Finite Group Databasebeta

← #21446052

Subgroups — #21446052

Order 7808.

286 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 93 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#16839805C211yesmaximal, characteristic, complemented
2C2×#14519704C211yesmaximal, characteristic
3#16839763C211yesmaximal, characteristic
4#16839627C211yesmaximal, characteristic, complemented
5#16839531C211yesmaximal, characteristic, complemented
6#16839521C211yesmaximal, characteristic, complemented
7C61×#520C211yesmaximal, characteristic
8C2×#11758194C2211yescharacteristic
9C2×#11758194C2211yescharacteristic
10C2×C4⋊Dic61C2211yescharacteristic
11C2×C4×Dic61C2211yescharacteristic
12#14519710—21no—
13#14519708—21no—
14#14519704C414yescomplemented
15#14519701—21no—
16#14519698—21no—
17#14519684—22no—
18C2×#41×C61C2211yescharacteristic
19C4×Q8×C61—21no—
20C4×D4×C61—21no—
21C4×D4×C61—22no—
22#117×C61—21no—
23#117×C61C2211yescharacteristic
24C2×C4⋊C4×C61—21no—
25C2×C4⋊C4×C61C2211yescharacteristic
26#41×C61—21no—
27#41×C61—21no—
28#41×C61C2×C412yes—
29#41×C61Q812yes—
30C2×Q8×C61D411yescharacteristic
31C2×D4×C61—21no—
32C2×D4×C61D411yescharacteristic
33C22×C4×C61—21no—
34C22×C4×C61—22no—
35C22×C4×C61D412yes—
36C22×C4×C61C2311yescharacteristic
37C22×Dic61—21no—
38C22×Dic61—21no—
39C4⋊C4×C61—22no—
40C4⋊C4×C61—21no—
41C4⋊C4×C61—21no—
42C4⋊C4×C61D411yescharacteristic
43C4⋊C4×C61D411yescharacteristic
44C22⋊C4×C61—22no—
45C22⋊C4×C61—21no—
46C42×C61—22no—
47C42×C61—21no—
48C4⋊Dic61—21no—
49C4⋊Dic61—21no—
50C4×Dic61—21no—
51C4×Dic61C2×C412yescomplemented
52#11758194—21no—
53#11758194—21no—
54#11758194—21no—
55#11758194C2×C412yescomplemented
56C2×#92418—21no—
57C2×#92418—21no—
58C23×C61—21no—
59C23×C61C2×D411yescharacteristic
60Q8×C61—21no—
61Q8×C61C4⋊C412yes—
62D4×C61—22no—
63D4×C61—22no—
64D4×C61—21no—
65D4×C61C4⋊C412yes—
66C2×C4×C61—21no—
67C2×C4×C61—22no—
68C2×C4×C61—22no—
69C2×C4×C61—21no—
70C2×C4×C61—22no—
71C2×C4×C61—21no—
72C2×C4×C61—42no—
73C2×C4×C61—82no—
74C2×C4×C61C22×C411yescharacteristic
75C2×C4×C61C2×D411yescharacteristic
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61C2×Q811yescharacteristic
78C2×C4×C61#4111yescharacteristic
79C2×C4×C61#4111yescharacteristic
80C2×Dic61—22no—
81C2×Dic61—41no—
82C2×Dic61—41no—
83C2×Dic61—42no—
84C2×Dic61—41no—
85#92418—22no—
86#92418—41no—
87C22×C61—21no—
88C22×C61—21no—
89C22×C61—22no—
90C22×C61—41no—
91C22×C61—41no—
92C22×C61C4×D411yescharacteristic
93C22×C61#12011yescharacteristic
94C22×C61C22⋊Q811yescharacteristic
95C4×C61—22no—
96C4×C61—41no—
97C4×C61—42no—
98C4×C61—41no—
99C4×C61C2×C4⋊C411yescharacteristic
100C4×C61C4×D411yescharacteristic
101C4×C61C22⋊Q811yescharacteristic
102C4×C61#12311yescharacteristic
103Dic61—42no—
104Dic61—81no—
105#1860—611nomaximal, Sylow
106C2×C61—21no—
107C2×C61—21no—
108C2×C61—42no—
109C2×C61#38511yescharacteristic
110C2×C61#45411yescharacteristic
111C2×C61#45511yescharacteristic
112#520D6111yescharacteristic
113#428—611no—
114C2×#104—611no—
115#417—611no—
116#382—611no—
117#343—611no—
118#339—611no—
119C61#186011yescharacteristic, complemented, Sylow
120C2×#41C2×D6111yescharacteristic
121C2×M16—611no—
122C2×M16—611no—
123C4×Q8—21no—
124C4×D4—21no—
125C4×D4—22no—
126#117—21no—
127#117C2×D6111yescharacteristic
128C2×C4⋊C4—21no—
129C2×C4⋊C4—611no—
130C2×C4⋊C4C2×D6111yescharacteristic
131C2×C42—611no—
132#107—1221no—
133#106—1221no—
134#104—614no—
135#103—1221no—
136#102—1221no—
137#95—1222no—
138#41—21no—
139#41—21no—
140#41Dic12212yes—
141#41C4×D6112yes—
142C2×Q8C22⋊D6111yescharacteristic
143C2×D4—21no—
144C2×D4C22⋊D6111yescharacteristic
145C22×C4—21no—
146C22×C4—22no—
147C22×C4—1221no—
148C22×C4—1221no—
149C22×C4C22⋊D6112yes—
150C22×C4C22×D6111yescharacteristic
151M16—612no—
152M16—1221no—
153M16—1221no—
154M16—1221no—
155C2×C8—1221no—
156C2×C8—1221no—
157C4⋊C4—22no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—1221no—
161C4⋊C4—1221no—
162C4⋊C4C22⋊D6111yescharacteristic
163C4⋊C4C22⋊D6111yescharacteristic
164C22⋊C4—22no—
165C22⋊C4—21no—
166C42—22no—
167C42—21no—
168C42—612no—
169C42—1221no—
170C23—21no—
171C23C2×C22⋊D6111yescharacteristic
172Q8—21no—
173Q8#1175819612yes—
174D4—22no—
175D4—22no—
176D4—21no—
177D4#1175819612yes—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—42no—
185C2×C4—82no—
186C2×C4—1222no—
187C2×C4—2442no—
188C2×C4—2441no—
189C2×C4—2441no—
190C2×C4—2441no—
191C2×C4C2×Dic12211yescharacteristic
192C2×C4C2×C4×D6111yescharacteristic
193C2×C4#1175822211yescharacteristic
194C2×C4#1175822211yescharacteristic
195C2×C4C2×C22⋊D6111yescharacteristic
196C2×C4C2×C22⋊D6111yescharacteristic
197C8—1222no—
198C8—2441no—
199C22—21no—
200C22—21no—
201C22—22no—
202C22—41no—
203C22—41no—
204C22C4×C22⋊D6111yescharacteristic
205C22#1451974611yescharacteristic
206C22#1451975611yescharacteristic
207C4—22no—
208C4—42no—
209C4—41no—
210C4—41no—
211C4—4881no—
212C4—2442no—
213C4C2×#1175819611yescharacteristic
214C4C4×C22⋊D6111yescharacteristic
215C4#1451975611yescharacteristic
216C4#1451976011yescharacteristic
217C2—21no—
218C2—21no—
219C2—42no—
220C2#1683963511yescharacteristic
221C2#1683993511yescharacteristic
222C2#1683994011yescharacteristic
subgroupG/H
centerC22#14519746
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#520C2
socleC22×C61#120
hypercenter#520D61
hypocenterC61#1860
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #16839805C2semidirect
4. #16839627C2semidirect
5. #16839531C2semidirect
6. #16839521C2semidirect
14. #14519704C4semidirect
51. C4×Dic61C2×C4semidirect
55. #11758194C2×C4semidirect
119. C61#1860semidirect