Finite Group Databasebeta

← #11867796

Subgroups — #11867796

Order 1152.

1004 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#907C211yesmaximal, characteristic, complemented
2#10594894C211yesmaximal, characteristic
3#10594884C211yesmaximal, characteristic, complemented
4C2×#63801C211yesmaximal, characteristic, complemented
5#10592833C211yesmaximal, characteristic, complemented
6C3×#5137C211yesmaximal, characteristic, complemented
7#10591187C211yesmaximal, characteristic, complemented
8#10591177C211yesmaximal, characteristic, complemented
9#10590851C211yesmaximal, characteristic, complemented
10#10590850C211yesmaximal, characteristic, complemented
11#10590849C211yesmaximal, characteristic, complemented
12#10590830C211yesmaximal, characteristic, complemented
13#10590690C211yesmaximal, characteristic, complemented
14#10590681C211yesmaximal, characteristic, complemented
15D3×#816C211yesmaximal, characteristic, complemented
16#83808—31nomaximal
17#80907—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21C2×C32×M16C2211yescharacteristic
22#64139C2211yescharacteristic
23#64133C2211yescharacteristic
24C2×#3744C2211yescharacteristic
25C3×#924C2211yescharacteristic
26C3×#924C2211yescharacteristic
27C22×C3×C3⋊C8C2211yescharacteristic
28C3×#907—24no—
29C2×C3×Dic12C2211yescharacteristic
30C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
31C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
32C2×C3×D3×C8C2211yescharacteristic
33C2×C3×D3×C8C2211yescharacteristic
34#63971—21no—
35#63969—21no—
36#63959—21no—
37#63958—21no—
38#63909C2211yescharacteristic
39D3×C4⋊Dic3C2211yescharacteristic
40#63888—21no—
41#63886—21no—
42#63884—21no—
43#63857C2211yescharacteristic
44#63856C2211yescharacteristic
45#63856C2211yescharacteristic
46#63841C2211yescharacteristic
47#63839—21no—
48C2×#3719C2211yescharacteristic
49C2×#3717C2211yescharacteristic
50#63801—24no—
51#63648C2211yescharacteristic
52#63645C2211yescharacteristic
53#63643C2211yescharacteristic
54C3×#817C2211yescharacteristic
55C3×#816C2211yescharacteristic
56C3×#816C2211yescharacteristic
57#63575C2211yescharacteristic
58#63573C2211yescharacteristic
59#63567C2211yescharacteristic
60#63566C2211yescharacteristic
61#63566C2211yescharacteristic
62#63564C2211yescharacteristic
63C2×C3×#131—31no—
64#5833—31no—
65#5825—31no—
66C2×#918—31no—
67C2×#909—31no—
68C2×#907D311yescharacteristic, complemented
69#5629—31no—
70#5628—31no—
71C3×#470—31no—
72#5188—31no—
73#5137—31no—
74#5137D311yescharacteristic, complemented
75#5134—31no—
76#5134—31no—
77#5134—31no—
78#5134—61no—
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#5048—31no—
88#4864—31no—
89#4861—31no—
90#4816—31no—
91#4812—31no—
92#4804—31no—
93D3×#103—31no—
94C22×C32×C4C2311yescharacteristic
95C2×#638—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C2×C3×#67D411yescharacteristic
99C2×C3×#67D411yescharacteristic
100C3×#235—22no—
101C3×#235—22no—
102C2×C3×D12D411yescharacteristic
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6D411yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×#627—21no—
109C2×#626—21no—
110C2×#626—21no—
111C2×#624—21no—
112C2×D3×Dic3—21no—
113C2×D3×Dic3—21no—
114#3799—22no—
115#3799—22no—
116D3×Dic6—22no—
117D3×Dic6—22no—
118C32×M16—22no—
119C2×C32×C8C2311yescharacteristic
120C2×C32×C8C2311yescharacteristic
121#3757—21no—
122#3752—21no—
123C4⋊(C3⋊Dic3)C2311yescharacteristic
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125#3750—21no—
126#3744—22no—
127C3×#217—21no—
128C3×#217—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C2×C3×C3⋊C8—22no—
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C3×Dic12—22no—
137C3×ΓL(1,𝔽25)—22no—
138C3×ΓL(1,𝔽25)D414yescomplemented
139C3×D3×C8—22no—
140C3×D3×C8—22no—
141#3724—21no—
142#3724—21no—
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3—21no—
145#3722—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#3717—22no—
153#3063—91noSylow
154C2×C3×#41—31no—
155C2×#239—31no—
156C2×D3×Q8—31no—
157C2×#235—31no—
158C2×#235C2×D311yescharacteristic
159C22×Dic6—31no—
160C2×C3×Q16—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×C22⋊Q8—31no—
172#946—31no—
173#946—31no—
174#946—61no—
175#944—61no—
176C2×#216—31no—
177C2×#215—31no—
178#939—61no—
179#939—61no—
180#938—61no—
181#936—61no—
182#935—61no—
183#935—61no—
184#930—31no—
185#930—31no—
186#930—31no—
187#930—61no—
188#926—31no—
189C2×C4⋊Dic3—31no—
190#924—31no—
191#924—31no—
192#924—31no—
193#924—31no—
194#924—31no—
195#924—61no—
196#924C2×D311yescharacteristic
197#924C2×D311yescharacteristic
198C22×C3⋊C8C2×D311yescharacteristic
199#918—64no—
200#909—64no—
201#907—24no—
202C2×Dic12—31no—
203C2×Dic12C2×D311yescharacteristic
204C2×#204—31no—
205C2×#204—31no—
206C2×#204—31no—
207C2×#204—61no—
208C2×ΓL(1,𝔽25)C2×D311yescharacteristic
209C2×ΓL(1,𝔽25)C2×D311yescharacteristic
210C2×D3×C8C2×D311yescharacteristic
211C2×D3×C8C2×D311yescharacteristic
212#897—31no—
213#896—61no—
214#895—31no—
215#895—61no—
216#894—61no—
217#892—31no—
218D3×C4⋊C4—31no—
219#888—61no—
220#885—61no—
221#884—61no—
222#884—61no—
223#883—61no—
224C3×#106—31no—
225C3×#103—31no—
226C3×#103—31no—
227#835—31no—
228#835—31no—
229#821—31no—
230#821—31no—
231#821—31no—
232#821—61no—
233#818—31no—
234#818—31no—
235#818—31no—
236#818—61no—
237#817—31no—
238#817C2×D311yescharacteristic
239#816—31no—
240#816—31no—
241#816—31no—
242#816—31no—
243#816—31no—
244#816—61no—
245#816C2×D311yescharacteristic
246#816C2×D311yescharacteristic
247#810—31no—
248#809—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
259#638—81no—
260C2×C3⋊Dic3—21no—
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3—21no—
263C4⋊(C3⋊D3)—21no—
264C4⋊(C3⋊D3)—21no—
265#634—21no—
266#634—21no—
267C3×#67—22no—
268C3×#67—22no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3C2×D411yescharacteristic
274C2×C3×Dic3C2×D411yescharacteristic
275C3×D12—22no—
276C3×C4×D3—21no—
277C3×C4×D3—21no—
278C3×C4×D3C2×D412yes—
279C3×C4×D3#4112yes—
280C3×Dic6—22no—
281C3×Dic6—21no—
282C3×Dic6—21no—
283C3×Dic6—21no—
284C3×Dic6—21no—
285#627—42no—
286#626—42no—
287#626—81no—
288#624—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—31no—
300#470—91no—
301#468—91no—
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×Q8—31no—
315C2×C3×D4—31no—
316C2×C3×D4—31no—
317C2×C3×D4—31no—
318C22×C3×C4—21no—
319C22×C3×C4—31no—
320C22×C3×C4—31no—
321C22×C3×C4C22×D311yescharacteristic
322C22×C3×C4C22×D311yescharacteristic
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—61no—
326C2×#67—61no—
327C2×#67—121no—
328C2×#67D1211yescharacteristic
329C2×#67D1211yescharacteristic
330C22×Dic3—61no—
331C22×Dic3—61no—
332#239—62no—
333#239—62no—
334D3×Q8—62no—
335D3×Q8—62no—
336#235—22no—
337#235—22no—
338#235—62no—
339#235—62no—
340C2×D12—31no—
341C2×D12—31no—
342C2×D12—61no—
343C2×D12—61no—
344C2×D12—61no—
345C2×D12D1211yescharacteristic
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3—61no—
349C2×C4×D3—61no—
350C2×C4×D3C22×D311yescharacteristic
351C2×C4×D3C22×D311yescharacteristic
352C2×Dic6—31no—
353C2×Dic6—31no—
354C2×Dic6—61no—
355C2×Dic6—62no—
356C2×Dic6—62no—
357C2×Dic6—61no—
358C2×Dic6—61no—
359C2×Dic6D1211yescharacteristic
360C2×Dic6C22×D311yescharacteristic
361C2×Dic6C22×D311yescharacteristic
362C3×Q16—62no—
363C3×M16—22no—
364C3×M16—22no—
365C3×M16—34no—
366C3×M16—42no—
367C3×M16—62no—
368C2×C3×C8—21no—
369C2×C3×C8—21no—
370C2×C3×C8—31no—
371C2×C3×C8—31no—
372C2×C3×C8—62no—
373C2×C3×C8—62no—
374C2×C3×C8—62no—
375C2×C3×C8C22×D311yescharacteristic
376C2×C3×C8C22×D311yescharacteristic
377C2×C3×C8C22×D311yescharacteristic
378C2×C3×C8C22×D311yescharacteristic
379C3×C4⋊C4—31no—
380C3×C4⋊C4—31no—
381C3×C4⋊C4—61no—
382C3×C4⋊C4—61no—
383C3×C22⋊C4—61no—
384C3×C22⋊C4—61no—
385#217—21no—
386#217—21no—
387#217—61no—
388#217—61no—
389#217—61no—
390#217—61no—
391#217—61no—
392#217—61no—
393#217—121no—
394#216—62no—
395#215—62no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4—61no—
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—
403(C2×D3)⋊C4—61no—
404(C2×D3)⋊C4—121no—
405C4⋊Dic3—31no—
406C4⋊Dic3—31no—
407C4⋊Dic3—31no—
408C4⋊Dic3—31no—
409C4⋊Dic3—61no—
410C4⋊Dic3—61no—
411C4⋊Dic3—61no—
412C4⋊Dic3—61no—
413C4⋊Dic3C22×D311yescharacteristic
414C4⋊Dic3C22×D311yescharacteristic
415Dic3⋊C4—21no—
416Dic3⋊C4—21no—
417Dic3⋊C4—61no—
418Dic3⋊C4—61no—
419Dic3⋊C4—61no—
420Dic3⋊C4—61no—
421Dic3⋊C4—61no—
422Dic3⋊C4—61no—
423Dic3⋊C4—61no—
424Dic3⋊C4—61no—
425Dic3⋊C4—121no—
426C4×Dic3—61no—
427C4×Dic3—61no—
428C2×C3⋊C8—22no—
429C2×C3⋊C8C22×D311yescharacteristic
430C2×C3⋊C8C22×D311yescharacteristic
431Dic12—22no—
432Dic12—62no—
433#204—62no—
434#204—62no—
435#204—62no—
436#204—122no—
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—41no—
446C2×C3⋊D3—41no—
447C2×C3⋊D3—41no—
448C2×C3×D3—21no—
449C2×C3×D3—21no—
450C2×C3×D3—21no—
451C2×C3×D3—21no—
452C2×C3×D3—21no—
453C2×C3×D3#12112yes—
454C32×C4—21no—
455C32×C4C22×D411yescharacteristic
456C32×C4C2×#4111yescharacteristic
457C3⋊Dic3—41no—
458C3⋊Dic3—41no—
459C3⋊Dic3—41no—
460C3×Dic3—21no—
461C3×Dic3—41no—
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—31no—
471C2×Q16—91no—
472C2×SD16—91no—
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—31no—
487C22⋊Q8—91no—
488C22⋊Q8—91no—
489C22⋊Q8—91no—
490C22⋊Q8—91no—
491C22⋊Q8—181no—
492#121—91no—
493#121—91no—
494#121—181no—
495#121—181no—
496#121—181no—
497#117—91no—
498C2×C4⋊C4—91no—
499#107—91no—
500#107—91no—
501#106—31no—
502#106—91no—
503#103—31no—
504#103—31no—
505#103—91no—
506#103—91no—
507#103—91no—
508#103—91no—
509#102—91no—
510#102—91no—
511C23×C3—21no—
512C23×C3—31no—
513C23×C3—31no—
514C23×C3C2×D1211yescharacteristic
515C23×C3D3×D411yescharacteristic
516C22×D3—61no—
517C22×D3—61no—
518C22×D3—121no—
519C22×D3C2×D1211yescharacteristic
520C22×D3C2×D1211yescharacteristic
521C3×Q8—62no—
522C3×Q8—61no—
523C3×Q8—61no—
524C3×Q8—61no—
525C3×Q8—61no—
526C3×D4—62no—
527C3×D4—62no—
528C3×D4—62no—
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×C4—61no—
547C2×C3×C4C2×D1211yescharacteristic
548C2×C3×C4D3×D411yescharacteristic
549C2×C3×C4C23×D311yescharacteristic
550C2×C3×C4C23×D311yescharacteristic
551#67—22no—
552#67—22no—
553#67—122no—
554#67—241no—
555#67—241no—
556#67—241no—
557#67—242no—
558C2×Dic3—21no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—21no—
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—122no—
572C2×Dic3—241no—
573C2×Dic3C2×D1211yescharacteristic
574C2×Dic3C2×D1211yescharacteristic
575D12—22no—
576D12—61no—
577D12—61no—
578D12—61no—
579D12—61no—
580D12—121no—
581D12—121no—
582D12—122no—
583D12—241no—
584C4×D3—21no—
585C4×D3—21no—
586C4×D3—122no—
587C4×D3—122no—
588C4×D3—122no—
589C4×D3—241no—
590C4×D3#23512yes—
591C4×D3C2×#6712yes—
592Dic6—22no—
593Dic6—21no—
594Dic6—21no—
595Dic6—21no—
596Dic6—21no—
597Dic6—61no—
598Dic6—61no—
599Dic6—61no—
600Dic6—61no—
601Dic6—121no—
602Dic6—121no—
603Dic6—122no—
604Dic6—122no—
605C3×C8—21no—
606C3×C8—21no—
607C3×C8—22no—
608C3×C8—32no—
609C3×C8—41no—
610C3×C8—61no—
611C3×C8D3×D412yes—
612C3×C8C2×#6712yes—
613C3⋊C8—21no—
614C3⋊C8C2×#6712yes—
615C2×C32—41no—
616C2×C32C2×#12111yescharacteristic
617C2×C32#57711yescharacteristic
618C2×C32#57811yescharacteristic
619C3⋊D3—81no—
620C3×D3—22no—
621C3×D3—41no—
622#41—62no—
623#41—62no—
624#41—182no—
625#41—182no—
626C2×Q8—31no—
627C2×Q8—31no—
628C2×Q8—31no—
629C2×Q8—91no—
630C2×Q8—181no—
631C2×Q8—182no—
632C2×Q8—182no—
633C2×D4—31no—
634C2×D4—31no—
635C2×D4—31no—
636C2×D4—91no—
637C2×D4—181no—
638C2×D4—181no—
639C2×D4—181no—
640C22×C4—31no—
641C22×C4—31no—
642C22×C4—181no—
643C22×C4—181no—
644C22×C4—181no—
645C22×C4C2×D3211yescharacteristic
646Q16—62no—
647Q16—182no—
648SD16—182no—
649SD16—182no—
650M16—22no—
651M16—34no—
652M16—62no—
653C2×C8—31no—
654C2×C8—31no—
655C2×C8—62no—
656C2×C8—62no—
657C2×C8—62no—
658C2×C8C2×D3211yescharacteristic
659C2×C8C2×D3211yescharacteristic
660C4⋊C4—31no—
661C4⋊C4—31no—
662C4⋊C4—61no—
663C4⋊C4—61no—
664C4⋊C4—91no—
665C4⋊C4—91no—
666C4⋊C4—181no—
667C4⋊C4—181no—
668C4⋊C4—181no—
669C4⋊C4—181no—
670C4⋊C4—181no—
671C22⋊C4—61no—
672C22⋊C4—61no—
673C22⋊C4—181no—
674C22⋊C4—181no—
675C22⋊C4—181no—
676C22⋊C4—181no—
677C22⋊C4—181no—
678C22⋊C4—181no—
679C22⋊C4—181no—
680C42—181no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—32no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—61no—
693C22×C3—61no—
694C22×C3—61no—
695C22×C3—61no—
696C22×C3—61no—
697C22×C3C22×D1211yescharacteristic
698C22×C3C2×D3×D411yescharacteristic
699C2×D3—21no—
700C2×D3—21no—
701C2×D3—21no—
702C2×D3—21no—
703C2×D3—21no—
704C2×D3—121no—
705C2×D3—121no—
706C2×D3—121no—
707C2×D3—121no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—241no—
711C2×D3—241no—
712C2×D3—241no—
713C2×D3#93012yes—
714C3×C4—21no—
715C3×C4—21no—
716C3×C4—21no—
717C3×C4—21no—
718C3×C4—32no—
719C3×C4—41no—
720C3×C4—61no—
721C3×C4—121no—
722C3×C4—121no—
723C3×C4—121no—
724C3×C4—121no—
725C3×C4C2×#23511yescharacteristic
726C3×C4C2×D3×D411yescharacteristic
727C3×C4D3×#4111yescharacteristic
728C3×C4C22×#6711yescharacteristic
729Dic3—21no—
730Dic3—41no—
731Dic3—41no—
732Dic3—41no—
733Dic3—41no—
734Dic3—121no—
735Dic3—121no—
736Dic3—121no—
737Dic3—121no—
738Dic3—121no—
739Dic3—121no—
740Dic3—241no—
741Dic3—241no—
742Dic3—241no—
743Dic3#93012yes—
744C32#306311yescharacteristic, complemented, Sylow
745C23—31no—
746C23—31no—
747C23—181no—
748C23D3×D1211yescharacteristic
749Q8—62no—
750Q8—61no—
751Q8—61no—
752Q8—61no—
753Q8—61no—
754Q8—181no—
755Q8—181no—
756Q8—362no—
757D4—62no—
758D4—62no—
759D4—62no—
760D4—181no—
761D4—181no—
762D4—362no—
763D4—721no—
764D4—721no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—31no—
768C2×C4—32no—
769C2×C4—32no—
770C2×C4—31no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—181no—
778C2×C4—181no—
779C2×C4—181no—
780C2×C4—362no—
781C2×C4—362no—
782C2×C4—721no—
783C2×C4D3×D1211yescharacteristic
784C2×C4C22×D3211yescharacteristic
785C8—21no—
786C8—32no—
787C8—61no—
788C8D3×#6712yes—
789C2×C3—21no—
790C2×C3—21no—
791C2×C3—21no—
792C2×C3—41no—
793C2×C3—41no—
794C2×C3—62no—
795C2×C3—81no—
796C2×C3—121no—
797C2×C3D3×#12111yescharacteristic
798C2×C3#575111yescharacteristic
799C2×C3#575311yescharacteristic
800C2×C3#577811yescharacteristic
801C2×C3#577911yescharacteristic
802C2×C3C2×#93011yescharacteristic
803D3—22no—
804D3—41no—
805D3—241no—
806D3—241no—
807D3—481no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—32no—
812C22—61no—
813C22—61no—
814C22—61no—
815C22—61no—
816C22—61no—
817C22—361no—
818C22—361no—
819C22—361no—
820C22C2×D3×D1211yescharacteristic
821C4—21no—
822C4—32no—
823C4—61no—
824C4—121no—
825C4—121no—
826C4—121no—
827C4—121no—
828C4—361no—
829C4—361no—
830C4—361no—
831C4D3×#23511yescharacteristic
832C4C2×D3×#6711yescharacteristic
833C3—21no—
834C3#8090711yescharacteristic, complemented
835C3#8380811yescharacteristic, complemented
836C2—41no—
837C2—62no—
838C2—121no—
839C2—721no—
840C2#1059471511yescharacteristic
841C2#1059472111yescharacteristic
842C2D3×#93011yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radical#10594894C2
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×#63801C2semidirect
5. #10592833C2semidirect
6. C3×#5137C2semidirect
7. #10591187C2semidirect
8. #10591177C2semidirect
9. #10590851C2semidirect
10. #10590850C2semidirect
11. #10590849C2semidirect
12. #10590830C2semidirect
13. #10590690C2semidirect
14. #10590681C2semidirect
15. D3×#816C2semidirect
68. C2×#907D3semidirect
74. #5137D3semidirect
138. C3×ΓL(1,𝔽25)D4semidirect
438. ΓL(1,𝔽25)#67semidirect
744. C32#3063semidirect
834. C3#80907semidirect
835. 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
#105948942
#105948842
C2×#638012
#105928332
C3×#51372
#105911872
#105911772
#105908512
#105908502
#105908492
#105908302
#105906902
#105906812
D3×#8162
#838083
#809073