Finite Group Databasebeta

← #11858684

Subgroups — #11858684

Order 1152.

931 conjugacy classes of subgroups.

The subgroup lattice has 561 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594722C212yesmaximal
2C2×#63804C211yesmaximal, characteristic
3#10592592C211yesmaximal, characteristic, complemented
4C3×#4893C211yesmaximal, characteristic, complemented
5C3×D3×#108C211yesmaximal, characteristic, complemented
6#10590973C212yesmaximal, complemented
7#10590972C212yesmaximal, complemented
8D3×#822C212yesmaximal, complemented
9#10590914C211yesmaximal, characteristic, complemented
10#10590912C211yesmaximal, characteristic, complemented
11D3×#819C211yesmaximal, characteristic, complemented
12#79260—31nomaximal
13#79252—31nomaximal
14C2×#3798C2211yescharacteristic
15M16×C3⋊D3C2212yes—
16C2×#3743C2211yescharacteristic
17C3×D3×M16C2212yes—
18C3×D3×M16C2212yes—
19C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
20C2×C3×D3×C8C2211yescharacteristic
21C2×#3711C2211yescharacteristic
22#63818C2212yes—
23C2×#3710C2211yescharacteristic
24D3×#208C2212yes—
25D3×#208C2212yes—
26C2×D3×C3⋊C8C2211yescharacteristic
27#63805—22no—
28#63804—22no—
29#63804—22no—
30#63804C414yes—
31#63804C414yes—
32#63803—22no—
33C32×#108C2211yescharacteristic
34#63649C2212yes—
35#63646C2211yescharacteristic
36C3×#822C2212yes—
37C3×#822C2212yes—
38C3×#819C2211yescharacteristic
39C3×#819C2211yescharacteristic
40#63578C2212yes—
41#63577C2212yes—
42#63577C2212yes—
43#5745—32no—
44#5745—32no—
45C2×#907—31no—
46C2×#901—31no—
47C3×#430—31no—
48C2×C3×#108—31no—
49#5125—31no—
50#5124—32no—
51C2×#822—32no—
52C2×#819—31no—
53#4893—32no—
54#4893—31no—
55#4893—31no—
56#4893—31no—
57#4893—31no—
58#4893—31no—
59#4893—61no—
60#4893D311yescharacteristic, complemented
61D3×#108—32no—
62D3×#108—31no—
63D3×#108—32no—
64D3×#108—32no—
65D3×#108D311yescharacteristic, complemented
66C2×C4×C3⋊D3C2311yescharacteristic
67C2×C3×C4×D3C2311yescharacteristic
68C2×C3×C4×D3C2311yescharacteristic
69C2×#627Q811yescharacteristic
70C2×#626Q811yescharacteristic
71C2×#626Q811yescharacteristic
72C2×#625Q811yescharacteristic
73#3798C2×C412yes—
74#3798C2×C412yes—
75#3798D412yes—
76#3798D412yes—
77C32×M16C2312yes—
78C2×C32×C8C2311yescharacteristic
79#3748C2312yes—
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81#3743—22no—
82#3743C2×C414yes—
83C8×C3⋊D3—22no—
84C3×#208C2312yes—
85C3×#208C2312yes—
86C2×C3×C3⋊C8C2311yescharacteristic
87C2×C3×C3⋊C8C2311yescharacteristic
88C3×ΓL(1,𝔽25)—22no—
89C3×ΓL(1,𝔽25)—22no—
90C3×ΓL(1,𝔽25)C2×C414yes—
91C3×D3×C8—22no—
92C3×D3×C8—22no—
93C3×D3×C8C2×C412yes—
94C3×D3×C8C2×C412yes—
95#3712—22no—
96#3711—22no—
97#3711—22no—
98#3711C2×C412yes—
99#3711C2×C412yes—
100#3710—22no—
101#3710C2×C414yes—
102D3×C3⋊C8—22no—
103D3×C3⋊C8—22no—
104D3×C3⋊C8C2×C414yes—
105#2916—91noSylow
106C2×#235—31no—
107C2×#235—31no—
108C2×C3×M16—31no—
109C2×C3×M16—32no—
110C2×C3×M16—32no—
111C22×C3×C8—31no—
112C2×#208—31no—
113C2×#208—32no—
114C2×#208—32no—
115C22×C3⋊C8—31no—
116#907—34no—
117#907—34no—
118#907—62no—
119#907—62no—
120#907—62no—
121#907—62no—
122D3×M16—32no—
123D3×M16—32no—
124D3×M16—32no—
125D3×M16—32no—
126D3×M16—32no—
127D3×M16—32no—
128D3×M16—62no—
129D3×M16C2×D312yes—
130D3×M16C2×D312yes—
131#901—34no—
132#901—34no—
133#901—62no—
134#901—62no—
135#901—62no—
136#901—62no—
137C2×ΓL(1,𝔽25)—31no—
138C2×ΓL(1,𝔽25)—31no—
139C2×ΓL(1,𝔽25)—31no—
140C2×ΓL(1,𝔽25)—61no—
141C2×ΓL(1,𝔽25)C2×D311yescharacteristic
142C2×D3×C8—31no—
143C2×D3×C8—31no—
144C2×D3×C8—31no—
145C2×D3×C8C2×D311yescharacteristic
146C3×#108—21no—
147C3×#108—32no—
148C3×#108—32no—
149C3×#108—31no—
150C3×#108—31no—
151C3×#108C2×D311yescharacteristic
152C3×#108C2×D311yescharacteristic
153#822—32no—
154#822—32no—
155#822—32no—
156#822—32no—
157#822—32no—
158#822—32no—
159#822—62no—
160#822C2×D312yes—
161#822C2×D312yes—
162#819—31no—
163#819—31no—
164#819—32no—
165#819—32no—
166#819—61no—
167#819C2×D311yescharacteristic
168#819C2×D311yescharacteristic
169C22×C3⋊D3C2×Q811yescharacteristic
170C22×C3×D3C2×Q811yescharacteristic
171C22×C3×D3C2×Q811yescharacteristic
172C2×C32×C4C2411yescharacteristic
173C2×C3⋊Dic3C2×Q811yescharacteristic
174C4×C3⋊D3C22×C412yes—
175C4×C3⋊D3C2×D412yes—
176C2×C3×Dic3C2×Q811yescharacteristic
177C2×C3×Dic3C2×Q811yescharacteristic
178C3×C4×D3C22×C412yes—
179C3×C4×D3C22×C411yescharacteristic
180C3×C4×D3C22×C411yescharacteristic
181C3×C4×D3C2×D411yescharacteristic
182C3×C4×D3C2×D412yes—
183C3×C4×D3C2×D411yescharacteristic
184#627C4⋊C412yes—
185#627C4⋊C412yes—
186#626C4⋊C412yes—
187#626C4⋊C412yes—
188#626C4⋊C412yes—
189#626C4⋊C412yes—
190#625C4⋊C412yes—
191#625C4⋊C412yes—
192C32×C8—22no—
193C32×C8C22×C412yes—
194C3⋊(C3⋊C8)—22no—
195C3⋊(C3⋊C8)C22×C412yes—
196C3×C3⋊C8—22no—
197C3×C3⋊C8—22no—
198C3×C3⋊C8C22×C412yes—
199C3×C3⋊C8C22×C412yes—
200#568—92no—
201C2×#131—91no—
202#430—31no—
203#430—91no—
204#430—92no—
205#430—91no—
206#430—91no—
207C2×#108—31no—
208C2×#108—92no—
209C2×#108—91no—
210C2×#108—92no—
211C22×C3×C4—31no—
212C22×C3×C4—31no—
213C2×#67—31no—
214C2×#67—31no—
215C2×#67—31no—
216C2×#67—31no—
217#235—32no—
218#235—32no—
219#235—32no—
220#235—32no—
221#235—32no—
222#235—32no—
223#235—32no—
224#235—32no—
225C2×D12—31no—
226C2×D12—31no—
227C2×C4×D3—31no—
228C2×C4×D3—31no—
229C2×C4×D3—61no—
230C2×C4×D3C22×D311yescharacteristic
231C2×C4×D3C22×D311yescharacteristic
232C2×Dic6—31no—
233C2×Dic6—31no—
234C3×M16—22no—
235C3×M16—34no—
236C3×M16—32no—
237C3×M16—32no—
238C3×M16—62no—
239C3×M16—62no—
240C3×M16C22×D312yes—
241C3×M16C22×D312yes—
242C2×C3×C8—21no—
243C2×C3×C8—31no—
244C2×C3×C8—31no—
245C2×C3×C8—32no—
246C2×C3×C8—32no—
247C2×C3×C8—62no—
248C2×C3×C8—62no—
249C2×C3×C8C22×D311yescharacteristic
250C2×C3×C8C22×D311yescharacteristic
251#208—32no—
252#208—32no—
253#208—32no—
254#208—32no—
255#208—62no—
256#208—62no—
257#208—62no—
258#208C22×D312yes—
259#208C22×D312yes—
260C2×C3⋊C8—31no—
261C2×C3⋊C8—31no—
262C2×C3⋊C8—34no—
263C2×C3⋊C8—61no—
264C2×C3⋊C8—62no—
265C2×C3⋊C8—62no—
266C2×C3⋊C8C22×D311yescharacteristic
267C2×C3⋊C8C22×D311yescharacteristic
268ΓL(1,𝔽25)—22no—
269ΓL(1,𝔽25)—22no—
270ΓL(1,𝔽25)—32no—
271ΓL(1,𝔽25)—32no—
272ΓL(1,𝔽25)—34no—
273ΓL(1,𝔽25)—34no—
274ΓL(1,𝔽25)—64no—
275ΓL(1,𝔽25)—62no—
276ΓL(1,𝔽25)—62no—
277ΓL(1,𝔽25)—62no—
278ΓL(1,𝔽25)—62no—
279ΓL(1,𝔽25)—62no—
280ΓL(1,𝔽25)—62no—
281ΓL(1,𝔽25)—122no—
282ΓL(1,𝔽25)C4×D314yes—
283D3×C8—22no—
284D3×C8—22no—
285D3×C8—34no—
286D3×C8—34no—
287D3×C8—34no—
288D3×C8—62no—
289D3×C8—62no—
290D3×C8—62no—
291D3×C8—62no—
292D3×C8—62no—
293D3×C8—62no—
294D3×C8—122no—
295D3×C8C4×D312yes—
296D3×C8C4×D312yes—
297C22×C32C22×Q811yescharacteristic
298C2×C3⋊D3—41no—
299C2×C3⋊D3C2×C4⋊C412yes—
300C2×C3×D3—41no—
301C2×C3×D3—41no—
302C2×C3×D3C2×C4⋊C412yes—
303C2×C3×D3C2×C4⋊C411yescharacteristic
304C2×C3×D3C2×C4⋊C411yescharacteristic
305C32×C4C23×C411yescharacteristic
306C32×C4C22×D411yescharacteristic
307C3⋊Dic3C2×C4⋊C412yes—
308C3×Dic3C2×C4⋊C412yes—
309C3×Dic3C2×C4⋊C411yescharacteristic
310C3×Dic3C2×C4⋊C411yescharacteristic
311C2×#41—91no—
312#131—94no—
313#131—94no—
314#131—182no—
315#131—182no—
316#131—182no—
317#131—182no—
318C2×M16—31no—
319C2×M16—32no—
320C2×M16—32no—
321C2×M16—91no—
322C2×M16—91no—
323C2×M16—92no—
324C2×M16—92no—
325C2×M16—92no—
326C2×M16—92no—
327C22×C8—31no—
328C22×C8—91no—
329C22×C8—91no—
330#108—32no—
331#108—32no—
332#108—31no—
333#108—31no—
334#108—92no—
335#108—92no—
336#108—92no—
337#108—92no—
338#108—91no—
339#108D3211yescharacteristic
340C23×C3—31no—
341C23×C3—31no—
342C22×D3—31no—
343C22×D3—31no—
344C22×D3—61no—
345C22×D3D3×Q811yescharacteristic
346C22×D3D3×Q811yescharacteristic
347C2×C3×C4—21no—
348C2×C3×C4—31no—
349C2×C3×C4—31no—
350C2×C3×C4—32no—
351C2×C3×C4—31no—
352C2×C3×C4—31no—
353C2×C3×C4—31no—
354C2×C3×C4—32no—
355C2×C3×C4—31no—
356C2×C3×C4C23×D311yescharacteristic
357C2×C3×C4C23×D311yescharacteristic
358#67—32no—
359#67—32no—
360#67—32no—
361#67—32no—
362#67—32no—
363#67—32no—
364#67—32no—
365#67—32no—
366C2×Dic3—31no—
367C2×Dic3—31no—
368C2×Dic3—61no—
369C2×Dic3D3×Q811yescharacteristic
370C2×Dic3D3×Q811yescharacteristic
371D12—32no—
372D12—32no—
373D12—32no—
374D12—32no—
375C4×D3—32no—
376C4×D3—32no—
377C4×D3—32no—
378C4×D3—32no—
379C4×D3—62no—
380C4×D3—62no—
381C4×D3C2×C4×D312yes—
382C4×D3C2×C4×D311yescharacteristic
383C4×D3C2×C4×D311yescharacteristic
384C4×D3D3×D411yescharacteristic
385C4×D3D3×D412yes—
386C4×D3D3×D411yescharacteristic
387Dic6—32no—
388Dic6—32no—
389Dic6—32no—
390Dic6—32no—
391C3×C8—22no—
392C3×C8—22no—
393C3×C8—22no—
394C3×C8—32no—
395C3×C8—32no—
396C3×C8—42no—
397C3×C8—62no—
398C3×C8—62no—
399C3×C8C2×C4×D312yes—
400C3×C8C2×C4×D312yes—
401C3⋊C8—22no—
402C3⋊C8—22no—
403C3⋊C8—32no—
404C3⋊C8—32no—
405C3⋊C8—62no—
406C3⋊C8—62no—
407C3⋊C8—62no—
408C3⋊C8—122no—
409C3⋊C8C2×C4×D312yes—
410C3⋊C8C2×C4×D312yes—
411C2×C32—21no—
412C2×C32C22×C4⋊C411yescharacteristic
413C3⋊D3—22no—
414C3×D3—21no—
415C3×D3—21no—
416C3×D3—22no—
417#41—92no—
418#41—92no—
419#41—92no—
420#41—92no—
421C2×Q8—91no—
422C2×D4—91no—
423C2×D4—91no—
424C2×D4—91no—
425C22×C4—31no—
426C22×C4—31no—
427C22×C4—91no—
428M16—34no—
429M16—32no—
430M16—32no—
431M16—62no—
432M16—62no—
433M16—92no—
434M16—92no—
435M16—94no—
436M16—92no—
437M16—182no—
438M16—182no—
439M16—182no—
440M16—182no—
441M16C2×D3212yes—
442C2×C8—31no—
443C2×C8—31no—
444C2×C8—32no—
445C2×C8—32no—
446C2×C8—62no—
447C2×C8—62no—
448C2×C8—94no—
449C2×C8—94no—
450C2×C8—91no—
451C2×C8—182no—
452C2×C8—182no—
453C2×C8—182no—
454C2×C8—182no—
455C2×C8C2×D3211yescharacteristic
456C22×C3—21no—
457C22×C3—32no—
458C22×C3—31no—
459C22×C3—31no—
460C22×C3—121no—
461C22×C3—121no—
462C22×C3C2×D3×Q811yescharacteristic
463C22×C3C2×D3×Q811yescharacteristic
464C2×D3—32no—
465C2×D3—32no—
466C2×D3—41no—
467C2×D3—41no—
468C2×D3—62no—
469C2×D3—121no—
470C2×D3—121no—
471C2×D3—241no—
472C2×D3D3×C4⋊C411yescharacteristic
473C2×D3D3×C4⋊C411yescharacteristic
474C2×D3D3×C4⋊C412yes—
475C3×C4—21no—
476C3×C4—21no—
477C3×C4—32no—
478C3×C4—31no—
479C3×C4—31no—
480C3×C4C22×C4×D311yescharacteristic
481C3×C4C22×C4×D311yescharacteristic
482C3×C4C2×D3×D411yescharacteristic
483C3×C4C2×D3×D411yescharacteristic
484Dic3—32no—
485Dic3—32no—
486Dic3—62no—
487Dic3D3×C4⋊C411yescharacteristic
488Dic3D3×C4⋊C411yescharacteristic
489Dic3D3×C4⋊C412yes—
490C32#291611yescharacteristic, complemented, Sylow
491C23—31no—
492C23—31no—
493C23—91no—
494Q8—92no—
495Q8—92no—
496D4—92no—
497D4—92no—
498D4—92no—
499D4—92no—
500D4—92no—
501D4—92no—
502C2×C4—31no—
503C2×C4—31no—
504C2×C4—31no—
505C2×C4—31no—
506C2×C4—32no—
507C2×C4—31no—
508C2×C4—32no—
509C2×C4—31no—
510C2×C4—91no—
511C2×C4—92no—
512C2×C4—92no—
513C2×C4C22×D3211yescharacteristic
514C8—22no—
515C8—32no—
516C8—32no—
517C8—62no—
518C8—62no—
519C8—92no—
520C8—182no—
521C8C4×D3212yes—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—41no—
526C2×C3—62no—
527C2×C3—61no—
528C2×C3—61no—
529C2×C3C2×D3×C4⋊C411yescharacteristic
530C2×C3C2×D3×C4⋊C411yescharacteristic
531D3—21no—
532D3—21no—
533D3—22no—
534D3—62no—
535D3—62no—
536D3—122no—
537C22—31no—
538C22—31no—
539C22—32no—
540C22—92no—
541C22—121no—
542C22—121no—
543C22—361no—
544C22D32×Q811yescharacteristic
545C4—31no—
546C4—31no—
547C4—32no—
548C4—92no—
549C4C2×C4×D3211yescharacteristic
550C4D32×D411yescharacteristic
551C3—21no—
552C3#7925211yescharacteristic, complemented
553C3#7926011yescharacteristic, complemented
554C2—21no—
555C2—61no—
556C2—61no—
557C2—62no—
558C2—182no—
559C2D32×C4⋊C411yescharacteristic
subgroupG/H
centerC4D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#108C22
socleC2×C32C22×C4⋊C4
prime radicalC2×#3798C22
cosocleC2×C32×C4C24
hypercenter#108D32
hypocenterC32#2916
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ #108

Complements

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

NH ≅ G/Ntype
3. #10592592C2semidirect
4. C3×#4893C2semidirect
5. C3×D3×#108C2semidirect
6. #10590973C2semidirect
7. #10590972C2semidirect
8. D3×#822C2semidirect
9. #10590914C2semidirect
10. #10590912C2semidirect
11. D3×#819C2semidirect
60. #4893D3semidirect
65. D3×#108D3semidirect
490. C32#2916semidirect
552. C3#79252semidirect
553. C3#79260semidirect

Maximal subgroups

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

subgroupindex
#105947222
C2×#638042
#105925922
C3×#48932
C3×D3×#1082
#105909732
#105909722
D3×#8222
#105909142
#105909122
D3×#8192
#792603
#792523