Finite Group Databasebeta

← #21445046

Subgroups — #21445046

Order 7808.

212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 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#16840477C211yesmaximal, characteristic
2#16840114C211yesmaximal, characteristic, complemented
3#16839964C211yesmaximal, characteristic, complemented
4#16839510C211yesmaximal, characteristic, complemented
5D4⋊#92418C211yesmaximal, characteristic, complemented
6#16839489C211yesmaximal, characteristic, complemented
7C61×#474C211yesmaximal, characteristic, complemented
8C2×#11758201—21no—
9#14519777C2211yescharacteristic
10#14519763—22no—
11#14519751—21no—
12#14519748—21no—
13C4×D244C2211yescharacteristic
14#14519736—21no—
15#14519735—21no—
16C4⋊#92418C2211yescharacteristic
17#14519701—21no—
18#14519700—22no—
19C4×#92418C2211yescharacteristic
20C4⋊Q8×C61C2211yescharacteristic
21C4×D4×C61C2211yescharacteristic
22#107×C61—21no—
23C4⋊C8×C61C2211yescharacteristic
24#102×C61—21no—
25C2×Q8×C61—21no—
26C2×D4×C61D411yescharacteristic
27C22×C4×C61—21no—
28C2×C22⋊D61—22no—
29C2×D244D411yescharacteristic
30C2×C4×D61—21no—
31C2×Dic122D412yes—
32C2×C8×C61—21no—
33C4⋊C4×C61—21no—
34C4⋊C4×C61—21no—
35C4⋊C4×C61D411yescharacteristic
36C22⋊C4×C61—21no—
37C42×C61C2311yescharacteristic
38C22⋊Dic61—22no—
39#11758201—42no—
40#11758198—22no—
41#11758198—21no—
42C4⋊Dic61—21no—
43C4⋊Dic61—21no—
44C4⋊Dic61D411yescharacteristic
45C4×Dic61—22no—
46C2×#92418—21no—
47C2×#92418—21no—
48C23×C61—21no—
49C22×D61—21no—
50Q8×C61—41no—
51Q8×C61—41no—
52D4×C61—21no—
53D4×C61—21no—
54C2×C4×C61—21no—
55C2×C4×C61—41no—
56C2×C4×C61—41no—
57C2×C4×C61—41no—
58C2×C4×C61C2×D411yescharacteristic
59C2×C4×C61C2×D411yescharacteristic
60C2×C4×C61C2×D411yescharacteristic
61C22⋊D61—82no—
62C2×Dic61—21no—
63C2×Dic61—22no—
64D244—21no—
65D244—21no—
66C4×D61—41no—
67C4×D61—41no—
68Dic122—42no—
69C8×C61—41no—
70#92418—41no—
71#92418—41no—
72C22×C61—41no—
73C22×C61—41no—
74C22×C61—41no—
75C22×C61#12011yescharacteristic
76C2×D61—41no—
77C2×D61—41no—
78C2×D61—41no—
79C4×C61—21no—
80C4×C61—41no—
81C4×C61—81no—
82C4×C61#13511yescharacteristic
83C4×C61#13511yescharacteristic
84C4×C61AGL(1,ℤ/8)11yescharacteristic
85C4×C61#13711yescharacteristic
86Dic61—41no—
87Dic61—42no—
88#1646—611nomaximal, Sylow
89C2×C61—81no—
90C2×C61#44911yescharacteristic
91C2×C61#45211yescharacteristic
92C2×C61#45511yescharacteristic
93D61—81no—
94#555—611no—
95#487—611no—
96#474D6111yescharacteristic, complemented
97#461—611no—
98#333—611no—
99D4⋊C8—611no—
100D4⋊C8—611no—
101C61#164611yescharacteristic, complemented, Sylow
102C2×SD16—1221no—
103C4⋊Q8—611no—
104C4⋊Q8C2×D6111yescharacteristic
105#124—1222no—
106#121—1221no—
107#121—1221no—
108C4×D4—611no—
109C4×D4C2×D6111yescharacteristic
110#117—1221no—
111#117—1221no—
112#107—21no—
113C4⋊C8—611no—
114C4⋊C8C2×D6111yescharacteristic
115#103—1222no—
116#103—1221no—
117#102—21no—
118C4×C8—611no—
119C2×Q8—21no—
120C2×Q8—612no—
121C2×D4—611no—
122C2×D4—1222no—
123C2×D4C22⋊D6111yescharacteristic
124C22×C4—21no—
125C22×C4—1221no—
126SD16—2442no—
127C2×C8—21no—
128C2×C8—1221no—
129C2×C8—1221no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—611no—
133C4⋊C4—1221no—
134C4⋊C4—1221no—
135C4⋊C4C22⋊D6111yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—1222no—
138C22⋊C4—1222no—
139C22⋊C4—1221no—
140C42—1222no—
141C42C22×D6111yescharacteristic
142C23—21no—
143C23—1221no—
144Q8—41no—
145Q8—41no—
146Q8—2442no—
147D4—21no—
148D4—21no—
149D4—1221no—
150D4—1221no—
151D4—4882no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—1221no—
157C2×C4—1222no—
158C2×C4—2441no—
159C2×C4—2441no—
160C2×C4D4×D6111yescharacteristic
161C2×C4D4×D6111yescharacteristic
162C2×C4C2×C22⋊D6111yescharacteristic
163C8—41no—
164C8—2441no—
165C8—2441no—
166C22—41no—
167C22—41no—
168C22—41no—
169C22—2441no—
170C22—2441no—
171C22—2441no—
172C22#1451974511yescharacteristic
173C4—21no—
174C4—41no—
175C4—81no—
176C4—2442no—
177C4—2441no—
178C4#1451979611yescharacteristic
179C4#1451979711yescharacteristic
180C4#1451980111yescharacteristic
181C4#1451980811yescharacteristic
182C2—81no—
183C2—4881no—
184C2#1683990411yescharacteristic
185C2#1683992211yescharacteristic
186C2#1683993811yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#474C2
socleC22×C61#120
hypercenter#474D61
hypocenterC61#1646
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
2. #16840114C2semidirect
3. #16839964C2semidirect
4. #16839510C2semidirect
5. D4⋊#92418C2semidirect
6. #16839489C2semidirect
7. C61×#474C2semidirect
96. #474D61semidirect
101. C61#1646semidirect