Finite Group Databasebeta

← #21461976

Subgroups — #21461976

Order 7808.

284 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 66 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
1#16840772C211yesmaximal, characteristic, complemented
2#16840760C212yesmaximal, complemented
3#16840742C212yesmaximal, complemented
4#16840725C211yesmaximal, characteristic, complemented
5C2×#14519796C211yesmaximal, characteristic
6D61⋊M16C2211yescharacteristic
7#14519856C2212yes—
8#14519856C2211yescharacteristic
9#14519846—21no—
10#14519845—21no—
11#14519841—24no—
12#14519835—24no—
13#14519831—21no—
14C8×#6923—21no—
15C2×#11758224C2212yes—
16#14519796—21no—
17#14519796—21no—
18#14519796—21no—
19#14519796—21no—
20C2×Dic244C411yescharacteristic, complemented
21C2×#11758200C412yescomplemented
22C2×C8×D61C2211yescharacteristic
23C2×D8×C61C411yescharacteristic, complemented
24C2×D4×C61C2×C412yes—
25C2×C22⋊D61—22no—
26C22×Dic61—22no—
27#11758224—22no—
28#11758224—22no—
29#11758224—22no—
30#11758224—22no—
31C2×C4×D61C2311yescharacteristic
32C2×Dic122C2×C412yes—
33C22⋊#6923—22no—
34C22⋊#6923D412yes—
35#11758217—21no—
36C4⋊#6923—22no—
37C4⋊#6923—21no—
38C4×#6923—21no—
39C4×#6923—22no—
40#11758213D412yes—
41D61⋊C8—21no—
42D8×C61—21no—
43D8×C61—21no—
44C2×C8×C61C2×C411yescharacteristic
45#11758200—22no—
46#11758200—22no—
47C2×#92418C2×C411yescharacteristic
48Dic244—21no—
49Dic244—21no—
50C8×D61D411yescharacteristic
51C8×D61D411yescharacteristic
52C8×D61D411yescharacteristic
53C8×D61D411yescharacteristic
54C23×C61—22no—
55C22×D61C2×D411yescharacteristic
56C2×#6923—22no—
57C2×#6923—42no—
58D4×C61—22no—
59D4×C61—22no—
60C2×C4×C61C22×C411yescharacteristic
61C22⋊D61—42no—
62C22⋊D61—42no—
63C2×Dic61—22no—
64C2×Dic61—42no—
65C2×Dic61—42no—
66C2×Dic61#4111yescharacteristic
67C4×D61C2×D411yescharacteristic
68C4×D61C2×D411yescharacteristic
69C4×D61C2×D411yescharacteristic
70C4×D61#4111yescharacteristic
71Dic122—22no—
72Dic122—22no—
73#92420—22no—
74C8×C61C22⋊C411yescharacteristic
75C8×C61C22⋊C411yescharacteristic
76#92418C22⋊C411yescharacteristic
77#92418C22⋊C411yescharacteristic
78C22×C61—42no—
79C22×C61—82no—
80C22×C61C4×D411yescharacteristic
81C2×D61—41no—
82C2×D61#12111yescharacteristic
83C2×D61#12711yescharacteristic
84#6923—42no—
85#6923—82no—
86C4×C61C2×C22⋊C411yescharacteristic
87C4×C61C4×D411yescharacteristic
88Dic61—42no—
89Dic61#12111yescharacteristic
90Dic61#12411yescharacteristic
91#1976—611nomaximal, Sylow
92C2×C61—21no—
93C2×C61—82no—
94C2×C61#39011yescharacteristic
95D61—21no—
96D61—21no—
97C2×#135—611no—
98#427—611no—
99#421—612no—
100#410—612no—
101#405—611no—
102C61#197611yescharacteristic, complemented, Sylow
103C2×#41—612no—
104#135—1221no—
105#135—1221no—
106#135—1221no—
107#135—1221no—
108C2×Q16—611no—
109C2×SD16—612no—
110C2×D8#692311yescharacteristic, complemented
111C2×M16—611no—
112C22×C8—611no—
113#117—611no—
114#117—612no—
115#107—1221no—
116#106—1221no—
117#104—1224no—
118#99—1224no—
119#97—1221no—
120C4×C8—1221no—
121#41—1222no—
122#41—1222no—
123#41—1222no—
124#41—1222no—
125C2×Q8—612no—
126C2×D4—1222no—
127C2×D4C2×#692312yes—
128C22×C4—611no—
129C22×C4—1222no—
130Q16—1221no—
131Q16—1221no—
132SD16—1222no—
133SD16—1222no—
134D8—21no—
135D8—21no—
136M16—612no—
137M16—1221no—
138C2×C8—611no—
139C2×C8—611no—
140C2×C8—611no—
141C2×C8—611no—
142C2×C8—611no—
143C2×C8—1221no—
144C2×C8C2×#692311yescharacteristic
145C4⋊C4—1221no—
146C4⋊C4—1222no—
147C22⋊C4—612no—
148C22⋊C4—1222no—
149C42—1221no—
150C42—1222no—
151C23—22no—
152C23—611no—
153Q8—1222no—
154Q8—1222no—
155D4—22no—
156D4—22no—
157D4—2442no—
158D4—2442no—
159C2×C4—611no—
160C2×C4—611no—
161C2×C4—611no—
162C2×C4—611no—
163C2×C4—611no—
164C2×C4—1222no—
165C2×C4—1222no—
166C2×C4—2442no—
167C2×C4—2442no—
168C2×C4—2442no—
169C2×C4C22×#692311yescharacteristic
170C8—611no—
171C8—611no—
172C8—1222no—
173C8C22⋊#692311yescharacteristic
174C8C22⋊#692311yescharacteristic
175C22—42no—
176C22—82no—
177C22—611no—
178C22—611no—
179C22—2441no—
180C22D4×#692311yescharacteristic
181C4—611no—
182C4—611no—
183C4—4882no—
184C4—2442no—
185C4—2442no—
186C4C2×C22⋊#692311yescharacteristic
187C4D4×#692311yescharacteristic
188C2—21no—
189C2—82no—
190C2—1221no—
191C2—1221no—
192C2#1684071411yescharacteristic
subgroupG/H
centerC2#16840714
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC2×D8×C61C4
socleC2×C61#390
hypercenterC2×D8#6923
hypocenterC61#1976
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #16840772C2semidirect
2. #16840760C2semidirect
3. #16840742C2semidirect
4. #16840725C2semidirect
20. C2×Dic244C4semidirect
21. C2×#11758200C4semidirect
23. C2×D8×C61C4semidirect
102. C61#1976semidirect
110. C2×D8#6923semidirect