Finite Group Databasebeta

← C2×#13092599 #15682738

Subgroups — C2×#13092599 #15682738

Order 2944.

708 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 149 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×#10625158C211yesmaximal, characteristic
2C2×#10625113C212yesmaximal, complemented
3#13092599C218yesmaximal, direct product factor
4C2×#10624987C212yesmaximal, complemented
5C2×#10625018C211yesmaximal, characteristic, complemented
6C2×C23×C4⋊Q8C211yesmaximal, characteristic, complemented
7C22×Q8×C23C2211yescharacteristic
8C22×Q8×C23C2211yescharacteristic
9#10625158—22no—
10#10625158—24no—
11#10625158C2214yes—
12C2×#67292—22no—
13C2×Q8×D23—22no—
14C2×#67288—22no—
15C2×#67288C2212yes—
16C23×C4⋊Q8—22no—
17C23×C4⋊Q8C2214yescomplemented
18C2×C4⋊C4×C23—22no—
19C2×C42×C23C2211yescharacteristic
20C2×#67275—22no—
21#10625113—24no—
22#10625113C2218yescomplemented
23C2×#67274—22no—
24C2×#67267C2212yes—
25#10625018C2214yescomplemented
26#10624987C2218yescomplemented
27C2×Q8×C23—22no—
28C2×Q8×C23—22no—
29C2×Q8×C23—21no—
30C2×Q8×C23—22no—
31C2×Q8×C23—22no—
32C2×Q8×C23D412yes—
33C2×Q8×C23C2312yes—
34C2×Q8×C23C2312yes—
35C22×C4×C23—21no—
36C22×C4×C23—21no—
37C22×C4×C23D412yes—
38C22×C4×C23C2311yescharacteristic
39C2×C22⋊D23—22no—
40#67292—28no—
41#67292—28no—
42Q8×D23—28no—
43Q8×D23—28no—
44#67288—28no—
45#67288—28no—
46#67288—22no—
47#67288—22no—
48#67288D414yes—
49#67288C2314yes—
50C2×D92—22no—
51C2×D92D412yes—
52C2×C4×D23—24no—
53C2×C4×D23—22no—
54C2×Dic46—22no—
55C2×Dic46D412yes—
56C4⋊C4×C23—28no—
57C42×C23—21no—
58C42×C23C2312yes—
59#67275—28no—
60#67274—28no—
61#67267—22no—
62#67267C2314yes—
63C2×C23⋊C8—22no—
64C23×C23C2×D411yescharacteristic
65C22×D23—22no—
66Q8×C23—24no—
67Q8×C23—24no—
68Q8×C23—24no—
69Q8×C23—42no—
70C2×C4×C23—24no—
71C2×C4×C23—22no—
72C2×C4×C23—22no—
73C2×C4×C23—22no—
74C2×C4×C23—22no—
75C2×C4×C23—41no—
76C2×C4×C23—41no—
77C2×C4×C23C2×D412yes—
78C2×C4×C23C2×D412yes—
79C2×C4×C23C2×D414yes—
80C2×C4×C23C2×D411yescharacteristic
81C2×C4×C23C2411yescharacteristic
82C22⋊D23—24no—
83C22⋊D23—24no—
84C2×Dic23—22no—
85D92—28no—
86D92—22no—
87D92C2×D414yes—
88C4×D23—216no—
89C4×D23—24no—
90C4×D23—24no—
91Dic46—28no—
92Dic46—22no—
93Dic46C2×D414yes—
94C23⋊C8—24no—
95C2×#456—231nomaximal, Sylow
96C22×C23—22no—
97C22×C23#12011yescharacteristic
98C22×C23#12011yescharacteristic
99C22×C23C22×D411yescharacteristic
100C2×D23—24no—
101C2×D23—44no—
102C4×C23—24no—
103C4×C23—24no—
104C4×C23—42no—
105C4×C23#12012yes—
106C4×C23C22×D412yes—
107Dic23—24no—
108C2×2−1+4—231no—
109C2×#137—232no—
110C2×C4⋊Q8D2311yescharacteristic, complemented
111#456—238no—
112C2×#104—232no—
113C2×#101—231no—
114C2×C23—21no—
115C2×C23—21no—
116C2×C23#45612yescomplemented
117C2×C23C2×#12011yescharacteristic
118D23—44no—
1192−1+4—234no—
1202−1+4—464no—
1212−1+4—462no—
122C2×#41—232no—
123C2×#41—462no—
124C2×#41—462no—
125C22×Q8—462no—
126C22×Q8C2×D2311yescharacteristic
127C22×Q8C2×D2311yescharacteristic
128#137—238no—
129#137—464no—
130C2×Q16—462no—
131C2×SD16—462no—
132C2×M16—232no—
133C4⋊Q8—22no—
134C4⋊Q8C2×D2314yescomplemented
135C2×C4⋊C4—22no—
136C2×C42C2×D2311yescharacteristic
137#104—238no—
138#101—234no—
139C23C2×#45611yescharacteristic, complemented, Sylow
140#41—234no—
141#41—234no—
142#41—468no—
143#41—468no—
144#41—468no—
145#41—462no—
146#41—462no—
147#41—468no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—21no—
151C2×Q8—22no—
152C2×Q8—22no—
153C2×Q8—232no—
154C2×Q8—462no—
155C2×Q8—468no—
156C2×Q8—468no—
157C2×Q8C22⋊D2312yes—
158C2×Q8C22×D2312yes—
159C2×Q8C22×D2312yes—
160C2×D4—232no—
161C2×D4—462no—
162C2×D4—462no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—464no—
166C22×C4—462no—
167C22×C4C22⋊D2312yes—
168C22×C4C22×D2311yescharacteristic
169Q16—468no—
170SD16—468no—
171M16—234no—
172M16—462no—
173C2×C8—462no—
174C4⋊C4—28no—
175C42—21no—
176C42C22×D2312yes—
177C23—462no—
178C23C2×C22⋊D2311yescharacteristic
179Q8—24no—
180Q8—24no—
181Q8—24no—
182Q8—42no—
183Q8—234no—
184Q8—468no—
185Q8—462no—
186D4—234no—
187D4—468no—
188D4—464no—
189D4—464no—
190D4—462no—
191C2×C4—24no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—4616no—
199C2×C4—462no—
200C2×C4—464no—
201C2×C4—464no—
202C2×C4D4×D2312yes—
203C2×C4D4×D2312yes—
204C2×C4C2×C22⋊D2314yes—
205C2×C4C2×C22⋊D2311yescharacteristic
206C2×C4C23×D2311yescharacteristic
207C8—464no—
208C22—22no—
209C22—464no—
210C22—924no—
211C22#1062510811yescharacteristic
212C22#1062510811yescharacteristic
213C22C22×C22⋊D2311yescharacteristic
214C4—24no—
215C4—24no—
216C4—42no—
217C4—464no—
218C4#1062510812yes—
219C4C2×D4×D2312yes—
220C2—21no—
221C2—21no—
222C2—924no—
223C2#1309259912yesdirect product factor
224C2C2×#1062510811yescharacteristic
subgroupG/H
centerC22#10625108
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC2×C23×C4⋊Q8C2
socleC22×C23#120
prime radicalC2×#10625158C2
hypercenterC2×C4⋊Q8D23
hypocenterC23C2×#456
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#10625113C2semidirect
3. #13092599C2direct (N × H)
4. C2×#10624987C2semidirect
5. C2×#10625018C2semidirect
6. C2×C23×C4⋊Q8C2semidirect
17. C23×C4⋊Q8C22semidirect
22. #10625113C22semidirect
25. #10625018C22semidirect
26. #10624987C22semidirect
110. C2×C4⋊Q8D23semidirect
116. C2×C23#456semidirect
134. C4⋊Q8C2×D23semidirect
139. C23C2×#456semidirect
223. C2#13092599direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106251582
C2×#106251132
#130925992
C2×#106249872
C2×#106250182
C2×C23×C4⋊Q82
C2×#45623