Finite Group Databasebeta

← #22621382

Subgroups — #22621382

Order 9344.

322 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 109 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#17989197C212yesmaximal
2#17988897C212yesmaximal, complemented
3#17988892C212yesmaximal, complemented
4#17988845C211yesmaximal, characteristic
5#17988826C212yesmaximal
6#17988796C212yesmaximal, complemented
7#17988795C212yesmaximal, complemented
8#17988615C211yesmaximal, characteristic
9#470×C73C211yesmaximal, characteristic
10C2×Dic292C2211yescharacteristic
11C2×#11924018C2212yes—
12C22×#10596831C2211yescharacteristic
13#14556589C2212yes—
14#14556584—22no—
15#14556584—22no—
16#14556582—22no—
17#14556582C2212yes—
18#14556581—22no—
19#14556570C2212yes—
20Q8×Dic73C2212yes—
21#14556556C2212yes—
22#14556550C2211yescharacteristic
23#14556524C2212yes—
24#14556523C2211yescharacteristic
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×Dic146C2312yes—
36Dic292—41no—
37#11924018—42no—
38C2×#10596831—41no—
39C2×#10596831C2312yes—
40C4⋊Dic73—22no—
41C4⋊Dic73—22no—
42C4⋊Dic73D412yes—
43C4⋊Dic73C2312yes—
44#11924007—22no—
45#11924007—22no—
46#11924007—22no—
47#11924007—22no—
48#11924007—22no—
49C22⋊Dic73—22no—
50C22⋊Dic73D411yescharacteristic
51C22⋊Dic73D411yescharacteristic
52C4×Dic73—22no—
53C4×Dic73—22no—
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—22no—
74C2×Dic73—22no—
75C2×Dic73C2×D412yes—
76C2×Dic73C2×D412yes—
77Dic146—22no—
78Dic146—22no—
79C8×C73—21no—
80C8×C73—21no—
81#10596831—22no—
82C22×C73—21no—
83C22×C73—22no—
84C22×C73C22×D411yescharacteristic
85C4×C73—21no—
86C4×C73—42no—
87C4×C73—42no—
88C4×C73H(5,𝔽2)11yescharacteristic
89C4×C732−1+411yescharacteristic
90Dic73—22no—
91Dic73—22no—
92Dic73—42no—
93Dic73—42no—
94C2×C73—41no—
95C2×C73#53711yescharacteristic
96C2×C73#57812yes—
97#3261—731nomaximal, Sylow
98C73#326111yescharacteristic, complemented, Sylow
99#541—732no—
100#479—732no—
101#479—732no—
102#470—731no—
103#470D7311yescharacteristic
104#467—732no—
105#462—732no—
106#462—732no—
107#424—731no—
108C2×Q16—732no—
109C2×Q16—731no—
110C2×Q16C2×D7311yescharacteristic
111C2×M16C2×D7311yescharacteristic
112C22×C8—731no—
113C4⋊Q8—732no—
114#126—1462no—
115#126—1462no—
116#125—732no—
117#125—1462no—
118#125—1462no—
119C22⋊Q8—732no—
120C22⋊Q8C2×D7312yes—
121C4×Q8—732no—
122C4×Q8—732no—
123#117—731no—
124#107—732no—
125#106—731no—
126#106C2×D7311yescharacteristic
127C4⋊C8—732no—
128C4⋊C8—732no—
129#103—732no—
130#103—732no—
131#103—732no—
132#103C2×D7312yes—
133C2×Q8—732no—
134C2×Q8C22×D7312yes—
135C22×C4C22×D7311yescharacteristic
136Q16—41no—
137Q16—2921no—
138Q16—2922no—
139M16—41no—
140C2×C8—2921no—
141C2×C8—732no—
142C2×C8C22×D7311yescharacteristic
143C2×C8C22×D7311yescharacteristic
144C4⋊C4—22no—
145C4⋊C4—732no—
146C4⋊C4—732no—
147C4⋊C4—1462no—
148C4⋊C4—1462no—
149C4⋊C4—1462no—
150C4⋊C4—1462no—
151C4⋊C4—1462no—
152C4⋊C4—1462no—
153C4⋊C4—1462no—
154C4⋊C4C22×D7312yes—
155C22⋊C4—22no—
156C22⋊C4—731no—
157C22⋊C4—731no—
158C22⋊C4—1462no—
159C42—732no—
160C42—1462no—
161C42—1462no—
162C23D4×D7311yescharacteristic
163Q8—22no—
164Q8—22no—
165Q8—1462no—
166Q8—1462no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—732no—
172C2×C4—732no—
173C2×C4—1462no—
174C2×C4—1462no—
175C2×C4D4×D7311yescharacteristic
176C2×C4C23×D7311yescharacteristic
177C8—21no—
178C8—21no—
179C8—1462no—
180C22—22no—
181C22—21no—
182C22C2×D4×D7311yescharacteristic
183C4—21no—
184C4—42no—
185C4—42no—
186C4—2922no—
187C4—2922no—
188C4—1462no—
189C4—1462no—
190C4#1455663611yescharacteristic
191C4#1455663811yescharacteristic
192C2—41no—
193C2#1798916411yescharacteristic
194C2#1798940312yes—
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#470×C73C2
socleC22×C73C22×D4
hypercenter#470D73
hypocenterC73#3261
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. #17988897C2semidirect
3. #17988892C2semidirect
6. #17988796C2semidirect
7. #17988795C2semidirect
98. C73#3261semidirect