Finite Group Databasebeta

← #22615757

Subgroups — #22615757

Order 9344.

488 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 143 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×#14556590C211yesmaximal, characteristic, complemented
2C2×#14556547C211yesmaximal, characteristic
3#17988527C211yesmaximal, characteristic, complemented
4#17988525C211yesmaximal, characteristic, complemented
5#17988523C211yesmaximal, characteristic
6#17988507C212yesmaximal, complemented
7#17988499C212yesmaximal
8#17988482C212yesmaximal, complemented
9#17988451C211yesmaximal, characteristic, complemented
10#17988445C212yesmaximal
11#399×C73C211yesmaximal, characteristic
12C22×Dic146C2212yes—
13C23×Dic73C2211yescharacteristic
14#14556590—24no—
15#14556547—24no—
16C2×C4⋊Dic73C2211yescharacteristic
17C2×#11924007C2212yes—
18C2×#11924007C2212yes—
19C2×#11924007C2211yescharacteristic
20C2×#11924007C2211yescharacteristic
21C2×#11924007C2212yes—
22C2×C22⋊Dic73C2211yescharacteristic
23C2×C22⋊Dic73C2212yes—
24C2×C4×Dic73C2211yescharacteristic
25C2×C4×Dic73C2211yescharacteristic
26#14556498C2212yes—
27#14556498C2212yes—
28#14556498C2212yes—
29#14556498C2211yescharacteristic
30#14556498C2212yes—
31#14556498C2212yes—
32C2×C4⋊C4×C73C2211yescharacteristic
33C2×C4⋊C4×C73C2212yes—
34C2×C22⋊C4×C73C2211yescharacteristic
35C2×C22⋊C4×C73C2212yes—
36#95×C73C2211yescharacteristic
37C2×Dic146—24no—
38C2×Dic146—42no—
39C2×Dic146—42no—
40C22×Dic73—22no—
41C22×Dic73—22no—
42C22×Dic73Q814yescomplemented
43C22×Dic73C2311yescharacteristic
44C22×Dic73C2312yes—
45C22×Dic73C2312yes—
46C22×Dic73C2311yescharacteristic
47C22×Dic73C2311yescharacteristic
48C22×Dic73C2311yescharacteristic
49C4⋊Dic73—22no—
50#11924007—22no—
51#11924007—22no—
52#11924007—24no—
53#11924007—24no—
54#11924007—42no—
55C22⋊Dic73—22no—
56C22⋊Dic73—42no—
57C4×Dic73—22no—
58C4×Dic73D414yes—
59C24×C73C2311yescharacteristic
60C22×C4×C73C2312yes—
61C22×C4×C73C2312yes—
62C22×C4×C73C2311yescharacteristic
63C22×C4×C73C2311yescharacteristic
64C4⋊C4×C73—22no—
65C4⋊C4×C73—42no—
66C22⋊C4×C73—22no—
67C22⋊C4×C73—42no—
68C23×C73—21no—
69C23×C73—21no—
70C23×C73—22no—
71C23×C73—22no—
72C23×C73C2×Q812yes—
73C23×C73C2411yescharacteristic
74C2×C4×C73—22no—
75C2×C4×C73—21no—
76C2×C4×C73—22no—
77C2×C4×C73—22no—
78C2×C4×C73—22no—
79C2×C4×C73—22no—
80C2×C4×C73—22no—
81C2×C4×C73—22no—
82C2×C4×C73—22no—
83C2×C4×C73C2×D412yes—
84C2×Dic73—21no—
85C2×Dic73—21no—
86C2×Dic73—22no—
87C2×Dic73—28no—
88C2×Dic73—21no—
89C2×Dic73—22no—
90C2×Dic73—22no—
91C2×Dic73—22no—
92C2×Dic73—22no—
93C2×Dic73—22no—
94C2×Dic73—22no—
95C2×Dic73—22no—
96C2×Dic73C2×D412yes—
97C2×Dic73C2×D412yes—
98C2×Dic73C2×Q812yes—
99C2×Dic73C2×Q812yes—
100C2×Dic73#4112yes—
101Dic146—48no—
102C22×C73—22no—
103C22×C73—24no—
104C22×C73—41no—
105C22×C73—41no—
106C22×C73—42no—
107C22×C73C22×D411yescharacteristic
108C22×C73C22×Q811yescharacteristic
109C22×C73C2×#4111yescharacteristic
110C22×C73H(5,𝔽2)12yes—
111C22×C732−1+412yes—
112C4×C73—22no—
113C4×C73—42no—
114C4×C73—41no—
115C4×C73—42no—
116Dic73—22no—
117Dic73—22no—
118Dic73—42no—
119Dic73—41no—
120Dic73—42no—
121Dic73C22⋊Q814yes—
122C2×C73—42no—
123C2×C73C2×C22⋊Q811yescharacteristic
124C2×C73#53511yescharacteristic
125C2×C73#53611yescharacteristic
126C2×C73#54212yes—
127C2×C73#54412yes—
128#2628—731nomaximal, Sylow
129C73#262811yescharacteristic, complemented, Sylow
130C2×C4⋊Q8—731no—
131C2×#117—731no—
132#400—731no—
133#400—731no—
134#399—731no—
135#399D7311yescharacteristic
136#395—732no—
137#393—732no—
138#389—732no—
139#382—731no—
140#380—732no—
141C22×Q8—732no—
142C23×C4—731no—
143C4⋊Q8—1464no—
144#117—1464no—
145C2×C4⋊C4—732no—
146C2×C4⋊C4—731no—
147C2×C4⋊C4—731no—
148C2×C4⋊C4—732no—
149C2×C4⋊C4—731no—
150C2×C4⋊C4—732no—
151C2×C4⋊C4C2×D7311yescharacteristic
152C2×C4⋊C4C2×D7312yes—
153C2×C22⋊C4—732no—
154C2×C22⋊C4—731no—
155C2×C22⋊C4C2×D7311yescharacteristic
156C2×C22⋊C4C2×D7312yes—
157C2×C42—731no—
158C2×C42—731no—
159#95—732no—
160#95—732no—
161#95—732no—
162#95—731no—
163#95—732no—
164#95—732no—
165#95C2×D7311yescharacteristic
166C24C22×D7311yescharacteristic
167C2×Q8—2922no—
168C2×Q8—2922no—
169C2×Q8—1464no—
170C22×C4—731no—
171C22×C4—734no—
172C22×C4—731no—
173C22×C4—731no—
174C22×C4—731no—
175C22×C4—732no—
176C22×C4—732no—
177C22×C4—1462no—
178C22×C4—1462no—
179C22×C4C22×D7312yes—
180C22×C4C22×D7312yes—
181C22×C4C22×D7311yescharacteristic
182C22×C4C22×D7311yescharacteristic
183C4⋊C4—22no—
184C4⋊C4—42no—
185C4⋊C4—2922no—
186C4⋊C4—1464no—
187C4⋊C4—1462no—
188C4⋊C4—1464no—
189C4⋊C4—1462no—
190C4⋊C4—1462no—
191C22⋊C4—22no—
192C22⋊C4—42no—
193C22⋊C4—2922no—
194C22⋊C4—1462no—
195C42—734no—
196C42—1462no—
197C23—21no—
198C23—21no—
199C23—22no—
200C23—22no—
201C23Q8×D7312yes—
202C23C23×D7311yescharacteristic
203Q8—2928no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—732no—
214C2×C4—732no—
215C2×C4—732no—
216C2×C4—732no—
217C2×C4—732no—
218C2×C4—1461no—
219C2×C4—1462no—
220C2×C4—1462no—
221C2×C4—1462no—
222C2×C4—1462no—
223C2×C4—1462no—
224C2×C4—1462no—
225C2×C4—1462no—
226C2×C4—1468no—
227C2×C4—1461no—
228C2×C4—1461no—
229C2×C4—1462no—
230C2×C4D4×D7312yes—
231C22—24no—
232C22—22no—
233C22—41no—
234C22—41no—
235C22—42no—
236C22C2×D4×D7311yescharacteristic
237C22C2×Q8×D7311yescharacteristic
238C22#41×D7311yescharacteristic
239C22#1455663612yes—
240C22#1455663812yes—
241C4—22no—
242C4—42no—
243C4—41no—
244C4—42no—
245C4—2922no—
246C4—2921no—
247C4—2922no—
248C4—734no—
249C4—1462no—
250C4—1462no—
251C2—42no—
252C2C22⋊Q8×D7311yescharacteristic
253C2#1798915011yescharacteristic
254C2#1798915911yescharacteristic
255C2#1798920512yes—
256C2#1798921612yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#399×C73C2
hypercenter#399D73
hypocenterC73#2628
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#14556590C2semidirect
3. #17988527C2semidirect
4. #17988525C2semidirect
6. #17988507C2semidirect
8. #17988482C2semidirect
9. #17988451C2semidirect
42. C22×Dic73Q8semidirect
129. C73#2628semidirect