Finite Group Databasebeta

← #21446978

Subgroups — #21446978

Order 7808.

246 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 69 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#16840390C211yesmaximal, characteristic
2#16839771C211yesmaximal, characteristic
3#16839669C211yesmaximal, characteristic
4#16839530C211yesmaximal, characteristic
5#16839523C211yesmaximal, characteristic
6#16839521C211yesmaximal, characteristic
7C61×#419C211yesmaximal, characteristic
8C2×#11758194C2211yescharacteristic
9#14519777—21no—
10#14519776—21no—
11#14519769—21no—
12#14519768—21no—
13#14519754—22no—
14#14519736C2211yescharacteristic
15C2×C4⋊Dic61C2211yescharacteristic
16C2×C4×Dic61C2211yescharacteristic
17#14519701—21no—
18#14519701—21no—
19#14519684—22no—
20C22×Q8×C61C2211yescharacteristic
21C2×M16×C61C2211yescharacteristic
22#117×C61C2211yescharacteristic
23#103×C61—21no—
24#103×C61—21no—
25C2×Q8×C61—21no—
26C2×Q8×C61—21no—
27C2×Q8×C61—21no—
28C2×Q8×C61—21no—
29C2×Q8×C61—21no—
30C2×Q8×C61Q812yescomplemented
31C22×C4×C61—21no—
32C22×C4×C61C2311yescharacteristic
33C22×Dic61—21no—
34C22×Dic61D412yes—
35C2×Dic122—22no—
36M16×C61—21no—
37M16×C61—21no—
38C2×C8×C61—21no—
39C4⋊C4×C61D411yescharacteristic
40C4⋊C4×C61D411yescharacteristic
41C22⋊C4×C61—21no—
42C42×C61—21no—
43C22⋊Dic61—21no—
44C4⋊Dic61—22no—
45C4⋊Dic61—21no—
46C4⋊Dic61—21no—
47C4⋊Dic61D411yescharacteristic
48C4⋊Dic61D411yescharacteristic
49#11758196—22no—
50#11758196—22no—
51C4×Dic61—21no—
52C4×Dic61—21no—
53C4×Dic61—21no—
54#11758194—21no—
55#11758194—21no—
56C2×#92418—21no—
57C23×C61C2×D411yescharacteristic
58Q8×C61—22no—
59Q8×C61—22no—
60Q8×C61—41no—
61Q8×C61—41no—
62C2×C4×C61—21no—
63C2×C4×C61—21no—
64C2×C4×C61—22no—
65C2×C4×C61—41no—
66C2×C4×C61—41no—
67C2×C4×C61C2×D411yescharacteristic
68C2×C4×C61C2×D411yescharacteristic
69C2×C4×C61C2×Q811yescharacteristic
70C2×C4×C61#4111yescharacteristic
71C2×C4×C61#4111yescharacteristic
72C2×C4×C61#4111yescharacteristic
73C2×Dic61—22no—
74C2×Dic61—21no—
75C2×Dic61—21no—
76C2×Dic61—22no—
77C2×Dic61—41no—
78C2×Dic61—41no—
79C2×Dic61—42no—
80Dic122—82no—
81C8×C61—41no—
82#92418—41no—
83C22×C61—21no—
84C22×C61—21no—
85C22×C61#12011yescharacteristic
86C22×C61C22⋊Q811yescharacteristic
87C22×C61#12411yescharacteristic
88C4×C61—42no—
89C4×C61—41no—
90C4×C61—41no—
91C4×C61C22⋊Q811yescharacteristic
92C4×C61C22⋊Q811yescharacteristic
93C4×C61#12411yescharacteristic
94C4×C61#12411yescharacteristic
95Dic61—42no—
96Dic61—41no—
97Dic61—42no—
98Dic61—41no—
99#2028—611nomaximal, Sylow
100C2×C61—21no—
101C2×C61—21no—
102C2×C61#39311yescharacteristic
103C2×C61#45511yescharacteristic
104C2×C61#45611yescharacteristic
105#544—611no—
106#419—611no—
107#419D6111yescharacteristic
108#391—611no—
109#343—611no—
110#339—611no—
111#339—611no—
112C61#202811yescharacteristic, complemented, Sylow
113C22×Q8C2×D6111yescharacteristic
114C2×M16—611no—
115C2×M16C2×D6111yescharacteristic
116C4⋊Q8—1221no—
117C4⋊Q8—1221no—
118#125—1221no—
119#125—1221no—
120C22⋊Q8—1222no—
121#117—611no—
122#117C2×D6111yescharacteristic
123C2×C4⋊C4—611no—
124C2×C42—611no—
125#103—21no—
126#103—21no—
127#103—1221no—
128#103—1221no—
129#95—1222no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—1222no—
136C2×Q8Dic12212yescomplemented
137C22×C4—21no—
138C22×C4—612no—
139C22×C4—1221no—
140C22×C4C22×D6111yescharacteristic
141M16—21no—
142M16—21no—
143M16—1221no—
144M16—1221no—
145C2×C8—21no—
146C2×C8—1221no—
147C4⋊C4—611no—
148C4⋊C4—611no—
149C4⋊C4—1222no—
150C4⋊C4—1222no—
151C4⋊C4—1222no—
152C4⋊C4—1221no—
153C4⋊C4—1221no—
154C4⋊C4C22⋊D6111yescharacteristic
155C4⋊C4C22⋊D6111yescharacteristic
156C22⋊C4—21no—
157C22⋊C4—1221no—
158C42—21no—
159C42—1221no—
160C42—1221no—
161C42—1221no—
162C23D4×D6111yescharacteristic
163Q8—22no—
164Q8—22no—
165Q8—41no—
166Q8—41no—
167Q8—4882no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—22no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—1222no—
174C2×C4—1221no—
175C2×C4—1221no—
176C2×C4—1222no—
177C2×C4—2441no—
178C2×C4—2441no—
179C2×C4—2442no—
180C2×C4C2×Dic12211yescharacteristic
181C2×C4#1175822211yescharacteristic
182C2×C4D4×D6111yescharacteristic
183C2×C4#1175822411yescharacteristic
184C2×C4#1175822411yescharacteristic
185C2×C4C2×C22⋊D6111yescharacteristic
186C8—41no—
187C8—2441no—
188C22—21no—
189C22—21no—
190C22#1451974511yescharacteristic
191C22#1451975411yescharacteristic
192C22#1451976311yescharacteristic
193C4—41no—
194C4—41no—
195C4—42no—
196C4—2442no—
197C4—2442no—
198C4—2441no—
199C4—2441no—
200C4#1451975411yescharacteristic
201C4#1451975611yescharacteristic
202C4#1451976311yescharacteristic
203C4#1451976411yescharacteristic
204C2—21no—
205C2—21no—
206C2#1683967411yescharacteristic
207C2#1683993811yescharacteristic
208C2#1683994311yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#419C2
socleC22×C61#120
hypercenter#419D61
hypocenterC61#2028
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
30. C2×Q8×C61Q8semidirect
112. C61#2028semidirect
136. C2×Q8Dic122semidirect