Finite Group Databasebeta

← #21456770

Subgroups — #21456770

Order 7808.

394 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 117 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#16840317C211yesmaximal, characteristic, complemented
2#16840310C211yesmaximal, characteristic
3#16840141C211yesmaximal, characteristic, complemented
4#16840113C211yesmaximal, characteristic, complemented
5#16840108C211yesmaximal, characteristic, complemented
6#16839982C214yesmaximal, complemented
7#16839921C214yesmaximal, complemented
8#16839813C211yesmaximal, characteristic, complemented
9C61×#492C211yesmaximal, characteristic, complemented
10C2×#11758224C2212yes—
11C2×#11758202C2214yes—
12#14519777C2211yescharacteristic
13#14519777C2211yescharacteristic
14#14519768—21no—
15#14519764C2212yes—
16#14519757—21no—
17#14519753C2212yes—
18#14519748—21no—
19#14519748—21no—
20Q8×Dic61C2212yes—
21#14519742—21no—
22D4×Dic61—21no—
23D4×Dic61—21no—
24#14519735—21no—
25C42×D61C2211yescharacteristic
26#14519706C2212yes—
27#14519702C2214yes—
28#14519698C2214yes—
29#14519689C2212yes—
30C4×#92418C2211yescharacteristic
31C2×SD16×C61C2214yes—
32C4⋊Q8×C61C2211yescharacteristic
33#127×C61C2211yescharacteristic
34C4×C8×C61C2211yescharacteristic
35C2×Q8×C61C2312yes—
36C2×D4×C61—21no—
37C2×D4×C61—21no—
38C2×D4×C61C2312yes—
39C2×C22⋊D61—22no—
40C22×Dic61—22no—
41#11758224—44no—
42C2×C4×D61D411yescharacteristic
43C2×C4×D61D411yescharacteristic
44C2×C4×D61C2311yescharacteristic
45C2×Dic122—21no—
46C2×Dic122C2312yes—
47SD16×C61—44no—
48C2×C8×C61C2312yes—
49C4⋊C4×C61—21no—
50C4⋊C4×C61—21no—
51C42×C61C2311yescharacteristic
52C22⋊Dic61—22no—
53C22⋊Dic61—22no—
54#11758202—44no—
55#11758198—22no—
56C4⋊Dic61—21no—
57C4⋊Dic61—21no—
58C4⋊Dic61—21no—
59C4⋊Dic61—22no—
60C4⋊Dic61C2312yes—
61#11758196—22no—
62C4×Dic61—22no—
63C4×Dic61D411yescharacteristic
64C4×Dic61D411yescharacteristic
65C4×Dic61C2311yescharacteristic
66C2×#92418C2312yes—
67C23×C61—22no—
68C22×D61C2×D411yescharacteristic
69Q8×C61—24no—
70D4×C61—24no—
71D4×C61—42no—
72D4×C61—42no—
73C2×C4×C61—22no—
74C2×C4×C61C2×D411yescharacteristic
75C2×C4×C61C2×D411yescharacteristic
76C2×C4×C61C2411yescharacteristic
77C22⋊D61—44no—
78C2×Dic61—22no—
79C2×Dic61—22no—
80C2×Dic61—44no—
81C2×Dic61C2×D411yescharacteristic
82C2×Dic61C2×D411yescharacteristic
83C2×Dic61C2×D411yescharacteristic
84C4×D61—22no—
85C4×D61—22no—
86C4×D61—22no—
87Dic122—24no—
88Dic122—42no—
89C8×C61—22no—
90#92418—22no—
91C22×C61—42no—
92C22×C61—42no—
93C22×C61—42no—
94C22×C61C22×D411yescharacteristic
95C2×D61—21no—
96C2×D61—21no—
97C2×D61—21no—
98C4×C61—42no—
99C4×C61#13512yes—
100C4×C61#13712yes—
101C4×C61H(5,𝔽2)12yes—
102Dic61—21no—
103Dic61—21no—
104Dic61—21no—
105Dic61—42no—
106Dic61—42no—
107#3210—611nomaximal, Sylow
108C2×C61—82no—
109C2×C61#53511yescharacteristic
110C2×C61C2×#13511yescharacteristic
111C2×C61C2×#13711yescharacteristic
112D61—41no—
113#533—611no—
114#532—611no—
115#494—611no—
116#492D6111yescharacteristic, complemented
117#487—611no—
118#486—611no—
119#464—614no—
120#452—614no—
121#431—611no—
122C61#321011yescharacteristic, complemented, Sylow
123C2×#41—612no—
124C2×Q16—614no—
125C2×SD16C2×D6114yes—
126C4⋊Q8—611no—
127C4⋊Q8—611no—
128C4⋊Q8C2×D6111yescharacteristic
129#127C2×D6111yescharacteristic
130#125—1221no—
131#124—612no—
132C22⋊Q8—612no—
133C22⋊Q8—1221no—
134#121—1221no—
135#121—1221no—
136C4×Q8—612no—
137C4×Q8—1221no—
138C4×D4—1221no—
139C4×D4—1221no—
140#117—1221no—
141C2×C42—611no—
142C4⋊C8—612no—
143#103—614no—
144#102—614no—
145C22⋊C8—612no—
146C4×C8—611no—
147C4×C8C2×D6111yescharacteristic
148#41—2444no—
149C2×Q8—612no—
150C2×Q8—1221no—
151C2×Q8C22×D6112yes—
152C2×D4—21no—
153C2×D4—21no—
154C2×D4—1222no—
155C2×D4C22×D6112yes—
156C22×C4—611no—
157C22×C4—611no—
158C22×C4—611no—
159C22×C4—1222no—
160Q16—2444no—
161SD16—44no—
162C2×C8—612no—
163C2×C8C22×D6112yes—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—612no—
167C4⋊C4—1222no—
168C4⋊C4—1222no—
169C4⋊C4—1221no—
170C4⋊C4—1221no—
171C4⋊C4—1221no—
172C22⋊C4—1222no—
173C22⋊C4—1222no—
174C22⋊C4—1222no—
175C42—611no—
176C42—611no—
177C42—611no—
178C42—1222no—
179C42C22×D6111yescharacteristic
180C23—22no—
181C23—611no—
182Q8—24no—
183Q8—1224no—
184Q8—2442no—
185D4—24no—
186D4—42no—
187D4—42no—
188D4—2444no—
189C2×C4—22no—
190C2×C4—611no—
191C2×C4—611no—
192C2×C4—611no—
193C2×C4—1222no—
194C2×C4—1222no—
195C2×C4—1222no—
196C2×C4—1222no—
197C2×C4—1222no—
198C2×C4—2444no—
199C2×C4D4×D6111yescharacteristic
200C2×C4D4×D6111yescharacteristic
201C2×C4C23×D6111yescharacteristic
202C8—22no—
203C8—1222no—
204C22—42no—
205C22—42no—
206C22—42no—
207C22—1221no—
208C22—1221no—
209C22—1221no—
210C22C2×D4×D6111yescharacteristic
211C4—42no—
212C4—1221no—
213C4—1221no—
214C4—1221no—
215C4—2442no—
216C4—2442no—
217C4#1451979812yes—
218C4#1451980612yes—
219C4#1451982212yes—
220C2—82no—
221C2—2441no—
222C2#1684032511yescharacteristic
223C2C2×#1451979811yescharacteristic
224C2C2×#1451980611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#492C2
socleC22×C61C22×D4
hypercenter#492D61
hypocenterC61#3210
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #16840317C2semidirect
3. #16840141C2semidirect
4. #16840113C2semidirect
5. #16840108C2semidirect
6. #16839982C2semidirect
7. #16839921C2semidirect
8. #16839813C2semidirect
9. C61×#492C2semidirect
116. #492D61semidirect
122. C61#3210semidirect