Finite Group Databasebeta

← #21447504

Subgroups — #21447504

Order 7808.

250 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 73 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#16839746C212yesmaximal, complemented
2#16839561C212yesmaximal, complemented
3#16839559C212yesmaximal, complemented
4C61×#532C211yesmaximal, characteristic
5C2×#11758194—22no—
6#14519696C2214yes—
7#14519694—22no—
8C2×#41×C61C411yescharacteristic
9C2×#41×C61C2211yescharacteristic
10C4⋊Q8×C61C2211yescharacteristic
11#127×C61C411yescharacteristic
12#124×C61C411yescharacteristic
13#124×C61C2211yescharacteristic
14#121×C61—22no—
15C4×D4×C61—22no—
16C2×C42×C61C411yescharacteristic
17#41×C61—41no—
18#41×C61—41no—
19#41×C61—41no—
20#41×C61—41no—
21C2×Q8×C61C2×C411yescharacteristic
22C2×Q8×C61C2311yescharacteristic
23C2×D4×C61—22no—
24C2×D4×C61—21no—
25C2×D4×C61C2×C411yescharacteristic
26C2×D4×C61C2×C411yescharacteristic
27C2×D4×C61D412yes—
28C22×C4×C61—21no—
29C22×C4×C61—21no—
30C22×C4×C61C2×C411yescharacteristic
31C22×C4×C61D412yes—
32C4⋊C4×C61—22no—
33C22⋊C4×C61—22no—
34C22⋊C4×C61—22no—
35C42×C61—21no—
36C42×C61C2×C411yescharacteristic
37C42×C61C2×C411yescharacteristic
38#11758194—24no—
39#11758194—42no—
40C2×#92418—42no—
41C23×C61—21no—
42C23×C61C22⋊C412yes—
43C23×C61C22⋊C411yescharacteristic
44Q8×C61—41no—
45Q8×C61—41no—
46D4×C61—41no—
47D4×C61—42no—
48D4×C61—41no—
49D4×C61—44no—
50D4×C61—42no—
51C2×C4×C61—21no—
52C2×C4×C61—22no—
53C2×C4×C61—22no—
54C2×C4×C61—21no—
55C2×C4×C61—21no—
56C2×C4×C61—21no—
57C2×C4×C61—21no—
58C2×C4×C61—42no—
59C2×C4×C61—41no—
60C2×C4×C61—41no—
61C2×C4×C61C22⋊C411yescharacteristic
62C2×C4×C61C22×C411yescharacteristic
63C2×C4×C61C2×D412yes—
64#92418—44no—
65C22×C61—21no—
66C22×C61—22no—
67C22×C61—41no—
68C22×C61—42no—
69C22×C61—42no—
70C22×C61—41no—
71C22×C61C2×C22⋊C411yescharacteristic
72C4×C61—22no—
73C4×C61—22no—
74C4×C61—21no—
75C4×C61—41no—
76C4×C61—41no—
77C4×C61#9911yescharacteristic
78C4×C61#9911yescharacteristic
79#2132—611nomaximal, Sylow
80C2×C61—21no—
81C2×C61—41no—
82C2×C61—42no—
83C2×C61—81no—
84C2×C61C2×#9911yescharacteristic
85#532D6111yescharacteristic
86#413—612no—
87#356—612no—
88#355—612no—
89C61#213211yescharacteristic, complemented, Sylow
90C2×#41Dic6111yescharacteristic
91C2×#41C2×D6111yescharacteristic
92C2×M16—1222no—
93C4⋊Q8C2×D6111yescharacteristic
94#127Dic6111yescharacteristic
95#124Dic6111yescharacteristic
96#124C2×D6111yescharacteristic
97#121—22no—
98C4×D4—22no—
99C2×C42Dic6111yescharacteristic
100#101—614no—
101#100—1222no—
102#41—41no—
103#41—41no—
104#41—41no—
105#41—41no—
106C2×Q8C2×Dic6111yescharacteristic
107C2×Q8C22×D6111yescharacteristic
108C2×D4—22no—
109C2×D4—21no—
110C2×D4C2×Dic6111yescharacteristic
111C2×D4C2×Dic6111yescharacteristic
112C2×D4C22⋊D6112yes—
113C22×C4—21no—
114C22×C4—21no—
115C22×C4C2×Dic6111yescharacteristic
116C22×C4C22⋊D6112yes—
117M16—1224no—
118M16—2442no—
119C2×C8—2442no—
120C4⋊C4—22no—
121C22⋊C4—22no—
122C22⋊C4—22no—
123C42—21no—
124C42C2×Dic6111yescharacteristic
125C42C2×Dic6111yescharacteristic
126C23—21no—
127C23C22⋊Dic6112yes—
128C23C22⋊Dic6111yescharacteristic
129Q8—41no—
130Q8—41no—
131D4—41no—
132D4—42no—
133D4—41no—
134D4—44no—
135D4—42no—
136C2×C4—21no—
137C2×C4—22no—
138C2×C4—21no—
139C2×C4—22no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—42no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4C22⋊Dic6111yescharacteristic
147C2×C4C22×Dic6111yescharacteristic
148C2×C4C2×C22⋊D6112yes—
149C8—2444no—
150C22—21no—
151C22—22no—
152C22—41no—
153C22—42no—
154C22—42no—
155C22—41no—
156C22C2×C22⋊Dic6111yescharacteristic
157C4—22no—
158C4—22no—
159C4—21no—
160C4—41no—
161C4—41no—
162C4#1451969211yescharacteristic
163C4#1451969211yescharacteristic
164C2—21no—
165C2—41no—
166C2—42no—
167C2—81no—
168C2C2×#1451969211yescharacteristic
subgroupG/H
centerC4#14519692
commutatorC2×C4×C61C22×C4
FrattiniC2×Q8C22×D61
FittingC61×#532C2
socleC2×C61C2×#99
hypercenter#532D61
hypocenterC61#2132
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #16839746C2semidirect
2. #16839561C2semidirect
3. #16839559C2semidirect
89. C61#2132semidirect