Finite Group Databasebeta

← #27204961

Subgroups — #27204961

Order 13184.

384 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#125×D103C211yesmaximal, characteristic, complemented
2C4×#13110104C211yesmaximal, characteristic
3#20268101C211yesmaximal, characteristic, complemented
4#20268099C211yesmaximal, characteristic, complemented
5#20268097C211yesmaximal, characteristic, complemented
6#20268095C211yesmaximal, characteristic, complemented
7#20268093C211yesmaximal, characteristic, complemented
8#20268091C211yesmaximal, characteristic, complemented
9#20268089C211yesmaximal, characteristic, complemented
10#20267832C211yesmaximal, characteristic, complemented
11#20267830C211yesmaximal, characteristic, complemented
12#20267813C211yesmaximal, characteristic, complemented
13#20267789C211yesmaximal, characteristic
14#20267789C211yesmaximal, characteristic
15#478×C103C211yesmaximal, characteristic, complemented
16C2×#13110104C2211yescharacteristic
17C2×#13110088C2211yescharacteristic
18C2×#13110088C2211yescharacteristic
19#15693013C2211yescharacteristic
20#15693012C2211yescharacteristic
21#15693012C2211yescharacteristic
22#15693011—21no—
23#15693011—21no—
24C4×Dic206C2211yescharacteristic
25#15692986C2211yescharacteristic
26D4×Dic103C2211yescharacteristic
27C4×C22⋊D103—21no—
28(C22⋊D103)⋊C4—21no—
29#15692979C2211yescharacteristic
30#15692977—21no—
31C4⋊C4×D103—21no—
32C4⋊C4×D103—21no—
33C4⋊C4×D103C2211yescharacteristic
34C4⋊C4×D103C2211yescharacteristic
35C2×C4×Dic103—21no—
36C42×D103C2211yescharacteristic
37#15692955C2211yescharacteristic
38#15692954C2211yescharacteristic
39#15692954C2211yescharacteristic
40#15692953C2211yescharacteristic
41#15692952C2211yescharacteristic
42#15692952C2211yescharacteristic
43C4⋊(C103⋊C8)C2211yescharacteristic
44Dic103⋊C8C2211yescharacteristic
45Dic103⋊C8C2211yescharacteristic
46#15692946C2211yescharacteristic
47#15692946C2211yescharacteristic
48#15692944C2211yescharacteristic
49#15692944C2211yescharacteristic
50#15692942C2211yescharacteristic
51#15692942C2211yescharacteristic
52#125×C103C2211yescharacteristic
53C4×D4×C103C2211yescharacteristic
54#107×C103C2211yescharacteristic
55#106×C103C2211yescharacteristic
56C4⋊C8×C103C2211yescharacteristic
57#102×C103C2211yescharacteristic
58#102×C103C2211yescharacteristic
59#13110104—22no—
60#13110104Q814yes—
61C2×Dic206C2311yescharacteristic
62C2×C22⋊D103—21no—
63C22×Dic103—21no—
64C22×Dic103—21no—
65C2×C4×D103—21no—
66C2×C4×D103—21no—
67C2×C4×D103D411yescharacteristic
68C2×C4×D103D411yescharacteristic
69C2×C4×D103C2311yescharacteristic
70#13110088—22no—
71#13110088—22no—
72C2×C103⋊C8C2311yescharacteristic
73C2×C103⋊C8C2311yescharacteristic
74C4⋊Dic103—21no—
75C4⋊Dic103—21no—
76C4⋊Dic103C2311yescharacteristic
77C4⋊Dic103C2311yescharacteristic
78C4⋊Dic103C2311yescharacteristic
79Dic103⋊C4—21no—
80Dic103⋊C4—21no—
81Dic103⋊C4—21no—
82Dic103⋊C4—21no—
83Dic103⋊C4—21no—
84Dic103⋊C4—21no—
85Dic103⋊C4—21no—
86Dic103⋊C4—21no—
87C22⋊Dic103—21no—
88(C2×D103)⋊C4—21no—
89C4×Dic103—21no—
90C4×Dic103—21no—
91C4×Dic103—21no—
92C4×Dic103D411yescharacteristic
93C4×Dic103D411yescharacteristic
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×D103C2×D411yescharacteristic
108D4×C103—21no—
109D4×C103C2×Q812yes—
110C2×C4×C103—21no—
111C2×C4×C103—21no—
112C2×C4×C103—21no—
113C2×C4×C103—42no—
114C2×C4×C103C2×D411yescharacteristic
115C2×C4×C103C2×D411yescharacteristic
116C2×C4×C103C2411yescharacteristic
117C22⋊D103—24no—
118C2×Dic103—21no—
119C2×Dic103—24no—
120C2×Dic103—21no—
121C2×Dic103—21no—
122C2×Dic103—21no—
123C2×Dic103—42no—
124C2×Dic103C2×D411yescharacteristic
125C2×Dic103C2×D411yescharacteristic
126C2×Dic103C2×D411yescharacteristic
127C4×D103—41no—
128C4×D103—41no—
129C4×D103—42no—
130C4×D103—42no—
131C4×D103C2×Q812yes—
132C4×D103#4112yes—
133Dic206—21no—
134Dic206C2×Q812yes—
135C8×C103—21no—
136C8×C103—21no—
137C103⋊C8—21no—
138C103⋊C8—21no—
139C22×C103—22no—
140C22×C103—41no—
141C22×C103—41no—
142C22×C103C22×D411yescharacteristic
143C2×D103—21no—
144C2×D103—21no—
145C2×D103C22⋊Q812yes—
146C4×C103—21no—
147C4×C103—21no—
148C4×C103—41no—
149C4×C103—41no—
150C4×C103—41no—
151C4×C103C22×Q811yescharacteristic
152C4×C103C2×#4111yescharacteristic
153Dic103—22no—
154Dic103—21no—
155Dic103—21no—
156Dic103—41no—
157Dic103—41no—
158Dic103—41no—
159Dic103C22⋊Q812yes—
160C2×C103—42no—
161C2×C103C2×C22⋊Q811yescharacteristic
162C2×C103#57511yescharacteristic
163C2×C103#57511yescharacteristic
164D103—22no—
165#3080—1031nomaximal, Sylow
166C103#308011yescharacteristic, complemented, Sylow
167C2×#125—1031no—
168C4×#41—1031no—
169#479—1031no—
170#479—1031no—
171#479—1031no—
172#479—1031no—
173#478—1031no—
174#478—1031no—
175#478—1031no—
176#478D10311yescharacteristic, complemented
177#428—1031no—
178#428—1031no—
179#423—1031no—
180#417—1031no—
181#417—1031no—
182C2×#41—1031no—
183C2×M16—1031no—
184C2×M16—1031no—
185#125—1031no—
186#125—1031no—
187#125—1031no—
188#125—2061no—
189#125—2061no—
190#125C2×D10311yescharacteristic
191C4×Q8—1031no—
192C4×Q8—1031no—
193C4×D4—1031no—
194C4×D4—2061no—
195C4×D4—2061no—
196C4×D4C2×D10311yescharacteristic
197#117—1031no—
198#117—2061no—
199C2×C4⋊C4—1031no—
200C2×C4⋊C4—1031no—
201C2×C4⋊C4—2061no—
202C2×C4⋊C4—2061no—
203C2×C42—1031no—
204C2×C42—2061no—
205#107—1031no—
206#107—1031no—
207#107—1031no—
208#107C2×D10311yescharacteristic
209#106—1031no—
210#106—1031no—
211#106—1031no—
212#106C2×D10311yescharacteristic
213C4⋊C8—1031no—
214C4⋊C8—1031no—
215C4⋊C8—1031no—
216C4⋊C8C2×D10311yescharacteristic
217#103—1031no—
218#103—1031no—
219#103—1031no—
220#103—1031no—
221#102—1031no—
222#102—1031no—
223#102C2×D10311yescharacteristic
224#102C2×D10311yescharacteristic
225#41—1034no—
226#41—2062no—
227C2×Q8—1031no—
228C2×D4—2061no—
229C2×D4C22×D10311yescharacteristic
230C22×C4—21no—
231C22×C4—1031no—
232C22×C4—1031no—
233C22×C4—1031no—
234C22×C4—2061no—
235C22×C4—2061no—
236C22×C4—2061no—
237C22×C4—2061no—
238M16—2062no—
239M16—2062no—
240C2×C8—1031no—
241C2×C8—1031no—
242C2×C8C22×D10311yescharacteristic
243C2×C8C22×D10311yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—1031no—
247C4⋊C4—1031no—
248C4⋊C4—1031no—
249C4⋊C4—2061no—
250C4⋊C4—2061no—
251C4⋊C4—2061no—
252C4⋊C4—2061no—
253C4⋊C4—2061no—
254C4⋊C4—2061no—
255C4⋊C4—2061no—
256C4⋊C4—2061no—
257C4⋊C4—2061no—
258C4⋊C4—2061no—
259C4⋊C4C22×D10311yescharacteristic
260C4⋊C4C22×D10311yescharacteristic
261C4⋊C4C22×D10311yescharacteristic
262C22⋊C4—21no—
263C22⋊C4—2061no—
264C22⋊C4—2061no—
265C42—1031no—
266C42—1031no—
267C42—1031no—
268C42—2061no—
269C42—2061no—
270C42—2061no—
271C42C22×D10311yescharacteristic
272C23—21no—
273C23—1031no—
274Q8—1032no—
275Q8—2061no—
276D4—21no—
277D4—2064no—
278D4Q8×D10312yes—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—42no—
283C2×C4—1031no—
284C2×C4—1032no—
285C2×C4—1032no—
286C2×C4—1031no—
287C2×C4—1031no—
288C2×C4—4121no—
289C2×C4—4121no—
290C2×C4—4122no—
291C2×C4—4122no—
292C2×C4—4122no—
293C2×C4—2064no—
294C2×C4—2061no—
295C2×C4—2061no—
296C2×C4—2061no—
297C2×C4—2061no—
298C2×C4D4×D10311yescharacteristic
299C2×C4D4×D10311yescharacteristic
300C2×C4C23×D10311yescharacteristic
301C8—21no—
302C8—21no—
303C8—2061no—
304C8—2061no—
305C22—22no—
306C22—41no—
307C22—41no—
308C22—1032no—
309C22—2061no—
310C22—2061no—
311C22C2×D4×D10311yescharacteristic
312C4—21no—
313C4—21no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—1032no—
318C4—4121no—
319C4—4121no—
320C4—4121no—
321C4—2061no—
322C4—2061no—
323C4—2062no—
324C4C2×Q8×D10311yescharacteristic
325C4#41×D10311yescharacteristic
326C2—42no—
327C2—2062no—
328C2C22⋊Q8×D10311yescharacteristic
329C2#2026858711yescharacteristic
330C2#2026858811yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#478×C103C2
socleC22×C103C22×D4
prime radicalC2×#13110104C22
hypercenter#478D103
hypocenterC103#3080
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. #125×D103C2semidirect
3. #20268101C2semidirect
4. #20268099C2semidirect
5. #20268097C2semidirect
6. #20268095C2semidirect
7. #20268093C2semidirect
8. #20268091C2semidirect
9. #20268089C2semidirect
10. #20267832C2semidirect
11. #20267830C2semidirect
12. #20267813C2semidirect
15. #478×C103C2semidirect
166. C103#3080semidirect
176. #478D103semidirect

Maximal subgroups

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

subgroupindex
#125×D1032
C4×#131101042
#202681012
#202680992
#202680972
#202680952
#202680932
#202680912
#202680892
#202678322
#202678302
#202678132
#202677892
#478×C1032
#3080103