Finite Group Databasebeta

← #22621321

Subgroups — #22621321

Order 9344.

342 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 113 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#17989139C212yesmaximal
2#17988871C212yesmaximal, complemented
3#17988870C212yesmaximal, complemented
4#17988845C211yesmaximal, characteristic
5#17988843C212yesmaximal
6#17988796C212yesmaximal, complemented
7#17988795C212yesmaximal, complemented
8#17988610C211yesmaximal, characteristic
9#470×C73C211yesmaximal, characteristic
10C2×Dic292C2211yescharacteristic
11C2×#11924018C2212yes—
12C2×#11924012C2211yescharacteristic
13#14556590C2212yes—
14#14556589C2212yes—
15#14556581—22no—
16#14556570C2212yes—
17#14556568—22no—
18Q8×Dic73C2212yes—
19#14556556—22no—
20#14556556C2212yes—
21#14556547—22no—
22C2×C4×Dic73C2211yescharacteristic
23#14556523C2211yescharacteristic
24#14556522C2212yes—
25#14556520C2212yes—
26#14556520C2212yes—
27#14556516C2212yes—
28#14556515C2212yes—
29#14556514C2212yes—
30C2×Q16×C73C2211yescharacteristic
31C2×M16×C73C2211yescharacteristic
32C22⋊Q8×C73C2212yes—
33#106×C73C2211yescharacteristic
34#103×C73C2212yes—
35C2×Dic146—22no—
36C2×Dic146C2312yes—
37C22×Dic73D412yes—
38Dic292—41no—
39#11924018—42no—
40#11924012—41no—
41C2×#10596831C2312yes—
42C4⋊Dic73—22no—
43C4⋊Dic73C2312yes—
44#11924007—22no—
45#11924007—22no—
46#11924007—22no—
47#11924007—22no—
48#11924007—22no—
49C22⋊Dic73—22no—
50C4×Dic73—22no—
51C4×Dic73—22no—
52C4×Dic73D411yescharacteristic
53C4×Dic73D411yescharacteristic
54C4×Dic73C2312yes—
55C2×Q8×C73C2312yes—
56C22×C4×C73C2311yescharacteristic
57Q16×C73—41no—
58M16×C73—41no—
59C2×C8×C73C2311yescharacteristic
60C2×C8×C73C2311yescharacteristic
61C4⋊C4×C73—22no—
62C4⋊C4×C73C2312yes—
63C22⋊C4×C73—22no—
64C23×C73C2×D411yescharacteristic
65Q8×C73—22no—
66Q8×C73—22no—
67C2×C4×C73—21no—
68C2×C4×C73—21no—
69C2×C4×C73—22no—
70C2×C4×C73—22no—
71C2×C4×C73C2×D411yescharacteristic
72C2×C4×C73C2411yescharacteristic
73C2×Dic73—24no—
74C2×Dic73—22no—
75C2×Dic73—22no—
76C2×Dic73C2×D412yes—
77C2×Dic73C2×D412yes—
78Dic146—22no—
79Dic146—22no—
80Dic146—44no—
81C8×C73—21no—
82C8×C73—21no—
83#10596831—22no—
84C22×C73—21no—
85C22×C73—22no—
86C22×C73C22×D411yescharacteristic
87C4×C73—21no—
88C4×C73—42no—
89C4×C73—42no—
90C4×C73H(5,𝔽2)11yescharacteristic
91C4×C732−1+411yescharacteristic
92Dic73—22no—
93Dic73—42no—
94Dic73—42no—
95Dic73#13714yes—
96C2×C73—41no—
97C2×C73#53711yescharacteristic
98C2×C73C2×#13712yes—
99#3255—731nomaximal, Sylow
100C73#325511yescharacteristic, complemented, Sylow
101#533—732no—
102#475—732no—
103#475—732no—
104#470—731no—
105#470—732no—
106#470D7311yescharacteristic
107#462—732no—
108#462—732no—
109#423—731no—
110C2×Q16—732no—
111C2×Q16—731no—
112C2×Q16C2×D7311yescharacteristic
113C2×M16—731no—
114C2×M16C2×D7311yescharacteristic
115C4⋊Q8—732no—
116C4⋊Q8—732no—
117#125—1462no—
118C22⋊Q8—732no—
119C22⋊Q8—1462no—
120C22⋊Q8C2×D7312yes—
121C4×Q8—732no—
122C4×Q8—732no—
123C4×Q8—1462no—
124#117—1462no—
125C2×C42—731no—
126#106—731no—
127#106—732no—
128#106C2×D7311yescharacteristic
129C4⋊C8—732no—
130C4⋊C8—732no—
131#103—732no—
132#103—732no—
133#103—732no—
134#103C2×D7312yes—
135C2×Q8—732no—
136C2×Q8—1462no—
137C2×Q8C22×D7312yes—
138C22×C4—732no—
139C22×C4C22×D7311yescharacteristic
140Q16—41no—
141Q16—2921no—
142Q16—2922no—
143M16—41no—
144M16—2921no—
145C2×C8—732no—
146C2×C8C22×D7311yescharacteristic
147C2×C8C22×D7311yescharacteristic
148C4⋊C4—22no—
149C4⋊C4—732no—
150C4⋊C4—1462no—
151C4⋊C4—1462no—
152C4⋊C4—1462no—
153C4⋊C4—1462no—
154C4⋊C4—1462no—
155C4⋊C4—1462no—
156C4⋊C4C22×D7312yes—
157C22⋊C4—22no—
158C22⋊C4—1462no—
159C42—731no—
160C42—731no—
161C42—732no—
162C42—1462no—
163C42—1462no—
164C23D4×D7311yescharacteristic
165Q8—22no—
166Q8—22no—
167Q8—2924no—
168Q8—1462no—
169Q8—1462no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—732no—
175C2×C4—732no—
176C2×C4—1462no—
177C2×C4—1462no—
178C2×C4—1464no—
179C2×C4D4×D7311yescharacteristic
180C2×C4C23×D7311yescharacteristic
181C8—21no—
182C8—21no—
183C8—1462no—
184C22—22no—
185C22—21no—
186C22C2×D4×D7311yescharacteristic
187C4—21no—
188C4—42no—
189C4—42no—
190C4—2922no—
191C4—2922no—
192C4—734no—
193C4—1462no—
194C4#1455663611yescharacteristic
195C4#1455663811yescharacteristic
196C2—41no—
197C2#1798916411yescharacteristic
198C2#137×D7312yes—
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#470×C73C2
socleC22×C73C22×D4
hypercenter#470D73
hypocenterC73#3255
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
2. #17988871C2semidirect
3. #17988870C2semidirect
6. #17988796C2semidirect
7. #17988795C2semidirect
100. C73#3255semidirect