Finite Group Databasebeta

← #21444828

Subgroups — #21444828

Order 7808.

210 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 51 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#16840391C211yesmaximal, characteristic
2#16840093C211yesmaximal, characteristic
3#16840090C211yesmaximal, characteristic
4#16839694C211yesmaximal, characteristic
5#16839498C211yesmaximal, characteristic
6#16839487C211yesmaximal, characteristic
7C61×#328C211yesmaximal, characteristic
8#14519776—21no—
9#14519775—21no—
10#14519767—21no—
11#14519767—21no—
12#14519756C2211yescharacteristic
13#14519754—21no—
14#14519733—21no—
15C2×C4⋊Dic61—21no—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×#11758196C2211yescharacteristic
18#14519709—21no—
19#14519708—21no—
20#14519702—21no—
21#14519701—21no—
22C22⋊#92418C2211yescharacteristic
23#14519684—21no—
24C22⋊Q8×C61C2211yescharacteristic
25C22⋊C8×C61C2211yescharacteristic
26#95×C61C2211yescharacteristic
27C2×Q8×C61D411yescharacteristic
28C22×C4×C61—21no—
29C22×C4×C61C2311yescharacteristic
30C22×Dic61—21no—
31C22×Dic61D411yescharacteristic
32C22×Dic61D411yescharacteristic
33C2×Dic122—21no—
34C2×Dic122D411yescharacteristic
35C2×C8×C61—21no—
36C4⋊C4×C61—21no—
37C4⋊C4×C61D411yescharacteristic
38C22⋊C4×C61—21no—
39C22⋊Dic61—21no—
40C4⋊Dic61—21no—
41C4⋊Dic61—21no—
42C4⋊Dic61—21no—
43C4⋊Dic61—42no—
44C4⋊Dic61D411yescharacteristic
45#11758196—21no—
46#11758196—21no—
47#11758196—21no—
48#11758196—21no—
49#11758196—21no—
50#11758196—21no—
51#11758196—21no—
52C4×Dic61—21no—
53C4×Dic61—21no—
54C2×#92418—21no—
55C23×C61C2×D411yescharacteristic
56Q8×C61—41no—
57C2×C4×C61—22no—
58C2×C4×C61—21no—
59C2×C4×C61—21no—
60C2×C4×C61—41no—
61C2×C4×C61—41no—
62C2×C4×C61—41no—
63C2×C4×C61C2×D411yescharacteristic
64C2×C4×C61C2×D411yescharacteristic
65C2×Dic61—21no—
66C2×Dic61—21no—
67C2×Dic61—21no—
68C2×Dic61—21no—
69C2×Dic61—21no—
70C2×Dic61—41no—
71C2×Dic61—41no—
72C2×Dic61—41no—
73C2×Dic61—41no—
74C2×Dic61SD1612yes—
75Dic122—41no—
76Dic122—81no—
77C8×C61—41no—
78#92418—41no—
79C22×C61—21no—
80C22×C61—21no—
81C22×C61#12011yescharacteristic
82C22×C61C2×SD1611yescharacteristic
83C22×C61#13711yescharacteristic
84C4×C61—21no—
85C4×C61—21no—
86C4×C61—42no—
87C4×C61—41no—
88C4×C61—41no—
89Dic61—22no—
90Dic61—41no—
91Dic61—41no—
92Dic61—41no—
93Dic61—81no—
94#1611—611nomaximal, Sylow
95C2×C61—21no—
96C2×C61—21no—
97C2×C61#44811yescharacteristic
98C2×C61#45611yescharacteristic
99C2×C61#45811yescharacteristic
100#544—611no—
101#483—611no—
102#483—611no—
103#398—611no—
104#328—611no—
105#328D6111yescharacteristic
106#324—611no—
107C61#161111yescharacteristic, complemented, Sylow
108C4⋊Q8—1221no—
109C4⋊Q8—1221no—
110#125—1221no—
111#125—1221no—
112C22⋊Q8—611no—
113C22⋊Q8—1221no—
114C22⋊Q8C2×D6111yescharacteristic
115#117—1221no—
116C2×C4⋊C4—611no—
117C2×C4⋊C4—611no—
118C2×C4⋊C4—1221no—
119#106—1221no—
120#106—1221no—
121#103—1221no—
122#103—1221no—
123C22⋊C8—611no—
124C22⋊C8C2×D6111yescharacteristic
125#95—1221no—
126#95C2×D6111yescharacteristic
127C2×Q8—611no—
128C2×Q8—1221no—
129C2×Q8D24411yescharacteristic
130C22×C4—21no—
131C22×C4—611no—
132C22×C4—611no—
133C22×C4—1221no—
134C22×C4C22×D6111yescharacteristic
135C2×C8—21no—
136C2×C8—1221no—
137C4⋊C4—21no—
138C4⋊C4—611no—
139C4⋊C4—1221no—
140C4⋊C4—1221no—
141C4⋊C4—1221no—
142C4⋊C4—1221no—
143C4⋊C4—1221no—
144C4⋊C4—1221no—
145C4⋊C4—1221no—
146C4⋊C4—1221no—
147C4⋊C4—1221no—
148C4⋊C4—1221no—
149C4⋊C4—2442no—
150C4⋊C4D24411yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—1221no—
153C42—1221no—
154C42—1221no—
155C23D4×D6111yescharacteristic
156Q8—41no—
157Q8—4881no—
158Q8—2441no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—612no—
166C2×C4—1221no—
167C2×C4—1221no—
168C2×C4—1221no—
169C2×C4—1221no—
170C2×C4—1221no—
171C2×C4—2441no—
172C2×C4—2441no—
173C2×C4—2441no—
174C2×C4—2441no—
175C2×C4C2×D24411yescharacteristic
176C2×C4D4×D6111yescharacteristic
177C8—41no—
178C8—2441no—
179C22—21no—
180C22—21no—
181C22#1451974711yescharacteristic
182C22SD16×D6111yescharacteristic
183C22#1451980911yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—41no—
188C4—41no—
189C4—1222no—
190C4—4881no—
191C4—2441no—
192C4—2441no—
193C4—2441no—
194C2—21no—
195C2—21no—
196C2#1683990211yescharacteristic
197C2#1683994611yescharacteristic
198C2#1683995311yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#328C2
socleC22×C61#120
hypercenter#328D61
hypocenterC61#1611
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
107. C61#1611semidirect