Finite Group Databasebeta

← #11859411

Subgroups — #11859411

Order 1152.

1149 conjugacy classes of subgroups.

The subgroup lattice has 947 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596018C211yesmaximal, characteristic
2C2×#63818C211yesmaximal, characteristic, complemented
3C2×#63817C211yesmaximal, characteristic, complemented
4C3×#5012C211yesmaximal, characteristic, complemented
5C3×#5011C211yesmaximal, characteristic, complemented
6#10591159C211yesmaximal, characteristic, complemented
7#10591157C211yesmaximal, characteristic, complemented
8#10591153C211yesmaximal, characteristic, complemented
9#10591149C211yesmaximal, characteristic, complemented
10#10591051C211yesmaximal, characteristic, complemented
11#10591051C211yesmaximal, characteristic, complemented
12#10590338C211yesmaximal, characteristic, complemented
13#10590332C211yesmaximal, characteristic, complemented
14#10590328C211yesmaximal, characteristic, complemented
15#10590321C211yesmaximal, characteristic, complemented
16#79537—31nomaximal
17#79479—31nomaximal
18C2×#3828C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21#64148C411yescharacteristic
22#64146C411yescharacteristic
23C4×#638C2211yescharacteristic
24C4×#638C2211yescharacteristic
25#64105C411yescharacteristic
26#64103C411yescharacteristic
27#64093C411yescharacteristic
28#64092C411yescharacteristic
29#64091C411yescharacteristic
30#64087C411yescharacteristic
31C4×C4⋊(C3⋊D3)C2211yescharacteristic
32#64081C2211yescharacteristic
33C2×C3×#208C2211yescharacteristic
34C2×C3×#208C2211yescharacteristic
35C2×C3×#208C2211yescharacteristic, complemented
36C22×C3×C3⋊C8C2211yescharacteristic, complemented
37C2×#3712C2211yescharacteristic
38C2×#3712C2211yescharacteristic
39C2×#3712C2211yescharacteristic
40C2×#3712C2211yescharacteristic
41C2×#3712C2211yescharacteristic, complemented
42#63818—24no—
43#63817—24no—
44C2×#3710C2211yescharacteristic
45C2×#3710C2211yescharacteristic
46C2×#3710C2211yescharacteristic, complemented
47C3×#830C2211yescharacteristic
48C3×#830C2211yescharacteristic
49C3×#830C2211yescharacteristic, complemented
50C3×#830C2211yescharacteristic, complemented
51C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
52C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
53C3×#803C2211yescharacteristic, complemented
54C3×C4×C3⋊C8C2211yescharacteristic, complemented
55#63572C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63557C2211yescharacteristic
58#63557C2211yescharacteristic
59#63557C2211yescharacteristic, complemented
60#63557C2211yescharacteristic, complemented
61#63555C2211yescharacteristic, complemented
62#63553C2211yescharacteristic, complemented
63C2×#907—31no—
64C2×D3×M16—31no—
65C2×D3×M16—31no—
66C2×#901—31no—
67#5547—31no—
68#5547—31no—
69#5547—61no—
70C3×#436—31no—
71C3×#435—31no—
72#5128—31no—
73#5128—31no—
74#5127—31no—
75#5111—31no—
76#5012D311yescharacteristic, complemented
77#5011D311yescharacteristic, complemented
78#4839—31no—
79#4839—31no—
80#4838—31no—
81#4836—31no—
82#4730—31no—
83#4729—31no—
84#4729—31no—
85#4728—31no—
86#4727—31no—
87#4727—31no—
88#4726—31no—
89#4726—31no—
90#4708—31no—
91#4706—31no—
92#4689—31no—
93#4688—31no—
94C23×C3⋊D3C2×C411yescharacteristic
95C2×C32×D4C2×C411yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C2×#638C2×C411yescharacteristic
99C2×#638C2×C411yescharacteristic
100C2×#638C2×C411yescharacteristic
101C2×#638C2×C411yescharacteristic
102C22×C3⋊Dic3C2×C411yescharacteristic
103#3828—22no—
104#3828—22no—
105C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
106C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
107C2×C4×C3⋊D3—22no—
108C2×C4×C3⋊D3—22no—
109C2×C4×C3⋊D3C2×C411yescharacteristic
110C2×C4×C3⋊D3C2×C411yescharacteristic
111C2×C4×C3⋊D3C2311yescharacteristic
112C2×C4×C3⋊D3C2311yescharacteristic
113C2×C4×C3⋊D3C2311yescharacteristic
114C2×#634C2×C411yescharacteristic
115C32×C4⋊C4C2×C411yescharacteristic
116C32×C22⋊C4C2×C411yescharacteristic
117C32×C22⋊C4C2×C411yescharacteristic
118C32×C42C2311yescharacteristic
119#3757C2×C411yescharacteristic
120#3757C2×C411yescharacteristic
121#3752C2×C411yescharacteristic
122#3752C2×C411yescharacteristic
123#3752C2×C411yescharacteristic
124#3752C2×C411yescharacteristic
125#3752C2×C411yescharacteristic
126#3752C2×C411yescharacteristic
127C4⋊(C3⋊Dic3)C2×C411yescharacteristic
128#3750C2×C411yescharacteristic
129#3750C2×C411yescharacteristic
130#3750C2×C411yescharacteristic
131#3750C2×C411yescharacteristic
132C4×C3⋊Dic3C2311yescharacteristic
133C3×#208—22no—
134C3×#208—22no—
135C3×#208—22no—
136C2×C3×C3⋊C8—22no—
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145#3712—22no—
146#3712—22no—
147#3712—22no—
148#3712—22no—
149#3712—22no—
150#3710—22no—
151#3710—22no—
152#3710D414yescomplemented
153#2930—91noSylow
154C2×#235—31no—
155C2×#235—31no—
156C2×#235—61no—
157C22×C4×D3—31no—
158C22×C4×D3—31no—
159C22×C4×D3—61no—
160C2×C3×M16—31no—
161C2×C3×M16—31no—
162C2×C3×M16—31no—
163C22×C3×C8—31no—
164C3×C4×D4—21no—
165C3×C4×D4C2×D311yescharacteristic
166C3×C4×D4C2×D311yescharacteristic
167#939—31no—
168#939—31no—
169#939—61no—
170#937—31no—
171#937—31no—
172#937—61no—
173C4×#67—31no—
174C4×#67—31no—
175C4×#67—31no—
176C4×#67—31no—
177C4×#67—61no—
178C4×#67—61no—
179C2×#208C2×D311yescharacteristic
180C2×#208C2×D311yescharacteristic
181C2×#208C2×D311yescharacteristic, complemented
182C22×C3⋊C8C2×D311yescharacteristic, complemented
183#907—64no—
184D3×M16—64no—
185D3×M16—64no—
186#901—64no—
187C2×ΓL(1,𝔽25)—31no—
188C2×ΓL(1,𝔽25)—31no—
189C2×ΓL(1,𝔽25)—31no—
190C2×ΓL(1,𝔽25)—31no—
191C2×ΓL(1,𝔽25)—31no—
192C2×ΓL(1,𝔽25)—31no—
193C2×ΓL(1,𝔽25)—31no—
194C2×ΓL(1,𝔽25)—31no—
195C2×ΓL(1,𝔽25)—31no—
196C2×ΓL(1,𝔽25)—31no—
197C2×D3×C8—31no—
198C2×D3×C8—31no—
199C2×D3×C8—31no—
200C2×D3×C8—31no—
201C2×D3×C8—31no—
202C2×D3×C8—31no—
203#896—31no—
204#896—31no—
205#896—61no—
206#894—31no—
207#894—31no—
208#894—61no—
209#884—31no—
210#884—31no—
211#884—61no—
212#883—31no—
213#883—31no—
214#883—61no—
215#882—31no—
216#882—31no—
217#882—61no—
218#878—31no—
219#878—31no—
220#878—61no—
221C4×D12—31no—
222C4×D12—31no—
223C4×D12—61no—
224#872—31no—
225#872—31no—
226#872—61no—
227C3×C4⋊C8—31no—
228C3×C4⋊C8—31no—
229C3×C22⋊C8—31no—
230C3×C22⋊C8—31no—
231C3×C22⋊C8—31no—
232C3×C22⋊C8—31no—
233C3×#97—31no—
234C3×C4×C8—31no—
235#830C2×D311yescharacteristic
236#830C2×D311yescharacteristic
237#830C2×D311yescharacteristic, complemented
238#830C2×D311yescharacteristic, complemented
239(C2×D3)⋊C8—31no—
240(C2×D3)⋊C8—31no—
241(C2×D3)⋊C8—31no—
242(C2×D3)⋊C8—31no—
243(C2×D3)⋊C8—31no—
244(C2×D3)⋊C8—31no—
245(C2×D3)⋊C8—31no—
246(C2×D3)⋊C8—31no—
247#815—31no—
248#815—31no—
249Dic3⋊C8—31no—
250Dic3⋊C8—31no—
251Dic3⋊C8—31no—
252Dic3⋊C8—31no—
253C8×Dic3—31no—
254C8×Dic3—31no—
255C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
256C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
257#803C2×D311yescharacteristic, complemented
258C4×C3⋊C8C2×D311yescharacteristic, complemented
259C23×C32C22×C411yescharacteristic
260C23×C32C22×C411yescharacteristic
261C22×C3⋊D3—22no—
262C22×C3⋊D3—41no—
263C22×C3⋊D3—41no—
264C22×C3⋊D3C22×C411yescharacteristic
265C22×C3⋊D3C22×C411yescharacteristic
266C22×C3⋊D3C22×C411yescharacteristic
267C32×D4—41no—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4C22×C411yescharacteristic
273C2×C32×C4C22×C411yescharacteristic
274C2×C32×C4C22×C411yescharacteristic
275C2×C32×C4C22×C411yescharacteristic
276C2×C32×C4C2411yescharacteristic
277#638—22no—
278#638—22no—
279#638—41no—
280#638—41no—
281C2×C3⋊Dic3—22no—
282C2×C3⋊Dic3C22×C411yescharacteristic
283C2×C3⋊Dic3C22×C411yescharacteristic
284C2×C3⋊Dic3C22×C411yescharacteristic
285C2×C3⋊Dic3C22×C411yescharacteristic
286C2×C3⋊Dic3C22×C411yescharacteristic
287C4⋊(C3⋊D3)—22no—
288C4⋊(C3⋊D3)—41no—
289C4×C3⋊D3—22no—
290C4×C3⋊D3—21no—
291C4×C3⋊D3—21no—
292C4×C3⋊D3—21no—
293C4×C3⋊D3—21no—
294C4×C3⋊D3—22no—
295C4×C3⋊D3C2×D412yes—
296C4×C3⋊D3#4112yes—
297#634—22no—
298C3×C3⋊C8—21no—
299C3×C3⋊C8—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8—21no—
302C3×C3⋊C8—21no—
303C3×C3⋊C8—21no—
304C3×C3⋊C8C2×D412yes—
305C3×C3⋊C8C2×D412yes—
306C2×#131—91no—
307C22×M16—91no—
308#525—91no—
309#436—31no—
310#436—91no—
311#436—91no—
312#436—91no—
313#435—31no—
314#435—91no—
315#435—91no—
316#435—91no—
317#424—91no—
318#408—91no—
319#407—91no—
320#405—91no—
321C23×D3—31no—
322C23×D3—31no—
323C23×D3—61no—
324C2×C3×D4—21no—
325C2×C3×D4C4×D311yescharacteristic
326C2×C3×D4C4×D311yescharacteristic
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4C22×D311yescharacteristic
330C22×C3×C4C22×D311yescharacteristic
331C22×C3×C4C22×D311yescharacteristic
332C22×C3×C4C22×D311yescharacteristic
333C2×#67—31no—
334C2×#67—31no—
335C2×#67—31no—
336C2×#67—31no—
337C2×#67—31no—
338C2×#67—31no—
339C2×#67—31no—
340C2×#67—31no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C22×Dic3—31no—
346C22×Dic3—31no—
347C22×Dic3—61no—
348#235—62no—
349#235—62no—
350#235—62no—
351#235—62no—
352#235—122no—
353#235—122no—
354C2×D12—31no—
355C2×D12—31no—
356C2×D12—31no—
357C2×D12—31no—
358C2×D12—61no—
359C2×D12—61no—
360C2×C4×D3—31no—
361C2×C4×D3—31no—
362C2×C4×D3—31no—
363C2×C4×D3—31no—
364C2×C4×D3—31no—
365C2×C4×D3—31no—
366C2×C4×D3—31no—
367C2×C4×D3—31no—
368C2×C4×D3—31no—
369C2×C4×D3—31no—
370C2×C4×D3—61no—
371C2×C4×D3—61no—
372C2×C4×D3—61no—
373C2×C4×D3—61no—
374C2×C4×D3—61no—
375C2×C4×D3—62no—
376C2×C4×D3—62no—
377C2×C4×D3—62no—
378C2×C4×D3—62no—
379C2×C4×D3—122no—
380C2×C4×D3—122no—
381C2×Dic6—31no—
382C2×Dic6—31no—
383C2×Dic6—61no—
384C3×M16—62no—
385C3×M16—62no—
386C3×M16—62no—
387C2×C3×C8—31no—
388C2×C3×C8—31no—
389C2×C3×C8—31no—
390C2×C3×C8—31no—
391C2×C3×C8—31no—
392C2×C3×C8—31no—
393C2×C3×C8—31no—
394C2×C3×C8—31no—
395C2×C3×C8—62no—
396C3×C4⋊C4—21no—
397C3×C4⋊C4C4×D311yescharacteristic
398C3×C4⋊C4C4×D311yescharacteristic
399C3×C22⋊C4—21no—
400C3×C22⋊C4—21no—
401C3×C22⋊C4C4×D311yescharacteristic
402C3×C22⋊C4C4×D311yescharacteristic
403C3×C22⋊C4C4×D311yescharacteristic
404C3×C22⋊C4C4×D311yescharacteristic
405C3×C42—21no—
406C3×C42C22×D311yescharacteristic
407C3×C42C22×D311yescharacteristic
408#217—31no—
409#217—31no—
410#217—31no—
411#217—31no—
412#217—61no—
413#217—61no—
414(C2×D3)⋊C4—31no—
415(C2×D3)⋊C4—31no—
416(C2×D3)⋊C4—31no—
417(C2×D3)⋊C4—31no—
418(C2×D3)⋊C4—31no—
419(C2×D3)⋊C4—31no—
420(C2×D3)⋊C4—31no—
421(C2×D3)⋊C4—31no—
422(C2×D3)⋊C4—31no—
423(C2×D3)⋊C4—31no—
424(C2×D3)⋊C4—31no—
425(C2×D3)⋊C4—31no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—61no—
432C4⋊Dic3—31no—
433C4⋊Dic3—31no—
434C4⋊Dic3—61no—
435Dic3⋊C4—31no—
436Dic3⋊C4—31no—
437Dic3⋊C4—31no—
438Dic3⋊C4—31no—
439Dic3⋊C4—31no—
440Dic3⋊C4—31no—
441Dic3⋊C4—31no—
442Dic3⋊C4—31no—
443Dic3⋊C4—61no—
444Dic3⋊C4—61no—
445Dic3⋊C4—61no—
446Dic3⋊C4—61no—
447C4×Dic3—31no—
448C4×Dic3—31no—
449C4×Dic3—61no—
450#208—22no—
451#208—22no—
452#208—22no—
453C2×C3⋊C8—22no—
454C2×C3⋊C8C22×D311yescharacteristic
455C2×C3⋊C8C22×D311yescharacteristic
456C2×C3⋊C8C22×D311yescharacteristic
457C2×C3⋊C8C22×D311yescharacteristic
458C2×C3⋊C8C22×D311yescharacteristic
459C2×C3⋊C8C22×D311yescharacteristic
460C2×C3⋊C8C22×D311yescharacteristic
461C2×C3⋊C8C22×D311yescharacteristic
462ΓL(1,𝔽25)—62no—
463ΓL(1,𝔽25)—62no—
464ΓL(1,𝔽25)—62no—
465ΓL(1,𝔽25)—62no—
466ΓL(1,𝔽25)—62no—
467ΓL(1,𝔽25)—62no—
468ΓL(1,𝔽25)—62no—
469ΓL(1,𝔽25)—62no—
470ΓL(1,𝔽25)—62no—
471ΓL(1,𝔽25)—62no—
472D3×C8—34no—
473D3×C8—34no—
474D3×C8—62no—
475D3×C8—62no—
476D3×C8—62no—
477D3×C8—62no—
478C22×C32—21no—
479C22×C32—21no—
480C22×C32—21no—
481C22×C32—21no—
482C22×C32—21no—
483C22×C32—21no—
484C22×C32C23×C411yescharacteristic
485C2×C3⋊D3—21no—
486C2×C3⋊D3—21no—
487C2×C3⋊D3—21no—
488C2×C3⋊D3—21no—
489C2×C3⋊D3—21no—
490C2×C3⋊D3—21no—
491C2×C3⋊D3—21no—
492C2×C3⋊D3—21no—
493C2×C3⋊D3—44no—
494C2×C3⋊D3C4×D412yes—
495C32×C4—21no—
496C32×C4—21no—
497C32×C4—21no—
498C32×C4—21no—
499C32×C4C22×D411yescharacteristic
500C32×C4C2×#4111yescharacteristic
501C3⋊Dic3—21no—
502C3⋊Dic3—21no—
503C3⋊Dic3—21no—
504C3⋊Dic3—21no—
505C3⋊Dic3C4×D412yes—
506C2×#41—91no—
507C23×C4—91no—
508#131—184no—
509C2×M16—31no—
510C2×M16—31no—
511C2×M16—31no—
512C2×M16—91no—
513C2×M16—91no—
514C2×M16—91no—
515C2×M16—91no—
516C2×M16—91no—
517C2×M16—184no—
518C22×C8—31no—
519C22×C8—91no—
520C22×C8—91no—
521C22×C8—91no—
522#123—91no—
523#123—91no—
524C22⋊Q8—91no—
525C22⋊Q8—91no—
526#121—91no—
527#121—91no—
528#120—91no—
529#120—91no—
530C4×D4—91no—
531C4×D4—91no—
532C4×D4—91no—
533C4×D4D3211yescharacteristic
534#117—91no—
535C4⋊C8—31no—
536C4⋊C8—31no—
537C4⋊C8—91no—
538C4⋊C8—91no—
539C22⋊C8—31no—
540C22⋊C8—31no—
541C22⋊C8—31no—
542C22⋊C8—31no—
543C22⋊C8—91no—
544C22⋊C8—91no—
545C22⋊C8—91no—
546C22⋊C8—91no—
547#97—31no—
548#97—91no—
549C4×C8—31no—
550C4×C8—91no—
551C23×C3—21no—
552C23×C3—21no—
553C23×C3C2×C4×D311yescharacteristic
554C23×C3C2×C4×D311yescharacteristic
555C23×C3C2×C4×D311yescharacteristic
556C23×C3C2×C4×D311yescharacteristic
557C22×D3—31no—
558C22×D3—31no—
559C22×D3—31no—
560C22×D3—31no—
561C22×D3—31no—
562C22×D3—31no—
563C22×D3—61no—
564C22×D3—61no—
565C22×D3—61no—
566C22×D3—62no—
567C22×D3—62no—
568C22×D3—122no—
569C22×D3—121no—
570C22×D3—121no—
571C22×D3—121no—
572C22×D3—121no—
573C22×D3—122no—
574C22×D3—122no—
575C3×D4—41no—
576C3×D4—41no—
577C3×D4—42no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4C2×C4×D311yescharacteristic
596C2×C3×C4C2×C4×D311yescharacteristic
597C2×C3×C4C2×C4×D311yescharacteristic
598C2×C3×C4C2×C4×D311yescharacteristic
599C2×C3×C4C2×C4×D311yescharacteristic
600C2×C3×C4C2×C4×D311yescharacteristic
601C2×C3×C4C2×C4×D311yescharacteristic
602C2×C3×C4C2×C4×D311yescharacteristic
603C2×C3×C4C23×D311yescharacteristic
604C2×C3×C4C23×D311yescharacteristic
605#67—62no—
606#67—62no—
607#67—62no—
608#67—62no—
609#67—122no—
610#67—122no—
611#67—121no—
612#67—121no—
613#67—121no—
614#67—121no—
615#67—122no—
616#67—122no—
617C2×Dic3—31no—
618C2×Dic3—31no—
619C2×Dic3—31no—
620C2×Dic3—31no—
621C2×Dic3—31no—
622C2×Dic3—31no—
623C2×Dic3—31no—
624C2×Dic3—31no—
625C2×Dic3—31no—
626C2×Dic3—31no—
627C2×Dic3—61no—
628C2×Dic3—61no—
629C2×Dic3—61no—
630C2×Dic3—61no—
631C2×Dic3—61no—
632C2×Dic3—62no—
633C2×Dic3—62no—
634C2×Dic3—122no—
635D12—62no—
636D12—62no—
637D12—122no—
638D12—121no—
639D12—121no—
640D12—122no—
641C4×D3—32no—
642C4×D3—32no—
643C4×D3—32no—
644C4×D3—32no—
645C4×D3—62no—
646C4×D3—62no—
647C4×D3—62no—
648C4×D3—62no—
649C4×D3—62no—
650C4×D3—62no—
651C4×D3—61no—
652C4×D3—61no—
653C4×D3—61no—
654C4×D3—61no—
655C4×D3—61no—
656C4×D3—61no—
657C4×D3—61no—
658C4×D3—61no—
659C4×D3—122no—
660C4×D3—121no—
661C4×D3—121no—
662C4×D3—121no—
663C4×D3—121no—
664C4×D3—122no—
665Dic6—62no—
666Dic6—62no—
667Dic6—122no—
668C3×C8—32no—
669C3×C8—32no—
670C3×C8—61no—
671C3×C8—61no—
672C3×C8—61no—
673C3×C8—61no—
674C3×C8—61no—
675C3×C8—61no—
676C3⋊C8—21no—
677C3⋊C8—21no—
678C3⋊C8—21no—
679C3⋊C8—21no—
680C3⋊C8—21no—
681C3⋊C8—21no—
682C3⋊C8D3×D412yes—
683C3⋊C8D3×D412yes—
684C2×C32—41no—
685C2×C32—41no—
686C2×C32C2×C4×D411yescharacteristic
687C2×C32#56811yescharacteristic
688C2×C32#56811yescharacteristic
689C3⋊D3—22no—
690C3⋊D3—41no—
691C3⋊D3—41no—
692C24—91no—
693#41—182no—
694#41—182no—
695C2×Q8—91no—
696C2×D4—91no—
697C2×D4—91no—
698C2×D4—91no—
699C2×D4—91no—
700C2×D4—91no—
701C2×D4—91no—
702C2×D4#62411yescharacteristic
703C22×C4—91no—
704C22×C4—91no—
705C22×C4—91no—
706C22×C4—91no—
707C22×C4—91no—
708C22×C4—91no—
709C22×C4—182no—
710C22×C4—182no—
711C22×C4C2×D3211yescharacteristic
712C22×C4C2×D3211yescharacteristic
713M16—62no—
714M16—62no—
715M16—62no—
716M16—182no—
717M16—182no—
718M16—182no—
719M16—182no—
720M16—182no—
721C2×C8—31no—
722C2×C8—31no—
723C2×C8—31no—
724C2×C8—31no—
725C2×C8—31no—
726C2×C8—31no—
727C2×C8—31no—
728C2×C8—31no—
729C2×C8—62no—
730C2×C8—94no—
731C2×C8—182no—
732C2×C8—182no—
733C4⋊C4—91no—
734C4⋊C4—91no—
735C4⋊C4—91no—
736C4⋊C4—91no—
737C4⋊C4—91no—
738C4⋊C4#62411yescharacteristic
739C22⋊C4—91no—
740C22⋊C4—91no—
741C22⋊C4—91no—
742C22⋊C4—91no—
743C22⋊C4—91no—
744C22⋊C4—91no—
745C22⋊C4—91no—
746C22⋊C4—91no—
747C22⋊C4#62411yescharacteristic
748C22⋊C4#62411yescharacteristic
749C42—91no—
750C42C2×D3211yescharacteristic
751C22×C3—22no—
752C22×C3—21no—
753C22×C3—21no—
754C22×C3—21no—
755C22×C3—21no—
756C22×C3—21no—
757C22×C3—21no—
758C22×C3—21no—
759C22×C3—21no—
760C22×C3—21no—
761C22×C3—21no—
762C22×C3—21no—
763C22×C3—21no—
764C22×C3—21no—
765C22×C3—41no—
766C22×C3—41no—
767C22×C3—41no—
768C22×C3—41no—
769C22×C3—41no—
770C22×C3C22×C4×D311yescharacteristic
771C22×C3C22×C4×D311yescharacteristic
772C2×D3—32no—
773C2×D3—32no—
774C2×D3—62no—
775C2×D3—61no—
776C2×D3—61no—
777C2×D3—61no—
778C2×D3—61no—
779C2×D3—62no—
780C2×D3—61no—
781C2×D3—61no—
782C2×D3—61no—
783C2×D3—61no—
784C2×D3—61no—
785C2×D3—61no—
786C2×D3—61no—
787C2×D3—61no—
788C2×D3—61no—
789C2×D3—61no—
790C2×D3—61no—
791C2×D3—61no—
792C2×D3—121no—
793C2×D3—121no—
794C2×D3—121no—
795C2×D3—121no—
796C2×D3—121no—
797C2×D3—121no—
798C2×D3—121no—
799C2×D3—124no—
800C2×D3—124no—
801C2×D3—128no—
802C3×C4—21no—
803C3×C4—21no—
804C3×C4—21no—
805C3×C4—21no—
806C3×C4—21no—
807C3×C4—21no—
808C3×C4—21no—
809C3×C4—21no—
810C3×C4—21no—
811C3×C4—21no—
812C3×C4—41no—
813C3×C4—41no—
814C3×C4—41no—
815C3×C4—41no—
816C3×C4C2×D3×D411yescharacteristic
817C3×C4C2×D3×D411yescharacteristic
818C3×C4D3×#4111yescharacteristic
819C3×C4D3×#4111yescharacteristic
820Dic3—32no—
821Dic3—32no—
822Dic3—62no—
823Dic3—61no—
824Dic3—61no—
825Dic3—61no—
826Dic3—61no—
827Dic3—61no—
828Dic3—61no—
829Dic3—61no—
830Dic3—61no—
831Dic3—121no—
832Dic3—121no—
833Dic3—121no—
834Dic3—121no—
835C32#293011yescharacteristic, complemented, Sylow
836C23—91no—
837C23—91no—
838C23—91no—
839C23—182no—
840C23—361no—
841C23—361no—
842C23C2×#62411yescharacteristic
843C23C2×#62411yescharacteristic
844Q8—182no—
845D4—41no—
846D4—182no—
847D4—182no—
848D4—182no—
849D4—361no—
850D4—361no—
851D4—361no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—91no—
857C2×C4—92no—
858C2×C4—92no—
859C2×C4—91no—
860C2×C4—91no—
861C2×C4—91no—
862C2×C4—91no—
863C2×C4—182no—
864C2×C4—182no—
865C2×C4—182no—
866C2×C4—181no—
867C2×C4—181no—
868C2×C4—181no—
869C2×C4—181no—
870C2×C4C2×#62411yescharacteristic
871C2×C4C2×#62411yescharacteristic
872C2×C4C2×#62411yescharacteristic
873C2×C4C2×#62411yescharacteristic
874C2×C4C22×D3211yescharacteristic
875C8—32no—
876C8—32no—
877C8—61no—
878C8—61no—
879C8—61no—
880C8—61no—
881C8—61no—
882C8—61no—
883C2×C3—21no—
884C2×C3—21no—
885C2×C3—21no—
886C2×C3—42no—
887C2×C3—41no—
888C2×C3—41no—
889C2×C3—41no—
890C2×C3—41no—
891C2×C3—81no—
892C2×C3C4×D3×D411yescharacteristic
893C2×C3C4×D3×D411yescharacteristic
894C2×C3#574511yescharacteristic
895C2×C3#574511yescharacteristic
896C2×C3#575011yescharacteristic
897C2×C3#575011yescharacteristic
898D3—62no—
899D3—62no—
900D3—122no—
901D3—122no—
902D3—121no—
903D3—121no—
904D3—121no—
905D3—121no—
906D3—241no—
907C22—21no—
908C22—21no—
909C22—21no—
910C22—21no—
911C22—21no—
912C22—21no—
913C22—92no—
914C22—181no—
915C22—181no—
916C22—181no—
917C22—181no—
918C22—181no—
919C22—181no—
920C22—181no—
921C22—181no—
922C22—364no—
923C22C22×#62411yescharacteristic
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—92no—
929C4—181no—
930C4—181no—
931C4—181no—
932C4—181no—
933C4D32×D411yescharacteristic
934C4#6431211yescharacteristic
935C3—21no—
936C3#7947911yescharacteristic, complemented
937C3#7953711yescharacteristic, complemented
938C2—41no—
939C2—41no—
940C2—182no—
941C2—361no—
942C2—361no—
943C2#1059478011yescharacteristic
944C2D4×#62411yescharacteristic
945C2#1059544311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×C4×D4C22
prime radical#10596018C2
cosocleC2×C32×C4C24
hypercenterC4×D4D32
hypocenterC32#2930
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63818C2semidirect
3. C2×#63817C2semidirect
4. C3×#5012C2semidirect
5. C3×#5011C2semidirect
6. #10591159C2semidirect
7. #10591157C2semidirect
8. #10591153C2semidirect
9. #10591149C2semidirect
10. #10591051C2semidirect
11. #10591051C2semidirect
12. #10590338C2semidirect
13. #10590332C2semidirect
14. #10590328C2semidirect
15. #10590321C2semidirect
35. C2×C3×#208C22semidirect
36. C22×C3×C3⋊C8C22semidirect
41. C2×#3712C22semidirect
46. C2×#3710C22semidirect
49. C3×#830C22semidirect
50. C3×#830C22semidirect
51. C3×C4⋊(C3⋊C8)C22semidirect
52. C3×C4⋊(C3⋊C8)C22semidirect
53. C3×#803C22semidirect
54. C3×C4×C3⋊C8C22semidirect
55. #63572C22semidirect
56. #63572C22semidirect
59. #63557C22semidirect
60. #63557C22semidirect
61. #63555C22semidirect
62. #63553C22semidirect
76. #5012D3semidirect
77. #5011D3semidirect
152. #3710D4semidirect
181. C2×#208C2×D3semidirect
182. C22×C3⋊C8C2×D3semidirect
237. #830C2×D3semidirect
238. #830C2×D3semidirect
255. C4⋊(C3⋊C8)C2×D3semidirect
256. C4⋊(C3⋊C8)C2×D3semidirect
257. #803C2×D3semidirect
258. C4×C3⋊C8C2×D3semidirect
835. C32#2930semidirect
936. C3#79479semidirect
937. C3#79537semidirect

Maximal subgroups

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

subgroupindex
#105960182
C2×#638182
C2×#638172
C3×#50122
C3×#50112
#105911592
#105911572
#105911532
#105911492
#105910512
#105903382
#105903322
#105903282
#105903212
#795373
#794793