Finite Group Databasebeta

← #28347030

Subgroups — #28347030

Order 13696.

380 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293162C211yesmaximal, characteristic, complemented
2#20293156C211yesmaximal, characteristic, complemented
3#20293026C211yesmaximal, characteristic, complemented
4#20293009C211yesmaximal, characteristic, complemented
5#20292982C211yesmaximal, characteristic, complemented
6#20292867C211yesmaximal, characteristic, complemented
7#20292862C211yesmaximal, characteristic
8#20292859C211yesmaximal, characteristic, complemented
9#20292855C211yesmaximal, characteristic, complemented
10#20292719C211yesmaximal, characteristic, complemented
11#20292718C211yesmaximal, characteristic, complemented
12#20292712C211yesmaximal, characteristic, complemented
13#20292707C211yesmaximal, characteristic, complemented
14C4×C8×D107C211yesmaximal, characteristic, complemented
15#488×C107C211yesmaximal, characteristic, complemented
16C2×#13133808C2211yescharacteristic
17C2×#13133806C2211yescharacteristic
18C2×#13133805C2211yescharacteristic
19C2×#13133803C2211yescharacteristic
20C2×C8×D107C2211yescharacteristic
21C2×C8×D107C2211yescharacteristic
22#16812104—21no—
23#16812102—21no—
24#16812101C2211yescharacteristic
25#16812097C2211yescharacteristic
26#16812094—21no—
27#16812091—21no—
28#16812089C2211yescharacteristic
29#16812085C2211yescharacteristic
30#16812084C2211yescharacteristic
31#16812080C2211yescharacteristic
32Q8×Dic107C2211yescharacteristic
33#16812074C2211yescharacteristic
34D4×Dic107C2211yescharacteristic
35#16812071—21no—
36#16812071C2211yescharacteristic
37(C22⋊D107)⋊C4—21no—
38#16812067—21no—
39#16812065—21no—
40C42×D107C2211yescharacteristic
41#16812042C2211yescharacteristic
42#16812042C2211yescharacteristic
43#16812040C2211yescharacteristic
44#16812040C2211yescharacteristic
45#16812034C2211yescharacteristic
46#16812034C2211yescharacteristic
47#16812031C2211yescharacteristic
48#16812031C2211yescharacteristic
49C4×C107⋊C8C2211yescharacteristic
50C8×Dic107C2211yescharacteristic
51C8×Dic107C2211yescharacteristic
52#125×C107C2211yescharacteristic
53#124×C107C2211yescharacteristic
54#103×C107C2211yescharacteristic
55#103×C107C2211yescharacteristic
56#102×C107C2211yescharacteristic
57#102×C107C2211yescharacteristic
58C4×C8×C107C2211yescharacteristic
59C2×Dic214C2311yescharacteristic
60C2×D428—21no—
61C2×D428C2311yescharacteristic
62C2×C22⋊D107—21no—
63C22×Dic107—21no—
64C2×C4×D107—21no—
65C2×C4×D107D411yescharacteristic
66C2×C4×D107D411yescharacteristic
67C2×C4×D107C2311yescharacteristic
68#13133808—22no—
69#13133806—22no—
70#13133805—22no—
71#13133803—22no—
72C2×C107⋊C8C2311yescharacteristic
73C2×C107⋊C8C2311yescharacteristic
74C8×D107—22no—
75C8×D107—22no—
76C4⋊Dic107—21no—
77C4⋊Dic107—21no—
78C4⋊Dic107C2311yescharacteristic
79C4⋊Dic107C2311yescharacteristic
80Dic107⋊C4—21no—
81Dic107⋊C4—21no—
82Dic107⋊C4—21no—
83Dic107⋊C4—21no—
84C22⋊Dic107—21no—
85C22⋊Dic107—21no—
86(C2×D107)⋊C4—21no—
87(C2×D107)⋊C4—21no—
88(C2×D107)⋊C4—21no—
89(C2×D107)⋊C4—21no—
90(C2×D107)⋊C4—21no—
91(C2×D107)⋊C4—21no—
92C4×Dic107—21no—
93C4×Dic107—21no—
94C4×Dic107D411yescharacteristic
95C4×Dic107D411yescharacteristic
96C4×Dic107C2311yescharacteristic
97C2×Q8×C107C2311yescharacteristic
98C2×D4×C107C2311yescharacteristic
99C2×C8×C107C2311yescharacteristic
100C2×C8×C107C2311yescharacteristic
101C4⋊C4×C107—21no—
102C4⋊C4×C107—21no—
103C4⋊C4×C107C2311yescharacteristic
104C4⋊C4×C107C2311yescharacteristic
105C22⋊C4×C107—21no—
106C22⋊C4×C107—21no—
107C42×C107C2311yescharacteristic
108C23×C107—21no—
109C22×D107—21no—
110C22×D107C2×D411yescharacteristic
111Q8×C107—21no—
112Q8×C107—21no—
113D4×C107—21no—
114D4×C107—21no—
115C2×C4×C107—21no—
116C2×C4×C107—21no—
117C2×C4×C107—21no—
118C2×C4×C107C2×D411yescharacteristic
119C2×C4×C107C2×D411yescharacteristic
120C2×C4×C107C2411yescharacteristic
121C22⋊D107—42no—
122C2×Dic107—21no—
123C2×Dic107—21no—
124C2×Dic107—21no—
125C2×Dic107—42no—
126C2×Dic107C2×D411yescharacteristic
127C2×Dic107C2×D411yescharacteristic
128C2×Dic107C2×D411yescharacteristic
129D428—21no—
130D428—21no—
131D428—42no—
132C4×D107—22no—
133C4×D107—21no—
134C4×D107—21no—
135C4×D107—22no—
136C4×D107—42no—
137Dic214—21no—
138Dic214—21no—
139C8×C107—21no—
140C8×C107—21no—
141C107⋊C8#4112yes—
142C107⋊C8#4112yes—
143C22×C107—41no—
144C22×C107—41no—
145C22×C107—41no—
146C22×C107C22×D411yescharacteristic
147C2×D107—21no—
148C2×D107—21no—
149C2×D107—41no—
150C2×D107—41no—
151C2×D107—41no—
152C2×D107#13512yes—
153C4×C107—21no—
154C4×C107—21no—
155C4×C107—41no—
156C4×C107—41no—
157C4×C107—41no—
158C4×C107C2×#4111yescharacteristic
159C4×C107C2×#4111yescharacteristic
160Dic107—21no—
161Dic107—21no—
162Dic107—41no—
163Dic107—41no—
164Dic107—41no—
165Dic107#13512yes—
166C2×C107—81no—
167C2×C107#53211yescharacteristic
168C2×C107C2×#13511yescharacteristic
169C2×C107C2×#13511yescharacteristic
170D107—22no—
171D107—81no—
172#3168—1071nomaximal, Sylow
173C107#316811yescharacteristic, complemented, Sylow
174#529—1071no—
175#529—1071no—
176#499—1071no—
177#495—1071no—
178#488—1071no—
179#488D10711yescharacteristic, complemented
180#467—1071no—
181#466—1071no—
182#465—1071no—
183#465—1071no—
184C4×Q16—1071no—
185C4×SD16—1071no—
186C4×SD16—1071no—
187C4×D8—1071no—
188C2×C4×C8—1071no—
189C2×Q16—1071no—
190C2×SD16—1071no—
191C2×SD16—1071no—
192C2×D8—1071no—
193C22×C8—1071no—
194C22×C8—1071no—
195#126—2141no—
196#126—2141no—
197#125—1071no—
198#125C2×D10711yescharacteristic
199#124—1071no—
200#124C2×D10711yescharacteristic
201#123—2141no—
202#123—2141no—
203C22⋊Q8—1071no—
204C22⋊Q8—1071no—
205#121—1071no—
206#121—1071no—
207C4×Q8—1071no—
208C4×Q8—1071no—
209C4×D4—1071no—
210C4×D4—1071no—
211C4×D4—2141no—
212C4×D4—2141no—
213#117—2141no—
214#117—2141no—
215C2×C42—1071no—
216#107—1071no—
217#107—1071no—
218#106—1071no—
219#106—1071no—
220#103—1071no—
221#103—1071no—
222#103C2×D10711yescharacteristic
223#103C2×D10711yescharacteristic
224#102—1071no—
225#102—1071no—
226#102C2×D10711yescharacteristic
227#102C2×D10711yescharacteristic
228C4×C8—1071no—
229C4×C8—1071no—
230C4×C8—1071no—
231C4×C8C2×D10711yescharacteristic
232C2×Q8—1071no—
233C2×Q8C22×D10711yescharacteristic
234C2×D4—1071no—
235C2×D4—2141no—
236C2×D4—2141no—
237C2×D4C22×D10711yescharacteristic
238C22×C4—1071no—
239C22×C4—1071no—
240C22×C4—1071no—
241C22×C4—2141no—
242C22×C4—2141no—
243Q16—2142no—
244SD16—2142no—
245SD16—2142no—
246D8—2142no—
247C2×C8—1071no—
248C2×C8—1071no—
249C2×C8—2142no—
250C2×C8—2142no—
251C2×C8C22×D10711yescharacteristic
252C2×C8C22×D10711yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—1071no—
256C4⋊C4—1071no—
257C4⋊C4—2141no—
258C4⋊C4—2141no—
259C4⋊C4—2141no—
260C4⋊C4—2141no—
261C4⋊C4—2141no—
262C4⋊C4—2141no—
263C4⋊C4C22×D10711yescharacteristic
264C4⋊C4C22×D10711yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—2141no—
268C22⋊C4—2141no—
269C22⋊C4—2141no—
270C22⋊C4—2141no—
271C22⋊C4—2141no—
272C22⋊C4—2141no—
273C22⋊C4—2141no—
274C22⋊C4—2141no—
275C42—1071no—
276C42—1071no—
277C42—1071no—
278C42—2141no—
279C42—2141no—
280C42C22×D10711yescharacteristic
281C23—21no—
282C23—1071no—
283C23—2141no—
284Q8—21no—
285Q8—21no—
286Q8—2141no—
287Q8—2141no—
288D4—21no—
289D4—21no—
290D4—4282no—
291D4—4282no—
292D4—2141no—
293D4—2141no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—1071no—
298C2×C4—1071no—
299C2×C4—1071no—
300C2×C4—4282no—
301C2×C4—4282no—
302C2×C4—2142no—
303C2×C4—2142no—
304C2×C4—2141no—
305C2×C4—2141no—
306C2×C4—2141no—
307C2×C4—2141no—
308C2×C4—2141no—
309C2×C4D4×D10711yescharacteristic
310C2×C4D4×D10711yescharacteristic
311C2×C4C23×D10711yescharacteristic
312C8—21no—
313C8—21no—
314C8—1072no—
315C8—1072no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—1072no—
320C22—4281no—
321C22—4281no—
322C22—4281no—
323C22—2141no—
324C22—2141no—
325C22C2×D4×D10711yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—1072no—
332C4—4281no—
333C4—4281no—
334C4—4281no—
335C4—2141no—
336C4—2141no—
337C4#41×D10711yescharacteristic
338C4#41×D10711yescharacteristic
339C2—81no—
340C2—8561no—
341C2—2142no—
342C2#2029317611yescharacteristic
343C2#135×D10711yescharacteristic
344C2#135×D10711yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#488×C107C2
socleC22×C107C22×D4
prime radical#20292862C2
hypercenter#488D107
hypocenterC107#3168
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #20293162C2semidirect
2. #20293156C2semidirect
3. #20293026C2semidirect
4. #20293009C2semidirect
5. #20292982C2semidirect
6. #20292867C2semidirect
8. #20292859C2semidirect
9. #20292855C2semidirect
10. #20292719C2semidirect
11. #20292718C2semidirect
12. #20292712C2semidirect
13. #20292707C2semidirect
14. C4×C8×D107C2semidirect
15. #488×C107C2semidirect
173. C107#3168semidirect
179. #488D107semidirect

Maximal subgroups

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

subgroupindex
#202931622
#202931562
#202930262
#202930092
#202929822
#202928672
#202928622
#202928592
#202928552
#202927192
#202927182
#202927122
#202927072
C4×C8×D1072
#488×C1072
#3168107