Finite Group Databasebeta

← #28349067

Subgroups — #28349067

Order 13696.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293325C211yesmaximal, characteristic, complemented
2#20293324C211yesmaximal, characteristic, complemented
3#20293028C211yesmaximal, characteristic, complemented
4#20292952C211yesmaximal, characteristic, complemented
5#20292949C211yesmaximal, characteristic, complemented
6#20292942C211yesmaximal, characteristic, complemented
7#20292930C211yesmaximal, characteristic, complemented
8#20292929C211yesmaximal, characteristic, complemented
9#20292879C211yesmaximal, characteristic, complemented
10#20292878C211yesmaximal, characteristic, complemented
11#20292707C211yesmaximal, characteristic, complemented
12#20292702C211yesmaximal, characteristic, complemented
13#20292668C211yesmaximal, characteristic, complemented
14#20292667C211yesmaximal, characteristic, complemented
15#480×C107C211yesmaximal, characteristic, complemented
16C2×#13133803C2211yescharacteristic
17C2×#13133802C2211yescharacteristic
18C2×#13133801C2211yescharacteristic
19#16812104—21no—
20#16812102—21no—
21#16812100C2211yescharacteristic
22#16812100C2211yescharacteristic
23#16812094—21no—
24#16812090—21no—
25#16812084C2211yescharacteristic
26#16812083—21no—
27#16812083C2211yescharacteristic
28#16812080—21no—
29#16812080C2211yescharacteristic
30D4×Dic107C2211yescharacteristic
31#16812071C2211yescharacteristic
32C4×C22⋊D107—21no—
33C4×C22⋊D107C2211yescharacteristic
34(C22⋊D107)⋊C4—21no—
35#16812068C2211yescharacteristic
36#16812067C2211yescharacteristic
37C4⋊C4×D107C2211yescharacteristic
38#16812043C2211yescharacteristic
39#16812042C2211yescharacteristic
40#16812042C2211yescharacteristic
41#16812041C2211yescharacteristic
42#16812040C2211yescharacteristic
43#16812040C2211yescharacteristic
44#16812040C2211yescharacteristic
45Dic107⋊C8C2211yescharacteristic
46#16812031C2211yescharacteristic
47#16812031C2211yescharacteristic
48#16812030C2211yescharacteristic
49#16812029C2211yescharacteristic
50(C2×D107)⋊C8C2211yescharacteristic
51C8×Dic107C2211yescharacteristic
52#121×C107C2211yescharacteristic
53C2×C4⋊C4×C107C2211yescharacteristic
54#107×C107C2211yescharacteristic
55#107×C107C2211yescharacteristic
56#102×C107C2211yescharacteristic
57#102×C107C2211yescharacteristic
58C22⋊C8×C107C2211yescharacteristic
59C2×D428—21no—
60C2×D428C2311yescharacteristic
61C2×C22⋊D107—21no—
62C2×C22⋊D107—21no—
63C2×C22⋊D107D411yescharacteristic
64C22×Dic107—21no—
65C2×C4×D107—21no—
66C2×C4×D107—21no—
67C2×C4×D107C2311yescharacteristic
68#13133803—22no—
69#13133802—22no—
70#13133801—22no—
71C2×C107⋊C8C2311yescharacteristic
72C2×C107⋊C8C2311yescharacteristic
73C4⋊Dic107—21no—
74C4⋊Dic107—21no—
75C4⋊Dic107C2311yescharacteristic
76C4⋊Dic107C2311yescharacteristic
77C4⋊Dic107C2311yescharacteristic
78Dic107⋊C4—21no—
79Dic107⋊C4—21no—
80Dic107⋊C4—21no—
81Dic107⋊C4D411yescharacteristic
82C22⋊Dic107—21no—
83C22⋊Dic107—21no—
84C22⋊Dic107—21no—
85C22⋊Dic107D411yescharacteristic
86(C2×D107)⋊C4—21no—
87(C2×D107)⋊C4—21no—
88(C2×D107)⋊C4—21no—
89(C2×D107)⋊C4—21no—
90(C2×D107)⋊C4D411yescharacteristic
91C4×Dic107—21no—
92C4×Dic107—21no—
93C4×Dic107C2311yescharacteristic
94C2×D4×C107—21no—
95C2×D4×C107C2311yescharacteristic
96C22×C4×C107—21no—
97C22×C4×C107C2311yescharacteristic
98C2×C8×C107C2311yescharacteristic
99C2×C8×C107C2311yescharacteristic
100C4⋊C4×C107—21no—
101C4⋊C4×C107C2311yescharacteristic
102C4⋊C4×C107C2311yescharacteristic
103C4⋊C4×C107C2311yescharacteristic
104C22⋊C4×C107—21no—
105C23×C107—21no—
106C23×C107C2×D411yescharacteristic
107C22×D107—21no—
108C22×D107C2×D411yescharacteristic
109D4×C107—21no—
110D4×C107—21no—
111D4×C107—81no—
112C2×C4×C107—21no—
113C2×C4×C107—21no—
114C2×C4×C107—21no—
115C2×C4×C107—21no—
116C2×C4×C107—21no—
117C2×C4×C107—81no—
118C2×C4×C107C2×D411yescharacteristic
119C2×C4×C107C2411yescharacteristic
120C22⋊D107—41no—
121C22⋊D107—42no—
122C22⋊D107—42no—
123C2×Dic107—21no—
124C2×Dic107—21no—
125C2×Dic107—21no—
126C2×Dic107—81no—
127C2×Dic107C2×D411yescharacteristic
128C2×Dic107C2×D411yescharacteristic
129C2×Dic107C2×D411yescharacteristic
130D428—21no—
131D428—21no—
132D428—81no—
133C4×D107—21no—
134C4×D107—21no—
135C4×D107—81no—
136C4×D107—81no—
137C8×C107—21no—
138C8×C107—21no—
139C107⋊C8—21no—
140C107⋊C8#4112yes—
141C22×C107—21no—
142C22×C107—21no—
143C22×C107—21no—
144C22×C107—41no—
145C22×C107—41no—
146C22×C107—41no—
147C22×C107C22×D411yescharacteristic
148C2×D107—21no—
149C2×D107—21no—
150C2×D107—21no—
151C2×D107—41no—
152C2×D107—41no—
153C2×D107—41no—
154C4×C107—21no—
155C4×C107—41no—
156C4×C107—41no—
157C4×C107—41no—
158C4×C107C2×#4111yescharacteristic
159C4×C1072−1+411yescharacteristic
160Dic107—21no—
161Dic107—21no—
162Dic107—21no—
163Dic107—41no—
164Dic107—41no—
165Dic107—41no—
166C2×C107—41no—
167C2×C107—81no—
168C2×C107#54711yescharacteristic
169C2×C107#57511yescharacteristic
170C2×C107#57611yescharacteristic
171D107—41no—
172D107—81no—
173#3355—1071nomaximal, Sylow
174C107#335511yescharacteristic, complemented, Sylow
175#553—1071no—
176#553—1071no—
177#499—1071no—
178#482—1071no—
179#482—1071no—
180#480—1071no—
181#480D10711yescharacteristic, complemented
182#478—1071no—
183#478—1071no—
184#469—1071no—
185#469—1071no—
186C4×D8—1071no—
187#436—1071no—
188#428—1071no—
189#428—1071no—
190C2×D8—1071no—
191C2×M16—1071no—
192C2×M16—1071no—
193#126—2141no—
194#126—2141no—
195#125—1071no—
196#125—1071no—
197#123—2141no—
198#123—2141no—
199#121—1071no—
200#121—1071no—
201#121—1071no—
202#121—2141no—
203#121—2141no—
204#121C2×D10711yescharacteristic
205C4×D4—1071no—
206C4×D4—1071no—
207C4×D4—1071no—
208C4×D4—2141no—
209C4×D4—2141no—
210#117—1071no—
211#117—1071no—
212C2×C4⋊C4—1071no—
213C2×C4⋊C4C2×D10711yescharacteristic
214#107—1071no—
215#107—1071no—
216#107—1071no—
217#107C2×D10711yescharacteristic
218#107C2×D10711yescharacteristic
219#106—1071no—
220#106—1071no—
221#106—1071no—
222#106—1071no—
223C4⋊C8—1071no—
224#102—1071no—
225#102—1071no—
226#102—1071no—
227#102—1071no—
228#102C2×D10711yescharacteristic
229#102C2×D10711yescharacteristic
230C22⋊C8—1071no—
231C22⋊C8C2×D10711yescharacteristic
232C4×C8—1071no—
233C2×D4—21no—
234C2×D4—1071no—
235C2×D4—1071no—
236C2×D4—2141no—
237C2×D4—2141no—
238C2×D4—2141no—
239C2×D4C22×D10711yescharacteristic
240C22×C4—21no—
241C22×C4—1071no—
242C22×C4—2141no—
243C22×C4—2141no—
244C22×C4—2141no—
245C22×C4C22×D10711yescharacteristic
246D8—2142no—
247M16—2142no—
248M16—2142no—
249C2×C8—1071no—
250C2×C8—1071no—
251C2×C8C22×D10711yescharacteristic
252C2×C8C22×D10711yescharacteristic
253C4⋊C4—21no—
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⋊C4C22×D10711yescharacteristic
264C4⋊C4C22×D10711yescharacteristic
265C4⋊C4C22×D10711yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—1071no—
268C22⋊C4—1071no—
269C22⋊C4—2141no—
270C22⋊C4—2141no—
271C22⋊C4—2141no—
272C22⋊C4—2141no—
273C22⋊C4—2141no—
274C22⋊C4—2141no—
275C22⋊C4—2141no—
276C42—1071no—
277C42—2141no—
278C42—2141no—
279C23—21no—
280C23—1071no—
281C23—2141no—
282C23D4×D10711yescharacteristic
283D4—21no—
284D4—21no—
285D4—81no—
286D4—8561no—
287D4—4282no—
288D4—4282no—
289D4—4281no—
290D4—2141no—
291D4—2141no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—81no—
298C2×C4—8561no—
299C2×C4—8561no—
300C2×C4—8561no—
301C2×C4—1071no—
302C2×C4—1071no—
303C2×C4—1071no—
304C2×C4—2141no—
305C2×C4—2141no—
306C2×C4—2141no—
307C2×C4—2141no—
308C2×C4—2141no—
309C2×C4D4×D10711yescharacteristic
310C2×C4C23×D10711yescharacteristic
311C8—21no—
312C8—21no—
313C8—1072no—
314C8—2141no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—4281no—
322C22—4281no—
323C22—4281no—
324C22—2141no—
325C22—2141no—
326C22—2141no—
327C22C2×D4×D10711yescharacteristic
328C4—21no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—4281no—
333C4—4281no—
334C4—4281no—
335C4—2141no—
336C4—2141no—
337C4—2141no—
338C4#41×D10711yescharacteristic
339C4#1681215611yescharacteristic
340C2—41no—
341C2—81no—
342C2—8561no—
343C2—4281no—
344C2#2029327511yescharacteristic
345C2#2029342611yescharacteristic
346C2#2029342811yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#480×C107C2
socleC22×C107C22×D4
hypercenter#480D107
hypocenterC107#3355
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #20293325C2semidirect
2. #20293324C2semidirect
3. #20293028C2semidirect
4. #20292952C2semidirect
5. #20292949C2semidirect
6. #20292942C2semidirect
7. #20292930C2semidirect
8. #20292929C2semidirect
9. #20292879C2semidirect
10. #20292878C2semidirect
11. #20292707C2semidirect
12. #20292702C2semidirect
13. #20292668C2semidirect
14. #20292667C2semidirect
15. #480×C107C2semidirect
174. C107#3355semidirect
181. #480D107semidirect

Maximal subgroups

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

subgroupindex
#202933252
#202933242
#202930282
#202929522
#202929492
#202929422
#202929302
#202929292
#202928792
#202928782
#202927072
#202927022
#202926682
#202926672
#480×C1072
#3355107