Finite Group Databasebeta

← #21456978

Subgroups — #21456978

Order 7808.

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

normal subgroups only

This group has 326 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
2#16840165C211yesmaximal, characteristic, complemented
3#16840158C211yesmaximal, characteristic, complemented
4#16840114C211yesmaximal, characteristic, complemented
5#16840114C211yesmaximal, characteristic, complemented
6#16840103C214yesmaximal
7#16840066C214yesmaximal, complemented
8#16839815C211yesmaximal, characteristic
9C61×#533C211yesmaximal, characteristic
10#14519777C2211yescharacteristic
11#14519777C2211yescharacteristic
12#14519769—21no—
13#14519756—21no—
14#14519756C2212yes—
15C4×Dic122—21no—
16C4×Dic122C2212yes—
17#14519736—21no—
18#14519710C2214yes—
19#14519708C2214yes—
20C4⋊#92418C2212yes—
21#14519700C2214yes—
22#14519700C2214yes—
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×Dic122—21no—
41C2×Dic122C2312yes—
42C4⋊C4×C61—22no—
43C4⋊C4×C61—22no—
44C4⋊C4×C61—21no—
45C4⋊C4×C61—21no—
46C4⋊C4×C61C2312yes—
47C4⋊C4×C61C2312yes—
48C22⋊C4×C61—22no—
49C42×C61—22no—
50C42×C61D411yescharacteristic
51C42×C61D411yescharacteristic
52C42×C61C2311yescharacteristic
53C42×C61C2311yescharacteristic
54C22⋊Dic61—22no—
55C4⋊Dic61—21no—
56C4⋊Dic61—21no—
57C4⋊Dic61—21no—
58C4⋊Dic61C2312yes—
59#11758196—22no—
60#11758196—22no—
61C4×Dic61—22no—
62C2×#92418C2312yes—
63C2×#92418C2312yes—
64C23×C61C2×D411yescharacteristic
65Q8×C61—42no—
66Q8×C61—42no—
67C2×C4×C61—22no—
68C2×C4×C61—22no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2×D411yescharacteristic
74C2×C4×C61C2×D411yescharacteristic
75C2×C4×C61C2×D411yescharacteristic
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61C2411yescharacteristic
78C2×Dic61—22no—
79C2×Dic61—22no—
80Dic122—24no—
81Dic122—42no—
82#92418—22no—
83#92418—22no—
84C22×C61—21no—
85C22×C61—21no—
86C22×C61—21no—
87C22×C61C22×D411yescharacteristic
88C4×C61—21no—
89C4×C61—21no—
90C4×C61—21no—
91C4×C61—42no—
92C4×C61—42no—
93C4×C61#13512yes—
94C4×C61#13712yes—
95C4×C612−1+412yes—
96Dic61—42no—
97Dic61—42no—
98#3231—611nomaximal, Sylow
99C2×C61—41no—
100C2×C61#53611yescharacteristic
101C2×C61C2×#13511yescharacteristic
102C2×C61C2×#13711yescharacteristic
103#533—611no—
104#533D6111yescharacteristic
105#500—611no—
106#498—611no—
107#487—611no—
108#487—611no—
109#485—614no—
110#479—614no—
111#431—611no—
112C61#323111yescharacteristic, complemented, Sylow
113C4⋊Q8—611no—
114C4⋊Q8—611no—
115C4⋊Q8C2×D6111yescharacteristic
116C4⋊Q8C2×D6111yescharacteristic
117#125—1221no—
118#125C2×D6112yes—
119C22⋊Q8—21no—
120C22⋊Q8—21no—
121C22⋊Q8—612no—
122C22⋊Q8—1221no—
123C4×Q8—21no—
124C4×Q8—21no—
125C4×Q8—612no—
126C4×Q8—1221no—
127#117—1221no—
128#117C2×D6112yes—
129C2×C42C2×D6111yescharacteristic
130#107—614no—
131#106—614no—
132C4⋊C8—612no—
133#103—614no—
134#103—614no—
135C22⋊C8—612no—
136C4×C8—611no—
137C4×C8—611no—
138C2×Q8—21no—
139C2×Q8—21no—
140C2×Q8—612no—
141C2×Q8—1221no—
142C22×C4C22⋊D6111yescharacteristic
143C22×C4C22⋊D6111yescharacteristic
144C22×C4C22×D6111yescharacteristic
145C2×C8—612no—
146C2×C8—612no—
147C4⋊C4—22no—
148C4⋊C4—22no—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—612no—
152C4⋊C4—1222no—
153C4⋊C4—1222no—
154C4⋊C4—1221no—
155C4⋊C4—1221no—
156C4⋊C4—1221no—
157C4⋊C4C22×D6112yes—
158C4⋊C4C22×D6112yes—
159C22⋊C4—22no—
160C22⋊C4—1222no—
161C42—22no—
162C42—1222no—
163C42C22⋊D6111yescharacteristic
164C42C22⋊D6111yescharacteristic
165C42C22×D6111yescharacteristic
166C42C22×D6111yescharacteristic
167C23C2×C22⋊D6111yescharacteristic
168Q8—42no—
169Q8—42no—
170Q8—1224no—
171Q8—2442no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—1222no—
178C2×C4—1222no—
179C2×C4C2×C22⋊D6111yescharacteristic
180C2×C4C2×C22⋊D6111yescharacteristic
181C2×C4C2×C22⋊D6111yescharacteristic
182C2×C4C2×C22⋊D6111yescharacteristic
183C2×C4C2×C22⋊D6111yescharacteristic
184C2×C4C23×D6111yescharacteristic
185C8—1222no—
186C8—1222no—
187C22—21no—
188C22—21no—
189C22—21no—
190C22C22×C22⋊D6111yescharacteristic
191C4—21no—
192C4—21no—
193C4—21no—
194C4—42no—
195C4—42no—
196C4—2442no—
197C4—2442no—
198C4#1451979712yes—
199C4#1451980712yes—
200C4#1451982512yes—
201C2—41no—
202C2#1684033611yescharacteristic
203C2C2×#1451979711yescharacteristic
204C2C2×#1451980711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#533C2
socleC22×C61C22×D4
hypercenter#533D61
hypocenterC61#3231
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. #16840114C2semidirect
5. #16840114C2semidirect
7. #16840066C2semidirect
112. C61#3231semidirect