Finite Group Databasebeta

← #22615283

Subgroups — #22615283

Order 9344.

584 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 153 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×#14556551C211yesmaximal, characteristic
2C22×#11924007C211yesmaximal, characteristic, complemented
3#17988518C212yesmaximal, complemented
4#17988511C212yesmaximal, complemented
5#17988469C212yesmaximal, complemented
6#17988466C211yesmaximal, characteristic
7#17988464C211yesmaximal, characteristic
8#17988459C211yesmaximal, characteristic, complemented
9#17988458C212yesmaximal, complemented
10#17988445C211yesmaximal, characteristic, complemented
11#385×C73C211yesmaximal, characteristic, complemented
12C22×C22⋊D73C2211yescharacteristic
13C23×Dic73C2211yescharacteristic
14C23×Dic73C2211yescharacteristic
15C22×C4×D73C2211yescharacteristic
16#14556551—24no—
17C2×#11924007—24no—
18C2×#11924007C2212yes—
19C2×#11924007C2212yes—
20C2×#11924007C2212yes—
21C2×#11924007C2211yescharacteristic
22C2×#11924007C2212yes—
23C2×C22⋊Dic73C2211yescharacteristic
24C2×#11924005C2212yes—
25C2×#11924005C2211yescharacteristic
26C2×#11924005C2212yes—
27C2×C4×Dic73C2211yescharacteristic
28#14556498C2212yes—
29#14556498C2212yes—
30#14556498C2212yes—
31#14556498C2212yes—
32C23×C4×C73C2211yescharacteristic
33C2×C4⋊C4×C73C2212yes—
34C2×C22⋊C4×C73C2211yescharacteristic
35C2×C22⋊C4×C73C2211yescharacteristic
36#95×C73C2212yes—
37C23×D73C2311yescharacteristic
38C2×C22⋊D73—22no—
39C2×C22⋊D73—22no—
40C2×C22⋊D73Q814yes—
41C22×Dic73—22no—
42C22×Dic73—24no—
43C22×Dic73—42no—
44C22×Dic73D414yes—
45C22×Dic73C2312yes—
46C22×Dic73C2311yescharacteristic
47C22×Dic73C2311yescharacteristic
48C22×Dic73C2311yescharacteristic
49C22×Dic73C2312yes—
50C2×C4×D73—22no—
51C2×C4×D73—42no—
52#11924007—24no—
53#11924007—24no—
54#11924007—22no—
55#11924007—24no—
56#11924007—42no—
57C22⋊Dic73—22no—
58#11924005—22no—
59#11924005—24no—
60#11924005—42no—
61C4×Dic73—22no—
62C24×C73C2311yescharacteristic
63C22×C4×C73—22no—
64C22×C4×C73—42no—
65C22×C4×C73C2311yescharacteristic
66C22×C4×C73C2312yes—
67C22×C4×C73C2312yes—
68C22×C4×C73C2311yescharacteristic
69C4⋊C4×C73—42no—
70C22⋊C4×C73—22no—
71C22⋊C4×C73—22no—
72C23×C73—22no—
73C23×C73—22no—
74C23×C73C2×D412yes—
75C23×C73C2×Q812yes—
76C23×C73#4112yes—
77C23×C73C2411yescharacteristic
78C22×D73—21no—
79C22×D73—22no—
80C22×D73—21no—
81C22×D73—22no—
82C22×D73C2×Q812yes—
83C2×C4×C73—21no—
84C2×C4×C73—21no—
85C2×C4×C73—22no—
86C2×C4×C73—22no—
87C2×C4×C73—22no—
88C2×C4×C73—22no—
89C2×C4×C73—22no—
90C2×C4×C73—22no—
91C2×C4×C73—22no—
92C2×C4×C73—22no—
93C2×C4×C73—44no—
94C22⋊D73—28no—
95C2×Dic73—28no—
96C2×Dic73—21no—
97C2×Dic73—22no—
98C2×Dic73—22no—
99C2×Dic73—21no—
100C2×Dic73—22no—
101C2×Dic73—22no—
102C2×Dic73—22no—
103C2×Dic73—22no—
104C2×Dic73—22no—
105C2×Dic73—44no—
106C2×Dic73C2×D412yes—
107C2×Dic73C2×D412yes—
108C2×Dic73C2×Q812yes—
109C2×Dic73#4114yes—
110C4×D73—44no—
111C22×C73—22no—
112C22×C73—22no—
113C22×C73—24no—
114C22×C73—24no—
115C22×C73C22⋊Q814yes—
116C22×C73C22×D411yescharacteristic
117C22×C73C22×Q811yescharacteristic
118C22×C73C2×#4112yes—
119C22×C73C2×#4111yescharacteristic
120C22×C73H(5,𝔽2)12yes—
121C2×D73—22no—
122C2×D73—24no—
123C2×D73—41no—
124C2×D73—41no—
125C2×D73—42no—
126C4×C73—41no—
127C4×C73—41no—
128C4×C73—42no—
129C4×C73—42no—
130Dic73—22no—
131Dic73—24no—
132Dic73—22no—
133Dic73—22no—
134Dic73—42no—
135C2×C73—24no—
136C2×C73C2×C22⋊Q811yescharacteristic
137C2×C73#52511yescharacteristic
138C2×C73#53411yescharacteristic
139C2×C73#55312yes—
140C2×C73#55412yes—
141D73—42no—
142#2579—731nomaximal, Sylow
143C73#257911yescharacteristic, complemented, Sylow
144C2×C4×D4—731no—
145C22×C4⋊C4—731no—
146#398—732no—
147#396—732no—
148#387—732no—
149#386—731no—
150#386—731no—
151#385—732no—
152#385—731no—
153#385D7311yescharacteristic, complemented
154#380—731no—
155C22×D4—731no—
156C23×C4—731no—
157C23×C4—731no—
158C23×C4—731no—
159C23×C4C2×D7311yescharacteristic
160C4×D4—1464no—
161C2×C4⋊C4—732no—
162C2×C4⋊C4—732no—
163C2×C4⋊C4—732no—
164C2×C4⋊C4—731no—
165C2×C4⋊C4—732no—
166C2×C4⋊C4—1464no—
167C2×C4⋊C4C2×D7312yes—
168C2×C22⋊C4—732no—
169C2×C22⋊C4—731no—
170C2×C22⋊C4—731no—
171C2×C22⋊C4—732no—
172C2×C22⋊C4C2×D7311yescharacteristic
173C2×C22⋊C4C2×D7311yescharacteristic
174C2×C42—731no—
175#95—732no—
176#95—732no—
177#95—732no—
178#95—732no—
179#95C2×D7312yes—
180C24—731no—
181C24C22×D7311yescharacteristic
182C2×D4—734no—
183C2×D4—1462no—
184C2×D4—1462no—
185C22×C4—22no—
186C22×C4—42no—
187C22×C4—2922no—
188C22×C4—2922no—
189C22×C4—734no—
190C22×C4—731no—
191C22×C4—731no—
192C22×C4—732no—
193C22×C4—731no—
194C22×C4—732no—
195C22×C4—1462no—
196C22×C4—1464no—
197C22×C4—1462no—
198C22×C4C22×D7312yes—
199C22×C4C22×D7311yescharacteristic
200C22×C4C22×D7312yes—
201C22×C4C22×D7311yescharacteristic
202C4⋊C4—42no—
203C4⋊C4—2922no—
204C4⋊C4—1464no—
205C4⋊C4—1464no—
206C4⋊C4—1464no—
207C4⋊C4—1462no—
208C22⋊C4—22no—
209C22⋊C4—22no—
210C22⋊C4—2922no—
211C22⋊C4—1464no—
212C22⋊C4—1462no—
213C22⋊C4—1462no—
214C42—1462no—
215C23—22no—
216C23—22no—
217C23—732no—
218C23—1461no—
219C23—1462no—
220C23—1461no—
221C23—1462no—
222C23D4×D7312yes—
223C23Q8×D7312yes—
224C23#1192402812yes—
225C23C23×D7311yescharacteristic
226D4—1468no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—44no—
238C2×C4—2924no—
239C2×C4—2924no—
240C2×C4—732no—
241C2×C4—732no—
242C2×C4—732no—
243C2×C4—734no—
244C2×C4—1462no—
245C2×C4—1462no—
246C2×C4—1462no—
247C2×C4—1468no—
248C2×C4—1461no—
249C2×C4—1462no—
250C2×C4—1462no—
251C2×C4—1461no—
252C2×C4—1462no—
253C2×C4—1462no—
254C22—22no—
255C22—24no—
256C22—24no—
257C22—22no—
258C22—2921no—
259C22—2922no—
260C22—2921no—
261C22—1464no—
262C22—1462no—
263C22#1455656914yes—
264C22C2×D4×D7311yescharacteristic
265C22C2×Q8×D7311yescharacteristic
266C22#41×D7312yes—
267C22C2×#1192402811yescharacteristic
268C22#1455663612yes—
269C4—42no—
270C4—41no—
271C4—42no—
272C4—41no—
273C4—2922no—
274C4—1462no—
275C4—1462no—
276C4—1462no—
277C4—1464no—
278C2—24no—
279C2—2922no—
280C2C2×#1455656911yescharacteristic
281C2#1798909511yescharacteristic
282C2#1798914711yescharacteristic
283C2#1798928612yes—
284C2#1798929112yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#385×C73C2
hypercenter#385D73
hypocenterC73#2579
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C22×#11924007C2semidirect
3. #17988518C2semidirect
4. #17988511C2semidirect
5. #17988469C2semidirect
8. #17988459C2semidirect
9. #17988458C2semidirect
10. #17988445C2semidirect
11. #385×C73C2semidirect
143. C73#2579semidirect
153. #385D73semidirect