Finite Group Databasebeta

← #28346467

Subgroups — #28346467

Order 13696.

448 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293181C211yesmaximal, characteristic, complemented
2C4×D4×D107C211yesmaximal, characteristic
3#20292959C211yesmaximal, characteristic, complemented
4#20292956C211yesmaximal, characteristic, complemented
5#20292916C211yesmaximal, characteristic, complemented
6#20292915C211yesmaximal, characteristic, complemented
7#20292831C211yesmaximal, characteristic, complemented
8#20292830C211yesmaximal, characteristic, complemented
9#20292779C211yesmaximal, characteristic
10#20292776C211yesmaximal, characteristic
11C4×#13133807C211yesmaximal, characteristic, complemented
12C4×#13133805C211yesmaximal, characteristic, complemented
13C4×#13133806C211yesmaximal, characteristic, complemented
14#20292678C211yesmaximal, characteristic, complemented
15C4×SD16×C107C211yesmaximal, characteristic, complemented
16C2×D4×D107C2211yescharacteristic
17C22×C4×D107—21no—
18C2×#13133807C2211yescharacteristic
19C2×#13133806C2211yescharacteristic
20C2×#13133805C2211yescharacteristic
21#16812108C2211yescharacteristic, complemented
22#16812107C2211yescharacteristic, complemented
23#16812099—21no—
24#16812089C2211yescharacteristic
25#16812087—21no—
26#16812085C2211yescharacteristic
27C4×Dic214—21no—
28C4×Dic214C2211yescharacteristic, complemented
29C4×D428C2211yescharacteristic
30D4×Dic107C2211yescharacteristic
31#16812071C2211yescharacteristic
32C4×C22⋊D107—21no—
33(C22⋊D107)⋊C4—21no—
34#16812066—21no—
35C4⋊C4×D107C2211yescharacteristic
36C22⋊C4×D107—21no—
37C42×D107C2211yescharacteristic
38#16812041C2211yescharacteristic, complemented
39#16812040C2211yescharacteristic, complemented
40#16812040C2211yescharacteristic, complemented
41Dic107⋊C8C2211yescharacteristic, complemented
42Dic107⋊C8C2211yescharacteristic, complemented
43#16812034C2211yescharacteristic, complemented
44#16812033C2211yescharacteristic, complemented
45#16812032C2211yescharacteristic, complemented
46#16812031C2211yescharacteristic
47#16812030C2211yescharacteristic
48#16812029C2211yescharacteristic
49(C2×D107)⋊C8C2211yescharacteristic
50(C2×D107)⋊C8C2211yescharacteristic
51C4×C107⋊C8C2211yescharacteristic, complemented
52C2×SD16×C107C2211yescharacteristic
53C4×Q8×C107C2211yescharacteristic, complemented
54C4×D4×C107C2211yescharacteristic
55#106×C107C2211yescharacteristic, complemented
56#103×C107C2211yescharacteristic, complemented
57#102×C107C2211yescharacteristic
58C4×C8×C107C2211yescharacteristic, complemented
59C23×D107—21no—
60C2×Dic214—21no—
61C2×Dic214C2311yescharacteristic
62C2×D428C2311yescharacteristic
63C2×C22⋊D107—21no—
64D4×D107—22no—
65D4×D107—22no—
66C22×Dic107—21no—
67C2×C4×D107—21no—
68C2×C4×D107—21no—
69C2×C4×D107—21no—
70C2×C4×D107—44no—
71C2×C4×D107D411yescharacteristic
72C2×C4×D107D411yescharacteristic
73C2×C4×D107C2311yescharacteristic
74#13133807—22no—
75#13133806—22no—
76#13133805—22no—
77C2×C107⋊C8C2311yescharacteristic
78C2×C107⋊C8C2311yescharacteristic
79C4⋊Dic107—21no—
80C4⋊Dic107C2311yescharacteristic
81C4⋊Dic107C2311yescharacteristic
82Dic107⋊C4—21no—
83Dic107⋊C4—21no—
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—
93C4×Dic107—21no—
94C4×Dic107D411yescharacteristic
95C4×Dic107D411yescharacteristic
96C4×Dic107C2311yescharacteristic
97C2×Q8×C107C2311yescharacteristic
98C2×D4×C107C2311yescharacteristic
99C22×C4×C107—21no—
100SD16×C107—22no—
101C2×C8×C107C2311yescharacteristic
102C2×C8×C107C2311yescharacteristic
103C4⋊C4×C107—21no—
104C4⋊C4×C107C2311yescharacteristic
105C4⋊C4×C107C2311yescharacteristic
106C22⋊C4×C107—21no—
107C42×C107—21no—
108C42×C107C2311yescharacteristic
109C23×C107—21no—
110C22×D107—24no—
111C22×D107—21no—
112C22×D107—42no—
113C22×D107—42no—
114C22×D107C2×D411yescharacteristic
115Q8×C107—21no—
116Q8×C107—21no—
117D4×C107—21no—
118D4×C107#4112yes—
119C2×C4×C107—21no—
120C2×C4×C107—21no—
121C2×C4×C107—21no—
122C2×C4×C107—42no—
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—42no—
131C2×Dic107C2×D411yescharacteristic
132C2×Dic107C2×D411yescharacteristic
133C2×Dic107C2×D411yescharacteristic
134D428—21no—
135D428#4112yes—
136C4×D107—21no—
137C4×D107—21no—
138C4×D107—41no—
139C4×D107—42no—
140C4×D107—42no—
141C4×D107—42no—
142C4×D107SD1614yescomplemented
143Dic214—21no—
144Dic214—21no—
145Dic214—42no—
146C8×C107—21no—
147C8×C107—21no—
148C107⋊C8—21no—
149C107⋊C8—21no—
150C22×C107—22no—
151C22×C107—41no—
152C22×C107—41no—
153C22×C107C22×D411yescharacteristic
154C2×D107—21no—
155C2×D107—21no—
156C2×D107—22no—
157C2×D107—48no—
158C2×D107—41no—
159C2×D107—41no—
160C2×D107C2×SD1612yes—
161C4×C107—21no—
162C4×C107—41no—
163C4×C107—41no—
164C4×C107—41no—
165C4×C107C2×SD1612yes—
166C4×C107C2×#4111yescharacteristic
167C4×C107C2×#4111yescharacteristic
168Dic107—21no—
169Dic107—21no—
170Dic107—41no—
171Dic107—41no—
172Dic107—41no—
173Dic107C2×SD1612yes—
174C2×C107—42no—
175C2×C107#52511yescharacteristic
176C2×C107C22×SD1611yescharacteristic
177C2×C107#57511yescharacteristic
178D107—22no—
179D107—42no—
180#3101—1071nomaximal, Sylow
181C107#310111yescharacteristic, complemented, Sylow
182#533—1071no—
183C2×C4×D4—1071no—
184#483—1071no—
185#483—1071no—
186#476—1071no—
187#476—1071no—
188#461—1071no—
189#461—1071no—
190#450—1071no—
191#450—1071no—
192C4×SD16—1071no—
193C4×SD16—1071no—
194C4×SD16—1071no—
195C4×SD16D10711yescharacteristic, complemented
196#431—1071no—
197C22×D4—1071no—
198C23×C4—2141no—
199C2×SD16—1071no—
200C2×SD16—1071no—
201C2×SD16—1071no—
202C2×SD16C2×D10711yescharacteristic
203C4⋊Q8—1071no—
204C4⋊Q8—1071no—
205#125—2141no—
206C22⋊Q8—1071no—
207C22⋊Q8—1071no—
208C22⋊Q8—2141no—
209C4×Q8—1071no—
210C4×Q8—2141no—
211C4×Q8C2×D10711yescharacteristic, complemented
212C4×D4—1071no—
213C4×D4—1071no—
214C4×D4—1071no—
215C4×D4—2141no—
216C4×D4—2141no—
217C4×D4C2×D10711yescharacteristic
218#117—2141no—
219C2×C4⋊C4—1071no—
220C2×C22⋊C4—2141no—
221C2×C42—1071no—
222#106—1071no—
223#106—1071no—
224#106—1071no—
225#106C2×D10711yescharacteristic, complemented
226C4⋊C8—1071no—
227C4⋊C8—1071no—
228#103—1071no—
229#103—1071no—
230#103—1071no—
231#103C2×D10711yescharacteristic, complemented
232#102—1071no—
233#102—1071no—
234#102—1071no—
235#102C2×D10711yescharacteristic
236C22⋊C8—1071no—
237C22⋊C8—1071no—
238C4×C8—1071no—
239C4×C8C2×D10711yescharacteristic, complemented
240C24—2141no—
241C2×Q8—1071no—
242C2×Q8—2141no—
243C2×Q8C22×D10711yescharacteristic
244C2×D4—1071no—
245C2×D4—2141no—
246C2×D4—2142no—
247C2×D4—2142no—
248C2×D4C22×D10711yescharacteristic
249C22×C4—21no—
250C22×C4—1071no—
251C22×C4—1071no—
252C22×C4—1071no—
253C22×C4—4284no—
254C22×C4—2141no—
255C22×C4—2141no—
256C22×C4—2141no—
257C22×C4—2141no—
258SD16—22no—
259SD16—2142no—
260SD16—2142no—
261SD16—2142no—
262C2×C8—1071no—
263C2×C8—1071no—
264C2×C8C22×D10711yescharacteristic
265C2×C8C22×D10711yescharacteristic
266C4⋊C4—21no—
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⋊C4—2141no—
276C4⋊C4C22×D10711yescharacteristic
277C4⋊C4C22×D10711yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—2141no—
280C22⋊C4—2141no—
281C22⋊C4—2141no—
282C22⋊C4—2141no—
283C22⋊C4—2141no—
284C42—21no—
285C42—1071no—
286C42—1071no—
287C42—1071no—
288C42—2141no—
289C42C22×D10711yescharacteristic
290C23—21no—
291C23—1071no—
292C23—4282no—
293C23—4282no—
294C23—2144no—
295C23—2141no—
296Q8—21no—
297Q8—21no—
298Q8—4282no—
299Q8—2141no—
300Q8—2141no—
301D4—21no—
302D4—1072no—
303D4—2144no—
304D4—2141no—
305D4#1313381812yes—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—1071no—
311C2×C4—1074no—
312C2×C4—1071no—
313C2×C4—1071no—
314C2×C4—4281no—
315C2×C4—4282no—
316C2×C4—4282no—
317C2×C4—4282no—
318C2×C4—4282no—
319C2×C4—2141no—
320C2×C4—2141no—
321C2×C4—2141no—
322C2×C4—2141no—
323C2×C4—2141no—
324C2×C4D4×D10711yescharacteristic
325C2×C4D4×D10711yescharacteristic
326C2×C4C23×D10711yescharacteristic
327C8—21no—
328C8—21no—
329C8—2141no—
330C8—2141no—
331C22—22no—
332C22—41no—
333C22—41no—
334C22—1072no—
335C22—4288no—
336C22—4281no—
337C22—4281no—
338C22—2142no—
339C22—2141no—
340C22—2141no—
341C22C2×D4×D10711yescharacteristic
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—1072no—
347C4—4281no—
348C4—4281no—
349C4—4281no—
350C4—2141no—
351C4—2141no—
352C4SD16×D10712yes—
353C4#41×D10711yescharacteristic
354C4C2×#1313381811yescharacteristic
355C2—42no—
356C2—4282no—
357C2—2142no—
358C2#2029313611yescharacteristic
359C2C2×SD16×D10711yescharacteristic
360C2#2029342411yescharacteristic
subgroupG/H
centerC2×C4D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
FittingC4×SD16×C107C2
socleC22×C107C22×D4
prime radicalC2×D4×D107C22
hypercenterC4×SD16D107
hypocenterC107#3101
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #20293181C2semidirect
3. #20292959C2semidirect
4. #20292956C2semidirect
5. #20292916C2semidirect
6. #20292915C2semidirect
7. #20292831C2semidirect
8. #20292830C2semidirect
11. C4×#13133807C2semidirect
12. C4×#13133805C2semidirect
13. C4×#13133806C2semidirect
14. #20292678C2semidirect
15. C4×SD16×C107C2semidirect
21. #16812108C22semidirect
22. #16812107C22semidirect
28. C4×Dic214C22semidirect
38. #16812041C22semidirect
39. #16812040C22semidirect
40. #16812040C22semidirect
41. Dic107⋊C8C22semidirect
42. Dic107⋊C8C22semidirect
43. #16812034C22semidirect
44. #16812033C22semidirect
45. #16812032C22semidirect
51. C4×C107⋊C8C22semidirect
53. C4×Q8×C107C22semidirect
55. #106×C107C22semidirect
56. #103×C107C22semidirect
58. C4×C8×C107C22semidirect
142. C4×D107SD16semidirect
181. C107#3101semidirect
195. C4×SD16D107semidirect
211. C4×Q8C2×D107semidirect
225. #106C2×D107semidirect
231. #103C2×D107semidirect
239. C4×C8C2×D107semidirect

Maximal subgroups

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

subgroupindex
#202931812
C4×D4×D1072
#202929592
#202929562
#202929162
#202929152
#202928312
#202928302
#202927792
#202927762
C4×#131338072
C4×#131338052
C4×#131338062
#202926782
C4×SD16×C1072
#3101107