Finite Group Databasebeta

← #28346320

Subgroups — #28346320

Order 13696.

376 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293254C211yesmaximal, characteristic, complemented
2#20293109C211yesmaximal, characteristic
3#20292936C211yesmaximal, characteristic, complemented
4#20292934C211yesmaximal, characteristic, complemented
5#20292928C211yesmaximal, characteristic, complemented
6#20292926C211yesmaximal, characteristic, complemented
7#20292916C211yesmaximal, characteristic, complemented
8#20292914C211yesmaximal, characteristic, complemented
9#20292910C211yesmaximal, characteristic, complemented
10#20292666C211yesmaximal, characteristic, complemented
11#106×D107C211yesmaximal, characteristic, complemented
12#20292652C211yesmaximal, characteristic, complemented
13#20292627C211yesmaximal, characteristic
14#20292622C211yesmaximal, characteristic
15#475×C107C211yesmaximal, characteristic, complemented
16C2×#13133819C2211yescharacteristic
17C2×#13133801C2211yescharacteristic
18C2×C8×D107C2211yescharacteristic
19#16812108C2211yescharacteristic
20#16812107—21no—
21#16812101C2211yescharacteristic
22#16812100C2211yescharacteristic
23#16812099—21no—
24#16812087—21no—
25#16812085—21no—
26Q8×Dic107C2211yescharacteristic
27C4×D428—21no—
28C4×D428C2211yescharacteristic
29#16812071—21no—
30#16812071C2211yescharacteristic
31#16812067C2211yescharacteristic
32#16812066—21no—
33#16812066C2211yescharacteristic
34C4⋊C4×D107—21no—
35C4⋊C4×D107C2211yescharacteristic
36C4⋊C4×D107C2211yescharacteristic
37#16812043C2211yescharacteristic
38#16812042C2211yescharacteristic
39#16812041C2211yescharacteristic
40#16812040C2211yescharacteristic
41#16812040C2211yescharacteristic
42#16812040C2211yescharacteristic
43C4⋊(C107⋊C8)C2211yescharacteristic
44Dic107⋊C8C2211yescharacteristic
45Dic107⋊C8C2211yescharacteristic
46#16812033C2211yescharacteristic
47#16812033C2211yescharacteristic
48#16812031C2211yescharacteristic
49#16812031C2211yescharacteristic
50#16812029C2211yescharacteristic
51#16812029C2211yescharacteristic
52C4⋊Q8×C107C2211yescharacteristic
53C4×Q8×C107C2211yescharacteristic
54#106×C107C2211yescharacteristic
55#106×C107C2211yescharacteristic
56C4⋊C8×C107C2211yescharacteristic
57#103×C107C2211yescharacteristic
58#103×C107C2211yescharacteristic
59#13133819—22no—
60#13133819Q814yescomplemented
61C2×Dic214—21no—
62C2×D428—21no—
63C2×D428C2311yescharacteristic
64C2×C4×D107—21no—
65C2×C4×D107—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⋊Dic107—21no—
76C4⋊Dic107C2311yescharacteristic
77C4⋊Dic107C2311yescharacteristic
78C4⋊Dic107C2311yescharacteristic
79Dic107⋊C4—21no—
80Dic107⋊C4—21no—
81Dic107⋊C4—21no—
82Dic107⋊C4—21no—
83Dic107⋊C4—21no—
84Dic107⋊C4—21no—
85Dic107⋊C4D411yescharacteristic
86Dic107⋊C4D411yescharacteristic
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×Q8×C107C2311yescharacteristic
97C2×C8×C107C2311yescharacteristic
98C2×C8×C107C2311yescharacteristic
99C4⋊C4×C107—21no—
100C4⋊C4×C107—21no—
101C4⋊C4×C107C2311yescharacteristic
102C4⋊C4×C107C2311yescharacteristic
103C4⋊C4×C107C2311yescharacteristic
104C42×C107—21no—
105C42×C107C2311yescharacteristic
106C22×D107—21no—
107C22×D107C2×D411yescharacteristic
108Q8×C107—21no—
109Q8×C107—81no—
110Q8×C107C2×Q812yes—
111C2×C4×C107—21no—
112C2×C4×C107—21no—
113C2×C4×C107—21no—
114C2×C4×C107—21no—
115C2×C4×C107C2×D411yescharacteristic
116C2×C4×C107C2×D411yescharacteristic
117C2×C4×C107C2411yescharacteristic
118C2×Dic107—21no—
119C2×Dic107—21no—
120C2×Dic107—21no—
121C2×Dic107C2×D411yescharacteristic
122C2×Dic107C2×D411yescharacteristic
123C2×Dic107C2×D411yescharacteristic
124D428—24no—
125D428—21no—
126D428C2×Q812yes—
127C4×D107—24no—
128C4×D107—81no—
129C4×D107—81no—
130C4×D107—81no—
131C4×D107—81no—
132C4×D107C2×Q812yes—
133C4×D107#4112yes—
134Dic214—81no—
135C8×C107—21no—
136C8×C107—21no—
137C107⋊C8—21no—
138C107⋊C8—21no—
139C22×C107C22×D411yescharacteristic
140C2×D107—21no—
141C2×D107—21no—
142C2×D107—22no—
143C2×D107—41no—
144C2×D107—41no—
145C2×D107C22⋊Q812yes—
146C4×C107—22no—
147C4×C107—21no—
148C4×C107—21no—
149C4×C107—41no—
150C4×C107—41no—
151C4×C107—41no—
152C4×C107C22×Q811yescharacteristic
153C4×C107C2×#4111yescharacteristic
154Dic107—21no—
155Dic107—21no—
156Dic107—41no—
157Dic107—41no—
158Dic107—41no—
159Dic107C22⋊Q812yes—
160C2×C107C2×C22⋊Q811yescharacteristic
161C2×C107#57711yescharacteristic
162C2×C107#57711yescharacteristic
163D107—22no—
164D107—42no—
165#3084—1071nomaximal, Sylow
166C107#308411yescharacteristic, complemented, Sylow
167#544—1071no—
168#520—1071no—
169#479—1071no—
170#479—1071no—
171#478—1071no—
172#478—1071no—
173#476—1071no—
174#476—1071no—
175#475—1071no—
176#475D10711yescharacteristic, complemented
177#428—1071no—
178C2×#106—1071no—
179#424—1071no—
180#417—1071no—
181#416—1071no—
182C2×#41—1071no—
183C2×M16—1071no—
184C22×C8—1071no—
185C4⋊Q8—1071no—
186C4⋊Q8—2141no—
187C4⋊Q8C2×D10711yescharacteristic
188#125—1071no—
189#125—1071no—
190#125—2141no—
191C22⋊Q8—2141no—
192C22⋊Q8—2141no—
193C4×Q8—1071no—
194C4×Q8C2×D10711yescharacteristic
195C4×D4—1071no—
196C4×D4—1071no—
197C4×D4—2141no—
198C4×D4—2141no—
199#117—1071no—
200#117—1071no—
201#117—2141no—
202C2×C4⋊C4—1071no—
203C2×C4⋊C4—1071no—
204C2×C4⋊C4—2141no—
205#107—1071no—
206#107—1071no—
207#106—1071no—
208#106—1071no—
209#106—1071no—
210#106—1071no—
211#106C2×D10711yescharacteristic
212#106C2×D10711yescharacteristic
213C4⋊C8—1071no—
214C4⋊C8—1071no—
215C4⋊C8—1071no—
216C4⋊C8C2×D10711yescharacteristic
217#103—1071no—
218#103—1071no—
219#103C2×D10711yescharacteristic
220#103C2×D10711yescharacteristic
221#102—1071no—
222#102—1071no—
223#102—1071no—
224#102—1071no—
225#41—1074no—
226#41—2142no—
227C2×Q8—21no—
228C2×Q8—2141no—
229C2×Q8C22×D10711yescharacteristic
230C2×D4—1071no—
231C2×D4—2141no—
232C22×C4—1071no—
233C22×C4—2141no—
234C22×C4—2141no—
235C22×C4—2141no—
236C22×C4—2141no—
237C22×C4—2141no—
238M16—2142no—
239C2×C8—1071no—
240C2×C8—1071no—
241C2×C8—2142no—
242C2×C8C22×D10711yescharacteristic
243C2×C8C22×D10711yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—1071no—
247C4⋊C4—1071no—
248C4⋊C4—1071no—
249C4⋊C4—1071no—
250C4⋊C4—1071no—
251C4⋊C4—2141no—
252C4⋊C4—2141no—
253C4⋊C4—2141no—
254C4⋊C4—2141no—
255C4⋊C4—2141no—
256C4⋊C4—2141no—
257C4⋊C4—2141no—
258C4⋊C4—2141no—
259C4⋊C4C22×D10711yescharacteristic
260C4⋊C4C22×D10711yescharacteristic
261C4⋊C4C22×D10711yescharacteristic
262C22⋊C4—1071no—
263C22⋊C4—1071no—
264C22⋊C4—2141no—
265C22⋊C4—2141no—
266C22⋊C4—2141no—
267C42—21no—
268C42—1071no—
269C42—2141no—
270C42—2141no—
271C42C22×D10711yescharacteristic
272C23—1071no—
273C23—2141no—
274Q8—21no—
275Q8—81no—
276Q8—8561no—
277Q8Q8×D10712yes—
278D4—1072no—
279D4—2144no—
280D4—2141no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—8561no—
286C2×C4—8561no—
287C2×C4—8561no—
288C2×C4—8561no—
289C2×C4—1071no—
290C2×C4—1072no—
291C2×C4—1072no—
292C2×C4—1071no—
293C2×C4—1071no—
294C2×C4—2144no—
295C2×C4—2141no—
296C2×C4—2141no—
297C2×C4—2141no—
298C2×C4D4×D10711yescharacteristic
299C2×C4D4×D10711yescharacteristic
300C2×C4C23×D10711yescharacteristic
301C8—21no—
302C8—21no—
303C8—2141no—
304C8—2141no—
305C22—1072no—
306C22—4281no—
307C22—4281no—
308C22—2142no—
309C22—2141no—
310C22—2141no—
311C22C2×D4×D10711yescharacteristic
312C4—22no—
313C4—21no—
314C4—21no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—1072no—
319C4—4281no—
320C4—4281no—
321C4—4281no—
322C4—2141no—
323C4—2141no—
324C4C2×Q8×D10711yescharacteristic
325C4#41×D10711yescharacteristic
326C2—4282no—
327C2—2142no—
328C2C22⋊Q8×D10711yescharacteristic
329C2#2029343311yescharacteristic
330C2#2029343611yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#475×C107C2
socleC22×C107C22×D4
prime radicalC2×#13133819C22
hypercenter#475D107
hypocenterC107#3084
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
1. #20293254C2semidirect
3. #20292936C2semidirect
4. #20292934C2semidirect
5. #20292928C2semidirect
6. #20292926C2semidirect
7. #20292916C2semidirect
8. #20292914C2semidirect
9. #20292910C2semidirect
10. #20292666C2semidirect
11. #106×D107C2semidirect
12. #20292652C2semidirect
15. #475×C107C2semidirect
60. #13133819Q8semidirect
166. C107#3084semidirect
176. #475D107semidirect

Maximal subgroups

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

subgroupindex
#202932542
#202931092
#202929362
#202929342
#202929282
#202929262
#202929162
#202929142
#202929102
#202926662
#106×D1072
#202926522
#202926272
#202926222
#475×C1072
#3084107