Finite Group Databasebeta

← #11867794

Subgroups — #11867794

Order 1152.

999 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
1C2×C3×#907C211yesmaximal, characteristic, complemented
2#10595004C211yesmaximal, characteristic
3#10594884C211yesmaximal, characteristic, complemented
4C2×#63800C211yesmaximal, characteristic, complemented
5#10592836C211yesmaximal, characteristic, complemented
6C3×#5134C211yesmaximal, characteristic, complemented
7#10591187C211yesmaximal, characteristic, complemented
8#10591175C211yesmaximal, characteristic, complemented
9#10590954C211yesmaximal, characteristic, complemented
10#10590852C211yesmaximal, characteristic, complemented
11#10590849C211yesmaximal, characteristic, complemented
12#10590829C211yesmaximal, characteristic, complemented
13#10590828C211yesmaximal, characteristic, complemented
14#10590683C211yesmaximal, characteristic, complemented
15D3×#816C211yesmaximal, characteristic, complemented
16#83808—31nomaximal
17#80810—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21C2×C32×M16C2211yescharacteristic
22#64133C2211yescharacteristic
23#64133C2211yescharacteristic
24C2×#3746C2211yescharacteristic
25C3×#930C2211yescharacteristic
26C3×#924C2211yescharacteristic
27C22×C3×C3⋊C8C2211yescharacteristic
28C3×#907—24no—
29C2×C3×#204C2211yescharacteristic
30C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
31C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
32C2×C3×D3×C8C2211yescharacteristic
33C2×C3×D3×C8C2211yescharacteristic
34#63970—21no—
35#63970—21no—
36#63969—21no—
37#63959—21no—
38#63908C2211yescharacteristic
39D3×C4⋊Dic3C2211yescharacteristic
40#63887—21no—
41#63885—21no—
42#63884—21no—
43#63857C2211yescharacteristic
44#63857C2211yescharacteristic
45#63856C2211yescharacteristic
46#63841C2211yescharacteristic
47#63839—21no—
48C2×#3719C2211yescharacteristic
49C2×#3716C2211yescharacteristic
50#63800—24no—
51#63644C2211yescharacteristic
52#63643C2211yescharacteristic
53#63643C2211yescharacteristic
54C3×#821C2211yescharacteristic
55C3×#818C2211yescharacteristic
56C3×#816C2211yescharacteristic
57#63575C2211yescharacteristic
58#63573C2211yescharacteristic
59#63567C2211yescharacteristic
60#63567C2211yescharacteristic
61#63566C2211yescharacteristic
62#63563C2211yescharacteristic
63C2×C3×#131—31no—
64#5833—31no—
65#5825—31no—
66C2×#915—31no—
67C2×#909—31no—
68C2×#907D311yescharacteristic, complemented
69#5628—31no—
70#5608—31no—
71C3×#468—31no—
72#5171—31no—
73#5137—31no—
74#5137—31no—
75#5137—31no—
76#5137—61no—
77#5134—31no—
78#5134D311yescharacteristic, complemented
79#5121—31no—
80#5116—31no—
81#5116—31no—
82#5114—31no—
83#5114—31no—
84#5113—31no—
85C2×#816—31no—
86#5051—31no—
87#5041—31no—
88#4887—31no—
89#4881—31no—
90#4816—31no—
91D3×#103—31no—
92#4780—31no—
93#4772—31no—
94C22×C32×C4C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×#634C2311yescharacteristic
97C2×C3×#67—21no—
98C2×C3×#67D411yescharacteristic
99C2×C3×#67D411yescharacteristic
100C3×#235—22no—
101C3×#235—22no—
102C2×C3×D12D411yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6D411yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×#627—21no—
109C2×#625—21no—
110C2×#625—21no—
111C2×D3×Dic3—21no—
112C2×D3×Dic3—21no—
113C2×D3×Dic3—21no—
114#3795—22no—
115#3795—22no—
116D3×Dic6—22no—
117D3×Dic6—22no—
118C32×M16—22no—
119C2×C32×C8C2311yescharacteristic
120C2×C32×C8C2311yescharacteristic
121#3757—21no—
122#3757—21no—
123C4⋊(C3⋊Dic3)C2311yescharacteristic
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125#3750—21no—
126#3750—21no—
127#3746—22no—
128C3×#217—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C2×C3×C3⋊C8—22no—
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C3×#204—22no—
137C3×ΓL(1,𝔽25)—22no—
138C3×ΓL(1,𝔽25)D414yescomplemented
139C3×D3×C8—22no—
140C3×D3×C8—22no—
141#3724—21no—
142Dic3⋊Dic3—21no—
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150Dic32—21no—
151#3719—22no—
152#3716—22no—
153#3063—91noSylow
154C2×C3×#41—31no—
155C2×D3×Q8—31no—
156C2×#237—31no—
157C2×#235—31no—
158C2×#235C2×D311yescharacteristic
159C22×Dic6—31no—
160C2×C3×SD16—31no—
161C3×#131—64no—
162C2×C3×M16—21no—
163C2×C3×M16—31no—
164C2×C3×M16—31no—
165C2×C3×M16C2×D311yescharacteristic
166C2×C3×M16C2×D311yescharacteristic
167C22×C3×C8—31no—
168C22×C3×C8—31no—
169C22×C3×C8—31no—
170C3×C22⋊Q8—31no—
171C3×#121—31no—
172#946—31no—
173#946—61no—
174#944—61no—
175C2×#216—31no—
176#939—61no—
177#939—61no—
178#939—61no—
179#938—31no—
180#938—61no—
181#938—61no—
182#936—61no—
183#935—61no—
184#935—61no—
185C2×#214—31no—
186#930—31no—
187#930C2×D311yescharacteristic
188#926—31no—
189C2×C4⋊Dic3—31no—
190#924—31no—
191#924—31no—
192#924—31no—
193#924—31no—
194#924—31no—
195#924—31no—
196#924—31no—
197#924—61no—
198#924—61no—
199#924C2×D311yescharacteristic
200C22×C3⋊C8C2×D311yescharacteristic
201#915—64no—
202#909—64no—
203#907—24no—
204C2×Dic12—31no—
205C2×Dic12—31no—
206C2×Dic12—31no—
207C2×Dic12—61no—
208C2×#204—31no—
209C2×#204C2×D311yescharacteristic
210C2×ΓL(1,𝔽25)C2×D311yescharacteristic
211C2×ΓL(1,𝔽25)C2×D311yescharacteristic
212C2×D3×C8C2×D311yescharacteristic
213C2×D3×C8C2×D311yescharacteristic
214#897—31no—
215#897—31no—
216#894—61no—
217#892—31no—
218D3×C4⋊C4—31no—
219#888—61no—
220#885—61no—
221#884—61no—
222#883—61no—
223#878—61no—
224C3×#107—31no—
225C3×#103—31no—
226C3×#102—31no—
227#835—31no—
228#832—31no—
229#821—31no—
230#821C2×D311yescharacteristic
231#818—31no—
232#818C2×D311yescharacteristic
233#817—31no—
234#817—31no—
235#817—31no—
236#817—61no—
237#816—31no—
238#816—31no—
239#816—31no—
240#816—31no—
241#816—31no—
242#816—31no—
243#816—31no—
244#816—61no—
245#816—61no—
246#816C2×D311yescharacteristic
247#810—31no—
248#810—31no—
249#808—31no—
250#807—31no—
251C23×C32C2×D411yescharacteristic
252C22×C3×D3—21no—
253C22×C3×D3C2×D411yescharacteristic
254C22×C3×D3C2×D411yescharacteristic
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4C2×D411yescharacteristic
258C2×C32×C4C2411yescharacteristic
259C2×C3⋊Dic3—21no—
260C2×C3⋊Dic3—21no—
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3—21no—
263#634—21no—
264#634—21no—
265#634—21no—
266#634—21no—
267C3×#67—22no—
268C3×#67—22no—
269C3×#67—81no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3C2×D411yescharacteristic
274C2×C3×Dic3C2×D411yescharacteristic
275C3×D12—22no—
276C3×D12—21no—
277C3×D12—21no—
278C3×C4×D3—21no—
279C3×C4×D3—21no—
280C3×C4×D3C2×D412yes—
281C3×C4×D3#4112yes—
282C3×Dic6—22no—
283C3×Dic6—21no—
284C3×Dic6—21no—
285#627—42no—
286#625—42no—
287#625—81no—
288D3×Dic3—42no—
289D3×Dic3—42no—
290D3×Dic3—81no—
291C32×C8—21no—
292C32×C8C2×D412yes—
293C3×C3⋊C8—21no—
294C3×C3⋊C8C2×D412yes—
295C2×#137—91no—
296C2×#131—31no—
297#537—91no—
298#536—91no—
299#470—91no—
300#470—91no—
301#468—31no—
302#468—91no—
303#467—91no—
304#467—91no—
305#465—91no—
306#465—91no—
307#428—91no—
308#416—91no—
309C2×#103—91no—
310C3×#41—62no—
311C3×#41—62no—
312C2×C3×Q8—31no—
313C2×C3×Q8—31no—
314C2×C3×D4—31no—
315C2×C3×D4—31no—
316C2×C3×D4—31no—
317C2×C3×D4—31no—
318C2×C3×D4—61no—
319C22×C3×C4—21no—
320C22×C3×C4—31no—
321C22×C3×C4—31no—
322C22×C3×C4C22×D311yescharacteristic
323C22×C3×C4C22×D311yescharacteristic
324C2×#67—21no—
325C2×#67—61no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67D1211yescharacteristic
330C2×#67D1211yescharacteristic
331C22×Dic3—61no—
332C22×Dic3—61no—
333C22×Dic3—61no—
334D3×Q8—62no—
335D3×Q8—62no—
336#237—62no—
337#237—62no—
338#235—22no—
339#235—22no—
340#235—62no—
341#235—62no—
342C2×D12D1211yescharacteristic
343C2×D12C22×D311yescharacteristic
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3—61no—
347C2×C4×D3C22×D311yescharacteristic
348C2×C4×D3C22×D311yescharacteristic
349C2×Dic6—31no—
350C2×Dic6—31no—
351C2×Dic6—31no—
352C2×Dic6—31no—
353C2×Dic6—61no—
354C2×Dic6—61no—
355C2×Dic6—62no—
356C2×Dic6—62no—
357C2×Dic6—61no—
358C2×Dic6—61no—
359C2×Dic6D1211yescharacteristic
360C2×Dic6C22×D311yescharacteristic
361C3×SD16—62no—
362C3×M16—22no—
363C3×M16—22no—
364C3×M16—34no—
365C3×M16—42no—
366C3×M16—62no—
367C2×C3×C8—21no—
368C2×C3×C8—21no—
369C2×C3×C8—31no—
370C2×C3×C8—31no—
371C2×C3×C8—62no—
372C2×C3×C8—62no—
373C2×C3×C8—62no—
374C2×C3×C8C22×D311yescharacteristic
375C2×C3×C8C22×D311yescharacteristic
376C2×C3×C8C22×D311yescharacteristic
377C2×C3×C8C22×D311yescharacteristic
378C3×C4⋊C4—31no—
379C3×C4⋊C4—31no—
380C3×C4⋊C4—61no—
381C3×C22⋊C4—61no—
382C3×C22⋊C4—61no—
383#217—21no—
384#217—61no—
385#217—61no—
386#217—61no—
387#217—61no—
388#217—61no—
389#217—61no—
390#217—61no—
391#217—61no—
392#217—61no—
393#217—121no—
394#217—121no—
395#216—62no—
396#214—62no—
397(C2×D3)⋊C4—21no—
398(C2×D3)⋊C4—61no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4—61no—
401(C2×D3)⋊C4—61no—
402(C2×D3)⋊C4—61no—
403C4⋊Dic3—31no—
404C4⋊Dic3—31no—
405C4⋊Dic3—31no—
406C4⋊Dic3—31no—
407C4⋊Dic3—61no—
408C4⋊Dic3—61no—
409C4⋊Dic3—61no—
410C4⋊Dic3—61no—
411C4⋊Dic3—61no—
412C4⋊Dic3C22×D311yescharacteristic
413C4⋊Dic3C22×D311yescharacteristic
414Dic3⋊C4—21no—
415Dic3⋊C4—61no—
416Dic3⋊C4—61no—
417Dic3⋊C4—61no—
418Dic3⋊C4—61no—
419Dic3⋊C4—61no—
420Dic3⋊C4—61no—
421Dic3⋊C4—61no—
422Dic3⋊C4—61no—
423Dic3⋊C4—61no—
424Dic3⋊C4—121no—
425Dic3⋊C4—121no—
426C4×Dic3—61no—
427C4×Dic3—61no—
428C2×C3⋊C8—22no—
429C2×C3⋊C8C22×D311yescharacteristic
430C2×C3⋊C8C22×D311yescharacteristic
431Dic12—62no—
432Dic12—62no—
433Dic12—62no—
434Dic12—122no—
435#204—22no—
436#204—62no—
437ΓL(1,𝔽25)—22no—
438ΓL(1,𝔽25)#6714yescomplemented
439D3×C8—22no—
440D3×C8—22no—
441C22×C32—21no—
442C22×C32—21no—
443C22×C32—21no—
444C22×C32C22×D411yescharacteristic
445C2×C3×D3—21no—
446C2×C3×D3—21no—
447C2×C3×D3—21no—
448C2×C3×D3—21no—
449C2×C3×D3—21no—
450C2×C3×D3—41no—
451C2×C3×D3—41no—
452C2×C3×D3—41no—
453C2×C3×D3#12112yes—
454C32×C4—21no—
455C32×C4C22×D411yescharacteristic
456C32×C4C2×#4111yescharacteristic
457C3⋊Dic3—41no—
458C3⋊Dic3—41no—
459C3⋊Dic3—41no—
460C3⋊Dic3—41no—
461C3×Dic3—21no—
462C3×Dic3—41no—
463C3×Dic3—41no—
464C3×Dic3—41no—
465C3×Dic3#12112yes—
466C2×#41—31no—
467C2×#41—91no—
468C22×Q8—91no—
469#137—184no—
470C2×Q16—91no—
471C2×Q16—91no—
472C2×SD16—31no—
473C2×SD16—91no—
474#131—64no—
475C2×M16—31no—
476C2×M16—31no—
477C2×M16D3211yescharacteristic
478C22×C8—31no—
479C22×C8—31no—
480C22×C8—31no—
481C4⋊Q8—181no—
482#124—181no—
483#123—181no—
484#123—181no—
485C22⋊Q8—31no—
486C22⋊Q8—91no—
487C22⋊Q8—91no—
488C22⋊Q8—91no—
489C22⋊Q8—91no—
490C22⋊Q8—91no—
491C22⋊Q8—181no—
492#121—31no—
493#121—91no—
494#121—181no—
495#121—181no—
496#121—181no—
497#117—91no—
498C2×C4⋊C4—91no—
499#107—31no—
500#107—91no—
501#106—91no—
502#106—91no—
503#103—31no—
504#103—91no—
505#103—91no—
506#103—91no—
507#103—91no—
508#103—91no—
509#102—31no—
510#102—91no—
511C23×C3—21no—
512C23×C3—31no—
513C23×C3—31no—
514C23×C3—61no—
515C23×C3C2×D1211yescharacteristic
516C23×C3D3×D411yescharacteristic
517C22×D3—21no—
518C22×D3C2×D1211yescharacteristic
519C22×D3C2×D1211yescharacteristic
520C3×Q8—62no—
521C3×Q8—61no—
522C3×Q8—61no—
523C3×D4—62no—
524C3×D4—62no—
525C3×D4—62no—
526C3×D4—61no—
527C3×D4—61no—
528C3×D4—241no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—31no—
536C2×C3×C4—32no—
537C2×C3×C4—32no—
538C2×C3×C4—31no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4C2×D1211yescharacteristic
547C2×C3×C4D3×D411yescharacteristic
548C2×C3×C4C23×D311yescharacteristic
549C2×C3×C4C23×D311yescharacteristic
550#67—22no—
551#67—22no—
552#67—81no—
553#67—122no—
554#67—122no—
555#67—241no—
556#67—241no—
557C2×Dic3—21no—
558C2×Dic3—21no—
559C2×Dic3—21no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—121no—
569C2×Dic3—121no—
570C2×Dic3—121no—
571C2×Dic3—121no—
572C2×Dic3—122no—
573C2×Dic3—122no—
574C2×Dic3—241no—
575C2×Dic3C2×D1211yescharacteristic
576C2×Dic3C2×D1211yescharacteristic
577D12—22no—
578D12—21no—
579D12—21no—
580C4×D3—21no—
581C4×D3—21no—
582C4×D3—122no—
583C4×D3—122no—
584C4×D3—241no—
585C4×D3#23512yes—
586C4×D3C2×#6712yes—
587Dic6—22no—
588Dic6—21no—
589Dic6—21no—
590Dic6—61no—
591Dic6—61no—
592Dic6—61no—
593Dic6—61no—
594Dic6—61no—
595Dic6—61no—
596Dic6—61no—
597Dic6—61no—
598Dic6—121no—
599Dic6—121no—
600Dic6—121no—
601Dic6—121no—
602Dic6—122no—
603Dic6—122no—
604C3×C8—21no—
605C3×C8—21no—
606C3×C8—22no—
607C3×C8—32no—
608C3×C8—41no—
609C3×C8—61no—
610C3×C8D3×D412yes—
611C3×C8C2×#6712yes—
612C3⋊C8—21no—
613C3⋊C8C2×#6712yes—
614C2×C32—41no—
615C2×C32C2×#12111yescharacteristic
616C2×C32#57711yescharacteristic
617C2×C32#57811yescharacteristic
618C3×D3—22no—
619C3×D3—41no—
620C3×D3—81no—
621#41—62no—
622#41—62no—
623#41—182no—
624#41—182no—
625C2×Q8—31no—
626C2×Q8—31no—
627C2×Q8—91no—
628C2×Q8—91no—
629C2×Q8—181no—
630C2×Q8—182no—
631C2×Q8—182no—
632C2×D4—31no—
633C2×D4—31no—
634C2×D4—31no—
635C2×D4—31no—
636C2×D4—61no—
637C2×D4—181no—
638C2×D4—181no—
639C22×C4—31no—
640C22×C4—31no—
641C22×C4—181no—
642C22×C4—181no—
643C22×C4—181no—
644C22×C4C2×D3211yescharacteristic
645Q16—182no—
646Q16—182no—
647SD16—62no—
648SD16—182no—
649M16—22no—
650M16—34no—
651M16—62no—
652C2×C8—31no—
653C2×C8—31no—
654C2×C8—62no—
655C2×C8—62no—
656C2×C8—62no—
657C2×C8C2×D3211yescharacteristic
658C2×C8C2×D3211yescharacteristic
659C4⋊C4—31no—
660C4⋊C4—31no—
661C4⋊C4—61no—
662C4⋊C4—91no—
663C4⋊C4—91no—
664C4⋊C4—181no—
665C4⋊C4—181no—
666C4⋊C4—181no—
667C4⋊C4—181no—
668C4⋊C4—181no—
669C4⋊C4—181no—
670C22⋊C4—61no—
671C22⋊C4—61no—
672C22⋊C4—181no—
673C22⋊C4—181no—
674C22⋊C4—181no—
675C22⋊C4—181no—
676C22⋊C4—181no—
677C22⋊C4—181no—
678C22⋊C4—181no—
679C42—181no—
680C22×C3—21no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—32no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—61no—
692C22×C3—61no—
693C22×C3—61no—
694C22×C3—61no—
695C22×C3—61no—
696C22×C3—121no—
697C22×C3—121no—
698C22×C3—121no—
699C22×C3C22×D1211yescharacteristic
700C22×C3C2×D3×D411yescharacteristic
701C2×D3—21no—
702C2×D3—21no—
703C2×D3—21no—
704C2×D3—21no—
705C2×D3—21no—
706C2×D3—41no—
707C2×D3—41no—
708C2×D3—41no—
709C2×D3#93012yes—
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—21no—
713C3×C4—21no—
714C3×C4—32no—
715C3×C4—41no—
716C3×C4—61no—
717C3×C4—121no—
718C3×C4—121no—
719C3×C4—121no—
720C3×C4C2×#23511yescharacteristic
721C3×C4C2×D3×D411yescharacteristic
722C3×C4D3×#4111yescharacteristic
723C3×C4C22×#6711yescharacteristic
724Dic3—21no—
725Dic3—41no—
726Dic3—41no—
727Dic3—41no—
728Dic3—121no—
729Dic3—121no—
730Dic3—121no—
731Dic3—121no—
732Dic3—121no—
733Dic3—121no—
734Dic3—121no—
735Dic3—121no—
736Dic3—241no—
737Dic3—241no—
738Dic3—241no—
739Dic3—241no—
740Dic3#93012yes—
741C32#306311yescharacteristic, complemented, Sylow
742C23—31no—
743C23—31no—
744C23—61no—
745C23D3×D1211yescharacteristic
746Q8—62no—
747Q8—61no—
748Q8—61no—
749Q8—181no—
750Q8—181no—
751Q8—181no—
752Q8—181no—
753Q8—362no—
754D4—62no—
755D4—62no—
756D4—62no—
757D4—61no—
758D4—61no—
759D4—241no—
760D4—362no—
761D4—721no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—31no—
765C2×C4—32no—
766C2×C4—32no—
767C2×C4—31no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—181no—
774C2×C4—181no—
775C2×C4—181no—
776C2×C4—181no—
777C2×C4—362no—
778C2×C4—362no—
779C2×C4—721no—
780C2×C4D3×D1211yescharacteristic
781C2×C4C22×D3211yescharacteristic
782C8—21no—
783C8—32no—
784C8—61no—
785C8D3×#6712yes—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—41no—
790C2×C3—41no—
791C2×C3—62no—
792C2×C3—81no—
793C2×C3—121no—
794C2×C3—241no—
795C2×C3D3×#12111yescharacteristic
796C2×C3#575111yescharacteristic
797C2×C3#575311yescharacteristic
798C2×C3#577511yescharacteristic
799C2×C3#577911yescharacteristic
800C2×C3C2×#93011yescharacteristic
801D3—22no—
802D3—41no—
803D3—81no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—32no—
808C22—61no—
809C22—61no—
810C22—61no—
811C22—61no—
812C22—61no—
813C22—121no—
814C22—121no—
815C22—121no—
816C22C2×D3×D1211yescharacteristic
817C4—21no—
818C4—32no—
819C4—61no—
820C4—121no—
821C4—121no—
822C4—121no—
823C4—361no—
824C4—361no—
825C4—361no—
826C4—361no—
827C4D3×#23511yescharacteristic
828C4C2×D3×#6711yescharacteristic
829C3—21no—
830C3#8081011yescharacteristic, complemented
831C3#8380811yescharacteristic, complemented
832C2—41no—
833C2—62no—
834C2—121no—
835C2—241no—
836C2#1059471311yescharacteristic
837C2#1059472111yescharacteristic
838C2D3×#93011yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radical#10595004C2
hypercenterC2×M16D32
hypocenterC32#3063
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#907C2semidirect
3. #10594884C2semidirect
4. C2×#63800C2semidirect
5. #10592836C2semidirect
6. C3×#5134C2semidirect
7. #10591187C2semidirect
8. #10591175C2semidirect
9. #10590954C2semidirect
10. #10590852C2semidirect
11. #10590849C2semidirect
12. #10590829C2semidirect
13. #10590828C2semidirect
14. #10590683C2semidirect
15. D3×#816C2semidirect
68. C2×#907D3semidirect
78. #5134D3semidirect
138. C3×ΓL(1,𝔽25)D4semidirect
438. ΓL(1,𝔽25)#67semidirect
741. C32#3063semidirect
830. C3#80810semidirect
831. C3#83808semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9072
#105950042
#105948842
C2×#638002
#105928362
C3×#51342
#105911872
#105911752
#105909542
#105908522
#105908492
#105908292
#105908282
#105906832
D3×#8162
#838083
#808103