Finite Group Databasebeta

← #22614411

Subgroups — #22614411

Order 9344.

512 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14556569C211yesmaximal, characteristic
2C2×C4⋊C4×D73C211yesmaximal, characteristic
3#17988527C211yesmaximal, characteristic, complemented
4#17988526C211yesmaximal, characteristic, complemented
5#17988525C211yesmaximal, characteristic, complemented
6#17988491C212yesmaximal, complemented
7#17988451C212yesmaximal, complemented
8#17988449C212yesmaximal
9#17988449C212yesmaximal
10#17988434C211yesmaximal, characteristic
11#400×C73C211yesmaximal, characteristic, complemented
12C22×Dic146C2211yescharacteristic
13C22×C4×D73C2212yes—
14C22×C4×D73C2211yescharacteristic
15#14556569—24no—
16C2×C4⋊Dic73C2211yescharacteristic
17C2×#11924007C2211yescharacteristic
18C2×#11924007C2212yes—
19C2×#11924007C2211yescharacteristic
20C4⋊C4×D73—24no—
21C2×#11924005C2212yes—
22C2×#11924005C2211yescharacteristic
23C2×#11924005C2211yescharacteristic
24C2×C4×Dic73C2212yes—
25#14556498C2211yescharacteristic
26#14556498C2212yes—
27#14556498C2212yes—
28#14556498C2212yes—
29#14556498C2212yes—
30#14556498C2212yes—
31#14556498C2212yes—
32C2×C4⋊C4×C73C2211yescharacteristic
33C2×C4⋊C4×C73C2211yescharacteristic
34#95×C73C2211yescharacteristic
35#95×C73C2212yes—
36#95×C73C2212yes—
37C23×D73C2311yescharacteristic
38C2×Dic146—22no—
39C2×Dic146—24no—
40C22×Dic73C2312yes—
41C22×Dic73C2311yescharacteristic
42C22×Dic73C2311yescharacteristic
43C22×Dic73C2312yes—
44C22×Dic73C2311yescharacteristic
45C2×C4×D73—24no—
46C2×C4×D73—24no—
47C2×C4×D73—28no—
48C2×C4×D73D414yes—
49C4⋊Dic73—22no—
50#11924007—22no—
51#11924007—24no—
52#11924007—22no—
53#11924005—22no—
54#11924005—22no—
55#11924005—24no—
56C4×Dic73—24no—
57C22×C4×C73C2312yes—
58C22×C4×C73C2311yescharacteristic
59C22×C4×C73C2311yescharacteristic
60C22×C4×C73C2312yes—
61C22×C4×C73C2311yescharacteristic
62C4⋊C4×C73—22no—
63C4⋊C4×C73—22no—
64C23×C73C2411yescharacteristic
65C22×D73—22no—
66C22×D73—21no—
67C22×D73—21no—
68C22×D73C2×D412yes—
69C22×D73#4114yes—
70C2×C4×C73—22no—
71C2×C4×C73—21no—
72C2×C4×C73—21no—
73C2×C4×C73—22no—
74C2×C4×C73—22no—
75C2×C4×C73—22no—
76C2×C4×C73—24no—
77C2×C4×C73—22no—
78C2×C4×C73—21no—
79C2×C4×C73—22no—
80C2×C4×C73—21no—
81C2×C4×C73C2×D412yes—
82C2×Dic73—21no—
83C2×Dic73—21no—
84C2×Dic73—22no—
85C2×Dic73—22no—
86C2×Dic73—22no—
87C2×Dic73—24no—
88C2×Dic73—22no—
89C2×Dic73—21no—
90C2×Dic73—21no—
91C2×Dic73—22no—
92C2×Dic73C2×D412yes—
93C2×Dic73#4114yes—
94C4×D73—28no—
95C4×D73—48no—
96Dic146—44no—
97C22×C73C22×D411yescharacteristic
98C22×C73C2×#4112yes—
99C22×C73C2×#4112yes—
100C22×C732−1+411yescharacteristic
101C22×C732−1+411yescharacteristic
102C2×D73—22no—
103C2×D73—22no—
104C2×D73—24no—
105C2×D73—24no—
106C2×D73#12414yes—
107C4×C73—22no—
108C4×C73—41no—
109C4×C73—42no—
110C4×C73—41no—
111C4×C73—42no—
112Dic73—41no—
113Dic73—42no—
114Dic73—41no—
115Dic73—42no—
116Dic73#12314yes—
117C2×C73C2×#12311yescharacteristic
118C2×C73C2×#12411yescharacteristic
119C2×C73#53611yescharacteristic
120C2×C73#55212yes—
121C2×C73#55212yes—
122D73—24no—
123#2503—731nomaximal, Sylow
124C73#250311yescharacteristic, complemented, Sylow
125C2×C22⋊Q8—731no—
126C22×C4⋊C4—731no—
127#400—731no—
128#400—731no—
129#400—731no—
130#400D7311yescharacteristic, complemented
131#391—732no—
132#382—732no—
133#381—732no—
134#381—732no—
135C4×C22⋊C4—731no—
136C22×Q8—731no—
137C23×C4—731no—
138C23×C4—732no—
139C22⋊Q8—1464no—
140C2×C4⋊C4—732no—
141C2×C4⋊C4—731no—
142C2×C4⋊C4—731no—
143C2×C4⋊C4—731no—
144C2×C4⋊C4—1464no—
145C2×C4⋊C4C2×D7311yescharacteristic
146C2×C4⋊C4C2×D7311yescharacteristic
147C2×C22⋊C4—731no—
148C2×C22⋊C4—731no—
149C2×C22⋊C4—732no—
150C2×C42—732no—
151#95—731no—
152#95—732no—
153#95—732no—
154#95—732no—
155#95—732no—
156#95—732no—
157#95—732no—
158#95C2×D7311yescharacteristic
159#95C2×D7312yes—
160#95C2×D7312yes—
161C24—731no—
162C2×Q8—1462no—
163C2×Q8—1464no—
164C22×C4—731no—
165C22×C4—734no—
166C22×C4—732no—
167C22×C4—731no—
168C22×C4—731no—
169C22×C4—732no—
170C22×C4—1464no—
171C22×C4—1468no—
172C22×C4—1464no—
173C22×C4C22×D7312yes—
174C22×C4C22×D7311yescharacteristic
175C22×C4C22×D7311yescharacteristic
176C22×C4C22×D7312yes—
177C22×C4C22×D7311yescharacteristic
178C4⋊C4—22no—
179C4⋊C4—22no—
180C4⋊C4—1464no—
181C4⋊C4—1462no—
182C4⋊C4—1462no—
183C4⋊C4—1462no—
184C22⋊C4—1464no—
185C22⋊C4—1462no—
186C22⋊C4—1462no—
187C42—1464no—
188C23—732no—
189C23—734no—
190C23—1462no—
191C23—1461no—
192C23—1461no—
193C23C23×D7311yescharacteristic
194Q8—2924no—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—24no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—2928no—
207C2×C4—732no—
208C2×C4—734no—
209C2×C4—1468no—
210C2×C4—1461no—
211C2×C4—1461no—
212C2×C4—1462no—
213C2×C4—1462no—
214C2×C4—1462no—
215C2×C4—1464no—
216C2×C4—1462no—
217C2×C4—1461no—
218C2×C4—1461no—
219C2×C4—1462no—
220C2×C4D4×D7312yes—
221C22—734no—
222C22—1462no—
223C22—1464no—
224C22—1464no—
225C22—1462no—
226C22C2×D4×D7311yescharacteristic
227C22#41×D7312yes—
228C22#41×D7312yes—
229C22#1455663811yescharacteristic
230C22#1455663911yescharacteristic
231C4—22no—
232C4—41no—
233C4—42no—
234C4—41no—
235C4—42no—
236C4—2921no—
237C4—2922no—
238C4—2921no—
239C4—2922no—
240C4—734no—
241C2—1464no—
242C2#123×D7311yescharacteristic
243C2#124×D7311yescharacteristic
244C2#1798916011yescharacteristic
245C2#1798926912yes—
246C2#1798927312yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#400×C73C2
hypercenter#400D73
hypocenterC73#2503
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
3. #17988527C2semidirect
4. #17988526C2semidirect
5. #17988525C2semidirect
6. #17988491C2semidirect
7. #17988451C2semidirect
11. #400×C73C2semidirect
124. C73#2503semidirect
130. #400D73semidirect