Finite Group Databasebeta

← #21444862

Subgroups — #21444862

Order 7808.

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

normal subgroups only

This group has 202 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#16840098C211yesmaximal, characteristic
3#16840095C211yesmaximal, characteristic
4#16839702C211yesmaximal, 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⋊Dic61C2211yescharacteristic
16C2×#11758196C2211yescharacteristic
17#14519711—21no—
18#14519710—21no—
19#14519702—21no—
20#14519701—21no—
21C22⋊#92418C2211yescharacteristic
22#14519684—21no—
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⋊Dic61D411yescharacteristic
44#11758196—21no—
45#11758196—21no—
46#11758196—21no—
47#11758196—21no—
48#11758196—21no—
49#11758196—21no—
50#11758196—21no—
51C4×Dic61—21no—
52C4×Dic61—21no—
53C2×#92418—21no—
54C23×C61C2×D411yescharacteristic
55Q8×C61—41no—
56C2×C4×C61—21no—
57C2×C4×C61—21no—
58C2×C4×C61—41no—
59C2×C4×C61—41no—
60C2×C4×C61—41no—
61C2×C4×C61—41no—
62C2×C4×C61C2×D411yescharacteristic
63C2×C4×C61C2×D411yescharacteristic
64C2×Dic61—21no—
65C2×Dic61—21no—
66C2×Dic61—21no—
67C2×Dic61—21no—
68C2×Dic61—21no—
69C2×Dic61—41no—
70C2×Dic61—42no—
71C2×Dic61—41no—
72C2×Dic61Q1612yes—
73Dic122—41no—
74Dic122—81no—
75C8×C61—41no—
76#92418—41no—
77C22×C61—21no—
78C22×C61—21no—
79C22×C61#12011yescharacteristic
80C22×C61C2×Q1611yescharacteristic
81C22×C61#13711yescharacteristic
82C4×C61—21no—
83C4×C61—21no—
84C4×C61—41no—
85C4×C61—41no—
86C4×C61—81no—
87Dic61—22no—
88Dic61—41no—
89Dic61—41no—
90Dic61—41no—
91Dic61—81no—
92#1617—611nomaximal, Sylow
93C2×C61—21no—
94C2×C61—21no—
95C2×C61#45111yescharacteristic
96C2×C61#45411yescharacteristic
97C2×C61#45811yescharacteristic
98#544—611no—
99#484—611no—
100#484—611no—
101#400—611no—
102#328—611no—
103#328D6111yescharacteristic
104#324—611no—
105C61#161711yescharacteristic, complemented, Sylow
106C4⋊Q8—1221no—
107C4⋊Q8—1221no—
108#125—1221no—
109#125—1221no—
110C22⋊Q8—611no—
111C22⋊Q8—1221no—
112C22⋊Q8C2×D6111yescharacteristic
113#117—1221no—
114C2×C4⋊C4—611no—
115C2×C4⋊C4—611no—
116#107—1221no—
117#107—1221no—
118#103—1221no—
119#103—1221no—
120C22⋊C8—611no—
121C22⋊C8C2×D6111yescharacteristic
122#95—1221no—
123#95—1221no—
124#95C2×D6111yescharacteristic
125C2×Q8—611no—
126C2×Q8—1221no—
127C2×Q8D24411yescharacteristic
128C22×C4—21no—
129C22×C4—611no—
130C22×C4—611no—
131C22×C4—1221no—
132C22×C4C22×D6111yescharacteristic
133C2×C8—21no—
134C2×C8—1221no—
135C4⋊C4—21no—
136C4⋊C4—611no—
137C4⋊C4—1221no—
138C4⋊C4—1221no—
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⋊C4D24411yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—1221no—
150C42—1221no—
151C42—1221no—
152C23D4×D6111yescharacteristic
153Q8—41no—
154Q8—4881no—
155Q8—2441no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—612no—
163C2×C4—1221no—
164C2×C4—1221no—
165C2×C4—1221no—
166C2×C4—1221no—
167C2×C4—1221no—
168C2×C4—2442no—
169C2×C4—2441no—
170C2×C4—2441no—
171C2×C4C2×D24411yescharacteristic
172C2×C4D4×D6111yescharacteristic
173C8—41no—
174C8—2441no—
175C22—21no—
176C22—21no—
177C22#1451974711yescharacteristic
178C22Q16×D6111yescharacteristic
179C22#1451980611yescharacteristic
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—81no—
185C4—1222no—
186C4—4881no—
187C4—2441no—
188C4—2441no—
189C4—2441no—
190C2—21no—
191C2—21no—
192C2#1683991911yescharacteristic
193C2#1683993611yescharacteristic
194C2#1683995311yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#328C2
socleC22×C61#120
hypercenter#328D61
hypocenterC61#1617
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
105. C61#1617semidirect