Finite Group Databasebeta

← #27204974

Subgroups — #27204974

Order 13184.

398 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268421C211yesmaximal, characteristic, complemented
2#20268263C211yesmaximal, characteristic
3#20268093C211yesmaximal, characteristic, complemented
4#20268090C211yesmaximal, characteristic, complemented
5#20268088C211yesmaximal, characteristic, complemented
6#20268082C211yesmaximal, characteristic, complemented
7#20268079C211yesmaximal, characteristic, complemented
8#20268071C211yesmaximal, characteristic, complemented
9#20268070C211yesmaximal, characteristic, complemented
10#20267832C211yesmaximal, characteristic, complemented
11#20267826C211yesmaximal, characteristic, complemented
12#20267816C211yesmaximal, characteristic, complemented
13#20267794C211yesmaximal, characteristic
14#102×D103C211yesmaximal, characteristic
15#478×C103C211yesmaximal, characteristic, complemented
16C2×D4×D103C2211yescharacteristic
17C2×#13110088C2211yescharacteristic
18C2×C8×D103C2211yescharacteristic
19#15693021C2211yescharacteristic, complemented
20#15693020—21no—
21#15693020C2211yescharacteristic, complemented
22#15693012C2211yescharacteristic, complemented
23#15693011—21no—
24#15693001—21no—
25#15692999—21no—
26C4×D412C2211yescharacteristic
27D4×Dic103C2211yescharacteristic
28#15692983C2211yescharacteristic
29C4×C22⋊D103—21no—
30(C22⋊D103)⋊C4—21no—
31#15692979C2211yescharacteristic
32#15692979C2211yescharacteristic
33#15692978C2211yescharacteristic
34C4⋊C4×D103C2211yescharacteristic
35C2×(C2×D103)⋊C4—21no—
36C22⋊C4×D103—21no—
37#15692954C2211yescharacteristic, complemented
38#15692954C2211yescharacteristic, complemented
39#15692954C2211yescharacteristic, complemented
40#15692953C2211yescharacteristic, complemented
41#15692953C2211yescharacteristic, 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×D103C2311yescharacteristic
71#13110088—22no—
72C2×C103⋊C8C2311yescharacteristic
73C2×C103⋊C8C2311yescharacteristic
74C8×D103—22no—
75C4⋊Dic103—21no—
76C4⋊Dic103—21no—
77C4⋊Dic103C2311yescharacteristic
78C4⋊Dic103C2311yescharacteristic
79C4⋊Dic103C2311yescharacteristic
80Dic103⋊C4—21no—
81Dic103⋊C4—21no—
82Dic103⋊C4—21no—
83Dic103⋊C4D411yescharacteristic
84Dic103⋊C4D411yescharacteristic
85C22⋊Dic103—21no—
86(C2×D103)⋊C4—21no—
87(C2×D103)⋊C4—21no—
88(C2×D103)⋊C4—21no—
89(C2×D103)⋊C4—21no—
90(C2×D103)⋊C4D411yescharacteristic
91(C2×D103)⋊C4D411yescharacteristic
92C4×Dic103—21no—
93C4×Dic103—21no—
94C4×Dic103C2311yescharacteristic
95C2×D4×C103C2311yescharacteristic
96C22×C4×C103—21no—
97C2×C8×C103C2311yescharacteristic
98C2×C8×C103C2311yescharacteristic
99C4⋊C4×C103—21no—
100C4⋊C4×C103—21no—
101C4⋊C4×C103C2311yescharacteristic
102C4⋊C4×C103C2311yescharacteristic
103C4⋊C4×C103C2311yescharacteristic
104C22⋊C4×C103—21no—
105C42×C103C2311yescharacteristic
106C23×C103—21no—
107C22×D103—21no—
108C22×D103—24no—
109C22×D103—81no—
110C22×D103—81no—
111C22×D103C2×D411yescharacteristic
112D4×C103—21no—
113D4×C103C2×Q812yes—
114C2×C4×C103—21no—
115C2×C4×C103—21no—
116C2×C4×C103—21no—
117C2×C4×C103—81no—
118C2×C4×C103C2×D411yescharacteristic
119C2×C4×C103C2×D411yescharacteristic
120C2×C4×C103C2411yescharacteristic
121C22⋊D103—24no—
122C2×Dic103—21no—
123C2×Dic103—21no—
124C2×Dic103—21no—
125C2×Dic103—81no—
126C2×Dic103C2×D411yescharacteristic
127C2×Dic103C2×D411yescharacteristic
128C2×Dic103C2×D411yescharacteristic
129D412—21no—
130D412C2×Q812yes—
131C4×D103—81no—
132C4×D103—81no—
133C4×D103—81no—
134C4×D103C2×Q812yes—
135C4×D103#4112yes—
136Dic206—81no—
137Dic206—81no—
138C8×C103—21no—
139C8×C103—21no—
140C103⋊C8—21no—
141C103⋊C8—21no—
142C22×C103—22no—
143C22×C103—41no—
144C22×C103—41no—
145C22×C103C22×D411yescharacteristic
146C2×D103—21no—
147C2×D103—21no—
148C2×D103—22no—
149C2×D103—41no—
150C2×D103—41no—
151C2×D103—84no—
152C2×D103C22⋊Q812yes—
153C4×C103—21no—
154C4×C103—21no—
155C4×C103—41no—
156C4×C103—41no—
157C4×C103—41no—
158C4×C103C22×Q811yescharacteristic
159C4×C103C2×#4111yescharacteristic
160Dic103—21no—
161Dic103—21no—
162Dic103—41no—
163Dic103—41no—
164Dic103—41no—
165Dic103C22⋊Q812yes—
166C2×C103—42no—
167C2×C103C2×C22⋊Q811yescharacteristic
168C2×C103#57611yescharacteristic
169C2×C103#57711yescharacteristic
170D103—22no—
171D103—42no—
172#3081—1031nomaximal, Sylow
173C103#308111yescharacteristic, complemented, Sylow
174#544—1031no—
175#518—1031no—
176#478—1031no—
177#478—1031no—
178#478—1031no—
179#478D10311yescharacteristic, complemented
180#476—1031no—
181#476—1031no—
182#474—1031no—
183#474—1031no—
184#428—1031no—
185#427—1031no—
186#424—1031no—
187#418—1031no—
188C2×#102—1031no—
189C22×D4—1031no—
190C2×M16—1031no—
191C22×C8—1031no—
192C4⋊Q8—1031no—
193C4⋊Q8—1031no—
194C4⋊Q8—2061no—
195#125—1031no—
196#125—2061no—
197#125C2×D10311yescharacteristic, complemented
198C22⋊Q8—2061no—
199C22⋊Q8—2061no—
200C4×D4—1031no—
201C4×D4—1031no—
202C4×D4—1031no—
203C4×D4—2061no—
204C4×D4—2061no—
205C4×D4C2×D10311yescharacteristic
206#117—1031no—
207#117—1031no—
208#117—1031no—
209C2×C4⋊C4—1031no—
210C2×C22⋊C4—2061no—
211C2×C22⋊C4—2061no—
212#107—1031no—
213#107—1031no—
214#107—1031no—
215#107C2×D10311yescharacteristic, complemented
216#106—1031no—
217#106—1031no—
218#106—1031no—
219#106C2×D10311yescharacteristic, complemented
220C4⋊C8—1031no—
221C4⋊C8—1031no—
222C4⋊C8—1031no—
223C4⋊C8C2×D10311yescharacteristic, complemented
224#102—1031no—
225#102—1031no—
226#102—1031no—
227#102—1031no—
228#102—1031no—
229#102—1031no—
230#102C2×D10311yescharacteristic
231#102C2×D10311yescharacteristic
232C24—2061no—
233C2×Q8—2061no—
234C2×Q8—2061no—
235C2×D4—1034no—
236C2×D4—1031no—
237C2×D4—2062no—
238C2×D4—2061no—
239C2×D4C22×D10311yescharacteristic
240C22×C4—21no—
241C22×C4—1031no—
242C22×C4—2061no—
243C22×C4—2061no—
244C22×C4—2061no—
245C22×C4—2061no—
246M16—2062no—
247C2×C8—1031no—
248C2×C8—1031no—
249C2×C8—2062no—
250C2×C8C22×D10311yescharacteristic
251C2×C8C22×D10311yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—1031no—
255C4⋊C4—1031no—
256C4⋊C4—1031no—
257C4⋊C4—1031no—
258C4⋊C4—1031no—
259C4⋊C4—2061no—
260C4⋊C4—2061no—
261C4⋊C4—2061no—
262C4⋊C4—2061no—
263C4⋊C4—2061no—
264C4⋊C4C22×D10311yescharacteristic
265C4⋊C4C22×D10311yescharacteristic
266C4⋊C4C22×D10311yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—1031no—
269C22⋊C4—1031no—
270C22⋊C4—2061no—
271C22⋊C4—2061no—
272C22⋊C4—2061no—
273C22⋊C4—2061no—
274C22⋊C4—2061no—
275C42—1031no—
276C42—2061no—
277C42—2061no—
278C42C22×D10311yescharacteristic
279C23—21no—
280C23—8241no—
281C23—8241no—
282C23—1031no—
283C23—2064no—
284C23—2061no—
285Q8—8241no—
286Q8—8241no—
287D4—21no—
288D4—1032no—
289D4—2064no—
290D4—2061no—
291D4Q8×D10312yes—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—81no—
296C2×C4—8241no—
297C2×C4—8241no—
298C2×C4—8241no—
299C2×C4—8241no—
300C2×C4—1031no—
301C2×C4—1032no—
302C2×C4—1032no—
303C2×C4—1031no—
304C2×C4—1031no—
305C2×C4—2061no—
306C2×C4—2061no—
307C2×C4—2061no—
308C2×C4D4×D10311yescharacteristic
309C2×C4D4×D10311yescharacteristic
310C2×C4C23×D10311yescharacteristic
311C8—21no—
312C8—21no—
313C8—2061no—
314C8—2061no—
315C22—22no—
316C22—41no—
317C22—41no—
318C22—8244no—
319C22—1032no—
320C22—4121no—
321C22—4121no—
322C22—2062no—
323C22—2061no—
324C22—2061no—
325C22C2×D4×D10311yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—1032no—
332C4—4121no—
333C4—4121no—
334C4—4121no—
335C4—2061no—
336C4—2061no—
337C4C2×Q8×D10311yescharacteristic
338C4#41×D10311yescharacteristic
339C2—42no—
340C2—4122no—
341C2—2062no—
342C2C22⋊Q8×D10311yescharacteristic
343C2#2026859511yescharacteristic
344C2#2026859811yescharacteristic
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#3081
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. #20268421C2semidirect
3. #20268093C2semidirect
4. #20268090C2semidirect
5. #20268088C2semidirect
6. #20268082C2semidirect
7. #20268079C2semidirect
8. #20268071C2semidirect
9. #20268070C2semidirect
10. #20267832C2semidirect
11. #20267826C2semidirect
12. #20267816C2semidirect
15. #478×C103C2semidirect
19. #15693021C22semidirect
21. #15693020C22semidirect
22. #15693012C22semidirect
37. #15692954C22semidirect
38. #15692954C22semidirect
39. #15692954C22semidirect
40. #15692953C22semidirect
41. #15692953C22semidirect
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
173. C103#3081semidirect
179. #478D103semidirect
197. #125C2×D103semidirect
215. #107C2×D103semidirect
219. #106C2×D103semidirect
223. C4⋊C8C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202684212
#202682632
#202680932
#202680902
#202680882
#202680822
#202680792
#202680712
#202680702
#202678322
#202678262
#202678162
#202677942
#102×D1032
#478×C1032
#3081103