Finite Group Databasebeta

← #21446974

Subgroups — #21446974

Order 7808.

282 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 67 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#16840390C211yesmaximal, characteristic, complemented
2#16839768C211yesmaximal, characteristic
3#16839766C211yesmaximal, characteristic
4#16839664C211yesmaximal, characteristic
5#16839530C211yesmaximal, characteristic, complemented
6#16839522C211yesmaximal, characteristic, complemented
7C61×#339C211yesmaximal, characteristic, complemented
8C22×D244C2211yescharacteristic
9C2×#11758194C2211yescharacteristic
10#14519777—21no—
11#14519776—21no—
12#14519769—21no—
13#14519768—21no—
14#14519754—22no—
15#14519736C2211yescharacteristic
16C2×C4⋊Dic61C2211yescharacteristic
17C2×#11758198—22no—
18#14519699—21no—
19#14519699—21no—
20#14519697—21no—
21#14519697—21no—
22C2×M16×C61C2211yescharacteristic
23#117×C61C2211yescharacteristic
24C2×C42×C61C2211yescharacteristic
25C23×D61—21no—
26C22×C4×C61—21no—
27C22×C4×C61C2311yescharacteristic
28C22×Dic61D412yes—
29C2×D244—21no—
30C2×D244—21no—
31C2×D244—21no—
32C2×D244—21no—
33C2×D244—21no—
34C2×D244Q812yescomplemented
35C2×Dic122—22no—
36M16×C61—21no—
37M16×C61—21no—
38C2×C8×C61—21no—
39C4⋊C4×C61D411yescharacteristic
40C4⋊C4×C61D411yescharacteristic
41C22⋊C4×C61—21no—
42C42×C61—21no—
43C42×C61—21no—
44C42×C61—21no—
45C22⋊Dic61—21no—
46#11758198—44no—
47C4⋊Dic61—22no—
48C4⋊Dic61—21no—
49C4⋊Dic61—21no—
50C4⋊Dic61D411yescharacteristic
51C4⋊Dic61D411yescharacteristic
52#11758196—22no—
53#11758196—22no—
54C4×Dic61—21no—
55#11758194—21no—
56#11758194—21no—
57C2×#92418—21no—
58C23×C61C2×D411yescharacteristic
59C22×D61—22no—
60C22×D61—42no—
61C22×D61—42no—
62C22×D61—41no—
63C22×D61—41no—
64C2×C4×C61—22no—
65C2×C4×C61—21no—
66C2×C4×C61—21no—
67C2×C4×C61—41no—
68C2×C4×C61—41no—
69C2×C4×C61C2×D411yescharacteristic
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2×Q811yescharacteristic
72C2×C4×C61#4111yescharacteristic
73C2×C4×C61#4111yescharacteristic
74C2×C4×C61#4111yescharacteristic
75C2×Dic61—21no—
76C2×Dic61—21no—
77C2×Dic61—22no—
78C2×Dic61—42no—
79D244—22no—
80D244—22no—
81D244—41no—
82D244—41no—
83Dic122—82no—
84C8×C61—41no—
85#92418—41no—
86C22×C61—21no—
87C22×C61—21no—
88C22×C61#12011yescharacteristic
89C22×C61C22⋊Q811yescharacteristic
90C22×C61#12411yescharacteristic
91C2×D61—44no—
92C2×D61—42no—
93C2×D61—82no—
94C2×D61—81no—
95C2×D61—81no—
96C4×C61—42no—
97C4×C61—41no—
98C4×C61—41no—
99C4×C61C22⋊Q811yescharacteristic
100C4×C61C22⋊Q811yescharacteristic
101C4×C61#12411yescharacteristic
102C4×C61#12411yescharacteristic
103Dic61—41no—
104Dic61—42no—
105Dic61—41no—
106#2027—611nomaximal, Sylow
107C2×C61—21no—
108C2×C61—21no—
109C2×C61#39311yescharacteristic
110C2×C61#45311yescharacteristic
111C2×C61#45411yescharacteristic
112D61—82no—
113#544—611no—
114#418—611no—
115#418—611no—
116#390—611no—
117#343—611no—
118#339—611no—
119#339D6111yescharacteristic, complemented
120C61#202711yescharacteristic, complemented, Sylow
121C22×D4—611no—
122C2×M16—611no—
123C2×M16C2×D6111yescharacteristic
124C4⋊Q8—1221no—
125C4⋊Q8—1221no—
126#125—1221no—
127#125—1221no—
128C22⋊Q8—1222no—
129#117—611no—
130#117C2×D6111yescharacteristic
131C2×C4⋊C4—611no—
132C2×C22⋊C4—1222no—
133C2×C42C2×D6111yescharacteristic
134#102—1221no—
135#102—1221no—
136#102—1221no—
137#102—1221no—
138C24—1221no—
139C2×Q8—1222no—
140C2×D4—612no—
141C2×D4—1221no—
142C2×D4—1221no—
143C2×D4—1221no—
144C2×D4—1221no—
145C2×D4—1221no—
146C22×C4—21no—
147C22×C4—612no—
148C22×C4C22×D6111yescharacteristic
149M16—21no—
150M16—21no—
151M16—1221no—
152M16—1221no—
153C2×C8—21no—
154C2×C8—1221no—
155C4⋊C4—611no—
156C4⋊C4—611no—
157C4⋊C4—1222no—
158C4⋊C4—1222no—
159C4⋊C4—1222no—
160C4⋊C4—1221no—
161C4⋊C4—1221no—
162C4⋊C4D24411yescharacteristic
163C4⋊C4D24411yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—1221no—
166C22⋊C4—2444no—
167C42—21no—
168C42—21no—
169C42—21no—
170C42—1221no—
171C23—1222no—
172C23—2442no—
173C23—2442no—
174C23—2441no—
175C23—2441no—
176C23D4×D6111yescharacteristic
177Q8—4882no—
178D4—1222no—
179D4—1222no—
180D4—2441no—
181D4—2441no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—1221no—
188C2×C4—1221no—
189C2×C4—1222no—
190C2×C4—2442no—
191C2×C4C2×D24411yescharacteristic
192C2×C4#1175822211yescharacteristic
193C2×C4#1175822211yescharacteristic
194C2×C4D4×D6111yescharacteristic
195C2×C4#1175822411yescharacteristic
196C2×C4Q8×D6111yescharacteristic
197C8—41no—
198C8—2441no—
199C22—21no—
200C22—21no—
201C22—4882no—
202C22—4881no—
203C22—4881no—
204C22—2444no—
205C22—2442no—
206C22#1451974711yescharacteristic
207C22#1451975511yescharacteristic
208C22#1451976311yescharacteristic
209C4—42no—
210C4—41no—
211C4—41no—
212C4—2441no—
213C4—2442no—
214C4—2441no—
215C4#1451975511yescharacteristic
216C4#1451975711yescharacteristic
217C4#1451976311yescharacteristic
218C4#1451976511yescharacteristic
219C2—21no—
220C2—21no—
221C2—4882no—
222C2#1683967511yescharacteristic
223C2#1683993111yescharacteristic
224C2#1683993611yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#339C2
socleC22×C61#120
hypercenter#339D61
hypocenterC61#2027
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. #16840390C2semidirect
5. #16839530C2semidirect
6. #16839522C2semidirect
7. C61×#339C2semidirect
34. C2×D244Q8semidirect
119. #339D61semidirect
120. C61#2027semidirect