Finite Group Databasebeta

← #22621272

Subgroups — #22621272

Order 9344.

348 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 121 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#17988881C212yesmaximal, complemented
3#17988880C212yesmaximal, complemented
4#17988828C211yesmaximal, characteristic
5#17988826C212yesmaximal
6#17988796C212yesmaximal, complemented
7#17988795C212yesmaximal, complemented
8C2×#14556520C211yesmaximal, characteristic
9#467×C73C211yesmaximal, characteristic
10C2×Dic292C2211yescharacteristic
11C2×#11924018C2212yes—
12C22×#10596831C2211yescharacteristic
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#14556525C2211yescharacteristic
24#14556524C2212yes—
25#14556520C2212yes—
26#14556520C2212yes—
27#14556516C2212yes—
28#14556515C2212yes—
29#14556514C2212yes—
30C2×Q16×C73C2211yescharacteristic
31C22×C8×C73C2211yescharacteristic
32C22⋊Q8×C73C2212yes—
33#107×C73C2211yescharacteristic
34#103×C73C2212yes—
35C2×Dic146—22no—
36C2×Dic146C2312yes—
37C22×Dic73D411yescharacteristic
38C22×Dic73D411yescharacteristic
39Dic292—41no—
40#11924018—42no—
41C2×#10596831—41no—
42C2×#10596831C2312yes—
43C4⋊Dic73—22no—
44C4⋊Dic73C2312yes—
45#11924007—22no—
46#11924007—22no—
47#11924007—22no—
48#11924007—22no—
49#11924007—22no—
50C22⋊Dic73—22no—
51C4×Dic73—22no—
52C4×Dic73—22no—
53C4×Dic73D412yes—
54C4×Dic73C2312yes—
55C2×Q8×C73C2312yes—
56C22×C4×C73C2311yescharacteristic
57Q16×C73—41no—
58C2×C8×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×Dic73—41no—
76C2×Dic73Q1614yescomplemented
77C2×Dic73C2×D412yes—
78C2×Dic73C2×D412yes—
79Dic146—22no—
80Dic146—22no—
81Dic146—44no—
82C8×C73—21no—
83C8×C73—21no—
84#10596831—22no—
85C22×C73—21no—
86C22×C73—21no—
87C22×C73C2×Q1612yes—
88C22×C73C22×D411yescharacteristic
89C4×C73—21no—
90C4×C73—42no—
91C4×C73—42no—
92C4×C73H(5,𝔽2)11yescharacteristic
93C4×C732−1+411yescharacteristic
94Dic73—22no—
95Dic73—42no—
96Dic73—42no—
97Dic73C2×Q1614yes—
98C2×C73—22no—
99C2×C73#53711yescharacteristic
100C2×C73C22×Q1611yescharacteristic
101C2×C73#57511yescharacteristic
102#3249—731nomaximal, Sylow
103C73#324911yescharacteristic, complemented, Sylow
104#533—732no—
105#477—732no—
106#477—732no—
107#467—731no—
108#467—732no—
109#467D7311yescharacteristic
110#462—732no—
111#462—732no—
112C2×C4⋊C8—731no—
113C2×Q16—732no—
114C2×Q16—731no—
115C2×Q16C2×D7311yescharacteristic
116C22×C8—731no—
117C22×C8C2×D7311yescharacteristic
118C4⋊Q8—732no—
119C4⋊Q8—732no—
120#125—1462no—
121C22⋊Q8—732no—
122C22⋊Q8—1462no—
123C22⋊Q8C2×D7312yes—
124C4×Q8—732no—
125C4×Q8—732no—
126C4×Q8—1462no—
127#117—1462no—
128C2×C42—731no—
129#107—731no—
130#107—732no—
131#107C2×D7311yescharacteristic
132C4⋊C8—732no—
133C4⋊C8—732no—
134#103—732no—
135#103—732no—
136#103—732no—
137#103C2×D7312yes—
138C2×Q8—732no—
139C2×Q8—1462no—
140C2×Q8C22×D7312yes—
141C22×C4—731no—
142C22×C4—731no—
143C22×C4C22×D7311yescharacteristic
144Q16—41no—
145Q16—2921no—
146Q16—2922no—
147C2×C8—41no—
148C2×C8—2921no—
149C2×C8—732no—
150C2×C8C22×D7311yescharacteristic
151C2×C8C22×D7311yescharacteristic
152C4⋊C4—22no—
153C4⋊C4—732no—
154C4⋊C4—1462no—
155C4⋊C4—1462no—
156C4⋊C4—1462no—
157C4⋊C4—1462no—
158C4⋊C4—1462no—
159C4⋊C4—1462no—
160C4⋊C4C22×D7312yes—
161C22⋊C4—22no—
162C22⋊C4—1462no—
163C42—732no—
164C42—732no—
165C42—1462no—
166C42—1462no—
167C23D4×D7311yescharacteristic
168Q8—22no—
169Q8—22no—
170Q8—2924no—
171Q8—1462no—
172Q8—1462no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—2921no—
178C2×C4—734no—
179C2×C4—732no—
180C2×C4—732no—
181C2×C4—1462no—
182C2×C4—1462no—
183C2×C4D4×D7311yescharacteristic
184C2×C4C23×D7311yescharacteristic
185C8—21no—
186C8—21no—
187C8—1462no—
188C22—21no—
189C22—21no—
190C22Q16×D7312yes—
191C22C2×D4×D7311yescharacteristic
192C4—21no—
193C4—42no—
194C4—42no—
195C4—2922no—
196C4—2922no—
197C4—734no—
198C4—1462no—
199C4#1455663611yescharacteristic
200C4#1455663811yescharacteristic
201C2—22no—
202C2#1798916411yescharacteristic
203C2C2×Q16×D7311yescharacteristic
204C2#1798938411yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#467×C73C2
socleC22×C73C22×D4
hypercenter#467D73
hypocenterC73#3249
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
2. #17988881C2semidirect
3. #17988880C2semidirect
6. #17988796C2semidirect
7. #17988795C2semidirect
76. C2×Dic73Q16semidirect
103. C73#3249semidirect