Finite Group Databasebeta

← #11889748

Subgroups — #11889748

Order 1152.

880 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594007C211yesmaximal, characteristic
2#10593956C211yesmaximal, characteristic, complemented
3#10592409C211yesmaximal, characteristic, complemented
4C3×#4714C211yesmaximal, characteristic, complemented
5C3×#4706C211yesmaximal, characteristic, complemented
6#10590970C211yesmaximal, characteristic, complemented
7#10590946C211yesmaximal, characteristic, complemented
8D3×#821C211yesmaximal, characteristic, complemented
9#10590848C211yesmaximal, characteristic, complemented
10#10590828C211yesmaximal, characteristic, complemented
11#10590682C211yesmaximal, characteristic, complemented
12#10590680C211yesmaximal, characteristic, complemented
13#10590671C211yesmaximal, characteristic, complemented
14#10590378C211yesmaximal, characteristic, complemented
15#10590313C211yesmaximal, characteristic, complemented
16#81700—31nomaximal
17#79503—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C2×#3744C2211yescharacteristic
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22C4×#634C2211yescharacteristic, complemented
23C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
24C2×C3×D3×C8C2211yescharacteristic
25C3×#875C2211yescharacteristic
26C3×C4×D12C2211yescharacteristic
27C3×#869C2211yescharacteristic, complemented
28#63922—21no—
29#63921—21no—
30#63912—21no—
31#63908C2211yescharacteristic
32#63898—21no—
33D3×C4⋊Dic3C2211yescharacteristic
34D3×C4⋊Dic3C2211yescharacteristic, complemented
35#63887—21no—
36#63887—21no—
37#63872—21no—
38#63857C2211yescharacteristic
39#63857C2211yescharacteristic, complemented
40#63856C2211yescharacteristic
41#63854—21no—
42C2×#3719C2211yescharacteristic, complemented
43C2×#3716C2211yescharacteristic
44C32×#97C2211yescharacteristic, complemented
45#63648C2211yescharacteristic
46#63645C2211yescharacteristic, complemented
47#63643C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
52C3×#816C2211yescharacteristic, complemented
53C3×#816C2211yescharacteristic, complemented
54C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63575C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic
60#63563C2211yescharacteristic
61#5730—31no—
62#5676—31no—
63#5550—31no—
64#5543—31no—
65C3×#489—31no—
66C3×#435—31no—
67#5134—31no—
68#5133—31no—
69#5116—31no—
70C2×#821—31no—
71#5087—31no—
72#5054—31no—
73#4846—31no—
74#4845—31no—
75#4813—31no—
76#4811—31no—
77#4808—31no—
78#4803—31no—
79#4780—31no—
80#4776—31no—
81#4774—31no—
82D3×#102—31no—
83#4736—31no—
84#4733—31no—
85#4731—31no—
86#4722—31no—
87#4714D311yescharacteristic, complemented
88#4710—31no—
89#4710—31no—
90#4710—61no—
91#4706D311yescharacteristic, complemented
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×#634C2311yescharacteristic
96C2×C3×D12D411yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×Dic6—21no—
101C2×C3×Dic6C2311yescharacteristic
102C2×#626—21no—
103C2×#626—21no—
104C2×#625—21no—
105C2×#624—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108D3×D12—22no—
109D3×D12—41no—
110#3799—22no—
111#3799—41no—
112C2×C32×C8C2311yescharacteristic
113C2×C32×C8C2311yescharacteristic
114C32×C42C2311yescharacteristic
115#3752—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3750—21no—
119C4×C3⋊Dic3—21no—
120#3744—22no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×(C2×D3)⋊C4D411yescharacteristic
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3D411yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×ΓL(1,𝔽25)—41no—
132C3×D3×C8—41no—
133#3724—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142#3719—41no—
143#3716—41no—
144#3314—91noSylow
145C2×#239—31no—
146C2×D3×D4—31no—
147C2×#235—31no—
148C22×D12—31no—
149C2×C3×M16—31no—
150C22×C3×C8—31no—
151C3×C4⋊Q8—31no—
152C3×#124—31no—
153C3×C4×D4—31no—
154#946—31no—
155#946—61no—
156#946—61no—
157C2×#216—31no—
158#938—31no—
159#937—61no—
160D4×Dic3—61no—
161C2×#214—31no—
162#930—31no—
163C2×C4⋊Dic3—31no—
164C2×C4⋊Dic3—31no—
165#924—31no—
166#924—31no—
167#924—31no—
168C2×Dic12—31no—
169C2×#204—31no—
170C2×#204—31no—
171C2×#204—31no—
172C2×#204—61no—
173C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
174C2×D3×C8C2×D311yescharacteristic
175#897—31no—
176#897—31no—
177#894—61no—
178#893—61no—
179D3×C4⋊C4—31no—
180D3×C4⋊C4—31no—
181#890—61no—
182#890—61no—
183#884—61no—
184#884—61no—
185#883—61no—
186#882—61no—
187D3×C22⋊C4—61no—
188D3×C22⋊C4—61no—
189#878—61no—
190#878—61no—
191#875C2×D311yescharacteristic
192C4×D12—31no—
193C4×D12—31no—
194C4×D12—61no—
195C4×D12C2×D311yescharacteristic
196#869C2×D311yescharacteristic, complemented
197C4×Dic6—31no—
198C4×Dic6—31no—
199C4×Dic6—61no—
200C3×C4⋊C8—31no—
201C3×#103—31no—
202C3×#103—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×C22⋊C8—31no—
206C3×C22⋊C8—31no—
207C3×#97—21no—
208C3×#97C2×D311yescharacteristic, complemented
209C3×#97C2×D311yescharacteristic, complemented
210#835—31no—
211#832—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—61no—
218#821C2×D311yescharacteristic
219#821C2×D311yescharacteristic
220(C2×D3)⋊C8C2×D311yescharacteristic
221(C2×D3)⋊C8C2×D311yescharacteristic, complemented
222#818—31no—
223#818—31no—
224#818—31no—
225#818—31no—
226#818—61no—
227#816—31no—
228#816—31no—
229#816—31no—
230#816—61no—
231#816C2×D311yescharacteristic, complemented
232#816C2×D311yescharacteristic, complemented
233#809—31no—
234#809—31no—
235#807—31no—
236#807—31no—
237C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
238C22×C3⋊D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C2×D32—42no—
243C2×D32—42no—
244C2×D32—81no—
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)#4112yes—
253C4×C3⋊D3—81no—
254#634—21no—
255#634—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—22no—
262C3×D12—21no—
263C3×D12—21no—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—81no—
271#626—42no—
272#626—42no—
273#625—81no—
274#624—42no—
275D3×Dic3—81no—
276D3×Dic3—81no—
277C32×C8—21no—
278C32×C8—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281#554—91no—
282#546—91no—
283#489—31no—
284#484—91no—
285#480—91no—
286#474—91no—
287#468—91no—
288#467—91no—
289#464—91no—
290#452—91no—
291#450—91no—
292#440—91no—
293#435—31no—
294#417—91no—
295C2×#102—91no—
296C23×D3—61no—
297C23×D3—61no—
298C2×C3×Q8—31no—
299C2×C3×Q8—61no—
300C2×C3×D4—31no—
301C2×C3×D4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—31no—
304C2×#67—61no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—61no—
308C22×Dic3—61no—
309C22×Dic3—61no—
310#239—62no—
311#239—121no—
312D3×D4—62no—
313D3×D4—121no—
314#235—62no—
315#235—121no—
316C2×D12—31no—
317C2×D12—31no—
318C2×D12—61no—
319C2×D12—62no—
320C2×D12—61no—
321C2×D12—61no—
322C2×D12—121no—
323C2×D12D1211yescharacteristic
324C2×D12C22×D311yescharacteristic
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—121no—
332C2×C4×D3C22×D311yescharacteristic
333C2×C4×D3C22×D311yescharacteristic
334C2×Dic6—21no—
335C2×Dic6—31no—
336C2×Dic6—31no—
337C2×Dic6—61no—
338C2×Dic6C22×D311yescharacteristic
339C3×M16—121no—
340C2×C3×C8—21no—
341C2×C3×C8—21no—
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C2×C3×C8—121no—
345C2×C3×C8C22×D311yescharacteristic
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C22×D311yescharacteristic
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—61no—
353C3×C22⋊C4—31no—
354C3×C22⋊C4—31no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C42—21no—
358C3×C42C22×D311yescharacteristic
359C3×C42C22×D311yescharacteristic
360#217—61no—
361#217—61no—
362#217—61no—
363#217—61no—
364#216—121no—
365#214—121no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—121no—
375(C2×D3)⋊C4D1211yescharacteristic
376(C2×D3)⋊C4D1211yescharacteristic
377C4⋊Dic3—21no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3D1211yescharacteristic
389C4⋊Dic3C22×D311yescharacteristic
390C4⋊Dic3C22×D311yescharacteristic
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—121no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—121no—
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405Dic12—121no—
406#204—62no—
407#204—62no—
408#204—64no—
409#204—121no—
410ΓL(1,𝔽25)—41no—
411D3×C8—41no—
412C22×C32C22×D411yescharacteristic
413C2×C3⋊D3—22no—
414C2×C3⋊D3—41no—
415C2×C3⋊D3—41no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3#13712yes—
425D32—84no—
426C32×C4—21no—
427C32×C4—21no—
428C32×C4C2×#4111yescharacteristic
429C32×C4H(5,𝔽2)11yescharacteristic
430C3⋊Dic3—41no—
431C3⋊Dic3—41no—
432C3⋊Dic3—41no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C2×#41—91no—
439C22×D4—91no—
440C2×Q16—91no—
441C2×SD16—91no—
442C2×SD16—91no—
443C2×M16—31no—
444C22×C8—31no—
445C4⋊Q8—31no—
446#125—181no—
447#124—31no—
448#123—181no—
449C22⋊Q8—91no—
450C22⋊Q8—91no—
451C22⋊Q8—91no—
452C22⋊Q8—181no—
453C22⋊Q8—181no—
454#121—91no—
455#121—181no—
456#120—181no—
457C4×Q8—91no—
458C4×D4—31no—
459C4×D4—91no—
460C4×D4—181no—
461C2×C4⋊C4—91no—
462C2×C4⋊C4—91no—
463C2×C22⋊C4—181no—
464#107—91no—
465#107—91no—
466#107—91no—
467C4⋊C8—31no—
468#103—31no—
469#103—31no—
470#103—91no—
471#103—91no—
472#102—31no—
473#102—31no—
474#102—91no—
475#102—91no—
476#102—91no—
477#102—91no—
478C22⋊C8—31no—
479C22⋊C8—31no—
480#97D3211yescharacteristic, complemented
481C23×C3—31no—
482C23×C3—31no—
483C23×C3—61no—
484C22×D3—21no—
485C22×D3—61no—
486C22×D3—61no—
487C22×D3—121no—
488C22×D3—122no—
489C22×D3—122no—
490C22×D3—122no—
491C22×D3—122no—
492C22×D3—241no—
493C22×D3—241no—
494C22×D3C2×D1211yescharacteristic
495C22×D3C2×D1211yescharacteristic
496C3×Q8—61no—
497C3×Q8—61no—
498C3×Q8—241no—
499C3×D4—62no—
500C3×D4—61no—
501C3×D4—61no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4C2×D1211yescharacteristic
515C2×C3×C4C2×D1211yescharacteristic
516C2×C3×C4D3×D411yescharacteristic
517C2×C3×C4D3×D411yescharacteristic
518C2×C3×C4C23×D311yescharacteristic
519C2×C3×C4C23×D311yescharacteristic
520#67—122no—
521#67—122no—
522#67—241no—
523#67—241no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—121no—
534C2×Dic3—121no—
535C2×Dic3—121no—
536C2×Dic3—241no—
537C2×Dic3—241no—
538C2×Dic3C2×D1211yescharacteristic
539C2×Dic3C2×D1211yescharacteristic
540D12—22no—
541D12—21no—
542D12—21no—
543D12—32no—
544D12—32no—
545D12—62no—
546D12—61no—
547D12—61no—
548D12—121no—
549D12—122no—
550D12—122no—
551C4×D3—21no—
552C4×D3—21no—
553C4×D3—21no—
554C4×D3—21no—
555C4×D3—122no—
556C4×D3—122no—
557C4×D3—241no—
558C4×D3—241no—
559C4×D3—241no—
560C4×D3—241no—
561C4×D3—242no—
562Dic6—21no—
563Dic6—21no—
564Dic6—62no—
565Dic6—61no—
566Dic6—61no—
567Dic6—61no—
568Dic6—61no—
569Dic6—81no—
570Dic6—121no—
571C3×C8—22no—
572C3×C8—21no—
573C3×C8—21no—
574C3×C8—21no—
575C3×C8—21no—
576C3×C8—41no—
577C3×C8—61no—
578C3×C8—61no—
579C3⋊C8—21no—
580C3⋊C8—21no—
581C2×C32#54611yescharacteristic
582C2×C32C2×#13711yescharacteristic
583C2×C32#57611yescharacteristic
584C3⋊D3—42no—
585C3×D3—22no—
586C3×D3—41no—
587C3×D3—81no—
588C24—181no—
589#41—182no—
590#41—361no—
591C2×Q8—31no—
592C2×Q8—61no—
593C2×Q8—91no—
594C2×D4—31no—
595C2×D4—31no—
596C2×D4—91no—
597C2×D4—181no—
598C2×D4—182no—
599C2×D4—181no—
600C2×D4—181no—
601C2×D4—361no—
602C22×C4—31no—
603C22×C4—31no—
604C22×C4—181no—
605C22×C4—181no—
606C22×C4—181no—
607C22×C4—181no—
608Q16—361no—
609SD16—182no—
610SD16—361no—
611M16—121no—
612C2×C8—31no—
613C2×C8—31no—
614C2×C8—121no—
615C2×C8C2×D3211yescharacteristic
616C2×C8C2×D3211yescharacteristic
617C4⋊C4—31no—
618C4⋊C4—31no—
619C4⋊C4—31no—
620C4⋊C4—61no—
621C4⋊C4—91no—
622C4⋊C4—91no—
623C4⋊C4—181no—
624C4⋊C4—181no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C22⋊C4—31no—
630C22⋊C4—31no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—181no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C42—181no—
639C42C2×D3211yescharacteristic
640C22×C3—21no—
641C22×C3—32no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—61no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3C22×D1211yescharacteristic
651C22×C3C2×D3×D411yescharacteristic
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—41no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—62no—
661C2×D3—62no—
662C2×D3—122no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3—121no—
667C2×D3—241no—
668C2×D3—241no—
669C2×D3—244no—
670C2×D3—244no—
671C2×D3#90912yes—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—41no—
679C3×C4—41no—
680C3×C4—61no—
681C3×C4—61no—
682C3×C4—121no—
683C3×C4—121no—
684C3×C4—121no—
685C3×C4#100411yescharacteristic
686C3×C4D3×#4111yescharacteristic
687C3×C4D3×#4111yescharacteristic
688C3×C4#100911yescharacteristic
689Dic3—21no—
690Dic3—21no—
691Dic3—41no—
692Dic3—41no—
693Dic3—41no—
694Dic3—122no—
695Dic3—121no—
696Dic3—121no—
697Dic3—121no—
698Dic3—121no—
699Dic3—121no—
700Dic3—121no—
701Dic3—241no—
702Dic3—241no—
703C32#331411yescharacteristic, complemented, Sylow
704C23—31no—
705C23—31no—
706C23—61no—
707C23—181no—
708C23—362no—
709C23—362no—
710C23—721no—
711Q8—61no—
712Q8—61no—
713Q8—181no—
714Q8—181no—
715Q8—241no—
716D4—62no—
717D4—61no—
718D4—61no—
719D4—92no—
720D4—181no—
721D4—362no—
722D4—362no—
723D4—721no—
724C2×C4—31no—
725C2×C4—31no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—181no—
734C2×C4—181no—
735C2×C4—181no—
736C2×C4—362no—
737C2×C4—721no—
738C2×C4—721no—
739C2×C4—721no—
740C2×C4D3×D1211yescharacteristic
741C2×C4D3×D1211yescharacteristic
742C2×C4C22×D3211yescharacteristic
743C8—21no—
744C8—21no—
745C8—61no—
746C8—61no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—21no—
750C2×C3—62no—
751C2×C3—121no—
752C2×C3—241no—
753C2×C3#555411yescharacteristic
754C2×C3#567611yescharacteristic
755C2×C3C2×#90911yescharacteristic
756C2×C3#575211yescharacteristic
757C2×C3#577411yescharacteristic
758C2×C3D3×#13711yescharacteristic
759D3—22no—
760D3—41no—
761D3—81no—
762D3—122no—
763D3—122no—
764D3—242no—
765C22—32no—
766C22—61no—
767C22—61no—
768C22—61no—
769C22—61no—
770C22—61no—
771C22—121no—
772C22—121no—
773C22—121no—
774C22—182no—
775C22—361no—
776C22—361no—
777C22—724no—
778C22C2×D3×D1211yescharacteristic
779C4—21no—
780C4—21no—
781C4—61no—
782C4—61no—
783C4—121no—
784C4—121no—
785C4—121no—
786C4—361no—
787C4—361no—
788C4—361no—
789C4#6430611yescharacteristic
790C4#6430711yescharacteristic
791C3—21no—
792C3#7950311yescharacteristic, complemented
793C3#8170011yescharacteristic, complemented
794C2—62no—
795C2—121no—
796C2—241no—
797C2—362no—
798C2#1059400511yescharacteristic
799C2D3×#90911yescharacteristic
800C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
prime radical#10594007C2
hypercenter#97D32
hypocenterC32#3314
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
2. #10593956C2semidirect
3. #10592409C2semidirect
4. C3×#4714C2semidirect
5. C3×#4706C2semidirect
6. #10590970C2semidirect
7. #10590946C2semidirect
8. D3×#821C2semidirect
9. #10590848C2semidirect
10. #10590828C2semidirect
11. #10590682C2semidirect
12. #10590680C2semidirect
13. #10590671C2semidirect
14. #10590378C2semidirect
15. #10590313C2semidirect
22. C4×#634C22semidirect
23. C2×C3×ΓL(1,𝔽25)C22semidirect
27. C3×#869C22semidirect
34. D3×C4⋊Dic3C22semidirect
39. #63857C22semidirect
42. C2×#3719C22semidirect
44. C32×#97C22semidirect
46. #63645C22semidirect
47. #63643C22semidirect
51. C3×(C2×D3)⋊C8C22semidirect
52. C3×#816C22semidirect
53. C3×#816C22semidirect
54. C3×C4⋊(C3⋊C8)C22semidirect
55. #63575C22semidirect
56. #63575C22semidirect
57. #63566C22semidirect
87. #4714D3semidirect
91. #4706D3semidirect
173. C2×ΓL(1,𝔽25)C2×D3semidirect
196. #869C2×D3semidirect
208. C3×#97C2×D3semidirect
209. C3×#97C2×D3semidirect
221. (C2×D3)⋊C8C2×D3semidirect
231. #816C2×D3semidirect
232. #816C2×D3semidirect
237. C4⋊(C3⋊C8)C2×D3semidirect
480. #97D32semidirect
703. C32#3314semidirect
792. C3#79503semidirect
793. C3#81700semidirect

Maximal subgroups

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

subgroupindex
#105940072
#105939562
#105924092
C3×#47142
C3×#47062
#105909702
#105909462
D3×#8212
#105908482
#105908282
#105906822
#105906802
#105906712
#105903782
#105903132
#817003
#795033