Finite Group Databasebeta

← #27204930

Subgroups — #27204930

Order 13184.

388 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268344C211yesmaximal, characteristic, complemented
2#20268259C211yesmaximal, characteristic
3#20268101C211yesmaximal, characteristic, complemented
4#20268097C211yesmaximal, characteristic, complemented
5#20268094C211yesmaximal, characteristic, complemented
6#20268090C211yesmaximal, characteristic, complemented
7#20268085C211yesmaximal, characteristic, complemented
8#20268080C211yesmaximal, characteristic, complemented
9#20268075C211yesmaximal, characteristic, complemented
10#20268070C211yesmaximal, characteristic, complemented
11#20267827C211yesmaximal, characteristic, complemented
12C2×Dic103⋊C8C211yesmaximal, characteristic, complemented
13#20267788C211yesmaximal, characteristic
14#20267785C211yesmaximal, characteristic
15#427×C103C211yesmaximal, characteristic, complemented
16C2×#13110105C2211yescharacteristic
17C22×C103⋊C8C2211yescharacteristic
18#15693020C2211yescharacteristic
19#15693020C2211yescharacteristic
20#15693012C2211yescharacteristic
21#15693012C2211yescharacteristic
22#15692998—21no—
23#15692998—21no—
24C4×Dic206—21no—
25C4×Dic206—21no—
26#15692986C2211yescharacteristic
27#15692986C2211yescharacteristic
28#15692983C2211yescharacteristic
29#15692983C2211yescharacteristic
30(C22⋊D103)⋊C4—21no—
31(C22⋊D103)⋊C4—21no—
32#15692980C2211yescharacteristic
33#15692978—21no—
34C2×C4×Dic103C2211yescharacteristic
35C42×D103—21no—
36#15692954C2211yescharacteristic
37#15692954C2211yescharacteristic
38#15692952C2211yescharacteristic
39#15692952C2211yescharacteristic
40Dic103⋊C8C2211yescharacteristic
41Dic103⋊C8C2211yescharacteristic
42Dic103⋊C8C2211yescharacteristic
43Dic103⋊C8C2211yescharacteristic
44#15692946C2211yescharacteristic
45#15692946C2211yescharacteristic
46#15692944C2211yescharacteristic
47#15692944C2211yescharacteristic
48#15692943C2211yescharacteristic
49#15692943C2211yescharacteristic
50#15692941C2211yescharacteristic
51#15692941C2211yescharacteristic
52C22×C8×C103C2211yescharacteristic
53#117×C103C2211yescharacteristic
54#117×C103C2211yescharacteristic
55#107×C103C2211yescharacteristic
56#107×C103C2211yescharacteristic
57#106×C103C2211yescharacteristic
58#106×C103C2211yescharacteristic
59#13110105—22no—
60#13110105Q814yescomplemented
61C2×Dic206—21no—
62C2×Dic206—21no—
63C2×Dic206C2311yescharacteristic
64C2×D412C2311yescharacteristic
65C2×C22⋊D103—21no—
66C22×Dic103D411yescharacteristic
67C22×Dic103D411yescharacteristic
68C2×C4×D103—21no—
69C2×C4×D103—21no—
70C2×C4×D103—21no—
71C2×C103⋊C8—22no—
72C2×C103⋊C8C2311yescharacteristic
73C2×C103⋊C8C2311yescharacteristic
74C4⋊Dic103—21no—
75C4⋊Dic103—21no—
76C4⋊Dic103C2311yescharacteristic
77C4⋊Dic103C2311yescharacteristic
78Dic103⋊C4—21no—
79Dic103⋊C4—21no—
80Dic103⋊C4—21no—
81Dic103⋊C4—21no—
82Dic103⋊C4—21no—
83Dic103⋊C4—21no—
84C22⋊Dic103—21no—
85(C2×D103)⋊C4—21no—
86(C2×D103)⋊C4—21no—
87C4×Dic103—21no—
88C4×Dic103—21no—
89C4×Dic103—21no—
90C4×Dic103D411yescharacteristic
91C4×Dic103D411yescharacteristic
92C4×Dic103C2311yescharacteristic
93C4×Dic103C2311yescharacteristic
94C22×C4×C103C2311yescharacteristic
95C2×C8×C103—22no—
96C2×C8×C103C2311yescharacteristic
97C2×C8×C103C2311yescharacteristic
98C4⋊C4×C103C2311yescharacteristic
99C4⋊C4×C103C2311yescharacteristic
100C4⋊C4×C103C2311yescharacteristic
101C4⋊C4×C103C2311yescharacteristic
102C22⋊C4×C103—21no—
103C22⋊C4×C103—21no—
104C42×C103—21no—
105C42×C103—21no—
106C23×C103C2×D411yescharacteristic
107C22×D103—21no—
108C2×C4×C103—21no—
109C2×C4×C103—21no—
110C2×C4×C103—21no—
111C2×C4×C103—21no—
112C2×C4×C103C2×D411yescharacteristic
113C2×C4×C103C2×Q812yes—
114C2×C4×C103#4112yes—
115C2×C4×C103C2411yescharacteristic
116C22⋊D103—24no—
117C2×Dic103—21no—
118C2×Dic103—22no—
119C2×Dic103—21no—
120C2×Dic103—21no—
121C2×Dic103—41no—
122C2×Dic103C2×D411yescharacteristic
123C2×Dic103C2×D411yescharacteristic
124C2×Dic103C2×D411yescharacteristic
125C2×Dic103C2×D411yescharacteristic
126D412—21no—
127D412C2×Q812yes—
128C4×D103—24no—
129C4×D103—42no—
130C4×D103—42no—
131Dic206—21no—
132Dic206—42no—
133Dic206—42no—
134Dic206C2×Q812yes—
135C8×C103—21no—
136C8×C103—21no—
137C103⋊C8—21no—
138C103⋊C8—21no—
139C22×C103—21no—
140C22×C103—21no—
141C22×C103C22⋊Q812yes—
142C22×C103C22×D411yescharacteristic
143C2×D103—22no—
144C2×D103—41no—
145C2×D103—41no—
146C4×C103—41no—
147C4×C103—41no—
148C4×C103—41no—
149C4×C103—41no—
150C4×C103C22⋊Q812yes—
151C4×C103C22×Q811yescharacteristic
152C4×C103C2×#4111yescharacteristic
153Dic103—22no—
154Dic103—21no—
155Dic103—21no—
156Dic103—21no—
157Dic103—41no—
158Dic103—41no—
159Dic103#13512yes—
160C2×C103—22no—
161C2×C103C2×C22⋊Q811yescharacteristic
162C2×C103C2×#13511yescharacteristic
163C2×C103#57511yescharacteristic
164D103—42no—
165#3076—1031nomaximal, Sylow
166C103#307611yescharacteristic, complemented, Sylow
167#533—1031no—
168C4×#41—1031no—
169#479—1031no—
170#479—1031no—
171#478—1031no—
172#478—1031no—
173#477—1031no—
174#476—1031no—
175#475—1031no—
176#474—1031no—
177#427—1031no—
178#427D10311yescharacteristic, complemented
179C2×C4⋊C8—1031no—
180#416—1031no—
181#416—1031no—
182C2×#41—1031no—
183C22×C8—1031no—
184C22×C8C2×D10311yescharacteristic
185C4⋊Q8—1031no—
186C4⋊Q8—1031no—
187#125—1031no—
188#125—1031no—
189C22⋊Q8—2061no—
190C22⋊Q8—2061no—
191C4×Q8—1031no—
192C4×Q8—1031no—
193C4×Q8—2061no—
194C4×Q8—2061no—
195C4×D4—1031no—
196C4×D4—1031no—
197C4×D4—2061no—
198C4×D4—2061no—
199#117—1031no—
200#117—2061no—
201#117C2×D10311yescharacteristic
202#117C2×D10311yescharacteristic
203C2×C42—1031no—
204C2×C42—2061no—
205#107—1031no—
206#107—1031no—
207#107C2×D10311yescharacteristic
208#107C2×D10311yescharacteristic
209#106—1031no—
210#106—1031no—
211#106C2×D10311yescharacteristic
212#106C2×D10311yescharacteristic
213C4⋊C8—1031no—
214C4⋊C8—1031no—
215C4⋊C8—1031no—
216C4⋊C8—1031no—
217#103—1031no—
218#103—1031no—
219#103—1031no—
220#103—1031no—
221#102—1031no—
222#102—1031no—
223#102—1031no—
224#102—1031no—
225#41—1034no—
226#41—2062no—
227C2×Q8—1031no—
228C2×Q8—2061no—
229C2×Q8—2061no—
230C2×D4—1031no—
231C2×D4—2061no—
232C22×C4—1031no—
233C22×C4—1031no—
234C22×C4—2061no—
235C22×C4—2061no—
236C22×C4—2061no—
237C22×C4C22×D10311yescharacteristic
238C2×C8—22no—
239C2×C8—1031no—
240C2×C8—1031no—
241C2×C8—2062no—
242C2×C8C22×D10311yescharacteristic
243C2×C8C22×D10311yescharacteristic
244C4⋊C4—1031no—
245C4⋊C4—1031no—
246C4⋊C4—2061no—
247C4⋊C4—2061no—
248C4⋊C4—2061no—
249C4⋊C4—2061no—
250C4⋊C4—2061no—
251C4⋊C4—2061no—
252C4⋊C4—2061no—
253C4⋊C4—2061no—
254C4⋊C4C22×D10311yescharacteristic
255C4⋊C4C22×D10311yescharacteristic
256C4⋊C4C22×D10311yescharacteristic
257C4⋊C4C22×D10311yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—2061no—
261C22⋊C4—2061no—
262C22⋊C4—2061no—
263C42—21no—
264C42—21no—
265C42—1031no—
266C42—1031no—
267C42—1031no—
268C42—1031no—
269C42—2061no—
270C42—2061no—
271C42—2061no—
272C23—2061no—
273C23D4×D10311yescharacteristic
274Q8—1032no—
275Q8—4122no—
276Q8—4122no—
277Q8—2061no—
278D4—1032no—
279D4—2064no—
280D4—2061no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—1031no—
286C2×C4—1031no—
287C2×C4—1031no—
288C2×C4—1031no—
289C2×C4—4122no—
290C2×C4—4122no—
291C2×C4—4121no—
292C2×C4—2062no—
293C2×C4—2061no—
294C2×C4—2061no—
295C2×C4—2061no—
296C2×C4—2064no—
297C2×C4D4×D10311yescharacteristic
298C2×C4Q8×D10312yes—
299C2×C4#1311010512yes—
300C2×C4C23×D10311yescharacteristic
301C8—21no—
302C8—21no—
303C8—2061no—
304C8—2061no—
305C22—21no—
306C22—21no—
307C22—4121no—
308C22—4121no—
309C22—2062no—
310C22#1569299912yes—
311C22C2×D4×D10311yescharacteristic
312C4—41no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—1032no—
317C4—4121no—
318C4—4121no—
319C4—2062no—
320C4—2061no—
321C4—2061no—
322C4—2061no—
323C4#1569299912yes—
324C4C2×Q8×D10311yescharacteristic
325C4C2×#1311010511yescharacteristic
326C2—22no—
327C2—4122no—
328C2C2×#1569299911yescharacteristic
329C2#135×D10311yescharacteristic
330C2#2026858811yescharacteristic
subgroupG/H
centerC2×C4D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#427×C103C2
socleC22×C103C22×D4
prime radicalC2×#13110105C22
hypercenter#427D103
hypocenterC103#3076
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
1. #20268344C2semidirect
3. #20268101C2semidirect
4. #20268097C2semidirect
5. #20268094C2semidirect
6. #20268090C2semidirect
7. #20268085C2semidirect
8. #20268080C2semidirect
9. #20268075C2semidirect
10. #20268070C2semidirect
11. #20267827C2semidirect
12. C2×Dic103⋊C8C2semidirect
15. #427×C103C2semidirect
60. #13110105Q8semidirect
166. C103#3076semidirect
178. #427D103semidirect

Maximal subgroups

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

subgroupindex
#202683442
#202682592
#202681012
#202680972
#202680942
#202680902
#202680852
#202680802
#202680752
#202680702
#202678272
C2×Dic103⋊C82
#202677882
#202677852
#427×C1032
#3076103