Finite Group Databasebeta

← #22614420

Subgroups — #22614420

Order 9344.

596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14556566C211yesmaximal, characteristic
2C2×C4⋊C4×D73C211yesmaximal, characteristic, complemented
3#17988516C214yesmaximal, complemented
4#17988489C211yesmaximal, characteristic, complemented
5#17988488C211yesmaximal, characteristic, complemented
6#17988465C214yesmaximal, complemented
7#17988452C211yesmaximal, characteristic, complemented
8C4×#11924005C211yesmaximal, characteristic, complemented
9#382×C73C211yesmaximal, characteristic, complemented
10C22×D292C2212yes—
11C22×D292C2211yescharacteristic
12C22×C4×D73C2211yescharacteristic
13C22×C4×D73C2212yes—
14#14556566—24no—
15C2×C4⋊Dic73C2211yescharacteristic
16C2×#11924007C2212yes—
17C4⋊C4×D73—24no—
18C2×#11924005C2212yes—
19C2×#11924005C2212yes—
20C2×#11924005C2214yes—
21C2×#11924005C2214yes—
22C2×C4×Dic73C2211yescharacteristic
23#14556498C2212yes—
24#14556498C2214yes—
25C2×C4⋊C4×C73C2211yescharacteristic
26C2×C4⋊C4×C73C2211yescharacteristic
27C2×C42×C73C2211yescharacteristic
28#95×C73C2214yes—
29C23×D73C2312yes—
30C23×D73C2311yescharacteristic
31C2×D292—24no—
32C2×D292—28no—
33C2×D292—22no—
34C2×D292—22no—
35C2×D292—22no—
36C22×Dic73C2312yes—
37C22×Dic73C2312yes—
38C22×Dic73C2311yescharacteristic
39C2×C4×D73—22no—
40C2×C4×D73—22no—
41C2×C4×D73—24no—
42C2×C4×D73—44no—
43C2×C4×D73D414yes—
44C4⋊Dic73—22no—
45#11924007—24no—
46#11924005—24no—
47#11924005—24no—
48#11924005—44no—
49#11924005—44no—
50C4×Dic73—22no—
51C22×C4×C73C2312yes—
52C22×C4×C73C2312yes—
53C22×C4×C73C2312yes—
54C22×C4×C73C2311yescharacteristic
55C4⋊C4×C73—22no—
56C4⋊C4×C73—22no—
57C42×C73—22no—
58C23×C73C2411yescharacteristic
59C22×D73—21no—
60C22×D73—21no—
61C22×D73—22no—
62C22×D73—22no—
63C22×D73—24no—
64C22×D73—22no—
65C22×D73—22no—
66C22×D73—24no—
67C22×D73C2×D412yes—
68C22×D73#4114yes—
69C2×C4×C73—22no—
70C2×C4×C73—22no—
71C2×C4×C73—22no—
72C2×C4×C73—22no—
73C2×C4×C73—24no—
74C2×C4×C73—22no—
75C2×C4×C73—24no—
76C2×C4×C73C2×D412yes—
77C2×C4×C73#4112yes—
78C2×C4×C73#4112yes—
79C2×Dic73—21no—
80C2×Dic73—21no—
81C2×Dic73—22no—
82C2×Dic73—22no—
83C2×Dic73—22no—
84C2×Dic73—22no—
85C2×Dic73—24no—
86C2×Dic73C2×D412yes—
87D292—48no—
88D292—44no—
89C4×D73—28no—
90C4×D73—48no—
91C22×C73C22×D411yescharacteristic
92C22×C73C2×#4112yes—
93C22×C73C2×#4111yescharacteristic
94C22×C73C2×#4111yescharacteristic
95C22×C73H(5,𝔽2)12yes—
96C2×D73—22no—
97C2×D73—22no—
98C2×D73—24no—
99C2×D73—24no—
100C2×D73—42no—
101C2×D73—42no—
102C2×D73—42no—
103C2×D73—44no—
104C2×D73—44no—
105C2×D73#12414yes—
106C4×C73—42no—
107C4×C73—42no—
108C4×C73—42no—
109C4×C73#12314yes—
110Dic73—22no—
111Dic73—42no—
112Dic73—42no—
113C2×C73C2×#12311yescharacteristic
114C2×C73C2×#12411yescharacteristic
115C2×C73#53511yescharacteristic
116C2×C73#55312yes—
117C2×C73#55312yes—
118D73—24no—
119D73—82no—
120#2504—731nomaximal, Sylow
121C73#250411yescharacteristic, complemented, Sylow
122C2×#121—731no—
123C22×C4⋊C4—731no—
124#397—734no—
125#390—731no—
126#390—731no—
127#386—734no—
128#382—731no—
129#382D7311yescharacteristic, complemented
130C4×C22⋊C4—731no—
131C22×D4—732no—
132C22×D4—731no—
133C23×C4—732no—
134C23×C4—731no—
135#121—1464no—
136C2×C4⋊C4—731no—
137C2×C4⋊C4—732no—
138C2×C4⋊C4—1464no—
139C2×C4⋊C4C2×D7311yescharacteristic
140C2×C4⋊C4C2×D7311yescharacteristic
141C2×C22⋊C4—734no—
142C2×C22⋊C4—734no—
143C2×C22⋊C4—732no—
144C2×C22⋊C4—732no—
145C2×C42—731no—
146C2×C42C2×D7311yescharacteristic
147#95—732no—
148#95—734no—
149#95C2×D7314yes—
150C24—731no—
151C24—732no—
152C2×D4—1464no—
153C2×D4—1468no—
154C2×D4—1462no—
155C2×D4—1462no—
156C2×D4—1462no—
157C22×C4—2924no—
158C22×C4—731no—
159C22×C4—734no—
160C22×C4—732no—
161C22×C4—732no—
162C22×C4—1464no—
163C22×C4—1462no—
164C22×C4—1462no—
165C22×C4C22×D7312yes—
166C22×C4C22×D7312yes—
167C22×C4C22×D7312yes—
168C22×C4C22×D7311yescharacteristic
169C4⋊C4—22no—
170C4⋊C4—22no—
171C4⋊C4—1464no—
172C4⋊C4—1462no—
173C22⋊C4—2924no—
174C22⋊C4—2924no—
175C22⋊C4—1464no—
176C22⋊C4—1464no—
177C42—22no—
178C42—1462no—
179C23—732no—
180C23—734no—
181C23—1462no—
182C23—1464no—
183C23—1462no—
184C23—1462no—
185C23—1464no—
186C23—1461no—
187C23—1461no—
188C23—1462no—
189C23C23×D7311yescharacteristic
190D4—2928no—
191D4—2924no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—24no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—24no—
199C2×C4—2928no—
200C2×C4—732no—
201C2×C4—1462no—
202C2×C4—1462no—
203C2×C4—1462no—
204C2×C4—1462no—
205C2×C4—1464no—
206C2×C4—1461no—
207C2×C4—1461no—
208C2×C4—1468no—
209C2×C4D4×D7312yes—
210C2×C4#1192402812yes—
211C2×C4#1192402912yes—
212C22—2922no—
213C22—2924no—
214C22—2924no—
215C22—2922no—
216C22—2922no—
217C22—734no—
218C22—1462no—
219C22—1464no—
220C22—1464no—
221C22—1462no—
222C22C2×D4×D7311yescharacteristic
223C22#41×D7312yes—
224C22C2×#1192402811yescharacteristic
225C22C2×#1192402911yescharacteristic
226C22#1455663712yes—
227C4—42no—
228C4—42no—
229C4—42no—
230C4—2922no—
231C4—2922no—
232C4—1462no—
233C4#1455657614yes—
234C2—5842no—
235C2—1464no—
236C2C2×#1455657611yescharacteristic
237C2#124×D7311yescharacteristic
238C2#1798915511yescharacteristic
239C2#1798928112yes—
240C2#1798929012yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#382×C73C2
hypercenter#382D73
hypocenterC73#2504
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D73C2semidirect
3. #17988516C2semidirect
4. #17988489C2semidirect
5. #17988488C2semidirect
6. #17988465C2semidirect
7. #17988452C2semidirect
8. C4×#11924005C2semidirect
9. #382×C73C2semidirect
121. C73#2504semidirect
129. #382D73semidirect