Finite Group Databasebeta

← #28337488

Subgroups — #28337488

Order 13696.

394 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C2×#16812139C211yesmaximal, characteristic, complemented
2C2×#16812096C211yesmaximal, characteristic, complemented
3C2×#16812036C211yesmaximal, characteristic, complemented
4#20292635C211yesmaximal, characteristic, complemented
5C2×#16812026C211yesmaximal, characteristic, complemented
6#20292386C211yesmaximal, characteristic, complemented
7#535×C107C211yesmaximal, characteristic
8C22×Dic214C2211yescharacteristic
9#16812139—22no—
10#16812139—22no—
11C2×#13133808—21no—
12C2×#13133806—21no—
13C2×#13133802C2211yescharacteristic
14C2×#13133802C2211yescharacteristic
15#16812096—22no—
16#16812096—22no—
17C2×C22⋊Dic107—22no—
18C2×C4×Dic107C2211yescharacteristic
19#16812036—22no—
20#16812032—22no—
21#16812026—22no—
22C2×#41×C107C2211yescharacteristic
23C22×D4×C107C2211yescharacteristic
24#127×C107—21no—
25#124×C107—21no—
26#121×C107—22no—
27#120×C107—22no—
28#117×C107C2211yescharacteristic
29C2×Dic214—21no—
30C2×Dic214—21no—
31C2×Dic214—21no—
32C2×Dic214—21no—
33C2×Dic214—21no—
34C2×Dic214D412yescomplemented
35C22×Dic107—21no—
36C22×Dic107—21no—
37#13133808—24no—
38#13133806—24no—
39#13133802—21no—
40#13133802—21no—
41#13133802—21no—
42#13133802D412yescomplemented
43C2×C107⋊C8—21no—
44C2×C107⋊C8—21no—
45C22⋊Dic107—28no—
46C4×Dic107—21no—
47C4×Dic107D412yescomplemented
48C24×C107D412yes—
49#41×C107—21no—
50#41×C107—21no—
51#41×C107—21no—
52#41×C107—21no—
53C2×Q8×C107D411yescharacteristic
54C2×D4×C107—21no—
55C2×D4×C107—24no—
56C2×D4×C107—21no—
57C2×D4×C107—21no—
58C2×D4×C107—21no—
59C2×D4×C107—21no—
60C2×D4×C107—21no—
61C2×D4×C107—21no—
62C2×D4×C107D411yescharacteristic
63C22×C4×C107—21no—
64C22×C4×C107C2311yescharacteristic
65C4⋊C4×C107D412yes—
66C22⋊C4×C107—24no—
67C22⋊C4×C107—21no—
68C42×C107—21no—
69C23×C107—22no—
70C23×C107—21no—
71C23×C107—22no—
72C23×C107—22no—
73C23×C107—44no—
74C23×C107C2×D411yescharacteristic
75Q8×C107—21no—
76Q8×C107—21no—
77D4×C107—21no—
78D4×C107—21no—
79D4×C107—41no—
80D4×C107—41no—
81D4×C107—41no—
82D4×C107—41no—
83D4×C107—41no—
84D4×C107—41no—
85D4×C107—84no—
86C2×C4×C107—22no—
87C2×C4×C107—21no—
88C2×C4×C107—41no—
89C2×C4×C107—41no—
90C2×C4×C107C2×D411yescharacteristic
91C2×C4×C107C2×D411yescharacteristic
92C2×C4×C107C2×D411yescharacteristic
93C2×C4×C107C2×D411yescharacteristic
94C2×C4×C107C2×D411yescharacteristic
95C2×C4×C107#4111yescharacteristic
96C2×Dic107—22no—
97C2×Dic107—22no—
98C2×Dic107—42no—
99C2×Dic107—41no—
100C2×Dic107—41no—
101Dic214—22no—
102Dic214—22no—
103Dic214—41no—
104Dic214—41no—
105C107⋊C8—22no—
106C107⋊C8—41no—
107C22×C107—22no—
108C22×C107—44no—
109C22×C107—41no—
110C22×C107—42no—
111C22×C107—42no—
112C22×C107—44no—
113C22×C107—82no—
114C22×C107#12011yescharacteristic
115C22×C107#12011yescharacteristic
116C22×C107#12111yescharacteristic
117C4×C107—41no—
118C4×C107—42no—
119C4×C107#12011yescharacteristic
120C4×C107#12111yescharacteristic
121C4×C107#12111yescharacteristic
122C4×C107#12711yescharacteristic
123Dic107—42no—
124Dic107—42no—
125C2×C107—21no—
126C2×C107—21no—
127C2×C107—81no—
128C2×C107—82no—
129C2×C107#39211yescharacteristic
130C2×C107#45512yes—
131#2004—1071nomaximal, Sylow
132C107#200411yescharacteristic, complemented, Sylow
133C2×#137—1071no—
134#535D10711yescharacteristic
135C2×#124—1071no—
136C2×#104—1071no—
137#419—1071no—
138C2×#100—1071no—
139#339—1071no—
140C2×#41C2×D10711yescharacteristic
141C22×Q8—1071no—
142C22×D4C2×D10711yescharacteristic
143#137—2142no—
144#137—2142no—
145C2×Q16—2141no—
146C2×SD16—2141no—
147C2×M16—1071no—
148C2×M16—1071no—
149#127—21no—
150#124—21no—
151#124—2142no—
152#124—2142no—
153#121—22no—
154#120—22no—
155#117C2×D10711yescharacteristic
156C2×C22⋊C4—2142no—
157C2×C42—1071no—
158#104—2142no—
159#103—2142no—
160#100—2142no—
161C24C22⋊D10712yes—
162#41—21no—
163#41—21no—
164#41—21no—
165#41—21no—
166C2×Q8—1072no—
167C2×Q8—2141no—
168C2×Q8—2141no—
169C2×Q8—2141no—
170C2×Q8—2141no—
171C2×Q8—2141no—
172C2×Q8C22⋊D10711yescharacteristic
173C2×D4—21no—
174C2×D4—24no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—21no—
180C2×D4—21no—
181C2×D4C22⋊D10711yescharacteristic
182C22×C4—21no—
183C22×C4—2141no—
184C22×C4—2141no—
185C22×C4C22×D10711yescharacteristic
186Q16—2144no—
187SD16—2144no—
188M16—1072no—
189M16—2141no—
190M16—2141no—
191M16—2141no—
192C2×C8—2141no—
193C2×C8—2141no—
194C4⋊C4C22⋊D10712yes—
195C22⋊C4—24no—
196C22⋊C4—21no—
197C22⋊C4—2148no—
198C42—21no—
199C42—1072no—
200C42—2141no—
201C23—22no—
202C23—22no—
203C23—21no—
204C23—22no—
205C23—44no—
206C23C2×C22⋊D10711yescharacteristic
207Q8—21no—
208Q8—21no—
209Q8—4281no—
210Q8—4281no—
211Q8—2142no—
212Q8—2142no—
213D4—21no—
214D4—21no—
215D4—41no—
216D4—41no—
217D4—41no—
218D4—41no—
219D4—41no—
220D4—41no—
221D4—84no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—4282no—
227C2×C4—4281no—
228C2×C4—4281no—
229C2×C4—2142no—
230C2×C4—2142no—
231C2×C4D4×D10711yescharacteristic
232C2×C4D4×D10711yescharacteristic
233C2×C4D4×D10711yescharacteristic
234C2×C4C2×C22⋊D10711yescharacteristic
235C2×C4C2×C22⋊D10711yescharacteristic
236C2×C4#1313381711yescharacteristic
237C8—4281no—
238C8—2142no—
239C22—22no—
240C22—44no—
241C22—41no—
242C22—42no—
243C22—42no—
244C22—44no—
245C22—82no—
246C22#1681207711yescharacteristic
247C22#1681207811yescharacteristic
248C22#1681208111yescharacteristic
249C4—41no—
250C4—42no—
251C4—4282no—
252C4—4282no—
253C4#1681207711yescharacteristic
254C4#1681208011yescharacteristic
255C4#1681208111yescharacteristic
256C4#1681210511yescharacteristic
257C2—21no—
258C2—21no—
259C2—82no—
260C2—81no—
261C2#2029253511yescharacteristic
262C2#2029280512yes—
subgroupG/H
centerC22#16812078
commutator, cosocleC22×C4×C107C23
FrattiniC22×C4C22×D107
Fitting, prime radical#535×C107C2
socleC22×C107#120
hypercenter#535D107
hypocenterC107#2004
LCSG ▷ C22×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#16812139C2semidirect
2. C2×#16812096C2semidirect
3. C2×#16812036C2semidirect
4. #20292635C2semidirect
5. C2×#16812026C2semidirect
6. #20292386C2semidirect
34. C2×Dic214D4semidirect
42. #13133802D4semidirect
47. C4×Dic107D4semidirect
132. C107#2004semidirect

Maximal subgroups

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

subgroupindex
C2×#168121392
C2×#168120962
C2×#168120362
#202926352
C2×#168120262
#202923862
#535×C1072
#2004107