Finite Group Databasebeta

← #22625391

Subgroups — #22625391

Order 9344.

264 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 58 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#17989610C211yesmaximal, characteristic, complemented
2C4×#11924038C211yesmaximal, characteristic, complemented
3#17989443C212yesmaximal, complemented
4#17989442C212yesmaximal, complemented
5#124×D73C211yesmaximal, characteristic
6C2×#11924038—21no—
7#14556658—21no—
8#14556648—21no—
9#14556646C2212yescomplemented
10#14556646C2212yescomplemented
11C4×#10596833—21no—
12C2×Q8×D73C411yescharacteristic
13C2×D4×D73C411yescharacteristic
14#14556580C2211yescharacteristic
15#14556579C411yescharacteristic
16#14556578C2211yescharacteristic
17#14556577—21no—
18#14556577—21no—
19C22⋊C4×D73—21no—
20C22⋊C4×D73—21no—
21C42×D73C2211yescharacteristic
22#124×C73C411yescharacteristic
23#11924038—24no—
24C2×#10596833—22no—
25C2×#10596833—22no—
26C23×D73—21no—
27C2×Dic146—21no—
28C2×Dic146C2×C411yescharacteristic
29Q8×D73—42no—
30C2×D292C2×C411yescharacteristic
31C2×C22⋊D73—21no—
32D4×D73—42no—
33C2×C4×D73—21no—
34C2×C4×D73C2×C411yescharacteristic
35C2×C4×D73D411yescharacteristic
36C2×C4×D73D411yescharacteristic
37C22⋊Dic73—21no—
38C22⋊Dic73—21no—
39#11924005—21no—
40#11924005—21no—
41#11924005—21no—
42#11924005—21no—
43C4×Dic73D411yescharacteristic
44C4×Dic73D411yescharacteristic
45C4×Dic73C2311yescharacteristic
46C2×Q8×C73C2×C411yescharacteristic
47C2×D4×C73C2×C411yescharacteristic
48C22⋊C4×C73—21no—
49C22⋊C4×C73—21no—
50C42×C73C2×C411yescharacteristic
51C23×C73—21no—
52C22×D73—21no—
53C22×D73—42no—
54C22×D73—42no—
55C22×D73—42no—
56C22×D73C22⋊C411yescharacteristic
57Q8×C73—41no—
58D4×C73—41no—
59C2×C4×C73—21no—
60C2×C4×C73C22⋊C411yescharacteristic
61C2×C4×C73C22⋊C411yescharacteristic
62C2×C4×C73C22×C411yescharacteristic
63C22⋊D73—42no—
64C2×Dic73—21no—
65C2×Dic73C22⋊C411yescharacteristic
66C2×Dic73C2×D411yescharacteristic
67C2×Dic73C2×D411yescharacteristic
68D292—41no—
69C4×D73—22no—
70C4×D73—22no—
71C4×D73—41no—
72C4×D73—42no—
73Dic146—42no—
74Dic146—41no—
75#10596833—24no—
76#10596833—42no—
77C22×C73—41no—
78C22×C73—41no—
79C22×C73—41no—
80C22×C73C2×C22⋊C411yescharacteristic
81C2×D73—21no—
82C2×D73—21no—
83C2×D73—41no—
84C2×D73—41no—
85C2×D73—41no—
86C2×D73—84no—
87C2×D73#10412yes—
88C4×C73—21no—
89C4×C73—21no—
90C4×C73—21no—
91C4×C73—41no—
92Dic73—21no—
93Dic73—21no—
94Dic73—41no—
95Dic73#10012yes—
96C2×C73—81no—
97C2×C73C2×#10011yescharacteristic
98C2×C73C2×#10411yescharacteristic
99C2×C73#42111yescharacteristic
100D73—22no—
101D73—81no—
102#1527—731nomaximal, Sylow
103C73#152711yescharacteristic, complemented, Sylow
104C2×#124—731no—
105#432—731no—
106C4×M16—731no—
107#329—732no—
108#329—732no—
109C22×Q8—731no—
110C22×D4—731no—
111C2×M16—1461no—
112#124—731no—
113#124—731no—
114#124—731no—
115#124—1461no—
116#124—1461no—
117#124#6440811yescharacteristic
118C2×C22⋊C4—1461no—
119C2×C22⋊C4—1461no—
120C2×C42—731no—
121C4⋊C8—1461no—
122C22⋊C8—1461no—
123#97—732no—
124#97—732no—
125C4×C8—1461no—
126C24—1461no—
127C2×Q8—2922no—
128C2×Q8—731no—
129C2×Q8—1461no—
130C2×Q8C2×#6440811yescharacteristic
131C2×D4—2922no—
132C2×D4—731no—
133C2×D4—1461no—
134C2×D4C2×#6440811yescharacteristic
135C22×C4—731no—
136C22×C4—731no—
137C22×C4—731no—
138C22×C4—1461no—
139M16—1464no—
140C2×C8—1462no—
141C2×C8—1462no—
142C22⋊C4—21no—
143C22⋊C4—21no—
144C22⋊C4—1461no—
145C22⋊C4—1461no—
146C22⋊C4—1461no—
147C22⋊C4—1461no—
148C22⋊C4—1461no—
149C22⋊C4—1461no—
150C42—731no—
151C42—731no—
152C42—731no—
153C42C2×#6440811yescharacteristic
154C23—21no—
155C23—2922no—
156C23—2922no—
157C23—2922no—
158C23—731no—
159C23—1461no—
160Q8—41no—
161Q8—2921no—
162Q8—2922no—
163D4—41no—
164D4—2921no—
165D4—2922no—
166C2×C4—21no—
167C2×C4—2921no—
168C2×C4—2922no—
169C2×C4—731no—
170C2×C4—731no—
171C2×C4—731no—
172C2×C4—1462no—
173C2×C4—1462no—
174C2×C4—1461no—
175C2×C4C22⋊#6440811yescharacteristic
176C2×C4C22⋊#6440811yescharacteristic
177C2×C4C22×#6440811yescharacteristic
178C8—2922no—
179C8—1464no—
180C22—41no—
181C22—41no—
182C22—41no—
183C22—2921no—
184C22—2921no—
185C22—2921no—
186C22—5844no—
187C22—732no—
188C22—1461no—
189C22—1461no—
190C22C2×C22⋊#6440811yescharacteristic
191C4—21no—
192C4—21no—
193C4—21no—
194C4—41no—
195C4—2921no—
196C4—732no—
197C4—1461no—
198C4—1461no—
199C2—81no—
200C2—5841no—
201C2—1462no—
202C2D73⋊#10011yescharacteristic
203C2D73⋊#10411yescharacteristic
204C2#1798958411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#124×C73C4
socleC22×C73C2×C22⋊C4
hypercenter#124#64408
hypocenterC73#1527
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #17989610C2semidirect
2. C4×#11924038C2semidirect
3. #17989443C2semidirect
4. #17989442C2semidirect
9. #14556646C22semidirect
10. #14556646C22semidirect
103. C73#1527semidirect