Finite Group Databasebeta

← C2×#101×D107 #28344929

Subgroups — C2×#101×D107 #28344929

Order 13696.

736 conjugacy classes of subgroups; only the 221 normal subgroups are shown.

normal subgroups only

This group has 736 conjugacy classes of subgroups — too many to draw. Only its 221 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
1C22×Q8×D107C211yesmaximal, characteristic
2C2×M16×D107C212yesmaximal
3C2×#16812028C211yesmaximal, characteristic, complemented
4C2×#16812027C212yesmaximal, complemented
5#101×D107C218yesmaximal, direct product factor
6C2×#101×C107C211yesmaximal, characteristic, complemented
7C22×Dic214C412yes—
8C22×Dic214C2211yescharacteristic
9C2×Q8×D107—22no—
10C2×Q8×D107—24no—
11C2×Q8×D107—22no—
12C2×Q8×D107C414yes—
13C2×Q8×D107C2214yes—
14C22×C4×D107C412yes—
15C22×C4×D107C2211yescharacteristic
16C2×#13133802C2212yes—
17C2×#13133801—22no—
18M16×D107—24no—
19M16×D107C2218yes—
20C2×C8×D107—22no—
21#16812028C2214yescomplemented
22#16812027C2218yescomplemented
23C22×Q8×C107C2211yescharacteristic
24C2×M16×C107C2212yes—
25#101×C107C2214yescomplemented
26C23×D107C2×C411yescharacteristic
27C2×Dic214—22no—
28C2×Dic214—22no—
29C2×Dic214—24no—
30C2×Dic214—24no—
31C2×Dic214C2×C412yes—
32C2×Dic214C2×C418yes—
33C2×Dic214C2312yes—
34Q8×D107—28no—
35Q8×D107—28no—
36Q8×D107—28no—
37Q8×D107—28no—
38C22×Dic107C2×C412yes—
39C22×Dic107C2×C411yescharacteristic
40C2×C4×D107—24no—
41C2×C4×D107—22no—
42C2×C4×D107—22no—
43C2×C4×D107C2×C418yes—
44C2×C4×D107C2×C412yes—
45C2×C4×D107D412yes—
46C2×C4×D107D414yes—
47C2×C4×D107D412yes—
48C2×C4×D107C2312yes—
49#13133802—22no—
50#13133802C2314yes—
51#13133801—28no—
52C2×C107⋊C8—22no—
53C8×D107—28no—
54C2×Q8×C107—22no—
55C2×Q8×C107—22no—
56C2×Q8×C107C2×C412yes—
57C2×Q8×C107C2312yes—
58C22×C4×C107C2×C412yes—
59C22×C4×C107C2311yescharacteristic
60M16×C107—22no—
61M16×C107C2314yes—
62C2×C8×C107—22no—
63C23×C107C22×C411yescharacteristic
64C22×D107—24no—
65C22×D107C22⋊C412yes—
66C22×D107C22⋊C411yescharacteristic
67C22×D107C22⋊C411yescharacteristic
68C22×D107C22×C412yes—
69Q8×C107—24no—
70Q8×C107—24no—
71C2×C4×C107—22no—
72C2×C4×C107—22no—
73C2×C4×C107C22×C414yes—
74C2×C4×C107C22×C411yescharacteristic
75C2×C4×C107C2×D412yes—
76C2×C4×C107C2×D412yes—
77C2×C4×C107C2411yescharacteristic
78C2×Dic107—22no—
79C2×Dic107—22no—
80C2×Dic107C22⋊C412yes—
81C2×Dic107C22⋊C412yes—
82C2×Dic107C22×C414yes—
83C2×Dic107C22×C412yes—
84C4×D107—28no—
85C4×D107—28no—
86C4×D107C22⋊C414yes—
87C4×D107C22⋊C414yes—
88C4×D107C2×D414yes—
89C4×D107C2×D414yes—
90Dic214—24no—
91Dic214—24no—
92Dic214—216no—
93C8×C107—24no—
94C107⋊C8—24no—
95C22×C107—22no—
96C22×C107C2×C22⋊C411yescharacteristic
97C22×C107C2×C22⋊C411yescharacteristic
98C22×C107C23×C411yescharacteristic
99C2×D107—22no—
100C2×D107—24no—
101C2×D107—24no—
102C2×D107#10114yesdirect product factor
103C2×D107C2×C22⋊C412yes—
104C2×D107C2×C22⋊C412yes—
105C4×C107—24no—
106C4×C107C2×C22⋊C412yes—
107C4×C107C22×D412yes—
108Dic107—24no—
109Dic107C2×C22⋊C414yes—
110C2×C107—21no—
111C2×C107—21no—
112C2×C107C2×#10112yescomplemented
113C2×C107C22×C22⋊C411yescharacteristic
114D107—22no—
115D107C2×#10114yesdirect product factor
116C22×#101—1071nomaximal, Sylow
117C107C22×#10111yescharacteristic, complemented, Sylow
118C23×Q8—1071no—
119C22×M16—1072no—
120C2×#101—1071no—
121C2×#101—1072no—
122C2×#101—1078no—
123C2×#101D10711yescharacteristic, direct product factor
124C22×Q8—1074no—
125C22×Q8—1074no—
126C22×Q8—1072no—
127C22×Q8—1071no—
128C22×Q8—2142no—
129C22×Q8—2144no—
130C22×Q8—2142no—
131C22×Q8C2×D10711yescharacteristic
132C23×C4—1071no—
133C23×C4—1072no—
134C2×M16—1072no—
135C2×M16—1078no—
136C2×M16—2142no—
137C2×M16—2144no—
138C2×M16C2×D10712yes—
139C22×C8—2142no—
140#101—1074no—
141#101—1078no—
142#101C2×D10714yesdirect product factor
143C24—1071no—
144C2×Q8—22no—
145C2×Q8—22no—
146C2×Q8—1078no—
147C2×Q8—1072no—
148C2×Q8—1072no—
149C2×Q8—2144no—
150C2×Q8—2144no—
151C2×Q8—2148no—
152C2×Q8—2148no—
153C2×Q8—2148no—
154C2×Q8—2148no—
155C2×Q8—2142no—
156C2×Q8—2142no—
157C2×Q8C4×D10712yes—
158C2×Q8C22×D10712yes—
159C22×C4—1071no—
160C22×C4—1072no—
161C22×C4—1072no—
162C22×C4—1074no—
163C22×C4—1072no—
164C22×C4—1072no—
165C22×C4—1072no—
166C22×C4—1078no—
167C22×C4—2144no—
168C22×C4—2142no—
169C22×C4—2142no—
170C22×C4C4×D10712yes—
171C22×C4C22×D10711yescharacteristic
172M16—22no—
173M16—1074no—
174M16—2148no—
175M16—2142no—
176M16C22×D10714yes—
177C2×C8—22no—
178C2×C8—2148no—
179C2×C8—2142no—
180C23—1071no—
181C23—1072no—
182C23—1071no—
183C23—1072no—
184C23—2144no—
185C23C2×C4×D10711yescharacteristic
186Q8—24no—
187Q8—24no—
188Q8—21416no—
189Q8—2144no—
190Q8—2144no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—1072no—
194C2×C4—1072no—
195C2×C4—1072no—
196C2×C4—1074no—
197C2×C4—1074no—
198C2×C4—1074no—
199C2×C4—1074no—
200C2×C4—1074no—
201C2×C4—2148no—
202C2×C4—2148no—
203C2×C4—2142no—
204C2×C4—2142no—
205C2×C4C2×C4×D10714yes—
206C2×C4C2×C4×D10711yescharacteristic
207C2×C4D4×D10712yes—
208C2×C4D4×D10712yes—
209C2×C4C23×D10711yescharacteristic
210C8—24no—
211C8—2144no—
212C22—22no—
213C22—1072no—
214C22—1074no—
215C22—1072no—
216C22—2144no—
217C22—2144no—
218C22—2142no—
219C22C22⋊C4×D10711yescharacteristic
220C22C22⋊C4×D10711yescharacteristic
221C22C22×C4×D10711yescharacteristic
222C4—24no—
223C4—1074no—
224C4—2144no—
225C4C22⋊C4×D10712yes—
226C4C2×D4×D10712yes—
227C2—21no—
228C2—21no—
229C2—1074no—
230C2—2142no—
231C2#101×D10712yesdirect product factor
232C2C2×C22⋊C4×D10711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D107
commutatorC22×C107C23×C4
FrattiniC2×C4C23×D107
FittingC2×#101×C107C2
socleC22×C107C2×C22⋊C4
prime radicalC23×D107C2×C4
cosocleC2×C4×C107C24
hypercenterC2×#101D107
hypocenterC107C22×#101
LCSG ▷ C22×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
3. C2×#16812028C2semidirect
4. C2×#16812027C2semidirect
5. #101×D107C2direct (N × H)
6. C2×#101×C107C2semidirect
21. #16812028C22semidirect
22. #16812027C22semidirect
25. #101×C107C22semidirect
102. C2×D107#101direct (N × H)
112. C2×C107C2×#101semidirect
115. D107C2×#101direct (N × H)
117. C107C22×#101semidirect
123. C2×#101D107direct (N × H)
142. #101C2×D107direct (N × H)
231. C2#101×D107direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×D1072
C2×M16×D1072
C2×#168120282
C2×#168120272
#101×D1072
C2×#101×C1072
C22×#101107