Finite Group Databasebeta

← #21456955

Subgroups — #21456955

Order 7808.

370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 125 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#16840312C211yesmaximal, characteristic
2#16840165C211yesmaximal, characteristic, complemented
3#16840158C211yesmaximal, characteristic, complemented
4#16840110C211yesmaximal, characteristic, complemented
5#16840110C211yesmaximal, characteristic, complemented
6#16840086C214yesmaximal, complemented
7#16840059C214yesmaximal, complemented
8#16839815C211yesmaximal, characteristic, complemented
9C61×#533C211yesmaximal, characteristic, complemented
10C2×#11758222—21no—
11#14519777C2211yescharacteristic
12#14519774C2211yescharacteristic
13#14519765—21no—
14#14519751—21no—
15#14519751C2212yes—
16C4×D244—21no—
17C4×D244C2212yes—
18#14519710C2214yes—
19#14519708C2214yes—
20C4⋊#92418C2212yes—
21#14519697C2214yes—
22#14519697C2214yes—
23C22⋊#92418C2212yes—
24C4×#92418C2211yescharacteristic
25C4×#92418C2211yescharacteristic
26C4⋊Q8×C61C2211yescharacteristic
27C4⋊Q8×C61C2211yescharacteristic
28#125×C61C2212yes—
29C22⋊Q8×C61—21no—
30C22⋊Q8×C61—21no—
31C4×Q8×C61—21no—
32C4×Q8×C61—21no—
33#117×C61C2212yes—
34C2×C42×C61C2211yescharacteristic
35C2×Q8×C61—21no—
36C2×Q8×C61—21no—
37C22×C4×C61D411yescharacteristic
38C22×C4×C61D411yescharacteristic
39C22×C4×C61C2311yescharacteristic
40C2×C22⋊D61—22no—
41#11758222—44no—
42C2×D244—21no—
43C2×D244—21no—
44C2×D244C2312yes—
45C2×C4×D61—22no—
46C2×Dic122—21no—
47C4⋊C4×C61—22no—
48C4⋊C4×C61—22no—
49C4⋊C4×C61—21no—
50C4⋊C4×C61—21no—
51C4⋊C4×C61C2312yes—
52C4⋊C4×C61C2312yes—
53C22⋊C4×C61—22no—
54C42×C61—22no—
55C42×C61D411yescharacteristic
56C42×C61D411yescharacteristic
57C42×C61C2311yescharacteristic
58C42×C61C2311yescharacteristic
59#11758198—22no—
60#11758198—22no—
61C4⋊Dic61—21no—
62C4⋊Dic61C2312yes—
63C2×#92418C2312yes—
64C2×#92418C2312yes—
65C23×C61C2×D411yescharacteristic
66C22×D61—22no—
67Q8×C61—42no—
68Q8×C61—42no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61C2×D411yescharacteristic
75C2×C4×C61C2×D411yescharacteristic
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2411yescharacteristic
80C22⋊D61—44no—
81C2×Dic61—22no—
82D244—24no—
83D244—42no—
84D244—42no—
85C4×D61—44no—
86Dic122—42no—
87#92418—22no—
88#92418—22no—
89C22×C61—21no—
90C22×C61—21no—
91C22×C61—21no—
92C22×C61C22×D411yescharacteristic
93C2×D61—42no—
94C2×D61—42no—
95C2×D61—42no—
96C4×C61—21no—
97C4×C61—21no—
98C4×C61—21no—
99C4×C61—42no—
100C4×C61—42no—
101C4×C61#13512yes—
102C4×C61AGL(1,ℤ/8)12yes—
103C4×C612−1+412yes—
104Dic61—42no—
105#3228—611nomaximal, Sylow
106C2×C61—41no—
107C2×C61#53611yescharacteristic
108C2×C61C2×#13511yescharacteristic
109C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
110D61—82no—
111#533D6111yescharacteristic, complemented
112#532—611no—
113#500—611no—
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#125C2×D6112yes—
127#124—1221no—
128C22⋊Q8—21no—
129C22⋊Q8—21no—
130#121—612no—
131#121—1221no—
132C4×Q8—21no—
133C4×Q8—21no—
134C4×D4—612no—
135C4×D4—1221no—
136#117C2×D6112yes—
137C2×C42C2×D6111yescharacteristic
138#107—614no—
139#106—614no—
140C4⋊C8—612no—
141#102—614no—
142#102—614no—
143C22⋊C8—612no—
144C4×C8—611no—
145C4×C8—611no—
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—1222no—
155C22×C4C22⋊D6111yescharacteristic
156C22×C4C22⋊D6111yescharacteristic
157C22×C4C22×D6111yescharacteristic
158C2×C8—612no—
159C2×C8—612no—
160C4⋊C4—22no—
161C4⋊C4—22no—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—612no—
165C4⋊C4—1221no—
166C4⋊C4C22×D6112yes—
167C4⋊C4C22×D6112yes—
168C22⋊C4—22no—
169C22⋊C4—1222no—
170C22⋊C4—1222no—
171C42—22no—
172C42C22⋊D6111yescharacteristic
173C42C22⋊D6111yescharacteristic
174C42C22×D6111yescharacteristic
175C42C22×D6111yescharacteristic
176C23—1222no—
177C23C2×C22⋊D6111yescharacteristic
178Q8—42no—
179Q8—42no—
180Q8—2442no—
181D4—1224no—
182D4—2444no—
183D4—2442no—
184D4—2442no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—1222no—
191C2×C4—2444no—
192C2×C4C2×C22⋊D6111yescharacteristic
193C2×C4C2×C22⋊D6111yescharacteristic
194C2×C4C2×C22⋊D6111yescharacteristic
195C2×C4C2×C22⋊D6111yescharacteristic
196C2×C4C2×C22⋊D6111yescharacteristic
197C2×C4C23×D6111yescharacteristic
198C8—1222no—
199C8—1222no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—2442no—
204C22—2442no—
205C22—2442no—
206C22C22×C22⋊D6111yescharacteristic
207C4—21no—
208C4—21no—
209C4—21no—
210C4—42no—
211C4—42no—
212C4—2442no—
213C4#1451979712yes—
214C4#1451980212yes—
215C4#1451982512yes—
216C2—41no—
217C2—4882no—
218C2#1684033611yescharacteristic
219C2C2×#1451979711yescharacteristic
220C2C2×#1451980211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#533C2
socleC22×C61C22×D4
hypercenter#533D61
hypocenterC61#3228
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #16840165C2semidirect
3. #16840158C2semidirect
4. #16840110C2semidirect
5. #16840110C2semidirect
6. #16840086C2semidirect
7. #16840059C2semidirect
8. #16839815C2semidirect
9. C61×#533C2semidirect
111. #533D61semidirect
120. C61#3228semidirect