Finite Group Databasebeta

← #46846362

Subgroups — #46846362

Order 34688.

492 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31774444C211yesmaximal, characteristic, complemented
2C4×D4×D271C211yesmaximal, characteristic, complemented
3#31774212C211yesmaximal, characteristic, complemented
4#31774209C211yesmaximal, characteristic, complemented
5#31774176C211yesmaximal, characteristic, complemented
6#31774175C211yesmaximal, characteristic, complemented
7#31774091C211yesmaximal, characteristic, complemented
8#31774090C211yesmaximal, characteristic, complemented
9#31774032C211yesmaximal, characteristic, complemented
10#31774029C211yesmaximal, characteristic, complemented
11C4×D2168C211yesmaximal, characteristic, complemented
12C4×#16864639C211yesmaximal, characteristic, complemented
13C4×#16864639C211yesmaximal, characteristic, complemented
14#31773948C211yesmaximal, characteristic, complemented
15C4×D8×C271C211yesmaximal, characteristic, complemented
16C2×#16864654—21no—
17C2×D4×D271C2211yescharacteristic
18C22×C4×D271—21no—
19C2×D2168C2211yescharacteristic
20C2×#16864639C2211yescharacteristic
21C2×#16864639C2211yescharacteristic
22#22576159C2211yescharacteristic, complemented
23#22576156C2211yescharacteristic, complemented
24#22576146—21no—
25#22576135C2211yescharacteristic
26#22576133—21no—
27#22576131C2211yescharacteristic
28C4×D1084C2211yescharacteristic
29C4×D1084C2211yescharacteristic, complemented
30D4×Dic271C2211yescharacteristic
31#22576122C2211yescharacteristic
32C4×C22⋊D271—21no—
33C4×C22⋊D271—21no—
34(C22⋊D271)⋊C4—21no—
35C4⋊C4×D271C2211yescharacteristic
36C22⋊C4×D271—21no—
37C42×D271C2211yescharacteristic
38#22576094C2211yescharacteristic, complemented
39#22576093C2211yescharacteristic, complemented
40#22576093C2211yescharacteristic, complemented
41Dic271⋊C8C2211yescharacteristic, complemented
42Dic271⋊C8C2211yescharacteristic, complemented
43#22576082C2211yescharacteristic
44#22576082C2211yescharacteristic, complemented
45#22576081C2211yescharacteristic
46#22576081C2211yescharacteristic, complemented
47#22576080C2211yescharacteristic
48#22576080C2211yescharacteristic, complemented
49(C2×D271)⋊C8C2211yescharacteristic
50(C2×D271)⋊C8C2211yescharacteristic
51C4×C271⋊C8C2211yescharacteristic, complemented
52C2×D8×C271C2211yescharacteristic
53C4×D4×C271C2211yescharacteristic
54C4×D4×C271C2211yescharacteristic, complemented
55#107×C271C2211yescharacteristic, complemented
56#102×C271C2211yescharacteristic
57#102×C271C2211yescharacteristic, complemented
58C4×C8×C271C2211yescharacteristic, complemented
59C23×D271—21no—
60#16864654—44no—
61C2×Dic542—21no—
62C2×D1084—21no—
63C2×D1084C2311yescharacteristic
64C2×D1084C2311yescharacteristic
65C2×C22⋊D271—21no—
66C2×C22⋊D271—21no—
67C2×C22⋊D271—21no—
68C2×C22⋊D271—21no—
69D4×D271—22no—
70D4×D271—22no—
71C22×Dic271—21no—
72C2×C4×D271—21no—
73C2×C4×D271—21no—
74C2×C4×D271—21no—
75C2×C4×D271—21no—
76C2×C4×D271—44no—
77C2×C4×D271D411yescharacteristic
78C2×C4×D271D411yescharacteristic
79C2×C4×D271C2311yescharacteristic
80D2168—22no—
81#16864639—22no—
82#16864639—22no—
83C2×C271⋊C8C2311yescharacteristic
84C2×C271⋊C8C2311yescharacteristic
85C4⋊Dic271C2311yescharacteristic
86C4⋊Dic271C2311yescharacteristic
87Dic271⋊C4—21no—
88Dic271⋊C4—21no—
89C22⋊Dic271—21no—
90C22⋊Dic271—21no—
91(C2×D271)⋊C4—21no—
92(C2×D271)⋊C4—21no—
93(C2×D271)⋊C4—21no—
94(C2×D271)⋊C4—21no—
95C4×Dic271D411yescharacteristic
96C4×Dic271D411yescharacteristic
97C4×Dic271C2311yescharacteristic
98C2×D4×C271C2311yescharacteristic
99C2×D4×C271C2311yescharacteristic
100C22×C4×C271—21no—
101C22×C4×C271—21no—
102D8×C271—22no—
103C2×C8×C271C2311yescharacteristic
104C2×C8×C271C2311yescharacteristic
105C4⋊C4×C271C2311yescharacteristic
106C4⋊C4×C271C2311yescharacteristic
107C22⋊C4×C271—21no—
108C22⋊C4×C271—21no—
109C42×C271C2311yescharacteristic
110C22×D271—24no—
111C22×D271—21no—
112C22×D271—21no—
113C22×D271—42no—
114C22×D271—42no—
115C22×D271C2×D411yescharacteristic
116Dic542—42no—
117D1084—21no—
118D1084—21no—
119D1084—21no—
120D1084—42no—
121D1084#4112yescomplemented
122C22⋊D271—24no—
123C22⋊D271—42no—
124C22⋊D271—42no—
125C22⋊D271—42no—
126C2×Dic271—21no—
127C2×Dic271—21no—
128C2×Dic271—42no—
129C2×Dic271C2×D411yescharacteristic
130C2×Dic271C2×D411yescharacteristic
131C2×Dic271C2×D411yescharacteristic
132C4×D271—21no—
133C4×D271—21no—
134C4×D271—41no—
135C4×D271—42no—
136C4×D271—42no—
137C4×D271—42no—
138C4×D271—42no—
139C4×D271D814yescomplemented
140C271⋊C8—21no—
141C271⋊C8—21no—
142C23×C271—21no—
143C23×C271—21no—
144D4×C271—21no—
145D4×C271—21no—
146D4×C271—21no—
147D4×C271#4112yescomplemented
148C2×C4×C271—21no—
149C2×C4×C271—21no—
150C2×C4×C271—42no—
151C2×C4×C271—42no—
152C2×C4×C271C2×D411yescharacteristic
153C2×C4×C271C2×D411yescharacteristic
154C2×C4×C271C2411yescharacteristic
155C8×C271—21no—
156C8×C271—21no—
157C22×C271—22no—
158C22×C271—41no—
159C22×C271—41no—
160C22×C271—41no—
161C22×C271—41no—
162C22×C271—41no—
163C22×C271C22×D411yescharacteristic
164C2×D271—21no—
165C2×D271—21no—
166C2×D271—22no—
167C2×D271—48no—
168C2×D271—41no—
169C2×D271—41no—
170C2×D271—41no—
171C2×D271—41no—
172C2×D271—41no—
173C2×D271C2×D812yes—
174C4×C271—21no—
175C4×C271—41no—
176C4×C271—41no—
177C4×C271C2×D812yes—
178C4×C271C2×#4111yescharacteristic
179C4×C271C2×#4111yescharacteristic
180Dic271—21no—
181Dic271—21no—
182Dic271—41no—
183Dic271—41no—
184Dic271C2×D812yes—
185C2×C271—42no—
186C2×C271—81no—
187C2×C271#52511yescharacteristic
188C2×C271C22×D811yescharacteristic
189C2×C271#57511yescharacteristic
190D271—22no—
191D271—42no—
192D271—81no—
193C271#310011yescharacteristic, complemented, Sylow
194#3100—2711nomaximal, Sylow
195#532—2711no—
196C2×C4×D4—2711no—
197#480—2711no—
198#480—2711no—
199#474—2711no—
200#474—2711no—
201#459—2711no—
202#459—2711no—
203#447—2711no—
204#447—2711no—
205C4×D8—2711no—
206C4×D8—2711no—
207C4×D8—2711no—
208C4×D8D27111yescharacteristic, complemented
209#431—2711no—
210C2×#41—5421no—
211C22×D4—2711no—
212C23×C4—5421no—
213C2×D8—2711no—
214C2×D8—2711no—
215C2×D8—2711no—
216C2×D8C2×D27111yescharacteristic
217C4⋊Q8—2711no—
218#127—2711no—
219#124—5421no—
220#121—2711no—
221#121—2711no—
222#121—5421no—
223C4×D4—2711no—
224C4×D4—2711no—
225C4×D4—2711no—
226C4×D4—2711no—
227C4×D4—5421no—
228C4×D4—5421no—
229C4×D4—5421no—
230C4×D4C2×D27111yescharacteristic
231C4×D4C2×D27111yescharacteristic, complemented
232C2×C4⋊C4—2711no—
233C2×C22⋊C4—5421no—
234C2×C42—2711no—
235#107—2711no—
236#107—2711no—
237#107—2711no—
238#107C2×D27111yescharacteristic, complemented
239C4⋊C8—2711no—
240C4⋊C8—2711no—
241#102—2711no—
242#102—2711no—
243#102—2711no—
244#102—2711no—
245#102—2711no—
246#102—2711no—
247#102C2×D27111yescharacteristic
248#102C2×D27111yescharacteristic, complemented
249C22⋊C8—2711no—
250C22⋊C8—2711no—
251C4×C8—2711no—
252C4×C8C2×D27111yescharacteristic, complemented
253C24—5421no—
254#41—10844no—
255C2×Q8—5421no—
256C2×D4—2711no—
257C2×D4—2711no—
258C2×D4—5421no—
259C2×D4—5421no—
260C2×D4—5421no—
261C2×D4—5421no—
262C2×D4—5422no—
263C2×D4—5422no—
264C2×D4—5421no—
265C2×D4C22×D27111yescharacteristic
266C2×D4C22×D27111yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—2711no—
270C22×C4—2711no—
271C22×C4—2711no—
272C22×C4—5421no—
273C22×C4—5421no—
274C22×C4—5421no—
275C22×C4—5421no—
276C22×C4—5421no—
277C22×C4—10844no—
278D8—22no—
279D8—5422no—
280D8—5422no—
281D8—5422no—
282C2×C8—2711no—
283C2×C8—2711no—
284C2×C8C22×D27111yescharacteristic
285C2×C8C22×D27111yescharacteristic
286C4⋊C4—2711no—
287C4⋊C4—2711no—
288C4⋊C4—5421no—
289C4⋊C4—5421no—
290C4⋊C4C22×D27111yescharacteristic
291C4⋊C4C22×D27111yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—5421no—
295C22⋊C4—5421no—
296C22⋊C4—5421no—
297C22⋊C4—5421no—
298C22⋊C4—5421no—
299C22⋊C4—5421no—
300C42—2711no—
301C42—2711no—
302C42—2711no—
303C42C22×D27111yescharacteristic
304C23—21no—
305C23—21no—
306C23—2711no—
307C23—5424no—
308C23—5421no—
309C23—5421no—
310C23—10842no—
311C23—10842no—
312Q8—10842no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—2712no—
317D4—5424no—
318D4—5421no—
319D4—5421no—
320D4—5421no—
321D4—10842no—
322D4—10842no—
323D4—10842no—
324D4—10842no—
325D4#1686465412yescomplemented
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—2711no—
331C2×C4—2714no—
332C2×C4—2711no—
333C2×C4—2711no—
334C2×C4—5421no—
335C2×C4—5421no—
336C2×C4—5421no—
337C2×C4—5421no—
338C2×C4—10841no—
339C2×C4—10842no—
340C2×C4—10842no—
341C2×C4—10842no—
342C2×C4—10842no—
343C2×C4—10842no—
344C2×C4D4×D27111yescharacteristic
345C2×C4D4×D27111yescharacteristic
346C2×C4C23×D27111yescharacteristic
347C8—21no—
348C8—21no—
349C8—5421no—
350C8—5421no—
351C22—22no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—2712no—
358C22—5421no—
359C22—5421no—
360C22—5422no—
361C22—10848no—
362C22—10841no—
363C22—10841no—
364C22—10841no—
365C22—10841no—
366C22—10841no—
367C22C2×D4×D27111yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—2712no—
372C4—5421no—
373C4—5421no—
374C4—10841no—
375C4—10841no—
376C4D8×D27112yes—
377C4#41×D27111yescharacteristic
378C4C2×#1686465411yescharacteristic
379C2—42no—
380C2—81no—
381C2—5422no—
382C2—10842no—
383C2—21681no—
384C2#3177440611yescharacteristic
385C2C2×D8×D27111yescharacteristic
386C2#3177469411yescharacteristic
subgroupG/H
centerC2×C4D4×D271
commutator, cosocleC2×C4×C271C24
FrattiniC2×C4C23×D271
FittingC4×D8×C271C2
socleC22×C271C22×D4
hypercenterC4×D8D271
hypocenterC271#3100
LCSG ▷ C2×C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #31774444C2semidirect
2. C4×D4×D271C2semidirect
3. #31774212C2semidirect
4. #31774209C2semidirect
5. #31774176C2semidirect
6. #31774175C2semidirect
7. #31774091C2semidirect
8. #31774090C2semidirect
9. #31774032C2semidirect
10. #31774029C2semidirect
11. C4×D2168C2semidirect
12. C4×#16864639C2semidirect
13. C4×#16864639C2semidirect
14. #31773948C2semidirect
15. C4×D8×C271C2semidirect
22. #22576159C22semidirect
23. #22576156C22semidirect
29. C4×D1084C22semidirect
38. #22576094C22semidirect
39. #22576093C22semidirect
40. #22576093C22semidirect
41. Dic271⋊C8C22semidirect
42. Dic271⋊C8C22semidirect
44. #22576082C22semidirect
46. #22576081C22semidirect
48. #22576080C22semidirect
51. C4×C271⋊C8C22semidirect
54. C4×D4×C271C22semidirect
55. #107×C271C22semidirect
57. #102×C271C22semidirect
58. C4×C8×C271C22semidirect
121. D1084#41semidirect
139. C4×D271D8semidirect
147. D4×C271#41semidirect
193. C271#3100semidirect
208. C4×D8D271semidirect
231. C4×D4C2×D271semidirect
238. #107C2×D271semidirect
248. #102C2×D271semidirect
252. C4×C8C2×D271semidirect
325. D4#16864654semidirect

Maximal subgroups

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

subgroupindex
#317744442
C4×D4×D2712
#317742122
#317742092
#317741762
#317741752
#317740912
#317740902
#317740322
#317740292
C4×D21682
C4×#168646392
#317739482
C4×D8×C2712
#3100271