Finite Group Databasebeta

← #11807569

Subgroups — #11807569

Order 1152.

1233 conjugacy classes of subgroups.

The subgroup lattice has 887 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63966C211yesmaximal, characteristic
2#10592656C211yesmaximal, characteristic
3C3×#4945C211yesmaximal, characteristic, complemented
4C3×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
5#10591722C211yesmaximal, characteristic
6#10591701C211yesmaximal, characteristic, complemented
7Dic3×#217C211yesmaximal, characteristic, complemented
8#10591332C211yesmaximal, characteristic, complemented
9C4×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
10#10591289C211yesmaximal, characteristic, complemented
11#10591259C211yesmaximal, characteristic, complemented
12#10591251C211yesmaximal, characteristic, complemented
13#10591241C211yesmaximal, characteristic, complemented
14#10591233C211yesmaximal, characteristic, complemented
15#10591233C211yesmaximal, characteristic, complemented
16#75488—31nomaximal
17#73478—31nomaximal
18C22×#638C2211yescharacteristic
19C23×C3×Dic3C2211yescharacteristic
20C22×#624C2211yescharacteristic
21C2×C32×C22⋊C4C2211yescharacteristic
22C2×#3757C2211yescharacteristic
23C2×#3752C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×#3750C2211yescharacteristic
26C2×C4×C3⋊Dic3C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34#63966C418yescomplemented
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×Dic32C2211yescharacteristic
42C2×Dic32C2211yescharacteristic
43C2×Dic32C2211yescharacteristic
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×#929—31no—
55C2×#886—31no—
56C3×#388—31no—
57C3×C4×C22⋊C4—31no—
58C4×#217—31no—
59#4990—31no—
60Dic3×C4⋊C4—31no—
61#4957—31no—
62#4957—31no—
63#4957—61no—
64#4956—31no—
65#4956—31no—
66#4951—31no—
67#4945D311yescharacteristic, complemented
68#4944—31no—
69Dic3×C22⋊C4—31no—
70Dic3×C22⋊C4D311yescharacteristic, complemented
71#4940—31no—
72C4×(C2×D3)⋊C4—31no—
73C4×(C2×D3)⋊C4—31no—
74C4×C4⋊Dic3—31no—
75#4933—31no—
76C4×Dic3⋊C4—31no—
77#4670—31no—
78#4669—31no—
79#4666—31no—
80#4666—31no—
81#4654—31no—
82#4653—31no—
83#4652—31no—
84#4649—31no—
85C24×C32C2311yescharacteristic
86C23×C3⋊D3C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C2×#638—41no—
90C2×#638—41no—
91C2×#638C2×C414yes—
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3×Dic3—41no—
96C22×C3×Dic3—41no—
97C22×C3×Dic3C2×C414yescomplemented
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—
109C32×C22⋊C4—22no—
110#3757—22no—
111#3752—22no—
112#3752—22no—
113#3750—41no—
114C4×C3⋊Dic3—41no—
115C3×#217—22no—
116C3×#217—22no—
117C3×#217C2×C414yescomplemented
118C3×Dic3⋊C4—22no—
119C3×C4×Dic3—22no—
120C3×C4×Dic3—41no—
121C3×C4×Dic3—41no—
122Dic3⋊Dic3—22no—
123Dic3⋊Dic3C2×C414yescomplemented
124Dic3⋊Dic3C2×C414yescomplemented
125#3722—41no—
126#3722C2×C414yes—
127#3722C2×C414yes—
128Dic32—22no—
129Dic32—41no—
130Dic32—41no—
131#2374—91noSylow
132C23×C3×C4—31no—
133C22×#67—31no—
134C22×#67—31no—
135C22×#67—61no—
136C23×Dic3C2×D311yescharacteristic
137C22×C4×D3—31no—
138C22×C4×D3—31no—
139C2×C3×C4⋊C4—31no—
140C2×C3×C22⋊C4—21no—
141C2×C3×C22⋊C4—31no—
142C2×C3×C22⋊C4—31no—
143C2×C3×C22⋊C4—31no—
144C2×C3×C22⋊C4C2×D311yescharacteristic
145C2×C3×C22⋊C4C2×D311yescharacteristic
146C2×C3×C42—31no—
147C2×C3×C42—31no—
148C2×C3×C42—31no—
149C2×#217—31no—
150C2×#217—31no—
151C2×#217—61no—
152C2×#217C2×D311yescharacteristic
153C2×#217C2×D311yescharacteristic
154C2×#217C2×D311yescharacteristic
155#929—38no—
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×C4⋊Dic3—31no—
169C2×C4⋊Dic3—31no—
170C2×C4⋊Dic3—31no—
171C2×Dic3⋊C4—31no—
172C2×Dic3⋊C4—31no—
173C2×Dic3⋊C4—31no—
174C2×Dic3⋊C4—31no—
175C2×Dic3⋊C4—31no—
176C2×Dic3⋊C4—61no—
177C2×Dic3⋊C4C2×D311yescharacteristic
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—31no—
185C2×C4×Dic3—31no—
186C2×C4×Dic3—61no—
187C2×C4×Dic3C2×D311yescharacteristic
188C2×C4×Dic3C2×D311yescharacteristic
189C2×C4×Dic3C2×D311yescharacteristic
190#886—38no—
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—31no—
207C3⋊#95C2×D311yescharacteristic
208C3⋊#95C2×D311yescharacteristic
209C3⋊#95C2×D311yescharacteristic
210C3⋊#95C2×D311yescharacteristic
211C23×C32—21no—
212C23×C32—21no—
213C23×C32—21no—
214C23×C32—21no—
215C23×C32—21no—
216C23×C32—21no—
217C23×C32C22×C412yes—
218C23×C32C2411yescharacteristic
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#4112yes—
232#638—44no—
233C2×C3⋊Dic3—21no—
234C2×C3⋊Dic3—21no—
235C2×C3⋊Dic3—21no—
236C2×C3⋊Dic3—21no—
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3C22×C412yes—
241C2×C3⋊Dic3#4112yes—
242C2×C3×Dic3—21no—
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—44no—
261C2×C3×Dic3C22×C412yes—
262C2×C3×Dic3C22×C412yes—
263C2×C3×Dic3C22×C412yes—
264C2×C3×Dic3C22×C412yes—
265C2×C3×Dic3#4112yes—
266C2×C3×Dic3#4112yes—
267#624—44no—
268C2×#123—91no—
269#390—91no—
270#388—31no—
271#388—91no—
272#388—91no—
273#388—91no—
274#387—91no—
275#387—91no—
276#386—91no—
277C4×C4⋊C4—91no—
278C4×C4⋊C4—91no—
279C4×C22⋊C4—31no—
280C4×C22⋊C4—91no—
281C4×C22⋊C4—91no—
282C4×C22⋊C4—91no—
283C24×C3—21no—
284C24×C3C22×D311yescharacteristic
285C24×C3C22×D311yescharacteristic
286C23×D3—31no—
287C23×D3—31no—
288C23×D3—61no—
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—34no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—121no—
301C22×C3×C4—121no—
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C2×#67—34no—
307C2×#67—34no—
308C2×#67—64no—
309C2×#67—121no—
310C2×#67—121no—
311C2×#67—121no—
312C2×#67—121no—
313C2×#67—122no—
314C2×#67—122no—
315C22×Dic3—31no—
316C22×Dic3—31no—
317C22×Dic3—31no—
318C22×Dic3—31no—
319C22×Dic3—31no—
320C22×Dic3—31no—
321C22×Dic3—41no—
322C22×Dic3—41no—
323C22×Dic3—61no—
324C22×Dic3—61no—
325C22×Dic3—61no—
326C22×Dic3C4×D314yescomplemented
327C22×Dic3C22×D311yescharacteristic
328C22×Dic3C22×D311yescharacteristic
329C22×Dic3C22×D311yescharacteristic
330C22×Dic3C22×D311yescharacteristic
331C22×Dic3C22×D311yescharacteristic
332C22×Dic3C22×D311yescharacteristic
333C22×Dic3C22×D311yescharacteristic
334C22×Dic3C22×D311yescharacteristic
335C2×C4×D3—62no—
336C2×C4×D3—62no—
337C2×C4×D3—62no—
338C2×C4×D3—62no—
339C2×C4×D3—121no—
340C2×C4×D3—121no—
341C3×C4⋊C4—62no—
342C3×C22⋊C4—22no—
343C3×C22⋊C4—22no—
344C3×C22⋊C4—34no—
345C3×C22⋊C4—42no—
346C3×C22⋊C4—62no—
347C3×C22⋊C4—62no—
348C3×C42—62no—
349C3×C42—121no—
350C3×C42—121no—
351#217—22no—
352#217—22no—
353#217—62no—
354#217—62no—
355#217—122no—
356#217C4×D314yescomplemented
357(C2×D3)⋊C4—34no—
358(C2×D3)⋊C4—34no—
359(C2×D3)⋊C4—34no—
360(C2×D3)⋊C4—34no—
361(C2×D3)⋊C4—62no—
362(C2×D3)⋊C4—62no—
363(C2×D3)⋊C4—62no—
364(C2×D3)⋊C4—62no—
365(C2×D3)⋊C4—122no—
366(C2×D3)⋊C4—122no—
367(C2×D3)⋊C4—121no—
368(C2×D3)⋊C4—121no—
369C4⋊Dic3—34no—
370C4⋊Dic3—34no—
371C4⋊Dic3—62no—
372Dic3⋊C4—22no—
373Dic3⋊C4—34no—
374Dic3⋊C4—34no—
375Dic3⋊C4—62no—
376Dic3⋊C4—121no—
377Dic3⋊C4—121no—
378Dic3⋊C4—122no—
379C4×Dic3—22no—
380C4×Dic3—41no—
381C4×Dic3—41no—
382C4×Dic3—62no—
383C4×Dic3—62no—
384C4×Dic3—121no—
385C4×Dic3—121no—
386C4×Dic3—121no—
387C4×Dic3—121no—
388C4×Dic3—121no—
389C4×Dic3—121no—
390C4×Dic3—122no—
391C22×C32—22no—
392C22×C32—22no—
393C22×C32—22no—
394C22×C32—41no—
395C22×C32—41no—
396C22×C32—41no—
397C22×C32—41no—
398C22×C32C23×C411yescharacteristic
399C22×C32C2×#4111yescharacteristic
400C22×C32C2×#4111yescharacteristic
401C22×C32C2×#4111yescharacteristic
402C22×C32C2×#4111yescharacteristic
403C22×C32H(5,𝔽2)11yescharacteristic
404C22×C32H(5,𝔽2)11yescharacteristic
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—
414C3⋊Dic3—22no—
415C3⋊Dic3—22no—
416C3⋊Dic3—41no—
417C3×Dic3—22no—
418C3×Dic3—22no—
419C3×Dic3—22no—
420C3×Dic3—22no—
421C3×Dic3—22no—
422C3×Dic3—22no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C22×D4—91no—
426C23×C4—31no—
427C23×C4—91no—
428#123—98no—
429C2×C4⋊C4—31no—
430C2×C4⋊C4—91no—
431C2×C4⋊C4—91no—
432C2×C4⋊C4—91no—
433C2×C4⋊C4—91no—
434C2×C22⋊C4—31no—
435C2×C22⋊C4—31no—
436C2×C22⋊C4—31no—
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⋊C4D3211yescharacteristic
444C2×C42—31no—
445C2×C42—31no—
446C2×C42—31no—
447C2×C42—91no—
448C2×C42—91no—
449C2×C42—91no—
450C2×C42—91no—
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—
461C23×C3—21no—
462C23×C3—21no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—22no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3—41no—
479C23×C3—41no—
480C23×C3—41no—
481C23×C3C2×C4×D312yes—
482C23×C3C2×C4×D312yes—
483C23×C3C23×D311yescharacteristic
484C23×C3C23×D311yescharacteristic
485C22×D3—32no—
486C22×D3—32no—
487C22×D3—62no—
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—61no—
499C22×D3—61no—
500C22×D3—121no—
501C22×D3—121no—
502C22×D3—121no—
503C22×D3—121no—
504C22×D3—121no—
505C22×D3—121no—
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—22no—
517C2×C3×C4—32no—
518C2×C3×C4—32no—
519C2×C3×C4—32no—
520C2×C3×C4—32no—
521C2×C3×C4—32no—
522C2×C3×C4—32no—
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—61no—
546C2×C3×C4—124no—
547C2×C3×C4#23512yes—
548C2×C3×C4#23712yes—
549#67—124no—
550#67—124no—
551#67—128no—
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—21no—
569C2×Dic3—21no—
570C2×Dic3—32no—
571C2×Dic3—32no—
572C2×Dic3—32no—
573C2×Dic3—32no—
574C2×Dic3—44no—
575C2×Dic3—62no—
576C2×Dic3—62no—
577C2×Dic3—62no—
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—61no—
592C2×Dic3—61no—
593C2×Dic3—121no—
594C2×Dic3—121no—
595C2×Dic3—121no—
596C2×Dic3—121no—
597C2×Dic3—121no—
598C2×Dic3C2×C4×D312yes—
599C2×Dic3C2×C4×D312yes—
600C2×Dic3C2×C4×D312yes—
601C2×Dic3C2×C4×D312yes—
602C2×Dic3#23512yes—
603C2×Dic3#23712yes—
604C4×D3—124no—
605C4×D3—124no—
606C2×C32—42no—
607C2×C32C4×#4111yescharacteristic
608C2×C32C4×#4111yescharacteristic
609C2×C32#51811yescharacteristic
610C2×C32#55111yescharacteristic
611C2×C32#55311yescharacteristic
612C2×C32#55311yescharacteristic
613C2×C32#55911yescharacteristic
614C3⋊D3—42no—
615C24—91no—
616C24C2×D3211yescharacteristic
617C2×D4—94no—
618C2×D4—361no—
619C2×D4—361no—
620C22×C4—31no—
621C22×C4—31no—
622C22×C4—31no—
623C22×C4—31no—
624C22×C4—31no—
625C22×C4—31no—
626C22×C4—34no—
627C22×C4—31no—
628C22×C4—31no—
629C22×C4—91no—
630C22×C4—91no—
631C22×C4—91no—
632C22×C4—121no—
633C22×C4—121no—
634C22×C4—182no—
635C22×C4—182no—
636C22×C4—361no—
637C22×C4C2×D3211yescharacteristic
638C22×C4C2×D3211yescharacteristic
639C4⋊C4—62no—
640C4⋊C4—94no—
641C4⋊C4—94no—
642C4⋊C4—182no—
643C4⋊C4—361no—
644C22⋊C4—22no—
645C22⋊C4—34no—
646C22⋊C4—62no—
647C22⋊C4—62no—
648C22⋊C4—94no—
649C22⋊C4—94no—
650C22⋊C4—182no—
651C22⋊C4—182no—
652C22⋊C4—182no—
653C22⋊C4—361no—
654C42—62no—
655C42—121no—
656C42—121no—
657C42—182no—
658C42—361no—
659C42—361no—
660C42—361no—
661C22×C3—22no—
662C22×C3—22no—
663C22×C3—22no—
664C22×C3—22no—
665C22×C3—22no—
666C22×C3—22no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—42no—
675C22×C3—42no—
676C22×C3—42no—
677C22×C3—41no—
678C22×C3—41no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—81no—
686C22×C3—81no—
687C22×C3—81no—
688C22×C3—81no—
689C22×C3C22×C4×D311yescharacteristic
690C22×C3C22×C4×D311yescharacteristic
691C22×C3C2×#23511yescharacteristic
692C22×C3C2×#23511yescharacteristic
693C22×C3C2×#23711yescharacteristic
694C22×C3C2×#23711yescharacteristic
695C22×C3#100411yescharacteristic
696C22×C3#100411yescharacteristic
697C22×C3D3×#4111yescharacteristic
698C22×C3D3×#4111yescharacteristic
699C22×C3D3×#4111yescharacteristic
700C22×C3D3×#4111yescharacteristic
701C22×C3#100911yescharacteristic
702C22×C3#100911yescharacteristic
703C2×D3—62no—
704C2×D3—62no—
705C2×D3—62no—
706C2×D3—62no—
707C2×D3—62no—
708C2×D3—62no—
709C2×D3—122no—
710C2×D3—122no—
711C2×D3—122no—
712C2×D3—121no—
713C2×D3—121no—
714C2×D3—121no—
715C2×D3—121no—
716C2×D3—121no—
717C2×D3—121no—
718C2×D3—121no—
719C2×D3—121no—
720C2×D3—241no—
721C2×D3—241no—
722C2×D3—241no—
723C2×D3—241no—
724C3×C4—22no—
725C3×C4—22no—
726C3×C4—42no—
727C3×C4—41no—
728C3×C4—41no—
729C3×C4—62no—
730C3×C4—62no—
731C3×C4—62no—
732C3×C4—62no—
733C3×C4—62no—
734C3×C4—62no—
735C3×C4—81no—
736C3×C4—121no—
737C3×C4—121no—
738Dic3—22no—
739Dic3—22no—
740Dic3—22no—
741Dic3—22no—
742Dic3—22no—
743Dic3—22no—
744Dic3—41no—
745Dic3—41no—
746Dic3—64no—
747Dic3—62no—
748Dic3—62no—
749Dic3—62no—
750Dic3—62no—
751Dic3—122no—
752Dic3—121no—
753Dic3—121no—
754Dic3—241no—
755C32#237411yescharacteristic, complemented, Sylow
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—92no—
763C23—181no—
764C23—181no—
765C23—181no—
766C23—181no—
767C23—181no—
768C23—181no—
769C23C4×D3212yes—
770C23C22×D3211yescharacteristic
771D4—364no—
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—32no—
781C2×C4—32no—
782C2×C4—32no—
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—61no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—92no—
802C2×C4—92no—
803C2×C4—124no—
804C2×C4—181no—
805C2×C4—181no—
806C2×C4—181no—
807C2×C4—181no—
808C2×C4—181no—
809C2×C4—181no—
810C2×C4—181no—
811C2×C4—364no—
812C2×C4#380412yes—
813C2×C3—21no—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—21no—
819C2×C3—21no—
820C2×C3—42no—
821C2×C3—42no—
822C2×C3—82no—
823C2×C3C4×#23511yescharacteristic
824C2×C3#548611yescharacteristic
825C2×C3#552111yescharacteristic
826C2×C3#552211yescharacteristic
827C2×C3C4×#23711yescharacteristic
828C2×C3C4×#23711yescharacteristic
829C2×C3#554011yescharacteristic
830C2×C3#555611yescharacteristic
831C2×C3#555811yescharacteristic
832C2×C3#555911yescharacteristic
833C2×C3#561811yescharacteristic
834C2×C3#565811yescharacteristic
835C2×C3#568111yescharacteristic
836C2×C3#570911yescharacteristic
837D3—122no—
838D3—122no—
839D3—242no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—41no—
844C22—41no—
845C22—41no—
846C22—41no—
847C22—182no—
848C22—182no—
849C22—182no—
850C22—361no—
851C22—361no—
852C22—361no—
853C22—361no—
854C22C2×C4×D3211yescharacteristic
855C22D3×#23511yescharacteristic
856C22D3×#23711yescharacteristic
857C22#6431211yescharacteristic
858C22#6431411yescharacteristic
859C22#6431411yescharacteristic
860C22C2×#380411yescharacteristic
861C4—22no—
862C4—41no—
863C4—62no—
864C4—62no—
865C4—62no—
866C4—62no—
867C4—62no—
868C4—62no—
869C4—121no—
870C4—121no—
871C4—182no—
872C4—182no—
873C4—361no—
874C3—21no—
875C3#7347811yescharacteristic, complemented
876C3#7548811yescharacteristic, complemented
877C2—42no—
878C2—362no—
879C2#1059404811yescharacteristic
880C2#1059418211yescharacteristic
881C2#1059420311yescharacteristic
882C2#1059429911yescharacteristic
883C2C4×#380411yescharacteristic
884C2#1059519311yescharacteristic
885C2#1059521011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC22×#638C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2374
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C3×#4945C2semidirect
4. C3×Dic3×C22⋊C4C2semidirect
6. #10591701C2semidirect
7. Dic3×#217C2semidirect
8. #10591332C2semidirect
9. C4×Dic3⋊Dic3C2semidirect
10. #10591289C2semidirect
11. #10591259C2semidirect
12. #10591251C2semidirect
13. #10591241C2semidirect
14. #10591233C2semidirect
15. #10591233C2semidirect
34. #63966C4semidirect
67. #4945D3semidirect
70. Dic3×C22⋊C4D3semidirect
97. C22×C3×Dic3C2×C4semidirect
117. C3×#217C2×C4semidirect
123. Dic3⋊Dic3C2×C4semidirect
124. Dic3⋊Dic3C2×C4semidirect
326. C22×Dic3C4×D3semidirect
356. #217C4×D3semidirect
755. C32#2374semidirect
875. C3#73478semidirect
876. C3#75488semidirect

Maximal subgroups

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

subgroupindex
C2×#639662
#105926562
C3×#49452
C3×Dic3×C22⋊C42
#105917222
#105917012
Dic3×#2172
#105913322
C4×Dic3⋊Dic32
#105912892
#105912592
#105912512
#105912412
#105912332
#754883
#734783