Finite Group Databasebeta

← #28344754

Subgroups — #28344754

Order 13696.

1102 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×D107C211yesmaximal, characteristic, complemented
2C2×#16812093C211yesmaximal, characteristic, complemented
3C2×#16812092C211yesmaximal, characteristic, complemented
4C2×#16812079C211yesmaximal, characteristic
5#20292505C214yesmaximal, complemented
6#20292501C214yesmaximal, complemented
7#20292488C211yesmaximal, characteristic, complemented
8#20292482C211yesmaximal, characteristic, complemented
9#381×C107C211yesmaximal, characteristic, complemented
10C24×D107C2211yescharacteristic
11C22×D428C2212yes—
12C22×C22⋊D107C2211yescharacteristic
13C23×Dic107C2211yescharacteristic
14C22×C4×D107—24no—
15C22×C4×D107—24no—
16C22×C4×D107—24no—
17C22×C4×D107C2214yes—
18#16812093—24no—
19#16812092—24no—
20#16812079—24no—
21C2×C4⋊Dic107C2212yescomplemented
22C2×Dic107⋊C4C2212yescomplemented
23C2×C22⋊Dic107C2211yescharacteristic
24C2×(C2×D107)⋊C4C2214yes—
25C2×(C2×D107)⋊C4C2212yes—
26C2×(C2×D107)⋊C4C2212yescomplemented
27C2×(C2×D107)⋊C4C2212yescomplemented
28C107⋊#95C2214yescomplemented
29C23×C4×C107C2211yescharacteristic
30C2×C22⋊C4×C107C2211yescharacteristic
31C2×C22⋊C4×C107C2211yescharacteristic
32#95×C107C2214yescomplemented
33C23×D107—22no—
34C23×D107—22no—
35C23×D107—28no—
36C23×D107D414yes—
37C23×D107C2311yescharacteristic
38C23×D107C2312yes—
39C2×D428—24no—
40C2×D428—28no—
41C2×C22⋊D107—22no—
42C2×C22⋊D107—22no—
43C2×C22⋊D107—22no—
44C22×Dic107—22no—
45C22×Dic107—22no—
46C22×Dic107D414yescomplemented
47C22×Dic107C2312yes—
48C22×Dic107C2311yescharacteristic
49C22×Dic107C2312yes—
50C2×C4×D107—232no—
51C2×C4×D107—28no—
52C2×C4×D107—28no—
53C2×C4×D107—28no—
54C4⋊Dic107—24no—
55Dic107⋊C4—24no—
56C22⋊Dic107—22no—
57(C2×D107)⋊C4—24no—
58(C2×D107)⋊C4—28no—
59(C2×D107)⋊C4—24no—
60(C2×D107)⋊C4—24no—
61C24×C107C2311yescharacteristic
62C22×C4×C107—22no—
63C22×C4×C107—22no—
64C22×C4×C107D414yescomplemented
65C22×C4×C107C2312yes—
66C22×C4×C107C2312yes—
67C22×C4×C107C2312yes—
68C22⋊C4×C107—22no—
69C22⋊C4×C107—22no—
70C23×C107—24no—
71C23×C107C2×D412yes—
72C23×C107C2×D412yes—
73C23×C107C2×D412yes—
74C23×C107C2411yescharacteristic
75C22×D107—216no—
76C22×D107—216no—
77C22×D107—28no—
78C22×D107—22no—
79C22×D107—22no—
80C22×D107—24no—
81C22×D107—216no—
82C22×D107—21no—
83C22×D107—21no—
84C22×D107—21no—
85C22×D107—24no—
86C22×D107C2×D414yes—
87C22×D107#4118yes—
88C2×C4×C107—28no—
89C2×C4×C107—22no—
90C2×C4×C107—22no—
91C2×C4×C107—22no—
92C2×C4×C107—22no—
93C2×C4×C107—24no—
94C2×C4×C107—24no—
95C2×C4×C107C2×D414yes—
96C22⋊D107—44no—
97C2×Dic107—28no—
98C2×Dic107—22no—
99C2×Dic107—22no—
100C2×Dic107—21no—
101C2×Dic107—22no—
102C2×Dic107—21no—
103C2×Dic107—21no—
104C2×Dic107—24no—
105C2×Dic107C2×D414yes—
106D428—48no—
107C4×D107—232no—
108C22×C107—24no—
109C22×C107—24no—
110C22×C107—24no—
111C22×C107#12014yes—
112C22×C107C22×D411yescharacteristic
113C22×C107C22×D411yescharacteristic
114C22×C107C22×D411yescharacteristic
115C22×C107C2×#4114yes—
116C2×D107—232no—
117C2×D107—24no—
118C2×D107—24no—
119C2×D107—28no—
120C2×D107—28no—
121C2×D107—41no—
122C2×D107—42no—
123C2×D107—42no—
124C2×D107—42no—
125C2×D107#12318yescomplemented
126C4×C107—24no—
127C4×C107—42no—
128C4×C107—42no—
129Dic107—24no—
130Dic107—41no—
131Dic107—42no—
132C2×C107—24no—
133C2×C107C2×#12011yescharacteristic
134C2×C107C2×#12312yes—
135C2×C107#52512yes—
136C2×C107#52512yes—
137D107—28no—
138D107—81no—
139#2849—1071nomaximal, Sylow
140C107#284911yescharacteristic, complemented, Sylow
141C24×C4—1071no—
142C2×#123—1071no—
143C2×#123—1071no—
144C2×#120—1071no—
145#386—1074no—
146#385—1074no—
147#381—1071no—
148#381D10711yescharacteristic, complemented
149#379—1071no—
150C25—1071no—
151C22×D4—1071no—
152C22×D4—1072no—
153C23×C4—1071no—
154C23×C4—1074no—
155C23×C4—2144no—
156C23×C4—2144no—
157C23×C4—2144no—
158C23×C4C2×D10711yescharacteristic
159#123—2144no—
160#123—2144no—
161#120—2144no—
162C2×C4⋊C4—1072no—
163C2×C4⋊C4—1072no—
164C2×C22⋊C4—1071no—
165C2×C22⋊C4—1072no—
166C2×C22⋊C4—1072no—
167C2×C22⋊C4—1072no—
168C2×C22⋊C4—1074no—
169C2×C22⋊C4C2×D10711yescharacteristic
170C2×C22⋊C4C2×D10711yescharacteristic
171#95—1074no—
172#95C2×D10714yescomplemented
173C24—1072no—
174C24—1074no—
175C24—1071no—
176C24—2148no—
177C24—2142no—
178C24—2142no—
179C24C22×D10711yescharacteristic
180C2×D4—2144no—
181C2×D4—2148no—
182C2×D4—2142no—
183C2×D4—2142no—
184C2×D4—2142no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—1074no—
188C22×C4—1072no—
189C22×C4—1072no—
190C22×C4—1071no—
191C22×C4—2148no—
192C22×C4—2148no—
193C22×C4—21432no—
194C22×C4—2142no—
195C22×C4—2142no—
196C22×C4—2148no—
197C22×C4D42814yescomplemented
198C22×C4C22×D10712yes—
199C22×C4C22×D10712yes—
200C22×C4C22×D10712yes—
201C4⋊C4—2144no—
202C4⋊C4—2144no—
203C22⋊C4—22no—
204C22⋊C4—22no—
205C22⋊C4—2144no—
206C22⋊C4—2144no—
207C22⋊C4—2148no—
208C22⋊C4—2142no—
209C22⋊C4—2144no—
210C23—24no—
211C23—1074no—
212C23—1078no—
213C23—21416no—
214C23—21416no—
215C23—21416no—
216C23—2141no—
217C23—2141no—
218C23—2141no—
219C23—2144no—
220C23—2148no—
221C23—2142no—
222C23—2142no—
223C23—2144no—
224C23D4×D10712yes—
225C23D4×D10712yes—
226C23C2×D42812yes—
227C23C23×D10711yescharacteristic
228D4—4288no—
229D4—4284no—
230C2×C4—28no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—24no—
236C2×C4—24no—
237C2×C4—1074no—
238C2×C4—21432no—
239C2×C4—2141no—
240C2×C4—2141no—
241C2×C4—2142no—
242C2×C4—2141no—
243C2×C4—2144no—
244C2×C4—2148no—
245C2×C4—2142no—
246C2×C4—2142no—
247C2×C4C2×D42814yes—
248C22—24no—
249C22—24no—
250C22—24no—
251C22—1078no—
252C22—4282no—
253C22—4282no—
254C22—4282no—
255C22—4281no—
256C22—21432no—
257C22—2144no—
258C22—2148no—
259C22—2148no—
260C22—2144no—
261C22#1681207914yes—
262C22C2×D4×D10711yescharacteristic
263C22C2×D4×D10711yescharacteristic
264C22C22×D42811yescharacteristic
265C22#41×D10714yes—
266C4—24no—
267C4—42no—
268C4—42no—
269C4—4282no—
270C4—4281no—
271C4—2144no—
272C2—24no—
273C2—8561no—
274C2—2148no—
275C2C2×#1681207911yescharacteristic
276C2#123×D10712yes—
277C2#2029313512yes—
278C2#2029313912yes—
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, cosocleC23×C107C24
Fitting#381×C107C2
prime radicalC2×#16812079C2
hypercenter#381D107
hypocenterC107#2849
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
1. C23×C4×D107C2semidirect
2. C2×#16812093C2semidirect
3. C2×#16812092C2semidirect
5. #20292505C2semidirect
6. #20292501C2semidirect
7. #20292488C2semidirect
8. #20292482C2semidirect
9. #381×C107C2semidirect
21. C2×C4⋊Dic107C22semidirect
22. C2×Dic107⋊C4C22semidirect
26. C2×(C2×D107)⋊C4C22semidirect
27. C2×(C2×D107)⋊C4C22semidirect
28. C107⋊#95C22semidirect
32. #95×C107C22semidirect
46. C22×Dic107D4semidirect
64. C22×C4×C107D4semidirect
125. C2×D107#123semidirect
140. C107#2849semidirect
148. #381D107semidirect
172. #95C2×D107semidirect
197. C22×C4D428semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D1072
C2×#168120932
C2×#168120922
C2×#168120792
#202925052
#202925012
#202924882
#202924822
#381×C1072
#2849107