Finite Group Databasebeta

← #11889109

Subgroups — #11889109

Order 1152.

994 conjugacy classes of subgroups.

The subgroup lattice has 851 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595074C211yesmaximal, characteristic
2#10594849C211yesmaximal, characteristic, complemented
3#10592430C211yesmaximal, characteristic, complemented
4C3×#4736C211yesmaximal, characteristic, complemented
5C3×#4730C211yesmaximal, characteristic, complemented
6#10591175C211yesmaximal, characteristic, complemented
7C2×#63564C211yesmaximal, characteristic, complemented
8#10590946C211yesmaximal, characteristic, complemented
9#10590939C211yesmaximal, characteristic, complemented
10#10590882C211yesmaximal, characteristic, complemented
11#10590879C211yesmaximal, characteristic, complemented
12#10590838C211yesmaximal, characteristic, complemented
13#10590774C211yesmaximal, characteristic, complemented
14#10590773C211yesmaximal, characteristic, complemented
15#10590705C211yesmaximal, characteristic, complemented
16#81303—31nomaximal
17#79501—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×#3811—21no—
20C2×D3×D12C2211yescharacteristic
21#64133C2211yescharacteristic, complemented
22C2×#3744C2211yescharacteristic
23C2×#3744C2211yescharacteristic, complemented
24C3×#930C2211yescharacteristic
25C3×C4×#67C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
27C22×C3×C3⋊C8C2211yescharacteristic, complemented
28C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
29#63981—21no—
30#63961—21no—
31#63955—21no—
32#63923—21no—
33#63911C2211yescharacteristic
34#63910—21no—
35#63909C2211yescharacteristic
36#63894C2211yescharacteristic
37#63869C2211yescharacteristic, complemented
38#63858—21no—
39#63857C2211yescharacteristic, complemented
40#63847—21no—
41#63844C2211yescharacteristic, complemented
42#63841C2211yescharacteristic, complemented
43C2×#3716C2211yescharacteristic, complemented
44C32×C22⋊C8C2211yescharacteristic, complemented
45#63648C2211yescharacteristic
46#63648C2211yescharacteristic, complemented
47C3×#821C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic, complemented
49C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
50C3×#818C2211yescharacteristic, complemented
51C3×#818C2211yescharacteristic, complemented
52C3×#815C2211yescharacteristic, complemented
53C3×Dic3⋊C8C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic, complemented
59#63564C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61#5609—31no—
62D4×D12—31no—
63#5541—31no—
64#5513—31no—
65C3×#480—31no—
66C3×#435—31no—
67#5134—31no—
68#5131—31no—
69#5114—31no—
70C2×#821—31no—
71#5041—31no—
72C2×#809—31no—
73#4891—31no—
74#4889—31no—
75#4886—31no—
76#4885—31no—
77#4848—31no—
78#4847—31no—
79#4776—31no—
80#4770—31no—
81#4764—31no—
82#4762—31no—
83#4737—31no—
84#4736D311yescharacteristic, complemented
85#4731—31no—
86#4731—31no—
87#4731—31no—
88#4731—61no—
89#4730D311yescharacteristic, complemented
90#4713—31no—
91#4710—31no—
92C23×C3⋊D3—21no—
93C22×D32—21no—
94C22×C32×C4C2311yescharacteristic
95C2×C4⋊(C3⋊D3)—22no—
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)—41no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×#634C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67D411yescharacteristic
103C22×C3×Dic3—21no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106#3811—44no—
107C2×#626—21no—
108C2×#626—21no—
109C2×#626—21no—
110C2×#626—21no—
111C2×#624—21no—
112D3×D12—22no—
113D3×D12—41no—
114C2×C32×C8C2311yescharacteristic
115C2×C32×C8C2311yescharacteristic
116#3757—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3750—21no—
119#3744—22no—
120#3744—41no—
121C3×#217D411yescharacteristic
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4D411yescharacteristic
129C3×C4×Dic3C2311yescharacteristic
130C2×C3×C3⋊C8—41no—
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C3×ΓL(1,𝔽25)—41no—
134#3724—21no—
135#3724—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138#3722—21no—
139#3722—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142Dic32—21no—
143Dic32—21no—
144#3716—41no—
145#3310—91noSylow
146C2×D3×D4—31no—
147C2×D3×D4—61no—
148C2×D3×D4—61no—
149C22×D12—31no—
150C22×D12—31no—
151C22×D12—31no—
152C22×D12—61no—
153C2×C3×M16—31no—
154C22×C3×C8—31no—
155C3×#121—31no—
156C3×C4×D4—31no—
157C2×C3×C4⋊C4—31no—
158#940—31no—
159#937—61no—
160#935—61no—
161C2×#214—31no—
162#930—31no—
163#930C2×D311yescharacteristic
164#929—61no—
165C4×#67C2×D311yescharacteristic
166#926—31no—
167#926—61no—
168C2×C4⋊Dic3C2×D311yescharacteristic, complemented
169#924—31no—
170#924—31no—
171#924—31no—
172#924—61no—
173C22×C3⋊C8C2×D311yescharacteristic, complemented
174C2×#204—31no—
175C2×#204—31no—
176C2×#204—31no—
177C2×#204—31no—
178C2×#204—31no—
179C2×#204—61no—
180C2×#204—61no—
181C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
182#898—61no—
183#897—31no—
184#895—31no—
185#895—61no—
186#893—31no—
187#892—31no—
188#890—31no—
189#889—61no—
190#889—61no—
191#887—31no—
192#884—61no—
193#882—61no—
194#882—61no—
195#882—61no—
196#879—61no—
197#877—61no—
198#874—31no—
199C4×D12—31no—
200#870—31no—
201C4×Dic6—31no—
202C3×#107—31no—
203C3×#107—31no—
204C3×C4⋊C8—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×C22⋊C8—21no—
208C3×C22⋊C8—31no—
209C3×C22⋊C8C2×D311yescharacteristic, complemented
210C3×C22⋊C8C2×D311yescharacteristic, complemented
211C3×#97—31no—
212#832—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—31no—
220#821—31no—
221#821—31no—
222#821—61no—
223#821—61no—
224#821C2×D311yescharacteristic, complemented
225#821C2×D311yescharacteristic, complemented
226(C2×D3)⋊C8C2×D311yescharacteristic, complemented
227#818C2×D311yescharacteristic, complemented
228#818C2×D311yescharacteristic, complemented
229#817—31no—
230#816—31no—
231#815C2×D311yescharacteristic, complemented
232Dic3⋊C8C2×D311yescharacteristic, complemented
233#810—31no—
234#809—31no—
235#809—31no—
236#809—31no—
237#809—31no—
238#808—31no—
239C23×C32C2×D411yescharacteristic
240C22×C3⋊D3—21no—
241C22×C3⋊D3—21no—
242C22×C3⋊D3—42no—
243C22×C3⋊D3—42no—
244C22×C3⋊D3—81no—
245C22×C3×D3—21no—
246C22×C3×D3C2×D411yescharacteristic
247C2×D32—42no—
248C2×D32—42no—
249C2×D32—81no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—21no—
256C4⋊(C3⋊D3)—21no—
257C4⋊(C3⋊D3)—21no—
258C4⋊(C3⋊D3)—21no—
259C4⋊(C3⋊D3)—42no—
260C4⋊(C3⋊D3)#4112yes—
261#634—21no—
262#634—21no—
263C3×#67—22no—
264C3×#67—42no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—42no—
269C2×C3×Dic3C2×D411yescharacteristic
270C2×C3×Dic3C2×D411yescharacteristic
271C2×C3×Dic3C2×D411yescharacteristic
272C3×D12—21no—
273C3×D12—21no—
274C3×C4×D3—21no—
275C3×C4×D3—21no—
276#626—42no—
277#626—42no—
278#626—42no—
279#626—81no—
280#624—42no—
281C32×C8—21no—
282C32×C8—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#552—91no—
286D42—91no—
287#490—91no—
288#482—91no—
289#480—31no—
290#478—91no—
291#468—91no—
292#465—91no—
293#460—91no—
294#450—91no—
295#450—91no—
296#440—91no—
297#435—31no—
298#418—91no—
299C2×#102—91no—
300C23×D3—61no—
301C23×D3—61no—
302C23×D3—61no—
303C23×D3—61no—
304C23×D3—121no—
305C2×C3×D4—31no—
306C2×C3×D4—31no—
307C2×C3×D4—61no—
308C22×C3×C4—21no—
309C22×C3×C4—31no—
310C22×C3×C4—61no—
311C22×C3×C4C22×D311yescharacteristic
312C22×C3×C4C22×D311yescharacteristic
313C2×#67—21no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67D1211yescharacteristic
319C22×Dic3—21no—
320D3×D4—62no—
321D3×D4—121no—
322D3×D4—124no—
323D3×D4—124no—
324C2×D12—31no—
325C2×D12—31no—
326C2×D12—31no—
327C2×D12—31no—
328C2×D12—61no—
329C2×D12—61no—
330C2×D12—62no—
331C2×D12—62no—
332C2×D12—62no—
333C2×D12—61no—
334C2×D12—61no—
335C2×D12—61no—
336C2×D12—61no—
337C2×D12—61no—
338C2×D12—61no—
339C2×D12—122no—
340C2×D12—121no—
341C2×D12—121no—
342C2×D12—121no—
343C2×D12—121no—
344C2×D12—122no—
345C2×D12C22×D311yescharacteristic
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3C22×D311yescharacteristic
349C2×Dic6—31no—
350C2×Dic6—31no—
351C2×Dic6—61no—
352C3×M16—121no—
353C2×C3×C8—21no—
354C2×C3×C8—21no—
355C2×C3×C8—31no—
356C2×C3×C8—31no—
357C2×C3×C8—121no—
358C2×C3×C8C22×D311yescharacteristic
359C2×C3×C8C22×D311yescharacteristic
360C2×C3×C8C22×D311yescharacteristic
361C2×C3×C8C22×D311yescharacteristic
362C3×C4⋊C4—31no—
363C3×C4⋊C4—31no—
364C3×C4⋊C4—31no—
365C3×C4⋊C4—31no—
366C3×C4⋊C4—61no—
367C3×C22⋊C4—31no—
368C3×C22⋊C4—31no—
369C3×C22⋊C4—61no—
370C3×C42—31no—
371#217—61no—
372#217—61no—
373#217—61no—
374#217—61no—
375#217—121no—
376#217D1211yescharacteristic
377#214—121no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4D1211yescharacteristic
386C4⋊Dic3—21no—
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3C22×D311yescharacteristic
393C4⋊Dic3C22×D311yescharacteristic
394C4⋊Dic3C22×D311yescharacteristic
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—121no—
404Dic3⋊C4D1211yescharacteristic
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3—61no—
408C4×Dic3—61no—
409C4×Dic3C22×D311yescharacteristic
410C2×C3⋊C8—41no—
411C2×C3⋊C8C22×D311yescharacteristic
412C2×C3⋊C8C22×D311yescharacteristic
413#204—62no—
414#204—62no—
415#204—122no—
416#204—121no—
417#204—121no—
418#204—122no—
419#204—121no—
420ΓL(1,𝔽25)—41no—
421C22×C32—21no—
422C22×C32—21no—
423C22×C32AGL(1,ℤ/8)12yes—
424C22×C32C22×D411yescharacteristic
425C2×C3⋊D3—22no—
426C2×C3⋊D3—41no—
427C2×C3⋊D3—41no—
428C2×C3⋊D3—41no—
429C2×C3⋊D3—41no—
430C2×C3⋊D3—41no—
431C2×C3⋊D3—84no—
432C2×C3×D3—21no—
433C2×C3×D3—21no—
434C2×C3×D3—21no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437C2×C3×D3—41no—
438D32—84no—
439C32×C4—21no—
440C32×C4C2×#4111yescharacteristic
441C32×C4H(5,𝔽2)11yescharacteristic
442C3⋊Dic3—41no—
443C3⋊Dic3—41no—
444C3×Dic3—21no—
445C3×Dic3—21no—
446C3×Dic3—21no—
447C3×Dic3—41no—
448C3×Dic3—41no—
449C3×Dic3—41no—
450C22×D4—91no—
451C22×D4—91no—
452C22×D4—181no—
453C2×SD16—91no—
454C2×SD16—91no—
455C2×SD16—91no—
456C2×M16—31no—
457C22×C8—31no—
458#127—91no—
459#126—181no—
460#125—91no—
461#125—181no—
462#123—181no—
463C22⋊Q8—91no—
464C22⋊Q8—91no—
465#121—31no—
466#121—91no—
467#121—181no—
468#120—181no—
469#120—181no—
470C4×Q8—91no—
471C4×D4—31no—
472C4×D4—91no—
473#117—91no—
474#117—181no—
475C2×C4⋊C4—31no—
476#107—31no—
477#107—31no—
478#106—91no—
479C4⋊C8—31no—
480#103—91no—
481#102—31no—
482#102—31no—
483#102—91no—
484#102—91no—
485#102—91no—
486#102—91no—
487#102—91no—
488#102—91no—
489#102—91no—
490C22⋊C8—31no—
491C22⋊C8D3211yescharacteristic, complemented
492#97—31no—
493C23×C3—21no—
494C23×C3—31no—
495C23×C3—61no—
496C23×C3C2×D1211yescharacteristic
497C23×C3D3×D411yescharacteristic
498C22×D3—21no—
499C22×D3—61no—
500C22×D3—61no—
501C22×D3—61no—
502C22×D3—61no—
503C22×D3—121no—
504C22×D3—121no—
505C22×D3—122no—
506C22×D3—122no—
507C22×D3—122no—
508C22×D3—122no—
509C22×D3—122no—
510C22×D3—122no—
511C22×D3—124no—
512C22×D3—122no—
513C22×D3—122no—
514C22×D3—242no—
515C22×D3—241no—
516C22×D3—241no—
517C22×D3—241no—
518C22×D3—241no—
519C22×D3—242no—
520C22×D3C2×D1211yescharacteristic
521C3×D4—62no—
522C3×D4—61no—
523C3×D4—61no—
524C3×D4—122no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—31no—
532C2×C3×C4—31no—
533C2×C3×C4—31no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—122no—
542C2×C3×C4C2×D1211yescharacteristic
543C2×C3×C4D3×D411yescharacteristic
544C2×C3×C4C23×D311yescharacteristic
545C2×C3×C4C23×D311yescharacteristic
546#67—22no—
547#67—42no—
548#67—122no—
549#67—122no—
550#67—122no—
551#67—241no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—42no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—121no—
561C2×Dic3—121no—
562C2×Dic3C2×D1211yescharacteristic
563C2×Dic3C2×D1211yescharacteristic
564C2×Dic3C2×D1211yescharacteristic
565D12—21no—
566D12—21no—
567D12—32no—
568D12—32no—
569D12—62no—
570D12—62no—
571D12—61no—
572D12—61no—
573D12—61no—
574D12—61no—
575D12—61no—
576D12—61no—
577D12—121no—
578D12—121no—
579D12—122no—
580D12—122no—
581D12—124no—
582D12—122no—
583D12—122no—
584D12—122no—
585D12—241no—
586C4×D3—21no—
587C4×D3—21no—
588C4×D3—122no—
589C4×D3—122no—
590Dic6—61no—
591Dic6—61no—
592Dic6—61no—
593Dic6—61no—
594Dic6—121no—
595Dic6—121no—
596C3×C8—21no—
597C3×C8—21no—
598C3×C8—21no—
599C3×C8—21no—
600C3×C8—41no—
601C3×C8—41no—
602C3×C8—61no—
603C3×C8—61no—
604C3⋊C8—21no—
605C3⋊C8—21no—
606C2×C32—22no—
607C2×C32#54611yescharacteristic
608C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
609C2×C32#57711yescharacteristic
610C3⋊D3—42no—
611C3⋊D3—81no—
612C3×D3—41no—
613C3×D3—81no—
614C24—181no—
615C24—181no—
616C2×Q8—91no—
617C2×D4—31no—
618C2×D4—31no—
619C2×D4—61no—
620C2×D4—91no—
621C2×D4—91no—
622C2×D4—182no—
623C2×D4—181no—
624C2×D4—181no—
625C2×D4—181no—
626C2×D4—182no—
627C2×D4—181no—
628C2×D4—181no—
629C2×D4—361no—
630C2×D4—361no—
631C2×D4—364no—
632C22×C4—31no—
633C22×C4—61no—
634C22×C4—181no—
635C22×C4C2×D3211yescharacteristic
636SD16—182no—
637SD16—361no—
638SD16—361no—
639M16—121no—
640C2×C8—31no—
641C2×C8—31no—
642C2×C8—121no—
643C2×C8C2×D3211yescharacteristic
644C2×C8C2×D3211yescharacteristic
645C4⋊C4—31no—
646C4⋊C4—31no—
647C4⋊C4—31no—
648C4⋊C4—31no—
649C4⋊C4—61no—
650C4⋊C4—91no—
651C4⋊C4—181no—
652C4⋊C4—181no—
653C4⋊C4—181no—
654C4⋊C4—181no—
655C4⋊C4—181no—
656C22⋊C4—31no—
657C22⋊C4—31no—
658C22⋊C4—61no—
659C22⋊C4—181no—
660C22⋊C4—181no—
661C22⋊C4—181no—
662C22⋊C4—181no—
663C22⋊C4—181no—
664C42—31no—
665C42—181no—
666C42—181no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—22no—
673C22×C3—41no—
674C22×C3—41no—
675C22×C3—61no—
676C22×C3—61no—
677C22×C3—61no—
678C22×C3—121no—
679C22×C3—121no—
680C22×C3—121no—
681C22×C3#90812yes—
682C22×C3#91112yes—
683C22×C3C22×D1211yescharacteristic
684C22×C3C2×D3×D411yescharacteristic
685C2×D3—21no—
686C2×D3—21no—
687C2×D3—21no—
688C2×D3—41no—
689C2×D3—41no—
690C2×D3—41no—
691C2×D3—62no—
692C2×D3—62no—
693C2×D3—122no—
694C2×D3—121no—
695C2×D3—121no—
696C2×D3—121no—
697C2×D3—121no—
698C2×D3—122no—
699C2×D3—121no—
700C2×D3—121no—
701C2×D3—121no—
702C2×D3—121no—
703C2×D3—121no—
704C2×D3—121no—
705C2×D3—241no—
706C2×D3—241no—
707C2×D3—241no—
708C2×D3—241no—
709C2×D3—244no—
710C2×D3—244no—
711C2×D3—244no—
712C2×D3—244no—
713C2×D3—248no—
714C3×C4—21no—
715C3×C4—21no—
716C3×C4—21no—
717C3×C4—21no—
718C3×C4—41no—
719C3×C4—61no—
720C3×C4—61no—
721C3×C4—61no—
722C3×C4—121no—
723C3×C4—121no—
724C3×C4—121no—
725C3×C4#100411yescharacteristic
726C3×C4D3×#4111yescharacteristic
727C3×C4D3×#4111yescharacteristic
728C3×C4#100911yescharacteristic
729Dic3—21no—
730Dic3—21no—
731Dic3—21no—
732Dic3—41no—
733Dic3—41no—
734Dic3—41no—
735Dic3—121no—
736Dic3—121no—
737Dic3—121no—
738Dic3—121no—
739Dic3—241no—
740Dic3—241no—
741C32#331011yescharacteristic, complemented, Sylow
742C23—31no—
743C23—61no—
744C23—181no—
745C23—181no—
746C23—362no—
747C23—362no—
748C23—362no—
749C23—362no—
750C23—721no—
751C23—721no—
752C23D3×D1211yescharacteristic
753Q8—181no—
754Q8—181no—
755D4—62no—
756D4—61no—
757D4—61no—
758D4—92no—
759D4—122no—
760D4—181no—
761D4—181no—
762D4—181no—
763D4—362no—
764D4—362no—
765D4—362no—
766D4—362no—
767D4—721no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—31no—
771C2×C4—31no—
772C2×C4—31no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—122no—
779C2×C4—181no—
780C2×C4—181no—
781C2×C4—362no—
782C2×C4D3×D1211yescharacteristic
783C2×C4C22×D3211yescharacteristic
784C8—21no—
785C8—21no—
786C8—61no—
787C8—61no—
788C2×C3—22no—
789C2×C3—22no—
790C2×C3—21no—
791C2×C3—21no—
792C2×C3—21no—
793C2×C3—42no—
794C2×C3—121no—
795C2×C3—241no—
796C2×C3#555411yescharacteristic
797C2×C3#565411yescharacteristic
798C2×C3C2×#90811yescharacteristic
799C2×C3#575111yescharacteristic
800C2×C3C2×#91111yescharacteristic
801C2×C3#577811yescharacteristic
802D3—41no—
803D3—81no—
804D3—122no—
805D3—122no—
806D3—242no—
807D3—242no—
808D3—241no—
809D3—241no—
810C22—21no—
811C22—21no—
812C22—61no—
813C22—61no—
814C22—61no—
815C22—121no—
816C22—121no—
817C22—121no—
818C22—182no—
819C22—361no—
820C22—361no—
821C22—361no—
822C22—361no—
823C22—361no—
824C22—724no—
825C22—724no—
826C22#6379512yes—
827C22C2×D3×D1211yescharacteristic
828C4—21no—
829C4—61no—
830C4—61no—
831C4—61no—
832C4—121no—
833C4—121no—
834C4—121no—
835C4—361no—
836C4—361no—
837C4#6431211yescharacteristic
838C4#6431411yescharacteristic
839C3—21no—
840C3#7950111yescharacteristic, complemented
841C3#8130311yescharacteristic, complemented
842C2—22no—
843C2—121no—
844C2—241no—
845C2—362no—
846C2—721no—
847C2#1059429311yescharacteristic
848C2C2×#6379511yescharacteristic
849C2#1059471511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10595074C2
hypercenterC22⋊C8D32
hypocenterC32#3310
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #10594849C2semidirect
3. #10592430C2semidirect
4. C3×#4736C2semidirect
5. C3×#4730C2semidirect
6. #10591175C2semidirect
7. C2×#63564C2semidirect
8. #10590946C2semidirect
9. #10590939C2semidirect
10. #10590882C2semidirect
11. #10590879C2semidirect
12. #10590838C2semidirect
13. #10590774C2semidirect
14. #10590773C2semidirect
15. #10590705C2semidirect
21. #64133C22semidirect
23. C2×#3744C22semidirect
26. C2×C3×C4⋊Dic3C22semidirect
27. C22×C3×C3⋊C8C22semidirect
28. C2×C3×ΓL(1,𝔽25)C22semidirect
37. #63869C22semidirect
39. #63857C22semidirect
41. #63844C22semidirect
42. #63841C22semidirect
43. C2×#3716C22semidirect
44. C32×C22⋊C8C22semidirect
46. #63648C22semidirect
47. C3×#821C22semidirect
48. C3×#821C22semidirect
49. C3×(C2×D3)⋊C8C22semidirect
50. C3×#818C22semidirect
51. C3×#818C22semidirect
52. C3×#815C22semidirect
53. C3×Dic3⋊C8C22semidirect
54. #63573C22semidirect
55. #63567C22semidirect
58. #63564C22semidirect
59. #63564C22semidirect
60. #63563C22semidirect
84. #4736D3semidirect
89. #4730D3semidirect
168. C2×C4⋊Dic3C2×D3semidirect
173. C22×C3⋊C8C2×D3semidirect
181. C2×ΓL(1,𝔽25)C2×D3semidirect
209. C3×C22⋊C8C2×D3semidirect
210. C3×C22⋊C8C2×D3semidirect
224. #821C2×D3semidirect
225. #821C2×D3semidirect
226. (C2×D3)⋊C8C2×D3semidirect
227. #818C2×D3semidirect
228. #818C2×D3semidirect
231. #815C2×D3semidirect
232. Dic3⋊C8C2×D3semidirect
491. C22⋊C8D32semidirect
741. C32#3310semidirect
840. C3#79501semidirect
841. C3#81303semidirect

Maximal subgroups

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

subgroupindex
#105950742
#105948492
#105924302
C3×#47362
C3×#47302
#105911752
C2×#635642
#105909462
#105909392
#105908822
#105908792
#105908382
#105907742
#105907732
#105907052
#813033
#795013