Finite Group Databasebeta

← #28346264

Subgroups — #28346264

Order 13696.

376 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293183C211yesmaximal, characteristic
2C4×Q8×D107C211yesmaximal, characteristic
3#20292935C211yesmaximal, characteristic, complemented
4#20292934C211yesmaximal, characteristic, complemented
5#20292931C211yesmaximal, characteristic, complemented
6#20292921C211yesmaximal, characteristic, complemented
7#20292920C211yesmaximal, characteristic, complemented
8#20292911C211yesmaximal, characteristic, complemented
9#20292910C211yesmaximal, characteristic, complemented
10#20292668C211yesmaximal, characteristic
11#20292666C211yesmaximal, characteristic
12#20292649C211yesmaximal, characteristic
13#20292634C211yesmaximal, characteristic
14#20292634C211yesmaximal, characteristic
15#479×C107C211yesmaximal, characteristic, complemented
16C2×Q8×D107C2211yescharacteristic
17C2×#13133801C2211yescharacteristic
18C2×#13133801C2211yescharacteristic
19#16812108C2211yescharacteristic
20#16812108C2211yescharacteristic
21#16812101C2211yescharacteristic
22#16812087—21no—
23#16812087—21no—
24Q8×Dic107C2211yescharacteristic
25C4×Dic214—21no—
26C4×Dic214C2211yescharacteristic
27#16812074—21no—
28#16812074—21no—
29#16812074—21no—
30#16812074C2211yescharacteristic
31#16812067C2211yescharacteristic
32#16812067C2211yescharacteristic
33C4⋊C4×D107—21no—
34C4⋊C4×D107C2211yescharacteristic
35C42×D107—21no—
36C42×D107C2211yescharacteristic
37#16812043C2211yescharacteristic
38#16812042C2211yescharacteristic
39#16812042C2211yescharacteristic
40#16812041C2211yescharacteristic
41#16812040C2211yescharacteristic
42#16812040C2211yescharacteristic
43C4⋊(C107⋊C8)C2211yescharacteristic
44Dic107⋊C8C2211yescharacteristic
45Dic107⋊C8C2211yescharacteristic
46#16812034C2211yescharacteristic
47#16812034C2211yescharacteristic
48#16812033C2211yescharacteristic
49#16812033C2211yescharacteristic
50#16812032C2211yescharacteristic
51#16812032C2211yescharacteristic
52#125×C107C2211yescharacteristic
53C4×Q8×C107C2211yescharacteristic
54#107×C107C2211yescharacteristic
55#106×C107C2211yescharacteristic
56C4⋊C8×C107C2211yescharacteristic
57#103×C107C2211yescharacteristic
58#103×C107C2211yescharacteristic
59C2×Dic214—21no—
60C2×Dic214—21no—
61C2×Dic214—21no—
62C2×Dic214C2311yescharacteristic
63Q8×D107—22no—
64Q8×D107Q814yescomplemented
65C2×C4×D107—21no—
66C2×C4×D107—21no—
67C2×C4×D107D411yescharacteristic
68C2×C4×D107D411yescharacteristic
69C2×C4×D107C2311yescharacteristic
70#13133801—22no—
71#13133801—22no—
72C2×C107⋊C8C2311yescharacteristic
73C2×C107⋊C8C2311yescharacteristic
74C4⋊Dic107—21no—
75C4⋊Dic107C2311yescharacteristic
76C4⋊Dic107C2311yescharacteristic
77C4⋊Dic107C2311yescharacteristic
78Dic107⋊C4—21no—
79Dic107⋊C4—21no—
80Dic107⋊C4—21no—
81Dic107⋊C4—21no—
82Dic107⋊C4—21no—
83Dic107⋊C4—21no—
84Dic107⋊C4—21no—
85(C2×D107)⋊C4—21no—
86(C2×D107)⋊C4—21no—
87C4×Dic107—21no—
88C4×Dic107—21no—
89C4×Dic107—21no—
90C4×Dic107—21no—
91C4×Dic107—21no—
92C4×Dic107D411yescharacteristic
93C4×Dic107D411yescharacteristic
94C4×Dic107C2311yescharacteristic
95C2×Q8×C107C2311yescharacteristic
96C2×C8×C107C2311yescharacteristic
97C2×C8×C107C2311yescharacteristic
98C4⋊C4×C107—21no—
99C4⋊C4×C107—21no—
100C4⋊C4×C107—21no—
101C4⋊C4×C107C2311yescharacteristic
102C4⋊C4×C107C2311yescharacteristic
103C4⋊C4×C107C2311yescharacteristic
104C42×C107—21no—
105C42×C107C2311yescharacteristic
106C22×D107C2×D411yescharacteristic
107Q8×C107—21no—
108Q8×C107C2×Q812yes—
109C2×C4×C107—21no—
110C2×C4×C107—21no—
111C2×C4×C107—21no—
112C2×C4×C107—21no—
113C2×C4×C107C2×D411yescharacteristic
114C2×C4×C107C2×D411yescharacteristic
115C2×C4×C107C2411yescharacteristic
116C2×Dic107—21no—
117C2×Dic107—21no—
118C2×Dic107—21no—
119C2×Dic107—21no—
120C2×Dic107C2×D411yescharacteristic
121C2×Dic107C2×D411yescharacteristic
122C2×Dic107C2×D411yescharacteristic
123C4×D107—24no—
124C4×D107—22no—
125C4×D107—41no—
126C4×D107—42no—
127C4×D107C2×Q812yes—
128C4×D107#4112yes—
129Dic214—21no—
130Dic214—24no—
131Dic214—42no—
132Dic214—42no—
133Dic214C2×Q812yes—
134C8×C107—21no—
135C8×C107—21no—
136C107⋊C8—21no—
137C107⋊C8—21no—
138C22×C107C22×D411yescharacteristic
139C2×D107—21no—
140C2×D107—21no—
141C2×D107C22⋊Q812yes—
142C4×C107—22no—
143C4×C107—21no—
144C4×C107—21no—
145C4×C107—41no—
146C4×C107—41no—
147C4×C107—41no—
148C4×C107C22×Q811yescharacteristic
149C4×C107C2×#4111yescharacteristic
150Dic107—22no—
151Dic107—21no—
152Dic107—41no—
153Dic107—41no—
154Dic107—41no—
155Dic107C22⋊Q812yes—
156Dic107#13712yes—
157C2×C107C2×C22⋊Q811yescharacteristic
158C2×C107C2×#13711yescharacteristic
159C2×C107#57511yescharacteristic
160D107—22no—
161#3078—1071nomaximal, Sylow
162C107#307811yescharacteristic, complemented, Sylow
163#533—1071no—
164C2×C4×Q8—1071no—
165#479—1071no—
166#479—1071no—
167#479—1071no—
168#479D10711yescharacteristic, complemented
169#477—1071no—
170#477—1071no—
171#475—1071no—
172#475—1071no—
173#428—1071no—
174#428—1071no—
175#423—1071no—
176#419—1071no—
177#419—1071no—
178C22×Q8—1071no—
179C2×M16—1071no—
180C2×M16—1071no—
181C4⋊Q8—1071no—
182C4⋊Q8—1071no—
183#125—1071no—
184#125C2×D10711yescharacteristic
185C22⋊Q8—2141no—
186C22⋊Q8—2141no—
187C4×Q8—1071no—
188C4×Q8—1071no—
189C4×Q8—1071no—
190C4×Q8—2141no—
191C4×Q8—2141no—
192C4×Q8—2141no—
193C4×Q8—2141no—
194C4×Q8C2×D10711yescharacteristic
195#117—1071no—
196#117—1071no—
197C2×C4⋊C4—1071no—
198C2×C4⋊C4—2141no—
199C2×C42—1071no—
200C2×C42—2141no—
201#107—1071no—
202#107—1071no—
203#107—1071no—
204#107C2×D10711yescharacteristic
205#106—1071no—
206#106—1071no—
207#106—1071no—
208#106C2×D10711yescharacteristic
209C4⋊C8—1071no—
210C4⋊C8—1071no—
211C4⋊C8—1071no—
212C4⋊C8C2×D10711yescharacteristic
213#103—1071no—
214#103—1071no—
215#103—1071no—
216#103—1071no—
217#103—1071no—
218#103—1071no—
219#103C2×D10711yescharacteristic
220#103C2×D10711yescharacteristic
221C2×Q8—1074no—
222C2×Q8—1071no—
223C2×Q8—2141no—
224C2×Q8—2141no—
225C2×Q8—2141no—
226C2×Q8—2142no—
227C2×Q8C22×D10711yescharacteristic
228C22×C4—1071no—
229C22×C4—1071no—
230C22×C4—1071no—
231C22×C4—2141no—
232C22×C4—2141no—
233M16—2142no—
234M16—2142no—
235C2×C8—1071no—
236C2×C8—1071no—
237C2×C8C22×D10711yescharacteristic
238C2×C8C22×D10711yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—1071no—
243C4⋊C4—1071no—
244C4⋊C4—1071no—
245C4⋊C4—2141no—
246C4⋊C4—2141no—
247C4⋊C4—2141no—
248C4⋊C4—2141no—
249C4⋊C4—2141no—
250C4⋊C4—2141no—
251C4⋊C4—2141no—
252C4⋊C4—2141no—
253C4⋊C4C22×D10711yescharacteristic
254C4⋊C4C22×D10711yescharacteristic
255C4⋊C4C22×D10711yescharacteristic
256C22⋊C4—2141no—
257C22⋊C4—2141no—
258C42—21no—
259C42—1071no—
260C42—1071no—
261C42—1071no—
262C42—2141no—
263C42—2141no—
264C42—2141no—
265C42—2141no—
266C42—2141no—
267C42C22×D10711yescharacteristic
268C23—1071no—
269Q8—21no—
270Q8—1072no—
271Q8—4282no—
272Q8—4282no—
273Q8—2144no—
274Q8—2141no—
275Q8Q8×D10712yes—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—1071no—
281C2×C4—1071no—
282C2×C4—1072no—
283C2×C4—1072no—
284C2×C4—1071no—
285C2×C4—4281no—
286C2×C4—4282no—
287C2×C4—2142no—
288C2×C4—2144no—
289C2×C4—2141no—
290C2×C4—2141no—
291C2×C4—2141no—
292C2×C4—2141no—
293C2×C4D4×D10711yescharacteristic
294C2×C4D4×D10711yescharacteristic
295C2×C4C23×D10711yescharacteristic
296C8—21no—
297C8—21no—
298C8—2141no—
299C8—2141no—
300C22—1072no—
301C22—2141no—
302C22—2141no—
303C22C2×D4×D10711yescharacteristic
304C4—22no—
305C4—21no—
306C4—21no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—1072no—
311C4—1072no—
312C4—4281no—
313C4—4281no—
314C4—4281no—
315C4—2142no—
316C4—2141no—
317C4C2×Q8×D10711yescharacteristic
318C4#41×D10711yescharacteristic
319C2—2142no—
320C2C22⋊Q8×D10711yescharacteristic
321C2#137×D10711yescharacteristic
322C2#2029342411yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#479×C107C2
socleC22×C107C22×D4
prime radicalC22×D107C2×D4
hypercenter#479D107
hypocenterC107#3078
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
3. #20292935C2semidirect
4. #20292934C2semidirect
5. #20292931C2semidirect
6. #20292921C2semidirect
7. #20292920C2semidirect
8. #20292911C2semidirect
9. #20292910C2semidirect
15. #479×C107C2semidirect
64. Q8×D107Q8semidirect
162. C107#3078semidirect
168. #479D107semidirect

Maximal subgroups

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

subgroupindex
#202931832
C4×Q8×D1072
#202929352
#202929342
#202929312
#202929212
#202929202
#202929112
#202929102
#202926682
#202926662
#202926492
#202926342
#479×C1072
#3078107