Finite Group Databasebeta

← #22621237

Subgroups — #22621237

Order 9344.

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

normal subgroups only

This group has 436 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#17989132C212yesmaximal, complemented
2#17988866C212yesmaximal, complemented
3#17988865C212yesmaximal, complemented
4#17988823C211yesmaximal, characteristic, complemented
5#17988821C212yesmaximal, complemented
6#17988781C212yesmaximal, complemented
7#17988780C212yesmaximal, complemented
8C2×#14556520C211yesmaximal, characteristic, complemented
9#466×C73C211yesmaximal, characteristic, complemented
10C2×#11924027—22no—
11C2×D584C2211yescharacteristic
12C2×#11924013C2212yes—
13C22×#10596831C2211yescharacteristic
14#14556590C2212yes—
15#14556587C2212yes—
16#14556577—22no—
17#14556565C2212yes—
18#14556563—22no—
19D4×Dic73C2212yes—
20#14556553C2212yes—
21#14556551—22no—
22C2×C4×Dic73C2211yescharacteristic
23#14556525C2211yescharacteristic
24#14556524C2212yes—
25#14556520C2212yes—
26#14556520C2212yes—
27#14556513C2212yes—
28#14556512C2212yes—
29#14556511C2212yes—
30C2×D8×C73C2211yescharacteristic
31C22×C8×C73C2211yescharacteristic
32#121×C73C2212yes—
33#107×C73C2211yescharacteristic
34#102×C73C2212yes—
35#11924027—48no—
36C2×Dic146—22no—
37C2×D292C2312yes—
38C2×C22⋊D73—22no—
39C2×C22⋊D73—22no—
40C2×C22⋊D73—22no—
41C22×Dic73—22no—
42C22×Dic73D411yescharacteristic
43C22×Dic73D411yescharacteristic
44C2×C4×D73—22no—
45D584—41no—
46#11924013—42no—
47C2×#10596831—41no—
48C2×#10596831C2312yes—
49C4⋊Dic73C2312yes—
50#11924007—22no—
51C22⋊Dic73—22no—
52#11924005—22no—
53#11924005—22no—
54C4×Dic73D412yes—
55C4×Dic73C2312yes—
56C2×D4×C73—22no—
57C2×D4×C73C2312yes—
58C22×C4×C73C2311yescharacteristic
59D8×C73—41no—
60C2×C8×C73—41no—
61C2×C8×C73C2311yescharacteristic
62C2×C8×C73C2311yescharacteristic
63C4⋊C4×C73C2312yes—
64C22⋊C4×C73—22no—
65C23×C73—22no—
66C23×C73C2×D411yescharacteristic
67C22×D73—22no—
68D4×C73—22no—
69D4×C73—22no—
70D4×C73—44no—
71C2×C4×C73—21no—
72C2×C4×C73—21no—
73C2×C4×C73—22no—
74C2×C4×C73C2×D411yescharacteristic
75C2×C4×C73C2411yescharacteristic
76C22⋊D73—44no—
77C22⋊D73—44no—
78C22⋊D73—44no—
79C2×Dic73—22no—
80C2×Dic73—41no—
81C2×Dic73—44no—
82C2×Dic73D814yescomplemented
83C2×Dic73C2×D412yes—
84C2×Dic73C2×D412yes—
85D292—22no—
86D292—22no—
87C4×D73—44no—
88Dic146—44no—
89C8×C73—21no—
90C8×C73—21no—
91#10596831—22no—
92C22×C73—21no—
93C22×C73—21no—
94C22×C73—42no—
95C22×C73—42no—
96C22×C73—42no—
97C22×C73C2×D812yes—
98C22×C73C22×D411yescharacteristic
99C2×D73—42no—
100C2×D73—42no—
101C2×D73—42no—
102C4×C73—21no—
103C4×C73—42no—
104C4×C73H(5,𝔽2)11yescharacteristic
105C4×C732−1+411yescharacteristic
106Dic73—22no—
107Dic73—42no—
108Dic73C2×D814yes—
109C2×C73—22no—
110C2×C73—82no—
111C2×C73#53711yescharacteristic
112C2×C73C22×D811yescharacteristic
113C2×C73#57511yescharacteristic
114D73—82no—
115#3245—731nomaximal, Sylow
116C73#324511yescharacteristic, complemented, Sylow
117#532—732no—
118#474—732no—
119#474—732no—
120#466—731no—
121#466—732no—
122#466D7311yescharacteristic, complemented
123#459—732no—
124#459—732no—
125C2×C4⋊C8—731no—
126C2×#41—1462no—
127C2×D8—732no—
128C2×D8—731no—
129C2×D8C2×D7311yescharacteristic
130C22×C8—731no—
131C22×C8C2×D7311yescharacteristic
132C4⋊Q8—732no—
133#127—732no—
134#124—1462no—
135#121—732no—
136#121—1462no—
137#121C2×D7312yes—
138C4×D4—732no—
139C4×D4—732no—
140C4×D4—1462no—
141C2×C42—731no—
142#107—731no—
143#107—732no—
144#107C2×D7311yescharacteristic
145C4⋊C8—732no—
146C4⋊C8—732no—
147#102—732no—
148#102—732no—
149#102—732no—
150#102C2×D7312yes—
151#41—2928no—
152C2×Q8—1462no—
153C2×D4—22no—
154C2×D4—732no—
155C2×D4—1462no—
156C2×D4—1462no—
157C2×D4—1462no—
158C2×D4C22×D7312yes—
159C22×C4—731no—
160C22×C4—731no—
161C22×C4—1462no—
162C22×C4—1462no—
163C22×C4C22×D7311yescharacteristic
164D8—41no—
165D8—2921no—
166D8—2922no—
167C2×C8—41no—
168C2×C8—2921no—
169C2×C8—732no—
170C2×C8C22×D7311yescharacteristic
171C2×C8C22×D7311yescharacteristic
172C4⋊C4—732no—
173C4⋊C4—1462no—
174C4⋊C4C22×D7312yes—
175C22⋊C4—22no—
176C22⋊C4—1462no—
177C22⋊C4—1462no—
178C22⋊C4—1462no—
179C42—732no—
180C42—732no—
181C23—22no—
182C23—1462no—
183C23D4×D7311yescharacteristic
184Q8—2924no—
185D4—22no—
186D4—22no—
187D4—44no—
188D4—2924no—
189D4—2924no—
190D4—2924no—
191D4—1462no—
192D4—1462no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—2924no—
197C2×C4—2924no—
198C2×C4—2921no—
199C2×C4—734no—
200C2×C4—732no—
201C2×C4—732no—
202C2×C4—1462no—
203C2×C4D4×D7311yescharacteristic
204C2×C4C23×D7311yescharacteristic
205C8—21no—
206C8—21no—
207C8—1462no—
208C22—21no—
209C22—21no—
210C22—42no—
211C22—42no—
212C22—42no—
213C22—2922no—
214C22—2922no—
215C22—2922no—
216C22D8×D7312yes—
217C22C2×D4×D7311yescharacteristic
218C4—21no—
219C4—42no—
220C4—2922no—
221C4—734no—
222C4—1462no—
223C4#1455663611yescharacteristic
224C4#1455663811yescharacteristic
225C2—22no—
226C2—82no—
227C2—5842no—
228C2#1798916411yescharacteristic
229C2C2×D8×D7311yescharacteristic
230C2#1798938411yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#466×C73C2
socleC22×C73C22×D4
hypercenter#466D73
hypocenterC73#3245
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #17989132C2semidirect
2. #17988866C2semidirect
3. #17988865C2semidirect
4. #17988823C2semidirect
5. #17988821C2semidirect
6. #17988781C2semidirect
7. #17988780C2semidirect
8. C2×#14556520C2semidirect
9. #466×C73C2semidirect
82. C2×Dic73D8semidirect
116. C73#3245semidirect
122. #466D73semidirect