Finite Group Databasebeta

← #28346285

Subgroups — #28346285

Order 13696.

398 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#20293254C211yesmaximal, characteristic, complemented
2#20293099C211yesmaximal, characteristic
3#20292930C211yesmaximal, characteristic, complemented
4#20292928C211yesmaximal, characteristic, complemented
5#20292927C211yesmaximal, characteristic, complemented
6#20292925C211yesmaximal, characteristic, complemented
7#20292915C211yesmaximal, characteristic, complemented
8#20292914C211yesmaximal, characteristic, complemented
9#20292906C211yesmaximal, characteristic, complemented
10#20292668C211yesmaximal, characteristic, complemented
11#20292664C211yesmaximal, characteristic, complemented
12#20292652C211yesmaximal, characteristic, complemented
13#20292630C211yesmaximal, characteristic
14#102×D107C211yesmaximal, characteristic
15#474×C107C211yesmaximal, characteristic, complemented
16C2×D4×D107C2211yescharacteristic
17C2×#13133801C2211yescharacteristic
18C2×C8×D107C2211yescharacteristic
19#16812108C2211yescharacteristic, complemented
20#16812107—21no—
21#16812101C2211yescharacteristic, complemented
22#16812100C2211yescharacteristic, complemented
23#16812099—21no—
24#16812087—21no—
25#16812085—21no—
26C4×D428C2211yescharacteristic
27D4×Dic107C2211yescharacteristic
28#16812071C2211yescharacteristic
29C4×C22⋊D107—21no—
30(C22⋊D107)⋊C4—21no—
31#16812067C2211yescharacteristic
32#16812067C2211yescharacteristic
33#16812066C2211yescharacteristic
34C4⋊C4×D107C2211yescharacteristic
35C2×(C2×D107)⋊C4—21no—
36C22⋊C4×D107—21no—
37#16812043C2211yescharacteristic, complemented
38#16812042C2211yescharacteristic, complemented
39#16812041C2211yescharacteristic, complemented
40#16812040C2211yescharacteristic, complemented
41#16812040C2211yescharacteristic, complemented
42#16812040C2211yescharacteristic, complemented
43C4⋊(C107⋊C8)C2211yescharacteristic, complemented
44Dic107⋊C8C2211yescharacteristic, complemented
45Dic107⋊C8C2211yescharacteristic, complemented
46#16812031C2211yescharacteristic
47#16812031C2211yescharacteristic
48#16812030C2211yescharacteristic
49#16812030C2211yescharacteristic
50#16812029C2211yescharacteristic
51#16812029C2211yescharacteristic
52C4⋊Q8×C107C2211yescharacteristic, complemented
53C4×D4×C107C2211yescharacteristic
54#107×C107C2211yescharacteristic, complemented
55#107×C107C2211yescharacteristic, complemented
56C4⋊C8×C107C2211yescharacteristic, complemented
57#102×C107C2211yescharacteristic
58#102×C107C2211yescharacteristic
59C23×D107—21no—
60C2×Dic214—21no—
61C2×D428C2311yescharacteristic
62C2×C22⋊D107—21no—
63D4×D107—22no—
64D4×D107Q814yescomplemented
65C22×Dic107—21no—
66C2×C4×D107—21no—
67C2×C4×D107—21no—
68C2×C4×D107—21no—
69C2×C4×D107C2311yescharacteristic
70#13133801—22no—
71C2×C107⋊C8C2311yescharacteristic
72C2×C107⋊C8C2311yescharacteristic
73C8×D107—22no—
74C4⋊Dic107—21no—
75C4⋊Dic107C2311yescharacteristic
76C4⋊Dic107C2311yescharacteristic
77C4⋊Dic107C2311yescharacteristic
78Dic107⋊C4—21no—
79Dic107⋊C4—21no—
80Dic107⋊C4—21no—
81Dic107⋊C4—21no—
82Dic107⋊C4—21no—
83Dic107⋊C4D411yescharacteristic
84Dic107⋊C4D411yescharacteristic
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)⋊C4D411yescharacteristic
91(C2×D107)⋊C4D411yescharacteristic
92C4×Dic107—21no—
93C4×Dic107—21no—
94C4×Dic107C2311yescharacteristic
95C2×Q8×C107—21no—
96C2×D4×C107C2311yescharacteristic
97C22×C4×C107—21no—
98C2×C8×C107C2311yescharacteristic
99C2×C8×C107C2311yescharacteristic
100C4⋊C4×C107—21no—
101C4⋊C4×C107C2311yescharacteristic
102C4⋊C4×C107C2311yescharacteristic
103C4⋊C4×C107C2311yescharacteristic
104C22⋊C4×C107—21no—
105C42×C107C2311yescharacteristic
106C23×C107—21no—
107C22×D107—21no—
108C22×D107—24no—
109C22×D107—81no—
110C22×D107—81no—
111C22×D107C2×D411yescharacteristic
112Q8×C107—81no—
113D4×C107—21no—
114D4×C107C2×Q812yes—
115C2×C4×C107—21no—
116C2×C4×C107—21no—
117C2×C4×C107—21no—
118C2×C4×C107—81no—
119C2×C4×C107C2×D411yescharacteristic
120C2×C4×C107C2×D411yescharacteristic
121C2×C4×C107C2411yescharacteristic
122C22⋊D107—24no—
123C2×Dic107—21no—
124C2×Dic107—21no—
125C2×Dic107—21no—
126C2×Dic107—81no—
127C2×Dic107C2×D411yescharacteristic
128C2×Dic107C2×D411yescharacteristic
129C2×Dic107C2×D411yescharacteristic
130D428—21no—
131D428C2×Q812yes—
132C4×D107—81no—
133C4×D107—81no—
134C4×D107—81no—
135C4×D107C2×Q812yes—
136C4×D107#4112yes—
137Dic214—81no—
138C8×C107—21no—
139C8×C107—21no—
140C107⋊C8—21no—
141C107⋊C8—21no—
142C22×C107—22no—
143C22×C107—41no—
144C22×C107—41no—
145C22×C107C22×D411yescharacteristic
146C2×D107—21no—
147C2×D107—21no—
148C2×D107—22no—
149C2×D107—41no—
150C2×D107—41no—
151C2×D107—84no—
152C2×D107C22⋊Q812yes—
153C4×C107—21no—
154C4×C107—21no—
155C4×C107—41no—
156C4×C107—41no—
157C4×C107—41no—
158C4×C107C22×Q811yescharacteristic
159C4×C107C2×#4111yescharacteristic
160Dic107—21no—
161Dic107—21no—
162Dic107—41no—
163Dic107—41no—
164Dic107—41no—
165Dic107C22⋊Q812yes—
166C2×C107—42no—
167C2×C107C2×C22⋊Q811yescharacteristic
168C2×C107#57611yescharacteristic
169C2×C107#57711yescharacteristic
170D107—22no—
171D107—42no—
172#3081—1071nomaximal, Sylow
173C107#308111yescharacteristic, complemented, Sylow
174#544—1071no—
175#518—1071no—
176#478—1071no—
177#478—1071no—
178#478—1071no—
179#478—1071no—
180#476—1071no—
181#476—1071no—
182#474—1071no—
183#474D10711yescharacteristic, complemented
184#428—1071no—
185#427—1071no—
186#424—1071no—
187#418—1071no—
188C2×#102—1071no—
189C22×D4—1071no—
190C2×M16—1071no—
191C22×C8—1071no—
192C4⋊Q8—1071no—
193C4⋊Q8—2141no—
194C4⋊Q8C2×D10711yescharacteristic, complemented
195#125—1071no—
196#125—1071no—
197#125—2141no—
198C22⋊Q8—2141no—
199C22⋊Q8—2141no—
200C4×D4—1071no—
201C4×D4—1071no—
202C4×D4—1071no—
203C4×D4—2141no—
204C4×D4—2141no—
205C4×D4C2×D10711yescharacteristic
206#117—1071no—
207#117—1071no—
208#117—1071no—
209C2×C4⋊C4—1071no—
210C2×C22⋊C4—2141no—
211C2×C22⋊C4—2141no—
212#107—1071no—
213#107—1071no—
214#107C2×D10711yescharacteristic, complemented
215#107C2×D10711yescharacteristic, complemented
216#106—1071no—
217#106—1071no—
218#106—1071no—
219#106—1071no—
220C4⋊C8—1071no—
221C4⋊C8—1071no—
222C4⋊C8—1071no—
223C4⋊C8C2×D10711yescharacteristic, complemented
224#102—1071no—
225#102—1071no—
226#102—1071no—
227#102—1071no—
228#102—1071no—
229#102—1071no—
230#102C2×D10711yescharacteristic
231#102C2×D10711yescharacteristic
232C24—2141no—
233C2×Q8—21no—
234C2×Q8—2141no—
235C2×D4—1074no—
236C2×D4—1071no—
237C2×D4—2142no—
238C2×D4—2141no—
239C2×D4C22×D10711yescharacteristic
240C22×C4—21no—
241C22×C4—1071no—
242C22×C4—2141no—
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—1071no—
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⋊C4C22×D10711yescharacteristic
265C4⋊C4C22×D10711yescharacteristic
266C4⋊C4C22×D10711yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—1071no—
269C22⋊C4—1071no—
270C22⋊C4—2141no—
271C22⋊C4—2141no—
272C22⋊C4—2141no—
273C22⋊C4—2141no—
274C22⋊C4—2141no—
275C42—1071no—
276C42—2141no—
277C42—2141no—
278C42C22×D10711yescharacteristic
279C23—21no—
280C23—8561no—
281C23—8561no—
282C23—1071no—
283C23—2144no—
284C23—2141no—
285Q8—81no—
286Q8—8561no—
287D4—21no—
288D4—1072no—
289D4—2144no—
290D4—2141no—
291D4Q8×D10712yes—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—81no—
296C2×C4—8561no—
297C2×C4—8561no—
298C2×C4—8561no—
299C2×C4—8561no—
300C2×C4—1071no—
301C2×C4—1072no—
302C2×C4—1072no—
303C2×C4—1071no—
304C2×C4—1071no—
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—22no—
316C22—41no—
317C22—41no—
318C22—8564no—
319C22—1072no—
320C22—4281no—
321C22—4281no—
322C22—2142no—
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—
337C4C2×Q8×D10711yescharacteristic
338C4#41×D10711yescharacteristic
339C2—42no—
340C2—4282no—
341C2—2142no—
342C2C22⋊Q8×D10711yescharacteristic
343C2#2029342811yescharacteristic
344C2#2029343611yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#474×C107C2
socleC22×C107C22×D4
prime radicalC2×D4×D107C22
hypercenter#474D107
hypocenterC107#3081
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #20293254C2semidirect
3. #20292930C2semidirect
4. #20292928C2semidirect
5. #20292927C2semidirect
6. #20292925C2semidirect
7. #20292915C2semidirect
8. #20292914C2semidirect
9. #20292906C2semidirect
10. #20292668C2semidirect
11. #20292664C2semidirect
12. #20292652C2semidirect
15. #474×C107C2semidirect
19. #16812108C22semidirect
21. #16812101C22semidirect
22. #16812100C22semidirect
37. #16812043C22semidirect
38. #16812042C22semidirect
39. #16812041C22semidirect
40. #16812040C22semidirect
41. #16812040C22semidirect
42. #16812040C22semidirect
43. C4⋊(C107⋊C8)C22semidirect
44. Dic107⋊C8C22semidirect
45. Dic107⋊C8C22semidirect
52. C4⋊Q8×C107C22semidirect
54. #107×C107C22semidirect
55. #107×C107C22semidirect
56. C4⋊C8×C107C22semidirect
64. D4×D107Q8semidirect
173. C107#3081semidirect
183. #474D107semidirect
194. C4⋊Q8C2×D107semidirect
214. #107C2×D107semidirect
215. #107C2×D107semidirect
223. C4⋊C8C2×D107semidirect

Maximal subgroups

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

subgroupindex
#202932542
#202930992
#202929302
#202929282
#202929272
#202929252
#202929152
#202929142
#202929062
#202926682
#202926642
#202926522
#202926302
#102×D1072
#474×C1072
#3081107