Finite Group Databasebeta

← #21444452

Subgroups — #21444452

Order 7808.

238 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 59 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#16840311C211yesmaximal, characteristic
2#16839817C212yesmaximal, complemented
3#16839502C211yesmaximal, characteristic, complemented
4#16839501C212yesmaximal, complemented
5C61×#329C211yesmaximal, characteristic, complemented
6C2×#11758226C411yescharacteristic
7C2×#11758224C411yescharacteristic
8#14519775C411yescharacteristic
9#14519773C411yescharacteristic
10#14519765C2211yescharacteristic
11#14519750—22no—
12#14519737—22no—
13C42×D61C2211yescharacteristic
14#14519706—22no—
15#14519689—22no—
16#14519688C2212yes—
17#124×C61C2211yescharacteristic
18#97×C61C2212yes—
19C2×Q8×C61C2×C411yescharacteristic
20C2×D4×C61C2×C411yescharacteristic
21C2×C22⋊D61—21no—
22C2×C22⋊D61—22no—
23C22×Dic61—21no—
24#11758226—42no—
25#11758224—42no—
26C2×D244—21no—
27C2×D244C2×C411yescharacteristic
28C2×C4×D61—21no—
29C2×C4×D61C2×C411yescharacteristic
30C2×C4×D61D412yes—
31C2×Dic122C2×C411yescharacteristic
32C2×C8×C61—22no—
33C22⋊C4×C61—22no—
34C42×C61C2311yescharacteristic
35#11758198—22no—
36#11758196—22no—
37C4×Dic61C2×C411yescharacteristic
38C4×Dic61D412yes—
39C2×#92418—22no—
40C23×C61—21no—
41C22×D61—21no—
42C22×D61C22⋊C411yescharacteristic
43Q8×C61—41no—
44D4×C61—41no—
45C2×C4×C61—21no—
46C2×C4×C61C22×C411yescharacteristic
47C2×C4×C61C2×D412yes—
48C22⋊D61—44no—
49C22⋊D61—42no—
50C2×Dic61—21no—
51C2×Dic61—42no—
52C2×Dic61C22⋊C412yes—
53C2×Dic61C22⋊C411yescharacteristic
54D244—41no—
55D244—42no—
56C4×D61—22no—
57C4×D61—42no—
58C4×D61—42no—
59Dic122—41no—
60C8×C61—42no—
61#92418—42no—
62C22×C61—41no—
63C22×C61—42no—
64C22×C61C2×C22⋊C411yescharacteristic
65C2×D61—21no—
66C2×D61—22no—
67C2×D61—41no—
68C2×D61—42no—
69C4×C61—21no—
70C4×C61—22no—
71C4×C61—41no—
72Dic61—22no—
73Dic61—41no—
74Dic61#10012yes—
75#1536—611nomaximal, Sylow
76C2×C61—81no—
77C2×C61C2×#10011yescharacteristic
78C2×C61#42112yes—
79D61—41no—
80D61—81no—
81#532—611no—
82#432—612no—
83#329—611no—
84#329—612no—
85#329D6111yescharacteristic, complemented
86C61#153611yescharacteristic, complemented, Sylow
87C2×#41—611no—
88C2×#41—611no—
89C4⋊Q8—611no—
90#127—611no—
91#124—611no—
92#124C2×D6111yescharacteristic
93#121—1222no—
94C4×D4—1222no—
95C2×C42—611no—
96C4⋊C8—1222no—
97C22⋊C8—1222no—
98#97—612no—
99#97C2×D6112yes—
100#41—2442no—
101#41—2442no—
102C2×Q8—611no—
103C2×Q8C4×D6111yescharacteristic
104C2×D4—611no—
105C2×D4—1221no—
106C2×D4—1222no—
107C2×D4—1221no—
108C2×D4C4×D6111yescharacteristic
109C22×C4—611no—
110C22×C4—612no—
111C22×C4—1221no—
112C22×C4—1221no—
113C2×C8—22no—
114C2×C8—1222no—
115C4⋊C4—1222no—
116C22⋊C4—22no—
117C22⋊C4—1222no—
118C42—611no—
119C42—612no—
120C42C22×D6111yescharacteristic
121C23—21no—
122C23—611no—
123C23—1221no—
124Q8—41no—
125Q8—2441no—
126D4—41no—
127D4—2441no—
128D4—2442no—
129D4—2444no—
130D4—2442no—
131C2×C4—21no—
132C2×C4—611no—
133C2×C4—612no—
134C2×C4—1222no—
135C2×C4—1221no—
136C2×C4—2442no—
137C2×C4—2442no—
138C2×C4—2442no—
139C2×C4C2×C4×D6111yescharacteristic
140C2×C4D4×D6112yes—
141C8—42no—
142C8—2442no—
143C22—41no—
144C22—42no—
145C22—1221no—
146C22—1222no—
147C22—2441no—
148C22—2442no—
149C22C22⋊C4×D6111yescharacteristic
150C4—21no—
151C4—22no—
152C4—41no—
153C4—612no—
154C4—1222no—
155C4—2441no—
156C2—81no—
157C2—4881no—
158C2—2441no—
159C2#100×D6111yescharacteristic
160C2#1683977712yes—
subgroupG/H
centerC22C22⋊C4×D61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#329C2
socleC22×C61C2×C22⋊C4
hypercenter#329D61
hypocenterC61#1536
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #16839817C2semidirect
3. #16839502C2semidirect
4. #16839501C2semidirect
5. C61×#329C2semidirect
85. #329D61semidirect
86. C61#1536semidirect