Finite Group Databasebeta

← #21446495

Subgroups — #21446495

Order 7808.

256 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 101 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×#14519702C211yesmaximal, characteristic
2C2×#14519702C211yesmaximal, characteristic
3#16839668C211yesmaximal, characteristic
4#16839660C211yesmaximal, characteristic
5#16839525C211yesmaximal, characteristic
6#16839525C211yesmaximal, characteristic
7C2×C4×C8×C61C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic
9C2×C4⋊Dic61C2211yescharacteristic
10C2×C4⋊Dic61C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12C2×#11758196—21no—
13#14519702—22no—
14#14519702C414yescomplemented
15#14519684—21no—
16#14519684—21no—
17#14519684—21no—
18C22×C8×C61C2211yescharacteristic
19C22×C8×C61C2211yescharacteristic
20C2×C42×C61C2211yescharacteristic
21C4×C8×C61—22no—
22C22×C4×C61D411yescharacteristic
23C22×C4×C61D411yescharacteristic
24C22×C4×C61C2311yescharacteristic
25C22×Dic61—21no—
26C22×Dic61—21no—
27C22×Dic61—21no—
28C22×Dic61—21no—
29C2×Dic122—21no—
30C2×Dic122—21no—
31C2×Dic122—21no—
32C2×Dic122—21no—
33C2×Dic122—21no—
34C2×Dic122C2×C412yes—
35C2×C8×C61—21no—
36C2×C8×C61—21no—
37C2×C8×C61—21no—
38C2×C8×C61—21no—
39C2×C8×C61C2×C412yes—
40C2×C8×C61D412yes—
41C42×C61—21no—
42C42×C61—21no—
43C4⋊Dic61—21no—
44C4⋊Dic61—21no—
45C4⋊Dic61—21no—
46C4⋊Dic61—21no—
47C4⋊Dic61—21no—
48C4⋊Dic61C2×C412yes—
49#11758196—42no—
50C23×C61C2×D411yescharacteristic
51C2×C4×C61—21no—
52C2×C4×C61—21no—
53C2×C4×C61—21no—
54C2×C4×C61—21no—
55C2×C4×C61SD1612yes—
56C2×C4×C61Q1612yes—
57C2×C4×C61C22×C411yescharacteristic
58C2×C4×C61C2×D411yescharacteristic
59C2×C4×C61#4111yescharacteristic
60C2×C4×C61#4111yescharacteristic
61C2×C4×C61#4111yescharacteristic
62C2×C4×C61#4111yescharacteristic
63C2×Dic61—22no—
64C2×Dic61—22no—
65C2×Dic61—41no—
66C2×Dic61—41no—
67C2×Dic61—41no—
68C2×Dic61—41no—
69C2×Dic61—41no—
70C2×Dic61—41no—
71C2×Dic61—41no—
72C2×Dic61—41no—
73C2×Dic61—41no—
74C2×Dic61—41no—
75Dic122—22no—
76Dic122—22no—
77Dic122—41no—
78Dic122—41no—
79C8×C61—22no—
80C8×C61—22no—
81C22×C61C4×D411yescharacteristic
82C22×C61#12111yescharacteristic
83C22×C61#12411yescharacteristic
84C22×C61C2×SD1611yescharacteristic
85C22×C61C2×Q1611yescharacteristic
86C22×C61#13511yescharacteristic
87C22×C61#13511yescharacteristic
88C4×C61—22no—
89C4×C61—22no—
90C4×C61#11711yescharacteristic
91C4×C61C4×D411yescharacteristic
92C4×C61#12311yescharacteristic
93C4×C61#12611yescharacteristic
94Dic61—42no—
95Dic61—42no—
96Dic61—81no—
97Dic61—81no—
98#1933—611nomaximal, Sylow
99C2×C61#38811yescharacteristic
100C2×C61C4×SD1611yescharacteristic
101C2×C61C4×Q1611yescharacteristic
102C2×C61#46511yescharacteristic
103C2×C61#46711yescharacteristic
104C2×C61#48711yescharacteristic
105C2×C61#48811yescharacteristic
106C2×#103—611no—
107C2×#103—611no—
108C2×C4×C8D6111yescharacteristic
109#391—611no—
110#389—611no—
111#340—611no—
112#340—611no—
113C61#193311yescharacteristic, complemented, Sylow
114C22×Q8—611no—
115C22×C8C2×D6111yescharacteristic
116C22×C8C2×D6111yescharacteristic
117C2×C4⋊C4—611no—
118C2×C4⋊C4—611no—
119C2×C4⋊C4—611no—
120C2×C4⋊C4—1221no—
121C2×C42C2×D6111yescharacteristic
122#103—614no—
123#103—1222no—
124C4×C8—22no—
125#95—1221no—
126#95—1221no—
127#95—1221no—
128C2×Q8—612no—
129C2×Q8—1221no—
130C2×Q8—1221no—
131C2×Q8—1221no—
132C2×Q8—1221no—
133C2×Q8—1221no—
134C22×C4—1221no—
135C22×C4—1221no—
136C22×C4—1221no—
137C22×C4—1221no—
138C22×C4D24411yescharacteristic
139C22×C4D24411yescharacteristic
140C22×C4C22×D6111yescharacteristic
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—21no—
144C2×C8—21no—
145C2×C8C4×D6112yes—
146C2×C8C22⋊D6112yes—
147C4⋊C4—612no—
148C4⋊C4—1221no—
149C4⋊C4—1221no—
150C4⋊C4—1221no—
151C4⋊C4—1221no—
152C4⋊C4—1221no—
153C4⋊C4—2442no—
154C42—21no—
155C42—21no—
156C23C2×D24411yescharacteristic
157Q8—1222no—
158Q8—1222no—
159Q8—2441no—
160Q8—2441no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—1222no—
166C2×C4—1222no—
167C2×C4—2441no—
168C2×C4—2441no—
169C2×C4—2441no—
170C2×C4—2441no—
171C2×C4—2441no—
172C2×C4—2441no—
173C2×C4—2441no—
174C2×C4—2441no—
175C2×C4—2441no—
176C2×C4—2441no—
177C2×C4#1175819012yes—
178C2×C4Dic24412yes—
179C2×C4C2×C4×D6111yescharacteristic
180C2×C4#1175822211yescharacteristic
181C2×C4#1175822211yescharacteristic
182C2×C4#1175822211yescharacteristic
183C2×C4#1175822211yescharacteristic
184C2×C4C2×C22⋊D6111yescharacteristic
185C8—22no—
186C8—22no—
187C22C4×D24411yescharacteristic
188C22#1451975111yescharacteristic
189C22#1451976511yescharacteristic
190C22C2×#1175819011yescharacteristic
191C22C2×Dic24411yescharacteristic
192C22#1451979911yescharacteristic
193C22#1451979911yescharacteristic
194C4—22no—
195C4—22no—
196C4—4881no—
197C4—4881no—
198C4—2442no—
199C4—2442no—
200C4#1451973411yescharacteristic
201C4C4×C22⋊D6111yescharacteristic
202C4#1451976011yescharacteristic
203C4#1451977111yescharacteristic
204C2#1683965311yescharacteristic
205C2C4×#1175819011yescharacteristic
206C2C4×Dic24411yescharacteristic
207C2#1683999111yescharacteristic
208C2#1684000311yescharacteristic
209C2#1684011311yescharacteristic
210C2#1684011711yescharacteristic
subgroupG/H
centerC23C2×D244
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×C4×C8×C61C2
socleC23×C61C2×D4
hypercenterC2×C4×C8D61
hypocenterC61#1933
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
14. #14519702C4semidirect
113. C61#1933semidirect