Finite Group Databasebeta

← #22625374

Subgroups — #22625374

Order 9344.

218 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 56 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#17989606C211yesmaximal, characteristic, complemented
2#17989532C211yesmaximal, characteristic, complemented
3#17989440C212yesmaximal, complemented
4#17989439C212yesmaximal
5#17989122C211yesmaximal, characteristic
6C4⋊#10596833—21no—
7#14556648C2212yes—
8C4×#10596833—21no—
9(C2×#64408)⋊C4—21no—
10(C2×#64408)⋊C4—21no—
11(C2×#64408)⋊C4C2212yes—
12#14556586—21no—
13#14556579C411yescharacteristic, complemented
14#14556576—21no—
15#14556571C2211yescharacteristic
16#14556566C2211yescharacteristic
17#14556556C411yescharacteristic, complemented
18#14556553—21no—
19#14556553C411yescharacteristic, complemented
20#14556549—21no—
21C42×D73C2211yescharacteristic
22#125×C73C411yescharacteristic, complemented
23C22×#64408—22no—
24C2×#10596833—22no—
25C2×Dic146C2×C411yescharacteristic
26C2×D292—21no—
27C2×D292C2×C411yescharacteristic
28C2×C4×D73—21no—
29C2×C4×D73D411yescharacteristic
30C2×C4×D73D411yescharacteristic
31C2×C4×D73C2311yescharacteristic
32C4⋊Dic73—21no—
33#11924007—21no—
34#11924005—21no—
35#11924005—21no—
36#11924005—21no—
37#11924005—21no—
38#11924005—21no—
39C4×Dic73—21no—
40C4×Dic73C2×C411yescharacteristic
41C4×Dic73D411yescharacteristic
42C4×Dic73D411yescharacteristic
43C4⋊C4×C73—21no—
44C4⋊C4×C73—21no—
45C4⋊C4×C73C2×C411yescharacteristic
46C4⋊C4×C73C2×C411yescharacteristic
47C42×C73C2×C411yescharacteristic
48C22×D73—21no—
49C22×D73C2×D411yescharacteristic
50C2×#64408—42no—
51C2×#64408—42no—
52C2×#64408—42no—
53C2×C4×C73—21no—
54C2×C4×C73—21no—
55C2×C4×C73C22⋊C411yescharacteristic
56C2×C4×C73C22⋊C411yescharacteristic
57C2×C4×C73C22×C411yescharacteristic
58C2×Dic73—21no—
59C2×Dic73C22⋊C411yescharacteristic
60C2×Dic73C22⋊C411yescharacteristic
61C2×Dic73C2×D411yescharacteristic
62D292—41no—
63D292—42no—
64C4×D73—22no—
65C4×D73—41no—
66C4×D73—41no—
67C4×D73—42no—
68Dic146—41no—
69#10596833—42no—
70C22×C73C2×C22⋊C411yescharacteristic
71C2×D73—21no—
72C2×D73—21no—
73C2×D73—41no—
74C2×D73—41no—
75C2×D73—41no—
76C2×D73#13512yes—
77#64408—82no—
78C4×C73—21no—
79C4×C73—21no—
80C4×C73—21no—
81C4×C73—41no—
82C4×C73—41no—
83Dic73—21no—
84Dic73—21no—
85Dic73—21no—
86Dic73—41no—
87C2×C73#41011yescharacteristic
88C2×C73#41611yescharacteristic
89C2×C73#42111yescharacteristic
90D73—22no—
91D73—81no—
92#1521—731nomaximal, Sylow
93C73#152111yescharacteristic, complemented, Sylow
94#529—731no—
95#431—731no—
96#383—731no—
97#328—732no—
98#327—732no—
99#126—1461no—
100#125#6440811yescharacteristic, complemented
101#124—731no—
102#123—1461no—
103C22⋊Q8—731no—
104#121—731no—
105C4×Q8—731no—
106C4×D4—731no—
107C4×D4—1461no—
108#117—1461no—
109C2×C42—731no—
110C4⋊C8—1461no—
111C22⋊C8—732no—
112C4×C8—1461no—
113#95—732no—
114#95—1461no—
115#95—1461no—
116C2×Q8—731no—
117C2×D4—731no—
118C2×D4—1461no—
119C22×C4—731no—
120C22×C4—731no—
121C22×C4—731no—
122C22×C4—1461no—
123C22×C4—1462no—
124C2×C8—1462no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—1461no—
128C4⋊C4—1461no—
129C4⋊C4C2×#6440811yescharacteristic
130C4⋊C4C2×#6440811yescharacteristic
131C22⋊C4—1461no—
132C22⋊C4—1461no—
133C22⋊C4—1461no—
134C22⋊C4—1461no—
135C22⋊C4—1461no—
136C42—731no—
137C42—731no—
138C42—731no—
139C42—1461no—
140C42C2×#6440811yescharacteristic
141C23—731no—
142C23—1461no—
143Q8—2921no—
144D4—2921no—
145D4—2922no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—2921no—
149C2×C4—2921no—
150C2×C4—2922no—
151C2×C4—2922no—
152C2×C4—2922no—
153C2×C4—2922no—
154C2×C4—731no—
155C2×C4—731no—
156C2×C4—731no—
157C2×C4—1462no—
158C2×C4—1461no—
159C2×C4C22⋊#6440811yescharacteristic
160C2×C4C22⋊#6440811yescharacteristic
161C2×C4C22×#6440811yescharacteristic
162C8—2922no—
163C22—2921no—
164C22—2921no—
165C22—2921no—
166C22—732no—
167C22—1461no—
168C22—1461no—
169C22C2×C22⋊#6440811yescharacteristic
170C4—21no—
171C4—21no—
172C4—21no—
173C4—41no—
174C4—41no—
175C4—2921no—
176C4—5842no—
177C4—1461no—
178C4—1461no—
179C4—1461no—
180C2—5841no—
181C2—1462no—
182C2#1798956811yescharacteristic
183C2#1798957711yescharacteristic
184C2#1798958411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#125×C73C4
socleC22×C73C2×C22⋊C4
hypercenter#125#64408
hypocenterC73#1521
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
1. #17989606C2semidirect
2. #17989532C2semidirect
3. #17989440C2semidirect
13. #14556579C4semidirect
17. #14556556C4semidirect
19. #14556553C4semidirect
22. #125×C73C4semidirect
93. C73#1521semidirect
100. #125#64408semidirect