Finite Group Databasebeta

← #46848312

Subgroups — #46848312

Order 34688.

408 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31774610C211yesmaximal, characteristic, complemented
2#31774565C211yesmaximal, characteristic, complemented
3#31774242C211yesmaximal, characteristic, complemented
4#31774223C211yesmaximal, characteristic, complemented
5#31774191C211yesmaximal, characteristic, complemented
6#31774134C211yesmaximal, characteristic, complemented
7#31774131C211yesmaximal, characteristic, complemented
8#31774091C211yesmaximal, characteristic, complemented
9#31774044C211yesmaximal, characteristic, complemented
10#31774043C211yesmaximal, characteristic, complemented
11#31773984C211yesmaximal, characteristic, complemented
12(C22⋊D271)⋊C8C211yesmaximal, characteristic, complemented
13#31773891C211yesmaximal, characteristic, complemented
14#31773890C211yesmaximal, characteristic, complemented
15#482×C271C211yesmaximal, characteristic, complemented
16C2×#16864654C2211yescharacteristic
17C2×#16864653C2211yescharacteristic
18C2×#16864643C2211yescharacteristic
19C2×D2168C2211yescharacteristic
20C2×#16864639C2211yescharacteristic
21C22×C271⋊C8C2211yescharacteristic
22C2×C8×D271C2211yescharacteristic
23#22576159C2211yescharacteristic
24#22576156—21no—
25#22576156C2211yescharacteristic
26#22576148—21no—
27#22576146—21no—
28#22576135C2211yescharacteristic
29#22576135C2211yescharacteristic
30#22576134C2211yescharacteristic
31#22576133—21no—
32#22576133—21no—
33#22576132—21no—
34#22576125C2211yescharacteristic
35#22576122C2211yescharacteristic
36C4×C22⋊D271C2211yescharacteristic
37(C22⋊D271)⋊C4—21no—
38#22576118C2211yescharacteristic
39#22576117—21no—
40#22576093C2211yescharacteristic
41Dic271⋊C8C2211yescharacteristic
42#22576085C2211yescharacteristic
43#22576083C2211yescharacteristic
44#22576083C2211yescharacteristic
45#22576082C2211yescharacteristic
46#22576081C2211yescharacteristic
47#22576080C2211yescharacteristic
48#22576080C2211yescharacteristic
49#22576080C2211yescharacteristic
50(C2×D271)⋊C8C2211yescharacteristic
51C8×Dic271C2211yescharacteristic
52#121×C271C2211yescharacteristic
53#117×C271C2211yescharacteristic
54#107×C271C2211yescharacteristic
55#106×C271C2211yescharacteristic
56#102×C271C2211yescharacteristic
57#102×C271C2211yescharacteristic
58C22⋊C8×C271C2211yescharacteristic
59#16864654—22no—
60#16864654—41no—
61#16864653—22no—
62#16864653—41no—
63C2×Dic542—21no—
64C2×Dic542C2311yescharacteristic
65C2×D1084—21no—
66C2×D1084—21no—
67C2×D1084C2311yescharacteristic
68C2×D1084C2311yescharacteristic
69C2×C22⋊D271—21no—
70C2×C22⋊D271—21no—
71C2×C22⋊D271—21no—
72C2×C22⋊D271—21no—
73C2×C22⋊D271—21no—
74C2×C22⋊D271D411yescharacteristic
75C22×Dic271—21no—
76C2×C4×D271—21no—
77C2×C4×D271—21no—
78C2×C4×D271C2311yescharacteristic
79#16864643—22no—
80D2168—41no—
81#16864639—41no—
82C2×C271⋊C8—41no—
83C2×C271⋊C8C2311yescharacteristic
84C2×C271⋊C8C2311yescharacteristic
85C8×D271—41no—
86C4⋊Dic271C2311yescharacteristic
87Dic271⋊C4—21no—
88Dic271⋊C4—21no—
89Dic271⋊C4D411yescharacteristic
90C22⋊Dic271D411yescharacteristic
91(C2×D271)⋊C4—21no—
92(C2×D271)⋊C4—21no—
93(C2×D271)⋊C4—21no—
94(C2×D271)⋊C4—21no—
95(C2×D271)⋊C4—21no—
96(C2×D271)⋊C4D411yescharacteristic
97C4×Dic271—21no—
98C4×Dic271—21no—
99C4×Dic271C2311yescharacteristic
100C2×D4×C271—21no—
101C2×D4×C271C2311yescharacteristic
102C22×C4×C271C2311yescharacteristic
103C2×C8×C271C2311yescharacteristic
104C2×C8×C271C2311yescharacteristic
105C4⋊C4×C271C2311yescharacteristic
106C4⋊C4×C271C2311yescharacteristic
107C4⋊C4×C271C2311yescharacteristic
108C22⋊C4×C271—21no—
109C22⋊C4×C271—21no—
110C42×C271—21no—
111C22×D271—21no—
112C22×D271—21no—
113C22×D271C2×D411yescharacteristic
114Dic542—21no—
115Dic542—81no—
116Dic542#4112yes—
117D1084—21no—
118D1084—21no—
119D1084—21no—
120D1084—21no—
121D1084—81no—
122D1084—81no—
123C22⋊D271—22no—
124C22⋊D271—42no—
125C22⋊D271—42no—
126C22⋊D271—42no—
127C22⋊D271—81no—
128C22⋊D271—81no—
129C2×Dic271—21no—
130C2×Dic271—21no—
131C2×Dic271—42no—
132C2×Dic271C2×D411yescharacteristic
133C2×Dic271C2×D411yescharacteristic
134C2×Dic271C2×D411yescharacteristic
135C4×D271—21no—
136C4×D271—21no—
137C4×D271—42no—
138C4×D271—42no—
139C271⋊C8—21no—
140C271⋊C8—21no—
141C23×C271—21no—
142C23×C271C2×D411yescharacteristic
143D4×C271—21no—
144D4×C271—21no—
145D4×C271—81no—
146C2×C4×C271—21no—
147C2×C4×C271—21no—
148C2×C4×C271—21no—
149C2×C4×C271—21no—
150C2×C4×C271—21no—
151C2×C4×C271C2×D411yescharacteristic
152C2×C4×C271C2411yescharacteristic
153C8×C271—21no—
154C8×C271—21no—
155C22×C271—21no—
156C22×C271—21no—
157C22×C271—21no—
158C22×C271—41no—
159C22×C271—41no—
160C22×C271—41no—
161C22×C271C22×D411yescharacteristic
162C2×D271—21no—
163C2×D271—21no—
164C2×D271—21no—
165C2×D271—41no—
166C2×D271—41no—
167C2×D271—41no—
168C2×D271—41no—
169C2×D271—41no—
170C2×D271—41no—
171C4×C271—21no—
172C4×C271—41no—
173C4×C271—41no—
174C4×C271—41no—
175C4×C271C2×#4111yescharacteristic
176C4×C271H(5,𝔽2)11yescharacteristic
177Dic271—21no—
178Dic271—22no—
179Dic271—21no—
180Dic271—41no—
181Dic271#13512yes—
182C2×C271—41no—
183C2×C271—81no—
184C2×C271#54611yescharacteristic
185C2×C271C2×#13511yescharacteristic
186C2×C271#57611yescharacteristic
187D271—41no—
188D271—81no—
189D271—81no—
190C271#330511yescharacteristic, complemented, Sylow
191#3305—2711nomaximal, Sylow
192#555—2711no—
193#550—2711no—
194#486—2711no—
195#482—2711no—
196#482D27111yescharacteristic, complemented
197#477—2711no—
198#466—2711no—
199#466—2711no—
200#459—2711no—
201#449—2711no—
202#449—2711no—
203C4×SD16—2711no—
204C8×D4—2711no—
205#416—2711no—
206#416—2711no—
207C2×#41—2711no—
208C2×#41—2711no—
209C2×SD16—2711no—
210C2×D8—2711no—
211C2×D8—2711no—
212C22×C8—2711no—
213C22×C8—2711no—
214C4⋊Q8—2711no—
215#127—2711no—
216#127—5421no—
217#124—5421no—
218#124—5421no—
219#121—2711no—
220#121—2711no—
221#121—2711no—
222#121—5421no—
223#121—5421no—
224#121—5421no—
225#121C2×D27111yescharacteristic
226C4×Q8—2711no—
227C4×D4—2711no—
228C4×D4—2711no—
229C4×D4—5421no—
230#117—2711no—
231#117—5421no—
232#117C2×D27111yescharacteristic
233#107—2711no—
234#107C2×D27111yescharacteristic
235#106C2×D27111yescharacteristic
236C4⋊C8—2711no—
237#103—2711no—
238#103—2711no—
239#103—2711no—
240#102—2711no—
241#102—2711no—
242#102—2711no—
243#102—2711no—
244#102—2711no—
245#102C2×D27111yescharacteristic
246#102C2×D27111yescharacteristic
247C22⋊C8—2711no—
248C22⋊C8C2×D27111yescharacteristic
249C4×C8—2711no—
250#41—5422no—
251#41—5422no—
252#41—10841no—
253#41—10841no—
254C2×Q8—2711no—
255C2×Q8—5421no—
256C2×D4—21no—
257C2×D4—2711no—
258C2×D4—2711no—
259C2×D4—2711no—
260C2×D4—5421no—
261C2×D4—5421no—
262C2×D4—5421no—
263C2×D4—5421no—
264C2×D4—5421no—
265C2×D4—5421no—
266C2×D4—5421no—
267C2×D4C22×D27111yescharacteristic
268C22×C4—2711no—
269C22×C4—5421no—
270C22×C4—5421no—
271C22×C4—5421no—
272C22×C4C22×D27111yescharacteristic
273SD16—5422no—
274D8—10841no—
275D8—10841no—
276C2×C8—2711no—
277C2×C8—2711no—
278C2×C8—10841no—
279C2×C8—10841no—
280C2×C8C22×D27111yescharacteristic
281C2×C8C22×D27111yescharacteristic
282C4⋊C4—2711no—
283C4⋊C4—2711no—
284C4⋊C4—5421no—
285C4⋊C4—5421no—
286C4⋊C4C22×D27111yescharacteristic
287C4⋊C4C22×D27111yescharacteristic
288C4⋊C4C22×D27111yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—2711no—
292C22⋊C4—2711no—
293C22⋊C4—5421no—
294C22⋊C4—5421no—
295C22⋊C4—5421no—
296C22⋊C4—5421no—
297C22⋊C4—5421no—
298C42—21no—
299C42—2711no—
300C42—5421no—
301C42—5421no—
302C23—21no—
303C23—2711no—
304C23—5421no—
305C23—5421no—
306C23D4×D27111yescharacteristic
307Q8—2712no—
308Q8—5421no—
309Q8—21681no—
310D4—21no—
311D4—21no—
312D4—81no—
313D4—5422no—
314D4—5421no—
315D4—5421no—
316D4—5421no—
317D4—5421no—
318D4—10842no—
319D4—10842no—
320D4—10842no—
321D4—21681no—
322D4—21681no—
323D4—21681no—
324D4—21681no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—2711no—
331C2×C4—2711no—
332C2×C4—2711no—
333C2×C4—5421no—
334C2×C4—5421no—
335C2×C4—5421no—
336C2×C4—5421no—
337C2×C4—10842no—
338C2×C4—10842no—
339C2×C4—10842no—
340C2×C4D4×D27111yescharacteristic
341C2×C4C23×D27111yescharacteristic
342C8—21no—
343C8—21no—
344C8—5421no—
345C8—5421no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—5421no—
353C22—5421no—
354C22—5421no—
355C22—10841no—
356C22—10841no—
357C22—10841no—
358C22—10841no—
359C22—10841no—
360C22—10841no—
361C22C2×D4×D27111yescharacteristic
362C4—21no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—2712no—
367C4—5421no—
368C4—5422no—
369C4—5421no—
370C4—10841no—
371C4#41×D27111yescharacteristic
372C4#2257620611yescharacteristic
373C2—41no—
374C2—81no—
375C2—10841no—
376C2—21681no—
377C2—21681no—
378C2#3177453911yescharacteristic
379C2#135×D27111yescharacteristic
380C2#3177470111yescharacteristic
subgroupG/H
centerC22C2×D4×D271
commutator, cosocleC2×C4×C271C24
FrattiniC2×C4C23×D271
Fitting#482×C271C2
socleC22×C271C22×D4
hypercenter#482D271
hypocenterC271#3305
LCSG ▷ C2×C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #31774610C2semidirect
2. #31774565C2semidirect
3. #31774242C2semidirect
4. #31774223C2semidirect
5. #31774191C2semidirect
6. #31774134C2semidirect
7. #31774131C2semidirect
8. #31774091C2semidirect
9. #31774044C2semidirect
10. #31774043C2semidirect
11. #31773984C2semidirect
12. (C22⋊D271)⋊C8C2semidirect
13. #31773891C2semidirect
14. #31773890C2semidirect
15. #482×C271C2semidirect
190. C271#3305semidirect
196. #482D271semidirect

Maximal subgroups

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

subgroupindex
#317746102
#317745652
#317742422
#317742232
#317741912
#317741342
#317741312
#317740912
#317740442
#317740432
#317739842
(C22⋊D271)⋊C82
#317738912
#317738902
#482×C2712
#3305271