Finite Group Databasebeta

← #21446992

Subgroups — #21446992

Order 7808.

244 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 63 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#16840319C211yesmaximal, characteristic, complemented
2#16839778C211yesmaximal, characteristic
3C2×#14519705C211yesmaximal, characteristic
4#16839735C211yesmaximal, characteristic
5#16839533C211yesmaximal, characteristic, complemented
6#16839518C211yesmaximal, characteristic, complemented
7C61×#339C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C2×#11758194C2211yescharacteristic
10#14519777—21no—
11#14519769—21no—
12#14519756—22no—
13C4×Dic122—22no—
14#14519736C2211yescharacteristic
15#14519736C2211yescharacteristic
16#14519705—21no—
17#14519705—21no—
18#14519703—22no—
19#14519691—22no—
20C2×M16×C61C2211yescharacteristic
21#117×C61C2211yescharacteristic
22C2×C42×C61C2211yescharacteristic
23C22×C4×C61—21no—
24C22×C4×C61C2311yescharacteristic
25C2×C22⋊D61—21no—
26#11758222—21no—
27#11758222—21no—
28#11758222—21no—
29#11758222—21no—
30C2×D244Q811yescharacteristic, complemented
31C2×C4×D61—21no—
32C2×Dic122—22no—
33C2×Dic122Q811yescharacteristic, complemented
34M16×C61—21no—
35M16×C61—21no—
36C2×C8×C61—21no—
37C4⋊C4×C61—21no—
38C22⋊C4×C61—21no—
39C42×C61—21no—
40C42×C61—21no—
41C42×C61D411yescharacteristic
42C42×C61D411yescharacteristic
43C22⋊Dic61—21no—
44C22⋊Dic61D412yes—
45C4⋊Dic61—22no—
46C4⋊Dic61—21no—
47C4⋊Dic61—21no—
48#11758196—24no—
49C4×Dic61—21no—
50C4×Dic61D412yes—
51#11758194—21no—
52#11758194—21no—
53C2×#92418—21no—
54C23×C61C2×D411yescharacteristic
55C22×D61—21no—
56C2×C4×C61—21no—
57C2×C4×C61—21no—
58C2×C4×C61—42no—
59C2×C4×C61—41no—
60C2×C4×C61C2×D411yescharacteristic
61C2×C4×C61C2×D411yescharacteristic
62C2×C4×C61C2×Q811yescharacteristic
63C2×C4×C61#4111yescharacteristic
64C2×C4×C61#4111yescharacteristic
65C2×C4×C61#4111yescharacteristic
66C22⋊D61—41no—
67C22⋊D61—41no—
68C2×Dic61—22no—
69C2×Dic61—22no—
70C2×Dic61—21no—
71D244—21no—
72D244—21no—
73C4×D61—41no—
74C4×D61—41no—
75Dic122—21no—
76Dic122—21no—
77Dic122—44no—
78C8×C61—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—81no—
89C4×C61C22⋊Q811yescharacteristic
90C4×C61C22⋊Q811yescharacteristic
91C4×C61#12411yescharacteristic
92C4×C61#12411yescharacteristic
93Dic61—42no—
94Dic61—42no—
95Dic61—41no—
96#2031—611nomaximal, Sylow
97C2×C61—21no—
98C2×C61—21no—
99C2×C61—21no—
100C2×C61#39311yescharacteristic
101D61—81no—
102#533—611no—
103#421—611no—
104C2×#104—611no—
105#410—611no—
106#344—611no—
107#339D6111yescharacteristic, complemented
108H(3,ℤ/4)—611no—
109C61#203111yescharacteristic, complemented, Sylow
110C2×#41—611no—
111C2×M16—611no—
112C2×M16C2×D6111yescharacteristic
113C4⋊Q8—1221no—
114#125—1221no—
115C22⋊Q8—1222no—
116C4×Q8—1222no—
117#117—611no—
118#117—611no—
119#117C2×D6111yescharacteristic
120C2×C42C2×D6111yescharacteristic
121#104—1222no—
122#104—1221no—
123#104—1221no—
124#99—1222no—
125#41—1221no—
126#41—1221no—
127#41—1221no—
128#41—1221no—
129C2×Q8—611no—
130C2×Q8—1222no—
131C2×D4—611no—
132C2×D4—1221no—
133C22×C4—21no—
134C22×C4—1221no—
135C22×C4C22×D6111yescharacteristic
136M16—21no—
137M16—21no—
138M16—1221no—
139M16—1221no—
140C2×C8—21no—
141C2×C8—1221no—
142C4⋊C4—21no—
143C4⋊C4—1224no—
144C4⋊C4—1222no—
145C4⋊C4—1221no—
146C4⋊C4—1221no—
147C22⋊C4—21no—
148C22⋊C4—612no—
149C22⋊C4—1221no—
150C42—21no—
151C42—21no—
152C42—612no—
153C42—1221no—
154C42D24411yescharacteristic
155C42D24411yescharacteristic
156C23—1221no—
157C23D4×D6111yescharacteristic
158Q8—1221no—
159Q8—1221no—
160Q8—2444no—
161D4—1221no—
162D4—1221no—
163D4—2441no—
164D4—2441no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—42no—
168C2×C4—41no—
169C2×C4—1222no—
170C2×C4—1222no—
171C2×C4—1221no—
172C2×C4—2441no—
173C2×C4—2441no—
174C2×C4C2×D24411yescharacteristic
175C2×C4#1175822211yescharacteristic
176C2×C4#1175822211yescharacteristic
177C2×C4D4×D6111yescharacteristic
178C2×C4#1175822411yescharacteristic
179C2×C4Q8×D6111yescharacteristic
180C8—41no—
181C8—2441no—
182C22—41no—
183C22—4881no—
184C22—2441no—
185C22#1451974711yescharacteristic
186C22#1451975511yescharacteristic
187C22#1451976311yescharacteristic
188C4—22no—
189C4—41no—
190C4—81no—
191C4—2442no—
192C4—2442no—
193C4—2441no—
194C4#1451975511yescharacteristic
195C4#1451975711yescharacteristic
196C4#1451976311yescharacteristic
197C4#1451976511yescharacteristic
198C2—21no—
199C2—21no—
200C2—21no—
201C2—4881no—
202C2#1683967511yescharacteristic
subgroupG/H
centerC4#14519763
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#339C2
socleC2×C61#393
hypercenter#339D61
hypocenterC61#2031
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. #16840319C2semidirect
5. #16839533C2semidirect
6. #16839518C2semidirect
7. C61×#339C2semidirect
30. C2×D244Q8semidirect
33. C2×Dic122Q8semidirect
107. #339D61semidirect
109. C61#2031semidirect