Finite Group Databasebeta

← #28349111

Subgroups — #28349111

Order 13696.

350 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293349C211yesmaximal, characteristic, complemented
2#20293336C211yesmaximal, characteristic, complemented
3#20292983C211yesmaximal, characteristic, complemented
4#20292982C211yesmaximal, characteristic, complemented
5#20292976C211yesmaximal, characteristic, complemented
6#20292937C211yesmaximal, characteristic, complemented
7#20292934C211yesmaximal, characteristic, complemented
8#20292916C211yesmaximal, characteristic, complemented
9#20292844C211yesmaximal, characteristic
10#20292842C211yesmaximal, characteristic
11#20292830C211yesmaximal, characteristic, complemented
12C8×Dic214C211yesmaximal, characteristic, complemented
13#20292718C211yesmaximal, characteristic, complemented
14#20292707C211yesmaximal, characteristic
15C4×SD16×C107C211yesmaximal, characteristic, complemented
16C2×#13133806C2211yescharacteristic
17C2×#13133803C2211yescharacteristic
18#16812108C2211yescharacteristic
19#16812107C2211yescharacteristic
20#16812104—21no—
21#16812103—21no—
22#16812101C2211yescharacteristic
23#16812100C2211yescharacteristic
24#16812098C2211yescharacteristic
25#16812097C2211yescharacteristic
26#16812088—21no—
27#16812087—21no—
28#16812086—21no—
29#16812086—21no—
30C4×Dic214C2211yescharacteristic
31#16812074C2211yescharacteristic
32D4×Dic107C2211yescharacteristic
33D4×Dic107C2211yescharacteristic
34#16812071C2211yescharacteristic
35#16812066—21no—
36C2×Dic107⋊C4—21no—
37#16812042C2211yescharacteristic
38#16812040C2211yescharacteristic
39C4⋊(C107⋊C8)C2211yescharacteristic
40Dic107⋊C8C2211yescharacteristic
41Dic107⋊C8C2211yescharacteristic
42#16812034C2211yescharacteristic
43#16812034C2211yescharacteristic
44#16812033C2211yescharacteristic
45#16812033C2211yescharacteristic
46#16812032C2211yescharacteristic
47#16812031C2211yescharacteristic
48#16812031C2211yescharacteristic
49#16812029C2211yescharacteristic
50C8×Dic107C2211yescharacteristic
51C8×Dic107C2211yescharacteristic
52C2×SD16×C107C2211yescharacteristic
53C4×Q8×C107C2211yescharacteristic
54C4×D4×C107C2211yescharacteristic
55#106×C107C2211yescharacteristic
56#103×C107C2211yescharacteristic
57#102×C107C2211yescharacteristic
58C4×C8×C107C2211yescharacteristic
59C2×Dic214—21no—
60C2×Dic214D411yescharacteristic
61C2×Dic214C2311yescharacteristic
62C2×D428C2311yescharacteristic
63C22×Dic107—21no—
64C22×Dic107—21no—
65C2×C4×D107—21no—
66#13133806—22no—
67#13133803—22no—
68C2×C107⋊C8C2311yescharacteristic
69C2×C107⋊C8C2311yescharacteristic
70C4⋊Dic107—21no—
71C4⋊Dic107D411yescharacteristic
72C4⋊Dic107C2311yescharacteristic
73C4⋊Dic107C2311yescharacteristic
74Dic107⋊C4—21no—
75Dic107⋊C4—21no—
76Dic107⋊C4—21no—
77Dic107⋊C4—21no—
78Dic107⋊C4—21no—
79Dic107⋊C4—21no—
80Dic107⋊C4—21no—
81Dic107⋊C4D411yescharacteristic
82Dic107⋊C4D411yescharacteristic
83C22⋊Dic107—21no—
84C22⋊Dic107—21no—
85(C2×D107)⋊C4—21no—
86(C2×D107)⋊C4—21no—
87(C2×D107)⋊C4—21no—
88(C2×D107)⋊C4—21no—
89(C2×D107)⋊C4—21no—
90C4×Dic107—21no—
91C4×Dic107C2311yescharacteristic
92C4×Dic107C2311yescharacteristic
93C2×Q8×C107C2311yescharacteristic
94C2×D4×C107C2311yescharacteristic
95C22×C4×C107—21no—
96SD16×C107—22no—
97C2×C8×C107C2311yescharacteristic
98C2×C8×C107C2311yescharacteristic
99C4⋊C4×C107—21no—
100C4⋊C4×C107C2311yescharacteristic
101C4⋊C4×C107C2311yescharacteristic
102C22⋊C4×C107—21no—
103C42×C107—21no—
104C42×C107C2311yescharacteristic
105C23×C107—21no—
106C22×D107—21no—
107Q8×C107—21no—
108Q8×C107—21no—
109D4×C107—21no—
110D4×C107#4112yes—
111C2×C4×C107—21no—
112C2×C4×C107—21no—
113C2×C4×C107—21no—
114C2×C4×C107—81no—
115C2×C4×C107C2×D411yescharacteristic
116C2×C4×C107C2×D411yescharacteristic
117C2×C4×C107C2411yescharacteristic
118C2×Dic107—21no—
119C2×Dic107—21no—
120C2×Dic107—21no—
121C2×Dic107—42no—
122C2×Dic107—81no—
123C2×Dic107C2×D411yescharacteristic
124C2×Dic107C2×D411yescharacteristic
125C2×Dic107C2×D411yescharacteristic
126C2×Dic107C2×D411yescharacteristic
127D428—21no—
128D428—21no—
129C4×D107—42no—
130Dic214—22no—
131Dic214—21no—
132Dic214—21no—
133Dic214—81no—
134C8×C107—21no—
135C8×C107—21no—
136C107⋊C8—21no—
137C107⋊C8—21no—
138C22×C107—22no—
139C22×C107—41no—
140C22×C107—41no—
141C22×C107C22×D411yescharacteristic
142C2×D107—41no—
143C2×D107—41no—
144C2×D107—41no—
145C4×C107—21no—
146C4×C107—21no—
147C4×C107—41no—
148C4×C107—41no—
149C4×C107—41no—
150C4×C107C2×#4111yescharacteristic
151C4×C1072−1+411yescharacteristic
152Dic107—21no—
153Dic107—21no—
154Dic107—21no—
155Dic107—41no—
156Dic107—41no—
157Dic107—41no—
158Dic107#13512yes—
159C2×C107—42no—
160C2×C107#54811yescharacteristic
161C2×C107C2×#13511yescharacteristic
162C2×C107#57711yescharacteristic
163D107—81no—
164#3360—1071nomaximal, Sylow
165C107#336011yescharacteristic, complemented, Sylow
166#556—1071no—
167#554—1071no—
168#488—1071no—
169#488—1071no—
170#487—1071no—
171#479—1071no—
172#479—1071no—
173#476—1071no—
174#463—1071no—
175#463—1071no—
176#461—1071no—
177C8×Q8—1071no—
178C4×SD16—1071no—
179C4×SD16D10711yescharacteristic, complemented
180C4×D8—1071no—
181C2×SD16—1071no—
182C2×SD16C2×D10711yescharacteristic
183C2×D8—1071no—
184C4⋊Q8—1071no—
185C4⋊Q8—1071no—
186#126—2141no—
187#126—2141no—
188#125—1071no—
189#125—1071no—
190#124—1071no—
191#124—1071no—
192C22⋊Q8—2141no—
193C22⋊Q8—2141no—
194C22⋊Q8—2141no—
195C22⋊Q8—2141no—
196C4×Q8—1071no—
197C4×Q8—1071no—
198C4×Q8C2×D10711yescharacteristic
199C4×D4—1071no—
200C4×D4—1071no—
201C4×D4—1071no—
202C4×D4C2×D10711yescharacteristic
203#117—2141no—
204C2×C4⋊C4—2141no—
205#107—1071no—
206#106—1071no—
207#106C2×D10711yescharacteristic
208C4⋊C8—1071no—
209C4⋊C8—1071no—
210C4⋊C8—1071no—
211#103—1071no—
212#103—1071no—
213#103—1071no—
214#103—1071no—
215#103—1071no—
216#103C2×D10711yescharacteristic
217#102—1071no—
218#102—1071no—
219#102—1071no—
220#102C2×D10711yescharacteristic
221C4×C8—1071no—
222C4×C8—1071no—
223C4×C8C2×D10711yescharacteristic
224C2×Q8—1071no—
225C2×Q8—1071no—
226C2×Q8—2141no—
227C2×Q8C22×D10711yescharacteristic
228C2×D4—1071no—
229C2×D4C22×D10711yescharacteristic
230C22×C4—21no—
231C22×C4—2141no—
232C22×C4—2141no—
233C22×C4—2141no—
234SD16—22no—
235SD16—2142no—
236D8—2142no—
237C2×C8—1071no—
238C2×C8—1071no—
239C2×C8C22×D10711yescharacteristic
240C2×C8C22×D10711yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—1071no—
243C4⋊C4—1071no—
244C4⋊C4—1071no—
245C4⋊C4—1071no—
246C4⋊C4—1071no—
247C4⋊C4—2141no—
248C4⋊C4—2141no—
249C4⋊C4—2141no—
250C4⋊C4—2141no—
251C4⋊C4—2141no—
252C4⋊C4—2141no—
253C4⋊C4—2141no—
254C4⋊C4—2141no—
255C4⋊C4C22×D10711yescharacteristic
256C4⋊C4C22×D10711yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—2141no—
259C22⋊C4—2141no—
260C22⋊C4—2141no—
261C22⋊C4—2141no—
262C22⋊C4—2141no—
263C22⋊C4—2141no—
264C22⋊C4—2141no—
265C42—21no—
266C42—1071no—
267C42—1071no—
268C42—2141no—
269C42C22×D10711yescharacteristic
270C23—21no—
271C23—2141no—
272Q8—21no—
273Q8—21no—
274Q8—8561no—
275Q8—2142no—
276Q8—2141no—
277Q8—2141no—
278D4—21no—
279D4—2141no—
280D4—2141no—
281D4#1313381812yes—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—81no—
286C2×C4—8561no—
287C2×C4—1071no—
288C2×C4—1071no—
289C2×C4—1071no—
290C2×C4—1071no—
291C2×C4—4282no—
292C2×C4—4282no—
293C2×C4—2141no—
294C2×C4—2141no—
295C2×C4—2141no—
296C2×C4D4×D10711yescharacteristic
297C2×C4D4×D10711yescharacteristic
298C2×C4C23×D10711yescharacteristic
299C8—21no—
300C8—21no—
301C8—2141no—
302C8—2141no—
303C22—22no—
304C22—41no—
305C22—41no—
306C22—4281no—
307C22—4281no—
308C22—4281no—
309C22C2×D4×D10711yescharacteristic
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—1072no—
316C4—4281no—
317C4—4281no—
318C4—4281no—
319C4—2141no—
320C4—2141no—
321C4—2141no—
322C4C2×#1313381811yescharacteristic
323C4#1681215611yescharacteristic
324C2—42no—
325C2—8561no—
326C2#2029328611yescharacteristic
327C2#135×D10711yescharacteristic
328C2#2029343311yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
FittingC4×SD16×C107C2
socleC22×C107C22×D4
prime radicalC2×#13133803C22
hypercenterC4×SD16D107
hypocenterC107#3360
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #20293349C2semidirect
2. #20293336C2semidirect
3. #20292983C2semidirect
4. #20292982C2semidirect
5. #20292976C2semidirect
6. #20292937C2semidirect
7. #20292934C2semidirect
8. #20292916C2semidirect
11. #20292830C2semidirect
12. C8×Dic214C2semidirect
13. #20292718C2semidirect
15. C4×SD16×C107C2semidirect
165. C107#3360semidirect
179. C4×SD16D107semidirect

Maximal subgroups

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

subgroupindex
#202933492
#202933362
#202929832
#202929822
#202929762
#202929372
#202929342
#202929162
#202928442
#202928422
#202928302
C8×Dic2142
#202927182
#202927072
C4×SD16×C1072
#3360107