Finite Group Databasebeta

← #21446994

Subgroups — #21446994

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#16840315C211yesmaximal, characteristic, complemented
2#16839778C211yesmaximal, characteristic
3C2×#14519703C211yesmaximal, characteristic
4#16839735C211yesmaximal, characteristic
5#16839523C211yesmaximal, characteristic, complemented
6#16839519C211yesmaximal, characteristic, complemented
7C61×#344C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9#14519776—21no—
10#14519768—21no—
11#14519754—22no—
12C4×Dic122—22no—
13#14519736C2211yescharacteristic
14#14519736C2211yescharacteristic
15C2×C4×Dic61C2211yescharacteristic
16#14519703—21no—
17#14519703—21no—
18#14519703—22no—
19#14519691—22no—
20C2×M16×C61C2211yescharacteristic
21C2×M16×C61C2211yescharacteristic
22#117×C61C2211yescharacteristic
23C22×C4×C61C2311yescharacteristic
24C2×C22⋊D61—21no—
25C22×Dic61—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—
36M16×C61—21no—
37M16×C61—21no—
38C2×C8×C61—21no—
39C2×C8×C61—21no—
40C4⋊C4×C61—21no—
41C22⋊C4×C61D412yes—
42C42×C61—21no—
43C22⋊Dic61—21no—
44C22⋊Dic61—21no—
45C4⋊Dic61—22no—
46C4⋊Dic61—21no—
47C4⋊Dic61—21no—
48#11758196—22no—
49#11758196—22no—
50C4×Dic61—21no—
51C4×Dic61—21no—
52C4×Dic61D411yescharacteristic
53C4×Dic61D411yescharacteristic
54C4×Dic61D412yes—
55C23×C61C2×D411yescharacteristic
56C22×D61—21no—
57C2×C4×C61—22no—
58C2×C4×C61C2×D411yescharacteristic
59C2×C4×C61C2×D411yescharacteristic
60C2×C4×C61C2×Q811yescharacteristic
61C2×C4×C61#4111yescharacteristic
62C2×C4×C61#4111yescharacteristic
63C2×C4×C61#4111yescharacteristic
64C22⋊D61—41no—
65C22⋊D61—41no—
66C2×Dic61—21no—
67C2×Dic61—21no—
68C2×Dic61—22no—
69C2×Dic61—21no—
70C2×Dic61—42no—
71C2×Dic61—41no—
72D244—21no—
73D244—21no—
74C4×D61—41no—
75C4×D61—41no—
76Dic122—21no—
77Dic122—21no—
78Dic122—44no—
79C8×C61—41no—
80C8×C61—41no—
81C22×C61—41no—
82C22×C61#12011yescharacteristic
83C22×C61C22⋊Q811yescharacteristic
84C22×C61#12411yescharacteristic
85C2×D61—41no—
86C2×D61—81no—
87C4×C61—42no—
88C4×C61C22⋊Q811yescharacteristic
89C4×C61C22⋊Q811yescharacteristic
90C4×C61#12411yescharacteristic
91C4×C61#12411yescharacteristic
92Dic61—22no—
93Dic61—42no—
94Dic61—41no—
95Dic61—41no—
96Dic61—81no—
97#2031—611nomaximal, Sylow
98C2×C61—21no—
99C2×C61—21no—
100C2×C61—21no—
101C2×C61#39311yescharacteristic
102D61—81no—
103#533—611no—
104#421—611no—
105C2×#104—611no—
106#410—611no—
107#344D6111yescharacteristic, complemented
108#339—611no—
109H(3,ℤ/4)—611no—
110C61#203111yescharacteristic, complemented, Sylow
111C2×#41—611no—
112C2×M16C2×D6111yescharacteristic
113C2×M16C2×D6111yescharacteristic
114C4⋊Q8—1221no—
115#125—1221no—
116C22⋊Q8—1222no—
117C4×Q8—1222no—
118#117—611no—
119#117—611no—
120#117C2×D6111yescharacteristic
121C2×C42—611no—
122#104—1221no—
123#104—1221no—
124#104—1222no—
125#99—1222no—
126#41—1221no—
127#41—1221no—
128#41—1221no—
129#41—1221no—
130C2×Q8—611no—
131C2×Q8—1222no—
132C2×D4—611no—
133C2×D4—1221no—
134C22×C4—1221no—
135C22×C4—1221no—
136C22×C4C22×D6111yescharacteristic
137M16—21no—
138M16—21no—
139M16—21no—
140M16—21no—
141C2×C8—21no—
142C2×C8—21no—
143C4⋊C4—21no—
144C4⋊C4—1222no—
145C4⋊C4—1222no—
146C4⋊C4—1222no—
147C4⋊C4—1221no—
148C4⋊C4—1221no—
149C22⋊C4—1221no—
150C22⋊C4—1221no—
151C22⋊C4D24412yes—
152C42—21no—
153C42—611no—
154C42—611no—
155C42—612no—
156C42—1221no—
157C42—1221no—
158C23—1221no—
159C23C2×D24411yescharacteristic
160Q8—1221no—
161Q8—1221no—
162Q8—2444no—
163D4—1221no—
164D4—1221no—
165D4—2441no—
166D4—2441no—
167C2×C4—22no—
168C2×C4—1221no—
169C2×C4—1221no—
170C2×C4—1222no—
171C2×C4—1221no—
172C2×C4—2442no—
173C2×C4—2441no—
174C2×C4—2441no—
175C2×C4—2441no—
176C2×C4#1175822211yescharacteristic
177C2×C4#1175822211yescharacteristic
178C2×C4D4×D6111yescharacteristic
179C2×C4D4×D6111yescharacteristic
180C2×C4#1175822411yescharacteristic
181C2×C4Q8×D6111yescharacteristic
182C8—41no—
183C8—41no—
184C22—41no—
185C22—4881no—
186C22—2441no—
187C22#1451974711yescharacteristic
188C22#1451975711yescharacteristic
189C22#1451976511yescharacteristic
190C4—42no—
191C4—1222no—
192C4—4881no—
193C4—2441no—
194C4—2442no—
195C4—2441no—
196C4#1451975511yescharacteristic
197C4#1451975511yescharacteristic
198C4#1451976311yescharacteristic
199C4#1451976311yescharacteristic
200C2—21no—
201C2—21no—
202C2—21no—
203C2—4881no—
204C2#1683967511yescharacteristic
subgroupG/H
centerC4#14519763
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#344C2
socleC2×C61#393
hypercenter#344D61
hypocenterC61#2031
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
1. #16840315C2semidirect
5. #16839523C2semidirect
6. #16839519C2semidirect
7. C61×#344C2semidirect
30. C2×D244Q8semidirect
33. C2×Dic122Q8semidirect
107. #344D61semidirect
110. C61#2031semidirect