Finite Group Databasebeta

← #11859364

Subgroups — #11859364

Order 1152.

1097 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63804C211yesmaximal, characteristic, complemented
2C2×D32×C8C211yesmaximal, characteristic, complemented
3#10594006C211yesmaximal, characteristic
4#10592538C211yesmaximal, characteristic, complemented
5C3×#4836C211yesmaximal, characteristic, complemented
6C3×#4834C211yesmaximal, characteristic, complemented
7#10590958C211yesmaximal, characteristic, complemented
8#10590937C211yesmaximal, characteristic, complemented
9#10590724C211yesmaximal, characteristic, complemented
10#10590723C211yesmaximal, characteristic, complemented
11#10590717C211yesmaximal, characteristic, complemented
12#10590717C211yesmaximal, characteristic, complemented
13#10590326C211yesmaximal, characteristic, complemented
14C3⋊C8×D12C211yesmaximal, characteristic, complemented
15#10590321C211yesmaximal, characteristic, complemented
16#79478—31nomaximal
17#79421—31nomaximal
18C2×C4×D32C2211yescharacteristic
19C2×#3798C2211yescharacteristic
20C2×#3743C2211yescharacteristic
21C2×C8×C3⋊D3C2211yescharacteristic
22#64081C2211yescharacteristic
23C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
24C2×C3×D3×C8C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26C2×C3×D3×C8C2211yescharacteristic, complemented
27C3×C4×D12C2211yescharacteristic
28C3×C4×D12C2211yescharacteristic
29#63922C411yescharacteristic
30#63922C411yescharacteristic
31C4×#625C2211yescharacteristic
32C4×#625C2211yescharacteristic
33#63899C411yescharacteristic
34#63899C411yescharacteristic
35#63885C411yescharacteristic
36#63885C411yescharacteristic
37#63854C411yescharacteristic
38#63854C411yescharacteristic
39C2×#3712C2211yescharacteristic
40C2×#3711C2211yescharacteristic, complemented
41C2×#3710C2211yescharacteristic
42C2×D3×C3⋊C8C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44C2×D3×C3⋊C8C2211yescharacteristic, complemented
45#63804—24no—
46D32×C8—24no—
47C32×C4⋊C8C2211yescharacteristic, complemented
48#63641C2211yescharacteristic, complemented
49#63641C2211yescharacteristic, complemented
50C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
54C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
55C3×#803C2211yescharacteristic, complemented
56C3×C4×C3⋊C8C2211yescharacteristic, complemented
57(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
58(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63555C2211yescharacteristic, complemented
62#63553C2211yescharacteristic, complemented
63C2×#907—31no—
64C2×#901—31no—
65C22×D3×C8—31no—
66C22×D3×C8—31no—
67#5547—31no—
68#5547—31no—
69C3×#435—31no—
70C3×C8×D4—31no—
71#5127—31no—
72#5111—31no—
73C8×#67—31no—
74C8×#67—31no—
75#5011—31no—
76D4×C3⋊C8—31no—
77#4839—31no—
78#4839—31no—
79#4839—61no—
80#4836D311yescharacteristic, complemented
81#4834D311yescharacteristic, complemented
82#4730—31no—
83#4728—31no—
84#4727—31no—
85#4727—31no—
86#4726—31no—
87#4726—31no—
88#67⋊C8—31no—
89#67⋊C8—31no—
90#4708—31no—
91#4706—31no—
92#4689—31no—
93C8×D12—31no—
94C22×D32C2×C411yescharacteristic
95C2×C4×C3⋊D3C2311yescharacteristic
96C2×C3×D12C2×C411yescharacteristic
97C2×C3×D12C2×C411yescharacteristic
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×#627C2×C411yescharacteristic
103C2×#626C2×C411yescharacteristic
104C2×#626C2×C411yescharacteristic
105C2×#625C2×C411yescharacteristic
106C2×#625C2×C411yescharacteristic
107C2×#625C2×C411yescharacteristic
108C2×#624C2×C411yescharacteristic
109C2×D3×Dic3C2×C411yescharacteristic
110C2×D3×Dic3C2×C411yescharacteristic
111C4×D32—22no—
112C4×D32—22no—
113#3798—22no—
114#3798—22no—
115C2×C32×C8C2311yescharacteristic
116C2×C32×C8C2311yescharacteristic
117C32×C42C2311yescharacteristic
118#3752C2×C411yescharacteristic
119#3752C2×C411yescharacteristic
120#3750C2×C411yescharacteristic
121#3750C2×C411yescharacteristic
122C4×C3⋊Dic3C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125#3743—22no—
126C8×C3⋊D3—22no—
127C3×(C2×D3)⋊C4C2×C411yescharacteristic
128C3×(C2×D3)⋊C4C2×C411yescharacteristic
129C3×(C2×D3)⋊C4C2×C411yescharacteristic
130C3×(C2×D3)⋊C4C2×C411yescharacteristic
131C3×C4⋊Dic3C2×C411yescharacteristic
132C3×C4⋊Dic3C2×C411yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C3×ΓL(1,𝔽25)—22no—
138C3×D3×C8—22no—
139C3×D3×C8—22no—
140C3×D3×C8—22no—
141#3724C2×C411yescharacteristic
142#3724C2×C411yescharacteristic
143(C2×D3)⋊Dic3C2×C411yescharacteristic
144(C2×D3)⋊Dic3C2×C411yescharacteristic
145(C2×D3)⋊Dic3C2×C411yescharacteristic
146(C2×D3)⋊Dic3C2×C411yescharacteristic
147#3712—22no—
148#3711—22no—
149#3710D414yescomplemented
150D3×C3⋊C8—22no—
151D3×C3⋊C8—22no—
152D3×C3⋊C8—22no—
153#2929—91noSylow
154C2×#235—31no—
155C2×#235—31no—
156C22×C4×D3—31no—
157C22×C4×D3—31no—
158C2×C3×M16—31no—
159C22×C3×C8—31no—
160C22×C3×C8—31no—
161C22×C3×C8—31no—
162C3×C4×D4—31no—
163C3×C4×D4—31no—
164#939—31no—
165#939—31no—
166#937—31no—
167#937—31no—
168C4×#67—31no—
169C4×#67—31no—
170C4×#67—31no—
171C4×#67—31no—
172C2×#208—31no—
173C22×C3⋊C8—31no—
174C22×C3⋊C8—31no—
175C22×C3⋊C8—31no—
176#907—64no—
177#901—64no—
178C2×ΓL(1,𝔽25)—31no—
179C2×ΓL(1,𝔽25)—31no—
180C2×ΓL(1,𝔽25)—31no—
181C2×ΓL(1,𝔽25)—31no—
182C2×ΓL(1,𝔽25)—31no—
183C2×ΓL(1,𝔽25)—61no—
184C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
185C2×D3×C8—31no—
186C2×D3×C8—31no—
187C2×D3×C8—31no—
188C2×D3×C8—31no—
189C2×D3×C8—31no—
190C2×D3×C8—31no—
191C2×D3×C8—31no—
192C2×D3×C8—61no—
193C2×D3×C8—64no—
194C2×D3×C8—64no—
195C2×D3×C8C2×D311yescharacteristic
196C2×D3×C8C2×D311yescharacteristic
197C2×D3×C8C2×D311yescharacteristic, complemented
198#896—31no—
199#896—31no—
200#894—31no—
201#894—31no—
202#884—31no—
203#884—31no—
204#883—31no—
205#883—31no—
206#882—31no—
207#882—31no—
208#878—31no—
209#878—31no—
210C4×D12C2×D311yescharacteristic
211C4×D12C2×D311yescharacteristic
212#872—31no—
213#872—31no—
214#872—61no—
215C3×C4⋊C8—21no—
216C3×C4⋊C8C2×D311yescharacteristic, complemented
217C3×C4⋊C8C2×D311yescharacteristic, complemented
218C3×C22⋊C8—31no—
219C3×C22⋊C8—31no—
220C3×C22⋊C8—31no—
221C3×C22⋊C8—31no—
222C3×#97—31no—
223C3×C4×C8—31no—
224#830—31no—
225#830—31no—
226#830—31no—
227#830—31no—
228(C2×D3)⋊C8—31no—
229(C2×D3)⋊C8—31no—
230(C2×D3)⋊C8—31no—
231(C2×D3)⋊C8—31no—
232(C2×D3)⋊C8C2×D311yescharacteristic
233(C2×D3)⋊C8C2×D311yescharacteristic
234(C2×D3)⋊C8C2×D311yescharacteristic, complemented
235(C2×D3)⋊C8C2×D311yescharacteristic, complemented
236#815—31no—
237#815—31no—
238Dic3⋊C8—31no—
239Dic3⋊C8—31no—
240Dic3⋊C8—31no—
241Dic3⋊C8—31no—
242Dic3⋊C8—61no—
243Dic3⋊C8—61no—
244C8×Dic3—31no—
245C8×Dic3—31no—
246C4⋊(C3⋊C8)—31no—
247C4⋊(C3⋊C8)—31no—
248C4⋊(C3⋊C8)—61no—
249#803C2×D311yescharacteristic, complemented
250C4×C3⋊C8C2×D311yescharacteristic, complemented
251C22×C3⋊D3C22×C411yescharacteristic
252C22×C3×D3C22×C411yescharacteristic
253C22×C3×D3C22×C411yescharacteristic
254C22×C3×D3C22×C411yescharacteristic
255C22×C3×D3C22×C411yescharacteristic
256C2×D32—22no—
257C2×D32—22no—
258C2×D32—22no—
259C2×C32×C4C22×C411yescharacteristic
260C2×C32×C4C22×C411yescharacteristic
261C2×C32×C4C2411yescharacteristic
262C2×C3⋊Dic3C22×C411yescharacteristic
263C2×C3⋊Dic3C22×C411yescharacteristic
264C2×C3⋊Dic3C22×C411yescharacteristic
265C4×C3⋊D3C2×D412yes—
266C4×C3⋊D3#4112yes—
267C2×C3×Dic3C22×C411yescharacteristic
268C2×C3×Dic3C22×C411yescharacteristic
269C2×C3×Dic3C22×C411yescharacteristic
270C2×C3×Dic3C22×C411yescharacteristic
271C3×D12—22no—
272C3×D12—22no—
273C3×C4×D3—21no—
274C3×C4×D3—21no—
275C3×C4×D3—21no—
276C3×C4×D3—21no—
277C3×C4×D3—21no—
278C3×C4×D3—21no—
279C3×C4×D3—21no—
280C3×C4×D3—21no—
281#627—22no—
282#626—22no—
283#626—22no—
284#625—22no—
285#625—22no—
286#625—22no—
287#624—22no—
288D3×Dic3—22no—
289D3×Dic3—22no—
290C32×C8—21no—
291C32×C8—21no—
292C3⋊(C3⋊C8)—21no—
293C3⋊(C3⋊C8)—21no—
294C3×C3⋊C8—21no—
295C3×C3⋊C8—21no—
296C3×C3⋊C8C2×D412yes—
297C3×C3⋊C8C2×D412yes—
298C2×#131—91no—
299C23×C8—91no—
300#525—91no—
301#435—31no—
302#435—91no—
303#435—91no—
304#435—91no—
305C8×D4—31no—
306C8×D4—91no—
307C8×D4—91no—
308C8×D4—91no—
309#424—91no—
310#408—91no—
311#407—91no—
312#405—91no—
313C23×D3—31no—
314C23×D3—31no—
315C2×C3×D4—31no—
316C2×C3×D4—31no—
317C22×C3×C4—31no—
318C22×C3×C4—31no—
319C22×C3×C4—31no—
320C22×C3×C4—31no—
321C2×#67—31no—
322C2×#67—31no—
323C2×#67—31no—
324C2×#67—31no—
325C2×#67—31no—
326C2×#67—31no—
327C2×#67—31no—
328C2×#67—31no—
329C22×Dic3—31no—
330C22×Dic3—31no—
331#235—62no—
332#235—62no—
333#235—62no—
334#235—62no—
335C2×D12—31no—
336C2×D12—31no—
337C2×D12C4×D311yescharacteristic
338C2×D12C4×D311yescharacteristic
339C2×C4×D3—31no—
340C2×C4×D3—31no—
341C2×C4×D3—31no—
342C2×C4×D3—31no—
343C2×C4×D3—31no—
344C2×C4×D3—31no—
345C2×C4×D3—61no—
346C2×C4×D3—62no—
347C2×C4×D3—62no—
348C2×C4×D3—62no—
349C2×C4×D3—62no—
350C2×C4×D3C22×D311yescharacteristic
351C2×C4×D3C22×D311yescharacteristic
352C2×C4×D3C22×D311yescharacteristic
353C2×C4×D3C22×D311yescharacteristic
354C2×Dic6—31no—
355C2×Dic6—31no—
356C3×M16—62no—
357C2×C3×C8—21no—
358C2×C3×C8—21no—
359C2×C3×C8—31no—
360C2×C3×C8—31no—
361C2×C3×C8—31no—
362C2×C3×C8—31no—
363C2×C3×C8—62no—
364C2×C3×C8—62no—
365C2×C3×C8—62no—
366C2×C3×C8C22×D311yescharacteristic
367C2×C3×C8C22×D311yescharacteristic
368C2×C3×C8C22×D311yescharacteristic
369C2×C3×C8C22×D311yescharacteristic
370C3×C4⋊C4—31no—
371C3×C4⋊C4—31no—
372C3×C22⋊C4—31no—
373C3×C22⋊C4—31no—
374C3×C22⋊C4—31no—
375C3×C22⋊C4—31no—
376C3×C42—21no—
377C3×C42C22×D311yescharacteristic
378C3×C42C22×D311yescharacteristic
379#217—31no—
380#217—31no—
381#217—31no—
382#217—31no—
383(C2×D3)⋊C4—31no—
384(C2×D3)⋊C4—31no—
385(C2×D3)⋊C4—31no—
386(C2×D3)⋊C4—31no—
387(C2×D3)⋊C4—31no—
388(C2×D3)⋊C4—31no—
389(C2×D3)⋊C4—31no—
390(C2×D3)⋊C4—31no—
391(C2×D3)⋊C4—61no—
392(C2×D3)⋊C4—61no—
393(C2×D3)⋊C4C4×D311yescharacteristic
394(C2×D3)⋊C4C4×D311yescharacteristic
395(C2×D3)⋊C4C4×D311yescharacteristic
396(C2×D3)⋊C4C4×D311yescharacteristic
397C4⋊Dic3C4×D311yescharacteristic
398C4⋊Dic3C4×D311yescharacteristic
399Dic3⋊C4—31no—
400Dic3⋊C4—31no—
401Dic3⋊C4—31no—
402Dic3⋊C4—31no—
403Dic3⋊C4—31no—
404Dic3⋊C4—31no—
405Dic3⋊C4—31no—
406Dic3⋊C4—31no—
407Dic3⋊C4—61no—
408Dic3⋊C4—61no—
409C4×Dic3—31no—
410C4×Dic3—31no—
411C4×Dic3—61no—
412#208—62no—
413C2×C3⋊C8—31no—
414C2×C3⋊C8—31no—
415C2×C3⋊C8—31no—
416C2×C3⋊C8—31no—
417C2×C3⋊C8—61no—
418C2×C3⋊C8—61no—
419C2×C3⋊C8—62no—
420C2×C3⋊C8—62no—
421C2×C3⋊C8—62no—
422C2×C3⋊C8C22×D311yescharacteristic
423C2×C3⋊C8C22×D311yescharacteristic
424C2×C3⋊C8C22×D311yescharacteristic
425C2×C3⋊C8C22×D311yescharacteristic
426ΓL(1,𝔽25)—22no—
427ΓL(1,𝔽25)—62no—
428ΓL(1,𝔽25)—62no—
429ΓL(1,𝔽25)—62no—
430ΓL(1,𝔽25)—62no—
431ΓL(1,𝔽25)—62no—
432ΓL(1,𝔽25)—122no—
433D3×C8—22no—
434D3×C8—22no—
435D3×C8—22no—
436D3×C8—34no—
437D3×C8—34no—
438D3×C8—62no—
439D3×C8—62no—
440D3×C8—62no—
441D3×C8—62no—
442D3×C8—62no—
443D3×C8—122no—
444C22×C32C23×C411yescharacteristic
445C2×C3⋊D3—21no—
446C2×C3⋊D3—21no—
447C2×C3⋊D3C4×D412yes—
448C2×C3×D3—21no—
449C2×C3×D3—21no—
450C2×C3×D3—21no—
451C2×C3×D3—21no—
452C2×C3×D3—21no—
453C2×C3×D3—21no—
454C2×C3×D3—21no—
455C2×C3×D3—21no—
456C2×C3×D3—21no—
457C2×C3×D3—21no—
458C2×C3×D3#13112yescomplemented
459C2×C3×D3#13112yescomplemented
460D32—28no—
461C32×C4—21no—
462C32×C4—21no—
463C32×C4C22×D411yescharacteristic
464C32×C4C2×#4111yescharacteristic
465C3⋊Dic3—21no—
466C3⋊Dic3—21no—
467C3⋊Dic3C4×D412yes—
468C3×Dic3—21no—
469C3×Dic3—21no—
470C3×Dic3—21no—
471C3×Dic3—21no—
472C2×#41—91no—
473C23×C4—91no—
474#131—184no—
475C2×M16—31no—
476C2×M16—91no—
477C2×M16—91no—
478C2×M16—91no—
479C22×C8—31no—
480C22×C8—31no—
481C22×C8—31no—
482C22×C8—91no—
483C22×C8—91no—
484C22×C8—91no—
485C22×C8—91no—
486C22×C8—91no—
487C22×C8—184no—
488#123—91no—
489#123—91no—
490C22⋊Q8—91no—
491C22⋊Q8—91no—
492#121—91no—
493#121—91no—
494#120—91no—
495#120—91no—
496C4×D4—31no—
497C4×D4—31no—
498C4×D4—91no—
499C4×D4—91no—
500#117—91no—
501C4⋊C8—91no—
502C4⋊C8—91no—
503C4⋊C8—91no—
504C4⋊C8D3211yescharacteristic, complemented
505C22⋊C8—31no—
506C22⋊C8—31no—
507C22⋊C8—31no—
508C22⋊C8—31no—
509C22⋊C8—91no—
510C22⋊C8—91no—
511C22⋊C8—91no—
512C22⋊C8—91no—
513#97—31no—
514#97—91no—
515C4×C8—31no—
516C4×C8—91no—
517C23×C3—31no—
518C23×C3—31no—
519C23×C3—31no—
520C23×C3—31no—
521C22×D3—31no—
522C22×D3—31no—
523C22×D3—61no—
524C22×D3—62no—
525C22×D3—62no—
526C22×D3—62no—
527C22×D3—62no—
528C22×D3—62no—
529C22×D3—62no—
530C22×D3C2×C4×D311yescharacteristic
531C22×D3C2×C4×D311yescharacteristic
532C22×D3C2×C4×D311yescharacteristic
533C22×D3C2×C4×D311yescharacteristic
534C3×D4—62no—
535C3×D4—62no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—31no—
540C2×C3×C4—31no—
541C2×C3×C4—31no—
542C2×C3×C4—31no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4C2×C4×D311yescharacteristic
552C2×C3×C4C2×C4×D311yescharacteristic
553C2×C3×C4C2×C4×D311yescharacteristic
554C2×C3×C4C2×C4×D311yescharacteristic
555C2×C3×C4C23×D311yescharacteristic
556C2×C3×C4C23×D311yescharacteristic
557#67—62no—
558#67—62no—
559#67—62no—
560#67—62no—
561#67—62no—
562#67—62no—
563#67—62no—
564#67—62no—
565C2×Dic3—31no—
566C2×Dic3—31no—
567C2×Dic3—31no—
568C2×Dic3—31no—
569C2×Dic3—31no—
570C2×Dic3—31no—
571C2×Dic3—61no—
572C2×Dic3—61no—
573C2×Dic3—61no—
574C2×Dic3—62no—
575C2×Dic3—62no—
576C2×Dic3C2×C4×D311yescharacteristic
577C2×Dic3C2×C4×D311yescharacteristic
578C2×Dic3C2×C4×D311yescharacteristic
579C2×Dic3C2×C4×D311yescharacteristic
580D12—22no—
581D12—22no—
582D12—62no—
583D12—62no—
584C4×D3—21no—
585C4×D3—21no—
586C4×D3—21no—
587C4×D3—21no—
588C4×D3—21no—
589C4×D3—21no—
590C4×D3—21no—
591C4×D3—21no—
592C4×D3—32no—
593C4×D3—32no—
594C4×D3—32no—
595C4×D3—32no—
596C4×D3—62no—
597C4×D3—62no—
598C4×D3—62no—
599C4×D3—62no—
600C4×D3—62no—
601C4×D3—62no—
602Dic6—62no—
603Dic6—62no—
604C3×C8—21no—
605C3×C8—21no—
606C3×C8—21no—
607C3×C8—21no—
608C3×C8—32no—
609C3×C8—32no—
610C3×C8—41no—
611C3×C8—41no—
612C3×C8—61no—
613C3×C8—61no—
614C3⋊C8—21no—
615C3⋊C8—21no—
616C3⋊C8—61no—
617C3⋊C8—61no—
618C3⋊C8—61no—
619C3⋊C8—61no—
620C3⋊C8—121no—
621C3⋊C8—121no—
622C3⋊C8D3×D412yes—
623C3⋊C8D3×D412yes—
624C2×C32C2×C4×D411yescharacteristic
625C2×C32C2×#13111yescharacteristic
626C2×C32C2×#13111yescharacteristic
627C3⋊D3—22no—
628C3×D3—22no—
629C3×D3—22no—
630C3×D3—41no—
631C3×D3—41no—
632C24—91no—
633#41—182no—
634#41—182no—
635C2×Q8—91no—
636C2×D4—31no—
637C2×D4—31no—
638C2×D4—91no—
639C2×D4—91no—
640C2×D4—91no—
641C2×D4—91no—
642C2×D4—91no—
643C22×C4—31no—
644C22×C4—31no—
645C22×C4—31no—
646C22×C4—31no—
647C22×C4—91no—
648C22×C4—91no—
649C22×C4—91no—
650C22×C4—91no—
651C22×C4—182no—
652C22×C4—182no—
653M16—62no—
654M16—182no—
655M16—182no—
656M16—182no—
657C2×C8—31no—
658C2×C8—31no—
659C2×C8—31no—
660C2×C8—31no—
661C2×C8—62no—
662C2×C8—62no—
663C2×C8—62no—
664C2×C8—94no—
665C2×C8—91no—
666C2×C8—91no—
667C2×C8—182no—
668C2×C8—182no—
669C2×C8—182no—
670C2×C8—182no—
671C2×C8C2×D3211yescharacteristic
672C2×C8C2×D3211yescharacteristic
673C4⋊C4—31no—
674C4⋊C4—31no—
675C4⋊C4—91no—
676C4⋊C4—91no—
677C4⋊C4—91no—
678C4⋊C4—91no—
679C22⋊C4—31no—
680C22⋊C4—31no—
681C22⋊C4—31no—
682C22⋊C4—31no—
683C22⋊C4—91no—
684C22⋊C4—91no—
685C22⋊C4—91no—
686C22⋊C4—91no—
687C22⋊C4—91no—
688C22⋊C4—91no—
689C42—91no—
690C42C2×D3211yescharacteristic
691C22×C3—21no—
692C22×C3—32no—
693C22×C3—32no—
694C22×C3—61no—
695C22×C3—61no—
696C22×C3—61no—
697C22×C3—61no—
698C22×C3—61no—
699C22×C3—61no—
700C22×C3—61no—
701C22×C3—61no—
702C22×C3—61no—
703C22×C3—61no—
704C22×C3C22×C4×D311yescharacteristic
705C22×C3C22×C4×D311yescharacteristic
706C2×D3—21no—
707C2×D3—21no—
708C2×D3—21no—
709C2×D3—21no—
710C2×D3—21no—
711C2×D3—21no—
712C2×D3—21no—
713C2×D3—21no—
714C2×D3—21no—
715C2×D3—21no—
716C2×D3—32no—
717C2×D3—32no—
718C2×D3—62no—
719C2×D3—68no—
720C2×D3—68no—
721C2×D3—61no—
722C2×D3—61no—
723C2×D3—61no—
724C2×D3—61no—
725C2×D3—121no—
726C2×D3—121no—
727C2×D3#90112yescomplemented
728C2×D3#90712yescomplemented
729C3×C4—21no—
730C3×C4—21no—
731C3×C4—21no—
732C3×C4—21no—
733C3×C4—21no—
734C3×C4—21no—
735C3×C4—41no—
736C3×C4—41no—
737C3×C4—61no—
738C3×C4—61no—
739C3×C4—61no—
740C3×C4—61no—
741C3×C4C2×D3×D411yescharacteristic
742C3×C4C2×D3×D411yescharacteristic
743C3×C4D3×#4111yescharacteristic
744C3×C4D3×#4111yescharacteristic
745Dic3—21no—
746Dic3—21no—
747Dic3—21no—
748Dic3—21no—
749Dic3—32no—
750Dic3—32no—
751Dic3—62no—
752Dic3—61no—
753Dic3—61no—
754Dic3—61no—
755Dic3—61no—
756Dic3—121no—
757Dic3—121no—
758C32#292911yescharacteristic, complemented, Sylow
759C23—31no—
760C23—31no—
761C23—31no—
762C23—31no—
763C23—91no—
764C23—182no—
765C23—182no—
766C23—182no—
767Q8—182no—
768D4—62no—
769D4—62no—
770D4—182no—
771D4—182no—
772D4—182no—
773D4—182no—
774D4—182no—
775C2×C4—31no—
776C2×C4—31no—
777C2×C4—31no—
778C2×C4—31no—
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—91no—
788C2×C4—92no—
789C2×C4—92no—
790C2×C4—91no—
791C2×C4—91no—
792C2×C4—182no—
793C2×C4—182no—
794C2×C4—182no—
795C2×C4C4×D3211yescharacteristic
796C2×C4C4×D3211yescharacteristic
797C2×C4C22×D3211yescharacteristic
798C8—21no—
799C8—21no—
800C8—32no—
801C8—32no—
802C8—61no—
803C8—61no—
804C8—181no—
805C8—181no—
806C2×C3—21no—
807C2×C3—21no—
808C2×C3—21no—
809C2×C3—62no—
810C2×C3—62no—
811C2×C3—121no—
812C2×C3—121no—
813C2×C3C4×D3×D411yescharacteristic
814C2×C3C4×D3×D411yescharacteristic
815C2×C3C2×#90111yescharacteristic
816C2×C3C2×#90711yescharacteristic
817C2×C3D3×#13111yescharacteristic
818C2×C3D3×#13111yescharacteristic
819D3—22no—
820D3—22no—
821D3—41no—
822D3—41no—
823D3—62no—
824D3—62no—
825D3—122no—
826C22—32no—
827C22—32no—
828C22—61no—
829C22—61no—
830C22—61no—
831C22—61no—
832C22—61no—
833C22—61no—
834C22—61no—
835C22—61no—
836C22—61no—
837C22—61no—
838C22—92no—
839C22—188no—
840C22—181no—
841C22—181no—
842C22C2×C4×D3211yescharacteristic
843C4—21no—
844C4—21no—
845C4—61no—
846C4—61no—
847C4—61no—
848C4—61no—
849C4—92no—
850C4—181no—
851C4—181no—
852C4D32×D411yescharacteristic
853C4#6431911yescharacteristic
854C3—21no—
855C3#7942111yescharacteristic, complemented
856C3#7947811yescharacteristic, complemented
857C2—62no—
858C2—62no—
859C2—121no—
860C2—121no—
861C2—182no—
862C2#1059460511yescharacteristic
863C2D3×#90111yescharacteristic
864C2D3×#90711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×C4⋊C8C22
prime radical#10594006C2
cosocleC2×C32×C4C24
hypercenterC4⋊C8D32
hypocenterC32#2929
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#63804C2semidirect
2. C2×D32×C8C2semidirect
4. #10592538C2semidirect
5. C3×#4836C2semidirect
6. C3×#4834C2semidirect
7. #10590958C2semidirect
8. #10590937C2semidirect
9. #10590724C2semidirect
10. #10590723C2semidirect
11. #10590717C2semidirect
12. #10590717C2semidirect
13. #10590326C2semidirect
14. C3⋊C8×D12C2semidirect
15. #10590321C2semidirect
23. C2×C3×ΓL(1,𝔽25)C22semidirect
26. C2×C3×D3×C8C22semidirect
40. C2×#3711C22semidirect
44. C2×D3×C3⋊C8C22semidirect
47. C32×C4⋊C8C22semidirect
48. #63641C22semidirect
49. #63641C22semidirect
50. C4⋊(C3⋊(C3⋊C8))C22semidirect
53. C3×(C2×D3)⋊C8C22semidirect
54. C3×(C2×D3)⋊C8C22semidirect
55. C3×#803C22semidirect
56. C3×C4×C3⋊C8C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
61. #63555C22semidirect
62. #63553C22semidirect
80. #4836D3semidirect
81. #4834D3semidirect
149. #3710D4semidirect
184. C2×ΓL(1,𝔽25)C2×D3semidirect
197. C2×D3×C8C2×D3semidirect
216. C3×C4⋊C8C2×D3semidirect
217. C3×C4⋊C8C2×D3semidirect
234. (C2×D3)⋊C8C2×D3semidirect
235. (C2×D3)⋊C8C2×D3semidirect
249. #803C2×D3semidirect
250. C4×C3⋊C8C2×D3semidirect
458. C2×C3×D3#131semidirect
459. C2×C3×D3#131semidirect
504. C4⋊C8D32semidirect
727. C2×D3#901semidirect
728. C2×D3#907semidirect
758. C32#2929semidirect
855. C3#79421semidirect
856. C3#79478semidirect

Maximal subgroups

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

subgroupindex
C2×#638042
C2×D32×C82
#105940062
#105925382
C3×#48362
C3×#48342
#105909582
#105909372
#105907242
#105907232
#105907172
#105903262
C3⋊C8×D122
#105903212
#794783
#794213