Finite Group Databasebeta

← D3×#5750 #11918493

Subgroups — D3×#5750 #11918493

Order 1152.

3049 conjugacy classes of subgroups.

The subgroup lattice has 1061 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D32×#41C211yesmaximal, characteristic
2#10596221C211yesmaximal, characteristic, complemented
3C3×#5750C211yesmaximal, characteristic, complemented
4C3×D3×#131C211yesmaximal, characteristic, complemented
5#10595443C211yesmaximal, characteristic, complemented
6#10595441C211yesmaximal, characteristic, complemented
7D3×#948C211yesmaximal, characteristic, complemented
8#10594708C213yesmaximal, complemented
9#10594706C213yesmaximal, complemented
10D3×#907C213yesmaximal, complemented
11D32×M16C213yesmaximal, complemented
12#10594670C213yesmaximal, complemented
13#10594668C213yesmaximal, complemented
14D3×#901C213yesmaximal, complemented
15C2×D3×ΓL(1,𝔽25)C213yesmaximal, complemented
16D3×#568—31nomaximal
17C2×#5750—31nomaximal
18#41×C3⋊D3C2211yescharacteristic
19C3×D3×#41C2211yescharacteristic
20C3×D3×#41C2211yescharacteristic
21#64319C411yescharacteristic
22D3×#239C411yescharacteristic
23D3×#239C411yescharacteristic
24D32×Q8C411yescharacteristic
25#64312C413yes—
26D3×#237C413yes—
27D3×#237C413yes—
28D32×D4C413yes—
29#64306C2213yes—
30D3×#235C2213yes—
31D3×#235C2213yes—
32C2×C4×D32C2213yes—
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×#3712C2213yescomplemented
50C2×#3711C2213yescomplemented
51#63818C2213yescomplemented
52#63817C2213yescomplemented
53#63817C2213yescomplemented
54#63815C2213yescomplemented
55#63815C2213yescomplemented
56#63814C2213yescomplemented
57#63814C2213yescomplemented
58D3×#208C2213yescomplemented
59D3×#208C2213yescomplemented
60C2×D3×C3⋊C8C2213yescomplemented
61#63805C2216yescomplemented
62#63804C2216yescomplemented
63#63804C2216yescomplemented
64#63803C2216yescomplemented
65#63791C2216yescomplemented
66D3×ΓL(1,𝔽25)C2211yescharacteristic
67D3×ΓL(1,𝔽25)C2213yes—
68D3×ΓL(1,𝔽25)C2213yescomplemented
69D3×ΓL(1,𝔽25)C2213yescomplemented
70D3×ΓL(1,𝔽25)C2213yescomplemented
71D3×ΓL(1,𝔽25)C2213yescomplemented
72D3×ΓL(1,𝔽25)C2213yescomplemented
73D3×ΓL(1,𝔽25)C2213yescomplemented
74D3×ΓL(1,𝔽25)C2216yescomplemented
75D32×C8C2216yescomplemented
76C2×D3×#41—31no—
77C2×D3×#41—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—31no—
86#5750—31no—
87#5750—33no—
88#5750—33no—
89#5750—33no—
90#5750—33no—
91#5750—33no—
92#5750—33no—
93#5750—61no—
94#5750D311yescharacteristic, direct product factor
95D3×#131—31no—
96D3×#131—33no—
97D3×#131—33no—
98D3×#131D311yescharacteristic, complemented
99#5745—33no—
100#5745—33no—
101C2×#907—33no—
102C2×D3×M16—33no—
103C2×D3×M16—33no—
104C2×D3×M16—33no—
105C2×#901—33no—
106C22×ΓL(1,𝔽25)—33no—
107C22×D32C2×C413yes—
108C32×#41C2311yescharacteristic
109#3832C2×C411yescharacteristic
110Q8×C3⋊D3C2×C411yescharacteristic
111#3830C2×C413yes—
112D4×C3⋊D3C2×C413yes—
113#3828C2313yes—
114C2×C4×C3⋊D3C2313yes—
115C3×#239C2×C411yescharacteristic
116C3×#239C2×C411yescharacteristic
117C3×D3×Q8C2×C411yescharacteristic
118C3×D3×Q8C2×C411yescharacteristic
119C3×#237C2×C413yes—
120C3×#237C2×C413yes—
121C3×D3×D4C2×C413yes—
122C3×D3×D4C2×C413yes—
123C3×#235C2313yes—
124C3×#235C2313yes—
125C2×C3×C4×D3C2313yes—
126C2×C3×C4×D3C2313yes—
127#3811C2×C416yes—
128D3×#67C2×C416yes—
129D3×#67C2×C416yes—
130C2×#624C2×C413yes—
131#3805C2×C416yes—
132#3804C2×C416yes—
133#3804C2×C416yes—
134C2×D3×Dic3C2×C413yes—
135C2×D3×Dic3C2×C413yes—
136#3802C2×C413yes—
137D3×D12C2×C413yes—
138D3×D12C2×C413yes—
139C4×D32C2×C413yes—
140C4×D32C2×C413yes—
141C4×D32C2×C413yes—
142C4×D32C2×C413yes—
143C4×D32C2313yes—
144C4×D32C2311yescharacteristic
145C4×D32C2313yes—
146C4×D32C2313yes—
147#3799C2×C413yes—
148#3799C2×C413yes—
149#3798C2316yes—
150#3797C2×C413yes—
151#3796C2×C413yes—
152#3796C2×C413yes—
153#3795C2×C413yes—
154#3795C2×C413yes—
155D3×Dic6C2×C413yes—
156D3×Dic6C2×C413yes—
157C32×M16C2313yescomplemented
158C2×C32×C8C2313yescomplemented
159#3748C2313yescomplemented
160C2×C3⋊(C3⋊C8)C2313yescomplemented
161#3743C2311yescharacteristic
162#3743C2313yes—
163#3743C2313yescomplemented
164#3743C2313yescomplemented
165C8×C3⋊D3C2316yescomplemented
166C3×#208C2313yescomplemented
167C3×#208C2313yescomplemented
168C2×C3×C3⋊C8C2313yescomplemented
169C2×C3×C3⋊C8C2313yescomplemented
170C3×ΓL(1,𝔽25)C2311yescharacteristic
171C3×ΓL(1,𝔽25)C2313yes—
172C3×ΓL(1,𝔽25)C2313yescomplemented
173C3×ΓL(1,𝔽25)C2313yescomplemented
174C3×ΓL(1,𝔽25)C2316yescomplemented
175C3×D3×C8C2311yescharacteristic
176C3×D3×C8C2313yes—
177C3×D3×C8C2313yescomplemented
178C3×D3×C8C2313yescomplemented
179C3×D3×C8C2316yescomplemented
180#3712C2313yes—
181#3712C2311yescharacteristic
182#3712C2313yescomplemented
183#3712C2313yescomplemented
184#3711C2311yescharacteristic
185#3711C2313yes—
186#3711C2313yescomplemented
187#3711C2313yescomplemented
188#3711C2316yescomplemented
189#3710C2316yescomplemented
190D3×C3⋊C8C2313yes—
191D3×C3⋊C8C2311yescharacteristic
192D3×C3⋊C8C2316yescomplemented
193D3×C3⋊C8C2313yescomplemented
194D3×C3⋊C8C2313yescomplemented
195C2×#568—91noSylow
196C2×C3×#41—31no—
197C2×C3×#41—31no—
198D3×#41—31no—
199D3×#41—31no—
200D3×#41—31no—
201D3×#41—31no—
202D3×#41—31no—
203D3×#41—31no—
204D3×#41—33no—
205D3×#41—33no—
206D3×#41—33no—
207D3×#41—33no—
208D3×#41—33no—
209D3×#41—33no—
210D3×#41—33no—
211D3×#41—33no—
212D3×#41—61no—
213D3×#41C2×D311yescharacteristic
214D3×#41C2×D311yescharacteristic
215C2×#239—31no—
216C2×#239—31no—
217C2×D3×Q8—31no—
218C2×D3×Q8—31no—
219C2×#237—33no—
220C2×#237—33no—
221C2×D3×D4—33no—
222C2×D3×D4—33no—
223C2×#235—33no—
224C2×#235—33no—
225C22×C4×D3—33no—
226C22×C4×D3—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—36no—
262#907—36no—
263#907—63no—
264#907C2×D313yescomplemented
265#907C2×D313yescomplemented
266D3×M16—33no—
267D3×M16—33no—
268D3×M16—33no—
269D3×M16—33no—
270D3×M16—33no—
271D3×M16—33no—
272D3×M16—36no—
273D3×M16—36no—
274D3×M16—33no—
275D3×M16—31no—
276D3×M16—33no—
277D3×M16—33no—
278D3×M16—33no—
279D3×M16—33no—
280D3×M16—36no—
281D3×M16—33no—
282D3×M16—33no—
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—36no—
293#901—36no—
294#901—36no—
295#901—36no—
296#901—63no—
297#901C2×D313yescomplemented
298#901C2×D313yescomplemented
299C2×ΓL(1,𝔽25)—33no—
300C2×ΓL(1,𝔽25)—33no—
301C2×ΓL(1,𝔽25)—33no—
302C2×ΓL(1,𝔽25)—33no—
303C2×ΓL(1,𝔽25)—33no—
304C2×ΓL(1,𝔽25)—31no—
305C2×ΓL(1,𝔽25)—33no—
306C2×ΓL(1,𝔽25)—33no—
307C2×ΓL(1,𝔽25)—33no—
308C2×ΓL(1,𝔽25)—33no—
309C2×ΓL(1,𝔽25)—33no—
310C2×ΓL(1,𝔽25)—33no—
311C2×ΓL(1,𝔽25)—33no—
312C2×ΓL(1,𝔽25)—36no—
313C2×ΓL(1,𝔽25)—63no—
314C2×ΓL(1,𝔽25)C2×D313yescomplemented
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×D32—46no—
323C2×D32C22×C411yescharacteristic
324C2×D32C22×C413yes—
325C2×D32C22×C413yes—
326C2×D32C22×C413yes—
327C32×Q8C22×C411yescharacteristic
328C32×D4C22×C413yes—
329C2×C32×C4C2413yes—
330#638C22×C416yes—
331C2×C3⋊Dic3C22×C413yes—
332C4⋊(C3⋊D3)C22×C413yes—
333C4×C3⋊D3C22×C413yes—
334C4×C3⋊D3C22×C413yes—
335C4×C3⋊D3C2413yes—
336C4×C3⋊D3C2411yescharacteristic
337#634C22×C413yes—
338C3×#67C22×C416yes—
339C3×#67C22×C416yes—
340C2×C3×Dic3C22×C413yes—
341C2×C3×Dic3C22×C413yes—
342C3×D12C22×C413yes—
343C3×D12C22×C413yes—
344C3×C4×D3C22×C413yes—
345C3×C4×D3C22×C413yes—
346C3×C4×D3C22×C413yes—
347C3×C4×D3C22×C413yes—
348C3×C4×D3C2411yescharacteristic
349C3×C4×D3C2413yes—
350C3×C4×D3C2413yes—
351C3×C4×D3C2411yescharacteristic
352C3×Dic6C22×C413yes—
353C3×Dic6C22×C413yes—
354#627C22×C416yes—
355#626C22×C416yes—
356#626C22×C416yes—
357#625C22×C416yes—
358#624C22×C413yes—
359#624C22×C413yes—
360#624C22×C413yes—
361#624C22×C411yescharacteristic
362D3×Dic3C22×C413yes—
363D3×Dic3C22×C413yes—
364D3×Dic3C22×C413yes—
365D3×Dic3C22×C413yes—
366D3×Dic3C22×C413yes—
367D3×Dic3C22×C413yes—
368D3×Dic3C22×C411yescharacteristic
369D3×Dic3C22×C411yescharacteristic
370C32×C8C2413yes—
371C32×C8C2411yescharacteristic
372C3⋊(C3⋊C8)C2413yes—
373C3⋊(C3⋊C8)C2411yescharacteristic
374C3×C3⋊C8C2411yescharacteristic
375C3×C3⋊C8C2413yes—
376C3×C3⋊C8C2413yes—
377C3×C3⋊C8C2411yescharacteristic
378C22×#41—91no—
379#568—31no—
380#568—93no—
381#568—93no—
382#568—91no—
383#568—93no—
384#568—93no—
385#568—91no—
386#568—91no—
387C2×#131—31no—
388C2×#131—93no—
389C2×#131—93no—
390C2×#131—91no—
391C22×M16—93no—
392C22×M16—93no—
393C23×D3—33no—
394C23×D3—33no—
395C3×#41—21no—
396C3×#41—31no—
397C3×#41—31no—
398C3×#41—33no—
399C3×#41—33no—
400C3×#41—33no—
401C3×#41—33no—
402C3×#41C22×D311yescharacteristic
403C3×#41C22×D311yescharacteristic
404C2×C3×Q8—31no—
405C2×C3×Q8—31no—
406C2×C3×D4—33no—
407C2×C3×D4—33no—
408C22×C3×C4—33no—
409C22×C3×C4—33no—
410C2×#67—36no—
411C2×#67—36no—
412C22×Dic3—33no—
413C22×Dic3—33no—
414#239—31no—
415#239—31no—
416#239—33no—
417#239—33no—
418#239—33no—
419#239—33no—
420#239—61no—
421#239C4×D311yescharacteristic
422#239C4×D311yescharacteristic
423D3×Q8—31no—
424D3×Q8—31no—
425D3×Q8—33no—
426D3×Q8—33no—
427D3×Q8—33no—
428D3×Q8—33no—
429D3×Q8—61no—
430D3×Q8C4×D311yescharacteristic
431D3×Q8C4×D311yescharacteristic
432#237—33no—
433#237—33no—
434#237—36no—
435#237—36no—
436#237—36no—
437#237—36no—
438#237—33no—
439#237—33no—
440#237—33no—
441#237—33no—
442#237—63no—
443#237C4×D313yes—
444#237C4×D313yes—
445D3×D4—36no—
446D3×D4—36no—
447D3×D4—33no—
448D3×D4—33no—
449D3×D4—36no—
450D3×D4—36no—
451D3×D4—33no—
452D3×D4—33no—
453D3×D4—33no—
454D3×D4—33no—
455D3×D4—63no—
456D3×D4C4×D313yes—
457D3×D4C4×D313yes—
458#235—33no—
459#235—33no—
460#235—36no—
461#235—36no—
462#235—33no—
463#235—33no—
464#235—36no—
465#235—36no—
466#235—33no—
467#235—33no—
468#235—63no—
469#235C22×D313yes—
470#235C22×D313yes—
471C2×D12—33no—
472C2×D12—33no—
473C2×C4×D3—33no—
474C2×C4×D3—33no—
475C2×C4×D3—33no—
476C2×C4×D3—33no—
477C2×C4×D3—33no—
478C2×C4×D3—33no—
479C2×C4×D3—33no—
480C2×C4×D3—33no—
481C2×C4×D3—33no—
482C2×C4×D3—33no—
483C2×C4×D3—33no—
484C2×C4×D3—33no—
485C2×C4×D3—33no—
486C2×C4×D3—33no—
487C2×C4×D3—33no—
488C2×C4×D3—33no—
489C2×C4×D3—31no—
490C2×C4×D3—33no—
491C2×C4×D3—33no—
492C2×C4×D3—33no—
493C2×C4×D3—31no—
494C2×C4×D3—33no—
495C2×C4×D3—63no—
496C2×C4×D3C22×D313yes—
497C2×C4×D3C22×D313yes—
498C2×Dic6—33no—
499C2×Dic6—33no—
500C3×M16—23no—
501C3×M16—33no—
502C3×M16—33no—
503C3×M16—33no—
504C3×M16—31no—
505C3×M16—33no—
506C3×M16—36no—
507C3×M16—33no—
508C3×M16C22×D313yescomplemented
509C3×M16C22×D313yescomplemented
510C2×C3×C8—23no—
511C2×C3×C8—33no—
512C2×C3×C8—33no—
513C2×C3×C8—33no—
514C2×C3×C8—36no—
515C2×C3×C8—31no—
516C2×C3×C8—33no—
517C2×C3×C8—33no—
518C2×C3×C8C22×D313yescomplemented
519C2×C3×C8C22×D313yescomplemented
520#208—33no—
521#208—33no—
522#208—33no—
523#208—31no—
524#208—33no—
525#208—36no—
526#208—33no—
527#208—63no—
528#208C22×D313yescomplemented
529#208C22×D313yescomplemented
530C2×C3⋊C8—33no—
531C2×C3⋊C8—33no—
532C2×C3⋊C8—33no—
533C2×C3⋊C8—31no—
534C2×C3⋊C8—36no—
535C2×C3⋊C8—33no—
536C2×C3⋊C8—33no—
537C2×C3⋊C8—63no—
538C2×C3⋊C8C22×D313yescomplemented
539C2×C3⋊C8C22×D313yescomplemented
540ΓL(1,𝔽25)—31no—
541ΓL(1,𝔽25)—33no—
542ΓL(1,𝔽25)—33no—
543ΓL(1,𝔽25)—33no—
544ΓL(1,𝔽25)—36no—
545ΓL(1,𝔽25)—31no—
546ΓL(1,𝔽25)—33no—
547ΓL(1,𝔽25)—33no—
548ΓL(1,𝔽25)—33no—
549ΓL(1,𝔽25)—31no—
550ΓL(1,𝔽25)—33no—
551ΓL(1,𝔽25)—33no—
552ΓL(1,𝔽25)—33no—
553ΓL(1,𝔽25)—31no—
554ΓL(1,𝔽25)—33no—
555ΓL(1,𝔽25)—33no—
556ΓL(1,𝔽25)—31no—
557ΓL(1,𝔽25)—33no—
558ΓL(1,𝔽25)—33no—
559ΓL(1,𝔽25)—33no—
560ΓL(1,𝔽25)—33no—
561ΓL(1,𝔽25)—61no—
562ΓL(1,𝔽25)—63no—
563ΓL(1,𝔽25)—63no—
564ΓL(1,𝔽25)—63no—
565ΓL(1,𝔽25)C22×D311yescharacteristic
566ΓL(1,𝔽25)C22×D313yes—
567ΓL(1,𝔽25)C22×D313yescomplemented
568ΓL(1,𝔽25)C22×D313yescomplemented
569ΓL(1,𝔽25)C22×D316yescomplemented
570D3×C8—33no—
571D3×C8—31no—
572D3×C8—36no—
573D3×C8—33no—
574D3×C8—33no—
575D3×C8—36no—
576D3×C8—36no—
577D3×C8—36no—
578D3×C8—36no—
579D3×C8—66no—
580D3×C8C22×D313yes—
581D3×C8C22×D311yescharacteristic
582D3×C8C22×D316yescomplemented
583D3×C8C22×D313yescomplemented
584D3×C8C22×D313yescomplemented
585C22×C32C23×C413yes—
586C2×C3⋊D3—43no—
587C2×C3⋊D3C23×C411yescharacteristic
588C2×C3⋊D3C23×C413yes—
589C2×C3×D3—26no—
590C2×C3×D3—43no—
591C2×C3×D3C23×C411yescharacteristic
592C2×C3×D3C23×C413yes—
593C2×C3×D3C23×C413yes—
594C2×C3×D3C23×C411yescharacteristic
595D32—22no—
596D32—26no—
597D32—43no—
598D32—43no—
599C32×C4C23×C413yes—
600C32×C4C2511yescharacteristic
601C3⋊Dic3C23×C411yescharacteristic
602C3⋊Dic3C23×C413yes—
603C3×Dic3C23×C411yescharacteristic
604C3×Dic3C23×C411yescharacteristic
605C3×Dic3C23×C413yes—
606C3×Dic3C23×C413yes—
607C2×#41—31no—
608C2×#41—31no—
609C2×#41—93no—
610C2×#41—93no—
611C2×#41—93no—
612C2×#41—93no—
613C2×#41—91no—
614C2×#41—91no—
615C2×#41—93no—
616C2×#41—91no—
617C2×#41—93no—
618C2×#41—91no—
619C22×Q8—91no—
620C22×D4—93no—
621C23×C4—93no—
622#131—31no—
623#131—31no—
624#131—33no—
625#131—33no—
626#131—33no—
627#131—33no—
628#131—96no—
629#131—93no—
630#131—93no—
631#131—96no—
632#131—96no—
633#131—93no—
634#131—93no—
635#131—96no—
636#131—93no—
637#131—93no—
638#131—91no—
639#131—93no—
640#131—93no—
641#131D3211yescharacteristic, complemented
642C2×M16—33no—
643C2×M16—33no—
644C2×M16—33no—
645C2×M16—93no—
646C2×M16—91no—
647C2×M16—93no—
648C2×M16—93no—
649C2×M16—93no—
650C2×M16—93no—
651C2×M16—93no—
652C2×M16—93no—
653C2×M16—93no—
654C2×M16—96no—
655C2×M16—93no—
656C2×M16—93no—
657C2×M16—96no—
658C2×M16—93no—
659C2×M16—93no—
660C2×M16—93no—
661C2×M16—93no—
662C22×C8—33no—
663C22×C8—96no—
664C22×C8—93no—
665C23×C3—33no—
666C23×C3—33no—
667C22×D3—33no—
668C22×D3—33no—
669C22×D3—31no—
670C22×D3—31no—
671C22×D3—33no—
672C22×D3—33no—
673C22×D3—33no—
674C22×D3—33no—
675C22×D3—33no—
676C22×D3—33no—
677C22×D3—63no—
678C22×D3—126no—
679C22×D3—126no—
680C22×D3C2×C4×D313yes—
681C22×D3C2×C4×D313yes—
682C3×Q8—21no—
683C3×Q8—33no—
684C3×Q8—33no—
685C3×Q8C2×C4×D311yescharacteristic
686C3×Q8C2×C4×D311yescharacteristic
687C3×D4—23no—
688C3×D4—36no—
689C3×D4—36no—
690C3×D4—33no—
691C3×D4—33no—
692C3×D4C2×C4×D313yes—
693C3×D4C2×C4×D313yes—
694C2×C3×C4—23no—
695C2×C3×C4—33no—
696C2×C3×C4—33no—
697C2×C3×C4—33no—
698C2×C3×C4—33no—
699C2×C3×C4—33no—
700C2×C3×C4—33no—
701C2×C3×C4—31no—
702C2×C3×C4—33no—
703C2×C3×C4—33no—
704C2×C3×C4—31no—
705C2×C3×C4C23×D313yes—
706C2×C3×C4C23×D313yes—
707#67—36no—
708#67—36no—
709#67—36no—
710#67—36no—
711#67—36no—
712#67—36no—
713#67—66no—
714#67C2×C4×D316yes—
715#67C2×C4×D316yes—
716C2×Dic3—33no—
717C2×Dic3—33no—
718C2×Dic3—33no—
719C2×Dic3—33no—
720C2×Dic3—31no—
721C2×Dic3—31no—
722C2×Dic3—33no—
723C2×Dic3—33no—
724C2×Dic3—33no—
725C2×Dic3—33no—
726C2×Dic3—63no—
727C2×Dic3C2×C4×D313yes—
728C2×Dic3C2×C4×D313yes—
729D12—36no—
730D12—36no—
731D12—33no—
732D12—33no—
733D12—63no—
734D12C2×C4×D313yes—
735D12C2×C4×D313yes—
736C4×D3—31no—
737C4×D3—31no—
738C4×D3—33no—
739C4×D3—33no—
740C4×D3—33no—
741C4×D3—33no—
742C4×D3—33no—
743C4×D3—33no—
744C4×D3—33no—
745C4×D3—33no—
746C4×D3—33no—
747C4×D3—33no—
748C4×D3—33no—
749C4×D3—33no—
750C4×D3—31no—
751C4×D3—31no—
752C4×D3—31no—
753C4×D3—31no—
754C4×D3—33no—
755C4×D3—33no—
756C4×D3—33no—
757C4×D3—33no—
758C4×D3—33no—
759C4×D3—33no—
760C4×D3—63no—
761C4×D3—63no—
762C4×D3—63no—
763C4×D3—61no—
764C4×D3C2×C4×D313yes—
765C4×D3C2×C4×D313yes—
766C4×D3C2×C4×D313yes—
767C4×D3C2×C4×D313yes—
768C4×D3C23×D311yescharacteristic
769C4×D3C23×D313yes—
770C4×D3C23×D313yes—
771C4×D3C23×D311yescharacteristic
772Dic6—33no—
773Dic6—33no—
774Dic6—36no—
775Dic6—36no—
776Dic6—63no—
777Dic6C2×C4×D313yes—
778Dic6C2×C4×D313yes—
779C3×C8—23no—
780C3×C8—21no—
781C3×C8—31no—
782C3×C8—33no—
783C3×C8—33no—
784C3×C8—31no—
785C3×C8C23×D313yes—
786C3×C8C23×D313yes—
787C3×C8C23×D311yescharacteristic
788C3×C8C23×D311yescharacteristic
789C3⋊C8—33no—
790C3⋊C8—33no—
791C3⋊C8—31no—
792C3⋊C8—31no—
793C3⋊C8—63no—
794C3⋊C8—61no—
795C3⋊C8C23×D313yes—
796C3⋊C8C23×D313yes—
797C3⋊C8C23×D311yescharacteristic
798C3⋊C8C23×D311yescharacteristic
799C2×C32—23no—
800C2×C32C24×C411yescharacteristic
801C3⋊D3—21no—
802C3⋊D3—23no—
803C3×D3—21no—
804C3×D3—23no—
805C3×D3—23no—
806C3×D3#56812yescomplemented
807C24—93no—
808#41—31no—
809#41—31no—
810#41—33no—
811#41—33no—
812#41—33no—
813#41—33no—
814#41—96no—
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—91no—
834C2×D4—33no—
835C2×D4—33no—
836C2×D4—93no—
837C2×D4—93no—
838C2×D4—96no—
839C2×D4—93no—
840C2×D4—96no—
841C2×D4—96no—
842C2×D4—93no—
843C22×C4—33no—
844C22×C4—33no—
845C22×C4—93no—
846C22×C4—91no—
847C22×C4—93no—
848C22×C4—93no—
849C22×C4—93no—
850C22×C4—93no—
851C22×C4—93no—
852C22×C4—93no—
853C22×C4—93no—
854C22×C4—93no—
855C22×C4—93no—
856C22×C4—93no—
857M16—33no—
858M16—33no—
859M16—33no—
860M16—31no—
861M16—36no—
862M16—33no—
863M16—33no—
864M16—91no—
865M16—93no—
866M16—93no—
867M16—93no—
868M16—91no—
869M16—93no—
870M16—93no—
871M16—93no—
872M16—96no—
873M16—93no—
874M16—93no—
875M16—91no—
876M16—93no—
877M16—93no—
878M16C2×D3213yescomplemented
879C2×C8—33no—
880C2×C8—33no—
881C2×C8—31no—
882C2×C8—33no—
883C2×C8—33no—
884C2×C8—33no—
885C2×C8—36no—
886C2×C8—96no—
887C2×C8—93no—
888C2×C8—91no—
889C2×C8—96no—
890C2×C8—93no—
891C2×C8—93no—
892C2×C8—93no—
893C2×C8—96no—
894C2×C8C2×D3213yescomplemented
895C22×C3—23no—
896C22×C3—31no—
897C22×C3—31no—
898C22×C3—33no—
899C22×C3—33no—
900C22×C3—66no—
901C22×C3—123no—
902C22×C3C22×C4×D313yes—
903C22×C3C22×C4×D313yes—
904C2×D3—26no—
905C2×D3—31no—
906C2×D3—31no—
907C2×D3—33no—
908C2×D3—33no—
909C2×D3—43no—
910C2×D3—61no—
911C2×D3—63no—
912C2×D3—62no—
913C2×D3—66no—
914C2×D3—62no—
915C2×D3—66no—
916C2×D3—123no—
917C2×D3—123no—
918C2×D3—123no—
919C2×D3—123no—
920C2×D3—123no—
921C2×D3—123no—
922C2×D3—243no—
923C2×D3C22×C4×D311yescharacteristic
924C2×D3C22×C4×D313yes—
925C2×D3C22×C4×D313yes—
926C2×D3C22×C4×D311yescharacteristic
927C3×C4—23no—
928C3×C4—21no—
929C3×C4—33no—
930C3×C4—33no—
931C3×C4—31no—
932C3×C4—31no—
933C3×C4C22×C4×D313yes—
934C3×C4C22×C4×D313yes—
935C3×C4C24×D311yescharacteristic
936C3×C4C24×D311yescharacteristic
937Dic3—33no—
938Dic3—33no—
939Dic3—31no—
940Dic3—31no—
941Dic3—63no—
942Dic3—61no—
943Dic3C22×C4×D313yes—
944Dic3C22×C4×D313yes—
945Dic3C22×C4×D311yescharacteristic
946Dic3C22×C4×D311yescharacteristic
947C32C2×#56811yescharacteristic, complemented, Sylow
948C23—33no—
949C23—33no—
950C23—91no—
951C23—93no—
952C23—93no—
953C23—93no—
954C23—93no—
955C23—366no—
956Q8—33no—
957Q8—33no—
958Q8—96no—
959Q8—93no—
960Q8C4×D3211yescharacteristic
961D4—36no—
962D4—36no—
963D4—33no—
964D4—33no—
965D4—96no—
966D4—96no—
967D4—96no—
968D4—96no—
969D4—93no—
970D4C4×D3213yes—
971C2×C4—33no—
972C2×C4—33no—
973C2×C4—33no—
974C2×C4—33no—
975C2×C4—33no—
976C2×C4—33no—
977C2×C4—31no—
978C2×C4—33no—
979C2×C4—33no—
980C2×C4—31no—
981C2×C4—91no—
982C2×C4—93no—
983C2×C4—93no—
984C2×C4—93no—
985C2×C4—91no—
986C2×C4—91no—
987C2×C4—93no—
988C2×C4—93no—
989C2×C4—93no—
990C2×C4—93no—
991C2×C4—93no—
992C2×C4—93no—
993C2×C4—93no—
994C2×C4—93no—
995C2×C4—93no—
996C2×C4—93no—
997C2×C4—91no—
998C2×C4C22×D3213yes—
999C8—31no—
1000C8—33no—
1001C8—31no—
1002C8—33no—
1003C8—91no—
1004C8—93no—
1005C8C22×D3213yes—
1006C8C22×D3211yescharacteristic
1007C2×C3—23no—
1008C2×C3—23no—
1009C2×C3—21no—
1010C2×C3—32no—
1011C2×C3—43no—
1012C2×C3—61no—
1013C2×C3—63no—
1014C2×C3—63no—
1015C2×C3C23×C4×D311yescharacteristic
1016C2×C3C23×C4×D311yescharacteristic
1017D3—23no—
1018D3—21no—
1019D3—23no—
1020D3—61no—
1021D3—63no—
1022D3—61no—
1023D3—63no—
1024D3—121no—
1025D3—123no—
1026D3#575012yesdirect product factor
1027C22—31no—
1028C22—31no—
1029C22—33no—
1030C22—33no—
1031C22—66no—
1032C22—91no—
1033C22—93no—
1034C22—123no—
1035C22—182no—
1036C22—186no—
1037C22—363no—
1038C22—363no—
1039C22—363no—
1040C22C2×C4×D3213yes—
1041C4—31no—
1042C4—31no—
1043C4—33no—
1044C4—33no—
1045C4—91no—
1046C4—93no—
1047C4C2×C4×D3213yes—
1048C4C23×D3211yescharacteristic
1049C3—21no—
1050C3C2×#575011yescharacteristic, complemented
1051C3D3×#56811yescharacteristic, complemented
1052C2—23no—
1053C2—32no—
1054C2—63no—
1055C2—61no—
1056C2—63no—
1057C2—181no—
1058C2—183no—
1059C2C22×C4×D3211yescharacteristic
subgroupG/H
center, FrattiniC4C23×D32
commutator, socleC2×C32C24×C4
FittingC32×#131C22
prime radicalD32×#41C2
cosocleC32×C4C25
hypercenter#131D32
hypocenterC32C2×#568
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. #10595443C2semidirect
6. #10595441C2semidirect
7. D3×#948C2semidirect
8. #10594708C2semidirect
9. #10594706C2semidirect
10. D3×#907C2semidirect
11. D32×M16C2semidirect
12. #10594670C2semidirect
13. #10594668C2semidirect
14. D3×#901C2semidirect
15. C2×D3×ΓL(1,𝔽25)C2semidirect
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×#3712C22semidirect
50. C2×#3711C22semidirect
51. #63818C22semidirect
52. #63817C22semidirect
53. #63817C22semidirect
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. #63803C22semidirect
65. #63791C22semidirect
68. D3×ΓL(1,𝔽25)C22semidirect
69. D3×ΓL(1,𝔽25)C22semidirect
70. D3×ΓL(1,𝔽25)C22semidirect
71. D3×ΓL(1,𝔽25)C22semidirect
72. D3×ΓL(1,𝔽25)C22semidirect
73. D3×ΓL(1,𝔽25)C22semidirect
74. D3×ΓL(1,𝔽25)C22semidirect
75. D32×C8C22semidirect
94. #5750D3direct (N × H)
98. D3×#131D3semidirect
157. C32×M16C23semidirect
158. C2×C32×C8C23semidirect
159. #3748C23semidirect
160. C2×C3⋊(C3⋊C8)C23semidirect
163. #3743C23semidirect
164. #3743C23semidirect
165. C8×C3⋊D3C23semidirect
166. C3×#208C23semidirect
167. C3×#208C23semidirect
168. C2×C3×C3⋊C8C23semidirect
169. C2×C3×C3⋊C8C23semidirect
172. C3×ΓL(1,𝔽25)C23semidirect
173. C3×ΓL(1,𝔽25)C23semidirect
174. C3×ΓL(1,𝔽25)C23semidirect
177. C3×D3×C8C23semidirect
178. C3×D3×C8C23semidirect
179. C3×D3×C8C23semidirect
182. #3712C23semidirect
183. #3712C23semidirect
186. #3711C23semidirect
187. #3711C23semidirect
188. #3711C23semidirect
189. #3710C23semidirect
192. D3×C3⋊C8C23semidirect
193. D3×C3⋊C8C23semidirect
194. D3×C3⋊C8C23semidirect
234. C3×#131C2×D3semidirect
235. C3×#131C2×D3semidirect
247. #948C2×D3semidirect
248. #948C2×D3semidirect
264. #907C2×D3semidirect
265. #907C2×D3semidirect
284. D3×M16C2×D3semidirect
285. D3×M16C2×D3semidirect
297. #901C2×D3semidirect
298. #901C2×D3semidirect
314. C2×ΓL(1,𝔽25)C2×D3semidirect
318. C2×D3×C8C2×D3semidirect
508. C3×M16C22×D3semidirect
509. C3×M16C22×D3semidirect
518. C2×C3×C8C22×D3semidirect
519. C2×C3×C8C22×D3semidirect
528. #208C22×D3semidirect
529. #208C22×D3semidirect
538. C2×C3⋊C8C22×D3semidirect
539. C2×C3⋊C8C22×D3semidirect
567. ΓL(1,𝔽25)C22×D3semidirect
568. ΓL(1,𝔽25)C22×D3semidirect
569. ΓL(1,𝔽25)C22×D3semidirect
582. D3×C8C22×D3semidirect
583. D3×C8C22×D3semidirect
584. D3×C8C22×D3semidirect
641. #131D32semidirect
806. C3×D3#568semidirect
878. M16C2×D32semidirect
894. C2×C8C2×D32semidirect
947. C32C2×#568semidirect
1026. D3#5750direct (N × H)
1050. C3C2×#5750semidirect
1051. C3D3×#568semidirect

Maximal subgroups

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

subgroupindex
D32×#412
#105962212
C3×#57502
C3×D3×#1312
#105954432
#105954412
D3×#9482
#105947082
#105947062
D3×#9072
D32×M162
#105946702
#105946682
D3×#9012
C2×D3×ΓL(1,𝔽25)2
D3×#5683
C2×#57503