Finite Group Databasebeta

← #21456957

Subgroups — #21456957

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#16840319C211yesmaximal, characteristic, complemented
2#16840312C211yesmaximal, characteristic
3#16840167C211yesmaximal, characteristic, complemented
4#16840160C211yesmaximal, characteristic, complemented
5#16840109C211yesmaximal, characteristic, complemented
6#16840109C211yesmaximal, characteristic, complemented
7#16840087C214yesmaximal, complemented
8#16840063C214yesmaximal, complemented
9C61×#431C211yesmaximal, characteristic, complemented
10C2×#11758222—21no—
11#14519777C2211yescharacteristic
12#14519777C2211yescharacteristic
13#14519777C2211yescharacteristic
14#14519774C2211yescharacteristic
15#14519769C2212yes—
16#14519765—21no—
17#14519756—21no—
18#14519756—21no—
19#14519751—21no—
20#14519751C2212yes—
21C4×Dic122—21no—
22C4×Dic122—21no—
23C4×D244—21no—
24C4×D244C2212yes—
25#14519736C2212yes—
26#14519711C2214yes—
27#14519709C2214yes—
28#14519699C2214yes—
29#14519699C2214yes—
30C2×C42×C61C2211yescharacteristic
31C4⋊C8×C61C2212yes—
32C22⋊C8×C61C2212yes—
33C4×C8×C61C2211yescharacteristic
34C4×C8×C61C2211yescharacteristic
35C22×C4×C61D411yescharacteristic
36C22×C4×C61D411yescharacteristic
37C22×C4×C61C2311yescharacteristic
38C2×C22⋊D61—22no—
39#11758222—44no—
40C2×D244—21no—
41C2×D244—21no—
42C2×D244C2312yes—
43C2×C4×D61—22no—
44C2×Dic122—21no—
45C2×Dic122—21no—
46C2×Dic122—21no—
47C2×C8×C61C2312yes—
48C2×C8×C61C2312yes—
49C42×C61D411yescharacteristic
50C42×C61D411yescharacteristic
51C42×C61C2311yescharacteristic
52C42×C61C2311yescharacteristic
53C22⋊Dic61—22no—
54#11758198—22no—
55#11758198—22no—
56C4⋊Dic61—21no—
57C4⋊Dic61—21no—
58C4⋊Dic61—21no—
59C4⋊Dic61C2312yes—
60C4⋊Dic61C2312yes—
61C4⋊Dic61C2312yes—
62#11758196—22no—
63#11758196—22no—
64C4×Dic61—22no—
65C23×C61C2×D411yescharacteristic
66C22×D61—22no—
67C2×C4×C61—22no—
68C2×C4×C61—22no—
69C2×C4×C61—22no—
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2×D411yescharacteristic
74C2×C4×C61C2×D411yescharacteristic
75C2×C4×C61C2411yescharacteristic
76C22⋊D61—44no—
77C2×Dic61—22no—
78C2×Dic61—22no—
79C2×Dic61—22no—
80D244—24no—
81D244—42no—
82D244—42no—
83C4×D61—44no—
84Dic122—42no—
85Dic122—42no—
86Dic122—42no—
87C8×C61—22no—
88C8×C61—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#13512yes—
100C4×C61AGL(1,ℤ/8)12yes—
101C4×C612−1+412yes—
102Dic61—42no—
103Dic61—42no—
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#533—611no—
112#532—611no—
113#500—611no—
114#498—611no—
115#486—611no—
116#486—611no—
117#482—614no—
118#478—614no—
119#431D6111yescharacteristic, complemented
120C61#322811yescharacteristic, complemented, Sylow
121C2×#41—1221no—
122C4⋊Q8—611no—
123C4⋊Q8—611no—
124C4⋊Q8—611no—
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×C42C2×D6111yescharacteristic
138#107—614no—
139#106—614no—
140C4⋊C8C2×D6112yes—
141#102—614no—
142#102—614no—
143C22⋊C8C2×D6112yes—
144C4×C8C2×D6111yescharacteristic
145C4×C8C2×D6111yescharacteristic
146#41—2444no—
147C2×Q8—1221no—
148C2×Q8—1221no—
149C2×Q8—1221no—
150C2×D4—612no—
151C2×D4—1222no—
152C2×D4—1221no—
153C2×D4—1221no—
154C22×C4—1222no—
155C22×C4D24411yescharacteristic
156C22×C4D24411yescharacteristic
157C22×C4C22×D6111yescharacteristic
158C2×C8C22×D6112yes—
159C2×C8C22×D6112yes—
160C4⋊C4—612no—
161C4⋊C4—612no—
162C4⋊C4—612no—
163C4⋊C4—1222no—
164C4⋊C4—1222no—
165C4⋊C4—1221no—
166C4⋊C4—1221no—
167C4⋊C4—1221no—
168C22⋊C4—1222no—
169C22⋊C4—1222no—
170C22⋊C4—1222no—
171C42—1222no—
172C42D24411yescharacteristic
173C42D24411yescharacteristic
174C42C22×D6111yescharacteristic
175C42C22×D6111yescharacteristic
176C23—1222no—
177C23C2×D24411yescharacteristic
178Q8—2442no—
179Q8—2442no—
180Q8—2442no—
181D4—1224no—
182D4—2444no—
183D4—2442no—
184D4—2442no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—1222no—
189C2×C4—1222no—
190C2×C4—1222no—
191C2×C4—2444no—
192C2×C4C2×D24411yescharacteristic
193C2×C4C2×D24411yescharacteristic
194C2×C4C2×D24411yescharacteristic
195C2×C4C2×D24411yescharacteristic
196C2×C4C2×D24411yescharacteristic
197C2×C4C23×D6111yescharacteristic
198C8—22no—
199C8—22no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—2442no—
204C22—2442no—
205C22—2442no—
206C22C22×D24411yescharacteristic
207C4—21no—
208C4—21no—
209C4—21no—
210C4—2442no—
211C4—2442no—
212C4—2442no—
213C4#1451979912yes—
214C4#1451980512yes—
215C4#1451982412yes—
216C2—41no—
217C2—4882no—
218C2#1684033811yescharacteristic
219C2C2×#1451979911yescharacteristic
220C2C2×#1451980511yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#431C2
socleC22×C61C22×D4
hypercenter#431D61
hypocenterC61#3228
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
1. #16840319C2semidirect
3. #16840167C2semidirect
4. #16840160C2semidirect
5. #16840109C2semidirect
6. #16840109C2semidirect
7. #16840087C2semidirect
8. #16840063C2semidirect
9. C61×#431C2semidirect
119. #431D61semidirect
120. C61#3228semidirect