Finite Group Databasebeta

← #11889121

Subgroups — #11889121

Order 1152.

962 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595293C211yesmaximal, characteristic
2#10594584C211yesmaximal, characteristic, complemented
3#10592477C211yesmaximal, characteristic, complemented
4C3×#4770C211yesmaximal, characteristic, complemented
5C3×#4764C211yesmaximal, characteristic, complemented
6#10591459C211yesmaximal, characteristic, complemented
7#10591439C211yesmaximal, characteristic, complemented
8#10591417C211yesmaximal, characteristic, complemented
9#10590940C211yesmaximal, characteristic, complemented
10#10590828C211yesmaximal, characteristic, complemented
11#10590747C211yesmaximal, characteristic, complemented
12#10590736C211yesmaximal, characteristic, complemented
13#10590597C211yesmaximal, characteristic, complemented
14#10590505C211yesmaximal, characteristic, complemented
15#10590469C211yesmaximal, characteristic, complemented
16#81725—31nomaximal
17#78934—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×#67—21no—
20C2×#3802C2211yescharacteristic
21#64147C2211yescharacteristic
22C2×#3754C2211yescharacteristic, complemented
23C2×C8×C3⋊D3C2211yescharacteristic, complemented
24#64106C2211yescharacteristic, complemented
25C3×#940C2211yescharacteristic
26C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
27C3×#892C2211yescharacteristic, complemented
28C3×#890C2211yescharacteristic, complemented
29#63983—21no—
30#63976—21no—
31#63970—21no—
32#63908C2211yescharacteristic
33C4×#626C2211yescharacteristic
34#63900C2211yescharacteristic, complemented
35Dic3×D12C2211yescharacteristic
36#63869—21no—
37#63861—21no—
38#63857C2211yescharacteristic, complemented
39#63854—21no—
40#63844C2211yescharacteristic, complemented
41#63836—21no—
42C2×#3716C2211yescharacteristic
43C2×#3716C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic, complemented
45#63643C2211yescharacteristic, complemented
46#63635C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic, complemented
51C3×#815C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#809C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic, complemented
59#63557C2211yescharacteristic, complemented
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61D4×#67—31no—
62#5717—31no—
63#5694—31no—
64#5529—31no—
65C3×#490—31no—
66C3×#418—31no—
67#5218—31no—
68#5134—31no—
69#5127—31no—
70#5075—31no—
71#5066—31no—
72#5003—31no—
73#4784—31no—
74#4780—31no—
75#4778—31no—
76#4778—31no—
77#4778—61no—
78#4776—31no—
79#4776—31no—
80#4776—31no—
81#4774—31no—
82#4774—31no—
83#4770D311yescharacteristic, complemented
84D3×#102—31no—
85D3×#102—31no—
86#4766—31no—
87#4764D311yescharacteristic, complemented
88#4762—31no—
89#4757—31no—
90#4710—31no—
91#4706—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C3×D3×D4—22no—
102C3×D3×D4—41no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106D3×#67—44no—
107C2×#626D411yescharacteristic
108C2×#625—21no—
109C2×#625—21no—
110C2×#624—21no—
111C2×D3×Dic3—21no—
112#3802—22no—
113#3802—41no—
114C2×C32×C8C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116#3757—21no—
117#3754—41no—
118#3752—21no—
119C4⋊(C3⋊Dic3)—21no—
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C8×C3⋊D3—41no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3—21no—
129C3×C4×Dic3C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C3×ΓL(1,𝔽25)—41no—
133#3724—21no—
134#3724—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3D411yescharacteristic
137#3722D411yescharacteristic
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3D411yescharacteristic
142Dic32—21no—
143#3716—22no—
144#3716—41no—
145#3310—91noSylow
146C22×C3×D4—31no—
147C22×#67—61no—
148C2×D3×D4—31no—
149C2×D3×D4—31no—
150C2×D3×D4—61no—
151C2×D3×D4C2×D311yescharacteristic
152C2×C3×M16—31no—
153C3×#127—31no—
154C3×#125—31no—
155C3×#117—31no—
156#953—61no—
157#940C2×D311yescharacteristic
158#939—61no—
159#938—31no—
160#938—31no—
161#938—31no—
162#938—61no—
163#938—61no—
164#937—61no—
165#937—61no—
166#937—61no—
167D4×Dic3—31no—
168C2×#214—31no—
169C2×#214—31no—
170C2×#214—31no—
171C2×#214—31no—
172C2×#214—61no—
173#930—31no—
174C4×#67—31no—
175#924—31no—
176C2×#204—31no—
177C2×#204—31no—
178C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
179C2×D3×C8—31no—
180C2×D3×C8—31no—
181C2×D3×C8—61no—
182#898—61no—
183#897—31no—
184#897—31no—
185#897—31no—
186#897—61no—
187#894—61no—
188#892—61no—
189#892C2×D311yescharacteristic, complemented
190D3×C4⋊C4—31no—
191D3×C4⋊C4—31no—
192#890—61no—
193#890C2×D311yescharacteristic, complemented
194#887—31no—
195#883—61no—
196#879—61no—
197C4×D12—31no—
198C4×D12—31no—
199#872—61no—
200#870—61no—
201C4×Dic6—31no—
202C3×#102—21no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102C2×D311yescharacteristic, complemented
210C3×#102C2×D311yescharacteristic, complemented
211C3×#97—31no—
212#832—31no—
213#832—31no—
214#832C2×D311yescharacteristic, complemented
215#832C2×D311yescharacteristic, complemented
216#830—31no—
217#821C2×D311yescharacteristic
218#821C2×D311yescharacteristic, complemented
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—31no—
222#818—31no—
223#818—31no—
224#816—31no—
225#816—31no—
226#816—61no—
227#815C2×D311yescharacteristic, complemented
228Dic3⋊C8—31no—
229#809—31no—
230#809—31no—
231#809C2×D311yescharacteristic
232#809C2×D311yescharacteristic, complemented
233#808—31no—
234#808—31no—
235#808—61no—
236#807—31no—
237#807—31no—
238C4⋊(C3⋊C8)—31no—
239C23×C32—21no—
240C22×C3⋊D3C2×D411yescharacteristic
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—42no—
244C22×C3×D3—42no—
245C22×C3×D3—81no—
246C22×C3×D3C2×D411yescharacteristic
247C2×D32—42no—
248C2×D32—42no—
249C2×D32—81no—
250C32×D4—21no—
251C32×D4—21no—
252C2×C32×C4—21no—
253C2×C32×C4C2411yescharacteristic
254#638—42no—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3C2×D411yescharacteristic
258C4×C3⋊D3—21no—
259C4×C3⋊D3—21no—
260#634—21no—
261#634—21no—
262C3×#67—42no—
263C3×#67—42no—
264C3×#67—81no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C2×C3×Dic3C2×D411yescharacteristic
270C3×D12—21no—
271C3×D12—21no—
272C3×D12—21no—
273C3×D12#4112yes—
274C3×C4×D3—21no—
275C3×C4×D3—21no—
276#626—22no—
277#625—42no—
278#625—42no—
279#624—42no—
280D3×Dic3—42no—
281C32×C8—21no—
282C3⋊(C3⋊C8)—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#552—91no—
286D42—91no—
287#490—31no—
288#482—91no—
289#480—91no—
290#478—91no—
291#468—91no—
292#465—91no—
293#460—91no—
294#450—91no—
295#450—91no—
296#440—91no—
297#435—91no—
298#418—31no—
299C2×#102—91no—
300C24×C3—61no—
301C23×D3—21no—
302C23×D3—61no—
303C23×D3—61no—
304C2×C3×D4—21no—
305C2×C3×D4—31no—
306C2×C3×D4—31no—
307C2×C3×D4—61no—
308C2×C3×D4—61no—
309C2×C3×D4—61no—
310C2×C3×D4—62no—
311C2×C3×D4—121no—
312C2×C3×D4C22×D311yescharacteristic
313C2×C3×D4C22×D311yescharacteristic
314C22×C3×C4—31no—
315C2×#67—21no—
316C2×#67—21no—
317C2×#67—21no—
318C2×#67—31no—
319C2×#67—61no—
320C2×#67—61no—
321C2×#67—61no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—121no—
326C2×#67—124no—
327C22×Dic3—61no—
328D3×D4—22no—
329D3×D4—41no—
330D3×D4—62no—
331D3×D4—62no—
332D3×D4—121no—
333D3×D4—121no—
334D3×D4—124no—
335C2×D12—31no—
336C2×D12C22×D311yescharacteristic
337C2×D12C22×D311yescharacteristic
338C2×C4×D3—31no—
339C2×C4×D3—31no—
340C2×C4×D3—61no—
341C2×C4×D3—61no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3C22×D311yescharacteristic
345C2×Dic6—31no—
346C2×Dic6—31no—
347C2×Dic6—61no—
348C3×M16—121no—
349C2×C3×C8—21no—
350C2×C3×C8—31no—
351C2×C3×C8—31no—
352C2×C3×C8C22×D311yescharacteristic
353C2×C3×C8C22×D311yescharacteristic
354C3×C4⋊C4—21no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4C22×D311yescharacteristic
360C3×C4⋊C4C22×D311yescharacteristic
361C3×C22⋊C4—61no—
362C3×C42—31no—
363C3×C42—61no—
364#217—31no—
365#217—61no—
366#217—61no—
367#217—61no—
368#217—61no—
369#217—61no—
370#217—121no—
371#214—62no—
372#214—121no—
373#214—121no—
374#214—121no—
375#214—122no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—31no—
378(C2×D3)⋊C4—31no—
379(C2×D3)⋊C4—31no—
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)⋊C4—121no—
386C4⋊Dic3—21no—
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3—121no—
395C4⋊Dic3C22×D311yescharacteristic
396C4⋊Dic3C22×D311yescharacteristic
397Dic3⋊C4—21no—
398Dic3⋊C4—31no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404C4×Dic3—21no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3C22×D311yescharacteristic
408C2×C3⋊C8—31no—
409C2×C3⋊C8—31no—
410C2×C3⋊C8—61no—
411C2×C3⋊C8C22×D311yescharacteristic
412C2×C3⋊C8C22×D311yescharacteristic
413#204—62no—
414#204—121no—
415ΓL(1,𝔽25)—41no—
416D3×C8—121no—
417D3×C8—121no—
418D3×C8—122no—
419C22×C32—41no—
420C22×C32—41no—
421C22×C32—41no—
422C22×C32C22×D411yescharacteristic
423C2×C3⋊D3—21no—
424C2×C3⋊D3—21no—
425C2×C3⋊D3AGL(1,ℤ/8)12yes—
426C2×C3×D3—22no—
427C2×C3×D3—21no—
428C2×C3×D3—21no—
429C2×C3×D3—21no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
435C2×C3×D3—84no—
436D32—84no—
437C32×C4—41no—
438C32×C4C2×#4111yescharacteristic
439C32×C4H(5,𝔽2)11yescharacteristic
440C3⋊Dic3—21no—
441C3⋊Dic3—41no—
442C3⋊Dic3—41no—
443C3×Dic3—21no—
444C3×Dic3—21no—
445C3×Dic3—21no—
446C3×Dic3—41no—
447C3×Dic3—41no—
448C22×D4—31no—
449C22×D4—91no—
450C22×D4—181no—
451C2×SD16—91no—
452C2×SD16—91no—
453C2×SD16—91no—
454C2×M16—31no—
455C22×C8—91no—
456#127—31no—
457#126—181no—
458#125—31no—
459#125—181no—
460#123—181no—
461C22⋊Q8—91no—
462C22⋊Q8—91no—
463#121—91no—
464#121—91no—
465#121—181no—
466#120—181no—
467#120—181no—
468C4×Q8—91no—
469C4×D4—91no—
470C4×D4—91no—
471#117—31no—
472#117—181no—
473C2×C4⋊C4—91no—
474#107—91no—
475#107—91no—
476#106—91no—
477C4⋊C8—91no—
478#103—91no—
479#102—31no—
480#102—31no—
481#102—31no—
482#102—31no—
483#102—31no—
484#102—31no—
485#102—91no—
486#102—91no—
487#102D3211yescharacteristic, complemented
488C22⋊C8—91no—
489C22⋊C8—91no—
490#97—31no—
491C23×C3—21no—
492C23×C3—21no—
493C23×C3—31no—
494C23×C3—41no—
495C23×C3—61no—
496C23×C3—61no—
497C23×C3—122no—
498C23×C3—122no—
499C23×C3—241no—
500C22×D3—21no—
501C22×D3—21no—
502C22×D3—31no—
503C22×D3—31no—
504C22×D3—42no—
505C22×D3—42no—
506C22×D3—61no—
507C22×D3—81no—
508C22×D3—122no—
509C22×D3—122no—
510C22×D3—122no—
511C22×D3—122no—
512C22×D3—241no—
513C22×D3—241no—
514C22×D3D3×D411yescharacteristic
515C3×D4—21no—
516C3×D4—21no—
517C3×D4—21no—
518C3×D4—21no—
519C3×D4—32no—
520C3×D4—41no—
521C3×D4—41no—
522C3×D4—61no—
523C3×D4—61no—
524C3×D4—61no—
525C3×D4—122no—
526C3×D4—122no—
527C3×D4—241no—
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—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4C23×D311yescharacteristic
540C2×C3×C4C23×D311yescharacteristic
541#67—42no—
542#67—42no—
543#67—62no—
544#67—81no—
545#67—122no—
546#67—122no—
547#67—122no—
548#67—122no—
549#67—122no—
550#67—122no—
551#67—242no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—31no—
555C2×Dic3—31no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—121no—
562C2×Dic3—121no—
563C2×Dic3—122no—
564C2×Dic3D3×D411yescharacteristic
565C2×Dic3D3×D411yescharacteristic
566C2×Dic3D3×D411yescharacteristic
567D12—21no—
568D12—21no—
569D12—21no—
570D12—62no—
571D12#23512yes—
572C4×D3—21no—
573C4×D3—21no—
574C4×D3—61no—
575C4×D3—61no—
576C4×D3—61no—
577C4×D3—61no—
578C4×D3—121no—
579C4×D3—121no—
580C4×D3—122no—
581C4×D3—122no—
582C4×D3—122no—
583Dic6—61no—
584Dic6—61no—
585Dic6—61no—
586Dic6—61no—
587Dic6—121no—
588Dic6—121no—
589C3×C8—21no—
590C3×C8—21no—
591C3×C8—41no—
592C3×C8—61no—
593C3×C8—61no—
594C3⋊C8—21no—
595C3⋊C8—21no—
596C3⋊C8—62no—
597C3⋊C8—61no—
598C3⋊C8—61no—
599C2×C32—81no—
600C2×C32#54611yescharacteristic
601C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
602C2×C32#57711yescharacteristic
603C3⋊D3—22no—
604C3×D3—42no—
605C3×D3—41no—
606C3×D3—81no—
607C24—61no—
608C24—181no—
609C2×Q8—91no—
610C2×D4—31no—
611C2×D4—31no—
612C2×D4—61no—
613C2×D4—61no—
614C2×D4—61no—
615C2×D4—62no—
616C2×D4—91no—
617C2×D4—121no—
618C2×D4—181no—
619C2×D4—182no—
620C2×D4—181no—
621C2×D4—181no—
622C2×D4—361no—
623C2×D4—364no—
624C2×D4C2×D3211yescharacteristic
625C22×C4—31no—
626C22×C4—91no—
627C22×C4—181no—
628C22×C4—181no—
629SD16—182no—
630SD16—361no—
631SD16—361no—
632M16—121no—
633C2×C8—31no—
634C2×C8—31no—
635C2×C8—91no—
636C2×C8—361no—
637C2×C8C2×D3211yescharacteristic
638C4⋊C4—31no—
639C4⋊C4—31no—
640C4⋊C4—61no—
641C4⋊C4—61no—
642C4⋊C4—91no—
643C4⋊C4—91no—
644C4⋊C4—181no—
645C4⋊C4—181no—
646C4⋊C4—181no—
647C4⋊C4—181no—
648C4⋊C4C2×D3211yescharacteristic
649C22⋊C4—61no—
650C22⋊C4—91no—
651C22⋊C4—91no—
652C22⋊C4—181no—
653C22⋊C4—181no—
654C22⋊C4—181no—
655C22⋊C4—181no—
656C22⋊C4—181no—
657C42—31no—
658C42—61no—
659C42—181no—
660C22×C3—21no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—62no—
668C22×C3—61no—
669C22×C3—61no—
670C22×C3—61no—
671C22×C3—81no—
672C22×C3—81no—
673C22×C3—81no—
674C22×C3—121no—
675C22×C3—121no—
676C22×C3—121no—
677C22×C3—121no—
678C22×C3—121no—
679C22×C3—244no—
680C22×C3C2×D3×D411yescharacteristic
681C22×C3C2×D3×D411yescharacteristic
682C2×D3—21no—
683C2×D3—22no—
684C2×D3—21no—
685C2×D3—21no—
686C2×D3—32no—
687C2×D3—32no—
688C2×D3—41no—
689C2×D3—41no—
690C2×D3—41no—
691C2×D3—41no—
692C2×D3—41no—
693C2×D3—62no—
694C2×D3—61no—
695C2×D3—61no—
696C2×D3—61no—
697C2×D3—61no—
698C2×D3—84no—
699C2×D3—121no—
700C2×D3—121no—
701C2×D3—244no—
702C2×D3—244no—
703C3×C4—21no—
704C3×C4—21no—
705C3×C4—41no—
706C3×C4—41no—
707C3×C4—61no—
708C3×C4—61no—
709C3×C4—61no—
710C3×C4—81no—
711C3×C4—121no—
712C3×C4—121no—
713C3×C4C2×#23511yescharacteristic
714C3×C4#100411yescharacteristic
715C3×C4D3×#4111yescharacteristic
716C3×C4#100911yescharacteristic
717Dic3—21no—
718Dic3—21no—
719Dic3—21no—
720Dic3—41no—
721Dic3—41no—
722Dic3—61no—
723Dic3—61no—
724Dic3—121no—
725Dic3—121no—
726Dic3—121no—
727Dic3—121no—
728Dic3—121no—
729Dic3—241no—
730Dic3—241no—
731C32#331011yescharacteristic, complemented, Sylow
732C23—21no—
733C23—31no—
734C23—61no—
735C23—61no—
736C23—91no—
737C23—122no—
738C23—122no—
739C23—241no—
740C23—362no—
741C23—362no—
742C23—721no—
743Q8—181no—
744Q8—181no—
745D4—21no—
746D4—21no—
747D4—32no—
748D4—61no—
749D4—61no—
750D4—61no—
751D4—122no—
752D4—122no—
753D4—182no—
754D4—241no—
755D4—362no—
756D4—362no—
757D4—362no—
758C2×C4—21no—
759C2×C4—31no—
760C2×C4—31no—
761C2×C4—31no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—91no—
767C2×C4—181no—
768C2×C4—181no—
769C2×C4—181no—
770C2×C4—181no—
771C2×C4—362no—
772C2×C4—362no—
773C2×C4C22×D3211yescharacteristic
774C8—21no—
775C8—61no—
776C8—61no—
777C8—181no—
778C2×C3—21no—
779C2×C3—21no—
780C2×C3—21no—
781C2×C3—81no—
782C2×C3—81no—
783C2×C3—122no—
784C2×C3—121no—
785C2×C3—161no—
786C2×C3—241no—
787C2×C3#549011yescharacteristic
788C2×C3#567611yescharacteristic
789C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
790C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
791C2×C3#577511yescharacteristic
792C2×C3#577511yescharacteristic
793D3—41no—
794D3—42no—
795D3—62no—
796D3—62no—
797D3—81no—
798D3—122no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—61no—
803C22—61no—
804C22—61no—
805C22—62no—
806C22—92no—
807C22—121no—
808C22—121no—
809C22—121no—
810C22—121no—
811C22—121no—
812C22—181no—
813C22—181no—
814C22—244no—
815C22—724no—
816C22D32×D411yescharacteristic
817C4—41no—
818C4—61no—
819C4—61no—
820C4—61no—
821C4—121no—
822C4—121no—
823C4—181no—
824C4—361no—
825C4—361no—
826C4D3×#23511yescharacteristic
827C4#6431411yescharacteristic
828C3—21no—
829C3#7893411yescharacteristic, complemented
830C3#8172511yescharacteristic, complemented
831C2—81no—
832C2—121no—
833C2—122no—
834C2—182no—
835C2—241no—
836C2#1059428011yescharacteristic
837C2#1059473311yescharacteristic
838C2#1059474011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595293C2
hypercenter#102D32
hypocenterC32#3310
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. #10594584C2semidirect
3. #10592477C2semidirect
4. C3×#4770C2semidirect
5. C3×#4764C2semidirect
6. #10591459C2semidirect
7. #10591439C2semidirect
8. #10591417C2semidirect
9. #10590940C2semidirect
10. #10590828C2semidirect
11. #10590747C2semidirect
12. #10590736C2semidirect
13. #10590597C2semidirect
14. #10590505C2semidirect
15. #10590469C2semidirect
22. C2×#3754C22semidirect
23. C2×C8×C3⋊D3C22semidirect
24. #64106C22semidirect
26. C2×C3×ΓL(1,𝔽25)C22semidirect
27. C3×#892C22semidirect
28. C3×#890C22semidirect
34. #63900C22semidirect
38. #63857C22semidirect
40. #63844C22semidirect
43. C2×#3716C22semidirect
44. C32×#102C22semidirect
45. #63643C22semidirect
46. #63635C22semidirect
47. C3×#832C22semidirect
48. C3×#832C22semidirect
50. C3×#821C22semidirect
51. C3×#815C22semidirect
53. C3×#809C22semidirect
54. #63575C22semidirect
55. #63575C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
58. #63562C22semidirect
59. #63557C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
83. #4770D3semidirect
87. #4764D3semidirect
178. C2×ΓL(1,𝔽25)C2×D3semidirect
189. #892C2×D3semidirect
193. #890C2×D3semidirect
209. C3×#102C2×D3semidirect
210. C3×#102C2×D3semidirect
214. #832C2×D3semidirect
215. #832C2×D3semidirect
218. #821C2×D3semidirect
227. #815C2×D3semidirect
232. #809C2×D3semidirect
487. #102D32semidirect
731. C32#3310semidirect
829. C3#78934semidirect
830. C3#81725semidirect

Maximal subgroups

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

subgroupindex
#105952932
#105945842
#105924772
C3×#47702
C3×#47642
#105914592
#105914392
#105914172
#105909402
#105908282
#105907472
#105907362
#105905972
#105905052
#105904692
#817253
#789343