Finite Group Databasebeta

← #21461135

Subgroups — #21461135

Order 7808.

234 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 62 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
1D61⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
2C4×#11758213C211yesmaximal, characteristic, complemented
3Q8⋊#92420C212yesmaximal, complemented
4D4⋊#92420C212yesmaximal, complemented
5#16840291C211yesmaximal, characteristic
6C2×#11758213—21no—
7C2×D61⋊C8—21no—
8#14519844—21no—
9C4⋊#92420C2212yes—
10#14519832—21no—
11C4×#92420C2212yes—
12#14519770—21no—
13#14519769C411yescharacteristic
14#14519759—21no—
15#14519753C411yescharacteristic
16#14519748C411yescharacteristic
17Q8×Dic61C2211yescharacteristic
18D4×Dic61C2211yescharacteristic
19#14519737—21no—
20#14519733—21no—
21C42×D61C2211yescharacteristic
22#124×C61C411yescharacteristic
23C2×Q8×C61C2×C411yescharacteristic
24C2×D4×C61C2×C411yescharacteristic
25C2×C22⋊D61—21no—
26C22×Dic61—21no—
27C2×C4×D61C2×C411yescharacteristic
28C2×C4×D61D411yescharacteristic
29C2×C4×D61D411yescharacteristic
30C2×#92420—22no—
31C2×#92420—22no—
32#11758213—24no—
33D61⋊C8—42no—
34C22⋊C4×C61—21no—
35C22⋊C4×C61—21no—
36C42×C61C2×C411yescharacteristic
37C22⋊Dic61—21no—
38C22⋊Dic61—21no—
39#11758198—21no—
40C4⋊Dic61—21no—
41C4⋊Dic61C2×C411yescharacteristic
42C4⋊Dic61C2×C411yescharacteristic
43#11758196—21no—
44#11758196—21no—
45#11758196—21no—
46C4×Dic61—21no—
47C4×Dic61D411yescharacteristic
48C4×Dic61D411yescharacteristic
49C4×Dic61C2311yescharacteristic
50C23×C61—21no—
51C22×D61C22⋊C411yescharacteristic
52Q8×C61—22no—
53D4×C61—22no—
54C2×C4×C61—21no—
55C2×C4×C61C22⋊C411yescharacteristic
56C2×C4×C61C22⋊C411yescharacteristic
57C2×C4×C61C22×C411yescharacteristic
58C22⋊D61—42no—
59C2×Dic61—21no—
60C2×Dic61—21no—
61C2×Dic61—41no—
62C2×Dic61—41no—
63C2×Dic61C22⋊C411yescharacteristic
64C2×Dic61C2×D411yescharacteristic
65C2×Dic61C2×D411yescharacteristic
66C4×D61—22no—
67C4×D61—22no—
68C4×D61—21no—
69C4×D61—21no—
70#92420—24no—
71#92420—42no—
72C22×C61—41no—
73C22×C61—41no—
74C22×C61—41no—
75C22×C61C2×C22⋊C411yescharacteristic
76C2×D61—21no—
77C2×D61—21no—
78C2×D61#10412yes—
79C4×C61—21no—
80C4×C61—21no—
81C4×C61—41no—
82C4×C61#13112yes—
83Dic61—21no—
84Dic61—21no—
85Dic61—41no—
86Dic61—41no—
87Dic61AGL(1,ℤ/8)11yescharacteristic
88Dic61#13711yescharacteristic
89#1483—611nomaximal, Sylow
90C2×C61—81no—
91C2×C61#40811yescharacteristic
92C2×C61#41711yescharacteristic
93C2×C61C2×#10411yescharacteristic
94D61—22no—
95#529—611no—
96C2×C4⋊C8—611no—
97C4×M16—611no—
98Q8⋊C8—612no—
99D4⋊C8—612no—
100C61#148311yescharacteristic, complemented, Sylow
101C2×M16—1221no—
102C22×C8—1221no—
103#126—1221no—
104#125—611no—
105#124#692311yescharacteristic
106#123—1221no—
107C22⋊Q8—611no—
108#121—611no—
109C4×Q8—611no—
110C4×D4—611no—
111C4×D4—1221no—
112#117—1221no—
113C2×C42—611no—
114C4⋊C8—612no—
115C4⋊C8—1221no—
116#97—1221no—
117C4×C8—612no—
118C2×Q8C2×#692311yescharacteristic
119C2×D4—1221no—
120C2×D4C2×#692311yescharacteristic
121C22×C4—611no—
122C22×C4—611no—
123C22×C4—611no—
124C22×C4—1221no—
125M16—1224no—
126C2×C8—1222no—
127C2×C8—1222no—
128C2×C8—2442no—
129C4⋊C4—611no—
130C4⋊C4—611no—
131C4⋊C4—1221no—
132C4⋊C4—1221no—
133C4⋊C4—1221no—
134C4⋊C4—1221no—
135C22⋊C4—21no—
136C22⋊C4—21no—
137C22⋊C4—1221no—
138C22⋊C4—1221no—
139C22⋊C4—1221no—
140C42—611no—
141C42—611no—
142C42—611no—
143C42—1221no—
144C42C2×#692311yescharacteristic
145C23—21no—
146C23—611no—
147Q8—22no—
148D4—22no—
149D4—2442no—
150C2×C4—21no—
151C2×C4—611no—
152C2×C4—611no—
153C2×C4—611no—
154C2×C4—1221no—
155C2×C4—1221no—
156C2×C4—1222no—
157C2×C4—1222no—
158C2×C4—1221no—
159C2×C4—1221no—
160C2×C4—2441no—
161C2×C4—2441no—
162C2×C4C22⋊#692311yescharacteristic
163C2×C4C22⋊#692311yescharacteristic
164C2×C4C22×#692311yescharacteristic
165C8—1224no—
166C8—2442no—
167C22—41no—
168C22—41no—
169C22—41no—
170C22—612no—
171C22—1221no—
172C22—1221no—
173C22C2×C22⋊#692311yescharacteristic
174C4—21no—
175C4—21no—
176C4—41no—
177C4—611no—
178C4—611no—
179C4—1221no—
180C4—1221no—
181C4—2441no—
182C4—2441no—
183C4#1451986412yes—
184C2—81no—
185C2—1222no—
186C2#1684073611yescharacteristic
187C2#1684075311yescharacteristic
188C2D61⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#124×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#124#6923
hypocenterC61#1483
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. D61⋊(C4⋊C8)C2semidirect
2. C4×#11758213C2semidirect
3. Q8⋊#92420C2semidirect
4. D4⋊#92420C2semidirect
100. C61#1483semidirect