Finite Group Databasebeta

← #21446988

Subgroups — #21446988

Order 7808.

244 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 67 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#16839780C211yesmaximal, characteristic
2C2×#14519705C211yesmaximal, characteristic
3#16839735C211yesmaximal, characteristic
4#16839532C211yesmaximal, characteristic, complemented
5#16839522C211yesmaximal, characteristic, complemented
6#16839518C211yesmaximal, characteristic, complemented
7C61×#533C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C2×#11758194C2211yescharacteristic
10C2×#11758194C2211yescharacteristic
11#14519736C2211yescharacteristic
12#14519705—21no—
13#14519705—21no—
14#14519705—22no—
15#14519691—22no—
16C4⋊Q8×C61—21no—
17#125×C61—21no—
18C22⋊Q8×C61—22no—
19C4×Q8×C61—22no—
20#117×C61C2211yescharacteristic
21#117×C61C2211yescharacteristic
22C2×C42×C61C2211yescharacteristic
23C2×Q8×C61—22no—
24C22×C4×C61—21no—
25C22×C4×C61C2311yescharacteristic
26C2×C22⋊D61—21no—
27#11758222—21no—
28#11758222—21no—
29#11758222—21no—
30#11758222—21no—
31C2×D244Q811yescharacteristic, complemented
32C2×C4×D61—21no—
33C2×Dic122Q811yescharacteristic, complemented
34C4⋊C4×C61—24no—
35C4⋊C4×C61—22no—
36C4⋊C4×C61—21no—
37C4⋊C4×C61—21no—
38C22⋊C4×C61—21no—
39C22⋊C4×C61D412yes—
40C42×C61—21no—
41C42×C61—21no—
42C42×C61D411yescharacteristic
43C42×C61D411yescharacteristic
44C42×C61D412yes—
45C22⋊Dic61—21no—
46C4⋊Dic61—21no—
47C4×Dic61—21no—
48#11758194—21no—
49#11758194—21no—
50#11758194—21no—
51#11758194—21no—
52C2×#92418—21no—
53C2×#92418—21no—
54C23×C61C2×D411yescharacteristic
55C22×D61—21no—
56Q8×C61—44no—
57C2×C4×C61—21no—
58C2×C4×C61—21no—
59C2×C4×C61—22no—
60C2×C4×C61—22no—
61C2×C4×C61—42no—
62C2×C4×C61C2×D411yescharacteristic
63C2×C4×C61C2×D411yescharacteristic
64C2×C4×C61C2×Q811yescharacteristic
65C2×C4×C61#4111yescharacteristic
66C2×C4×C61#4111yescharacteristic
67C2×C4×C61#4111yescharacteristic
68C22⋊D61—41no—
69C22⋊D61—41no—
70C2×Dic61—21no—
71C2×Dic61—41no—
72D244—21no—
73D244—21no—
74C4×D61—41no—
75C4×D61—41no—
76Dic122—21no—
77Dic122—21no—
78#92418—41no—
79#92418—41no—
80C22×C61—41no—
81C22×C61#12011yescharacteristic
82C22×C61C22⋊Q811yescharacteristic
83C22×C61#12411yescharacteristic
84C2×D61—41no—
85C2×D61—81no—
86C4×C61—22no—
87C4×C61—41no—
88C4×C61—42no—
89C4×C61—42no—
90C4×C61C22⋊Q811yescharacteristic
91C4×C61C22⋊Q811yescharacteristic
92C4×C61#12411yescharacteristic
93C4×C61#12411yescharacteristic
94Dic61—41no—
95Dic61—81no—
96#2031—611nomaximal, Sylow
97C2×C61—21no—
98C2×C61—21no—
99C2×C61—21no—
100C2×C61#39311yescharacteristic
101D61—81no—
102#533D6111yescharacteristic, complemented
103#421—611no—
104C2×#104—611no—
105#410—611no—
106#344—611no—
107#339—611no—
108H(3,ℤ/4)—611no—
109C61#203111yescharacteristic, complemented, Sylow
110C2×#41—611no—
111C2×M16—611no—
112C2×M16—611no—
113C4⋊Q8—21no—
114#125—21no—
115C22⋊Q8—22no—
116C4×Q8—22no—
117#117—611no—
118#117C2×D6111yescharacteristic
119#117C2×D6111yescharacteristic
120C2×C42C2×D6111yescharacteristic
121#104—1221no—
122#104—1221no—
123#104—1222no—
124#99—1222no—
125#41—1221no—
126#41—1221no—
127#41—1221no—
128#41—1221no—
129C2×Q8—22no—
130C2×Q8—611no—
131C2×D4—611no—
132C2×D4—1221no—
133C22×C4—21no—
134C22×C4—1221no—
135C22×C4C22×D6111yescharacteristic
136M16—1221no—
137M16—1221no—
138M16—1221no—
139M16—1221no—
140C2×C8—1221no—
141C2×C8—1221no—
142C4⋊C4—24no—
143C4⋊C4—22no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—1221no—
147C22⋊C4—21no—
148C22⋊C4—1221no—
149C22⋊C4C22⋊D6112yes—
150C42—21no—
151C42—21no—
152C42—1221no—
153C42C22⋊D6111yescharacteristic
154C42C22⋊D6111yescharacteristic
155C42C22⋊D6112yes—
156C23—1221no—
157C23C2×C22⋊D6111yescharacteristic
158Q8—44no—
159Q8—1221no—
160Q8—1221no—
161D4—1221no—
162D4—1221no—
163D4—2441no—
164D4—2441no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—42no—
170C2×C4—1221no—
171C2×C4—2441no—
172C2×C4—2441no—
173C2×C4—2441no—
174C2×C4Q8×D6111yescharacteristic
175C2×C4#1175822611yescharacteristic
176C2×C4#1175822611yescharacteristic
177C2×C4#1175822611yescharacteristic
178C2×C4C2×C22⋊D6111yescharacteristic
179C2×C4C2×C22⋊D6111yescharacteristic
180C8—2441no—
181C8—2441no—
182C22—41no—
183C22—4881no—
184C22—2441no—
185C22#1451974611yescharacteristic
186C22#1451975311yescharacteristic
187C22#1451976611yescharacteristic
188C4—22no—
189C4—41no—
190C4—42no—
191C4—42no—
192C4—4881no—
193C4—2441no—
194C4#1451975311yescharacteristic
195C4#1451975311yescharacteristic
196C4#1451976611yescharacteristic
197C4#1451976611yescharacteristic
198C2—21no—
199C2—21no—
200C2—21no—
201C2—4881no—
202C2#1683967311yescharacteristic
subgroupG/H
centerC4#14519766
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#533C2
socleC2×C61#393
hypercenter#533D61
hypocenterC61#2031
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #533

Complements

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

NH ≅ G/Ntype
4. #16839532C2semidirect
5. #16839522C2semidirect
6. #16839518C2semidirect
7. C61×#533C2semidirect
31. C2×D244Q8semidirect
33. C2×Dic122Q8semidirect
102. #533D61semidirect
109. C61#2031semidirect