Finite Group Databasebeta

← #21446969

Subgroups — #21446969

Order 7808.

258 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#14519768C211yesmaximal, characteristic
2C2×#14519702C211yesmaximal, characteristic
3C2×#14519700C211yesmaximal, characteristic
4#16839667C211yesmaximal, characteristic
5#16839524C211yesmaximal, characteristic
6#16839516C211yesmaximal, characteristic
7C61×#340C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic
9C22×#92418C2211yescharacteristic
10#14519768—22no—
11#14519768—22no—
12C2×C4⋊Dic61—21no—
13C2×C4⋊Dic61C2211yescharacteristic
14C2×#11758196—21no—
15C2×C4×Dic61C2211yescharacteristic
16#14519702—22no—
17#14519700—22no—
18#14519684—21no—
19#14519684—21no—
20C22×C8×C61C2211yescharacteristic
21C2×C4⋊C4×C61C2211yescharacteristic
22C2×C4⋊C4×C61C2211yescharacteristic
23C22×C4×C61—21no—
24C22×C4×C61—21no—
25C22×C4×C61C2311yescharacteristic
26C22×Dic61—21no—
27C22×Dic61—21no—
28C22×Dic61D411yescharacteristic
29C22×Dic61D411yescharacteristic
30C2×Dic122—21no—
31C2×Dic122—21no—
32C2×Dic122—21no—
33C2×Dic122—21no—
34C2×Dic122—21no—
35C2×Dic122Q812yes—
36C2×C8×C61—21no—
37C2×C8×C61—21no—
38C2×C8×C61—21no—
39C4⋊C4×C61—21no—
40C4⋊C4×C61—21no—
41C4⋊C4×C61—21no—
42C4⋊C4×C61D412yes—
43C4⋊Dic61—24no—
44C4⋊Dic61—21no—
45C4⋊Dic61D412yes—
46#11758196—24no—
47C4×Dic61—21no—
48C4×Dic61—21no—
49C2×#92418—21no—
50C2×#92418—21no—
51C2×#92418—21no—
52C23×C61C2×D411yescharacteristic
53C2×C4×C61—22no—
54C2×C4×C61—41no—
55C2×C4×C61—41no—
56C2×C4×C61—41no—
57C2×C4×C61—41no—
58C2×C4×C61—41no—
59C2×C4×C61C2×D411yescharacteristic
60C2×C4×C61C2×D411yescharacteristic
61C2×C4×C61C2×Q811yescharacteristic
62C2×C4×C61#4111yescharacteristic
63C2×C4×C61#4111yescharacteristic
64C2×C4×C61#4111yescharacteristic
65C2×Dic61—21no—
66C2×Dic61—21no—
67C2×Dic61—22no—
68C2×Dic61—22no—
69C2×Dic61—21no—
70C2×Dic61—21no—
71C2×Dic61—21no—
72C2×Dic61—21no—
73C2×Dic61—41no—
74C2×Dic61—41no—
75C2×Dic61—41no—
76C2×Dic61—41no—
77Dic122—22no—
78Dic122—22no—
79Dic122—41no—
80Dic122—41no—
81C8×C61—41no—
82#92418—41no—
83C22×C61#12011yescharacteristic
84C22×C61C22⋊Q811yescharacteristic
85C22×C61#12411yescharacteristic
86C22×C61#13511yescharacteristic
87C22×C61#13511yescharacteristic
88C22×C61#13711yescharacteristic
89C22×C61#13711yescharacteristic
90C4×C61—42no—
91C4×C61—81no—
92C4×C61C22⋊Q811yescharacteristic
93C4×C61C22⋊Q811yescharacteristic
94C4×C61#12411yescharacteristic
95C4×C61#12411yescharacteristic
96Dic61—42no—
97Dic61—41no—
98Dic61—41no—
99Dic61—42no—
100#2026—611nomaximal, Sylow
101C2×C61#39311yescharacteristic
102C2×C61#45211yescharacteristic
103C2×C61#45211yescharacteristic
104C2×C61#47911yescharacteristic
105C2×C61#47911yescharacteristic
106C2×C61#48811yescharacteristic
107C2×C61#49111yescharacteristic
108C2×#125—611no—
109C2×#103—611no—
110C2×#103—611no—
111#391—611no—
112#340—611no—
113#340D6111yescharacteristic
114#336—611no—
115C61#202611yescharacteristic, complemented, Sylow
116C22×Q8—611no—
117C22×C8—611no—
118C22×C8C2×D6111yescharacteristic
119#125—1222no—
120#125—1222no—
121C2×C4⋊C4—611no—
122C2×C4⋊C4—1221no—
123C2×C4⋊C4—1221no—
124C2×C4⋊C4C2×D6111yescharacteristic
125C2×C4⋊C4C2×D6111yescharacteristic
126C2×C42—611no—
127#103—1222no—
128#103—1222no—
129#95—1221no—
130#95—1221no—
131C2×Q8—612no—
132C2×Q8—1221no—
133C2×Q8—1221no—
134C2×Q8—1221no—
135C2×Q8—1221no—
136C2×Q8—1221no—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—611no—
140C22×C4—611no—
141C22×C4—1221no—
142C22×C4—1221no—
143C22×C4C22×D6111yescharacteristic
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8—1221no—
148C2×C8—1221no—
149C2×C8—1221no—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—612no—
154C4⋊C4—1224no—
155C4⋊C4—1224no—
156C4⋊C4—1221no—
157C4⋊C4D24412yes—
158C42—1221no—
159C42—1221no—
160C23D4×D6111yescharacteristic
161Q8—1222no—
162Q8—1222no—
163Q8—2441no—
164Q8—2441no—
165C2×C4—22no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—1221no—
172C2×C4—1221no—
173C2×C4—1221no—
174C2×C4—1222no—
175C2×C4—1222no—
176C2×C4—1221no—
177C2×C4—1221no—
178C2×C4—1221no—
179C2×C4—2441no—
180C2×C4—2441no—
181C2×C4—2441no—
182C2×C4—2441no—
183C2×C4C2×D24411yescharacteristic
184C2×C4#1175822211yescharacteristic
185C2×C4#1175822211yescharacteristic
186C2×C4D4×D6111yescharacteristic
187C2×C4#1175822411yescharacteristic
188C2×C4Q8×D6111yescharacteristic
189C8—41no—
190C8—2441no—
191C22#1451974711yescharacteristic
192C22#1451975511yescharacteristic
193C22#1451976311yescharacteristic
194C22#1451979611yescharacteristic
195C22#1451979811yescharacteristic
196C22#1451980611yescharacteristic
197C22#1451980911yescharacteristic
198C4—42no—
199C4—81no—
200C4—2441no—
201C4—2441no—
202C4—2442no—
203C4—2442no—
204C4#1451975511yescharacteristic
205C4#1451975711yescharacteristic
206C4#1451976311yescharacteristic
207C4#1451976511yescharacteristic
208C2#1683967511yescharacteristic
209C2#1683992511yescharacteristic
210C2#1683992711yescharacteristic
211C2#1684006811yescharacteristic
212C2#1684007211yescharacteristic
213C2#1684011511yescharacteristic
214C2#1684012911yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#340C2
socleC23×C61C2×D4
hypercenter#340D61
hypocenterC61#2026
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
115. C61#2026semidirect