Finite Group Databasebeta

← #21445080

Subgroups — #21445080

Order 7808.

234 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×Dic122C211yesmaximal, characteristic
2#16840158C211yesmaximal, characteristic, complemented
3#16840044C211yesmaximal, characteristic, complemented
4#16839507C211yesmaximal, characteristic, complemented
5#16839492C211yesmaximal, characteristic, complemented
6D4⋊#92418C211yesmaximal, characteristic
7C61×#461C211yesmaximal, characteristic
8C22×Dic122—21no—
9#14519777C2211yescharacteristic
10#14519776—21no—
11#14519756—21no—
12#14519754—22no—
13C4×Dic122C2211yescharacteristic
14D4×Dic61—21no—
15#14519708—21no—
16#14519708—22no—
17C4⋊#92418C2211yescharacteristic
18#14519700—21no—
19C4×#92418C2211yescharacteristic
20C2×SD16×C61—21no—
21C4⋊Q8×C61C2211yescharacteristic
22C4×D4×C61C2211yescharacteristic
23C4⋊C8×C61C2211yescharacteristic
24#103×C61—21no—
25C2×Q8×C61—21no—
26C2×D4×C61D411yescharacteristic
27C22×C4×C61—21no—
28C22×Dic61—22no—
29C2×Dic122—22no—
30C2×Dic122—21no—
31C2×Dic122—42no—
32C2×Dic122—42no—
33C2×Dic122D411yescharacteristic
34SD16×C61—42no—
35C2×C8×C61—21no—
36C4⋊C4×C61—21no—
37C4⋊C4×C61—21no—
38C4⋊C4×C61D411yescharacteristic
39C22⋊C4×C61—21no—
40C42×C61C2311yescharacteristic
41C22⋊Dic61—22no—
42C4⋊Dic61—21no—
43C4⋊Dic61D411yescharacteristic
44C4⋊Dic61D412yes—
45#11758196—22no—
46#11758196—21no—
47C4×Dic61—21no—
48C2×#92418—21no—
49C2×#92418—21no—
50C23×C61—21no—
51Q8×C61—41no—
52Q8×C61—41no—
53D4×C61—21no—
54D4×C61SD1612yes—
55C2×C4×C61—21no—
56C2×C4×C61—41no—
57C2×C4×C61—41no—
58C2×C4×C61—41no—
59C2×C4×C61C2×D411yescharacteristic
60C2×C4×C61C2×D411yescharacteristic
61C2×C4×C61C2×D411yescharacteristic
62C2×Dic61—21no—
63C2×Dic61—21no—
64C2×Dic61—22no—
65C2×Dic61—44no—
66Dic122—21no—
67Dic122—44no—
68Dic122—41no—
69Dic122—41no—
70Dic122SD1612yescomplemented
71C8×C61—41no—
72#92418—22no—
73#92418—41no—
74C22×C61—22no—
75C22×C61—41no—
76C22×C61—41no—
77C22×C61#12011yescharacteristic
78C4×C61—21no—
79C4×C61—41no—
80C4×C61—81no—
81C4×C61C2×SD1611yescharacteristic
82C4×C61C2×SD1611yescharacteristic
83C4×C61AGL(1,ℤ/8)11yescharacteristic
84C4×C61#13711yescharacteristic
85Dic61—22no—
86Dic61—42no—
87Dic61—41no—
88#1651—611nomaximal, Sylow
89C2×C61—42no—
90C2×C61#44811yescharacteristic
91C2×C61#45011yescharacteristic
92C2×C61#45611yescharacteristic
93D4×Q8—611no—
94#498—611no—
95#475—611no—
96#461D6111yescharacteristic
97#332—611no—
98Q8⋊C8—611no—
99D4⋊C8—611no—
100C61#165111yescharacteristic, complemented, Sylow
101C22×Q8—1221no—
102C2×SD16—21no—
103C4⋊Q8—611no—
104C4⋊Q8—1221no—
105C4⋊Q8C2×D6111yescharacteristic
106C22⋊Q8—1222no—
107C22⋊Q8—1221no—
108C4×Q8—611no—
109C4×D4—1221no—
110C4×D4C2×D6111yescharacteristic
111#106—1221no—
112#106—1222no—
113C4⋊C8—611no—
114C4⋊C8C2×D6111yescharacteristic
115#103—21no—
116#103—1221no—
117C4×C8—611no—
118C2×Q8—21no—
119C2×Q8—611no—
120C2×Q8—1222no—
121C2×Q8—1221no—
122C2×Q8—2442no—
123C2×Q8—2442no—
124C2×D4C22⋊D6111yescharacteristic
125C22×C4—21no—
126C22×C4—1222no—
127SD16—42no—
128C2×C8—21no—
129C2×C8—1221no—
130C2×C8—1221no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—611no—
134C4⋊C4—612no—
135C4⋊C4—1222no—
136C4⋊C4—1221no—
137C4⋊C4—1221no—
138C4⋊C4C22⋊D6111yescharacteristic
139C22⋊C4—21no—
140C22⋊C4—1222no—
141C42—1221no—
142C42C22×D6111yescharacteristic
143C23—21no—
144Q8—41no—
145Q8—41no—
146Q8—612no—
147Q8—1221no—
148Q8—2444no—
149Q8—2441no—
150Q8—2441no—
151D4—21no—
152D4#1175820012yes—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—1221no—
158C2×C4—1221no—
159C2×C4—1222no—
160C2×C4—2444no—
161C2×C4D4×D6111yescharacteristic
162C2×C4D4×D6111yescharacteristic
163C2×C4C2×C22⋊D6111yescharacteristic
164C8—41no—
165C8—1222no—
166C8—2441no—
167C22—22no—
168C22—41no—
169C22—41no—
170C22#1451974511yescharacteristic
171C4—21no—
172C4—41no—
173C4—81no—
174C4—1222no—
175C4—2441no—
176C4—2442no—
177C4SD16×D6111yescharacteristic
178C4C2×#1175820011yescharacteristic
179C4#1451980411yescharacteristic
180C4#1451980711yescharacteristic
181C2—42no—
182C2#1683990011yescharacteristic
183C2#1683991111yescharacteristic
184C2#1683994311yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#461C2
socleC22×C61#120
hypercenter#461D61
hypocenterC61#1651
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
2. #16840158C2semidirect
3. #16840044C2semidirect
4. #16839507C2semidirect
5. #16839492C2semidirect
70. Dic122SD16semidirect
100. C61#1651semidirect