Finite Group Databasebeta

← #21456958

Subgroups — #21456958

Order 7808.

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

normal subgroups only

This group has 370 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#16840313C211yesmaximal, characteristic
3#16840158C211yesmaximal, characteristic, complemented
4#16840110C211yesmaximal, characteristic, complemented
5#16840109C211yesmaximal, characteristic, complemented
6#16840089C214yesmaximal, complemented
7#16840065C214yesmaximal, complemented
8#16839813C211yesmaximal, characteristic, complemented
9C61×#500C211yesmaximal, characteristic, complemented
10C2×#11758226—21no—
11#14519777C2211yescharacteristic
12#14519774C2211yescharacteristic
13#14519768C2212yes—
14#14519766—21no—
15#14519757—21no—
16#14519753—21no—
17#14519752—21no—
18#14519752C2212yes—
19Q8×Dic61—21no—
20#14519742—21no—
21#14519739—21no—
22#14519739C2212yes—
23#14519735C2212yes—
24C42×D61C2211yescharacteristic
25#14519708C2214yes—
26#14519706C2212yes—
27#14519699C2214yes—
28#14519697C2214yes—
29#14519689C2212yes—
30C4×#92418C2211yescharacteristic
31C4⋊Q8×C61C2211yescharacteristic
32C4⋊Q8×C61C2211yescharacteristic
33#107×C61C2214yes—
34C4×C8×C61C2211yescharacteristic
35C2×Q8×C61—21no—
36C2×Q8×C61—21no—
37#11758226—44no—
38C2×D244—22no—
39C2×D244—21no—
40C2×D244—21no—
41C2×D244C2312yes—
42C2×C4×D61—22no—
43C2×C4×D61D411yescharacteristic
44C2×C4×D61D411yescharacteristic
45C2×C4×D61C2311yescharacteristic
46C2×Dic122—21no—
47C2×C8×C61C2312yes—
48C4⋊C4×C61—21no—
49C4⋊C4×C61—21no—
50C4⋊C4×C61C2312yes—
51C4⋊C4×C61C2312yes—
52C42×C61C2311yescharacteristic
53#11758198—22no—
54#11758198—22no—
55#11758198—22no—
56C4⋊Dic61—21no—
57C4⋊Dic61—22no—
58C4⋊Dic61C2312yes—
59#11758196—22no—
60C4×Dic61—22no—
61C4×Dic61D411yescharacteristic
62C4×Dic61D411yescharacteristic
63C4×Dic61C2311yescharacteristic
64C2×#92418C2312yes—
65C22×D61—22no—
66C22×D61C2×D411yescharacteristic
67Q8×C61—42no—
68Q8×C61—42no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2411yescharacteristic
74C2×Dic61—22no—
75C2×Dic61C2×D411yescharacteristic
76C2×Dic61C2×D411yescharacteristic
77C2×Dic61C2×D411yescharacteristic
78D244—24no—
79D244—44no—
80D244—42no—
81D244—42no—
82C4×D61—22no—
83C4×D61—22no—
84C4×D61—22no—
85C4×D61—44no—
86Dic122—42no—
87C8×C61—22no—
88#92418—22no—
89C22×C61C22×D411yescharacteristic
90C2×D61—21no—
91C2×D61—21no—
92C2×D61—21no—
93C2×D61—42no—
94C2×D61—42no—
95C2×D61—42no—
96C4×C61—42no—
97C4×C61—42no—
98C4×C61#13512yes—
99C4×C61AGL(1,ℤ/8)12yes—
100C4×C612−1+412yes—
101Dic61—21no—
102Dic61—21no—
103Dic61—21no—
104Dic61—42no—
105#3228—611nomaximal, Sylow
106C2×C61#53611yescharacteristic
107C2×C61C2×#13511yescharacteristic
108C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
109D61—41no—
110D61—82no—
111#533—611no—
112#532—611no—
113#500D6111yescharacteristic, complemented
114#498—611no—
115#486—611no—
116#486—611no—
117#482—614no—
118#478—614no—
119#431—611no—
120C61#322811yescharacteristic, complemented, Sylow
121C2×#41—1221no—
122C4⋊Q8—611no—
123C4⋊Q8C2×D6111yescharacteristic
124C4⋊Q8C2×D6111yescharacteristic
125#127—611no—
126#125—612no—
127#124—1221no—
128C22⋊Q8—1221no—
129C22⋊Q8—1221no—
130#121—612no—
131#121—1221no—
132C4×Q8—1221no—
133C4×Q8—1221no—
134C4×D4—612no—
135C4×D4—1221no—
136#117—612no—
137C2×C42—611no—
138#107C2×D6114yes—
139#106—614no—
140C4⋊C8—612no—
141#102—614no—
142#102—614no—
143C22⋊C8—612no—
144C4×C8—611no—
145C4×C8C2×D6111yescharacteristic
146#41—2444no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—1221no—
150C2×D4—612no—
151C2×D4—1222no—
152C2×D4—1221no—
153C2×D4—1221no—
154C22×C4—611no—
155C22×C4—611no—
156C22×C4—611no—
157C22×C4—1222no—
158C2×C8—612no—
159C2×C8C22×D6112yes—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—612no—
163C4⋊C4—1222no—
164C4⋊C4—1222no—
165C4⋊C4—1221no—
166C4⋊C4C22×D6112yes—
167C4⋊C4C22×D6112yes—
168C22⋊C4—1222no—
169C22⋊C4—1222no—
170C22⋊C4—1222no—
171C42—611no—
172C42—611no—
173C42—611no—
174C42—1222no—
175C42C22×D6111yescharacteristic
176C23—611no—
177C23—1222no—
178Q8—42no—
179Q8—42no—
180Q8—2442no—
181D4—1224no—
182D4—2444no—
183D4—2442no—
184D4—2442no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—611no—
188C2×C4—611no—
189C2×C4—611no—
190C2×C4—1222no—
191C2×C4—1222no—
192C2×C4—1222no—
193C2×C4—1222no—
194C2×C4—2444no—
195C2×C4D4×D6111yescharacteristic
196C2×C4D4×D6111yescharacteristic
197C2×C4C23×D6111yescharacteristic
198C8—22no—
199C8—1222no—
200C22—1221no—
201C22—1221no—
202C22—1221no—
203C22—2442no—
204C22—2442no—
205C22—2442no—
206C22C2×D4×D6111yescharacteristic
207C4—42no—
208C4—42no—
209C4—1221no—
210C4—1221no—
211C4—1221no—
212C4—2442no—
213C4#1451980012yes—
214C4#1451980112yes—
215C4#1451982512yes—
216C2—4882no—
217C2—2441no—
218C2#1684033711yescharacteristic
219C2C2×#1451980011yescharacteristic
220C2C2×#1451980111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#500C2
socleC22×C61C22×D4
hypercenter#500D61
hypocenterC61#3228
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
1. #16840317C2semidirect
3. #16840158C2semidirect
4. #16840110C2semidirect
5. #16840109C2semidirect
6. #16840089C2semidirect
7. #16840065C2semidirect
8. #16839813C2semidirect
9. C61×#500C2semidirect
113. #500D61semidirect
120. C61#3228semidirect