Finite Group Databasebeta

← #21447528

Subgroups — #21447528

Order 7808.

232 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 69 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×#14519796C211yesmaximal, characteristic
2C2×#14519716C211yesmaximal, characteristic, complemented
3#107×D61C211yesmaximal, characteristic, complemented
4#16839567C211yesmaximal, characteristic, complemented
5#16839565C211yesmaximal, characteristic, complemented
6#16839563C211yesmaximal, characteristic, complemented
7C61×#357C211yesmaximal, characteristic, complemented
8C2×#11758224—21no—
9#14519796—22no—
10#14519796C414yescomplemented
11C2×Dic244C2211yescharacteristic
12C2×#11758200—21no—
13C2×C8×D61C2211yescharacteristic
14C4⋊C4×D61—21no—
15#14519716—22no—
16C2×#11758185C2211yescharacteristic
17#14519711C2211yescharacteristic
18#14519710—21no—
19C2×D8×C61C2211yescharacteristic
20C2×C16×C61C2211yescharacteristic
21#107×C61C2211yescharacteristic
22C2×D4×C61—21no—
23C2×C22⋊D61—41no—
24C22×Dic61—41no—
25#11758224—24no—
26#11758224—42no—
27C2×C4×D61—41no—
28C2×C4×D61D411yescharacteristic
29C2×Dic122—21no—
30D8×C61—21no—
31D8×C61C2×C412yescomplemented
32C2×C8×C61C2311yescharacteristic
33C4⋊C4×C61—21no—
34#11758200—24no—
35C4⋊Dic61—21no—
36#11758196—41no—
37C2×#92418D411yescharacteristic
38Dic244—21no—
39Dic244C2×C412yescomplemented
40C8×D61C2×C412yes—
41C8×D61D412yes—
42C16×C61—21no—
43#11758185—21no—
44C23×C61—41no—
45C22×D61D811yescharacteristic
46D4×C61—22no—
47D4×C61—41no—
48C2×C4×C61—41no—
49C2×C4×C61C2×D411yescharacteristic
50C22⋊D61—44no—
51C2×Dic61—41no—
52C2×Dic61—44no—
53C2×Dic61—41no—
54C2×Dic61D811yescharacteristic
55C4×D61—82no—
56C4×D61C22⋊C412yes—
57C4×D61SD1612yes—
58Dic122—22no—
59Dic122—41no—
60C8×C61C22×C411yescharacteristic
61C8×C61C2×D411yescharacteristic
62#92418C22⋊C412yes—
63C22×C61—42no—
64C22×C61—81no—
65C22×C61—81no—
66C22×C61C2×D811yescharacteristic
67C2×D61—21no—
68C2×D61—21no—
69C2×D61#10212yes—
70C4×C61—81no—
71C4×C61C2×C22⋊C411yescharacteristic
72C4×C61C2×SD1611yescharacteristic
73Dic61—42no—
74Dic61—81no—
75Dic61#10212yes—
76#2139—611nomaximal, Sylow
77C2×C61—82no—
78C2×C61C2×#10211yescharacteristic
79C2×C61#50911yescharacteristic
80C2×C61#51011yescharacteristic
81D61—22no—
82C2×#135—611no—
83C2×M32—611no—
84C2×#107—611no—
85#358—611no—
86#358—611no—
87#357—611no—
88#357D6111yescharacteristic, complemented
89C61#213911yescharacteristic, complemented, Sylow
90C2×#41—1221no—
91#135—614no—
92#135—1222no—
93C2×Q16—611no—
94C2×SD16—1221no—
95C2×D8C2×D6111yescharacteristic
96C22×C8—611no—
97C2×C4⋊C4—1221no—
98M32—1222no—
99C2×C16—611no—
100C2×C16C2×D6111yescharacteristic
101#107—611no—
102#107—1221no—
103#107C2×D6111yescharacteristic
104#41—1224no—
105#41—2442no—
106C2×Q8—1221no—
107C2×D4—21no—
108C2×D4—2441no—
109C22×C4—611no—
110C22×C4—2441no—
111C22×C4—2441no—
112Q16—612no—
113Q16—1221no—
114SD16—1224no—
115D8—21no—
116D8C4×D6112yescomplemented
117C2×C8—611no—
118C2×C8—612no—
119C2×C8—612no—
120C2×C8C22×D6111yescharacteristic
121C4⋊C4—21no—
122C4⋊C4—1221no—
123C4⋊C4—2441no—
124C16—21no—
125C16—1221no—
126C23—41no—
127C23—611no—
128Q8—1222no—
129Q8—2441no—
130D4—22no—
131D4—41no—
132D4—2444no—
133C2×C4—41no—
134C2×C4—611no—
135C2×C4—612no—
136C2×C4—612no—
137C2×C4—4882no—
138C2×C4—2444no—
139C2×C4—2441no—
140C2×C4—2441no—
141C2×C4D4×D6111yescharacteristic
142C8—612no—
143C8C2×C4×D6111yescharacteristic
144C8D4×D6111yescharacteristic
145C22—42no—
146C22—81no—
147C22—81no—
148C22—612no—
149C22—1221no—
150C22—1221no—
151C22D8×D6111yescharacteristic
152C4—81no—
153C4—612no—
154C4—4881no—
155C4—2442no—
156C4C22⋊C4×D6111yescharacteristic
157C4SD16×D6111yescharacteristic
158C2—82no—
159C2—1222no—
160C2#102×D6111yescharacteristic
161C2#1684019611yescharacteristic
162C2#1684020111yescharacteristic
subgroupG/H
centerC22D8×D61
commutatorC8×C61C22×C4
FrattiniC2×C8C22×D61
FittingC61×#357C2
socleC22×C61C2×D8
hypercenter#357D61
hypocenterC61#2139
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #357

Complements

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

NH ≅ G/Ntype
2. C2×#14519716C2semidirect
3. #107×D61C2semidirect
4. #16839567C2semidirect
5. #16839565C2semidirect
6. #16839563C2semidirect
7. C61×#357C2semidirect
10. #14519796C4semidirect
31. D8×C61C2×C4semidirect
39. Dic244C2×C4semidirect
88. #357D61semidirect
89. C61#2139semidirect
116. D8C4×D61semidirect