Finite Group Databasebeta

← #21446474

Subgroups — #21446474

Order 7808.

212 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 77 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#16839805C211yesmaximal, characteristic
2#16839770C211yesmaximal, characteristic
3C2×#14519702C211yesmaximal, characteristic
4C2×#14519695C211yesmaximal, characteristic
5#16839530C211yesmaximal, characteristic
6#16839527C211yesmaximal, characteristic
7C61×#405C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic
9C2×#11758194C2211yescharacteristic
10C2×#11758194C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12#14519710—21no—
13#14519708—21no—
14#14519702—21no—
15#14519702—21no—
16#14519700—21no—
17#14519700—21no—
18#14519695C414yescomplemented
19C2×M16×C61C2211yescharacteristic
20C22×C8×C61C2211yescharacteristic
21#117×C61C2211yescharacteristic
22#97×C61—21no—
23C4×C8×C61—21no—
24C22×C4×C61C2311yescharacteristic
25C22×Dic61—21no—
26C22×Dic61—21no—
27C2×Dic122—21no—
28C2×Dic122—21no—
29C2×Dic122—21no—
30C2×Dic122—21no—
31C2×Dic122—21no—
32C2×Dic122C2×C412yes—
33M16×C61—21no—
34M16×C61C2×C412yes—
35C2×C8×C61—21no—
36C2×C8×C61—21no—
37C2×C8×C61—21no—
38C2×C8×C61D411yescharacteristic
39C2×C8×C61D411yescharacteristic
40C4⋊C4×C61D411yescharacteristic
41C4⋊C4×C61D411yescharacteristic
42C22⋊C4×C61—21no—
43C42×C61—21no—
44C4⋊Dic61—21no—
45C4⋊Dic61—21no—
46#11758194—21no—
47#11758194—21no—
48#11758194—21no—
49#11758194C2×C412yes—
50C2×#92418—21no—
51C2×#92418—21no—
52C23×C61#4111yescharacteristic
53C2×C4×C61—21no—
54C2×C4×C61—21no—
55C2×C4×C61C22×C411yescharacteristic
56C2×C4×C61C2×D411yescharacteristic
57C2×C4×C61C2×D411yescharacteristic
58C2×C4×C61#4111yescharacteristic
59C2×C4×C61#4111yescharacteristic
60C2×C4×C61#4111yescharacteristic
61C2×Dic61—22no—
62C2×Dic61—41no—
63C2×Dic61—41no—
64C2×Dic61—41no—
65C2×Dic61—81no—
66Dic122—22no—
67Dic122—22no—
68Dic122—41no—
69Dic122—41no—
70C8×C61—22no—
71C8×C61—21no—
72C8×C61—21no—
73#92418—22no—
74#92418—41no—
75C22×C61—21no—
76C22×C61—21no—
77C22×C61#11711yescharacteristic
78C22×C61#12111yescharacteristic
79C22×C61#12611yescharacteristic
80C4×C61—41no—
81C4×C61—41no—
82C4×C61C4×D411yescharacteristic
83C4×C61C4×D411yescharacteristic
84C4×C61#12311yescharacteristic
85C4×C61#12411yescharacteristic
86Dic61—42no—
87Dic61—81no—
88#1930—611nomaximal, Sylow
89C2×C61—21no—
90C2×C61—21no—
91C2×C61#38811yescharacteristic
92C2×C61#47111yescharacteristic
93C2×C61#47311yescharacteristic
94#428—611no—
95#419—611no—
96C2×#103—611no—
97C2×#101—611no—
98#405D6111yescharacteristic
99#343—611no—
100#341—611no—
101C61#193011yescharacteristic, complemented, Sylow
102C22×Q8—611no—
103C2×M16—611no—
104C2×M16—611no—
105C2×M16C2×D6111yescharacteristic
106C22×C8C2×D6111yescharacteristic
107#117C2×D6111yescharacteristic
108C2×C4⋊C4—611no—
109#107—1221no—
110#106—1221no—
111#103—1221no—
112#103—1221no—
113#103—1221no—
114#103—1221no—
115#101—614no—
116#97—21no—
117C4×C8—21no—
118C2×Q8—612no—
119C2×Q8—1221no—
120C2×Q8—1221no—
121C2×Q8—1221no—
122C2×Q8—1221no—
123C2×Q8—1221no—
124C22×C4—1221no—
125C22×C4—1221no—
126C22×C4C22×D6111yescharacteristic
127M16—21no—
128M16—612no—
129M16—1221no—
130M16—1221no—
131M16—1221no—
132M16C4×D6112yes—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—1221no—
137C2×C8—1221no—
138C2×C8C22⋊D6111yescharacteristic
139C2×C8C22⋊D6111yescharacteristic
140C4⋊C4—1221no—
141C4⋊C4—1221no—
142C4⋊C4D24411yescharacteristic
143C4⋊C4D24411yescharacteristic
144C22⋊C4—21no—
145C42—21no—
146C23#1175822211yescharacteristic
147Q8—1222no—
148Q8—1222no—
149Q8—2441no—
150Q8—2441no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—1222no—
154C2×C4—4881no—
155C2×C4—2441no—
156C2×C4—2441no—
157C2×C4—2441no—
158C2×C4C2×C4×D6111yescharacteristic
159C2×C4C2×D24411yescharacteristic
160C2×C4#1175822211yescharacteristic
161C2×C4#1175822211yescharacteristic
162C2×C4#1175822211yescharacteristic
163C2×C4C2×C22⋊D6111yescharacteristic
164C8—22no—
165C8—21no—
166C8—21no—
167C8—1222no—
168C8—2441no—
169C22—21no—
170C22—21no—
171C22#1451973411yescharacteristic
172C22#1451975111yescharacteristic
173C22#1451977111yescharacteristic
174C4—41no—
175C4—41no—
176C4—4881no—
177C4—2442no—
178C4C4×C22⋊D6111yescharacteristic
179C4C4×D24411yescharacteristic
180C4#1451976011yescharacteristic
181C4#1451976511yescharacteristic
182C2—21no—
183C2—21no—
184C2#1683965311yescharacteristic
185C2#1684002511yescharacteristic
186C2#1684003711yescharacteristic
subgroupG/H
centerC22#14519751
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#405C2
socleC22×C61#121
hypercenter#405D61
hypocenterC61#1930
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #405

Complements

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

NH ≅ G/Ntype
18. #14519695C4semidirect
101. C61#1930semidirect