Finite Group Databasebeta

← #22625689

Subgroups — #22625689

Order 9344.

284 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 86 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
1C2×#14556678C211yesmaximal, characteristic
2#17989574C211yesmaximal, characteristic
3#17989551C212yesmaximal, complemented
4#17989468C212yesmaximal, complemented
5#17988559C211yesmaximal, characteristic
6#14556678—22no—
7#14556678—22no—
8C2×#11924038C411yescharacteristic, complemented
9C2×#11924037C411yescharacteristic, complemented
10C2×#11924037C2212yes—
11C2×#11924037C2211yescharacteristic
12C2×#11924036C411yescharacteristic, complemented
13C22×#10596833C411yescharacteristic, complemented
14C22×#10596833C2211yescharacteristic
15#14556652C412yescomplemented
16#14556651C412yescomplemented
17#14556646—22no—
18C4×#10596833—22no—
19C2×#11924027C2211yescharacteristic
20#14556547C2212yes—
21#14556506C411yescharacteristic
22#14556505C412yes—
23#99×C73C411yescharacteristic
24#11924038—22no—
25#11924037—22no—
26#11924037—22no—
27#11924037—22no—
28#11924037C2×C414yes—
29#11924036—21no—
30#11924036—21no—
31C2×#10596833—22no—
32C2×#10596833—21no—
33C2×#10596833—21no—
34C2×#10596833C2×C411yescharacteristic
35C2×#10596833C2×C411yescharacteristic
36C2×#10596833C2×C411yescharacteristic
37C2×#10596833C2×C411yescharacteristic
38C2×#10596833D412yes—
39C2×#10596833D412yes—
40#11924027—22no—
41#11924027—22no—
42C2×Dic146C2×C411yescharacteristic
43C2×C22⋊D73C2×C411yescharacteristic
44C2×C22⋊D73C2×C411yescharacteristic
45C22×Dic73C2×C411yescharacteristic
46C22×Dic73C2311yescharacteristic
47C2×C4×D73C2×C411yescharacteristic
48#11924007—22no—
49C22⋊Dic73C2×C412yes—
50C4×Dic73—22no—
51C2×D4×C73C2×C411yescharacteristic
52C22⋊C4×C73C2×C412yes—
53C23×C73C4211yescharacteristic
54C23×C73C22×C411yescharacteristic
55C22×D73C4211yescharacteristic
56D4×C73—22no—
57C2×C4×C73—22no—
58C2×C4×C73C4211yescharacteristic
59C22⋊D73—22no—
60C22⋊D73—22no—
61C2×Dic73—21no—
62C2×Dic73—21no—
63C2×Dic73—22no—
64C2×Dic73C4211yescharacteristic
65C2×Dic73C22×C411yescharacteristic
66C2×Dic73C22×C411yescharacteristic
67C2×Dic73C2×D412yes—
68C2×Dic73#4112yes—
69C4×D73—21no—
70C4×D73—21no—
71Dic146—22no—
72#10596833—21no—
73#10596833—21no—
74#10596833—24no—
75#10596833C22⋊C411yescharacteristic
76#10596833C22⋊C411yescharacteristic
77#10596833C22⋊C412yes—
78C22×C73—21no—
79C22×C73—41no—
80C22×C73—41no—
81C22×C73C2×C4211yescharacteristic
82C22×C73C4×D412yes—
83C2×D73—21no—
84C2×D73—41no—
85C4×C73—21no—
86C4×C73—42no—
87Dic73—21no—
88Dic73—42no—
89Dic73C2×C22⋊C411yescharacteristic
90Dic73#11711yescharacteristic
91Dic73C4×D412yes—
92C2×C73—22no—
93C2×C73—21no—
94C2×C73—41no—
95C2×C73C4×C22⋊C411yescharacteristic
96D73—41no—
97#1757—731nomaximal, Sylow
98C73#175711yescharacteristic, complemented, Sylow
99C2×#131—731no—
100#413—731no—
101#410—731no—
102#405—732no—
103#344—732no—
104C2×#41—731no—
105#131—1462no—
106#131—1462no—
107C2×M16—731no—
108C2×M16—731no—
109C2×M16—731no—
110C2×M16—732no—
111C22×C8—731no—
112C22×C8—731no—
113C22×C8—731no—
114#117—732no—
115#101—732no—
116#100—732no—
117#99—731no—
118#99—732no—
119#99#6440811yescharacteristic
120#97—1462no—
121C4×C8—1462no—
122#41—1462no—
123#41—1462no—
124C2×Q8—731no—
125C2×D4—731no—
126C2×D4—731no—
127C2×D4C2×#6440811yescharacteristic
128C22×C4—731no—
129C22×C4—731no—
130C22×C4—731no—
131M16—734no—
132M16—1462no—
133M16—1462no—
134M16—1462no—
135M16—1462no—
136C2×C8—731no—
137C2×C8—731no—
138C2×C8—732no—
139C2×C8—732no—
140C2×C8—731no—
141C2×C8—731no—
142C2×C8—1461no—
143C2×C8—1461no—
144C2×C8—1461no—
145C2×C8—1461no—
146C2×C8—1462no—
147C4⋊C4—1462no—
148C22⋊C4—732no—
149C22⋊C4C2×#6440812yes—
150C42—1462no—
151C23—731no—
152C23C4×#6440811yescharacteristic
153C23C22×#6440811yescharacteristic
154Q8—1462no—
155D4—22no—
156D4—1462no—
157D4—1462no—
158C2×C4—22no—
159C2×C4—731no—
160C2×C4—731no—
161C2×C4—732no—
162C2×C4—732no—
163C2×C4—731no—
164C2×C4—1461no—
165C2×C4—1461no—
166C2×C4—1462no—
167C2×C4—1461no—
168C2×C4—1461no—
169C2×C4C4×#6440811yescharacteristic
170C8—731no—
171C8—731no—
172C8—732no—
173C8—1461no—
174C8—1461no—
175C8—1464no—
176C22—21no—
177C22—41no—
178C22—41no—
179C22—2921no—
180C22—1461no—
181C22C2×C4×#6440811yescharacteristic
182C22D4×#6440812yes—
183C4—21no—
184C4—42no—
185C4—2922no—
186C4—731no—
187C4—732no—
188C4—731no—
189C4—1461no—
190C2—22no—
191C2—21no—
192C2—41no—
193C2—2921no—
194C2C22⋊C4×#6440811yescharacteristic
subgroupG/H
centerC2C22⋊C4×#64408
commutatorC22×C73C2×C42
FrattiniC23C22×#64408
Fitting#99×C73C4
socleC2×C73C4×C22⋊C4
hypercenter#99#64408
hypocenterC73#1757
LCSG ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
3. #17989551C2semidirect
4. #17989468C2semidirect
8. C2×#11924038C4semidirect
9. C2×#11924037C4semidirect
12. C2×#11924036C4semidirect
13. C22×#10596833C4semidirect
15. #14556652C4semidirect
16. #14556651C4semidirect
98. C73#1757semidirect