Finite Group Databasebeta

← #27205392

Subgroups — #27205392

Order 13184.

394 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#20268401C211yesmaximal, characteristic, complemented
2#20268265C211yesmaximal, characteristic
3#20268132C211yesmaximal, characteristic, complemented
4#20268094C211yesmaximal, characteristic, complemented
5#20268090C211yesmaximal, characteristic, complemented
6#20267995C211yesmaximal, characteristic, complemented
7#20267995C211yesmaximal, characteristic, complemented
8#20267944C211yesmaximal, characteristic
9#20267941C211yesmaximal, characteristic
10#20267894C211yesmaximal, characteristic, complemented
11#20267890C211yesmaximal, characteristic, complemented
12#20267878C211yesmaximal, characteristic, complemented
13#20267876C211yesmaximal, characteristic, complemented
14#20267849C211yesmaximal, characteristic, complemented
15#485×C103C211yesmaximal, characteristic, complemented
16C22×D412C2211yescharacteristic
17C2×#13110094C2211yescharacteristic
18C2×#13110094C2211yescharacteristic
19C2×#13110092C2211yescharacteristic
20C2×#13110092C2211yescharacteristic
21#15693019C2211yescharacteristic, complemented
22#15693014—21no—
23#15693014—21no—
24#15693012—21no—
25#15693012C2211yescharacteristic, complemented
26#15693011—21no—
27#15693000C2211yescharacteristic
28Q8×Dic103C2211yescharacteristic, complemented
29#15692986C2211yescharacteristic, complemented
30C4×D412—21no—
31C4×D412—21no—
32#15692983C2211yescharacteristic
33#15692983C2211yescharacteristic
34#15692983C2211yescharacteristic
35#15692983C2211yescharacteristic
36#15692980C2211yescharacteristic
37C22⋊C4×D103—21no—
38C22⋊C4×D103—21no—
39#15692954C2211yescharacteristic, complemented
40#15692952C2211yescharacteristic, complemented
41Dic103⋊C8C2211yescharacteristic, complemented
42Dic103⋊C8C2211yescharacteristic, complemented
43#15692944C2211yescharacteristic, complemented
44#15692944C2211yescharacteristic, complemented
45#15692943C2211yescharacteristic
46#15692943C2211yescharacteristic
47#15692941C2211yescharacteristic
48#15692941C2211yescharacteristic
49C22⋊(C103⋊C8)C2211yescharacteristic
50#15692931C2211yescharacteristic, complemented
51C8×Dic103C2211yescharacteristic, complemented
52C22⋊Q8×C103C2211yescharacteristic
53#117×C103C2211yescharacteristic
54#107×C103C2211yescharacteristic, complemented
55#106×C103C2211yescharacteristic, complemented
56#103×C103C2211yescharacteristic, complemented
57#103×C103C2211yescharacteristic, complemented
58C22⋊C8×C103C2211yescharacteristic
59C23×D103—21no—
60C2×Dic206C2311yescharacteristic
61C2×D412—21no—
62C2×D412—22no—
63C2×D412—22no—
64C2×D412C2311yescharacteristic
65C2×D412C2311yescharacteristic
66C2×C4×D103—21no—
67C2×C4×D103—21no—
68C2×C4×D103—21no—
69C2×C4×D103—21no—
70#13110094—22no—
71#13110094—22no—
72#13110092—22no—
73#13110092—22no—
74C2×C103⋊C8C2311yescharacteristic
75C2×C103⋊C8C2311yescharacteristic
76C4⋊Dic103—21no—
77C4⋊Dic103—21no—
78C4⋊Dic103D411yescharacteristic
79C4⋊Dic103D411yescharacteristic
80C4⋊Dic103C2311yescharacteristic
81Dic103⋊C4—21no—
82Dic103⋊C4—21no—
83Dic103⋊C4—21no—
84Dic103⋊C4—21no—
85Dic103⋊C4—21no—
86C22⋊Dic103—21no—
87C22⋊Dic103D411yescharacteristic
88C22⋊Dic103D411yescharacteristic
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×Dic103C2311yescharacteristic
96C4×Dic103C2311yescharacteristic
97C2×Q8×C103C2311yescharacteristic
98C22×C4×C103C2311yescharacteristic
99C2×C8×C103C2311yescharacteristic
100C2×C8×C103C2311yescharacteristic
101C4⋊C4×C103—21no—
102C4⋊C4×C103C2311yescharacteristic
103C4⋊C4×C103C2311yescharacteristic
104C4⋊C4×C103C2311yescharacteristic
105C22⋊C4×C103—21no—
106C22⋊C4×C103—21no—
107C42×C103—21no—
108C23×C103C2×D411yescharacteristic
109C22×D103—21no—
110C22×D103—21no—
111C22×D103—24no—
112C22×D103—81no—
113C22×D103—81no—
114Q8×C103—21no—
115Q8×C103—21no—
116C2×C4×C103—21no—
117C2×C4×C103—21no—
118C2×C4×C103—21no—
119C2×C4×C103—21no—
120C2×C4×C103—21no—
121C2×C4×C103—21no—
122C2×C4×C103C2×D411yescharacteristic
123C2×C4×C103C2411yescharacteristic
124C2×Dic103—21no—
125C2×Dic103—21no—
126C2×Dic103C2×D411yescharacteristic
127C2×Dic103C2×D411yescharacteristic
128C2×Dic103C2×D411yescharacteristic
129C2×Dic103C2×D411yescharacteristic
130D412—24no—
131D412—21no—
132D412—21no—
133D412#4112yes—
134D412#4112yes—
135C4×D103—81no—
136C4×D103—81no—
137C4×D103—81no—
138C4×D103—81no—
139Dic206—21no—
140Dic206—21no—
141C8×C103—21no—
142C8×C103—21no—
143C103⋊C8—21no—
144C103⋊C8—21no—
145C22×C103—21no—
146C22×C103—21no—
147C22×C103—21no—
148C22×C103C22×D411yescharacteristic
149C2×D103—22no—
150C2×D103—22no—
151C2×D103—41no—
152C2×D103—41no—
153C2×D103—41no—
154C2×D103—41no—
155C2×D103—84no—
156C4×C103—21no—
157C4×C103—41no—
158C4×C103—41no—
159C4×C103—41no—
160C4×C103—41no—
161C4×C103C2×#4111yescharacteristic
162C4×C103C2×#4111yescharacteristic
163Dic103—21no—
164Dic103—21no—
165Dic103—21no—
166Dic103—21no—
167Dic103—41no—
168Dic103—41no—
169C2×C103—41no—
170C2×C103#52511yescharacteristic
171C2×C103#57711yescharacteristic
172C2×C103#57711yescharacteristic
173D103—42no—
174D103—42no—
175#3123—1031nomaximal, Sylow
176C103#312311yescharacteristic, complemented, Sylow
177#541—1031no—
178#518—1031no—
179#485—1031no—
180#485D10311yescharacteristic, complemented
181#478—1031no—
182#478—1031no—
183#461—1031no—
184#461—1031no—
185#450—1031no—
186#450—1031no—
187#440—1031no—
188#440—1031no—
189C4×SD16—1031no—
190C4×SD16—1031no—
191#433—1031no—
192C22×D4—1031no—
193C2×SD16—1031no—
194C2×SD16—1031no—
195C2×SD16—1031no—
196C2×SD16—1031no—
197C4⋊Q8—1031no—
198#126—2061no—
199#126—2061no—
200#125—1031no—
201#125—2061no—
202#125—2061no—
203C22⋊Q8—1031no—
204C22⋊Q8C2×D10311yescharacteristic
205C4×Q8—1031no—
206C4×Q8—1031no—
207C4×D4—1031no—
208C4×D4—1031no—
209C4×D4—1031no—
210C4×D4—1031no—
211C4×D4—2061no—
212C4×D4—2061no—
213#117—1031no—
214#117C2×D10311yescharacteristic
215C2×C22⋊C4—2061no—
216C2×C22⋊C4—2061no—
217#107—1031no—
218#107C2×D10311yescharacteristic, complemented
219#106—1031no—
220#106C2×D10311yescharacteristic, complemented
221C4⋊C8—1031no—
222C4⋊C8—1031no—
223#103—1031no—
224#103—1031no—
225#103C2×D10311yescharacteristic, complemented
226#103C2×D10311yescharacteristic, complemented
227#102—1031no—
228#102—1031no—
229#102—1031no—
230#102—1031no—
231C22⋊C8—1031no—
232C22⋊C8C2×D10311yescharacteristic
233#97—1031no—
234C4×C8—1031no—
235C24—2061no—
236C2×Q8—1031no—
237C2×Q8C22×D10311yescharacteristic
238C2×D4—1031no—
239C2×D4—1031no—
240C2×D4—2062no—
241C2×D4—2062no—
242C2×D4—2061no—
243C22×C4—2061no—
244C22×C4—2061no—
245C22×C4—2061no—
246C22×C4—2061no—
247C22×C4C22×D10311yescharacteristic
248SD16—2062no—
249SD16—2062no—
250SD16—2062no—
251SD16—2062no—
252C2×C8—1031no—
253C2×C8—1031no—
254C2×C8C22×D10311yescharacteristic
255C2×C8C22×D10311yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—1031no—
258C4⋊C4—1031no—
259C4⋊C4—1031no—
260C4⋊C4—2061no—
261C4⋊C4—2061no—
262C4⋊C4—2061no—
263C4⋊C4—2061no—
264C4⋊C4—2061no—
265C4⋊C4—2061no—
266C4⋊C4—2061no—
267C4⋊C4C22×D10311yescharacteristic
268C4⋊C4C22×D10311yescharacteristic
269C4⋊C4C22×D10311yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—1031no—
273C22⋊C4—1031no—
274C22⋊C4—2061no—
275C22⋊C4—2061no—
276C22⋊C4—2061no—
277C22⋊C4—2061no—
278C22⋊C4—2061no—
279C42—21no—
280C42—1031no—
281C42—1031no—
282C42—2061no—
283C42—2061no—
284C23—8241no—
285C23—8241no—
286C23—2064no—
287C23—2061no—
288C23—2061no—
289C23D4×D10311yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—2061no—
293Q8—2061no—
294D4—1032no—
295D4—1032no—
296D4—2064no—
297D4—2061no—
298D4—2061no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—8241no—
306C2×C4—8241no—
307C2×C4—8241no—
308C2×C4—8241no—
309C2×C4—1031no—
310C2×C4—1031no—
311C2×C4—1031no—
312C2×C4—1031no—
313C2×C4—2061no—
314C2×C4—2061no—
315C2×C4D4×D10311yescharacteristic
316C2×C4C23×D10311yescharacteristic
317C8—21no—
318C8—21no—
319C8—2061no—
320C8—2061no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—8244no—
325C22—4121no—
326C22—4121no—
327C22—4121no—
328C22—4121no—
329C22—2062no—
330C22—2062no—
331C22C2×D4×D10311yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—4121no—
338C4—4121no—
339C4—2061no—
340C4—2061no—
341C4—2061no—
342C4—2061no—
343C4#41×D10311yescharacteristic
344C4#41×D10311yescharacteristic
345C2—41no—
346C2—4122no—
347C2—4122no—
348C2#2026829911yescharacteristic
349C2#2026859811yescharacteristic
350C2#2026860011yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#485×C103C2
socleC22×C103C22×D4
prime radicalC22×D412C22
hypercenter#485D103
hypocenterC103#3123
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #20268401C2semidirect
3. #20268132C2semidirect
4. #20268094C2semidirect
5. #20268090C2semidirect
6. #20267995C2semidirect
7. #20267995C2semidirect
10. #20267894C2semidirect
11. #20267890C2semidirect
12. #20267878C2semidirect
13. #20267876C2semidirect
14. #20267849C2semidirect
15. #485×C103C2semidirect
21. #15693019C22semidirect
25. #15693012C22semidirect
28. Q8×Dic103C22semidirect
29. #15692986C22semidirect
39. #15692954C22semidirect
40. #15692952C22semidirect
41. Dic103⋊C8C22semidirect
42. Dic103⋊C8C22semidirect
43. #15692944C22semidirect
44. #15692944C22semidirect
50. #15692931C22semidirect
51. C8×Dic103C22semidirect
54. #107×C103C22semidirect
55. #106×C103C22semidirect
56. #103×C103C22semidirect
57. #103×C103C22semidirect
176. C103#3123semidirect
180. #485D103semidirect
218. #107C2×D103semidirect
220. #106C2×D103semidirect
225. #103C2×D103semidirect
226. #103C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202684012
#202682652
#202681322
#202680942
#202680902
#202679952
#202679442
#202679412
#202678942
#202678902
#202678782
#202678762
#202678492
#485×C1032
#3123103