Finite Group Databasebeta

← #28348373

Subgroups — #28348373

Order 13696.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293348C211yesmaximal, characteristic, complemented
2#20293279C211yesmaximal, characteristic
3#20292976C211yesmaximal, characteristic, complemented
4#20292970C211yesmaximal, characteristic, complemented
5#20292965C211yesmaximal, characteristic, complemented
6#20292906C211yesmaximal, characteristic, complemented
7#20292867C211yesmaximal, characteristic, complemented
8#20292835C211yesmaximal, characteristic, complemented
9#20292788C211yesmaximal, characteristic, complemented
10#20292787C211yesmaximal, characteristic, complemented
11#20292712C211yesmaximal, characteristic, complemented
12C8×C22⋊D107C211yesmaximal, characteristic, complemented
13#20292624C211yesmaximal, characteristic, complemented
14#20292622C211yesmaximal, characteristic, complemented
15#467×C107C211yesmaximal, characteristic, complemented
16C2×#13133819C2211yescharacteristic
17C2×#13133818C2211yescharacteristic
18C2×#13133808C2211yescharacteristic
19C2×#13133805C2211yescharacteristic
20C2×C8×D107C2211yescharacteristic
21#16812108C2211yescharacteristic
22#16812107C2211yescharacteristic
23#16812104—21no—
24#16812102—21no—
25#16812095—21no—
26#16812094—21no—
27#16812091—21no—
28#16812089C2211yescharacteristic
29#16812085C2211yescharacteristic
30#16812082—21no—
31Q8×Dic107C2211yescharacteristic
32#16812074—21no—
33#16812071C2211yescharacteristic
34C4×C22⋊D107C2211yescharacteristic
35#16812068C2211yescharacteristic
36#16812067C2211yescharacteristic
37C4⋊C4×D107—21no—
38#16812042C2211yescharacteristic
39#16812040C2211yescharacteristic
40Dic107⋊C8C2211yescharacteristic
41#16812034C2211yescharacteristic
42#16812034C2211yescharacteristic
43#16812033C2211yescharacteristic
44#16812033C2211yescharacteristic
45#16812032C2211yescharacteristic
46#16812031C2211yescharacteristic
47#16812031C2211yescharacteristic
48#16812029C2211yescharacteristic
49C22⋊(C107⋊C8)C2211yescharacteristic
50(C2×D107)⋊C8C2211yescharacteristic
51C8×Dic107C2211yescharacteristic
52C2×Q16×C107C2211yescharacteristic
53C22×C8×C107C2211yescharacteristic
54C22⋊Q8×C107C2211yescharacteristic
55C22⋊Q8×C107C2211yescharacteristic
56#107×C107C2211yescharacteristic
57#103×C107C2211yescharacteristic
58#103×C107C2211yescharacteristic
59#13133819—22no—
60#13133819—41no—
61#13133818—22no—
62#13133818—41no—
63C2×Dic214—21no—
64C2×Dic214C2311yescharacteristic
65C2×D428—21no—
66C2×D428C2311yescharacteristic
67C2×C22⋊D107—21no—
68C2×C22⋊D107D411yescharacteristic
69C2×C4×D107—21no—
70C2×C4×D107—21no—
71C2×C4×D107—21no—
72C2×C4×D107C2311yescharacteristic
73#13133808—41no—
74#13133805—22no—
75C2×C107⋊C8C2311yescharacteristic
76C2×C107⋊C8C2311yescharacteristic
77C8×D107—41no—
78C4⋊Dic107—21no—
79C4⋊Dic107—21no—
80C4⋊Dic107C2311yescharacteristic
81C4⋊Dic107C2311yescharacteristic
82Dic107⋊C4—21no—
83Dic107⋊C4—21no—
84Dic107⋊C4—21no—
85Dic107⋊C4—21no—
86Dic107⋊C4D411yescharacteristic
87C22⋊Dic107—21no—
88C22⋊Dic107D411yescharacteristic
89(C2×D107)⋊C4—21no—
90(C2×D107)⋊C4—21no—
91(C2×D107)⋊C4—21no—
92(C2×D107)⋊C4—21no—
93(C2×D107)⋊C4D411yescharacteristic
94C4×Dic107—21no—
95C4×Dic107—21no—
96C4×Dic107—21no—
97C4×Dic107C2311yescharacteristic
98C2×Q8×C107C2311yescharacteristic
99C2×Q8×C107C2311yescharacteristic
100C22×C4×C107C2311yescharacteristic
101Q16×C107—41no—
102C2×C8×C107—41no—
103C2×C8×C107C2311yescharacteristic
104C2×C8×C107C2311yescharacteristic
105C4⋊C4×C107—21no—
106C4⋊C4×C107—21no—
107C4⋊C4×C107C2311yescharacteristic
108C4⋊C4×C107C2311yescharacteristic
109C22⋊C4×C107—21no—
110C22⋊C4×C107—21no—
111C23×C107C2×D411yescharacteristic
112C22×D107—21no—
113C22×D107C2×D411yescharacteristic
114Q8×C107—21no—
115Q8×C107—21no—
116Q8×C107—21no—
117Q8×C107—21no—
118C2×C4×C107—21no—
119C2×C4×C107—21no—
120C2×C4×C107—21no—
121C2×C4×C107—21no—
122C2×C4×C107—21no—
123C2×C4×C107—21no—
124C2×C4×C107C2×D411yescharacteristic
125C2×C4×C107C2411yescharacteristic
126C22⋊D107—22no—
127C22⋊D107—42no—
128C2×Dic107—21no—
129C2×Dic107—21no—
130C2×Dic107—21no—
131C2×Dic107C2×D411yescharacteristic
132C2×Dic107C2×D411yescharacteristic
133C2×Dic107C2×D411yescharacteristic
134D428—21no—
135D428—42no—
136D428#4112yes—
137C4×D107—21no—
138C4×D107—21no—
139C4×D107—42no—
140C4×D107—42no—
141C4×D107—42no—
142Dic214—21no—
143Dic214—21no—
144Dic214—42no—
145C8×C107—21no—
146C8×C107—21no—
147C107⋊C8—21no—
148C107⋊C8—21no—
149C22×C107—21no—
150C22×C107—21no—
151C22×C107—21no—
152C22×C107C22×D411yescharacteristic
153C2×D107—21no—
154C2×D107—22no—
155C2×D107—21no—
156C2×D107—21no—
157C2×D107—41no—
158C2×D107—41no—
159C4×C107—21no—
160C4×C107—41no—
161C4×C107—41no—
162C4×C107—41no—
163C4×C107—41no—
164C4×C107C2×#4111yescharacteristic
165C4×C107H(5,𝔽2)11yescharacteristic
166Dic107—21no—
167Dic107—21no—
168Dic107—41no—
169Dic107—41no—
170Dic107—41no—
171Dic107#13512yes—
172C2×C107—41no—
173C2×C107#54611yescharacteristic
174C2×C107C2×#13511yescharacteristic
175C2×C107#57811yescharacteristic
176D107—41no—
177D107—42no—
178#3302—1071nomaximal, Sylow
179C107#330211yescharacteristic, complemented, Sylow
180#556—1071no—
181#547—1071no—
182#487—1071no—
183#485—1071no—
184#485—1071no—
185#474—1071no—
186#467—1071no—
187#467D10711yescharacteristic, complemented
188#462—1071no—
189#452—1071no—
190#452—1071no—
191C4×SD16—1071no—
192C8×D4—1071no—
193#416—1071no—
194#416—1071no—
195C2×#41—1071no—
196C2×#41—1071no—
197C2×Q16—1071no—
198C2×Q16C2×D10711yescharacteristic
199C2×SD16—1071no—
200C22×C8—1071no—
201C22×C8C2×D10711yescharacteristic
202C4⋊Q8—1071no—
203C4⋊Q8—1071no—
204#126—2141no—
205#126—2141no—
206#124—2141no—
207#123—2141no—
208#123—2141no—
209C22⋊Q8—1071no—
210C22⋊Q8—1071no—
211C22⋊Q8C2×D10711yescharacteristic
212C22⋊Q8C2×D10711yescharacteristic
213#121—2141no—
214C4×Q8—1071no—
215C4×Q8—2141no—
216C4×D4—1071no—
217C4×D4—1071no—
218#117—1071no—
219#117—1071no—
220C2×C4⋊C4—2141no—
221#107—1071no—
222#107C2×D10711yescharacteristic
223#106—1071no—
224C4⋊C8—1071no—
225#103—1071no—
226#103—1071no—
227#103—1071no—
228#103—1071no—
229#103—1071no—
230#103C2×D10711yescharacteristic
231#103C2×D10711yescharacteristic
232#102—1071no—
233#102—1071no—
234#102—1071no—
235C22⋊C8—1071no—
236C22⋊C8—1071no—
237C4×C8—1071no—
238#41—4281no—
239#41—4281no—
240#41—2142no—
241#41—2142no—
242C2×Q8—1071no—
243C2×Q8—2141no—
244C2×Q8C22×D10711yescharacteristic
245C2×Q8C22×D10711yescharacteristic
246C2×D4—1071no—
247C2×D4—1071no—
248C2×D4—2141no—
249C2×D4—2141no—
250C22×C4—1071no—
251C22×C4—2141no—
252C22×C4—2141no—
253C22×C4—2141no—
254C22×C4C22×D10711yescharacteristic
255Q16—41no—
256Q16—4281no—
257SD16—2142no—
258C2×C8—41no—
259C2×C8—1071no—
260C2×C8—1071no—
261C2×C8—4281no—
262C2×C8C22×D10711yescharacteristic
263C2×C8C22×D10711yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—1071no—
267C4⋊C4—1071no—
268C4⋊C4—1071no—
269C4⋊C4—2141no—
270C4⋊C4—2141no—
271C4⋊C4—2141no—
272C4⋊C4—2141no—
273C4⋊C4—2141no—
274C4⋊C4—2141no—
275C4⋊C4C22×D10711yescharacteristic
276C4⋊C4C22×D10711yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—1071no—
280C22⋊C4—1071no—
281C22⋊C4—2141no—
282C22⋊C4—2141no—
283C22⋊C4—2141no—
284C22⋊C4—2141no—
285C22⋊C4—2141no—
286C42—1071no—
287C42—2141no—
288C42—2141no—
289C42—2141no—
290C23—1071no—
291C23—2141no—
292C23D4×D10711yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—4282no—
298Q8—2141no—
299Q8—2141no—
300D4—1072no—
301D4—4282no—
302D4—4282no—
303D4—2142no—
304D4—2141no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—1071no—
312C2×C4—1071no—
313C2×C4—1071no—
314C2×C4—4282no—
315C2×C4—4282no—
316C2×C4—4282no—
317C2×C4—2141no—
318C2×C4—2141no—
319C2×C4—2141no—
320C2×C4—2141no—
321C2×C4—2141no—
322C2×C4D4×D10711yescharacteristic
323C2×C4C23×D10711yescharacteristic
324C8—21no—
325C8—21no—
326C8—2141no—
327C8—2141no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—4281no—
332C22—4281no—
333C22—2141no—
334C22—2141no—
335C22—2142no—
336C22—2141no—
337C22C2×D4×D10711yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—1072no—
344C4—4281no—
345C4—4281no—
346C4—4281no—
347C4—2141no—
348C4—2141no—
349C4#41×D10711yescharacteristic
350C4#1681215411yescharacteristic
351C2—41no—
352C2—4282no—
353C2—4281no—
354C2#2029326611yescharacteristic
355C2#135×D10711yescharacteristic
356C2#2029344011yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#467×C107C2
socleC22×C107C22×D4
prime radical#20293279C2
hypercenter#467D107
hypocenterC107#3302
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #20293348C2semidirect
3. #20292976C2semidirect
4. #20292970C2semidirect
5. #20292965C2semidirect
6. #20292906C2semidirect
7. #20292867C2semidirect
8. #20292835C2semidirect
9. #20292788C2semidirect
10. #20292787C2semidirect
11. #20292712C2semidirect
12. C8×C22⋊D107C2semidirect
13. #20292624C2semidirect
14. #20292622C2semidirect
15. #467×C107C2semidirect
179. C107#3302semidirect
187. #467D107semidirect

Maximal subgroups

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

subgroupindex
#202933482
#202932792
#202929762
#202929702
#202929652
#202929062
#202928672
#202928352
#202927882
#202927872
#202927122
C8×C22⋊D1072
#202926242
#202926222
#467×C1072
#3302107