Finite Group Databasebeta

← #21446493

Subgroups — #21446493

Order 7808.

256 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 93 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×#14519700C211yesmaximal, characteristic
3C2×C8×Dic61C211yesmaximal, characteristic
4#16839667C211yesmaximal, characteristic
5#16839658C211yesmaximal, characteristic
6#16839524C211yesmaximal, characteristic
7C61×#340C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic
9C22×#92418C2211yescharacteristic
10C2×C4⋊Dic61C2211yescharacteristic
11C2×#11758196—21no—
12C2×C4×Dic61C2211yescharacteristic
13#14519702C414yescomplemented
14#14519700—22no—
15C8×Dic61—22no—
16#14519684—21no—
17#14519684—21no—
18#14519684—21no—
19C22×C8×C61C2211yescharacteristic
20C2×C4⋊C4×C61C2211yescharacteristic
21C2×C4⋊C4×C61C2211yescharacteristic
22C22×C4×C61—21no—
23C22×C4×C61—21no—
24C22×C4×C61C2311yescharacteristic
25C22×Dic61—21no—
26C22×Dic61—21no—
27C22×Dic61D411yescharacteristic
28C22×Dic61D411yescharacteristic
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×C61C2×C412yes—
38C4⋊C4×C61—21no—
39C4⋊C4×C61—21no—
40C4⋊C4×C61—21no—
41C4⋊C4×C61—21no—
42C4⋊Dic61—21no—
43C4⋊Dic61C2×C412yes—
44#11758196—42no—
45C4×Dic61—21no—
46C4×Dic61—21no—
47C2×#92418—21no—
48C2×#92418—21no—
49C2×#92418D412yes—
50C23×C61C2×D411yescharacteristic
51C2×C4×C61—41no—
52C2×C4×C61—41no—
53C2×C4×C61—41no—
54C2×C4×C61—41no—
55C2×C4×C61—41no—
56C2×C4×C61—41no—
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—21no—
64C2×Dic61—21no—
65C2×Dic61—21no—
66C2×Dic61—21no—
67C2×Dic61—22no—
68C2×Dic61—22no—
69C2×Dic61—41no—
70C2×Dic61—41no—
71C2×Dic61—41no—
72C2×Dic61—41no—
73C2×Dic61SD1612yes—
74C2×Dic61Q1612yes—
75Dic122—22no—
76Dic122—22no—
77Dic122—41no—
78Dic122—41no—
79C8×C61—22no—
80#92418—22no—
81C22×C61C4×D411yescharacteristic
82C22×C61#12111yescharacteristic
83C22×C61#12411yescharacteristic
84C22×C61C2×SD1611yescharacteristic
85C22×C61C2×Q1611yescharacteristic
86C22×C61#13511yescharacteristic
87C22×C61#13511yescharacteristic
88C4×C61—81no—
89C4×C61—81no—
90C4×C61#11711yescharacteristic
91C4×C61C4×D411yescharacteristic
92C4×C61#12311yescharacteristic
93C4×C61#12611yescharacteristic
94Dic61—22no—
95Dic61—22no—
96Dic61—42no—
97Dic61—42no—
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×C8—611no—
109#391—611no—
110#389—611no—
111#340—611no—
112#340D6111yescharacteristic
113C61#193311yescharacteristic, complemented, Sylow
114C22×Q8—611no—
115C22×C8—611no—
116C22×C8C2×D6111yescharacteristic
117C2×C4⋊C4—611no—
118C2×C4⋊C4—1221no—
119C2×C4⋊C4C2×D6111yescharacteristic
120C2×C4⋊C4C2×D6111yescharacteristic
121C2×C42—611no—
122#103—614no—
123#103—1222no—
124C4×C8—1222no—
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—21no—
135C22×C4—21no—
136C22×C4—611no—
137C22×C4—611no—
138C22×C4—1221no—
139C22×C4—1221no—
140C22×C4C22×D6111yescharacteristic
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—612no—
144C2×C8—1221no—
145C2×C8—1221no—
146C2×C8C4×D6112yes—
147C4⋊C4—21no—
148C4⋊C4—21no—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—612no—
152C4⋊C4—1221no—
153C4⋊C4—2442no—
154C42—1221no—
155C42—1221no—
156C23D4×D6111yescharacteristic
157Q8—1222no—
158Q8—1222no—
159Q8—2441no—
160Q8—2441no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—612no—
168C2×C4—612no—
169C2×C4—1221no—
170C2×C4—1221no—
171C2×C4—1221no—
172C2×C4—1221no—
173C2×C4—1222no—
174C2×C4—1222no—
175C2×C4—2441no—
176C2×C4—2441no—
177C2×C4—2441no—
178C2×C4—2441no—
179C2×C4C2×C4×D6111yescharacteristic
180C2×C4#1175822211yescharacteristic
181C2×C4#1175822211yescharacteristic
182C2×C4D4×D6111yescharacteristic
183C2×C4#1175822411yescharacteristic
184C2×C4#1175822611yescharacteristic
185C8—22no—
186C8—1222no—
187C22#1451973911yescharacteristic
188C22#1451975011yescharacteristic
189C22#1451976311yescharacteristic
190C22SD16×D6111yescharacteristic
191C22Q16×D6111yescharacteristic
192C22#1451979611yescharacteristic
193C22#1451979811yescharacteristic
194C4—81no—
195C4—81no—
196C4—1222no—
197C4—1222no—
198C4—2442no—
199C4—2442no—
200C4#1451973411yescharacteristic
201C4#1451973711yescharacteristic
202C4#1451976211yescharacteristic
203C4#1451977211yescharacteristic
204C2#1683965111yescharacteristic
205C2#1683984911yescharacteristic
206C2#1683985611yescharacteristic
207C2#1683999011yescharacteristic
208C2#1684000211yescharacteristic
209C2#1684011111yescharacteristic
210C2#1684011511yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#340C2
socleC23×C61C2×D4
hypercenter#340D61
hypocenterC61#1933
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
13. #14519702C4semidirect
113. C61#1933semidirect