Finite Group Databasebeta

← #27205061

Subgroups — #27205061

Order 13184.

420 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268303C211yesmaximal, characteristic
2#117×D103C211yesmaximal, characteristic, complemented
3#20268135C211yesmaximal, characteristic, complemented
4#20268134C211yesmaximal, characteristic, complemented
5#20268128C211yesmaximal, characteristic, complemented
6#20268123C211yesmaximal, characteristic, complemented
7#20268118C211yesmaximal, characteristic, complemented
8#20268117C211yesmaximal, characteristic, complemented
9#20268111C211yesmaximal, characteristic, complemented
10#20268106C211yesmaximal, characteristic, complemented
11#20267827C211yesmaximal, characteristic, complemented
12#20267788C211yesmaximal, characteristic, complemented
13#20267785C211yesmaximal, characteristic, complemented
14C2×(C2×D103)⋊C8C211yesmaximal, characteristic, complemented
15#427×C103C211yesmaximal, characteristic, complemented
16C2×#13110105C2211yescharacteristic
17C22×C4×D103C2211yescharacteristic
18C22×C103⋊C8C2211yescharacteristic
19#15693005—21no—
20#15693001C2211yescharacteristic
21#15693001C2211yescharacteristic
22#15692996C2211yescharacteristic
23#15692996C2211yescharacteristic
24#15692991—21no—
25C4×D412—21no—
26C4×D412—21no—
27#15692980C2211yescharacteristic
28#15692979C2211yescharacteristic
29#15692979C2211yescharacteristic
30#15692978—21no—
31#15692977—21no—
32C4⋊C4×D103C2211yescharacteristic
33C4⋊C4×D103C2211yescharacteristic
34C22⋊C4×D103—21no—
35C42×D103—21no—
36#15692954C2211yescharacteristic, complemented
37#15692954C2211yescharacteristic, complemented
38#15692952C2211yescharacteristic, complemented
39#15692952C2211yescharacteristic, complemented
40#15692946C2211yescharacteristic, complemented
41#15692946C2211yescharacteristic, complemented
42#15692944C2211yescharacteristic, complemented
43#15692944C2211yescharacteristic, complemented
44#15692943C2211yescharacteristic, complemented
45#15692943C2211yescharacteristic, complemented
46#15692941C2211yescharacteristic, complemented
47#15692941C2211yescharacteristic, complemented
48(C2×D103)⋊C8C2211yescharacteristic
49(C2×D103)⋊C8C2211yescharacteristic
50(C2×D103)⋊C8C2211yescharacteristic
51(C2×D103)⋊C8C2211yescharacteristic
52C22×C8×C103C2211yescharacteristic
53#117×C103C2211yescharacteristic
54#117×C103C2211yescharacteristic
55#107×C103C2211yescharacteristic, complemented
56#107×C103C2211yescharacteristic, complemented
57#106×C103C2211yescharacteristic, complemented
58#106×C103C2211yescharacteristic, complemented
59C23×D103D411yescharacteristic
60#13110105—22no—
61#13110105—22no—
62C2×Dic206C2311yescharacteristic
63C2×D412—21no—
64C2×D412—21no—
65C2×D412C2311yescharacteristic
66C2×C22⋊D103—21no—
67C22×Dic103D411yescharacteristic
68C2×C4×D103—22no—
69C2×C4×D103—22no—
70C2×C4×D103—21no—
71C2×C4×D103—21no—
72C2×C4×D103—21no—
73C2×C4×D103D411yescharacteristic
74C2×C4×D103D411yescharacteristic
75C2×C4×D103C2311yescharacteristic
76C2×C4×D103C2311yescharacteristic
77C2×C103⋊C8—22no—
78C2×C103⋊C8C2311yescharacteristic
79C2×C103⋊C8C2311yescharacteristic
80C4⋊Dic103—21no—
81C4⋊Dic103—21no—
82C4⋊Dic103C2311yescharacteristic
83C4⋊Dic103C2311yescharacteristic
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—
91(C2×D103)⋊C4—21no—
92(C2×D103)⋊C4—21no—
93C4×Dic103—21no—
94C4×Dic103—21no—
95C4×Dic103—21no—
96C22×C4×C103C2311yescharacteristic
97C2×C8×C103—22no—
98C2×C8×C103C2311yescharacteristic
99C2×C8×C103C2311yescharacteristic
100C4⋊C4×C103C2311yescharacteristic
101C4⋊C4×C103C2311yescharacteristic
102C4⋊C4×C103C2311yescharacteristic
103C4⋊C4×C103C2311yescharacteristic
104C22⋊C4×C103—21no—
105C22⋊C4×C103—21no—
106C42×C103—21no—
107C42×C103—21no—
108C23×C103C2×D411yescharacteristic
109C22×D103—22no—
110C22×D103—22no—
111C22×D103—21no—
112C22×D103—41no—
113C22×D103C2×D411yescharacteristic
114C22×D103C2×D411yescharacteristic
115C2×C4×C103—21no—
116C2×C4×C103—21no—
117C2×C4×C103—21no—
118C2×C4×C103—21no—
119C2×C4×C103C2×D411yescharacteristic
120C2×C4×C103#4112yes—
121C2×C4×C103#4112yes—
122C2×C4×C103C2411yescharacteristic
123C22⋊D103—42no—
124C2×Dic103—22no—
125C2×Dic103—21no—
126C2×Dic103—21no—
127C2×Dic103—21no—
128C2×Dic103C2×D411yescharacteristic
129C2×Dic103C2×D411yescharacteristic
130D412—21no—
131D412—21no—
132D412—42no—
133D412—42no—
134C4×D103—22no—
135C4×D103—22no—
136C4×D103—21no—
137C4×D103—21no—
138C4×D103—21no—
139C4×D103—21no—
140C4×D103—42no—
141C4×D103—42no—
142C4×D103—42no—
143Dic206—21no—
144Dic206—21no—
145C8×C103—21no—
146C8×C103—21no—
147C103⋊C8—21no—
148C103⋊C8—21no—
149C22×C103—21no—
150C22×C103—21no—
151C22×C103#12312yes—
152C22×C103C22×D411yescharacteristic
153C2×D103—21no—
154C2×D103—21no—
155C2×D103—21no—
156C2×D103—21no—
157C2×D103—21no—
158C2×D103—44no—
159C2×D103—41no—
160C2×D103—41no—
161C2×D103—41no—
162C2×D103#13512yes—
163C4×C103—41no—
164C4×C103—41no—
165C4×C103—41no—
166C4×C103—41no—
167C4×C103#12312yes—
168C4×C103C2×#4111yescharacteristic
169C4×C103C2×#4111yescharacteristic
170Dic103—21no—
171Dic103—21no—
172Dic103—41no—
173Dic103—41no—
174Dic103—41no—
175C2×C103—22no—
176C2×C103C2×#12311yescharacteristic
177C2×C103C2×#13511yescharacteristic
178C2×C103#57511yescharacteristic
179D103—22no—
180D103—41no—
181D103—81no—
182#3091—1031nomaximal, Sylow
183C103#309111yescharacteristic, complemented, Sylow
184#525—1031no—
185C2×#117—1031no—
186#485—1031no—
187#485—1031no—
188#484—1031no—
189#483—1031no—
190#482—1031no—
191#482—1031no—
192#481—1031no—
193#480—1031no—
194#427—1031no—
195#427D10311yescharacteristic, complemented
196#416—1031no—
197#416—1031no—
198C2×C22⋊C8—1031no—
199C2×#41—1031no—
200C23×C4—1031no—
201C22×C8—1031no—
202C22×C8C2×D10311yescharacteristic
203#123—2061no—
204C22⋊Q8—1031no—
205C22⋊Q8—1031no—
206#121—1031no—
207#121—1031no—
208#120—2061no—
209C4×D4—2061no—
210C4×D4—2061no—
211#117—1031no—
212#117—1031no—
213#117—1031no—
214#117—2061no—
215#117—2061no—
216#117C2×D10311yescharacteristic
217#117C2×D10311yescharacteristic
218C2×C4⋊C4—1031no—
219C2×C4⋊C4—1031no—
220C2×C22⋊C4—2061no—
221C2×C42—2061no—
222#107—1031no—
223#107—1031no—
224#107C2×D10311yescharacteristic, complemented
225#107C2×D10311yescharacteristic, complemented
226#106—1031no—
227#106—1031no—
228#106C2×D10311yescharacteristic, complemented
229#106C2×D10311yescharacteristic, complemented
230#103—1031no—
231#103—1031no—
232#103—1031no—
233#103—1031no—
234#102—1031no—
235#102—1031no—
236#102—1031no—
237#102—1031no—
238C22⋊C8—1031no—
239C22⋊C8—1031no—
240C22⋊C8—1031no—
241C22⋊C8—1031no—
242C24—1031no—
243#41—2062no—
244#41—2062no—
245C2×Q8—1031no—
246C2×D4—1031no—
247C2×D4—2061no—
248C2×D4—2061no—
249C2×D4—2061no—
250C22×C4—1031no—
251C22×C4—1031no—
252C22×C4—1031no—
253C22×C4—1031no—
254C22×C4—1031no—
255C22×C4—2061no—
256C22×C4—2061no—
257C22×C4—2061no—
258C22×C4—2062no—
259C22×C4—2062no—
260C22×C4C22×D10311yescharacteristic
261C2×C8—22no—
262C2×C8—1031no—
263C2×C8—1031no—
264C2×C8—2062no—
265C2×C8C22×D10311yescharacteristic
266C2×C8C22×D10311yescharacteristic
267C4⋊C4—1031no—
268C4⋊C4—1031no—
269C4⋊C4—2061no—
270C4⋊C4—2061no—
271C4⋊C4—2061no—
272C4⋊C4—2061no—
273C4⋊C4C22×D10311yescharacteristic
274C4⋊C4C22×D10311yescharacteristic
275C4⋊C4C22×D10311yescharacteristic
276C4⋊C4C22×D10311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—2061no—
280C22⋊C4—2061no—
281C22⋊C4—2061no—
282C22⋊C4—2061no—
283C22⋊C4—2061no—
284C22⋊C4—2061no—
285C22⋊C4—2061no—
286C42—21no—
287C42—21no—
288C42—2061no—
289C42—2061no—
290C42—2061no—
291C23—1031no—
292C23—1031no—
293C23—4121no—
294C23—2062no—
295C23—2061no—
296C23—2062no—
297C23D4×D10311yescharacteristic
298Q8—2061no—
299Q8—2061no—
300D4—4122no—
301D4—4122no—
302D4—4122no—
303D4—2061no—
304D4—2061no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—1031no—
310C2×C4—1031no—
311C2×C4—4122no—
312C2×C4—4122no—
313C2×C4—4122no—
314C2×C4—2061no—
315C2×C4—2061no—
316C2×C4—2061no—
317C2×C4—2062no—
318C2×C4—2061no—
319C2×C4—2061no—
320C2×C4—2061no—
321C2×C4—2061no—
322C2×C4—2062no—
323C2×C4—2062no—
324C2×C4D4×D10311yescharacteristic
325C2×C4#1311010512yes—
326C2×C4#1311010612yes—
327C2×C4C23×D10311yescharacteristic
328C8—21no—
329C8—21no—
330C8—2061no—
331C8—2061no—
332C22—21no—
333C22—21no—
334C22—1032no—
335C22—4124no—
336C22—4121no—
337C22—4121no—
338C22—4121no—
339C22—2061no—
340C22—2061no—
341C22—2061no—
342C22—2061no—
343C22—2061no—
344C22#1569300612yes—
345C22C2×D4×D10311yescharacteristic
346C4—41no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—4121no—
351C4—4121no—
352C4—4121no—
353C4—2061no—
354C4—2061no—
355C4#1569300612yes—
356C4C2×#1311010511yescharacteristic
357C4C2×#1311010611yescharacteristic
358C2—22no—
359C2—8241no—
360C2—4121no—
361C2—2062no—
362C2C2×#1569300611yescharacteristic
363C2#135×D10311yescharacteristic
364C2#2026858811yescharacteristic
subgroupG/H
centerC2×C4D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#427×C103C2
socleC22×C103C22×D4
prime radical#20268303C2
hypercenter#427D103
hypocenterC103#3091
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
2. #117×D103C2semidirect
3. #20268135C2semidirect
4. #20268134C2semidirect
5. #20268128C2semidirect
6. #20268123C2semidirect
7. #20268118C2semidirect
8. #20268117C2semidirect
9. #20268111C2semidirect
10. #20268106C2semidirect
11. #20267827C2semidirect
12. #20267788C2semidirect
13. #20267785C2semidirect
14. C2×(C2×D103)⋊C8C2semidirect
15. #427×C103C2semidirect
36. #15692954C22semidirect
37. #15692954C22semidirect
38. #15692952C22semidirect
39. #15692952C22semidirect
40. #15692946C22semidirect
41. #15692946C22semidirect
42. #15692944C22semidirect
43. #15692944C22semidirect
44. #15692943C22semidirect
45. #15692943C22semidirect
46. #15692941C22semidirect
47. #15692941C22semidirect
55. #107×C103C22semidirect
56. #107×C103C22semidirect
57. #106×C103C22semidirect
58. #106×C103C22semidirect
183. C103#3091semidirect
195. #427D103semidirect
224. #107C2×D103semidirect
225. #107C2×D103semidirect
228. #106C2×D103semidirect
229. #106C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202683032
#117×D1032
#202681352
#202681342
#202681282
#202681232
#202681182
#202681172
#202681112
#202681062
#202678272
#202677882
#202677852
C2×(C2×D103)⋊C82
#427×C1032
#3091103