Finite Group Databasebeta

← #22608562

Subgroups — #22608562

Order 9344.

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

normal subgroups only

This group has 200 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#17988644C211yesmaximal, characteristic, complemented
2#17988644C211yesmaximal, characteristic, complemented
3#17988329C212yesmaximal, complemented
4#17988327C212yesmaximal, complemented
5#529×C73C211yesmaximal, characteristic
6C4⋊#10596831—21no—
7C4⋊#10596831—21no—
8C22⋊#10596831—21no—
9C22⋊#10596831—21no—
10#14556502C2212yes—
11#14556502C2212yes—
12#126×C73—21no—
13#125×C73C2211yescharacteristic
14#124×C73C2211yescharacteristic
15#123×C73—21no—
16C22⋊Q8×C73C411yescharacteristic
17#121×C73C411yescharacteristic
18C4×Q8×C73C411yescharacteristic
19C4×D4×C73—21no—
20C4×D4×C73C411yescharacteristic
21#117×C73—21no—
22C2×C42×C73C2211yescharacteristic
23C2×#10596831—22no—
24C2×#10596831—22no—
25C2×Q8×C73C2×C411yescharacteristic
26C2×D4×C73—21no—
27C2×D4×C73C2×C411yescharacteristic
28C22×C4×C73—21no—
29C22×C4×C73C2×C411yescharacteristic
30C22×C4×C73D411yescharacteristic
31C22×C4×C73D411yescharacteristic
32C4⋊C4×C73—21no—
33C4⋊C4×C73—21no—
34C4⋊C4×C73—21no—
35C4⋊C4×C73—21no—
36C4⋊C4×C73C2×C411yescharacteristic
37C4⋊C4×C73C2×C411yescharacteristic
38C22⋊C4×C73—21no—
39C22⋊C4×C73—21no—
40C22⋊C4×C73—21no—
41C22⋊C4×C73—21no—
42C22⋊C4×C73—21no—
43C42×C73—21no—
44C42×C73C2×C411yescharacteristic
45C42×C73D411yescharacteristic
46C42×C73D411yescharacteristic
47C42×C73C2311yescharacteristic
48C23×C73—21no—
49C23×C73C22⋊C411yescharacteristic
50Q8×C73—41no—
51D4×C73—41no—
52D4×C73—42no—
53C2×C4×C73—21no—
54C2×C4×C73—21no—
55C2×C4×C73—21no—
56C2×C4×C73—41no—
57C2×C4×C73—41no—
58C2×C4×C73—41no—
59C2×C4×C73—42no—
60C2×C4×C73C22⋊C411yescharacteristic
61C2×C4×C73C22⋊C411yescharacteristic
62C2×C4×C73C22⋊C411yescharacteristic
63C2×C4×C73C22×C411yescharacteristic
64C2×C4×C73C2×D411yescharacteristic
65C2×C4×C73C2×D411yescharacteristic
66#10596831—42no—
67#10596831—42no—
68C22×C73—21no—
69C22×C73—21no—
70C22×C73—21no—
71C22×C73—41no—
72C22×C73—41no—
73C22×C73—41no—
74C22×C73C2×C22⋊C411yescharacteristic
75C4×C73—21no—
76C4×C73—21no—
77C4×C73—21no—
78C4×C73—21no—
79C4×C73—21no—
80C4×C73—21no—
81C4×C73—41no—
82C4×C73—41no—
83C4×C73—41no—
84C2×C73—41no—
85C2×C73—81no—
86C2×C73#41311yescharacteristic
87C2×C73#42111yescharacteristic
88C2×C73#42111yescharacteristic
89#1535—731nomaximal, Sylow
90C73#153511yescharacteristic, complemented, Sylow
91#529D7311yescharacteristic
92#432—731no—
93#432—731no—
94#330—732no—
95#329—732no—
96#126—21no—
97#125C2×D7311yescharacteristic
98#124C2×D7311yescharacteristic
99#123—21no—
100C22⋊Q8Dic7311yescharacteristic
101#121Dic7311yescharacteristic
102C4×Q8Dic7311yescharacteristic
103C4×D4—21no—
104C4×D4Dic7311yescharacteristic
105#117—21no—
106C2×C42C2×D7311yescharacteristic
107C4⋊C8—1461no—
108C4⋊C8—1461no—
109C22⋊C8—1461no—
110C22⋊C8—1461no—
111#97—732no—
112#97—732no—
113C2×Q8C2×Dic7311yescharacteristic
114C2×D4—21no—
115C2×D4C2×Dic7311yescharacteristic
116C22×C4—21no—
117C22×C4C2×Dic7311yescharacteristic
118C22×C4C22⋊D7311yescharacteristic
119C22×C4C22⋊D7311yescharacteristic
120C2×C8—1462no—
121C2×C8—1462no—
122C4⋊C4—21no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4C2×Dic7311yescharacteristic
127C4⋊C4C2×Dic7311yescharacteristic
128C22⋊C4—21no—
129C22⋊C4—21no—
130C22⋊C4—21no—
131C22⋊C4—21no—
132C22⋊C4—21no—
133C42—21no—
134C42C2×Dic7311yescharacteristic
135C42C22⋊D7311yescharacteristic
136C42C22⋊D7311yescharacteristic
137C42C22×D7311yescharacteristic
138C23—21no—
139C23C22⋊Dic7311yescharacteristic
140Q8—41no—
141D4—41no—
142D4—42no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—42no—
150C2×C4C22⋊Dic7311yescharacteristic
151C2×C4C22⋊Dic7311yescharacteristic
152C2×C4C22⋊Dic7311yescharacteristic
153C2×C4C22×Dic7311yescharacteristic
154C2×C4C2×C22⋊D7311yescharacteristic
155C2×C4C2×C22⋊D7311yescharacteristic
156C8—2922no—
157C8—2922no—
158C22—21no—
159C22—21no—
160C22—21no—
161C22—41no—
162C22—41no—
163C22—41no—
164C22C2×C22⋊Dic7311yescharacteristic
165C4—21no—
166C4—21no—
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—41no—
172C4—41no—
173C4—41no—
174C2—41no—
175C2—81no—
176C2#1798857111yescharacteristic
177C2#1798860411yescharacteristic
178C2#1798860411yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic73
commutatorC2×C4×C73C22×C4
FrattiniC42C22×D73
Fitting#529×C73C2
socleC22×C73C2×C22⋊C4
hypercenter#529D73
hypocenterC73#1535
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #17988644C2semidirect
2. #17988644C2semidirect
3. #17988329C2semidirect
4. #17988327C2semidirect
90. C73#1535semidirect