Finite Group Databasebeta

← #21456198

Subgroups — #21456198

Order 7808.

380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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#16840318C211yesmaximal, characteristic
2C4⋊Q8×D61C211yesmaximal, characteristic
3#16840132C211yesmaximal, characteristic, complemented
4#16840131C211yesmaximal, characteristic, complemented
5#16840130C211yesmaximal, characteristic, complemented
6#16840111C214yesmaximal, complemented
7#16839769C214yesmaximal
8#16839714C211yesmaximal, characteristic
9C61×#491C211yesmaximal, characteristic, complemented
10C2×Q8×D61C2212yes—
11C2×#11758189C2212yes—
12#14519777C2211yescharacteristic
13#14519776—22no—
14#14519776C2212yes—
15#14519775C2212yes—
16#14519769C2211yescharacteristic
17#14519755—22no—
18#14519742—22no—
19#14519735C2212yes—
20C4⋊C4×D61—22no—
21C42×D61C2211yescharacteristic
22#14519702C2214yes—
23#14519701C2214yes—
24#14519700C2214yes—
25#14519688C2211yescharacteristic
26C8×Dic61C2212yes—
27C4⋊Q8×C61C2211yescharacteristic
28#125×C61C2211yescharacteristic
29#103×C61C2214yes—
30#97×C61C2211yescharacteristic
31C2×Q8×C61C2312yes—
32Q8×D61—28no—
33C2×C4×D61—22no—
34C2×C4×D61D412yes—
35C2×C4×D61C2311yescharacteristic
36C2×Dic122—22no—
37C2×Dic122—22no—
38C2×Dic122C2312yes—
39C2×C8×C61C2312yes—
40C4⋊C4×C61—22no—
41C4⋊C4×C61—22no—
42C4⋊C4×C61C2312yes—
43C42×C61C2311yescharacteristic
44#11758198—22no—
45C4⋊Dic61—22no—
46C4⋊Dic61C2312yes—
47#11758196—22no—
48#11758196—24no—
49#11758196—22no—
50C4×Dic61—22no—
51C4×Dic61D412yes—
52C4×Dic61C2311yescharacteristic
53C2×#92418C2312yes—
54#11758189—24no—
55C22×D61C2×D411yescharacteristic
56Q8×C61—24no—
57C2×C4×C61—22no—
58C2×C4×C61—22no—
59C2×C4×C61C2×D412yes—
60C2×C4×C61C2411yescharacteristic
61C2×Dic61—22no—
62C2×Dic61—22no—
63C2×Dic61C2×D411yescharacteristic
64C2×Dic61C2×D412yes—
65C4×D61—24no—
66C4×D61—44no—
67C4×D61#4114yes—
68Dic122—24no—
69Dic122—44no—
70Dic122—44no—
71C8×C61—22no—
72#92418—22no—
73C22×C61C22×D411yescharacteristic
74C2×D61—22no—
75C2×D61#12412yes—
76C4×C61—22no—
77C4×C61—42no—
78C4×C61—42no—
79C4×C61C2×#4112yes—
80Dic61—42no—
81Dic61—42no—
82Dic61#12412yes—
83Dic61#13714yes—
84#3139—611nomaximal, Sylow
85C2×C61C2×#12411yescharacteristic
86C2×C61C2×#13712yes—
87D61—22no—
88#533—611no—
89C2×C4⋊Q8—611no—
90#491—611no—
91#491—611no—
92#491—611no—
93#491D6111yescharacteristic, complemented
94#487—614no—
95#419—614no—
96C4×M16—611no—
97C61#313911yescharacteristic, complemented, Sylow
98C22×Q8—612no—
99C2×M16—612no—
100C4⋊Q8—612no—
101C4⋊Q8—612no—
102C4⋊Q8—611no—
103C4⋊Q8—1222no—
104C4⋊Q8C2×D6111yescharacteristic
105#125—611no—
106#125C2×D6111yescharacteristic
107C22⋊Q8—1222no—
108C4×Q8—1222no—
109#117—612no—
110C2×C4⋊C4—1222no—
111C2×C42—611no—
112#103—614no—
113#103—614no—
114#103—614no—
115#103C2×D6114yes—
116#97—611no—
117#97C2×D6111yescharacteristic
118C4×C8—612no—
119C2×Q8—612no—
120C2×Q8—1222no—
121C2×Q8—1222no—
122C2×Q8—1228no—
123C2×Q8C22×D6112yes—
124C22×C4—611no—
125C22×C4—612no—
126C22×C4—1222no—
127M16—1224no—
128C2×C8—612no—
129C2×C8C22×D6112yes—
130C4⋊C4—22no—
131C4⋊C4—22no—
132C4⋊C4—612no—
133C4⋊C4—1224no—
134C4⋊C4—1222no—
135C4⋊C4—1222no—
136C4⋊C4—1222no—
137C4⋊C4C22×D6112yes—
138C22⋊C4—1222no—
139C42—612no—
140C42—611no—
141C42—1222no—
142C42C22×D6111yescharacteristic
143C23—611no—
144Q8—24no—
145Q8—1224no—
146Q8—2444no—
147Q8—2444no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—611no—
151C2×C4—612no—
152C2×C4—614no—
153C2×C4—1224no—
154C2×C4—1222no—
155C2×C4—1222no—
156C2×C4—2444no—
157C2×C4D4×D6112yes—
158C2×C4C23×D6111yescharacteristic
159C8—22no—
160C8—1222no—
161C22—612no—
162C22—1222no—
163C22C2×D4×D6111yescharacteristic
164C4—22no—
165C4—42no—
166C4—42no—
167C4—612no—
168C4—614no—
169C4—2442no—
170C4—2442no—
171C4#41×D6112yes—
172C2—1222no—
173C2#124×D6111yescharacteristic
174C2#137×D6112yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#491C2
socleC22×C61C22×D4
hypercenter#491D61
hypocenterC61#3139
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
3. #16840132C2semidirect
4. #16840131C2semidirect
5. #16840130C2semidirect
6. #16840111C2semidirect
9. C61×#491C2semidirect
93. #491D61semidirect
97. C61#3139semidirect