Finite Group Databasebeta

← #11918524

Subgroups — #11918524

Order 1152.

2977 conjugacy classes of subgroups.

The subgroup lattice has 1045 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596695C211yesmaximal, characteristic
2#10596221C211yesmaximal, characteristic, complemented
3C3×#5750C211yesmaximal, characteristic, complemented
4C3×D3×#131C211yesmaximal, characteristic, complemented
5#10595442C211yesmaximal, characteristic, complemented
6#10595441C211yesmaximal, characteristic, complemented
7D3×#948C211yesmaximal, characteristic, complemented
8#10594722C213yesmaximal, complemented
9#10594707C213yesmaximal, complemented
10#10594706C213yesmaximal, complemented
11D3×#907C213yesmaximal, complemented
12C2×#63804C213yesmaximal, complemented
13#10594670C213yesmaximal, complemented
14#10594668C213yesmaximal, complemented
15D3×#901C213yesmaximal, complemented
16#87166—31nomaximal
17#87160—31nomaximal
18#41×C3⋊D3C2211yescharacteristic
19C3×D3×#41C2211yescharacteristic
20C3×D3×#41C2211yescharacteristic
21#64320C411yescharacteristic
22#64316C411yescharacteristic
23#64315C411yescharacteristic
24#64315C411yescharacteristic
25#64314C413yes—
26#64314C413yes—
27#64313C413yes—
28#64309C413yes—
29#64306C2213yes—
30D3×#235C2213yes—
31D3×#235C2213yes—
32C2×#3798C2213yes—
33C32×#131C2211yescharacteristic, complemented
34#64157C2211yescharacteristic, complemented
35#64116C2213yescomplemented
36M16×C3⋊D3C2213yescomplemented
37#64110C2213yescomplemented
38C2×#3743C2213yescomplemented
39C3×#948C2211yescharacteristic, complemented
40C3×#948C2211yescharacteristic, complemented
41C3×#907C2213yescomplemented
42C3×#907C2213yescomplemented
43C3×D3×M16C2213yescomplemented
44C3×D3×M16C2213yescomplemented
45C3×#901C2213yescomplemented
46C3×#901C2213yescomplemented
47C2×C3×ΓL(1,𝔽25)C2213yescomplemented
48C2×C3×D3×C8C2213yescomplemented
49C2×#3711C2213yescomplemented
50#63818C2213yescomplemented
51#63817C2213yescomplemented
52#63817C2213yescomplemented
53C2×#3710C2213yescomplemented
54#63815C2213yescomplemented
55#63815C2213yescomplemented
56#63814C2213yescomplemented
57#63814C2213yescomplemented
58D3×#208C2213yescomplemented
59D3×#208C2213yescomplemented
60C2×D3×C3⋊C8C2213yescomplemented
61#63805C2216yescomplemented
62#63804C2213yescomplemented
63#63804C2213yescomplemented
64#63804C2213yescomplemented
65#63804C2216yescomplemented
66#63804C2211yescharacteristic, complemented
67#63804C2213yescomplemented
68#63804C2213yescomplemented
69#63804C2213yescomplemented
70#63804C2213yescomplemented
71#63803C2216yescomplemented
72#63791C2216yescomplemented
73D3×ΓL(1,𝔽25)C2216yescomplemented
74D3×ΓL(1,𝔽25)C2216yescomplemented
75D32×C8C2216yescomplemented
76#5964—31no—
77#5964—31no—
78C3×#568—31no—
79C2×C3×#131—31no—
80#5819—31no—
81C2×#948—31no—
82#5750—31no—
83#5750—31no—
84#5750—31no—
85#5750—33no—
86#5750—33no—
87#5750—33no—
88#5750—33no—
89#5750—61no—
90#5750D311yescharacteristic, complemented
91D3×#131—31no—
92D3×#131—31no—
93D3×#131—31no—
94D3×#131—33no—
95D3×#131—33no—
96D3×#131—33no—
97D3×#131—33no—
98D3×#131D311yescharacteristic, complemented
99#5745—33no—
100#5745—33no—
101#5745—33no—
102#5745—33no—
103C2×#907—33no—
104C2×#907—33no—
105C2×#901—33no—
106C2×#901—33no—
107C32×#41C2311yescharacteristic
108#3832C2×C411yescharacteristic
109Q8×C3⋊D3C2×C411yescharacteristic
110#3830C2×C413yes—
111D4×C3⋊D3C2×C413yes—
112#3828C2313yes—
113C2×C4×C3⋊D3C2313yes—
114C3×#239C2×C411yescharacteristic
115C3×#239C2×C411yescharacteristic
116C3×D3×Q8C2×C411yescharacteristic
117C3×D3×Q8C2×C411yescharacteristic
118C3×#237C2×C413yes—
119C3×#237C2×C413yes—
120C3×D3×D4C2×C413yes—
121C3×D3×D4C2×C413yes—
122C3×#235C2313yes—
123C3×#235C2313yes—
124C2×C3×C4×D3C2313yes—
125C2×C3×C4×D3C2313yes—
126#3811C2×C416yes—
127D3×#67C2×C416yes—
128D3×#67C2×C416yes—
129C2×#627C2×C413yes—
130C2×#626C2×C413yes—
131C2×#626C2×C413yes—
132C2×#625C2×C413yes—
133#3805C2×C416yes—
134#3804C2×C416yes—
135#3804C2×C416yes—
136#3802C2×C413yes—
137D3×D12C2×C413yes—
138D3×D12C2×C413yes—
139C4×D32C2316yes—
140#3799C2×C413yes—
141#3799C2×C413yes—
142#3798C2×C413yes—
143#3798C2×C413yes—
144#3798C2×C413yes—
145#3798C2×C413yes—
146#3798C2311yescharacteristic
147#3798C2313yes—
148#3798C2313yes—
149#3798C2313yes—
150#3797C2×C413yes—
151#3796C2×C413yes—
152#3796C2×C413yes—
153#3795C2×C413yes—
154#3795C2×C413yes—
155D3×Dic6C2×C413yes—
156D3×Dic6C2×C413yes—
157C32×M16C2313yes—
158C2×C32×C8C2313yes—
159#3748C2313yes—
160C2×C3⋊(C3⋊C8)C2313yes—
161#3743C2313yes—
162#3743C2313yes—
163#3743C2311yescharacteristic
164#3743C2313yes—
165C8×C3⋊D3C2316yes—
166C3×#208C2313yes—
167C3×#208C2313yes—
168C2×C3×C3⋊C8C2313yes—
169C2×C3×C3⋊C8C2313yes—
170C3×ΓL(1,𝔽25)C2311yescharacteristic
171C3×ΓL(1,𝔽25)C2313yes—
172C3×ΓL(1,𝔽25)C2313yes—
173C3×ΓL(1,𝔽25)C2313yes—
174C3×ΓL(1,𝔽25)C2316yes—
175C3×D3×C8C2311yescharacteristic
176C3×D3×C8C2313yes—
177C3×D3×C8C2313yes—
178C3×D3×C8C2313yes—
179C3×D3×C8C2316yes—
180#3712C2316yes—
181#3711C2313yes—
182#3711C2316yes—
183#3711C2313yes—
184#3711C2313yes—
185#3711C2311yescharacteristic
186#3710C2313yes—
187#3710C2313yes—
188#3710C2311yescharacteristic
189#3710C2313yes—
190D3×C3⋊C8C2313yes—
191D3×C3⋊C8C2316yes—
192D3×C3⋊C8C2313yes—
193D3×C3⋊C8C2311yescharacteristic
194D3×C3⋊C8C2313yes—
195#3573—91noSylow
196C2×C3×#41—31no—
197C2×C3×#41—31no—
198#1010—31no—
199#1010—31no—
200#1010—33no—
201#1010—33no—
202#1009—31no—
203#1009—31no—
204#1009—33no—
205#1009—33no—
206D3×#41—31no—
207D3×#41—31no—
208D3×#41—33no—
209D3×#41—33no—
210D3×#41—33no—
211D3×#41—33no—
212D3×#41—61no—
213D3×#41C2×D311yescharacteristic
214D3×#41C2×D311yescharacteristic
215#1007—31no—
216#1007—31no—
217#1007—31no—
218#1007—31no—
219#1004—33no—
220#1004—33no—
221#1004—33no—
222#1004—33no—
223C2×#235—33no—
224C2×#235—33no—
225C2×#235—33no—
226C2×#235—33no—
227C3×#131—21no—
228C3×#131—31no—
229C3×#131—31no—
230C3×#131—33no—
231C3×#131—33no—
232C3×#131—33no—
233C3×#131—33no—
234C3×#131C2×D311yescharacteristic, complemented
235C3×#131C2×D311yescharacteristic, complemented
236C2×C3×M16—33no—
237C2×C3×M16—33no—
238C2×C3×M16—33no—
239C22×C3×C8—33no—
240#948—31no—
241#948—31no—
242#948—33no—
243#948—33no—
244#948—33no—
245#948—33no—
246#948—61no—
247#948C2×D311yescharacteristic, complemented
248#948C2×D311yescharacteristic, complemented
249C2×#208—33no—
250C2×#208—33no—
251C2×#208—33no—
252C22×C3⋊C8—33no—
253#907—33no—
254#907—33no—
255#907—33no—
256#907—33no—
257#907—33no—
258#907—33no—
259#907—36no—
260#907—36no—
261#907—33no—
262#907—31no—
263#907—33no—
264#907—33no—
265#907—33no—
266#907—33no—
267#907—33no—
268#907—33no—
269#907—36no—
270#907—63no—
271#907C2×D313yescomplemented
272#907C2×D313yescomplemented
273D3×M16—33no—
274D3×M16—33no—
275D3×M16—33no—
276D3×M16—33no—
277D3×M16—33no—
278D3×M16—33no—
279D3×M16—36no—
280D3×M16—36no—
281D3×M16—36no—
282D3×M16—36no—
283D3×M16—63no—
284D3×M16C2×D313yescomplemented
285D3×M16C2×D313yescomplemented
286#901—33no—
287#901—33no—
288#901—33no—
289#901—33no—
290#901—33no—
291#901—33no—
292#901—33no—
293#901—31no—
294#901—33no—
295#901—33no—
296#901—33no—
297#901—33no—
298#901—33no—
299#901—33no—
300#901—36no—
301#901—36no—
302#901—36no—
303#901—63no—
304#901C2×D313yescomplemented
305#901C2×D313yescomplemented
306C2×ΓL(1,𝔽25)—33no—
307C2×ΓL(1,𝔽25)—33no—
308C2×ΓL(1,𝔽25)—33no—
309C2×ΓL(1,𝔽25)—36no—
310C2×ΓL(1,𝔽25)—36no—
311C2×ΓL(1,𝔽25)—63no—
312C2×ΓL(1,𝔽25)C2×D313yescomplemented
313C2×D3×C8—33no—
314C2×D3×C8—33no—
315C2×D3×C8—33no—
316C2×D3×C8—36no—
317C2×D3×C8—36no—
318C2×D3×C8C2×D313yescomplemented
319C22×C3⋊D3C22×C413yes—
320C22×C3×D3C22×C413yes—
321C22×C3×D3C22×C413yes—
322C2×D32C22×C416yes—
323C32×Q8C22×C411yescharacteristic
324C32×D4C22×C413yes—
325C2×C32×C4C2413yes—
326#638C22×C416yes—
327C2×C3⋊Dic3C22×C413yes—
328C4⋊(C3⋊D3)C22×C413yes—
329C4×C3⋊D3C22×C413yes—
330C4×C3⋊D3C22×C413yes—
331C4×C3⋊D3C2411yescharacteristic
332C4×C3⋊D3C2413yes—
333#634C22×C413yes—
334C3×#67C22×C416yes—
335C3×#67C22×C416yes—
336C2×C3×Dic3C22×C413yes—
337C2×C3×Dic3C22×C413yes—
338C3×D12C22×C413yes—
339C3×D12C22×C413yes—
340C3×C4×D3C22×C413yes—
341C3×C4×D3C22×C413yes—
342C3×C4×D3C22×C413yes—
343C3×C4×D3C22×C413yes—
344C3×C4×D3C2411yescharacteristic
345C3×C4×D3C2413yes—
346C3×C4×D3C2413yes—
347C3×C4×D3C2411yescharacteristic
348C3×Dic6C22×C413yes—
349C3×Dic6C22×C413yes—
350#627C22×C413yes—
351#627C22×C413yes—
352#627C22×C413yes—
353#627C22×C411yescharacteristic
354#626C22×C413yes—
355#626C22×C413yes—
356#626C22×C411yescharacteristic
357#626C22×C411yescharacteristic
358#626C22×C413yes—
359#626C22×C413yes—
360#626C22×C413yes—
361#626C22×C413yes—
362#625C22×C413yes—
363#625C22×C413yes—
364#625C22×C411yescharacteristic
365#625C22×C413yes—
366#624C22×C416yes—
367D3×Dic3C22×C416yes—
368D3×Dic3C22×C416yes—
369C32×C8C2413yes—
370C32×C8C2411yescharacteristic
371C3⋊(C3⋊C8)C2413yes—
372C3⋊(C3⋊C8)C2411yescharacteristic
373C3×C3⋊C8C2411yescharacteristic
374C3×C3⋊C8C2413yes—
375C3×C3⋊C8C2413yes—
376C3×C3⋊C8C2411yescharacteristic
377#585—91no—
378#568—31no—
379#568—93no—
380#568—93no—
381#568—93no—
382#568—93no—
383#568—91no—
384#568—91no—
385C2×#131—31no—
386C2×#131—93no—
387C2×#131—93no—
388C2×#131—93no—
389C2×#131—91no—
390C2×#131—93no—
391C2×#131—91no—
392C3×#41—21no—
393C3×#41—31no—
394C3×#41—31no—
395C3×#41—33no—
396C3×#41—33no—
397C3×#41—33no—
398C3×#41—33no—
399C3×#41C22×D311yescharacteristic
400C3×#41C22×D311yescharacteristic
401C2×C3×Q8—31no—
402C2×C3×Q8—31no—
403C2×C3×D4—33no—
404C2×C3×D4—33no—
405C22×C3×C4—33no—
406C22×C3×C4—33no—
407C2×#67—33no—
408C2×#67—33no—
409C2×#67—36no—
410C2×#67—36no—
411C2×#67—33no—
412C2×#67—33no—
413#239—31no—
414#239—31no—
415#239—33no—
416#239—33no—
417#239—33no—
418#239—33no—
419#239—61no—
420#239C4×D311yescharacteristic
421#239C4×D311yescharacteristic
422D3×Q8—31no—
423D3×Q8—31no—
424D3×Q8—33no—
425D3×Q8—33no—
426D3×Q8—33no—
427D3×Q8—33no—
428D3×Q8—61no—
429D3×Q8C4×D311yescharacteristic
430D3×Q8C4×D311yescharacteristic
431#237—33no—
432#237—33no—
433#237—36no—
434#237—36no—
435#237—36no—
436#237—36no—
437#237—33no—
438#237—33no—
439#237—33no—
440#237—33no—
441#237—63no—
442#237C4×D313yes—
443#237C4×D313yes—
444D3×D4—36no—
445D3×D4—36no—
446D3×D4—33no—
447D3×D4—33no—
448D3×D4—36no—
449D3×D4—36no—
450D3×D4—33no—
451D3×D4—33no—
452D3×D4—33no—
453D3×D4—33no—
454D3×D4—63no—
455D3×D4C4×D313yes—
456D3×D4C4×D313yes—
457#235—33no—
458#235—33no—
459#235—36no—
460#235—36no—
461#235—33no—
462#235—33no—
463#235—33no—
464#235—33no—
465#235—33no—
466#235—33no—
467#235—33no—
468#235—33no—
469#235—33no—
470#235—33no—
471#235—31no—
472#235—33no—
473#235—33no—
474#235—33no—
475#235—33no—
476#235—33no—
477#235—33no—
478#235—31no—
479#235—33no—
480#235—33no—
481#235—63no—
482#235C22×D313yes—
483#235C22×D313yes—
484C2×D12—33no—
485C2×D12—33no—
486C2×D12—33no—
487C2×D12—33no—
488C2×C4×D3—33no—
489C2×C4×D3—33no—
490C2×C4×D3—36no—
491C2×C4×D3—36no—
492C2×C4×D3—63no—
493C2×C4×D3C22×D313yes—
494C2×C4×D3C22×D313yes—
495C2×Dic6—33no—
496C2×Dic6—33no—
497C2×Dic6—33no—
498C2×Dic6—33no—
499C3×M16—23no—
500C3×M16—33no—
501C3×M16—33no—
502C3×M16—33no—
503C3×M16—36no—
504C3×M16—33no—
505C3×M16—33no—
506C3×M16—31no—
507C3×M16C22×D313yes—
508C3×M16C22×D313yes—
509C2×C3×C8—23no—
510C2×C3×C8—33no—
511C2×C3×C8—33no—
512C2×C3×C8—33no—
513C2×C3×C8—36no—
514C2×C3×C8—33no—
515C2×C3×C8—31no—
516C2×C3×C8—33no—
517C2×C3×C8C22×D313yes—
518C2×C3×C8C22×D313yes—
519#208—33no—
520#208—33no—
521#208—31no—
522#208—33no—
523#208—33no—
524#208—33no—
525#208—36no—
526#208—63no—
527#208C22×D313yes—
528#208C22×D313yes—
529C2×C3⋊C8—33no—
530C2×C3⋊C8—33no—
531C2×C3⋊C8—33no—
532C2×C3⋊C8—36no—
533C2×C3⋊C8—33no—
534C2×C3⋊C8—31no—
535C2×C3⋊C8—33no—
536C2×C3⋊C8—63no—
537C2×C3⋊C8C22×D313yes—
538C2×C3⋊C8C22×D313yes—
539ΓL(1,𝔽25)—33no—
540ΓL(1,𝔽25)—31no—
541ΓL(1,𝔽25)—36no—
542ΓL(1,𝔽25)—33no—
543ΓL(1,𝔽25)—33no—
544ΓL(1,𝔽25)—31no—
545ΓL(1,𝔽25)—33no—
546ΓL(1,𝔽25)—33no—
547ΓL(1,𝔽25)—31no—
548ΓL(1,𝔽25)—33no—
549ΓL(1,𝔽25)—33no—
550ΓL(1,𝔽25)—33no—
551ΓL(1,𝔽25)—33no—
552ΓL(1,𝔽25)—36no—
553ΓL(1,𝔽25)—36no—
554ΓL(1,𝔽25)—61no—
555ΓL(1,𝔽25)—63no—
556ΓL(1,𝔽25)—63no—
557ΓL(1,𝔽25)—63no—
558ΓL(1,𝔽25)C22×D313yes—
559ΓL(1,𝔽25)C22×D316yes—
560ΓL(1,𝔽25)C22×D311yescharacteristic
561ΓL(1,𝔽25)C22×D313yes—
562ΓL(1,𝔽25)C22×D313yes—
563D3×C8—31no—
564D3×C8—33no—
565D3×C8—33no—
566D3×C8—36no—
567D3×C8—33no—
568D3×C8—36no—
569D3×C8—36no—
570D3×C8—31no—
571D3×C8—33no—
572D3×C8—33no—
573D3×C8—31no—
574D3×C8—33no—
575D3×C8—33no—
576D3×C8—33no—
577D3×C8—33no—
578D3×C8—66no—
579D3×C8C22×D313yes—
580D3×C8C22×D316yes—
581D3×C8C22×D311yescharacteristic
582D3×C8C22×D313yes—
583D3×C8C22×D313yes—
584C22×C32C23×C413yes—
585C2×C3⋊D3—43no—
586C2×C3⋊D3C23×C413yes—
587C2×C3⋊D3C23×C411yescharacteristic
588C2×C3×D3—43no—
589C2×C3×D3—43no—
590C2×C3×D3C23×C413yes—
591C2×C3×D3C23×C413yes—
592C2×C3×D3C23×C411yescharacteristic
593C2×C3×D3C23×C411yescharacteristic
594D32—46no—
595C32×C4C23×C413yes—
596C32×C4C2511yescharacteristic
597C3⋊Dic3C23×C413yes—
598C3⋊Dic3C23×C411yescharacteristic
599C3×Dic3C23×C413yes—
600C3×Dic3C23×C413yes—
601C3×Dic3C23×C411yescharacteristic
602C3×Dic3C23×C411yescharacteristic
6032−1+4—91no—
6042−1+4—91no—
6052−1+4—91no—
6062−1+4—93no—
607H(5,𝔽2)—93no—
608H(5,𝔽2)—93no—
609H(5,𝔽2)—93no—
610H(5,𝔽2)—91no—
611C2×#41—31no—
612C2×#41—31no—
613C2×#41—93no—
614C2×#41—93no—
615C2×#41—93no—
616C2×#41—93no—
617C2×#41—91no—
618#131—31no—
619#131—31no—
620#131—33no—
621#131—33no—
622#131—33no—
623#131—33no—
624#131—96no—
625#131—93no—
626#131—91no—
627#131—93no—
628#131—93no—
629#131—93no—
630#131—93no—
631#131—93no—
632#131—93no—
633#131—93no—
634#131—93no—
635#131—96no—
636#131—93no—
637#131—93no—
638#131—96no—
639#131—93no—
640#131—93no—
641#131—91no—
642#131—93no—
643#131—93no—
644#131D3211yescharacteristic, complemented
645C2×M16—33no—
646C2×M16—33no—
647C2×M16—33no—
648C2×M16—96no—
649C2×M16—96no—
650C2×M16—93no—
651C2×M16—93no—
652C2×M16—96no—
653C2×M16—93no—
654C2×M16—93no—
655C2×M16—93no—
656C2×M16—93no—
657C22×C8—33no—
658C22×C8—93no—
659C22×C8—96no—
660C22×C8—93no—
661C23×C3—33no—
662C23×C3—33no—
663C22×D3—33no—
664C22×D3—33no—
665C22×D3—36no—
666C22×D3—36no—
667C22×D3—63no—
668C22×D3C2×C4×D313yes—
669C22×D3C2×C4×D313yes—
670C3×Q8—21no—
671C3×Q8—33no—
672C3×Q8—33no—
673C3×Q8C2×C4×D311yescharacteristic
674C3×Q8C2×C4×D311yescharacteristic
675C3×D4—23no—
676C3×D4—36no—
677C3×D4—36no—
678C3×D4—33no—
679C3×D4—33no—
680C3×D4C2×C4×D313yes—
681C3×D4C2×C4×D313yes—
682C2×C3×C4—23no—
683C2×C3×C4—33no—
684C2×C3×C4—33no—
685C2×C3×C4—33no—
686C2×C3×C4—33no—
687C2×C3×C4—33no—
688C2×C3×C4—33no—
689C2×C3×C4—31no—
690C2×C3×C4—33no—
691C2×C3×C4—33no—
692C2×C3×C4—31no—
693C2×C3×C4C23×D313yes—
694C2×C3×C4C23×D313yes—
695#67—36no—
696#67—36no—
697#67—33no—
698#67—33no—
699#67—31no—
700#67—31no—
701#67—33no—
702#67—33no—
703#67—33no—
704#67—33no—
705#67—31no—
706#67—31no—
707#67—33no—
708#67—33no—
709#67—33no—
710#67—33no—
711#67—33no—
712#67—33no—
713#67—66no—
714#67C2×C4×D316yes—
715#67C2×C4×D316yes—
716C2×Dic3—33no—
717C2×Dic3—33no—
718C2×Dic3—36no—
719C2×Dic3—36no—
720C2×Dic3—63no—
721C2×Dic3C2×C4×D313yes—
722C2×Dic3C2×C4×D313yes—
723D12—33no—
724D12—33no—
725D12—31no—
726D12—31no—
727D12—33no—
728D12—33no—
729D12—33no—
730D12—33no—
731D12—33no—
732D12—33no—
733D12—63no—
734D12C2×C4×D313yes—
735D12C2×C4×D313yes—
736C4×D3—36no—
737C4×D3—36no—
738C4×D3—33no—
739C4×D3—33no—
740C4×D3—33no—
741C4×D3—33no—
742C4×D3—31no—
743C4×D3—31no—
744C4×D3—33no—
745C4×D3—33no—
746C4×D3—36no—
747C4×D3—36no—
748C4×D3—63no—
749C4×D3—63no—
750C4×D3—63no—
751C4×D3—61no—
752C4×D3C2×C4×D313yes—
753C4×D3C2×C4×D313yes—
754C4×D3C2×C4×D313yes—
755C4×D3C2×C4×D313yes—
756C4×D3C23×D311yescharacteristic
757C4×D3C23×D313yes—
758C4×D3C23×D313yes—
759C4×D3C23×D311yescharacteristic
760Dic6—33no—
761Dic6—33no—
762Dic6—31no—
763Dic6—31no—
764Dic6—33no—
765Dic6—33no—
766Dic6—33no—
767Dic6—33no—
768Dic6—33no—
769Dic6—33no—
770Dic6—63no—
771Dic6C2×C4×D313yes—
772Dic6C2×C4×D313yes—
773C3×C8—23no—
774C3×C8—21no—
775C3×C8—31no—
776C3×C8—33no—
777C3×C8—33no—
778C3×C8—31no—
779C3×C8C23×D313yes—
780C3×C8C23×D313yes—
781C3×C8C23×D311yescharacteristic
782C3×C8C23×D311yescharacteristic
783C3⋊C8—33no—
784C3⋊C8—33no—
785C3⋊C8—31no—
786C3⋊C8—31no—
787C3⋊C8—63no—
788C3⋊C8—61no—
789C3⋊C8C23×D311yescharacteristic
790C3⋊C8C23×D311yescharacteristic
791C3⋊C8C23×D313yes—
792C3⋊C8C23×D313yes—
793C2×C32—23no—
794C2×C32C24×C411yescharacteristic
795C3⋊D3—23no—
796C3⋊D3—21no—
797C3×D3—23no—
798C3×D3—23no—
799C3×D3—21no—
800C3×D3—21no—
801#41—31no—
802#41—31no—
803#41—33no—
804#41—33no—
805#41—33no—
806#41—33no—
807#41—93no—
808#41—91no—
809#41—93no—
810#41—93no—
811#41—93no—
812#41—93no—
813#41—93no—
814#41—93no—
815#41—96no—
816#41—96no—
817#41—93no—
818#41—93no—
819#41—93no—
820#41—93no—
821#41—96no—
822#41—93no—
823#41—93no—
824#41—91no—
825#41—93no—
826#41—93no—
827#41C2×D3211yescharacteristic
828C2×Q8—31no—
829C2×Q8—31no—
830C2×Q8—93no—
831C2×Q8—93no—
832C2×Q8—93no—
833C2×Q8—93no—
834C2×Q8—91no—
835C2×D4—33no—
836C2×D4—33no—
837C2×D4—93no—
838C2×D4—93no—
839C2×D4—93no—
840C2×D4—93no—
841C2×D4—96no—
842C2×D4—93no—
843C2×D4—96no—
844C2×D4—96no—
845C2×D4—93no—
846C2×D4—93no—
847C22×C4—33no—
848C22×C4—33no—
849C22×C4—96no—
850C22×C4—93no—
851M16—33no—
852M16—33no—
853M16—33no—
854M16—31no—
855M16—36no—
856M16—33no—
857M16—33no—
858M16—96no—
859M16—91no—
860M16—93no—
861M16—93no—
862M16—96no—
863M16—93no—
864M16—93no—
865M16—93no—
866M16—93no—
867M16—93no—
868M16—91no—
869M16C2×D3213yes—
870C2×C8—33no—
871C2×C8—33no—
872C2×C8—31no—
873C2×C8—33no—
874C2×C8—33no—
875C2×C8—33no—
876C2×C8—36no—
877C2×C8—91no—
878C2×C8—93no—
879C2×C8—93no—
880C2×C8—93no—
881C2×C8—93no—
882C2×C8—91no—
883C2×C8—96no—
884C2×C8—93no—
885C2×C8—93no—
886C2×C8—93no—
887C2×C8—96no—
888C2×C8C2×D3213yes—
889C22×C3—23no—
890C22×C3—33no—
891C22×C3—33no—
892C22×C3—31no—
893C22×C3—31no—
894C22×C3—123no—
895C22×C3—123no—
896C22×C3C22×C4×D313yes—
897C22×C3C22×C4×D313yes—
898C2×D3—31no—
899C2×D3—33no—
900C2×D3—31no—
901C2×D3—33no—
902C2×D3—43no—
903C2×D3—43no—
904C2×D3—61no—
905C2×D3—63no—
906C2×D3—126no—
907C2×D3—126no—
908C2×D3—123no—
909C2×D3—123no—
910C2×D3—243no—
911C2×D3C22×C4×D313yes—
912C2×D3C22×C4×D313yes—
913C2×D3C22×C4×D311yescharacteristic
914C2×D3C22×C4×D311yescharacteristic
915C3×C4—23no—
916C3×C4—21no—
917C3×C4—31no—
918C3×C4—31no—
919C3×C4—33no—
920C3×C4—33no—
921C3×C4C22×C4×D313yes—
922C3×C4C22×C4×D313yes—
923C3×C4C24×D311yescharacteristic
924C3×C4C24×D311yescharacteristic
925Dic3—33no—
926Dic3—31no—
927Dic3—33no—
928Dic3—31no—
929Dic3—63no—
930Dic3—61no—
931Dic3C22×C4×D311yescharacteristic
932Dic3C22×C4×D311yescharacteristic
933Dic3C22×C4×D313yes—
934Dic3C22×C4×D313yes—
935C32#357311yescharacteristic, complemented, Sylow
936C23—33no—
937C23—33no—
938C23—96no—
939C23—93no—
940Q8—33no—
941Q8—33no—
942Q8—91no—
943Q8—93no—
944Q8—93no—
945Q8—93no—
946Q8—93no—
947Q8C4×D3211yescharacteristic
948D4—36no—
949D4—36no—
950D4—33no—
951D4—33no—
952D4—91no—
953D4—91no—
954D4—93no—
955D4—93no—
956D4—93no—
957D4—93no—
958D4—93no—
959D4—93no—
960D4—91no—
961D4—93no—
962D4—93no—
963D4—93no—
964D4—96no—
965D4—93no—
966D4C4×D3213yes—
967C2×C4—33no—
968C2×C4—33no—
969C2×C4—33no—
970C2×C4—33no—
971C2×C4—33no—
972C2×C4—33no—
973C2×C4—31no—
974C2×C4—33no—
975C2×C4—33no—
976C2×C4—31no—
977C2×C4—96no—
978C2×C4—96no—
979C2×C4—96no—
980C2×C4—93no—
981C2×C4—93no—
982C2×C4—93no—
983C2×C4—91no—
984C2×C4—93no—
985C2×C4C22×D3213yes—
986C8—31no—
987C8—33no—
988C8—31no—
989C8—33no—
990C8—91no—
991C8—93no—
992C8C22×D3213yes—
993C8C22×D3211yescharacteristic
994C2×C3—23no—
995C2×C3—23no—
996C2×C3—21no—
997C2×C3—43no—
998C2×C3—63no—
999C2×C3—61no—
1000C2×C3—63no—
1001C2×C3—61no—
1002C2×C3C23×C4×D311yescharacteristic
1003C2×C3C23×C4×D311yescharacteristic
1004D3—21no—
1005D3—23no—
1006D3—21no—
1007D3—23no—
1008D3—63no—
1009D3—61no—
1010D3—63no—
1011D3—61no—
1012D3—121no—
1013D3—123no—
1014C22—31no—
1015C22—31no—
1016C22—33no—
1017C22—33no—
1018C22—93no—
1019C22—91no—
1020C22—123no—
1021C22—123no—
1022C22—363no—
1023C22—366no—
1024C22C2×C4×D3213yes—
1025C4—31no—
1026C4—31no—
1027C4—33no—
1028C4—33no—
1029C4—93no—
1030C4—91no—
1031C4C2×C4×D3213yes—
1032C4C23×D3211yescharacteristic
1033C3—21no—
1034C3#8716011yescharacteristic, complemented
1035C3#8716611yescharacteristic, complemented
1036C2—23no—
1037C2—61no—
1038C2—61no—
1039C2—63no—
1040C2—63no—
1041C2—181no—
1042C2—183no—
1043C2C22×C4×D3211yescharacteristic
subgroupG/H
center, FrattiniC4C23×D32
commutator, socleC2×C32C24×C4
FittingC32×#131C22
prime radical#10596695C2
cosocleC32×C4C25
hypercenter#131D32
hypocenterC32#3573
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ #131

Complements

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

NH ≅ G/Ntype
2. #10596221C2semidirect
3. C3×#5750C2semidirect
4. C3×D3×#131C2semidirect
5. #10595442C2semidirect
6. #10595441C2semidirect
7. D3×#948C2semidirect
8. #10594722C2semidirect
9. #10594707C2semidirect
10. #10594706C2semidirect
11. D3×#907C2semidirect
12. C2×#63804C2semidirect
13. #10594670C2semidirect
14. #10594668C2semidirect
15. D3×#901C2semidirect
33. C32×#131C22semidirect
34. #64157C22semidirect
35. #64116C22semidirect
36. M16×C3⋊D3C22semidirect
37. #64110C22semidirect
38. C2×#3743C22semidirect
39. C3×#948C22semidirect
40. C3×#948C22semidirect
41. C3×#907C22semidirect
42. C3×#907C22semidirect
43. C3×D3×M16C22semidirect
44. C3×D3×M16C22semidirect
45. C3×#901C22semidirect
46. C3×#901C22semidirect
47. C2×C3×ΓL(1,𝔽25)C22semidirect
48. C2×C3×D3×C8C22semidirect
49. C2×#3711C22semidirect
50. #63818C22semidirect
51. #63817C22semidirect
52. #63817C22semidirect
53. C2×#3710C22semidirect
54. #63815C22semidirect
55. #63815C22semidirect
56. #63814C22semidirect
57. #63814C22semidirect
58. D3×#208C22semidirect
59. D3×#208C22semidirect
60. C2×D3×C3⋊C8C22semidirect
61. #63805C22semidirect
62. #63804C22semidirect
63. #63804C22semidirect
64. #63804C22semidirect
65. #63804C22semidirect
66. #63804C22semidirect
67. #63804C22semidirect
68. #63804C22semidirect
69. #63804C22semidirect
70. #63804C22semidirect
71. #63803C22semidirect
72. #63791C22semidirect
73. D3×ΓL(1,𝔽25)C22semidirect
74. D3×ΓL(1,𝔽25)C22semidirect
75. D32×C8C22semidirect
90. #5750D3semidirect
98. D3×#131D3semidirect
234. C3×#131C2×D3semidirect
235. C3×#131C2×D3semidirect
247. #948C2×D3semidirect
248. #948C2×D3semidirect
271. #907C2×D3semidirect
272. #907C2×D3semidirect
284. D3×M16C2×D3semidirect
285. D3×M16C2×D3semidirect
304. #901C2×D3semidirect
305. #901C2×D3semidirect
312. C2×ΓL(1,𝔽25)C2×D3semidirect
318. C2×D3×C8C2×D3semidirect
644. #131D32semidirect
935. C32#3573semidirect
1034. C3#87160semidirect
1035. C3#87166semidirect

Maximal subgroups

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

subgroupindex
#105966952
#105962212
C3×#57502
C3×D3×#1312
#105954422
#105954412
D3×#9482
#105947222
#105947072
#105947062
D3×#9072
C2×#638042
#105946702
#105946682
D3×#9012
#871663
#871603