Finite Group Databasebeta

← #28346427

Subgroups — #28346427

Order 13696.

386 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293200C211yesmaximal, characteristic
2#20293107C211yesmaximal, characteristic
3#20292971C211yesmaximal, characteristic, complemented
4#20292968C211yesmaximal, characteristic, complemented
5#20292966C211yesmaximal, characteristic, complemented
6#20292964C211yesmaximal, characteristic, complemented
7#20292960C211yesmaximal, characteristic, complemented
8#20292958C211yesmaximal, characteristic, complemented
9#20292956C211yesmaximal, characteristic, complemented
10#20292668C211yesmaximal, characteristic, complemented
11#20292662C211yesmaximal, characteristic, complemented
12#20292634C211yesmaximal, characteristic, complemented
13#103×D107C211yesmaximal, characteristic, complemented
14#20292592C211yesmaximal, characteristic
15#485×C107C211yesmaximal, characteristic, complemented
16C2×#13133818C2211yescharacteristic
17C2×Q8×D107C2211yescharacteristic
18C2×#13133801C2211yescharacteristic
19C2×C8×D107C2211yescharacteristic
20#16812108—21no—
21#16812095—21no—
22#16812094—21no—
23#16812091—21no—
24#16812089C2211yescharacteristic
25#16812088C2211yescharacteristic
26#16812085C2211yescharacteristic
27C4×Dic214—21no—
28C4×D428—21no—
29(C22⋊D107)⋊C4—21no—
30(C22⋊D107)⋊C4—21no—
31#16812067C2211yescharacteristic
32#16812067C2211yescharacteristic
33#16812067C2211yescharacteristic
34C2×C4⋊Dic107C2211yescharacteristic
35C4⋊C4×D107C2211yescharacteristic
36C4⋊C4×D107C2211yescharacteristic
37#16812042C2211yescharacteristic
38#16812042C2211yescharacteristic
39#16812042C2211yescharacteristic
40#16812041C2211yescharacteristic
41#16812041C2211yescharacteristic
42#16812040C2211yescharacteristic
43#16812034C2211yescharacteristic
44#16812034C2211yescharacteristic
45#16812033C2211yescharacteristic
46#16812033C2211yescharacteristic
47#16812032C2211yescharacteristic
48#16812032C2211yescharacteristic
49C22⋊(C107⋊C8)C2211yescharacteristic
50(C2×D107)⋊C8C2211yescharacteristic
51(C2×D107)⋊C8C2211yescharacteristic
52C22⋊Q8×C107C2211yescharacteristic
53#117×C107C2211yescharacteristic
54#107×C107C2211yescharacteristic
55#106×C107C2211yescharacteristic
56#103×C107C2211yescharacteristic
57#103×C107C2211yescharacteristic
58C22⋊C8×C107C2211yescharacteristic
59#13133818—22no—
60#13133818—22no—
61C2×Dic214—21no—
62C2×Dic214D411yescharacteristic
63C2×Dic214C2311yescharacteristic
64Q8×D107—22no—
65Q8×D107—22no—
66C2×D428D411yescharacteristic
67C2×C22⋊D107D411yescharacteristic
68C2×C22⋊D107D411yescharacteristic
69C22×Dic107—21no—
70C2×C4×D107—21no—
71C2×C4×D107—21no—
72C2×C4×D107—21no—
73C2×C4×D107C2311yescharacteristic
74C2×C4×D107C2311yescharacteristic
75#13133801—22no—
76C2×C107⋊C8C2311yescharacteristic
77C2×C107⋊C8C2311yescharacteristic
78C8×D107—22no—
79C4⋊Dic107—21no—
80C4⋊Dic107—21no—
81C4⋊Dic107C2311yescharacteristic
82C4⋊Dic107C2311yescharacteristic
83C4⋊Dic107C2311yescharacteristic
84Dic107⋊C4—21no—
85Dic107⋊C4—21no—
86Dic107⋊C4—21no—
87Dic107⋊C4—21no—
88C22⋊Dic107—21no—
89(C2×D107)⋊C4—21no—
90(C2×D107)⋊C4—21no—
91(C2×D107)⋊C4—21no—
92(C2×D107)⋊C4—21no—
93(C2×D107)⋊C4—21no—
94C4×Dic107—21no—
95C4×Dic107—21no—
96C4×Dic107—21no—
97C2×Q8×C107C2311yescharacteristic
98C22×C4×C107C2311yescharacteristic
99C2×C8×C107C2311yescharacteristic
100C2×C8×C107C2311yescharacteristic
101C4⋊C4×C107—21no—
102C4⋊C4×C107C2311yescharacteristic
103C4⋊C4×C107C2311yescharacteristic
104C4⋊C4×C107C2311yescharacteristic
105C22⋊C4×C107—21no—
106C22⋊C4×C107—21no—
107C42×C107—21no—
108C23×C107C2×D411yescharacteristic
109C22×D107C2×D411yescharacteristic
110C22×D107C2×D411yescharacteristic
111Q8×C107—21no—
112Q8×C107—21no—
113C2×C4×C107—21no—
114C2×C4×C107—21no—
115C2×C4×C107—21no—
116C2×C4×C107—21no—
117C2×C4×C107—21no—
118C2×C4×C107—21no—
119C2×C4×C107C2×D411yescharacteristic
120C2×C4×C107C2411yescharacteristic
121C22⋊D107—22no—
122C22⋊D107—22no—
123C2×Dic107—21no—
124C2×Dic107—21no—
125C2×Dic107—21no—
126C2×Dic107—21no—
127C2×Dic107—81no—
128C2×Dic107C2×D411yescharacteristic
129C2×Dic107C2×D411yescharacteristic
130D428—22no—
131C4×D107—21no—
132C4×D107—21no—
133C4×D107—42no—
134C4×D107—81no—
135C4×D107—81no—
136C4×D107#4112yes—
137C4×D107#4112yes—
138Dic214—22no—
139Dic214—21no—
140Dic214—21no—
141Dic214—42no—
142C8×C107—21no—
143C8×C107—21no—
144C107⋊C8—21no—
145C107⋊C8—21no—
146C22×C107—21no—
147C22×C107—21no—
148C22×C107—21no—
149C22×C107C22×D411yescharacteristic
150C2×D107—21no—
151C2×D107—21no—
152C2×D107—21no—
153C2×D107—21no—
154C2×D107—21no—
155C2×D107#12312yes—
156C4×C107—21no—
157C4×C107—41no—
158C4×C107—41no—
159C4×C107—41no—
160C4×C107—41no—
161C4×C107C2×#4111yescharacteristic
162C4×C107C2×#4111yescharacteristic
163Dic107—21no—
164Dic107—41no—
165Dic107—41no—
166Dic107—41no—
167Dic107—41no—
168Dic107#12312yes—
169C2×C107—41no—
170C2×C107C2×#12311yescharacteristic
171C2×C107#57711yescharacteristic
172C2×C107#57811yescharacteristic
173D107—22no—
174D107—41no—
175#3097—1071nomaximal, Sylow
176C107#309711yescharacteristic, complemented, Sylow
177#536—1071no—
178#520—1071no—
179#485—1071no—
180#485—1071no—
181#485—1071no—
182#485D10711yescharacteristic, complemented
183#484—1071no—
184#484—1071no—
185#483—1071no—
186#483—1071no—
187#428—1071no—
188#427—1071no—
189#419—1071no—
190C2×#103—1071no—
191#408—1071no—
192C2×#41—1071no—
193C22×Q8—1071no—
194C2×M16—1071no—
195C22×C8—1071no—
196C4⋊Q8—2141no—
197#124—2141no—
198#123—2141no—
199#123—2141no—
200C22⋊Q8—1071no—
201C22⋊Q8—1071no—
202C22⋊Q8—1071no—
203C22⋊Q8C2×D10711yescharacteristic
204C4×Q8—2141no—
205C4×D4—2141no—
206C4×D4—2141no—
207C4×D4—2141no—
208#117—1071no—
209#117—1071no—
210#117—1071no—
211#117C2×D10711yescharacteristic
212C2×C4⋊C4—1071no—
213C2×C4⋊C4—1071no—
214C2×C4⋊C4—1071no—
215#107—1071no—
216#107—1071no—
217#107—1071no—
218#107C2×D10711yescharacteristic
219#106—1071no—
220#106—1071no—
221#106—1071no—
222#106C2×D10711yescharacteristic
223#103—1071no—
224#103—1071no—
225#103—1071no—
226#103—1071no—
227#103—1071no—
228#103—1071no—
229#103C2×D10711yescharacteristic
230#103C2×D10711yescharacteristic
231C22⋊C8—1071no—
232C22⋊C8—1071no—
233C22⋊C8—1071no—
234C22⋊C8C2×D10711yescharacteristic
235#41—2142no—
236#41—2142no—
237C2×Q8—1071no—
238C2×Q8—1071no—
239C2×Q8—2141no—
240C2×Q8—2142no—
241C2×Q8—2142no—
242C2×Q8C22×D10711yescharacteristic
243C2×D4—1071no—
244C2×D4—1071no—
245C2×D4—1071no—
246C22×C4—1071no—
247C22×C4—1071no—
248C22×C4—2141no—
249C22×C4—2141no—
250C22×C4—2141no—
251C22×C4—2141no—
252C22×C4C22×D10711yescharacteristic
253M16—2142no—
254C2×C8—1071no—
255C2×C8—1071no—
256C2×C8—2142no—
257C2×C8C22×D10711yescharacteristic
258C2×C8C22×D10711yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—1071no—
261C4⋊C4—1071no—
262C4⋊C4—1071no—
263C4⋊C4—2141no—
264C4⋊C4—2141no—
265C4⋊C4—2141no—
266C4⋊C4—2141no—
267C4⋊C4—2141no—
268C4⋊C4—2141no—
269C4⋊C4C22×D10711yescharacteristic
270C4⋊C4C22×D10711yescharacteristic
271C4⋊C4C22×D10711yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—2141no—
275C22⋊C4—2141no—
276C22⋊C4—2141no—
277C22⋊C4—2141no—
278C22⋊C4—2141no—
279C22⋊C4—2141no—
280C42—21no—
281C42—2141no—
282C42—2141no—
283C42—2141no—
284C23—1071no—
285C23—1071no—
286C23D4×D10711yescharacteristic
287Q8—21no—
288Q8—21no—
289Q8—4282no—
290Q8—2142no—
291Q8—2141no—
292Q8—2141no—
293D4—2142no—
294D4—2142no—
295D4—2142no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—8561no—
303C2×C4—8561no—
304C2×C4—8561no—
305C2×C4—1071no—
306C2×C4—1072no—
307C2×C4—1072no—
308C2×C4—1071no—
309C2×C4—4282no—
310C2×C4—2141no—
311C2×C4—2141no—
312C2×C4—2141no—
313C2×C4—2141no—
314C2×C4—2141no—
315C2×C4—2141no—
316C2×C4D4×D10711yescharacteristic
317C2×C4C23×D10711yescharacteristic
318C8—21no—
319C8—21no—
320C8—2141no—
321C8—2141no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—1072no—
326C22—2141no—
327C22—2141no—
328C22—2141no—
329C22—2141no—
330C22—2141no—
331C22C2×D4×D10711yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—1072no—
338C4—4281no—
339C4—4281no—
340C4—4281no—
341C4—4281no—
342C4—2141no—
343C4#41×D10711yescharacteristic
344C4#41×D10711yescharacteristic
345C2—41no—
346C2—4281no—
347C2—2142no—
348C2#123×D10711yescharacteristic
349C2#2029343411yescharacteristic
350C2#2029344311yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#485×C107C2
socleC22×C107C22×D4
prime radicalC2×#13133818C22
hypercenter#485D107
hypocenterC107#3097
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
3. #20292971C2semidirect
4. #20292968C2semidirect
5. #20292966C2semidirect
6. #20292964C2semidirect
7. #20292960C2semidirect
8. #20292958C2semidirect
9. #20292956C2semidirect
10. #20292668C2semidirect
11. #20292662C2semidirect
12. #20292634C2semidirect
13. #103×D107C2semidirect
15. #485×C107C2semidirect
176. C107#3097semidirect
182. #485D107semidirect

Maximal subgroups

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

subgroupindex
#202932002
#202931072
#202929712
#202929682
#202929662
#202929642
#202929602
#202929582
#202929562
#202926682
#202926622
#202926342
#103×D1072
#202925922
#485×C1072
#3097107