Finite Group Databasebeta

← #27205398

Subgroups — #27205398

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#20268404C211yesmaximal, characteristic, complemented
2#20268263C211yesmaximal, characteristic
3#20268135C211yesmaximal, characteristic, complemented
4#20268134C211yesmaximal, characteristic, complemented
5#20268088C211yesmaximal, characteristic, complemented
6#20267997C211yesmaximal, characteristic, complemented
7#20267996C211yesmaximal, characteristic, complemented
8#20267943C211yesmaximal, characteristic
9#20267943C211yesmaximal, characteristic
10#20267890C211yesmaximal, characteristic, complemented
11#20267888C211yesmaximal, characteristic, complemented
12#20267882C211yesmaximal, characteristic, complemented
13#20267878C211yesmaximal, characteristic, complemented
14#20267851C211yesmaximal, characteristic, complemented
15#478×C103C211yesmaximal, characteristic, complemented
16C2×D4×D103C2211yescharacteristic
17C2×#13110094C2211yescharacteristic
18C2×#13110094C2211yescharacteristic
19C2×#13110093C2211yescharacteristic
20C2×#13110093C2211yescharacteristic
21#15693021C2211yescharacteristic, complemented
22#15693016—21no—
23#15693016—21no—
24#15693012—21no—
25#15693012—21no—
26#15693001C2211yescharacteristic
27#15693001C2211yescharacteristic
28#15692986C2211yescharacteristic, complemented
29#15692986C2211yescharacteristic, complemented
30C4×D412C2211yescharacteristic
31D4×Dic103C2211yescharacteristic
32#15692983C2211yescharacteristic
33C4×C22⋊D103—21no—
34(C22⋊D103)⋊C4—21no—
35#15692979C2211yescharacteristic
36#15692978C2211yescharacteristic
37C2×(C2×D103)⋊C4—21no—
38C22⋊C4×D103—21no—
39#15692954C2211yescharacteristic, complemented
40#15692952C2211yescharacteristic, complemented
41C4⋊(C103⋊C8)C2211yescharacteristic, complemented
42#15692946C2211yescharacteristic, complemented
43#15692946C2211yescharacteristic, complemented
44#15692944C2211yescharacteristic, complemented
45#15692944C2211yescharacteristic, complemented
46#15692941C2211yescharacteristic
47#15692941C2211yescharacteristic
48(C2×D103)⋊C8C2211yescharacteristic
49(C2×D103)⋊C8C2211yescharacteristic
50#15692931C2211yescharacteristic, complemented
51C8×Dic103C2211yescharacteristic, complemented
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×Dic206C2311yescharacteristic
61C2×Dic206C2311yescharacteristic
62C2×D412C2311yescharacteristic
63C2×C22⋊D103—21no—
64D4×D103—22no—
65D4×D103—22no—
66C22×Dic103—21no—
67C2×C4×D103—21no—
68C2×C4×D103—21no—
69C2×C4×D103C2311yescharacteristic
70#13110094—22no—
71#13110094—22no—
72#13110093—22no—
73#13110093—22no—
74C2×C103⋊C8C2311yescharacteristic
75C2×C103⋊C8C2311yescharacteristic
76C4⋊Dic103—21no—
77C4⋊Dic103—21no—
78C4⋊Dic103—21no—
79C4⋊Dic103—21no—
80C4⋊Dic103C2311yescharacteristic
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)⋊C4—21no—
91(C2×D103)⋊C4D411yescharacteristic
92(C2×D103)⋊C4D411yescharacteristic
93C4×Dic103—21no—
94C4×Dic103—21no—
95C4×Dic103—21no—
96C4×Dic103C2311yescharacteristic
97C2×D4×C103C2311yescharacteristic
98C22×C4×C103—21no—
99C2×C8×C103C2311yescharacteristic
100C2×C8×C103C2311yescharacteristic
101C4⋊C4×C103—21no—
102C4⋊C4×C103—21no—
103C4⋊C4×C103C2311yescharacteristic
104C4⋊C4×C103C2311yescharacteristic
105C4⋊C4×C103C2311yescharacteristic
106C22⋊C4×C103—21no—
107C42×C103C2311yescharacteristic
108C23×C103—21no—
109C22×D103—21no—
110C22×D103—24no—
111C22×D103—81no—
112C22×D103—81no—
113C22×D103C2×D411yescharacteristic
114D4×C103—21no—
115D4×C103#4112yes—
116C2×C4×C103—21no—
117C2×C4×C103—21no—
118C2×C4×C103—21no—
119C2×C4×C103—81no—
120C2×C4×C103C2×D411yescharacteristic
121C2×C4×C103C2×D411yescharacteristic
122C2×C4×C103C2411yescharacteristic
123C22⋊D103—24no—
124C2×Dic103—21no—
125C2×Dic103—21no—
126C2×Dic103—21no—
127C2×Dic103—81no—
128C2×Dic103C2×D411yescharacteristic
129C2×Dic103C2×D411yescharacteristic
130C2×Dic103C2×D411yescharacteristic
131D412—21no—
132D412#4112yes—
133C4×D103—21no—
134C4×D103—21no—
135C4×D103—81no—
136C4×D103—81no—
137Dic206—21no—
138Dic206—21no—
139Dic206—21no—
140Dic206—21no—
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—22no—
151C2×D103—21no—
152C2×D103—21no—
153C2×D103—41no—
154C2×D103—41no—
155C2×D103—84no—
156C4×C103—21no—
157C4×C103—21no—
158C4×C103—41no—
159C4×C103—41no—
160C4×C103—41no—
161C4×C103C2×#4111yescharacteristic
162C4×C103C2×#4111yescharacteristic
163Dic103—21no—
164Dic103—21no—
165Dic103—21no—
166Dic103—41no—
167Dic103—41no—
168Dic103—41no—
169C2×C103—42no—
170C2×C103#52511yescharacteristic
171C2×C103#57711yescharacteristic
172C2×C103#57711yescharacteristic
173D103—41no—
174D103—42no—
175#3123—1031nomaximal, Sylow
176C103#312311yescharacteristic, complemented, Sylow
177#541—1031no—
178#518—1031no—
179#485—1031no—
180#485—1031no—
181#478—1031no—
182#478D10311yescharacteristic, complemented
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—2061no—
201#125—2061no—
202#125C2×D10311yescharacteristic, complemented
203C22⋊Q8—1031no—
204C22⋊Q8—1031no—
205C4×Q8—1031no—
206C4×Q8—1031no—
207C4×D4—1031no—
208C4×D4—1031no—
209C4×D4—1031no—
210C4×D4—2061no—
211C4×D4—2061no—
212C4×D4C2×D10311yescharacteristic
213#117—1031no—
214#117—1031no—
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⋊C8C2×D10311yescharacteristic, complemented
223#103—1031no—
224#103—1031no—
225#103—1031no—
226#103—1031no—
227#102—1031no—
228#102—1031no—
229#102C2×D10311yescharacteristic
230#102C2×D10311yescharacteristic
231C22⋊C8—1031no—
232C22⋊C8—1031no—
233#97—1031no—
234C4×C8—1031no—
235C24—2061no—
236C2×Q8—1031no—
237C2×Q8—1031no—
238C2×D4—1031no—
239C2×D4—2061no—
240C2×D4—2062no—
241C2×D4—2062no—
242C2×D4C22×D10311yescharacteristic
243C22×C4—21no—
244C22×C4—1031no—
245C22×C4—2061no—
246C22×C4—2061no—
247C22×C4—2061no—
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—21no—
258C4⋊C4—1031no—
259C4⋊C4—1031no—
260C4⋊C4—1031no—
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—1031no—
272C22⋊C4—1031no—
273C22⋊C4—2061no—
274C22⋊C4—2061no—
275C22⋊C4—2061no—
276C22⋊C4—2061no—
277C22⋊C4—2061no—
278C22⋊C4—2061no—
279C42—1031no—
280C42—2061no—
281C42—2061no—
282C42—2061no—
283C42C22×D10311yescharacteristic
284C23—21no—
285C23—8241no—
286C23—8241no—
287C23—1031no—
288C23—2064no—
289C23—2061no—
290Q8—2061no—
291Q8—2061no—
292Q8—2061no—
293Q8—2061no—
294D4—21no—
295D4—1032no—
296D4—2064no—
297D4—2061no—
298D4#1311010612yes—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—8241no—
304C2×C4—8241no—
305C2×C4—8241no—
306C2×C4—1031no—
307C2×C4—1031no—
308C2×C4—1031no—
309C2×C4—2061no—
310C2×C4—2061no—
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—8244no—
325C22—4121no—
326C22—4121no—
327C22—2061no—
328C22—2062no—
329C22—2061no—
330C22—2061no—
331C22C2×D4×D10311yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—4121no—
338C4—4121no—
339C4—4121no—
340C4—2061no—
341C4—2061no—
342C4—2061no—
343C4#41×D10311yescharacteristic
344C4C2×#1311010611yescharacteristic
345C2—42no—
346C2—4121no—
347C2—4122no—
348C2#2026830411yescharacteristic
349C2#2026859811yescharacteristic
350C2#2026860111yescharacteristic
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#3123
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. #20268404C2semidirect
3. #20268135C2semidirect
4. #20268134C2semidirect
5. #20268088C2semidirect
6. #20267997C2semidirect
7. #20267996C2semidirect
10. #20267890C2semidirect
11. #20267888C2semidirect
12. #20267882C2semidirect
13. #20267878C2semidirect
14. #20267851C2semidirect
15. #478×C103C2semidirect
21. #15693021C22semidirect
28. #15692986C22semidirect
29. #15692986C22semidirect
39. #15692954C22semidirect
40. #15692952C22semidirect
41. C4⋊(C103⋊C8)C22semidirect
42. #15692946C22semidirect
43. #15692946C22semidirect
44. #15692944C22semidirect
45. #15692944C22semidirect
50. #15692931C22semidirect
51. C8×Dic103C22semidirect
52. #125×C103C22semidirect
54. #107×C103C22semidirect
55. #106×C103C22semidirect
56. C4⋊C8×C103C22semidirect
176. C103#3123semidirect
182. #478D103semidirect
202. #125C2×D103semidirect
218. #107C2×D103semidirect
220. #106C2×D103semidirect
222. C4⋊C8C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202684042
#202682632
#202681352
#202681342
#202680882
#202679972
#202679962
#202679432
#202678902
#202678882
#202678822
#202678782
#202678512
#478×C1032
#3123103