Finite Group Databasebeta

← C2×#14271820 #16832956

Subgroups — C2×#14271820 #16832956

Order 3712.

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×D29C211yesmaximal, characteristic, complemented
2#14271820C2116yesmaximal, direct product factor
3C2×#11745298C213yesmaximal, complemented
4C2×#11745286C213yesmaximal, complemented
5C2×#11745300C213yesmaximal, complemented
6C2×Q8×Dic29C211yesmaximal, characteristic, complemented
7C2×C4×C22⋊D29C213yesmaximal, complemented
8C22×#41×C29C211yesmaximal, characteristic, complemented
9C2×#41×C29—28no—
10C2×#41×C29C2218yescomplemented
11C22×Q8×C29C2211yescharacteristic
12C22×D4×C29C2213yes—
13C23×C4×C29C2213yes—
14C22×C22⋊D29C2213yes—
15C2×Q8×D29—28no—
16C2×Q8×D29C2218yescomplemented
17C22×C4×D29C2213yes—
18C22×Dic58C2213yes—
19C2×C22⋊Dic29C2213yes—
20C2×C22⋊Dic29C2216yes—
21Q8×Dic29C2218yescomplemented
22#11745300C22124yescomplemented
23#11745298C22124yescomplemented
24C4×C22⋊D29C22124yescomplemented
25C2×#90781C2211yescharacteristic
26C2×C4⋊Dic29C2213yes—
27#11745286C22124yescomplemented
28C2×#90779C2213yes—
29C2×C4×Dic29C2213yes—
30C24×C29C2313yes—
31C23×D29C2311yescharacteristic
32#41×C29—232no—
33C2×Q8×C29D418yescomplemented
34C2×Q8×C29C2314yes—
35C2×D4×C29—212no—
36C2×D4×C29C23112yes—
37C22×C4×C29—212no—
38C22×C4×C29C2311yescharacteristic
39C22×C4×C29C23112yes—
40C22×C4×C29C2313yes—
41C2×C22⋊D29—212no—
42C2×C22⋊D29C23112yes—
43C22×Dic29C2311yescharacteristic
44C22×Dic29C2313yes—
45C22×Dic29C2313yes—
46Q8×D29—232no—
47C2×C4×D29—212no—
48C2×C4×D29C23112yes—
49C2×Dic58—212no—
50C2×Dic58C23112yes—
51C22⋊Dic29C23124yes—
52C22⋊Dic29C23112yes—
53#90781C2314yes—
54C4⋊Dic29C23112yes—
55#90779C23112yes—
56C4×Dic29C23112yes—
57C23×C29—26no—
58C23×C29—26no—
59C23×C29—26no—
60C23×C29C2416yes—
61C23×C29C2411yescharacteristic
62C22×D29—22no—
63C22×D29—22no—
64C22×D29#4114yescomplemented
65C22×D29C2412yes—
66Q8×C29C2×D4116yescomplemented
67D4×C29—224no—
68C2×C4×C29—22no—
69C2×C4×C29—224no—
70C2×C4×C29C2×D4112yes—
71C2×C4×C29C2412yes—
72C2×C4×C29C2416yes—
73C22⋊D29—224no—
74C2×Dic29—26no—
75C2×Dic29—26no—
76C2×Dic29—22no—
77C2×Dic29C2412yes—
78C2×Dic29C2416yes—
79C2×Dic29C2416yes—
80C4×D29—224no—
81Dic58—224no—
82C2×#548—291nomaximal, Sylow
83C22×C29—26no—
84C22×C29—26no—
85C22×C29—26no—
86C22×C29—412no—
87C22×C29C22×D412yes—
88C22×C29C2×#4112yes—
89C22×C292−1+412yes—
90C22×C29C2511yescharacteristic
91C2×D29—28no—
92C2×D29—22no—
93C2×D29—22no—
94C2×D29C2×#4114yescomplemented
95C4×C29—22no—
96C4×C29C22×D4112yes—
97Dic29—26no—
98Dic29—26no—
99Dic29—22no—
100C22×#41D2911yescharacteristic, complemented
101C23×Q8—291no—
102#548—2916no—
103C2×#124—293no—
104C2×C22⋊Q8—293no—
105C2×#121—293no—
106C2×C4×Q8—291no—
107C2×C4×D4—293no—
108C2×C29—46no—
109C2×C29#54814yescomplemented
110C2×C29C23×D411yescharacteristic
111C2×C29C22×#4111yescharacteristic
112C2×C29C2×2−1+411yescharacteristic
113D29—24no—
114C2×#41—28no—
115C2×#41C2×D2918yescomplemented
116C22×Q8—298no—
117C22×Q8—293no—
118C22×Q8—588no—
119C22×Q8C2×D2911yescharacteristic
120C22×D4—293no—
121C22×D4C2×D2913yes—
122C23×C4—293no—
123C23×C4C2×D2913yes—
124#124—2924no—
125C22⋊Q8—2924no—
126#121—2924no—
127C4×Q8—298no—
128C4×D4—2924no—
129C2×C4⋊C4—293no—
130C2×C4⋊C4—293no—
131C2×C22⋊C4—293no—
132C2×C22⋊C4—296no—
133C2×C22⋊C4—291no—
134C2×C42—293no—
135C29C2×#54811yescharacteristic, complemented, Sylow
136C24—291no—
137C24C22×D2913yes—
138#41—232no—
139C2×Q8—2912no—
140C2×Q8—5832no—
141C2×Q8—5812no—
142C2×Q8C22⋊D2918yescomplemented
143C2×Q8C22×D2914yes—
144C2×D4—212no—
145C2×D4—2912no—
146C2×D4—5812no—
147C2×D4C22×D29112yes—
148C22×C4—212no—
149C22×C4—291no—
150C22×C4—293no—
151C22×C4—293no—
152C22×C4—2912no—
153C22×C4—5812no—
154C22×C4C22×D29112yes—
155C22×C4C22×D2911yescharacteristic
156C22×C4C22×D2913yes—
157C4⋊C4—2912no—
158C4⋊C4—2912no—
159C22⋊C4—2912no—
160C22⋊C4—2924no—
161C22⋊C4—294no—
162C42—2912no—
163C23—26no—
164C23—26no—
165C23—26no—
166C23—294no—
167C23—292no—
168C23—582no—
169C23—582no—
170C23C23×D2916yes—
171C23C23×D2911yescharacteristic
172Q8—5824no—
173Q8C2×C22⋊D29116yescomplemented
174D4—224no—
175D4—5824no—
176C2×C4—22no—
177C2×C4—224no—
178C2×C4—292no—
179C2×C4—296no—
180C2×C4—296no—
181C2×C4—586no—
182C2×C4—582no—
183C2×C4—586no—
184C2×C4—5824no—
185C2×C4C2×C22⋊D29112yes—
186C2×C4C23×D2912yes—
187C2×C4C23×D2916yes—
188C22—26no—
189C22—26no—
190C22—26no—
191C22—412no—
192C22—294no—
193C22—588no—
194C22—582no—
195C22—582no—
196C22#41×D2912yes—
197C22#1174536512yes—
198C22C22×C22⋊D2912yes—
199C22C24×D2911yescharacteristic
200C4—22no—
201C4—586no—
202C4—586no—
203C4—582no—
204C4C22×C22⋊D29112yes—
205C2—46no—
206C2—584no—
207C2#1427182014yesdirect product factor
208C2C23×C22⋊D2911yescharacteristic
209C2C2×#41×D2911yescharacteristic
210C2C2×#1174536511yescharacteristic
subgroupG/H
centerC23C23×D29
commutator, cosocleC22×C29C25
FrattiniC22C24×D29
FittingC22×#41×C29C2
socleC23×C29C24
hypercenterC22×#41D29
hypocenterC29C2×#548
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C23 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D29C2semidirect
2. #14271820C2direct (N × H)
3. C2×#11745298C2semidirect
4. C2×#11745286C2semidirect
5. C2×#11745300C2semidirect
6. C2×Q8×Dic29C2semidirect
7. C2×C4×C22⋊D29C2semidirect
8. C22×#41×C29C2semidirect
10. C2×#41×C29C22semidirect
16. C2×Q8×D29C22semidirect
21. Q8×Dic29C22semidirect
22. #11745300C22semidirect
23. #11745298C22semidirect
24. C4×C22⋊D29C22semidirect
27. #11745286C22semidirect
33. C2×Q8×C29D4semidirect
64. C22×D29#41semidirect
66. Q8×C29C2×D4semidirect
94. C2×D29C2×#41semidirect
100. C22×#41D29semidirect
109. C2×C29#548semidirect
115. C2×#41C2×D29semidirect
135. C29C2×#548semidirect
142. C2×Q8C22⋊D29semidirect
173. Q8C2×C22⋊D29semidirect
207. C2#14271820direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×D292
#142718202
C2×#117452982
C2×#117452862
C2×#117453002
C2×Q8×Dic292
C2×C4×C22⋊D292
C22×#41×C292
C2×#54829