Finite Group Databasebeta

← C2×#13093074 #15686861

Subgroups — C2×#13093074 #15686861

Order 2944.

1620 conjugacy classes of subgroups; only the 573 normal subgroups are shown.

normal subgroups only

This group has 1620 conjugacy classes of subgroups — too many to draw. Only its 573 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×D23C211yesmaximal, characteristic, complemented
2#13093074C2116yesmaximal, direct product factor
3C2×#10625107C213yesmaximal, complemented
4C2×#10625095C213yesmaximal, complemented
5C2×#10625109C213yesmaximal, complemented
6C2×Q8×Dic23C211yesmaximal, characteristic, complemented
7C2×C4×C22⋊D23C213yesmaximal, complemented
8C22×#41×C23C211yesmaximal, characteristic, complemented
9C2×#41×C23—28no—
10C2×#41×C23C2218yescomplemented
11C22×Q8×C23C2211yescharacteristic
12C22×D4×C23C2213yes—
13C23×C4×C23C2213yes—
14C22×C22⋊D23C2213yes—
15C2×Q8×D23—28no—
16C2×Q8×D23C2218yescomplemented
17C22×C4×D23C2213yes—
18C22×Dic46C2213yes—
19C2×C22⋊Dic23C2213yes—
20C2×C22⋊Dic23C2216yes—
21Q8×Dic23C2218yescomplemented
22#10625109C22124yescomplemented
23#10625107C22124yescomplemented
24C4×C22⋊D23C22124yescomplemented
25C2×(C2×D23)⋊C4C2211yescharacteristic
26C2×C4⋊Dic23C2213yes—
27#10625095C22124yescomplemented
28C2×Dic23⋊C4C2213yes—
29C2×C4×Dic23C2213yes—
30C24×C23C2313yes—
31C23×D23C2311yescharacteristic
32#41×C23—232no—
33C2×Q8×C23D418yescomplemented
34C2×Q8×C23C2314yes—
35C2×D4×C23—212no—
36C2×D4×C23C23112yes—
37C22×C4×C23—212no—
38C22×C4×C23C2311yescharacteristic
39C22×C4×C23C23112yes—
40C22×C4×C23C2313yes—
41C2×C22⋊D23—212no—
42C2×C22⋊D23C23112yes—
43C22×Dic23C2311yescharacteristic
44C22×Dic23C2313yes—
45C22×Dic23C2313yes—
46Q8×D23—232no—
47C2×C4×D23—212no—
48C2×C4×D23C23112yes—
49C2×Dic46—212no—
50C2×Dic46C23112yes—
51C22⋊Dic23C23124yes—
52C22⋊Dic23C23112yes—
53(C2×D23)⋊C4C2314yes—
54C4⋊Dic23C23112yes—
55Dic23⋊C4C23112yes—
56C4×Dic23C23112yes—
57C23×C23—26no—
58C23×C23—26no—
59C23×C23—26no—
60C23×C23C2416yes—
61C23×C23C2411yescharacteristic
62C22×D23—22no—
63C22×D23—22no—
64C22×D23#4114yescomplemented
65C22×D23C2412yes—
66Q8×C23C2×D4116yescomplemented
67D4×C23—224no—
68C2×C4×C23—22no—
69C2×C4×C23—224no—
70C2×C4×C23C2×D4112yes—
71C2×C4×C23C2412yes—
72C2×C4×C23C2416yes—
73C22⋊D23—224no—
74C2×Dic23—26no—
75C2×Dic23—26no—
76C2×Dic23—22no—
77C2×Dic23C2412yes—
78C2×Dic23C2416yes—
79C2×Dic23C2416yes—
80C4×D23—224no—
81Dic46—224no—
82C2×#548—231nomaximal, Sylow
83C22×C23—26no—
84C22×C23—26no—
85C22×C23—26no—
86C22×C23—412no—
87C22×C23C22×D412yes—
88C22×C23C2×#4112yes—
89C22×C232−1+412yes—
90C22×C23C2511yescharacteristic
91C2×D23—28no—
92C2×D23—22no—
93C2×D23—22no—
94C2×D23C2×#4114yescomplemented
95C4×C23—22no—
96C4×C23C22×D4112yes—
97Dic23—26no—
98Dic23—26no—
99Dic23—22no—
100C22×#41D2311yescharacteristic, complemented
101C23×Q8—231no—
102#548—2316no—
103C2×#124—233no—
104C2×C22⋊Q8—233no—
105C2×#121—233no—
106C2×C4×Q8—231no—
107C2×C4×D4—233no—
108C2×C23—46no—
109C2×C23#54814yescomplemented
110C2×C23C23×D411yescharacteristic
111C2×C23C22×#4111yescharacteristic
112C2×C23C2×2−1+411yescharacteristic
113D23—24no—
114C2×#41—28no—
115C2×#41C2×D2318yescomplemented
116C22×Q8—238no—
117C22×Q8—233no—
118C22×Q8—468no—
119C22×Q8C2×D2311yescharacteristic
120C22×D4—233no—
121C22×D4C2×D2313yes—
122C23×C4—233no—
123C23×C4C2×D2313yes—
124#124—2324no—
125C22⋊Q8—2324no—
126#121—2324no—
127C4×Q8—238no—
128C4×D4—2324no—
129C2×C4⋊C4—233no—
130C2×C4⋊C4—233no—
131C2×C22⋊C4—233no—
132C2×C22⋊C4—236no—
133C2×C22⋊C4—231no—
134C2×C42—233no—
135C23C2×#54811yescharacteristic, complemented, Sylow
136C24—231no—
137C24C22×D2313yes—
138#41—232no—
139C2×Q8—2312no—
140C2×Q8—4632no—
141C2×Q8—4612no—
142C2×Q8C22⋊D2318yescomplemented
143C2×Q8C22×D2314yes—
144C2×D4—212no—
145C2×D4—2312no—
146C2×D4—4612no—
147C2×D4C22×D23112yes—
148C22×C4—212no—
149C22×C4—231no—
150C22×C4—233no—
151C22×C4—233no—
152C22×C4—2312no—
153C22×C4—4612no—
154C22×C4C22×D23112yes—
155C22×C4C22×D2311yescharacteristic
156C22×C4C22×D2313yes—
157C4⋊C4—2312no—
158C4⋊C4—2312no—
159C22⋊C4—2312no—
160C22⋊C4—2324no—
161C22⋊C4—234no—
162C42—2312no—
163C23—26no—
164C23—26no—
165C23—26no—
166C23—234no—
167C23—232no—
168C23—462no—
169C23—462no—
170C23C23×D2316yes—
171C23C23×D2311yescharacteristic
172Q8—4624no—
173Q8C2×C22⋊D23116yescomplemented
174D4—224no—
175D4—4624no—
176C2×C4—22no—
177C2×C4—224no—
178C2×C4—232no—
179C2×C4—236no—
180C2×C4—236no—
181C2×C4—466no—
182C2×C4—462no—
183C2×C4—466no—
184C2×C4—4624no—
185C2×C4C2×C22⋊D23112yes—
186C2×C4C23×D2312yes—
187C2×C4C23×D2316yes—
188C22—26no—
189C22—26no—
190C22—26no—
191C22—412no—
192C22—234no—
193C22—462no—
194C22—462no—
195C22—468no—
196C22#41×D2312yes—
197C22#1062516112yes—
198C22C22×C22⋊D2312yes—
199C22C24×D2311yescharacteristic
200C4—22no—
201C4—466no—
202C4—466no—
203C4—462no—
204C4C22×C22⋊D23112yes—
205C2—46no—
206C2—464no—
207C2#1309307414yesdirect product factor
208C2C23×C22⋊D2311yescharacteristic
209C2C2×#41×D2311yescharacteristic
210C2C2×#1062516111yescharacteristic
subgroupG/H
centerC23C23×D23
commutator, cosocleC22×C23C25
FrattiniC22C24×D23
FittingC22×#41×C23C2
socleC23×C23C24
hypercenterC22×#41D23
hypocenterC23C2×#548
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D23C2semidirect
2. #13093074C2direct (N × H)
3. C2×#10625107C2semidirect
4. C2×#10625095C2semidirect
5. C2×#10625109C2semidirect
6. C2×Q8×Dic23C2semidirect
7. C2×C4×C22⋊D23C2semidirect
8. C22×#41×C23C2semidirect
10. C2×#41×C23C22semidirect
16. C2×Q8×D23C22semidirect
21. Q8×Dic23C22semidirect
22. #10625109C22semidirect
23. #10625107C22semidirect
24. C4×C22⋊D23C22semidirect
27. #10625095C22semidirect
33. C2×Q8×C23D4semidirect
64. C22×D23#41semidirect
66. Q8×C23C2×D4semidirect
94. C2×D23C2×#41semidirect
100. C22×#41D23semidirect
109. C2×C23#548semidirect
115. C2×#41C2×D23semidirect
135. C23C2×#548semidirect
142. C2×Q8C22⋊D23semidirect
173. Q8C2×C22⋊D23semidirect
207. C2#13093074direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×D232
#130930742
C2×#106251072
C2×#106250952
C2×#106251092
C2×Q8×Dic232
C2×C4×C22⋊D232
C22×#41×C232
C2×#54823