Finite Group Databasebeta

← #28346669

Subgroups — #28346669

Order 13696.

372 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293107C211yesmaximal, characteristic
2#20292960C211yesmaximal, characteristic, complemented
3#20292955C211yesmaximal, characteristic, complemented
4#20292931C211yesmaximal, characteristic, complemented
5#20292924C211yesmaximal, characteristic, complemented
6#20292834C211yesmaximal, characteristic, complemented
7#20292829C211yesmaximal, characteristic, complemented
8#20292787C211yesmaximal, characteristic
9#20292787C211yesmaximal, characteristic
10#20292732C211yesmaximal, characteristic, complemented
11#20292725C211yesmaximal, characteristic, complemented
12C4×#13133808C211yesmaximal, characteristic, complemented
13C4×#13133805C211yesmaximal, characteristic, complemented
14#20292688C211yesmaximal, characteristic, complemented
15#541×C107C211yesmaximal, characteristic, complemented
16C2×#13133818C2211yescharacteristic
17C2×#13133808C2211yescharacteristic
18C2×#13133808C2211yescharacteristic
19C2×#13133805C2211yescharacteristic
20C2×#13133805C2211yescharacteristic
21C4×Dic214C2211yescharacteristic
22C4×Dic214C2211yescharacteristic
23C4×D428C2211yescharacteristic
24C4×D428C2211yescharacteristic
25(C22⋊D107)⋊C4—21no—
26(C22⋊D107)⋊C4—21no—
27#16812067—21no—
28C2×C4⋊Dic107C2211yescharacteristic
29C4⋊C4×D107—21no—
30#16812042C2211yescharacteristic
31#16812042C2211yescharacteristic
32#16812040C2211yescharacteristic
33#16812040C2211yescharacteristic
34C4⋊(C107⋊C8)C2211yescharacteristic
35C4⋊(C107⋊C8)C2211yescharacteristic
36#16812033C2211yescharacteristic
37#16812033C2211yescharacteristic
38#16812033C2211yescharacteristic
39#16812033C2211yescharacteristic
40#16812032C2211yescharacteristic
41#16812032C2211yescharacteristic
42#16812029C2211yescharacteristic
43#16812029C2211yescharacteristic
44C22⋊(C107⋊C8)C2211yescharacteristic
45C22⋊(C107⋊C8)C2211yescharacteristic
46#16812020C2211yescharacteristic
47C4×C107⋊C8C2211yescharacteristic
48C4⋊Q8×C107C2211yescharacteristic
49#126×C107—21no—
50#126×C107—21no—
51#125×C107—21no—
52#125×C107—21no—
53#125×C107C2211yescharacteristic
54C22⋊Q8×C107C2211yescharacteristic
55C22⋊Q8×C107C2211yescharacteristic
56C4×Q8×C107C2211yescharacteristic
57C4×Q8×C107C2211yescharacteristic
58#117×C107C2211yescharacteristic
59#13133818—22no—
60#13133818—22no—
61C2×Dic214C2311yescharacteristic
62C2×D428C2311yescharacteristic
63C2×C22⋊D107—21no—
64C22×Dic107—21no—
65C2×C4×D107—21no—
66C2×C4×D107—21no—
67C2×C4×D107—21no—
68#13133808—22no—
69#13133808—22no—
70#13133805—22no—
71#13133805—22no—
72C2×C107⋊C8C2311yescharacteristic
73C2×C107⋊C8C2311yescharacteristic
74C2×C107⋊C8C2311yescharacteristic
75C2×C107⋊C8C2311yescharacteristic
76C4⋊Dic107—21no—
77C4⋊Dic107C2311yescharacteristic
78C4⋊Dic107C2311yescharacteristic
79Dic107⋊C4—21no—
80Dic107⋊C4—21no—
81(C2×D107)⋊C4—21no—
82(C2×D107)⋊C4—21no—
83C4×Dic107—21no—
84C4×Dic107—21no—
85C2×Q8×C107C2311yescharacteristic
86C2×Q8×C107C2311yescharacteristic
87C22×C4×C107C2311yescharacteristic
88C4⋊C4×C107—21no—
89C4⋊C4×C107—21no—
90C4⋊C4×C107—21no—
91C4⋊C4×C107—21no—
92C4⋊C4×C107—21no—
93C4⋊C4×C107—21no—
94C4⋊C4×C107—21no—
95C4⋊C4×C107—21no—
96C4⋊C4×C107D411yescharacteristic
97C4⋊C4×C107D411yescharacteristic
98C4⋊C4×C107C2311yescharacteristic
99C4⋊C4×C107C2311yescharacteristic
100C22⋊C4×C107—21no—
101C22⋊C4×C107—21no—
102C22⋊C4×C107D411yescharacteristic
103C22⋊C4×C107D411yescharacteristic
104C42×C107—21no—
105C42×C107—21no—
106C42×C107C2311yescharacteristic
107C42×C107C2311yescharacteristic
108C23×C107C2×D411yescharacteristic
109C22×D107—21no—
110Q8×C107—21no—
111Q8×C107—21no—
112Q8×C107—21no—
113Q8×C107—21no—
114C2×C4×C107—21no—
115C2×C4×C107—21no—
116C2×C4×C107—21no—
117C2×C4×C107—21no—
118C2×C4×C107—21no—
119C2×C4×C107—21no—
120C2×C4×C107C2×D411yescharacteristic
121C2×C4×C107C2×D411yescharacteristic
122C2×C4×C107C2×D411yescharacteristic
123C2×C4×C107C2×D411yescharacteristic
124C2×C4×C107C2×D411yescharacteristic
125C2×C4×C107C2411yescharacteristic
126C22⋊D107—24no—
127C2×Dic107—21no—
128C2×Dic107—21no—
129C2×Dic107—21no—
130C2×Dic107—81no—
131D428—21no—
132D428#4112yes—
133C4×D107—24no—
134C4×D107—81no—
135C4×D107—81no—
136Dic214—21no—
137Dic214#4112yes—
138C107⋊C8—21no—
139C107⋊C8—21no—
140C107⋊C8—21no—
141C107⋊C8—21no—
142C22×C107—21no—
143C22×C107—21no—
144C22×C107—21no—
145C22×C107C22×D411yescharacteristic
146C2×D107—22no—
147C2×D107—41no—
148C2×D107—41no—
149C4×C107—21no—
150C4×C107—21no—
151C4×C107—21no—
152C4×C107—21no—
153C4×C107—21no—
154C4×C107—41no—
155C4×C107—41no—
156C4×C107—41no—
157C4×C107—41no—
158C4×C107C2×#4111yescharacteristic
159C4×C107C2×#4111yescharacteristic
160Dic107—22no—
161Dic107—41no—
162Dic107—41no—
163C2×C107—41no—
164C2×C107#52511yescharacteristic
165C2×C107#57711yescharacteristic
166C2×C107#57811yescharacteristic
167D107—42no—
168#3120—1071nomaximal, Sylow
169C107#312011yescharacteristic, complemented, Sylow
170#541D10711yescharacteristic, complemented
171#520—1071no—
172#484—1071no—
173#483—1071no—
174#479—1071no—
175#478—1071no—
176#462—1071no—
177#461—1071no—
178#452—1071no—
179#452—1071no—
180#441—1071no—
181#440—1071no—
182C4×Q16—1071no—
183C4×SD16—1071no—
184#433—1071no—
185C2×#41—1071no—
186C2×Q16—1071no—
187C2×Q16—1071no—
188C2×SD16—1071no—
189C2×SD16—1071no—
190C4⋊Q8C2×D10711yescharacteristic
191#126—21no—
192#126—21no—
193#125—21no—
194#125—21no—
195#125C2×D10711yescharacteristic
196C22⋊Q8C2×D10711yescharacteristic
197C22⋊Q8C2×D10711yescharacteristic
198C4×Q8—1071no—
199C4×Q8—1071no—
200C4×Q8C2×D10711yescharacteristic
201C4×Q8C2×D10711yescharacteristic
202C4×D4—1071no—
203C4×D4—1071no—
204C4×D4—2141no—
205C4×D4—2141no—
206#117—2141no—
207#117C2×D10711yescharacteristic
208C2×C4⋊C4—1071no—
209C2×C4⋊C4—2141no—
210#107—1071no—
211#107—1071no—
212#106—1071no—
213#106—1071no—
214C4⋊C8—1071no—
215C4⋊C8—1071no—
216#103—1071no—
217#103—1071no—
218#103—1071no—
219#103—1071no—
220#103—1071no—
221#103—1071no—
222#102—1071no—
223#102—1071no—
224C22⋊C8—1071no—
225C22⋊C8—1071no—
226#97—1071no—
227C4×C8—1071no—
228#41—2142no—
229#41—2142no—
230C2×Q8—1071no—
231C2×Q8C22×D10711yescharacteristic
232C2×Q8C22×D10711yescharacteristic
233C2×D4—1071no—
234C2×D4—2141no—
235C22×C4—2141no—
236C22×C4—2141no—
237C22×C4—2141no—
238C22×C4—2141no—
239C22×C4C22×D10711yescharacteristic
240Q16—2142no—
241Q16—2142no—
242SD16—2142no—
243SD16—2142no—
244C2×C8—1071no—
245C2×C8—1071no—
246C2×C8—1071no—
247C2×C8—1071no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—1071no—
257C4⋊C4—1071no—
258C4⋊C4—2141no—
259C4⋊C4—2141no—
260C4⋊C4—2141no—
261C4⋊C4C22⋊D10711yescharacteristic
262C4⋊C4C22⋊D10711yescharacteristic
263C4⋊C4C22×D10711yescharacteristic
264C4⋊C4C22×D10711yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—2141no—
268C22⋊C4—2141no—
269C22⋊C4C22⋊D10711yescharacteristic
270C22⋊C4C22⋊D10711yescharacteristic
271C42—21no—
272C42—21no—
273C42—2141no—
274C42—2141no—
275C42C22×D10711yescharacteristic
276C42C22×D10711yescharacteristic
277C23—2141no—
278C23C2×C22⋊D10711yescharacteristic
279Q8—21no—
280Q8—21no—
281Q8—21no—
282Q8—21no—
283Q8—1072no—
284Q8—2141no—
285D4—1072no—
286D4—2144no—
287D4—2141no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—8561no—
295C2×C4—8561no—
296C2×C4—8561no—
297C2×C4—2144no—
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×C4C23×D10711yescharacteristic
307C8—2141no—
308C8—2141no—
309C8—2141no—
310C8—2141no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—4281no—
315C22—4281no—
316C22—2142no—
317C22C22×C22⋊D10711yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—4281no—
328C4—4281no—
329C4—2142no—
330C4#41×D10711yescharacteristic
331C4#41×D10711yescharacteristic
332C2—41no—
333C2—4282no—
334C2#2029313411yescharacteristic
335C2#2029343511yescharacteristic
336C2#2029344211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#541×C107C2
socleC22×C107C22×D4
prime radicalC2×#13133818C22
hypercenter#541D107
hypocenterC107#3120
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
2. #20292960C2semidirect
3. #20292955C2semidirect
4. #20292931C2semidirect
5. #20292924C2semidirect
6. #20292834C2semidirect
7. #20292829C2semidirect
10. #20292732C2semidirect
11. #20292725C2semidirect
12. C4×#13133808C2semidirect
13. C4×#13133805C2semidirect
14. #20292688C2semidirect
15. #541×C107C2semidirect
169. C107#3120semidirect
170. #541D107semidirect

Maximal subgroups

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

subgroupindex
#202931072
#202929602
#202929552
#202929312
#202929242
#202928342
#202928292
#202927872
#202927322
#202927252
C4×#131338082
C4×#131338052
#202926882
#541×C1072
#3120107