Finite Group Databasebeta

← #21444951

Subgroups — #21444951

Order 7808.

214 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 57 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#16840469C211yesmaximal, characteristic
2#16840141C211yesmaximal, characteristic, complemented
3#16840054C211yesmaximal, characteristic, complemented
4#16839510C211yesmaximal, characteristic, complemented
5#16839492C211yesmaximal, characteristic, complemented
6D4⋊#92418C211yesmaximal, characteristic
7C61×#476C211yesmaximal, characteristic
8C2×#11758202—22no—
9#14519777C2211yescharacteristic
10#14519768—21no—
11#14519756—21no—
12#14519754—22no—
13C4×Dic122C2211yescharacteristic
14D4×Dic61—21no—
15C2×C4⋊Dic61—21no—
16#14519710—21no—
17C4⋊#92418C2211yescharacteristic
18#14519700—21no—
19C4×#92418C2211yescharacteristic
20C4⋊Q8×C61C2211yescharacteristic
21C4×D4×C61C2211yescharacteristic
22#106×C61—21no—
23C4⋊C8×C61C2211yescharacteristic
24#102×C61—21no—
25C2×Q8×C61—21no—
26C2×D4×C61D411yescharacteristic
27C22×C4×C61—21no—
28C22×Dic61—22no—
29C2×Dic122D411yescharacteristic
30C2×Dic122D412yes—
31C2×C8×C61—21no—
32C4⋊C4×C61—21no—
33C4⋊C4×C61—21no—
34C4⋊C4×C61D411yescharacteristic
35C22⋊C4×C61—21no—
36C42×C61C2311yescharacteristic
37C22⋊Dic61—22no—
38#11758202—44no—
39C4⋊Dic61—22no—
40C4⋊Dic61—21no—
41C4⋊Dic61—21no—
42C4⋊Dic61D411yescharacteristic
43#11758196—22no—
44#11758196—21no—
45C4×Dic61—21no—
46C2×#92418—21no—
47C2×#92418—21no—
48C23×C61—21no—
49Q8×C61—42no—
50D4×C61—21no—
51D4×C61Q1612yescomplemented
52C2×C4×C61—21no—
53C2×C4×C61—41no—
54C2×C4×C61—41no—
55C2×C4×C61—41no—
56C2×C4×C61C2×D411yescharacteristic
57C2×C4×C61C2×D411yescharacteristic
58C2×C4×C61C2×D411yescharacteristic
59C2×Dic61—21no—
60C2×Dic61—21no—
61C2×Dic61—22no—
62C2×Dic61—82no—
63Dic122—21no—
64Dic122—21no—
65Dic122—42no—
66C8×C61—41no—
67#92418—22no—
68#92418—41no—
69C22×C61—22no—
70C22×C61—41no—
71C22×C61—41no—
72C22×C61#12011yescharacteristic
73C4×C61—21no—
74C4×C61—41no—
75C4×C61—81no—
76C4×C61C2×Q1611yescharacteristic
77C4×C61#13511yescharacteristic
78C4×C61#13711yescharacteristic
79C4×C61#13711yescharacteristic
80Dic61—41no—
81Dic61—42no—
82Dic61—41no—
83#1632—611nomaximal, Sylow
84C2×C61—42no—
85C2×C61#45111yescharacteristic
86C2×C61#45211yescharacteristic
87C2×C61#45311yescharacteristic
88#554—611no—
89#494—611no—
90#477—611no—
91#476D6111yescharacteristic
92#333—611no—
93Q8⋊C8—611no—
94D4⋊C8—611no—
95C61#163211yescharacteristic, complemented, Sylow
96C2×Q16—1222no—
97C4⋊Q8—611no—
98C4⋊Q8C2×D6111yescharacteristic
99#125—1221no—
100C22⋊Q8—1222no—
101C22⋊Q8—1221no—
102C4×Q8—611no—
103C4×D4—1221no—
104C4×D4C2×D6111yescharacteristic
105C2×C4⋊C4—1221no—
106#107—1221no—
107#106—21no—
108C4⋊C8—611no—
109C4⋊C8C2×D6111yescharacteristic
110#103—1221no—
111#102—21no—
112C4×C8—611no—
113C2×Q8—21no—
114C2×Q8—611no—
115C2×Q8—612no—
116C2×D4C22⋊D6111yescharacteristic
117C22×C4—21no—
118C22×C4—1222no—
119Q16—2444no—
120C2×C8—21no—
121C2×C8—1221no—
122C2×C8—1221no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—611no—
126C4⋊C4—1222no—
127C4⋊C4—1222no—
128C4⋊C4—1221no—
129C4⋊C4—1221no—
130C4⋊C4—1221no—
131C4⋊C4C22⋊D6111yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—1222no—
134C42—1221no—
135C42C22×D6111yescharacteristic
136C23—21no—
137Q8—42no—
138Q8—1221no—
139Q8—1221no—
140Q8—2442no—
141D4—21no—
142D4#1175820212yescomplemented
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—1221no—
148C2×C4—1221no—
149C2×C4—1222no—
150C2×C4—4882no—
151C2×C4D4×D6111yescharacteristic
152C2×C4D4×D6111yescharacteristic
153C2×C4C2×C22⋊D6111yescharacteristic
154C8—41no—
155C8—1222no—
156C8—2441no—
157C22—22no—
158C22—41no—
159C22—41no—
160C22#1451974511yescharacteristic
161C4—21no—
162C4—41no—
163C4—81no—
164C4—2441no—
165C4—2441no—
166C4—2442no—
167C4C2×#1175820211yescharacteristic
168C4#1451979811yescharacteristic
169C4#1451980611yescharacteristic
170C4#1451980711yescharacteristic
171C2—42no—
172C2#1683991711yescharacteristic
173C2#1683992111yescharacteristic
174C2#1683992811yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#476C2
socleC22×C61#120
hypercenter#476D61
hypocenterC61#1632
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #16840141C2semidirect
3. #16840054C2semidirect
4. #16839510C2semidirect
5. #16839492C2semidirect
51. D4×C61Q16semidirect
95. C61#1632semidirect
142. D4#11758202semidirect