Finite Group Databasebeta

← #11807748

Subgroups — #11807748

Order 1152.

1295 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63978C211yesmaximal, characteristic
2#10592655C211yesmaximal, characteristic, complemented
3C3×#4957C211yesmaximal, characteristic, complemented
4C3×#4943C211yesmaximal, characteristic, complemented
5#10591721C211yesmaximal, characteristic, complemented
6#10591716C211yesmaximal, characteristic, complemented
7#10591704C211yesmaximal, characteristic, complemented
8#10591387C211yesmaximal, characteristic, complemented
9#10591373C211yesmaximal, characteristic, complemented
10#10591364C211yesmaximal, characteristic, complemented
11#10591331C211yesmaximal, characteristic, complemented
12#10591290C211yesmaximal, characteristic, complemented
13#10591284C211yesmaximal, characteristic, complemented
14#10591254C211yesmaximal, characteristic, complemented
15#10591194C211yesmaximal, characteristic, complemented
16#76310—31nomaximal
17#74124—31nomaximal
18C22×#638C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C2×C32×C22⋊C4C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33#63978C418yescomplemented
34C2×#3724C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×Dic32C2211yescharacteristic
44#63658C2211yescharacteristic
45#63658C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×#939—31no—
55C2×#930—31no—
56C3×#390—31no—
57C3×#381—31no—
58#5220—31no—
59#5212—31no—
60#4989—31no—
61#4978—31no—
62#4958—31no—
63#4957—31no—
64#4957—31no—
65#4957D311yescharacteristic, complemented
66#4956—31no—
67#4956—31no—
68#4956—31no—
69#4956—31no—
70#4956—61no—
71#4946—31no—
72#4945—31no—
73#4943D311yescharacteristic, complemented
74#4942—31no—
75#4940—31no—
76#4933—31no—
77#4670—31no—
78#4670—31no—
79#4668—31no—
80#4668—31no—
81#4665—31no—
82#4665—31no—
83#4654—31no—
84#4654—31no—
85C24×C32C2311yescharacteristic
86C23×C3⋊D3C2311yescharacteristic
87C23×C3×D3C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C2×#638—41no—
91C2×#638—41no—
92C2×#638C2×C414yescomplemented
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C2×C4×C3⋊D3—41no—
97C2×C4×C3⋊D3—41no—
98C2×C4×C3⋊D3—41no—
99C2×C3×#67—41no—
100C2×C3×#67—41no—
101C2×C3×#67C2×C414yescomplemented
102C22×C3×Dic3—41no—
103C22×C3×Dic3—41no—
104C22×C3×Dic3C2×C414yescomplemented
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C2×#626—41no—
113C2×#626—41no—
114C2×#626C2×C414yes—
115C2×D3×Dic3—41no—
116C2×D3×Dic3—41no—
117C2×D3×Dic3—41no—
118C32×C22⋊C4—41no—
119#3757—41no—
120#3752—41no—
121C3×#217—41no—
122C3×#217—41no—
123C3×(C2×D3)⋊C4—41no—
124C3×(C2×D3)⋊C4—41no—
125C3×Dic3⋊C4—41no—
126C3×C4×Dic3—41no—
127#3724—41no—
128Dic3⋊Dic3—41no—
129Dic3⋊Dic3—41no—
130Dic3⋊Dic3C2×C414yescomplemented
131#3722—41no—
132#3722—41no—
133#3722C2×C414yescomplemented
134(C2×D3)⋊Dic3—41no—
135(C2×D3)⋊Dic3C2×C414yescomplemented
136Dic32—41no—
137#2377—91noSylow
138C22×C3×D4—31no—
139C23×C3×C4—31no—
140C22×#67—31no—
141C22×#67—31no—
142C22×#67—31no—
143C22×#67—61no—
144C22×#67C2×D311yescharacteristic
145C23×Dic3—31no—
146C23×Dic3C2×D311yescharacteristic
147C22×D12—31no—
148C22×C4×D3—31no—
149C22×C4×D3—31no—
150C22×C4×D3—31no—
151C22×C4×D3—61no—
152C2×C3×C4⋊C4—31no—
153C2×C3×C22⋊C4—21no—
154C2×C3×C22⋊C4—31no—
155C2×C3×C22⋊C4—31no—
156C2×C3×C22⋊C4—31no—
157C2×C3×C22⋊C4—31no—
158C2×C3×C22⋊C4C2×D311yescharacteristic
159C2×C3×C22⋊C4C2×D311yescharacteristic
160C2×C3×C42—31no—
161C2×#217—31no—
162C2×#217—31no—
163C2×#217—31no—
164C2×#217—31no—
165C2×#217—61no—
166C2×#217C2×D311yescharacteristic
167C2×#217C2×D311yescharacteristic
168#939—38no—
169#930—38no—
170C2×(C2×D3)⋊C4—31no—
171C2×(C2×D3)⋊C4—31no—
172C2×(C2×D3)⋊C4—31no—
173C2×(C2×D3)⋊C4—31no—
174C2×(C2×D3)⋊C4—31no—
175C2×(C2×D3)⋊C4—31no—
176C2×(C2×D3)⋊C4—31no—
177C2×(C2×D3)⋊C4—31no—
178C2×(C2×D3)⋊C4—31no—
179C2×(C2×D3)⋊C4—31no—
180C2×(C2×D3)⋊C4—61no—
181C2×(C2×D3)⋊C4C2×D311yescharacteristic
182C2×(C2×D3)⋊C4C2×D311yescharacteristic
183C2×C4⋊Dic3—31no—
184C2×C4⋊Dic3—31no—
185C2×C4⋊Dic3—31no—
186C2×Dic3⋊C4—31no—
187C2×Dic3⋊C4—31no—
188C2×Dic3⋊C4—31no—
189C2×Dic3⋊C4—31no—
190C2×Dic3⋊C4—31no—
191C2×Dic3⋊C4C2×D311yescharacteristic
192C2×C4×Dic3—31no—
193C2×C4×Dic3—31no—
194C2×C4×Dic3C2×D311yescharacteristic
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⋊#95—31no—
208C3⋊#95—31no—
209C3⋊#95—31no—
210C3⋊#95—31no—
211C3⋊#95—61no—
212C3⋊#95—61no—
213C3⋊#95C2×D311yescharacteristic
214C3⋊#95C2×D311yescharacteristic
215C3⋊#95C2×D311yescharacteristic
216C3⋊#95C2×D311yescharacteristic
217C23×C32—21no—
218C23×C32—21no—
219C23×C32—21no—
220C23×C32—21no—
221C23×C32—21no—
222C23×C32—21no—
223C23×C32C22×C412yes—
224C23×C32C2411yescharacteristic
225C22×C3⋊D3—21no—
226C22×C3⋊D3—21no—
227C22×C3⋊D3—21no—
228C22×C3⋊D3—21no—
229C22×C3⋊D3—21no—
230C22×C3⋊D3—21no—
231C22×C3⋊D3C22×C412yes—
232C22×C3×D3—21no—
233C22×C3×D3—21no—
234C22×C3×D3—21no—
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3C22×C412yes—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245#638—44no—
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⋊Dic3C22×C412yes—
255C4×C3⋊D3—44no—
256C3×#67—44no—
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×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—44no—
276C2×C3×Dic3C22×C412yes—
277C2×C3×Dic3C22×C412yes—
278C2×C3×Dic3C22×C412yes—
279#626—44no—
280D3×Dic3—44no—
281C2×#121—91no—
282#390—31no—
283#390—91no—
284#388—91no—
285#388—91no—
286#387—91no—
287#387—91no—
288#386—91no—
289#386—91no—
290#386—91no—
291#386—91no—
292#385—91no—
293#385—91no—
294#381—31no—
295#380—91no—
296C24×C3—21no—
297C24×C3—31no—
298C24×C3C22×D311yescharacteristic
299C24×C3C22×D311yescharacteristic
300C23×D3—31no—
301C23×D3—31no—
302C23×D3—61no—
303C23×D3C22×D311yescharacteristic
304C2×C3×D4—34no—
305C2×C3×D4—121no—
306C2×C3×D4—121no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—31no—
312C22×C3×C4—34no—
313C22×C3×C4—31no—
314C22×C3×C4—31no—
315C22×C3×C4—31no—
316C22×C3×C4—31no—
317C22×C3×C4—121no—
318C22×C3×C4—121no—
319C22×C3×C4C22×D311yescharacteristic
320C22×C3×C4C22×D311yescharacteristic
321C22×C3×C4C22×D311yescharacteristic
322C22×C3×C4C22×D311yescharacteristic
323C2×#67—34no—
324C2×#67—34no—
325C2×#67—34no—
326C2×#67—41no—
327C2×#67—41no—
328C2×#67—64no—
329C2×#67—121no—
330C2×#67—121no—
331C2×#67—121no—
332C2×#67—121no—
333C2×#67—121no—
334C2×#67—121no—
335C2×#67—122no—
336C2×#67—122no—
337C2×#67C4×D314yescomplemented
338C22×Dic3—31no—
339C22×Dic3—31no—
340C22×Dic3—31no—
341C22×Dic3—31no—
342C22×Dic3—31no—
343C22×Dic3—31no—
344C22×Dic3—41no—
345C22×Dic3—41no—
346C22×Dic3—61no—
347C22×Dic3—61no—
348C22×Dic3—61no—
349C22×Dic3—121no—
350C22×Dic3—121no—
351C22×Dic3—121no—
352C22×Dic3C4×D314yescomplemented
353C22×Dic3C22×D311yescharacteristic
354C22×Dic3C22×D311yescharacteristic
355C22×Dic3C22×D311yescharacteristic
356C22×Dic3C22×D311yescharacteristic
357C22×Dic3C22×D311yescharacteristic
358C22×Dic3C22×D311yescharacteristic
359C22×Dic3C22×D311yescharacteristic
360C2×D12—34no—
361C2×D12—121no—
362C2×D12—121no—
363C2×C4×D3—121no—
364C2×C4×D3—121no—
365C2×C4×D3—121no—
366C2×C4×D3—121no—
367C2×C4×D3—121no—
368C2×C4×D3—121no—
369C2×C4×D3—122no—
370C2×C4×D3—121no—
371C2×C4×D3—121no—
372C2×C4×D3—121no—
373C2×C4×D3—122no—
374C2×C4×D3—122no—
375C3×C4⋊C4—121no—
376C3×C22⋊C4—41no—
377C3×C22⋊C4—41no—
378C3×C22⋊C4—42no—
379C3×C22⋊C4—121no—
380C3×C22⋊C4—121no—
381C3×C22⋊C4—121no—
382C3×C22⋊C4—121no—
383C3×C42—121no—
384#217—34no—
385#217—41no—
386#217—41no—
387#217—121no—
388#217—121no—
389#217—121no—
390#217—122no—
391(C2×D3)⋊C4—34no—
392(C2×D3)⋊C4—34no—
393(C2×D3)⋊C4—34no—
394(C2×D3)⋊C4—41no—
395(C2×D3)⋊C4—41no—
396(C2×D3)⋊C4—121no—
397(C2×D3)⋊C4—121no—
398(C2×D3)⋊C4—121no—
399(C2×D3)⋊C4—121no—
400(C2×D3)⋊C4—121no—
401(C2×D3)⋊C4—121no—
402(C2×D3)⋊C4—121no—
403(C2×D3)⋊C4—122no—
404C4⋊Dic3—34no—
405C4⋊Dic3—121no—
406C4⋊Dic3—121no—
407Dic3⋊C4—34no—
408Dic3⋊C4—41no—
409Dic3⋊C4—121no—
410Dic3⋊C4—121no—
411Dic3⋊C4—121no—
412Dic3⋊C4—121no—
413C4×Dic3—41no—
414C4×Dic3—121no—
415C4×Dic3—121no—
416C22×C32—22no—
417C22×C32—22no—
418C22×C32—22no—
419C22×C32—41no—
420C22×C32—41no—
421C22×C32—41no—
422C22×C32—41no—
423C22×C32C23×C411yescharacteristic
424C22×C32H(5,𝔽2)11yescharacteristic
425C22×C32H(5,𝔽2)11yescharacteristic
426C22×C32H(5,𝔽2)11yescharacteristic
427C22×C32H(5,𝔽2)11yescharacteristic
428C22×C32H(5,𝔽2)11yescharacteristic
429C22×C322−1+411yescharacteristic
430C2×C3⋊D3—22no—
431C2×C3⋊D3—22no—
432C2×C3⋊D3—22no—
433C2×C3⋊D3—41no—
434C2×C3⋊D3—41no—
435C2×C3⋊D3—41no—
436C2×C3⋊D3—41no—
437C2×C3×D3—22no—
438C2×C3×D3—22no—
439C2×C3×D3—22no—
440C2×C3×D3—41no—
441C2×C3×D3—41no—
442C2×C3×D3—41no—
443C2×C3×D3—41no—
444C32×C4—41no—
445C32×C4—41no—
446C3⋊Dic3—22no—
447C3⋊Dic3—41no—
448C3⋊Dic3—41no—
449C3×Dic3—22no—
450C3×Dic3—22no—
451C3×Dic3—22no—
452C3×Dic3—41no—
453C3×Dic3—41no—
454C3×Dic3—41no—
455C3×Dic3—41no—
456C22×D4—31no—
457C22×D4—91no—
458C22×D4—91no—
459C23×C4—31no—
460C23×C4—91no—
461C23×C4—91no—
462#121—98no—
463C2×C4⋊C4—31no—
464C2×C4⋊C4—91no—
465C2×C4⋊C4—91no—
466C2×C4⋊C4—91no—
467C2×C4⋊C4—91no—
468C2×C22⋊C4—31no—
469C2×C22⋊C4—31no—
470C2×C22⋊C4—31no—
471C2×C22⋊C4—31no—
472C2×C22⋊C4—91no—
473C2×C22⋊C4—91no—
474C2×C22⋊C4—91no—
475C2×C22⋊C4—91no—
476C2×C22⋊C4—91no—
477C2×C22⋊C4—91no—
478C2×C22⋊C4—91no—
479C2×C22⋊C4D3211yescharacteristic
480C2×C42—31no—
481C2×C42—91no—
482#95—31no—
483#95—31no—
484#95—31no—
485#95—31no—
486#95—91no—
487#95—91no—
488#95—91no—
489#95—91no—
490#95—91no—
491#95—91no—
492C23×C3—21no—
493C23×C3—21no—
494C23×C3—21no—
495C23×C3—21no—
496C23×C3—21no—
497C23×C3—21no—
498C23×C3—21no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—21no—
502C23×C3—21no—
503C23×C3—21no—
504C23×C3—21no—
505C23×C3—22no—
506C23×C3—32no—
507C23×C3—41no—
508C23×C3—41no—
509C23×C3—41no—
510C23×C3—41no—
511C23×C3—41no—
512C23×C3—41no—
513C23×C3—61no—
514C23×C3—61no—
515C23×C3—61no—
516C23×C3—61no—
517C23×C3—61no—
518C23×C3—61no—
519C23×C3C2×C4×D312yes—
520C23×C3C2×C4×D312yes—
521C23×C3C23×D311yescharacteristic
522C23×C3C23×D311yescharacteristic
523C22×D3—21no—
524C22×D3—21no—
525C22×D3—21no—
526C22×D3—21no—
527C22×D3—21no—
528C22×D3—21no—
529C22×D3—32no—
530C22×D3—32no—
531C22×D3—62no—
532C22×D3—62no—
533C22×D3—62no—
534C22×D3—61no—
535C22×D3—61no—
536C22×D3—61no—
537C22×D3—61no—
538C22×D3—61no—
539C22×D3—61no—
540C22×D3—61no—
541C22×D3—61no—
542C22×D3—61no—
543C22×D3—61no—
544C22×D3—61no—
545C22×D3—61no—
546C22×D3—121no—
547C22×D3—121no—
548C22×D3—121no—
549C22×D3—121no—
550C22×D3C2×C4×D312yes—
551C3×D4—124no—
552C2×C3×C4—22no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—32no—
566C2×C3×C4—32no—
567C2×C3×C4—32no—
568C2×C3×C4—41no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—41no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—124no—
592#67—44no—
593#67—124no—
594#67—124no—
595#67—124no—
596#67—128no—
597C2×Dic3—21no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3—21no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3—21no—
606C2×Dic3—21no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—21no—
612C2×Dic3—21no—
613C2×Dic3—21no—
614C2×Dic3—21no—
615C2×Dic3—32no—
616C2×Dic3—32no—
617C2×Dic3—44no—
618C2×Dic3—62no—
619C2×Dic3—61no—
620C2×Dic3—61no—
621C2×Dic3—61no—
622C2×Dic3—61no—
623C2×Dic3—62no—
624C2×Dic3—61no—
625C2×Dic3—61no—
626C2×Dic3—61no—
627C2×Dic3—61no—
628C2×Dic3—61no—
629C2×Dic3—61no—
630C2×Dic3—61no—
631C2×Dic3—61no—
632C2×Dic3—61no—
633C2×Dic3—61no—
634C2×Dic3—61no—
635C2×Dic3—61no—
636C2×Dic3—121no—
637C2×Dic3—121no—
638C2×Dic3—121no—
639C2×Dic3—121no—
640C2×Dic3—121no—
641C2×Dic3—121no—
642C2×Dic3—121no—
643C2×Dic3—124no—
644C2×Dic3C2×C4×D312yes—
645C2×Dic3C2×C4×D312yes—
646C2×Dic3C2×C4×D312yes—
647D12—124no—
648C4×D3—128no—
649C4×D3—124no—
650C4×D3—124no—
651C4×D3—124no—
652C2×C32—42no—
653C2×C32#51811yescharacteristic
654C2×C32#51811yescharacteristic
655C2×C32#52011yescharacteristic
656C2×C32#56011yescharacteristic
657C2×C32#56011yescharacteristic
658C2×C32#56211yescharacteristic
659C2×C32#56211yescharacteristic
660C3⋊D3—42no—
661C3×D3—42no—
662C24—31no—
663C24—91no—
664C24C2×D3211yescharacteristic
665C2×D4—34no—
666C2×D4—94no—
667C2×D4—94no—
668C2×D4—121no—
669C2×D4—121no—
670C2×D4—361no—
671C2×D4—361no—
672C2×D4—361no—
673C2×D4—361no—
674C22×C4—31no—
675C22×C4—31no—
676C22×C4—31no—
677C22×C4—34no—
678C22×C4—31no—
679C22×C4—31no—
680C22×C4—31no—
681C22×C4—31no—
682C22×C4—91no—
683C22×C4—91no—
684C22×C4—91no—
685C22×C4—121no—
686C22×C4—121no—
687C22×C4—361no—
688C22×C4—361no—
689C22×C4—361no—
690C22×C4—361no—
691C22×C4—361no—
692C22×C4—361no—
693C22×C4C2×D3211yescharacteristic
694C22×C4C2×D3211yescharacteristic
695C4⋊C4—94no—
696C4⋊C4—121no—
697C4⋊C4—361no—
698C4⋊C4—361no—
699C4⋊C4—361no—
700C22⋊C4—41no—
701C22⋊C4—94no—
702C22⋊C4—94no—
703C22⋊C4—121no—
704C22⋊C4—121no—
705C22⋊C4—121no—
706C22⋊C4—121no—
707C22⋊C4—361no—
708C22⋊C4—361no—
709C22⋊C4—361no—
710C22⋊C4—361no—
711C22⋊C4—361no—
712C42—121no—
713C42—361no—
714C22×C3—22no—
715C22×C3—22no—
716C22×C3—22no—
717C22×C3—22no—
718C22×C3—22no—
719C22×C3—22no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—21no—
723C22×C3—21no—
724C22×C3—21no—
725C22×C3—21no—
726C22×C3—21no—
727C22×C3—42no—
728C22×C3—42no—
729C22×C3—42no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—62no—
739C22×C3—62no—
740C22×C3—62no—
741C22×C3—81no—
742C22×C3—81no—
743C22×C3—81no—
744C22×C3—81no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3—121no—
749C22×C3C22×C4×D311yescharacteristic
750C22×C3C22×C4×D311yescharacteristic
751C22×C3#100411yescharacteristic
752C22×C3#100411yescharacteristic
753C22×C3#100411yescharacteristic
754C22×C3#100411yescharacteristic
755C22×C3#100411yescharacteristic
756C22×C3#100411yescharacteristic
757C22×C3#100911yescharacteristic
758C22×C3#100911yescharacteristic
759C22×C3#100911yescharacteristic
760C22×C3#100911yescharacteristic
761C22×C3#101011yescharacteristic
762C22×C3#101011yescharacteristic
763C2×D3—22no—
764C2×D3—22no—
765C2×D3—22no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—64no—
771C2×D3—62no—
772C2×D3—62no—
773C2×D3—62no—
774C2×D3—62no—
775C2×D3—62no—
776C2×D3—62no—
777C2×D3—122no—
778C2×D3—122no—
779C2×D3—122no—
780C2×D3—122no—
781C2×D3—122no—
782C2×D3—122no—
783C2×D3—121no—
784C2×D3—121no—
785C2×D3—121no—
786C2×D3—121no—
787C2×D3—121no—
788C2×D3—121no—
789C2×D3—121no—
790C2×D3—121no—
791C3×C4—42no—
792C3×C4—41no—
793C3×C4—41no—
794C3×C4—41no—
795C3×C4—41no—
796C3×C4—62no—
797C3×C4—62no—
798C3×C4—62no—
799C3×C4—81no—
800C3×C4—121no—
801C3×C4—121no—
802C3×C4—121no—
803C3×C4—121no—
804Dic3—22no—
805Dic3—22no—
806Dic3—22no—
807Dic3—41no—
808Dic3—41no—
809Dic3—41no—
810Dic3—41no—
811Dic3—62no—
812Dic3—62no—
813Dic3—122no—
814Dic3—122no—
815Dic3—121no—
816Dic3—121no—
817Dic3—121no—
818Dic3—121no—
819Dic3—241no—
820C32#237711yescharacteristic, complemented, Sylow
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—32no—
828C23—61no—
829C23—61no—
830C23—61no—
831C23—61no—
832C23—61no—
833C23—61no—
834C23—92no—
835C23—181no—
836C23—181no—
837C23—181no—
838C23—181no—
839C23—181no—
840C23—181no—
841C23C4×D3212yes—
842C23C22×D3211yescharacteristic
843D4—124no—
844D4—364no—
845D4—364no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—32no—
853C2×C4—32no—
854C2×C4—32no—
855C2×C4—61no—
856C2×C4—61no—
857C2×C4—61no—
858C2×C4—61no—
859C2×C4—61no—
860C2×C4—61no—
861C2×C4—61no—
862C2×C4—61no—
863C2×C4—61no—
864C2×C4—61no—
865C2×C4—61no—
866C2×C4—61no—
867C2×C4—61no—
868C2×C4—61no—
869C2×C4—61no—
870C2×C4—61no—
871C2×C4—61no—
872C2×C4—61no—
873C2×C4—92no—
874C2×C4—124no—
875C2×C4—181no—
876C2×C4—181no—
877C2×C4—181no—
878C2×C4—181no—
879C2×C4—181no—
880C2×C4—181no—
881C2×C4—181no—
882C2×C4—181no—
883C2×C4—364no—
884C2×C4—364no—
885C2×C3—21no—
886C2×C3—21no—
887C2×C3—21no—
888C2×C3—21no—
889C2×C3—21no—
890C2×C3—21no—
891C2×C3—21no—
892C2×C3—42no—
893C2×C3—42no—
894C2×C3—82no—
895C2×C3—122no—
896C2×C3#548611yescharacteristic
897C2×C3#548611yescharacteristic
898C2×C3#552111yescharacteristic
899C2×C3#552311yescharacteristic
900C2×C3#554511yescharacteristic
901C2×C3#554611yescharacteristic
902C2×C3#562011yescharacteristic
903C2×C3#562111yescharacteristic
904C2×C3#566611yescharacteristic
905C2×C3#566611yescharacteristic
906C2×C3#566711yescharacteristic
907C2×C3#566711yescharacteristic
908C2×C3#568411yescharacteristic
909C2×C3#572011yescharacteristic
910D3—42no—
911D3—124no—
912D3—122no—
913D3—122no—
914C22—22no—
915C22—22no—
916C22—22no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—62no—
922C22—62no—
923C22—62no—
924C22—121no—
925C22—121no—
926C22—121no—
927C22—121no—
928C22—182no—
929C22—182no—
930C22—182no—
931C22—361no—
932C22—361no—
933C22—361no—
934C22—361no—
935C22C2×C4×D3211yescharacteristic
936C22#6430711yescharacteristic
937C22#6430911yescharacteristic
938C22#6431411yescharacteristic
939C22#6431411yescharacteristic
940C22#6431411yescharacteristic
941C22#6433011yescharacteristic
942C4—41no—
943C4—41no—
944C4—62no—
945C4—62no—
946C4—62no—
947C4—121no—
948C4—121no—
949C4—121no—
950C4—121no—
951C4—182no—
952C4—361no—
953C4—361no—
954C3—21no—
955C3#7412411yescharacteristic, complemented
956C3#7631011yescharacteristic, complemented
957C2—42no—
958C2—122no—
959C2—362no—
960C2#1059404911yescharacteristic
961C2#1059418211yescharacteristic
962C2#1059423711yescharacteristic
963C2#1059430811yescharacteristic
964C2#1059505611yescharacteristic
965C2#1059526511yescharacteristic
966C2#1059526611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63978C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2377
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #10592655C2semidirect
3. C3×#4957C2semidirect
4. C3×#4943C2semidirect
5. #10591721C2semidirect
6. #10591716C2semidirect
7. #10591704C2semidirect
8. #10591387C2semidirect
9. #10591373C2semidirect
10. #10591364C2semidirect
11. #10591331C2semidirect
12. #10591290C2semidirect
13. #10591284C2semidirect
14. #10591254C2semidirect
15. #10591194C2semidirect
33. #63978C4semidirect
65. #4957D3semidirect
73. #4943D3semidirect
92. C2×#638C2×C4semidirect
101. C2×C3×#67C2×C4semidirect
104. C22×C3×Dic3C2×C4semidirect
130. Dic3⋊Dic3C2×C4semidirect
133. #3722C2×C4semidirect
135. (C2×D3)⋊Dic3C2×C4semidirect
337. C2×#67C4×D3semidirect
352. C22×Dic3C4×D3semidirect
820. C32#2377semidirect
955. C3#74124semidirect
956. C3#76310semidirect

Maximal subgroups

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

subgroupindex
C2×#639782
#105926552
C3×#49572
C3×#49432
#105917212
#105917162
#105917042
#105913872
#105913732
#105913642
#105913312
#105912902
#105912842
#105912542
#105911942
#763103
#741243