Finite Group Databasebeta

← #28346825

Subgroups — #28346825

Order 13696.

372 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#20293257C211yesmaximal, characteristic, complemented
2#20293197C211yesmaximal, characteristic
3#20292997C211yesmaximal, characteristic, complemented
4#20292994C211yesmaximal, characteristic, complemented
5#20292986C211yesmaximal, characteristic, complemented
6#20292985C211yesmaximal, characteristic, complemented
7#20292980C211yesmaximal, characteristic, complemented
8#20292978C211yesmaximal, characteristic, complemented
9#20292976C211yesmaximal, characteristic, complemented
10#20292634C211yesmaximal, characteristic, complemented
11#20292625C211yesmaximal, characteristic
12#20292620C211yesmaximal, characteristic
13#103×D107C211yesmaximal, characteristic, complemented
14#20292581C211yesmaximal, characteristic, complemented
15#488×C107C211yesmaximal, characteristic, complemented
16C2×#13133817C2211yescharacteristic
17C2×Q8×D107C2211yescharacteristic
18C2×#13133801C2211yescharacteristic
19C2×C8×D107C2211yescharacteristic
20#16812109C2211yescharacteristic
21#16812109C2211yescharacteristic
22#16812108—21no—
23#16812108C2211yescharacteristic
24#16812107C2211yescharacteristic
25#16812100C2211yescharacteristic
26#16812099—21no—
27#16812096C2211yescharacteristic
28#16812091—21no—
29#16812091—21no—
30#16812089—21no—
31#16812087—21no—
32#16812086—21no—
33#16812086—21no—
34#16812067C2211yescharacteristic
35#16812066C2211yescharacteristic
36C4⋊C4×D107C2211yescharacteristic
37#16812034C2211yescharacteristic
38#16812034C2211yescharacteristic
39#16812034C2211yescharacteristic
40#16812034C2211yescharacteristic
41#16812033C2211yescharacteristic
42#16812033C2211yescharacteristic
43#16812032C2211yescharacteristic
44#16812032C2211yescharacteristic
45#16812032C2211yescharacteristic
46#16812032C2211yescharacteristic
47#16812030C2211yescharacteristic
48#16812030C2211yescharacteristic
49#16812020C2211yescharacteristic
50#16812019C2211yescharacteristic
51C8×Dic107C2211yescharacteristic
52#125×C107C2211yescharacteristic
53#124×C107C2211yescharacteristic
54#103×C107C2211yescharacteristic
55#103×C107C2211yescharacteristic
56#102×C107C2211yescharacteristic
57#102×C107C2211yescharacteristic
58C4×C8×C107C2211yescharacteristic
59#13133817—22no—
60#13133817—22no—
61C2×Dic214—21no—
62C2×Dic214—21no—
63C2×Dic214—21no—
64C2×Dic214C2311yescharacteristic
65C2×Dic214C2311yescharacteristic
66Q8×D107—22no—
67Q8×D107—22no—
68C2×C22⋊D107—21no—
69C22×Dic107—21no—
70C2×C4×D107—21no—
71C2×C4×D107—21no—
72C2×C4×D107C2311yescharacteristic
73#13133801—22no—
74C2×C107⋊C8C2311yescharacteristic
75C2×C107⋊C8C2311yescharacteristic
76C8×D107—22no—
77C4⋊Dic107—21no—
78C4⋊Dic107—21no—
79C4⋊Dic107—21no—
80C4⋊Dic107—21no—
81C4⋊Dic107C2311yescharacteristic
82C4⋊Dic107C2311yescharacteristic
83Dic107⋊C4—21no—
84Dic107⋊C4—21no—
85Dic107⋊C4—21no—
86Dic107⋊C4—21no—
87Dic107⋊C4—21no—
88Dic107⋊C4D411yescharacteristic
89Dic107⋊C4D411yescharacteristic
90C22⋊Dic107—21no—
91C22⋊Dic107—21no—
92(C2×D107)⋊C4—21no—
93(C2×D107)⋊C4D411yescharacteristic
94(C2×D107)⋊C4D411yescharacteristic
95C4×Dic107—21no—
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×D107C2×D411yescharacteristic
110Q8×C107—21no—
111Q8×C107—21no—
112D4×C107—21no—
113D4×C107—21no—
114C2×C4×C107—21no—
115C2×C4×C107—21no—
116C2×C4×C107—21no—
117C2×C4×C107C2×D411yescharacteristic
118C2×C4×C107C2×D411yescharacteristic
119C2×C4×C107C2411yescharacteristic
120C22⋊D107—42no—
121C2×Dic107—21no—
122C2×Dic107—21no—
123C2×Dic107—21no—
124C2×Dic107—21no—
125C2×Dic107—42no—
126C2×Dic107C2×D411yescharacteristic
127C2×Dic107C2×D411yescharacteristic
128C2×Dic107C2×D411yescharacteristic
129C4×D107—42no—
130C4×D107—81no—
131C4×D107#4112yes—
132C4×D107#4112yes—
133Dic214—21no—
134Dic214—21no—
135Dic214—21no—
136Dic214—21no—
137Dic214—42no—
138Dic214—81no—
139Dic214—81no—
140C8×C107—21no—
141C8×C107—21no—
142C107⋊C8—21no—
143C107⋊C8—21no—
144C22×C107—41no—
145C22×C107—41no—
146C22×C107—41no—
147C22×C107C22×D411yescharacteristic
148C2×D107—21no—
149C2×D107—21no—
150C2×D107#12412yes—
151C4×C107—21no—
152C4×C107—21no—
153C4×C107—41no—
154C4×C107—41no—
155C4×C107—41no—
156C4×C107C2×#4111yescharacteristic
157C4×C107C2×#4111yescharacteristic
158Dic107—21no—
159Dic107—21no—
160Dic107—41no—
161Dic107—41no—
162Dic107—41no—
163Dic107—41no—
164Dic107#12412yes—
165C2×C107—81no—
166C2×C107C2×#12411yescharacteristic
167C2×C107#57711yescharacteristic
168C2×C107#57811yescharacteristic
169D107—22no—
170#3137—1071nomaximal, Sylow
171C107#313711yescharacteristic, complemented, Sylow
172#544—1071no—
173#536—1071no—
174#491—1071no—
175#491—1071no—
176#489—1071no—
177#489—1071no—
178#488—1071no—
179#488D10711yescharacteristic, complemented
180#487—1071no—
181#487—1071no—
182#419—1071no—
183#417—1071no—
184#416—1071no—
185C2×#103—1071no—
186#405—1071no—
187C2×#41—1071no—
188C22×Q8—1071no—
189C2×M16—1071no—
190C22×C8—1071no—
191C4⋊Q8—1071no—
192C4⋊Q8—1071no—
193C4⋊Q8—1071no—
194C4⋊Q8—1071no—
195C4⋊Q8—2141no—
196#125—1071no—
197#125—2141no—
198#125C2×D10711yescharacteristic
199#124—1071no—
200#124C2×D10711yescharacteristic
201#123—2141no—
202#123—2141no—
203C22⋊Q8—2141no—
204C22⋊Q8—2141no—
205C22⋊Q8—2141no—
206C22⋊Q8—2141no—
207#117—1071no—
208#117—1071no—
209C2×C4⋊C4—1071no—
210#103—1071no—
211#103—1071no—
212#103—1071no—
213#103—1071no—
214#103—1071no—
215#103—1071no—
216#103—1071no—
217#103—1071no—
218#103—1071no—
219#103—1071no—
220#103C2×D10711yescharacteristic
221#103C2×D10711yescharacteristic
222#102—1071no—
223#102—1071no—
224#102C2×D10711yescharacteristic
225#102C2×D10711yescharacteristic
226#97—1071no—
227#97—1071no—
228C4×C8—1071no—
229C4×C8C2×D10711yescharacteristic
230#41—2142no—
231#41—2142no—
232C2×Q8—1071no—
233C2×Q8—1071no—
234C2×Q8—2141no—
235C2×Q8—2141no—
236C2×Q8—2142no—
237C2×Q8—2142no—
238C2×Q8—2141no—
239C2×Q8C22×D10711yescharacteristic
240C2×D4—2141no—
241C2×D4C22×D10711yescharacteristic
242C22×C4—1071no—
243C22×C4—2141no—
244C22×C4—2141no—
245C22×C4—2141no—
246M16—2142no—
247C2×C8—1071no—
248C2×C8—1071no—
249C2×C8—2142no—
250C2×C8C22×D10711yescharacteristic
251C2×C8C22×D10711yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—1071no—
255C4⋊C4—1071no—
256C4⋊C4—1071no—
257C4⋊C4—1071no—
258C4⋊C4—2141no—
259C4⋊C4—2141no—
260C4⋊C4—2141no—
261C4⋊C4—2141no—
262C4⋊C4—2141no—
263C4⋊C4—2141no—
264C4⋊C4—2141no—
265C4⋊C4—2141no—
266C4⋊C4—2141no—
267C4⋊C4C22×D10711yescharacteristic
268C4⋊C4C22×D10711yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—1071no—
272C22⋊C4—1071no—
273C22⋊C4—2141no—
274C22⋊C4—2141no—
275C22⋊C4—2141no—
276C42—1071no—
277C42—2141no—
278C42C22×D10711yescharacteristic
279C23—21no—
280C23—1071no—
281Q8—21no—
282Q8—21no—
283Q8—8561no—
284Q8—8561no—
285Q8—4282no—
286Q8—2141no—
287Q8—2141no—
288Q8—2141no—
289Q8—2141no—
290D4—21no—
291D4—21no—
292D4—4282no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—8561no—
297C2×C4—1071no—
298C2×C4—1072no—
299C2×C4—1072no—
300C2×C4—1071no—
301C2×C4—1071no—
302C2×C4—4282no—
303C2×C4—4282no—
304C2×C4—2141no—
305C2×C4—2141no—
306C2×C4—2141no—
307C2×C4—2141no—
308C2×C4D4×D10711yescharacteristic
309C2×C4D4×D10711yescharacteristic
310C2×C4C23×D10711yescharacteristic
311C8—21no—
312C8—21no—
313C8—2141no—
314C8—2141no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—1072no—
319C22—2141no—
320C22—2141no—
321C22C2×D4×D10711yescharacteristic
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—1072no—
328C4—4281no—
329C4—4281no—
330C4—4281no—
331C4—4281no—
332C4—2141no—
333C4—2141no—
334C4#41×D10711yescharacteristic
335C4#41×D10711yescharacteristic
336C2—81no—
337C2—2142no—
338C2#124×D10711yescharacteristic
339C2#2029343411yescharacteristic
340C2#2029344111yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#488×C107C2
socleC22×C107C22×D4
prime radicalC2×#13133817C22
hypercenter#488D107
hypocenterC107#3137
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. #20293257C2semidirect
3. #20292997C2semidirect
4. #20292994C2semidirect
5. #20292986C2semidirect
6. #20292985C2semidirect
7. #20292980C2semidirect
8. #20292978C2semidirect
9. #20292976C2semidirect
10. #20292634C2semidirect
13. #103×D107C2semidirect
14. #20292581C2semidirect
15. #488×C107C2semidirect
171. C107#3137semidirect
179. #488D107semidirect

Maximal subgroups

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

subgroupindex
#202932572
#202931972
#202929972
#202929942
#202929862
#202929852
#202929802
#202929782
#202929762
#202926342
#202926252
#202926202
#103×D1072
#202925812
#488×C1072
#3137107