Finite Group Databasebeta

← #27204939

Subgroups — #27204939

Order 13184.

440 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268347C211yesmaximal, characteristic, complemented
2C4×D4×D103C211yesmaximal, characteristic
3#20268092C211yesmaximal, characteristic, complemented
4#20268091C211yesmaximal, characteristic, complemented
5#20268088C211yesmaximal, characteristic, complemented
6#20268080C211yesmaximal, characteristic, complemented
7#20268079C211yesmaximal, characteristic, complemented
8#20268070C211yesmaximal, characteristic, complemented
9#20268069C211yesmaximal, characteristic, complemented
10#20267832C211yesmaximal, characteristic, complemented
11#20267830C211yesmaximal, characteristic, complemented
12#20267813C211yesmaximal, characteristic, complemented
13#20267794C211yesmaximal, characteristic
14#20267794C211yesmaximal, characteristic
15#478×C103C211yesmaximal, characteristic, complemented
16C2×D4×D103C2211yescharacteristic
17C22×C4×D103—21no—
18C2×#13110088C2211yescharacteristic
19C2×#13110088C2211yescharacteristic
20#15693020C2211yescharacteristic, complemented
21#15693020C2211yescharacteristic, complemented
22#15693013C2211yescharacteristic, complemented
23#15692999—21no—
24#15692999—21no—
25#15692986—21no—
26#15692986—21no—
27C4×D412C2211yescharacteristic
28D4×Dic103C2211yescharacteristic
29#15692983C2211yescharacteristic
30C4×C22⋊D103—21no—
31(C22⋊D103)⋊C4—21no—
32#15692979C2211yescharacteristic
33#15692979C2211yescharacteristic
34C4⋊C4×D103C2211yescharacteristic
35C22⋊C4×D103—21no—
36C42×D103C2211yescharacteristic
37#15692955C2211yescharacteristic, complemented
38#15692954C2211yescharacteristic, complemented
39#15692954C2211yescharacteristic, complemented
40#15692953C2211yescharacteristic, complemented
41#15692952C2211yescharacteristic, complemented
42#15692952C2211yescharacteristic, complemented
43C4⋊(C103⋊C8)C2211yescharacteristic, complemented
44Dic103⋊C8C2211yescharacteristic, complemented
45Dic103⋊C8C2211yescharacteristic, complemented
46#15692943C2211yescharacteristic
47#15692943C2211yescharacteristic
48#15692942C2211yescharacteristic
49#15692942C2211yescharacteristic
50#15692941C2211yescharacteristic
51#15692941C2211yescharacteristic
52#125×C103C2211yescharacteristic, complemented
53C4×D4×C103C2211yescharacteristic
54#107×C103C2211yescharacteristic, complemented
55#106×C103C2211yescharacteristic, complemented
56C4⋊C8×C103C2211yescharacteristic, complemented
57#102×C103C2211yescharacteristic
58#102×C103C2211yescharacteristic
59C23×D103—21no—
60C2×Dic206—21no—
61C2×Dic206—21no—
62C2×D412C2311yescharacteristic
63C2×C22⋊D103—21no—
64D4×D103—22no—
65D4×D103Q814yescomplemented
66C22×Dic103—21no—
67C2×C4×D103—21no—
68C2×C4×D103—21no—
69C2×C4×D103—21no—
70C2×C4×D103—44no—
71C2×C4×D103D411yescharacteristic
72C2×C4×D103D411yescharacteristic
73C2×C4×D103C2311yescharacteristic
74#13110088—22no—
75#13110088—22no—
76C2×C103⋊C8C2311yescharacteristic
77C2×C103⋊C8C2311yescharacteristic
78C4⋊Dic103C2311yescharacteristic
79C4⋊Dic103C2311yescharacteristic
80C4⋊Dic103C2311yescharacteristic
81Dic103⋊C4—21no—
82Dic103⋊C4—21no—
83Dic103⋊C4—21no—
84Dic103⋊C4—21no—
85Dic103⋊C4—21no—
86C22⋊Dic103—21no—
87(C2×D103)⋊C4—21no—
88(C2×D103)⋊C4—21no—
89(C2×D103)⋊C4—21no—
90(C2×D103)⋊C4—21no—
91C4×Dic103—21no—
92C4×Dic103—21no—
93C4×Dic103D411yescharacteristic
94C4×Dic103D411yescharacteristic
95C4×Dic103C2311yescharacteristic
96C2×D4×C103C2311yescharacteristic
97C22×C4×C103—21no—
98C2×C8×C103C2311yescharacteristic
99C2×C8×C103C2311yescharacteristic
100C4⋊C4×C103—21no—
101C4⋊C4×C103—21no—
102C4⋊C4×C103C2311yescharacteristic
103C4⋊C4×C103C2311yescharacteristic
104C4⋊C4×C103C2311yescharacteristic
105C22⋊C4×C103—21no—
106C42×C103C2311yescharacteristic
107C23×C103—21no—
108C22×D103—21no—
109C22×D103—24no—
110C22×D103—42no—
111C22×D103—42no—
112C22×D103C2×D411yescharacteristic
113D4×C103—21no—
114D4×C103C2×Q812yes—
115C2×C4×C103—21no—
116C2×C4×C103—21no—
117C2×C4×C103—21no—
118C2×C4×C103—42no—
119C2×C4×C103C2×D411yescharacteristic
120C2×C4×C103C2×D411yescharacteristic
121C2×C4×C103C2411yescharacteristic
122C22⋊D103—24no—
123C2×Dic103—21no—
124C2×Dic103—21no—
125C2×Dic103—21no—
126C2×Dic103—42no—
127C2×Dic103C2×D411yescharacteristic
128C2×Dic103C2×D411yescharacteristic
129C2×Dic103C2×D411yescharacteristic
130D412—21no—
131D412C2×Q812yes—
132C4×D103—22no—
133C4×D103—41no—
134C4×D103—42no—
135C4×D103—42no—
136C4×D103—42no—
137C4×D103C2×Q812yes—
138C4×D103#4112yes—
139Dic206—42no—
140Dic206—42no—
141C8×C103—21no—
142C8×C103—21no—
143C103⋊C8—21no—
144C103⋊C8—21no—
145C22×C103—22no—
146C22×C103—41no—
147C22×C103—41no—
148C22×C103C22×D411yescharacteristic
149C2×D103—21no—
150C2×D103—21no—
151C2×D103—22no—
152C2×D103—48no—
153C2×D103—41no—
154C2×D103—41no—
155C2×D103C22⋊Q812yes—
156C4×C103—21no—
157C4×C103—21no—
158C4×C103—41no—
159C4×C103—41no—
160C4×C103—41no—
161C4×C103C22×Q811yescharacteristic
162C4×C103C2×#4111yescharacteristic
163Dic103—21no—
164Dic103—41no—
165Dic103—41no—
166Dic103—41no—
167Dic103C22⋊Q812yes—
168Dic103AGL(1,ℤ/8)12yes—
169C2×C103—42no—
170C2×C103C2×C22⋊Q811yescharacteristic
171C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
172C2×C103#57511yescharacteristic
173D103—22no—
174D103—42no—
175#3077—1031nomaximal, Sylow
176C103#307711yescharacteristic, complemented, Sylow
177#533—1031no—
178C2×C4×D4—1031no—
179#478—1031no—
180#478—1031no—
181#478—1031no—
182#478D10311yescharacteristic, complemented
183#476—1031no—
184#476—1031no—
185#474—1031no—
186#474—1031no—
187#428—1031no—
188#428—1031no—
189#423—1031no—
190#418—1031no—
191#418—1031no—
192C22×D4—1031no—
193C23×C4—2061no—
194C2×M16—1031no—
195C2×M16—1031no—
196C4⋊Q8—1031no—
197C4⋊Q8—1031no—
198#125—1031no—
199#125C2×D10311yescharacteristic, complemented
200C22⋊Q8—2061no—
201C22⋊Q8—2061no—
202C4×Q8—2061no—
203C4×Q8—2061no—
204C4×D4—1031no—
205C4×D4—1031no—
206C4×D4—1031no—
207C4×D4—2061no—
208C4×D4—2061no—
209C4×D4C2×D10311yescharacteristic
210#117—1031no—
211#117—1031no—
212C2×C4⋊C4—1031no—
213C2×C22⋊C4—2061no—
214C2×C42—1031no—
215#107—1031no—
216#107—1031no—
217#107—1031no—
218#107C2×D10311yescharacteristic, complemented
219#106—1031no—
220#106—1031no—
221#106—1031no—
222#106C2×D10311yescharacteristic, complemented
223C4⋊C8—1031no—
224C4⋊C8—1031no—
225C4⋊C8—1031no—
226C4⋊C8C2×D10311yescharacteristic, complemented
227#102—1031no—
228#102—1031no—
229#102—1031no—
230#102—1031no—
231#102—1031no—
232#102—1031no—
233#102C2×D10311yescharacteristic
234#102C2×D10311yescharacteristic
235C24—2061no—
236C2×Q8—2061no—
237C2×Q8—2061no—
238C2×D4—1034no—
239C2×D4—1031no—
240C2×D4—2062no—
241C2×D4—2061no—
242C2×D4C22×D10311yescharacteristic
243C22×C4—21no—
244C22×C4—1031no—
245C22×C4—1031no—
246C22×C4—1031no—
247C22×C4—4124no—
248C22×C4—2061no—
249C22×C4—2061no—
250C22×C4—2061no—
251C22×C4—2061no—
252M16—2062no—
253M16—2062no—
254C2×C8—1031no—
255C2×C8—1031no—
256C2×C8C22×D10311yescharacteristic
257C2×C8C22×D10311yescharacteristic
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—1031no—
261C4⋊C4—1031no—
262C4⋊C4—1031no—
263C4⋊C4—2061no—
264C4⋊C4—2061no—
265C4⋊C4—2061no—
266C4⋊C4—2061no—
267C4⋊C4—2061no—
268C4⋊C4C22×D10311yescharacteristic
269C4⋊C4C22×D10311yescharacteristic
270C4⋊C4C22×D10311yescharacteristic
271C22⋊C4—21no—
272C22⋊C4—2061no—
273C22⋊C4—2061no—
274C22⋊C4—2061no—
275C22⋊C4—2061no—
276C22⋊C4—2061no—
277C42—1031no—
278C42—1031no—
279C42—1031no—
280C42—2061no—
281C42—2061no—
282C42C22×D10311yescharacteristic
283C23—21no—
284C23—1031no—
285C23—4122no—
286C23—4122no—
287C23—2064no—
288C23—2061no—
289Q8—4122no—
290Q8—4122no—
291D4—21no—
292D4—1032no—
293D4—2064no—
294D4—2061no—
295D4Q8×D10312yes—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—42no—
300C2×C4—1031no—
301C2×C4—1031no—
302C2×C4—1032no—
303C2×C4—1032no—
304C2×C4—1031no—
305C2×C4—4122no—
306C2×C4—4121no—
307C2×C4—4122no—
308C2×C4—4122no—
309C2×C4—4122no—
310C2×C4—2062no—
311C2×C4—2061no—
312C2×C4—2061no—
313C2×C4—2061no—
314C2×C4D4×D10311yescharacteristic
315C2×C4D4×D10311yescharacteristic
316C2×C4C23×D10311yescharacteristic
317C8—21no—
318C8—21no—
319C8—2061no—
320C8—2061no—
321C22—22no—
322C22—41no—
323C22—41no—
324C22—1032no—
325C22—4128no—
326C22—4121no—
327C22—4121no—
328C22—2062no—
329C22—2061no—
330C22—2061no—
331C22C2×D4×D10311yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—1032no—
338C4—1032no—
339C4—4121no—
340C4—4121no—
341C4—4121no—
342C4—2061no—
343C4C2×Q8×D10311yescharacteristic
344C4#41×D10311yescharacteristic
345C2—42no—
346C2—4122no—
347C2—2062no—
348C2C22⋊Q8×D10311yescharacteristic
349C2AGL(1,ℤ/8)×D10311yescharacteristic
350C2#2026858811yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#478×C103C2
socleC22×C103C22×D4
prime radicalC2×D4×D103C22
hypercenter#478D103
hypocenterC103#3077
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #20268347C2semidirect
3. #20268092C2semidirect
4. #20268091C2semidirect
5. #20268088C2semidirect
6. #20268080C2semidirect
7. #20268079C2semidirect
8. #20268070C2semidirect
9. #20268069C2semidirect
10. #20267832C2semidirect
11. #20267830C2semidirect
12. #20267813C2semidirect
15. #478×C103C2semidirect
20. #15693020C22semidirect
21. #15693020C22semidirect
22. #15693013C22semidirect
37. #15692955C22semidirect
38. #15692954C22semidirect
39. #15692954C22semidirect
40. #15692953C22semidirect
41. #15692952C22semidirect
42. #15692952C22semidirect
43. C4⋊(C103⋊C8)C22semidirect
44. Dic103⋊C8C22semidirect
45. Dic103⋊C8C22semidirect
52. #125×C103C22semidirect
54. #107×C103C22semidirect
55. #106×C103C22semidirect
56. C4⋊C8×C103C22semidirect
65. D4×D103Q8semidirect
176. C103#3077semidirect
182. #478D103semidirect
199. #125C2×D103semidirect
218. #107C2×D103semidirect
222. #106C2×D103semidirect
226. C4⋊C8C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202683472
C4×D4×D1032
#202680922
#202680912
#202680882
#202680802
#202680792
#202680702
#202680692
#202678322
#202678302
#202678132
#202677942
#478×C1032
#3077103