊Dic3C2×C414yes—
126(C2×D3)⋊Dic3C2×C414yes—
127(C2×D3)⋊Dic3C2×C414yescomplemented
128Dic32—22no—
129Dic32—41no—
130Dic32—41no—
131#2374—91noSylow
132C22×C3×D4—31no—
133C23×C3×C4—31no—
134C23×Dic3—31no—
135C22×D12C2×D311yescharacteristic
136C22×C4×D3—31no—
137C22×C4×D3C2×D311yescharacteristic
138C2×C3×C4⋊C4—31no—
139C2×C3×C4⋊C4—31no—
140C2×C3×C22⋊C4—31no—
141C2×C3×C22⋊C4—31no—
142C2×C3×C22⋊C4—31no—
143C2×C3×C42—31no—
144C2×#217—31no—
145C2×#217—31no—
146C2×#217—31no—
147C2×#217—31no—
148C2×#217—31no—
149C2×#217—31no—
150C2×#217—31no—
151#935—38no—
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)⋊C4C2×D311yescharacteristic
160C2×(C2×D3)⋊C4C2×D311yescharacteristic
161C2×(C2×D3)⋊C4C2×D311yescharacteristic
162C2×C4⋊Dic3—31no—
163C2×C4⋊Dic3C2×D311yescharacteristic
164C2×Dic3⋊C4—31no—
165C2×Dic3⋊C4—31no—
166C2×Dic3⋊C4—31no—
167C2×Dic3⋊C4—31no—
168C2×Dic3⋊C4—31no—
169C2×Dic3⋊C4—61no—
170C2×Dic3⋊C4—61no—
171C2×Dic3⋊C4C2×D311yescharacteristic
172C2×C4×Dic3—31no—
173C2×C4×Dic3—31no—
174C2×C4×Dic3—31no—
175C2×C4×Dic3—31no—
176C2×C4×Dic3—31no—
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×Dic3—31no—
184C2×C4×Dic3—61no—
185C2×C4×Dic3—61no—
186C2×C4×Dic3—61no—
187C2×C4×Dic3C2×D311yescharacteristic
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—21no—
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3C22×C412yes—
244C2×C3⋊Dic3C22×C412yes—
245C2×C3⋊Dic3#4112yes—
246C2×C3⋊Dic3#4112yes—
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×Dic3#4112yes—
265C3×D12—44no—
266C3×C4×D3—44no—
267D3×Dic3—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—31no—
277C4×C4⋊C4—91no—
278C4×C4⋊C4—91no—
279C4×C22⋊C4—91no—
280C4×C22⋊C4—91no—
281C4×C22⋊C4—91no—
282C4×C22⋊C4—91no—
283C24×C3—31no—
284C24×C3—31no—
285C23×D3C22×D311yescharacteristic
286C23×D3C22×D311yescharacteristic
287C2×C3×D4—34no—
288C2×C3×D4—121no—
289C2×C3×D4—121no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
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—62no—
300C22×C3×C4—62no—
301C22×C3×C4—121no—
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—31no—
313C22×Dic3—31no—
314C22×Dic3—31no—
315C22×Dic3—31no—
316C22×Dic3—34no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321C22×Dic3—121no—
322C22×Dic3—121no—
323C22×Dic3C22×D311yescharacteristic
324C22×Dic3C22×D311yescharacteristic
325C22×Dic3C22×D311yescharacteristic
326C22×Dic3C22×D311yescharacteristic
327C22×Dic3C22×D311yescharacteristic
328C22×Dic3C22×D311yescharacteristic
329C2×D12—41no—
330C2×D12—41no—
331C2×D12C4×D314yes—
332C2×C4×D3—22no—
333C2×C4×D3—22no—
334C2×C4×D3—34no—
335C2×C4×D3—41no—
336C2×C4×D3—121no—
337C2×C4×D3—121no—
338C3×C4⋊C4—34no—
339C3×C4⋊C4—121no—
340C3×C22⋊C4—62no—
341C3×C22⋊C4—62no—
342C3×C22⋊C4—121no—
343C3×C42—121no—
344#217—34no—
345#217—34no—
346#217—34no—
347#217—62no—
348#217—62no—
349#217—62no—
350#217—62no—
351(C2×D3)⋊C4—22no—
352(C2×D3)⋊C4—22no—
353(C2×D3)⋊C4—34no—
354(C2×D3)⋊C4—34no—
355(C2×D3)⋊C4—34no—
356(C2×D3)⋊C4—41no—
357(C2×D3)⋊C4—62no—
358(C2×D3)⋊C4—62no—
359(C2×D3)⋊C4—62no—
360(C2×D3)⋊C4—62no—
361C4⋊Dic3—41no—
362C4⋊Dic3—62no—
363Dic3⋊C4—34no—
364Dic3⋊C4—34no—
365Dic3⋊C4—64no—
366Dic3⋊C4—62no—
367Dic3⋊C4—62no—
368Dic3⋊C4—62no—
369Dic3⋊C4—64no—
370Dic3⋊C4C4×D314yescomplemented
371C4×Dic3—41no—
372C4×Dic3—62no—
373C4×Dic3—64no—
374C4×Dic3—62no—
375C4×Dic3—62no—
376C4×Dic3—62no—
377C4×Dic3—121no—
378C4×Dic3—121no—
379C4×Dic3—121no—
380C4×Dic3—121no—
381C4×Dic3—121no—
382C4×Dic3—121no—
383C4×Dic3—121no—
384C4×Dic3—121no—
385C4×Dic3—122no—
386C4×Dic3—122no—
387C22×C32C23×C411yescharacteristic
388C22×C32C2×#4111yescharacteristic
389C22×C32C2×#4111yescharacteristic
390C22×C32C2×#4111yescharacteristic
391C22×C32C2×#4111yescharacteristic
392C22×C32H(5,𝔽2)11yescharacteristic
393C22×C32H(5,𝔽2)11yescharacteristic
394C2×C3×D3—22no—
395C2×C3×D3—22no—
396C2×C3×D3—22no—
397C2×C3×D3—22no—
398C2×C3×D3—22no—
399C2×C3×D3—22no—
400C2×C3×D3—41no—
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—
408C32×C4—22no—
409C32×C4—22no—
410C32×C4—41no—
411C3⋊Dic3—22no—
412C3⋊Dic3—22no—
413C3⋊Dic3—22no—
414C3⋊Dic3—22no—
415C3×Dic3—22no—
416C3×Dic3—22no—
417C3×Dic3—22no—
418C3×Dic3—41no—
419C3×Dic3—41no—
420C3×Dic3—41no—
421C22×D4—31no—
422C23×C4—31no—
423C23×C4—91no—
424#123—98no—
425C2×C4⋊C4—31no—
426C2×C4⋊C4—31no—
427C2×C4⋊C4—91no—
428C2×C4⋊C4—91no—
429C2×C4⋊C4—91no—
430C2×C22⋊C4—31no—
431C2×C22⋊C4—31no—
432C2×C22⋊C4—31no—
433C2×C22⋊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×C42—31no—
441C2×C42—91no—
442C2×C42—91no—
443C2×C42—91no—
444C2×C42—91no—
445C2×C42—91no—
446C2×C42—91no—
447#95—31no—
448#95—31no—
449#95—31no—
450#95—31no—
451#95—91no—
452#95—91no—
453#95—91no—
454#95—91no—
455#95—91no—
456#95D3211yescharacteristic
457C23×C3—21no—
458C23×C3—32no—
459C23×C3—32no—
460C23×C3—61no—
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×C3C23×D311yescharacteristic
473C23×C3C23×D311yescharacteristic
474C22×D3—21no—
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×D3C2×C4×D312yes—
487C22×D3C2×C4×D312yes—
488C3×D4—124no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—22no—
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—22no—
505C2×C3×C4—22no—
506C2×C3×C4—32no—
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—61no—
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—124no—
531C2×C3×C4C2×C4×D312yes—
532C2×C3×C4C2×C4×D312yes—
533C2×C3×C4#23712yes—
534C2×C3×C4#23912yes—
535C2×Dic3—21no—
536C2×Dic3—21no—
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—32no—
551C2×Dic3—32no—
552C2×Dic3—32no—
553C2×Dic3—32no—
554C2×Dic3—32no—
555C2×Dic3—32no—
556C2×Dic3—32no—
557C2×Dic3—32no—
558C2×Dic3—62no—
559C2×Dic3—62no—
560C2×Dic3—62no—
561C2×Dic3—62no—
562C2×Dic3—62no—
563C2×Dic3—62no—
564C2×Dic3—62no—
565C2×Dic3—62no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—61no—
569C2×Dic3—61no—
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—124no—
587C2×Dic3C2×C4×D312yes—
588C2×Dic3C2×C4×D312yes—
589C2×Dic3#23712yes—
590D12—44no—
591C4×D3—44no—
592C4×D3—124no—
593C2×C32C4×#4111yescharacteristic
594C2×C32C4×#4111yescharacteristic
595C2×C32#51811yescharacteristic
596C2×C32#55111yescharacteristic
597C2×C32#55311yescharacteristic
598C2×C32#55311yescharacteristic
599C2×C32#55911yescharacteristic
600C3×D3—42no—
601C3×D3—42no—
602C24—31no—
603C24—31no—
604C2×D4—34no—
605C2×D4—121no—
606C2×D4—121no—
607C22×C4—31no—
608C22×C4—31no—
609C22×C4—31no—
610C22×C4—31no—
611C22×C4—31no—
612C22×C4—31no—
613C22×C4—62no—
614C22×C4—62no—
615C22×C4—94no—
616C22×C4—91no—
617C22×C4—91no—
618C22×C4—91no—
619C22×C4—91no—
620C22×C4—121no—
621C22×C4—361no—
622C22×C4—361no—
623C22×C4C2×D3211yescharacteristic
624C22×C4C2×D3211yescharacteristic
625C22×C4C2×D3211yescharacteristic
626C4⋊C4—34no—
627C4⋊C4—94no—
628C4⋊C4—121no—
629C4⋊C4—182no—
630C4⋊C4—182no—
631C22⋊C4—62no—
632C22⋊C4—62no—
633C22⋊C4—94no—
634C22⋊C4—94no—
635C22⋊C4—94no—
636C22⋊C4—121no—
637C22⋊C4—182no—
638C22⋊C4—182no—
639C22⋊C4—182no—
640C22⋊C4—182no—
641C42—121no—
642C42—182no—
643C42—182no—
644C42—361no—
645C42—361no—
646C42—361no—
647C42—361no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—62no—
656C22×C3—62no—
657C22×C3—62no—
658C22×C3—62no—
659C22×C3—62no—
660C22×C3—62no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3—121no—
667C22×C3—121no—
668C22×C3—121no—
669C22×C3C22×C4×D311yescharacteristic
670C22×C3C22×C4×D311yescharacteristic
671C22×C3C2×#23711yescharacteristic
672C22×C3C2×#23711yescharacteristic
673C22×C3#100411yescharacteristic
674C22×C3#100411yescharacteristic
675C22×C3#100411yescharacteristic
676C22×C3C2×#23911yescharacteristic
677C22×C3D3×#4111yescharacteristic
678C22×C3D3×#4111yescharacteristic
679C22×C3D3×#4111yescharacteristic
680C22×C3D3×#4111yescharacteristic
681C22×C3D3×#4111yescharacteristic
682C22×C3#100911yescharacteristic
683C2×D3—22no—
684C2×D3—22no—
685C2×D3—22no—
686C2×D3—22no—
687C2×D3—22no—
688C2×D3—22no—
689C2×D3—41no—
690C2×D3—41no—
691C2×D3—41no—
692C2×D3—41no—
693C2×D3—41no—
694C2×D3—41no—
695C2×D3—41no—
696C2×D3—41no—
697C3×C4—22no—
698C3×C4—22no—
699C3×C4—22no—
700C3×C4—22no—
701C3×C4—42no—
702C3×C4—42no—
703C3×C4—42no—
704C3×C4—41no—
705C3×C4—41no—
706C3×C4—62no—
707C3×C4—62no—
708C3×C4—62no—
709C3×C4—121no—
710C3×C4—121no—
711C3×C4—121no—
712Dic3—22no—
713Dic3—22no—
714Dic3—22no—
715Dic3—41no—
716Dic3—41no—
717Dic3—41no—
718Dic3—64no—
719Dic3—64no—
720Dic3—62no—
721Dic3—62no—
722Dic3—62no—
723Dic3—62no—
724Dic3—62no—
725Dic3—62no—
726Dic3—62no—
727Dic3—62no—
728Dic3—122no—
729Dic3—122no—
730C32#237411yescharacteristic, complemented, Sylow
731C23—32no—
732C23—32no—
733C23—61no—
734C23—61no—
735C23—61no—
736C23—61no—
737C23—61no—
738C23—61no—
739C23—61no—
740C23—61no—
741C23—61no—
742C23—61no—
743C23—61no—
744C23—61no—
745C23C22×D3211yescharacteristic
746D4—124no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—32no—
755C2×C4—32no—
756C2×C4—32no—
757C2×C4—61no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—61no—
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—92no—
773C2×C4—92no—
774C2×C4—92no—
775C2×C4—92no—
776C2×C4—124no—
777C2×C4—181no—
778C2×C4—181no—
779C2×C4—181no—
780C2×C4—181no—
781C2×C4—181no—
782C2×C4—181no—
783C2×C4—181no—
784C2×C4—181no—
785C2×C4—364no—
786C2×C4#379612yes—
787C2×C4C4×D3212yes—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—21no—
791C2×C3—21no—
792C2×C3—21no—
793C2×C3—21no—
794C2×C3—21no—
795C2×C3—122no—
796C2×C3—122no—
797C2×C3#548611yescharacteristic
798C2×C3#552211yescharacteristic
799C2×C3C4×#23711yescharacteristic
800C2×C3C4×#23711yescharacteristic
801C2×C3#554511yescharacteristic
802C2×C3C4×#23911yescharacteristic
803C2×C3#558711yescharacteristic
804C2×C3#561411yescharacteristic
805C2×C3#561411yescharacteristic
806C2×C3#563711yescharacteristic
807C2×C3#566411yescharacteristic
808C2×C3#566411yescharacteristic
809C2×C3#569511yescharacteristic
810C2×C3#570911yescharacteristic
811D3—42no—
812D3—42no—
813C22—62no—
814C22—62no—
815C22—62no—
816C22—62no—
817C22—62no—
818C22—62no—
819C22—121no—
820C22—121no—
821C22—121no—
822C22—121no—
823C22—121no—
824C22—121no—
825C22—121no—
826C22—121no—
827C22C2×#379611yescharacteristic
828C22C2×C4×D3211yescharacteristic
829C22#6430611yescharacteristic
830C22D3×#23711yescharacteristic
831C22#6431311yescharacteristic
832C22#6431411yescharacteristic
833C22#6431911yescharacteristic
834C4—22no—
835C4—22no—
836C4—41no—
837C4—62no—
838C4—62no—
839C4—62no—
840C4—121no—
841C4—121no—
842C4—121no—
843C4—182no—
844C4—182no—
845C4—182no—
846C4—182no—
847C3—21no—
848C3#7468111yescharacteristic, complemented
849C3#7497511yescharacteristic, complemented
850C2—122no—
851C2—122no—
852C2C4×#379611yescharacteristic
853C2#1059411911yescharacteristic
854C2#1059421711yescharacteristic
855C2#1059425411yescharacteristic
856C2#1059435811yescharacteristic
857C2#1059448911yescharacteristic
858C2#1059457011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC22×C3×D12C22
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
2. #10592348C2semidirect
4. C3×#4655C2semidirect
5. #10591368C2semidirect
6. Dic3×(C2×D3)⋊C4C2semidirect
8. #10591287C2semidirect
9. #10591287C2semidirect
10. #10591281C2semidirect
11. #10591281C2semidirect
12. C4×(C2×D3)⋊Dic3C2semidirect
13. #10591263C2semidirect
14. #10591241C2semidirect
15. #10591237C2semidirect
43. #63884C4semidirect
80. #4655D3semidirect
108. C2×D3×Dic3C2×C4semidirect
110. #3750C2×C4semidirect
118. C3×Dic3⋊C4C2×C4semidirect
127. (C2×D3)⋊Dic3C2×C4semidirect
370. Dic3⋊C4C4×D3semidirect
730. C32#2374semidirect
848. C3#74681semidirect
849. C3#74975semidirect

Maximal subgroups

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

subgroupindex
C2×#638842
#105923482
C3×#46652
C3×#46552
#105913682
Dic3×(C2×D3)⋊C42
#105913232
#105912872
#105912812
C4×(C2×D3)⋊Dic32
#105912632
#105912412
#105912372
#749753
#746813