Finite Group Databasebeta

← #11805803

Subgroups — #11805803

Order 1152.

1341 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63881C211yesmaximal, characteristic
2C3⋊D3×#95C211yesmaximal, characteristic, complemented
3C3×#4670C211yesmaximal, characteristic, complemented
4C3×#4655C211yesmaximal, characteristic, complemented
5#10591387C211yesmaximal, characteristic
6#10591387C211yesmaximal, characteristic
7Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
8#10591362C211yesmaximal, characteristic, complemented
9#10591325C211yesmaximal, characteristic, complemented
10#10591307C211yesmaximal, characteristic, complemented
11C4×#3722C211yesmaximal, characteristic, complemented
12#10591262C211yesmaximal, characteristic, complemented
13#10591260C211yesmaximal, characteristic, complemented
14#10591248C211yesmaximal, characteristic, complemented
15#10591239C211yesmaximal, characteristic, complemented
16#75835—31nomaximal
17#75306—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×#626C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C2×C3×(C2×D3)⋊C4C2211yescharacteristic
24C2×C3×(C2×D3)⋊C4C2211yescharacteristic
25C2×C3×(C2×D3)⋊C4C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×#3722C2211yescharacteristic
32C2×#3722C2211yescharacteristic
33C2×#3722C2211yescharacteristic
34C2×(C2×D3)⋊Dic3C2211yescharacteristic
35C2×(C2×D3)⋊Dic3C2211yescharacteristic
36C2×Dic32C2211yescharacteristic
37C2×Dic32C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39#63881C418yescomplemented
40C32×#95C2211yescharacteristic
41#63658C2211yescharacteristic
42#63658C2211yescharacteristic
43#63658C2211yescharacteristic
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×#67⋊C4—31no—
56C3×#388—31no—
57C3×#387—31no—
58#4990—31no—
59#4987—31no—
60#4987—31no—
61#4980—31no—
62#4978—31no—
63#4956—31no—
64#4956—31no—
65#4951—31no—
66#4943—31no—
67Dic3×C22⋊C4—31no—
68C4×(C2×D3)⋊C4—31no—
69C4×(C2×D3)⋊C4—31no—
70C4×(C2×D3)⋊C4—31no—
71#4932—31no—
72#4670D311yescharacteristic, complemented
73#4666—31no—
74#4666—31no—
75#4665—31no—
76#4665—31no—
77#4664—31no—
78D3×#95—31no—
79D3×#95—31no—
80D3×#95—61no—
81#4655D311yescharacteristic, complemented
82#4651—31no—
83#4651—31no—
84#4648—31no—
85C23×C3⋊D3C2311yescharacteristic
86C23×C3×D3C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C2×C4×C3⋊D3—22no—
94C2×C4×C3⋊D3—22no—
95C2×C4×C3⋊D3—22no—
96C2×C4×C3⋊D3—22no—
97C2×C4×C3⋊D3—41no—
98C2×C4×C3⋊D3—41no—
99C2×C4×C3⋊D3—41no—
100C2×C4×C3⋊D3—41no—
101C2×C4×C3⋊D3C2×C414yes—
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C2×#626—22no—
110C2×#626—22no—
111C2×#626C2×C414yes—
112C2×D3×Dic3—41no—
113C2×D3×Dic3—41no—
114C2×D3×Dic3C2×C414yescomplemented
115C3×(C2×D3)⋊C4—22no—
116C3×(C2×D3)⋊C4—41no—
117C3×(C2×D3)⋊C4C2×C414yescomplemented
118C3×C4⋊Dic3—41no—
119C3×C4⋊Dic3—41no—
120C3×Dic3⋊C4C2×C414yescomplemented
121C3×C4×Dic3—22no—
122C3×C4×Dic3—41no—
123#3722—22no—
124#3722—22no—
125#3722C2×C414yes—
126(C2×D3)⋊Dic3—22no—
127(C2×D3)⋊Dic3—41no—
128Dic32—22no—
129Dic32—41no—
130Dic32C2×C414yescomplemented
131#2353—91noSylow
132C22×#67—31no—
133C23×Dic3—31no—
134C22×D12—31no—
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—61no—
143C22×C4×D3—61no—
144C22×C4×D3—61no—
145C2×C3×C4⋊C4—31no—
146C2×C3×C4⋊C4—31no—
147C2×C3×C4⋊C4—31no—
148C2×C3×C22⋊C4—31no—
149C2×C3×C22⋊C4—31no—
150C2×C3×C22⋊C4—31no—
151C2×C3×C42—31no—
152C2×C3×C42—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)⋊C4—31no—
161C2×(C2×D3)⋊C4—31no—
162C2×(C2×D3)⋊C4—31no—
163C2×(C2×D3)⋊C4C2×D311yescharacteristic
164C2×(C2×D3)⋊C4C2×D311yescharacteristic
165C2×(C2×D3)⋊C4C2×D311yescharacteristic
166C2×C4⋊Dic3C2×D311yescharacteristic
167C2×C4⋊Dic3C2×D311yescharacteristic
168C2×Dic3⋊C4C2×D311yescharacteristic
169C2×C4×Dic3—31no—
170C2×C4×Dic3—31no—
171C2×C4×Dic3—31no—
172C2×C4×Dic3—31no—
173C2×C4×Dic3—31no—
174C2×C4×Dic3—31no—
175C2×C4×Dic3C2×D311yescharacteristic
176C2×C4×Dic3C2×D311yescharacteristic
177#893—38no—
178#67⋊C4—38no—
179C3×#95—21no—
180C3×#95—31no—
181C3×#95—31no—
182C3×#95—31no—
183C3×#95—31no—
184C3×#95C2×D311yescharacteristic
185C3×#95C2×D311yescharacteristic
186C3⋊#95—31no—
187C3⋊#95—31no—
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—61no—
205C3⋊#95—61no—
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⋊D3C22×C412yes—
217C22×C3⋊D3#4112yes—
218C22×C3⋊D3#4112yes—
219C22×C3×D3—21no—
220C22×C3×D3—21no—
221C22×C3×D3—21no—
222C22×C3×D3—21no—
223C22×C3×D3—21no—
224C22×C3×D3—21no—
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⋊Dic3C22×C412yes—
243C2×C3⋊Dic3#4112yes—
244C4×C3⋊D3—44no—
245C4×C3⋊D3—44no—
246C4×C3⋊D3—44no—
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×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3C22×C412yes—
266C2×C3×Dic3C22×C412yes—
267C2×C3×Dic3C22×C412yes—
268#626—28no—
269D3×Dic3—44no—
270C2×C4×D4—91no—
271#388—31no—
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—91no—
284C2×#95—91no—
285C24×C3—31no—
286C23×D3—31no—
287C23×D3—31no—
288C23×D3—61no—
289C23×D3C22×D311yescharacteristic
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—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
306C2×#67—34no—
307C2×#67—62no—
308C2×#67—62no—
309C22×Dic3—31no—
310C22×Dic3—31no—
311C22×Dic3—31no—
312C22×Dic3—31no—
313C22×Dic3—34no—
314C22×Dic3—31no—
315C22×Dic3—31no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319C22×Dic3—121no—
320C22×Dic3—121no—
321C22×Dic3C22×D311yescharacteristic
322C22×Dic3C22×D311yescharacteristic
323C22×Dic3C22×D311yescharacteristic
324C22×Dic3C22×D311yescharacteristic
325C22×Dic3C22×D311yescharacteristic
326C22×Dic3C22×D311yescharacteristic
327C22×Dic3C22×D311yescharacteristic
328C2×D12—34no—
329C2×D12—62no—
330C2×D12—62no—
331C2×C4×D3—34no—
332C2×C4×D3—34no—
333C2×C4×D3—34no—
334C2×C4×D3—64no—
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—64no—
342C2×C4×D3—64no—
343C2×C4×D3—62no—
344C2×C4×D3—62no—
345C2×C4×D3—122no—
346C2×C4×D3—122no—
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—
358C2×C4×D3—122no—
359C2×C4×D3—122no—
360C2×C4×D3—122no—
361C3×C4⋊C4—34no—
362C3×C4⋊C4—121no—
363C3×C4⋊C4—121no—
364C3×C22⋊C4—34no—
365C3×C22⋊C4—62no—
366C3×C22⋊C4—121no—
367C3×C42—62no—
368C3×C42—121no—
369#217—62no—
370#217—121no—
371(C2×D3)⋊C4—22no—
372(C2×D3)⋊C4—34no—
373(C2×D3)⋊C4—34no—
374(C2×D3)⋊C4—41no—
375(C2×D3)⋊C4—62no—
376(C2×D3)⋊C4—62no—
377(C2×D3)⋊C4—62no—
378(C2×D3)⋊C4—62no—
379(C2×D3)⋊C4—62no—
380(C2×D3)⋊C4—121no—
381(C2×D3)⋊C4C4×D314yescomplemented
382C4⋊Dic3—41no—
383C4⋊Dic3—41no—
384Dic3⋊C4C4×D314yescomplemented
385C4×Dic3—22no—
386C4×Dic3—34no—
387C4×Dic3—34no—
388C4×Dic3—41no—
389C4×Dic3—62no—
390C4×Dic3—62no—
391C4×Dic3—121no—
392C4×Dic3—121no—
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#11714yes—
407C2×C3×D3—22no—
408C2×C3×D3—22no—
409C2×C3×D3—22no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C32×C4—22no—
415C32×C4—22no—
416C32×C4—41no—
417C3⋊Dic3—22no—
418C3⋊Dic3—22no—
419C3⋊Dic3—41no—
420C3×Dic3—22no—
421C3×Dic3—22no—
422C3×Dic3—22no—
423C3×Dic3—41no—
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—31no—
436C2×C22⋊C4—31no—
437C2×C22⋊C4—31no—
438C2×C22⋊C4—31no—
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—91no—
447C2×C42—91no—
448C2×C42—91no—
449#95—31no—
450#95—31no—
451#95—31no—
452#95—31no—
453#95—91no—
454#95—91no—
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×C3—32no—
465C23×C3—61no—
466C23×C3—61no—
467C23×C3—61no—
468C23×C3—61no—
469C23×C3—61no—
470C23×C3—61no—
471C23×C3C23×D311yescharacteristic
472C23×C3C23×D311yescharacteristic
473C22×D3—21no—
474C22×D3—21no—
475C22×D3—21no—
476C22×D3—21no—
477C22×D3—21no—
478C22×D3—21no—
479C22×D3—32no—
480C22×D3—32no—
481C22×D3—32no—
482C22×D3—32no—
483C22×D3—32no—
484C22×D3—32no—
485C22×D3—62no—
486C22×D3—62no—
487C22×D3—62no—
488C22×D3—62no—
489C22×D3—62no—
490C22×D3—62no—
491C22×D3—62no—
492C22×D3—61no—
493C22×D3—61no—
494C22×D3—61no—
495C22×D3—61no—
496C22×D3—61no—
497C22×D3—61no—
498C22×D3—61no—
499C22×D3—61no—
500C22×D3C2×C4×D312yes—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—22no—
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—22no—
517C2×C3×C4—22no—
518C2×C3×C4—32no—
519C2×C3×C4—32no—
520C2×C3×C4—32no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
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×C4C2×C4×D312yes—
546C2×C3×C4C2×C4×D312yes—
547C2×C3×C4#23712yes—
548C2×C3×C4#23912yes—
549#67—68no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—21no—
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—32no—
569C2×Dic3—32no—
570C2×Dic3—32no—
571C2×Dic3—32no—
572C2×Dic3—62no—
573C2×Dic3—62no—
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—62no—
583C2×Dic3—61no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—121no—
590C2×Dic3—121no—
591C2×Dic3—121no—
592C2×Dic3—121no—
593C2×Dic3—121no—
594C2×Dic3—121no—
595C2×Dic3—124no—
596C2×Dic3C2×C4×D312yes—
597C2×Dic3C2×C4×D312yes—
598C2×Dic3C2×C4×D312yes—
599D12—68no—
600C4×D3—124no—
601C4×D3—124no—
602C4×D3—124no—
603C4×D3—124no—
604C4×D3—124no—
605C4×D3—124no—
606C4×D3—124no—
607C4×D3—128no—
608C4×D3—128no—
609C4×D3—128no—
610C2×C32C2×#11711yescharacteristic
611C2×C32C4×#4111yescharacteristic
612C2×C32#51811yescharacteristic
613C2×C32#55111yescharacteristic
614C2×C32#55111yescharacteristic
615C2×C32#55311yescharacteristic
616C2×C32#55311yescharacteristic
617C3⋊D3—24no—
618C3×D3—42no—
619C24—31no—
620C24—91no—
621C2×D4—94no—
622C2×D4—182no—
623C2×D4—182no—
624C22×C4—31no—
625C22×C4—31no—
626C22×C4—31no—
627C22×C4—31no—
628C22×C4—31no—
629C22×C4—31no—
630C22×C4—31no—
631C22×C4—94no—
632C22×C4—91no—
633C22×C4—91no—
634C22×C4—94no—
635C22×C4—91no—
636C22×C4—182no—
637C22×C4—182no—
638C22×C4—182no—
639C22×C4—182no—
640C22×C4—361no—
641C22×C4—361no—
642C22×C4—361no—
643C22×C4—361no—
644C22×C4—361no—
645C22×C4—361no—
646C22×C4C2×D3211yescharacteristic
647C22×C4C2×D3211yescharacteristic
648C22×C4C2×D3211yescharacteristic
649C4⋊C4—34no—
650C4⋊C4—121no—
651C4⋊C4—121no—
652C22⋊C4—34no—
653C22⋊C4—62no—
654C22⋊C4—94no—
655C22⋊C4—121no—
656C22⋊C4—182no—
657C22⋊C4—182no—
658C22⋊C4—182no—
659C22⋊C4—361no—
660C42—62no—
661C42—94no—
662C42—121no—
663C42—182no—
664C42—361no—
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—62no—
673C22×C3—62no—
674C22×C3—62no—
675C22×C3—121no—
676C22×C3—121no—
677C22×C3—121no—
678C22×C3—121no—
679C22×C3C22×C4×D311yescharacteristic
680C22×C3C22×C4×D311yescharacteristic
681C22×C3C2×#23711yescharacteristic
682C22×C3#100411yescharacteristic
683C22×C3#100411yescharacteristic
684C22×C3C2×#23911yescharacteristic
685C22×C3D3×#4111yescharacteristic
686C22×C3D3×#4111yescharacteristic
687C22×C3D3×#4111yescharacteristic
688C22×C3D3×#4111yescharacteristic
689C22×C3D3×#4111yescharacteristic
690C22×C3D3×#4111yescharacteristic
691C22×C3#100911yescharacteristic
692C22×C3#100911yescharacteristic
693C2×D3—22no—
694C2×D3—22no—
695C2×D3—22no—
696C2×D3—34no—
697C2×D3—34no—
698C2×D3—41no—
699C2×D3—41no—
700C2×D3—41no—
701C2×D3—41no—
702C2×D3—64no—
703C2×D3—64no—
704C2×D3—64no—
705C2×D3—64no—
706C2×D3—64no—
707C2×D3—64no—
708C2×D3—64no—
709C2×D3—62no—
710C2×D3—62no—
711C2×D3—62no—
712C2×D3—62no—
713C2×D3—62no—
714C2×D3—62no—
715C2×D3—62no—
716C2×D3—62no—
717C2×D3—62no—
718C2×D3—62no—
719C2×D3—62no—
720C2×D3—62no—
721C3×C4—22no—
722C3×C4—22no—
723C3×C4—22no—
724C3×C4—22no—
725C3×C4—42no—
726C3×C4—42no—
727C3×C4—42no—
728C3×C4—41no—
729C3×C4—41no—
730C3×C4—62no—
731C3×C4—62no—
732C3×C4—62no—
733C3×C4—121no—
734C3×C4—121no—
735C3×C4—121no—
736C3×C4—121no—
737Dic3—22no—
738Dic3—22no—
739Dic3—22no—
740Dic3—41no—
741Dic3—41no—
742Dic3—41no—
743Dic3—41no—
744Dic3—62no—
745Dic3—62no—
746Dic3—62no—
747Dic3—62no—
748Dic3—122no—
749Dic3—122no—
750Dic3—122no—
751Dic3—121no—
752Dic3—121no—
753C32#235311yescharacteristic, complemented, Sylow
754C23—32no—
755C23—61no—
756C23—61no—
757C23—61no—
758C23—61no—
759C23—61no—
760C23—61no—
761C23—92no—
762C23—92no—
763C23—92no—
764C23—181no—
765C23—181no—
766C23—181no—
767C23—181no—
768C23C22×D3211yescharacteristic
769D4—188no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—32no—
778C2×C4—32no—
779C2×C4—32no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—61no—
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—92no—
799C2×C4—92no—
800C2×C4—181no—
801C2×C4—181no—
802C2×C4—181no—
803C2×C4—181no—
804C2×C4—181no—
805C2×C4—181no—
806C2×C4—181no—
807C2×C4—364no—
808C2×C4—364no—
809C2×C4—364no—
810C2×C4—364no—
811C2×C4#379612yes—
812C2×C4C4×D3212yes—
813C2×C3—21no—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—21no—
819C2×C3—21no—
820C2×C3—122no—
821C2×C3D3×#11711yescharacteristic
822C2×C3D3×#11711yescharacteristic
823C2×C3C4×#23711yescharacteristic
824C2×C3#554511yescharacteristic
825C2×C3#554511yescharacteristic
826C2×C3C4×#23911yescharacteristic
827C2×C3#561411yescharacteristic
828C2×C3#563711yescharacteristic
829C2×C3#565811yescharacteristic
830C2×C3#566111yescharacteristic
831C2×C3#567911yescharacteristic
832C2×C3#569511yescharacteristic
833C2×C3#570511yescharacteristic
834C2×C3#570911yescharacteristic
835D3—42no—
836D3—68no—
837D3—64no—
838D3—64no—
839C22—62no—
840C22—62no—
841C22—62no—
842C22—94no—
843C22—121no—
844C22—121no—
845C22—121no—
846C22—121no—
847C22—182no—
848C22—182no—
849C22—182no—
850C22—182no—
851C22—182no—
852C22—182no—
853C22C2×#379611yescharacteristic
854C22C2×C4×D3211yescharacteristic
855C22#6430611yescharacteristic
856C22#6431211yescharacteristic
857C22#6431411yescharacteristic
858C22#6431411yescharacteristic
859C22#6431911yescharacteristic
860C4—22no—
861C4—22no—
862C4—41no—
863C4—62no—
864C4—62no—
865C4—62no—
866C4—121no—
867C4—121no—
868C4—121no—
869C4—121no—
870C4—182no—
871C4—182no—
872C4—361no—
873C3—21no—
874C3#7530611yescharacteristic, complemented
875C3#7583511yescharacteristic, complemented
876C2—122no—
877C2—184no—
878C2C4×#379611yescharacteristic
879C2#1059415311yescharacteristic
880C2#1059416411yescharacteristic
881C2#1059425611yescharacteristic
882C2#1059447311yescharacteristic
883C2#1059448911yescharacteristic
884C2#1059460211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC22×#626C22
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
2. C3⋊D3×#95C2semidirect
3. C3×#4670C2semidirect
4. C3×#4655C2semidirect
7. Dic3×(C2×D3)⋊C4C2semidirect
8. #10591362C2semidirect
9. #10591325C2semidirect
10. #10591307C2semidirect
11. C4×#3722C2semidirect
12. #10591262C2semidirect
13. #10591260C2semidirect
14. #10591248C2semidirect
15. #10591239C2semidirect
39. #63881C4semidirect
72. #4670D3semidirect
81. #4655D3semidirect
114. C2×D3×Dic3C2×C4semidirect
117. C3×(C2×D3)⋊C4C2×C4semidirect
120. C3×Dic3⋊C4C2×C4semidirect
130. Dic32C2×C4semidirect
381. (C2×D3)⋊C4C4×D3semidirect
384. Dic3⋊C4C4×D3semidirect
753. C32#2353semidirect
874. C3#75306semidirect
875. C3#75835semidirect

Maximal subgroups

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

subgroupindex
C2×#638812
C3⋊D3×#952
C3×#46702
C3×#46552
#105913872
Dic3×(C2×D3)⋊C42
#105913622
#105913252
#105913072
C4×#37222
#105912622
#105912602
#105912482
#105912392
#758353
#753063