Finite Group Databasebeta

← C2×#20292810 #28345803

Subgroups — C2×#20292810 #28345803

Order 13696.

708 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 165 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×#16812139C212yesmaximal, complemented
2C2×#16812107C211yesmaximal, characteristic, complemented
3#20292810C218yesmaximal, direct product factor
4C2×#16812036C212yesmaximal, complemented
5C2×#16812028C211yesmaximal, characteristic, complemented
6C2×2−1+4×C107C211yesmaximal, characteristic
7C22×Dic214C2211yescharacteristic
8#16812139—24no—
9#16812139C2218yescomplemented
10C2×#13133808—22no—
11C2×#13133806—22no—
12C2×#13133802C2212yes—
13#16812107—22no—
14#16812107C2214yescomplemented
15C2×Dic107⋊C4—22no—
16C2×C4×Dic107C2211yescharacteristic
17#16812036C2218yescomplemented
18#16812028C2214yescomplemented
192−1+4×C107—24no—
202−1+4×C107—22no—
212−1+4×C107C2214yes—
22C2×#41×C107—22no—
23C2×#41×C107—22no—
24C2×#41×C107C2212yes—
25C22×Q8×C107—22no—
26C22×Q8×C107C2211yescharacteristic
27C2×Dic214—22no—
28C2×Dic214—22no—
29C2×Dic214—21no—
30C2×Dic214C2312yes—
31C22×Dic107—21no—
32C22×Dic107—21no—
33#13133808—28no—
34#13133806—28no—
35#13133802—22no—
36#13133802C2314yes—
37C2×C107⋊C8—22no—
38Dic107⋊C4—28no—
39C4×Dic107—21no—
40C4×Dic107C2312yes—
41#41×C107—28no—
42#41×C107—28no—
43#41×C107—28no—
44#41×C107—28no—
45#41×C107—22no—
46#41×C107—22no—
47#41×C107D414yes—
48#41×C107C2314yes—
49C2×Q8×C107—22no—
50C2×Q8×C107—28no—
51C2×Q8×C107—28no—
52C2×Q8×C107—22no—
53C2×Q8×C107—22no—
54C2×Q8×C107D412yes—
55C2×Q8×C107D412yes—
56C2×Q8×C107C2312yes—
57C2×D4×C107—22no—
58C2×D4×C107—22no—
59C2×D4×C107D412yes—
60C22×C4×C107—24no—
61C22×C4×C107—22no—
62C22×C4×C107D412yes—
63C22×C4×C107C2311yescharacteristic
64C23×C107—22no—
65C23×C107C2×D411yescharacteristic
66Q8×C107—28no—
67Q8×C107—22no—
68Q8×C107—24no—
69Q8×C107—24no—
70Q8×C107C2×D414yes—
71D4×C107—28no—
72D4×C107—24no—
73D4×C107—24no—
74D4×C107—22no—
75D4×C107C2×D414yes—
76C2×C4×C107—216no—
77C2×C4×C107—22no—
78C2×C4×C107—22no—
79C2×C4×C107—22no—
80C2×C4×C107—24no—
81C2×C4×C107—24no—
82C2×C4×C107C2×D414yes—
83C2×C4×C107C2×D411yescharacteristic
84C2×C4×C107C2×D412yes—
85C2×C4×C107C2×D412yes—
86C2×C4×C107C2411yescharacteristic
87C2×Dic107—24no—
88C2×Dic107—22no—
89C2×Dic107—22no—
90C2×Dic107—41no—
91C2×Dic107—41no—
92Dic214—24no—
93Dic214—42no—
94C107⋊C8—24no—
95C22×C107—22no—
96C22×C107—24no—
97C22×C107—44no—
98C22×C107#12011yescharacteristic
99C22×C107#12011yescharacteristic
100C22×C107C22×D411yescharacteristic
101C4×C107—24no—
102C4×C107—24no—
103C4×C107#12012yes—
104C4×C107C22×D412yes—
105Dic107—24no—
106Dic107—42no—
107C2×C107—21no—
108C2×C107—21no—
109C2×C107—44no—
110C2×C107#45612yescomplemented
111C2×C107C2×#12011yescharacteristic
112C2×#456—1071nomaximal, Sylow
113C107C2×#45611yescharacteristic, complemented, Sylow
114C2×2−1+4D10711yescharacteristic
115C2×#137—1072no—
116C2×C4⋊Q8—1071no—
117#456—1078no—
118C2×#104—1072no—
119C2×#101—1071no—
1202−1+4—24no—
1212−1+4—22no—
1222−1+4C2×D10714yes—
123C2×#41—22no—
124C2×#41—22no—
125C2×#41C2×D10712yes—
126C22×Q8—22no—
127C22×Q8—1071no—
128C22×Q8C2×D10711yescharacteristic
129#137—1078no—
130#137—2144no—
131C2×Q16—2142no—
132C2×SD16—2142no—
133C2×M16—1072no—
134C4⋊Q8—1074no—
135C4⋊Q8—2142no—
136C2×C4⋊C4—2142no—
137C2×C42—1071no—
138#104—1078no—
139#101—1074no—
140#41—28no—
141#41—28no—
142#41—28no—
143#41—28no—
144#41—22no—
145#41—22no—
146#41C22⋊D10714yes—
147#41C22×D10714yes—
148C2×Q8—22no—
149C2×Q8—28no—
150C2×Q8—28no—
151C2×Q8—22no—
152C2×Q8—22no—
153C2×Q8—1072no—
154C2×Q8—2142no—
155C2×Q8—2142no—
156C2×Q8—2141no—
157C2×Q8C22⋊D10712yes—
158C2×Q8C22⋊D10712yes—
159C2×Q8C22×D10712yes—
160C2×D4—22no—
161C2×D4—22no—
162C2×D4C22⋊D10712yes—
163C22×C4—24no—
164C22×C4—22no—
165C22×C4—2141no—
166C22×C4—2141no—
167C22×C4C22⋊D10712yes—
168C22×C4C22×D10711yescharacteristic
169Q16—2148no—
170SD16—2148no—
171M16—1074no—
172M16—2142no—
173C2×C8—2142no—
174C4⋊C4—2148no—
175C42—1072no—
176C42—2141no—
177C23—22no—
178C23C2×C22⋊D10711yescharacteristic
179Q8—28no—
180Q8—22no—
181Q8—24no—
182Q8—24no—
183Q8—4282no—
184Q8—2144no—
185Q8C2×C22⋊D10714yes—
186D4—28no—
187D4—24no—
188D4—24no—
189D4—22no—
190D4C2×C22⋊D10714yes—
191C2×C4—216no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—24no—
196C2×C4—24no—
197C2×C4—4281no—
198C2×C4—4281no—
199C2×C4—2142no—
200C2×C4—2144no—
201C2×C4—2142no—
202C2×C4C2×C22⋊D10714yes—
203C2×C4C2×C22⋊D10711yescharacteristic
204C2×C4C2×C22⋊D10712yes—
205C2×C4C2×C22⋊D10712yes—
206C2×C4C23×D10711yescharacteristic
207C8—2144no—
208C22—22no—
209C22—24no—
210C22—44no—
211C22#1681207811yescharacteristic
212C22#1681207811yescharacteristic
213C22C22×C22⋊D10711yescharacteristic
214C4—24no—
215C4—24no—
216C4—4282no—
217C4—2144no—
218C4#1681207812yes—
219C4C22×C22⋊D10712yes—
220C2—21no—
221C2—21no—
222C2—44no—
223C2#2029281012yesdirect product factor
224C2C2×#1681207811yescharacteristic
subgroupG/H
centerC22#16812078
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting, prime radicalC2×2−1+4×C107C2
socleC22×C107#120
hypercenterC2×2−1+4D107
hypocenterC107C2×#456
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
1. C2×#16812139C2semidirect
2. C2×#16812107C2semidirect
3. #20292810C2direct (N × H)
4. C2×#16812036C2semidirect
5. C2×#16812028C2semidirect
9. #16812139C22semidirect
14. #16812107C22semidirect
17. #16812036C22semidirect
18. #16812028C22semidirect
110. C2×C107#456semidirect
113. C107C2×#456semidirect
223. C2#20292810direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168121392
C2×#168121072
#202928102
C2×#168120362
C2×#168120282
C2×2−1+4×C1072
C2×#456107