Finite Group Databasebeta

← #11805797

Subgroups — #11805797

Order 1152.

1305 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63904C211yesmaximal, characteristic
2#10592365C211yesmaximal, characteristic, complemented
3C3×#4664C211yesmaximal, characteristic, complemented
4C3×#4652C211yesmaximal, characteristic, complemented
5#10591387C211yesmaximal, characteristic
6#10591370C211yesmaximal, characteristic, complemented
7#10591367C211yesmaximal, characteristic, complemented
8#10591284C211yesmaximal, characteristic, complemented
9#10591283C211yesmaximal, characteristic, complemented
10C4×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
11#10591275C211yesmaximal, characteristic
12#10591252C211yesmaximal, characteristic, complemented
13#10591248C211yesmaximal, characteristic, complemented
14#10591233C211yesmaximal, characteristic, complemented
15#10591192C211yesmaximal, characteristic, complemented
16#75306—31nomaximal
17#74123—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×#626C2211yescharacteristic
21C22×#624C2211yescharacteristic
22C22×#624C2211yescharacteristic
23C2×#3752C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
26C2×C4×C3⋊Dic3C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×Dic3⋊Dic3C2211yescharacteristic
33C2×#3722C2211yescharacteristic
34C2×(C2×D3)⋊Dic3C2211yescharacteristic
35C2×(C2×D3)⋊Dic3C2211yescharacteristic
36C2×(C2×D3)⋊Dic3C2211yescharacteristic
37C2×Dic32C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39#63904C418yescomplemented
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×C4×#67—31no—
55C2×#893—31no—
56C3×#387—31no—
57C3×#381—31no—
58C4×#217—31no—
59#4990—31no—
60#4987—31no—
61#4980—31no—
62#4956—31no—
63#4956—31no—
64#4945—31no—
65#4945—31no—
66C4×(C2×D3)⋊C4—31no—
67C4×(C2×D3)⋊C4—31no—
68#4670—31no—
69#4667—31no—
70#4666—31no—
71#4666—31no—
72#4666—31no—
73#4666—61no—
74#4665—31no—
75#4665—31no—
76#4664D311yescharacteristic, complemented
77D3×#95—31no—
78D3×#95—31no—
79#4652—31no—
80#4652D311yescharacteristic, complemented
81#4651—31no—
82#4651—31no—
83#4648—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—41no—
96C22×C3×Dic3C2311yescharacteristic
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×D3C2×C414yescomplemented
106C2×#626—22no—
107C2×#626—22no—
108C2×#626C2×C414yes—
109C2×#624—22no—
110C2×#624—22no—
111C2×#624—41no—
112C2×#624—41no—
113C2×#624—41no—
114C2×#624C2×C414yes—
115#3752—22no—
116#3752C2×C414yes—
117C4×C3⋊Dic3—22no—
118C4×C3⋊Dic3—41no—
119C3×(C2×D3)⋊C4—41no—
120C3×(C2×D3)⋊C4—41no—
121C3×Dic3⋊C4—41no—
122C3×Dic3⋊C4C2×C414yescomplemented
123C3×C4×Dic3—41no—
124Dic3⋊Dic3—41no—
125#3722—22no—
126(C2×D3)⋊Dic3—22no—
127(C2×D3)⋊Dic3—22no—
128(C2×D3)⋊Dic3C2×C414yescomplemented
129Dic32—22no—
130Dic32C2×C414yescomplemented
131#2353—91noSylow
132C23×C3×C4—31no—
133C22×#67—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—61no—
142C22×C4×D3C2×D311yescharacteristic
143C2×C3×C4⋊C4—31no—
144C2×C3×C4⋊C4—31no—
145C2×C3×C22⋊C4—31no—
146C2×C3×C22⋊C4—31no—
147C2×C3×C42—31no—
148C2×#217—31no—
149C2×#217—31no—
150C2×#217—31no—
151C4×#67—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)⋊C4—31no—
160C2×(C2×D3)⋊C4—31no—
161C2×(C2×D3)⋊C4—61no—
162C2×(C2×D3)⋊C4—61no—
163C2×(C2×D3)⋊C4C2×D311yescharacteristic
164C2×(C2×D3)⋊C4C2×D311yescharacteristic
165C2×C4⋊Dic3—31no—
166C2×Dic3⋊C4—31no—
167C2×Dic3⋊C4C2×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×Dic3—31no—
176C2×C4×Dic3—31no—
177C2×C4×Dic3—61no—
178C2×C4×Dic3—61no—
179C2×C4×Dic3C2×D311yescharacteristic
180#893—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⋊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×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⋊Dic3C22×C412yes—
243C2×C3⋊Dic3#4112yes—
244C4×C3⋊D3—44no—
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×Dic3#4112yes—
266C3×C4×D3—44no—
267#626—28no—
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—31no—
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—34no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—121no—
302C22×C3×C4—121no—
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C22×D311yescharacteristic
309C2×#67—34no—
310C2×#67—62no—
311C2×#67—62no—
312C22×Dic3—31no—
313C22×Dic3—31no—
314C22×Dic3—31no—
315C22×Dic3—31no—
316C22×Dic3—31no—
317C22×Dic3—31no—
318C22×Dic3—61no—
319C22×Dic3—61no—
320C22×Dic3—61no—
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—41no—
334C2×C4×D3—41no—
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—64no—
343C2×C4×D3—62no—
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—122no—
354C2×C4×D3C4×D314yescomplemented
355C3×C4⋊C4—34no—
356C3×C4⋊C4—121no—
357C3×C22⋊C4—121no—
358C3×C22⋊C4—121no—
359C3×C42—121no—
360#217—34no—
361#217—62no—
362#217—62no—
363(C2×D3)⋊C4—34no—
364(C2×D3)⋊C4—34no—
365(C2×D3)⋊C4—34no—
366(C2×D3)⋊C4—41no—
367(C2×D3)⋊C4—41no—
368(C2×D3)⋊C4—64no—
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—64no—
375(C2×D3)⋊C4—62no—
376C4⋊Dic3—121no—
377Dic3⋊C4—41no—
378Dic3⋊C4—121no—
379Dic3⋊C4C4×D314yescomplemented
380C4×Dic3—34no—
381C4×Dic3—34no—
382C4×Dic3—41no—
383C4×Dic3—62no—
384C4×Dic3—62no—
385C4×Dic3—62no—
386C4×Dic3—62no—
387C4×Dic3—122no—
388C4×Dic3—121no—
389C4×Dic3—121no—
390C4×Dic3—122no—
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#11714yes—
405C2×C3×D3—22no—
406C2×C3×D3—22no—
407C2×C3×D3—22no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C32×C4—22no—
413C32×C4—41no—
414C32×C4—41no—
415C3⋊Dic3—22no—
416C3⋊Dic3—22no—
417C3⋊Dic3—41no—
418C3×Dic3—22no—
419C3×Dic3—22no—
420C3×Dic3—22no—
421C3×Dic3—22no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C22×D4—91no—
426C23×C4—31no—
427C23×C4—91no—
428C23×C4—91no—
429C23×C4—91no—
430C4×D4—98no—
431C2×C4⋊C4—31no—
432C2×C4⋊C4—31no—
433C2×C4⋊C4—91no—
434C2×C22⋊C4—31no—
435C2×C22⋊C4—31no—
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×C42—31no—
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—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#95D3211yescharacteristic
461C23×C3—21no—
462C23×C3—32no—
463C23×C3—61no—
464C23×C3—61no—
465C23×C3—61no—
466C23×C3—61no—
467C23×C3—61no—
468C23×C3—61no—
469C23×C3C23×D311yescharacteristic
470C23×C3C23×D311yescharacteristic
471C22×D3—21no—
472C22×D3—21no—
473C22×D3—21no—
474C22×D3—21no—
475C22×D3—21no—
476C22×D3—21no—
477C22×D3—32no—
478C22×D3—32no—
479C22×D3—32no—
480C22×D3—32no—
481C22×D3—32no—
482C22×D3—32no—
483C22×D3—62no—
484C22×D3—62no—
485C22×D3—62no—
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—121no—
495C22×D3—121no—
496C22×D3—121no—
497C22×D3—121no—
498C22×D3C2×C4×D312yes—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—21no—
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—22no—
518C2×C3×C4—32no—
519C2×C3×C4—32no—
520C2×C3×C4—32no—
521C2×C3×C4—32no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
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×C4—124no—
546C2×C3×C4C2×C4×D312yes—
547C2×C3×C4C2×C4×D312yes—
548#67—68no—
549C2×Dic3—21no—
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—32no—
567C2×Dic3—32no—
568C2×Dic3—32no—
569C2×Dic3—32no—
570C2×Dic3—62no—
571C2×Dic3—62no—
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×Dic3C2×C4×D312yes—
594C2×Dic3C2×C4×D312yes—
595C2×Dic3C2×C4×D312yes—
596C2×Dic3#23912yes—
597D12—68no—
598C4×D3—44no—
599C4×D3—124no—
600C4×D3—124no—
601C4×D3—124no—
602C4×D3—124no—
603C4×D3—124no—
604C4×D3—124no—
605C4×D3—128no—
606C2×C32C2×#11711yescharacteristic
607C2×C32C4×#4111yescharacteristic
608C2×C32#51811yescharacteristic
609C2×C32#55111yescharacteristic
610C2×C32#55111yescharacteristic
611C2×C32#55311yescharacteristic
612C2×C32#55311yescharacteristic
613C3⋊D3—24no—
614C3×D3—42no—
615C24—31no—
616C24—91no—
617C2×D4—94no—
618C2×D4—182no—
619C2×D4—182no—
620C22×C4—31no—
621C22×C4—31no—
622C22×C4—31no—
623C22×C4—31no—
624C22×C4—34no—
625C22×C4—31no—
626C22×C4—31no—
627C22×C4—31no—
628C22×C4—94no—
629C22×C4—91no—
630C22×C4—91no—
631C22×C4—91no—
632C22×C4—121no—
633C22×C4—121no—
634C22×C4—182no—
635C22×C4—182no—
636C22×C4—182no—
637C22×C4—182no—
638C22×C4—361no—
639C22×C4—361no—
640C22×C4—361no—
641C22×C4—361no—
642C22×C4C2×D3211yescharacteristic
643C22×C4C2×D3211yescharacteristic
644C22×C4C2×D3211yescharacteristic
645C4⋊C4—34no—
646C4⋊C4—121no—
647C4⋊C4—361no—
648C22⋊C4—94no—
649C22⋊C4—94no—
650C22⋊C4—121no—
651C22⋊C4—121no—
652C22⋊C4—182no—
653C22⋊C4—182no—
654C22⋊C4—182no—
655C22⋊C4—182no—
656C42—94no—
657C42—121no—
658C42—182no—
659C42—182no—
660C42—361no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—62no—
669C22×C3—62no—
670C22×C3—62no—
671C22×C3—121no—
672C22×C3—121no—
673C22×C3—121no—
674C22×C3—121no—
675C22×C3C22×C4×D311yescharacteristic
676C22×C3C22×C4×D311yescharacteristic
677C22×C3#100411yescharacteristic
678C22×C3#100411yescharacteristic
679C22×C3#100411yescharacteristic
680C22×C3C2×#23911yescharacteristic
681C22×C3D3×#4111yescharacteristic
682C22×C3D3×#4111yescharacteristic
683C22×C3D3×#4111yescharacteristic
684C22×C3D3×#4111yescharacteristic
685C22×C3D3×#4111yescharacteristic
686C22×C3D3×#4111yescharacteristic
687C22×C3D3×#4111yescharacteristic
688C22×C3#100911yescharacteristic
689C2×D3—22no—
690C2×D3—22no—
691C2×D3—22no—
692C2×D3—34no—
693C2×D3—34no—
694C2×D3—41no—
695C2×D3—41no—
696C2×D3—41no—
697C2×D3—41no—
698C2×D3—64no—
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—62no—
711C2×D3—122no—
712C2×D3—122no—
713C2×D3—122no—
714C2×D3—122no—
715C2×D3—122no—
716C2×D3—122no—
717C3×C4—22no—
718C3×C4—22no—
719C3×C4—42no—
720C3×C4—42no—
721C3×C4—42no—
722C3×C4—41no—
723C3×C4—41no—
724C3×C4—41no—
725C3×C4—41no—
726C3×C4—62no—
727C3×C4—62no—
728C3×C4—62no—
729C3×C4—62no—
730C3×C4—121no—
731C3×C4—121no—
732C3×C4—121no—
733Dic3—22no—
734Dic3—22no—
735Dic3—22no—
736Dic3—22no—
737Dic3—41no—
738Dic3—41no—
739Dic3—41no—
740Dic3—64no—
741Dic3—62no—
742Dic3—62no—
743Dic3—62no—
744Dic3—62no—
745Dic3—122no—
746Dic3—122no—
747Dic3—121no—
748Dic3—121no—
749C32#235311yescharacteristic, complemented, Sylow
750C23—32no—
751C23—61no—
752C23—61no—
753C23—61no—
754C23—61no—
755C23—61no—
756C23—61no—
757C23—92no—
758C23—92no—
759C23—92no—
760C23—181no—
761C23—181no—
762C23—181no—
763C23—181no—
764C23C22×D3211yescharacteristic
765D4—188no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—32no—
775C2×C4—32no—
776C2×C4—32no—
777C2×C4—32no—
778C2×C4—61no—
779C2×C4—61no—
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—92no—
796C2×C4—92no—
797C2×C4—124no—
798C2×C4—181no—
799C2×C4—181no—
800C2×C4—181no—
801C2×C4—181no—
802C2×C4—181no—
803C2×C4—181no—
804C2×C4—181no—
805C2×C4—364no—
806C2×C4—364no—
807C2×C4—364no—
808C2×C4C4×D3212yes—
809C2×C3—21no—
810C2×C3—21no—
811C2×C3—21no—
812C2×C3—21no—
813C2×C3—21no—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—122no—
817C2×C3#548611yescharacteristic
818C2×C3D3×#11711yescharacteristic
819C2×C3D3×#11711yescharacteristic
820C2×C3#552211yescharacteristic
821C2×C3#554511yescharacteristic
822C2×C3C4×#23911yescharacteristic
823C2×C3#563711yescharacteristic
824C2×C3#565911yescharacteristic
825C2×C3#565911yescharacteristic
826C2×C3#566111yescharacteristic
827C2×C3#566111yescharacteristic
828C2×C3#566111yescharacteristic
829C2×C3#569511yescharacteristic
830C2×C3#570511yescharacteristic
831D3—42no—
832D3—64no—
833D3—64no—
834D3—124no—
835C22—62no—
836C22—62no—
837C22—62no—
838C22—94no—
839C22—121no—
840C22—121no—
841C22—121no—
842C22—121no—
843C22—182no—
844C22—182no—
845C22—182no—
846C22—182no—
847C22—182no—
848C22—182no—
849C22C2×C4×D3211yescharacteristic
850C22#6430611yescharacteristic
851C22#6430611yescharacteristic
852C22#6431211yescharacteristic
853C22#6431311yescharacteristic
854C22#6431411yescharacteristic
855C22D3×#23911yescharacteristic
856C4—22no—
857C4—41no—
858C4—41no—
859C4—62no—
860C4—62no—
861C4—62no—
862C4—62no—
863C4—121no—
864C4—121no—
865C4—121no—
866C4—182no—
867C4—182no—
868C4—361no—
869C3—21no—
870C3#7412311yescharacteristic, complemented
871C3#7530611yescharacteristic, complemented
872C2—122no—
873C2—184no—
874C2#1059399211yescharacteristic
875C2#1059422811yescharacteristic
876C2#1059422911yescharacteristic
877C2#1059425411yescharacteristic
878C2#1059436211yescharacteristic
879C2#1059446111yescharacteristic
880C2#1059465311yescharacteristic
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. #10592365C2semidirect
3. C3×#4664C2semidirect
4. C3×#4652C2semidirect
6. #10591370C2semidirect
7. #10591367C2semidirect
8. #10591284C2semidirect
9. #10591283C2semidirect
10. C4×(C2×D3)⋊Dic3C2semidirect
12. #10591252C2semidirect
13. #10591248C2semidirect
14. #10591233C2semidirect
15. #10591192C2semidirect
39. #63904C4semidirect
76. #4664D3semidirect
80. #4652D3semidirect
105. C2×C3×C4×D3C2×C4semidirect
122. C3×Dic3⋊C4C2×C4semidirect
128. (C2×D3)⋊Dic3C2×C4semidirect
130. Dic32C2×C4semidirect
354. C2×C4×D3C4×D3semidirect
379. Dic3⋊C4C4×D3semidirect
749. C32#2353semidirect
870. C3#74123semidirect
871. C3#75306semidirect

Maximal subgroups

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

subgroupindex
C2×#639042
#105923652
C3×#46642
C3×#46522
#105913872
#105913702
#105913672
#105912842
#105912832
C4×(C2×D3)⋊Dic32
#105912752
#105912522
#105912482
#105912332
#105911922
#753063
#741233