Finite Group Databasebeta

← #21445156

Subgroups — #21445156

Order 7808.

184 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 45 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#16840512C211yesmaximal, characteristic
2#16840171C211yesmaximal, characteristic, complemented
3#16840131C211yesmaximal, characteristic, complemented
4#16840121C211yesmaximal, characteristic
5#16839503C211yesmaximal, characteristic, complemented
6#16839503C211yesmaximal, characteristic, complemented
7C61×#329C211yesmaximal, characteristic
8#14519777C2211yescharacteristic
9#14519775—21no—
10#14519770—21no—
11#14519770—21no—
12#14519769C2211yescharacteristic
13#14519769C2211yescharacteristic
14#14519758—21no—
15#14519754—21no—
16#14519754—21no—
17#14519711—21no—
18#14519709—21no—
19#14519702—21no—
20#14519702—21no—
21#14519701—21no—
22#14519698—21no—
23#14519688C2211yescharacteristic
24#124×C61C2211yescharacteristic
25#97×C61C2211yescharacteristic
26#97×C61C2211yescharacteristic
27C2×Q8×C61D411yescharacteristic
28C2×D4×C61D411yescharacteristic
29C22×Dic61—21no—
30C2×Dic122—21no—
31C2×Dic122—21no—
32C2×C8×C61—21no—
33C2×C8×C61—21no—
34C22⋊C4×C61—21no—
35C22⋊C4×C61—21no—
36C42×C61C2311yescharacteristic
37C22⋊Dic61—21no—
38C22⋊Dic61—21no—
39C22⋊Dic61—21no—
40C4⋊Dic61—21no—
41C4⋊Dic61—21no—
42C4⋊Dic61D411yescharacteristic
43C4⋊Dic61D411yescharacteristic
44C4⋊Dic61D411yescharacteristic
45C4⋊Dic61D411yescharacteristic
46#11758196—21no—
47#11758196—21no—
48#11758196—21no—
49#11758196—21no—
50#11758196—21no—
51#11758196—21no—
52C4×Dic61—21no—
53C2×#92418—21no—
54C23×C61—21no—
55Q8×C61—41no—
56D4×C61—41no—
57C2×C4×C61—21no—
58C2×C4×C61C2×D411yescharacteristic
59C2×C4×C61C2×D411yescharacteristic
60C2×C4×C61C2×D411yescharacteristic
61C2×Dic61—21no—
62C2×Dic61—21no—
63C2×Dic61—21no—
64C2×Dic61—21no—
65C2×Dic61—41no—
66C2×Dic61—81no—
67Dic122—42no—
68Dic122—81no—
69C8×C61—22no—
70C8×C61—41no—
71#92418—41no—
72C22×C61—41no—
73C22×C61—41no—
74C22×C61—41no—
75C22×C61#12011yescharacteristic
76C4×C61—21no—
77C4×C61—21no—
78C4×C61—21no—
79C4×C61—41no—
80Dic61—41no—
81Dic61—41no—
82Dic61—41no—
83Dic61—41no—
84Dic61—81no—
85#1664—611nomaximal, Sylow
86C2×C61—81no—
87C2×C61#45411yescharacteristic
88C2×C61#45511yescharacteristic
89C2×C61#45611yescharacteristic
90#563—611no—
91#501—611no—
92#491—611no—
93#489—611no—
94#330—611no—
95#330—611no—
96#329D6111yescharacteristic
97C61#166411yescharacteristic, complemented, Sylow
98C4⋊Q8—611no—
99C4⋊Q8—1221no—
100#126—1221no—
101#126—1221no—
102#125—611no—
103#125—611no—
104#124C2×D6111yescharacteristic
105#123—1221no—
106C22⋊Q8—1221no—
107C22⋊Q8—1221no—
108#107—1221no—
109#106—1221no—
110#103—1221no—
111#103—1221no—
112#103—1221no—
113#102—1221no—
114#97—611no—
115#97C2×D6111yescharacteristic
116#97C2×D6111yescharacteristic
117C2×Q8—1221no—
118C2×Q8—1221no—
119C2×Q8D24411yescharacteristic
120C2×D4D24411yescharacteristic
121C22×C4—1221no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8—1221no—
125C4⋊C4—611no—
126C4⋊C4—611no—
127C4⋊C4—611no—
128C4⋊C4—611no—
129C4⋊C4—1221no—
130C4⋊C4—1221no—
131C4⋊C4—1221no—
132C4⋊C4—1221no—
133C4⋊C4—1221no—
134C4⋊C4—1221no—
135C4⋊C4—1221no—
136C4⋊C4—1221no—
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—1221no—
140C22⋊C4—1221no—
141C22⋊C4—1221no—
142C42—1221no—
143C42C22×D6111yescharacteristic
144C23—21no—
145Q8—41no—
146Q8—4881no—
147Q8—2442no—
148D4—41no—
149C2×C4—21no—
150C2×C4—1221no—
151C2×C4—1221no—
152C2×C4—1221no—
153C2×C4—1221no—
154C2×C4—4881no—
155C2×C4—2441no—
156C2×C4C2×D24411yescharacteristic
157C2×C4D4×D6111yescharacteristic
158C2×C4D4×D6111yescharacteristic
159C8—22no—
160C8—41no—
161C8—2441no—
162C22—41no—
163C22—41no—
164C22—41no—
165C22#1451974711yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—4881no—
171C4—2441no—
172C4—2441no—
173C4—2441no—
174C4—2441no—
175C2—81no—
176C2#1683993611yescharacteristic
177C2#1683994211yescharacteristic
178C2#1683994611yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#329C2
socleC22×C61#120
hypercenter#329D61
hypocenterC61#1664
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #16840171C2semidirect
3. #16840131C2semidirect
5. #16839503C2semidirect
6. #16839503C2semidirect
97. C61#1664semidirect