Finite Group Databasebeta

← #28349208

Subgroups — #28349208

Order 13696.

358 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293337C211yesmaximal, characteristic, complemented
2#20292991C211yesmaximal, characteristic, complemented
3#20292986C211yesmaximal, characteristic, complemented
4#20292981C211yesmaximal, characteristic, complemented
5#20292934C211yesmaximal, characteristic, complemented
6#20292927C211yesmaximal, characteristic, complemented
7#20292907C211yesmaximal, characteristic, complemented
8#20292839C211yesmaximal, characteristic, complemented
9#20292839C211yesmaximal, characteristic, complemented
10#20292819C211yesmaximal, characteristic
11#20292758C211yesmaximal, characteristic, complemented
12#20292737C211yesmaximal, characteristic, complemented
13#20292725C211yesmaximal, characteristic, complemented
14C4×#13133803C211yesmaximal, characteristic, complemented
15#559×C107C211yesmaximal, characteristic, complemented
16C2×#13133805C2211yescharacteristic
17C2×#13133803C2211yescharacteristic
18C2×#13133803C2211yescharacteristic
19#16812109C2211yescharacteristic
20#16812101C2211yescharacteristic
21#16812101C2211yescharacteristic
22#16812087—21no—
23#16812087—21no—
24#16812085—21no—
25C4×D428C2211yescharacteristic
26C4×D428C2211yescharacteristic
27C4×D428C2211yescharacteristic
28C4⋊C4×D107—21no—
29#16812042C2211yescharacteristic
30#16812042C2211yescharacteristic
31#16812040C2211yescharacteristic
32C4⋊(C107⋊C8)C2211yescharacteristic
33C4⋊(C107⋊C8)C2211yescharacteristic
34C4⋊(C107⋊C8)C2211yescharacteristic
35#16812033C2211yescharacteristic
36#16812033C2211yescharacteristic
37#16812033C2211yescharacteristic
38#16812030C2211yescharacteristic
39#16812030C2211yescharacteristic
40#16812030C2211yescharacteristic
41#16812030C2211yescharacteristic
42#16812030C2211yescharacteristic
43#16812030C2211yescharacteristic
44#16812029C2211yescharacteristic
45#16812020C2211yescharacteristic
46#16812020C2211yescharacteristic
47C4×C107⋊C8C2211yescharacteristic
48#127×C107C2211yescharacteristic
49#124×C107—21no—
50#124×C107C2211yescharacteristic
51#124×C107C2211yescharacteristic
52#123×C107—21no—
53#123×C107—21no—
54C4×Q8×C107C2211yescharacteristic
55C4×Q8×C107C2211yescharacteristic
56C4×D4×C107—21no—
57C4×D4×C107C2211yescharacteristic
58C4×D4×C107C2211yescharacteristic
59C2×Dic214—21no—
60C2×D428C2311yescharacteristic
61C2×C4×D107—21no—
62C2×C4×D107—21no—
63C2×C4×D107—21no—
64#13133805—22no—
65#13133803—22no—
66#13133803—22no—
67C2×C107⋊C8C2311yescharacteristic
68C2×C107⋊C8C2311yescharacteristic
69C2×C107⋊C8C2311yescharacteristic
70C2×C107⋊C8C2311yescharacteristic
71C4⋊Dic107—21no—
72C4⋊Dic107C2311yescharacteristic
73C4⋊Dic107C2311yescharacteristic
74C4⋊Dic107C2311yescharacteristic
75Dic107⋊C4—21no—
76Dic107⋊C4—21no—
77Dic107⋊C4—21no—
78Dic107⋊C4—21no—
79(C2×D107)⋊C4—21no—
80(C2×D107)⋊C4—21no—
81(C2×D107)⋊C4—21no—
82C2×Q8×C107D411yescharacteristic
83C2×Q8×C107C2311yescharacteristic
84C2×D4×C107—21no—
85C2×D4×C107—21no—
86C2×D4×C107C2311yescharacteristic
87C2×D4×C107C2311yescharacteristic
88C22×C4×C107—21no—
89C22×C4×C107—21no—
90C4⋊C4×C107—21no—
91C4⋊C4×C107D411yescharacteristic
92C4⋊C4×C107D411yescharacteristic
93C4⋊C4×C107D411yescharacteristic
94C4⋊C4×C107C2311yescharacteristic
95C22⋊C4×C107—21no—
96C22⋊C4×C107—21no—
97C22⋊C4×C107—21no—
98C22⋊C4×C107—21no—
99C22⋊C4×C107—21no—
100C22⋊C4×C107—21no—
101C42×C107—21no—
102C42×C107C2311yescharacteristic
103C42×C107C2311yescharacteristic
104C42×C107C2311yescharacteristic
105C23×C107—21no—
106C23×C107—21no—
107C22×D107—21no—
108Q8×C107—21no—
109Q8×C107—21no—
110Q8×C107—41no—
111D4×C107—21no—
112D4×C107—21no—
113D4×C107—21no—
114D4×C107—21no—
115D4×C107—42no—
116D4×C107—81no—
117C2×C4×C107—21no—
118C2×C4×C107—21no—
119C2×C4×C107—81no—
120C2×C4×C107—81no—
121C2×C4×C107C2×D411yescharacteristic
122C2×C4×C107C2×D411yescharacteristic
123C2×C4×C107C2×D411yescharacteristic
124C2×C4×C107C2×D411yescharacteristic
125C2×C4×C107C2×D411yescharacteristic
126C2×C4×C107C2×D411yescharacteristic
127C2×C4×C107C2411yescharacteristic
128C2×Dic107—21no—
129C2×Dic107—21no—
130C2×Dic107—21no—
131D428—21no—
132D428#4112yes—
133C4×D107—42no—
134C4×D107—81no—
135C4×D107—81no—
136Dic214—81no—
137C107⋊C8—21no—
138C107⋊C8—21no—
139C107⋊C8—21no—
140C107⋊C8—21no—
141C22×C107—41no—
142C22×C107—41no—
143C22×C107—41no—
144C22×C107—41no—
145C22×C107—41no—
146C22×C107—41no—
147C22×C107C22×D411yescharacteristic
148C2×D107—22no—
149C2×D107—41no—
150C2×D107—41no—
151C4×C107—21no—
152C4×C107—21no—
153C4×C107—21no—
154C4×C107—21no—
155C4×C107—21no—
156C4×C107—21no—
157C4×C107—41no—
158C4×C107—41no—
159C4×C107C2×#4111yescharacteristic
160C4×C1072−1+411yescharacteristic
161Dic107—41no—
162Dic107—41no—
163Dic107—41no—
164C2×C107—81no—
165C2×C107—81no—
166C2×C107#54811yescharacteristic
167C2×C107#57511yescharacteristic
168C2×C107#57611yescharacteristic
169D107—42no—
170#3370—1071nomaximal, Sylow
171C107#337011yescharacteristic, complemented, Sylow
172#559D10711yescharacteristic, complemented
173#554—1071no—
174#490—1071no—
175#489—1071no—
176#488—1071no—
177#479—1071no—
178#478—1071no—
179#474—1071no—
180#463—1071no—
181#463—1071no—
182#459—1071no—
183#446—1071no—
184#442—1071no—
185#440—1071no—
186C4×D8—1071no—
187C2×SD16—1071no—
188C2×D8—1071no—
189C2×D8—1071no—
190C4⋊Q8—1071no—
191#127C2×D10711yescharacteristic
192#125—1071no—
193#125—1071no—
194#124—21no—
195#124C2×D10711yescharacteristic
196#124C2×D10711yescharacteristic
197#123—21no—
198#123—21no—
199C22⋊Q8—2141no—
200C22⋊Q8—2141no—
201C22⋊Q8—2141no—
202C4×Q8C2×D10711yescharacteristic
203C4×Q8C2×D10711yescharacteristic
204C4×D4—21no—
205C4×D4—1071no—
206C4×D4—1071no—
207C4×D4—1071no—
208C4×D4C2×D10711yescharacteristic
209C4×D4C2×D10711yescharacteristic
210C2×C4⋊C4—2141no—
211#107—1071no—
212#107—1071no—
213#106—1071no—
214C4⋊C8—1071no—
215C4⋊C8—1071no—
216C4⋊C8—1071no—
217#103—1071no—
218#103—1071no—
219#103—1071no—
220#102—1071no—
221#102—1071no—
222#102—1071no—
223#102—1071no—
224#102—1071no—
225#102—1071no—
226#102—1071no—
227#97—1071no—
228#97—1071no—
229C4×C8—1071no—
230C2×Q8—2141no—
231C2×Q8C22⋊D10711yescharacteristic
232C2×Q8C22×D10711yescharacteristic
233C2×D4—21no—
234C2×D4—21no—
235C2×D4—1071no—
236C2×D4C22×D10711yescharacteristic
237C2×D4C22×D10711yescharacteristic
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—2141no—
241C22×C4—2141no—
242C22×C4—2141no—
243SD16—2142no—
244D8—2142no—
245D8—2142no—
246C2×C8—1071no—
247C2×C8—1071no—
248C2×C8—1071no—
249C2×C8—1071no—
250C4⋊C4—21no—
251C4⋊C4—1071no—
252C4⋊C4—1071no—
253C4⋊C4—1071no—
254C4⋊C4—2141no—
255C4⋊C4—2141no—
256C4⋊C4—2141no—
257C4⋊C4—2141no—
258C4⋊C4—2141no—
259C4⋊C4C22⋊D10711yescharacteristic
260C4⋊C4C22⋊D10711yescharacteristic
261C4⋊C4C22⋊D10711yescharacteristic
262C4⋊C4C22×D10711yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—2141no—
270C22⋊C4—2141no—
271C22⋊C4—2141no—
272C42—21no—
273C42C22×D10711yescharacteristic
274C42C22×D10711yescharacteristic
275C42C22×D10711yescharacteristic
276C23—21no—
277C23—21no—
278C23—2141no—
279Q8—21no—
280Q8—21no—
281Q8—41no—
282Q8—8561no—
283D4—21no—
284D4—21no—
285D4—21no—
286D4—21no—
287D4—42no—
288D4—81no—
289D4—1072no—
290D4—2141no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—8561no—
296C2×C4—8561no—
297C2×C4—4282no—
298C2×C4—2141no—
299C2×C4—2141no—
300C2×C4—2141no—
301C2×C4C2×C22⋊D10711yescharacteristic
302C2×C4C2×C22⋊D10711yescharacteristic
303C2×C4C2×C22⋊D10711yescharacteristic
304C2×C4C2×C22⋊D10711yescharacteristic
305C2×C4C2×C22⋊D10711yescharacteristic
306C2×C4C2×C22⋊D10711yescharacteristic
307C2×C4C23×D10711yescharacteristic
308C8—2141no—
309C8—2141no—
310C8—2141no—
311C8—2141no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—4281no—
319C22—4281no—
320C22—2142no—
321C22C22×C22⋊D10711yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—4281no—
331C4—4281no—
332C4—4281no—
333C4#41×D10711yescharacteristic
334C4#1681215611yescharacteristic
335C2—81no—
336C2—81no—
337C2—4282no—
338C2#2029328411yescharacteristic
339C2#2029342511yescharacteristic
340C2#2029343011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#559×C107C2
socleC22×C107C22×D4
prime radical#20292819C2
hypercenter#559D107
hypocenterC107#3370
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #559

Complements

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

NH ≅ G/Ntype
1. #20293337C2semidirect
2. #20292991C2semidirect
3. #20292986C2semidirect
4. #20292981C2semidirect
5. #20292934C2semidirect
6. #20292927C2semidirect
7. #20292907C2semidirect
8. #20292839C2semidirect
9. #20292839C2semidirect
11. #20292758C2semidirect
12. #20292737C2semidirect
13. #20292725C2semidirect
14. C4×#13133803C2semidirect
15. #559×C107C2semidirect
171. C107#3370semidirect
172. #559D107semidirect

Maximal subgroups

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

subgroupindex
#202933372
#202929912
#202929862
#202929812
#202929342
#202929272
#202929072
#202928392
#202928192
#202927582
#202927372
#202927252
C4×#131338032
#559×C1072
#3370107