Finite Group Databasebeta

← #22617930

Subgroups — #22617930

Order 9344.

578 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 125 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×#14556573C211yesmaximal, characteristic, complemented
2C2×#14556562C211yesmaximal, characteristic, complemented
3#17988527C211yesmaximal, characteristic, complemented
4#17988523C211yesmaximal, characteristic, complemented
5#17988510C212yesmaximal, complemented
6#17988502C212yesmaximal, complemented
7#17988501C211yesmaximal, characteristic, complemented
8#17988501C212yesmaximal, complemented
9#17988495C212yesmaximal, complemented
10#17988446C211yesmaximal, characteristic, complemented
11#392×C73C211yesmaximal, characteristic, complemented
12C22×C22⋊D73C2211yescharacteristic
13C22×C22⋊D73C2212yes—
14C22×C4×D73C2211yescharacteristic
15#14556573—24no—
16#14556562—24no—
17C2×C4⋊Dic73C2211yescharacteristic
18C2×C4⋊Dic73C2211yescharacteristic
19C2×#11924007C2211yescharacteristic
20C2×#11924007C2212yes—
21C2×#11924007C2212yes—
22C2×C22⋊Dic73C2211yescharacteristic
23C2×C22⋊Dic73C2212yes—
24C2×C22⋊Dic73C2212yes—
25C2×C22⋊Dic73C2212yes—
26C2×C22⋊Dic73C2212yes—
27C2×#11924005C2211yescharacteristic
28C2×#11924005C2212yes—
29#14556498C2211yescharacteristic
30#14556498C2212yes—
31#14556498C2212yes—
32C22×D4×C73C2211yescharacteristic
33C22×D4×C73C2212yes—
34C2×C22⋊C4×C73C2211yescharacteristic
35C2×C22⋊C4×C73C2212yes—
36#95×C73C2211yescharacteristic
37C23×D73C2311yescharacteristic
38C2×C22⋊D73—24no—
39C2×C22⋊D73—22no—
40C2×C22⋊D73—42no—
41C2×C22⋊D73—42no—
42C2×C22⋊D73—42no—
43C22×Dic73C2311yescharacteristic
44C22×Dic73C2312yes—
45C22×Dic73C2311yescharacteristic
46C22×Dic73C2312yes—
47C22×Dic73C2311yescharacteristic
48C2×C4×D73—42no—
49C2×C4×D73D414yescomplemented
50C4⋊Dic73—22no—
51C4⋊Dic73—22no—
52#11924007—22no—
53#11924007—42no—
54#11924007—42no—
55C22⋊Dic73—24no—
56C22⋊Dic73—22no—
57C22⋊Dic73—42no—
58C22⋊Dic73—42no—
59C22⋊Dic73—42no—
60#11924005—22no—
61#11924005—42no—
62C24×C73C2311yescharacteristic
63C24×C73C2312yes—
64C2×D4×C73—22no—
65C2×D4×C73—42no—
66C2×D4×C73—42no—
67C2×D4×C73—42no—
68C2×D4×C73—42no—
69C22×C4×C73C2312yes—
70C22×C4×C73C2311yescharacteristic
71C22×C4×C73C2311yescharacteristic
72C22⋊C4×C73—22no—
73C22⋊C4×C73—42no—
74C23×C73—21no—
75C23×C73—22no—
76C23×C73—22no—
77C23×C73—22no—
78C23×C73—21no—
79C23×C73—22no—
80C23×C73—22no—
81C23×C73—22no—
82C23×C73—22no—
83C23×C73—22no—
84C23×C73—21no—
85C23×C73—22no—
86C23×C73C2411yescharacteristic
87C22×D73—21no—
88C22×D73—22no—
89C22×D73—22no—
90C22×D73—21no—
91C22×D73C2×D412yes—
92D4×C73—44no—
93D4×C73—48no—
94C2×C4×C73—22no—
95C2×C4×C73—21no—
96C2×C4×C73—22no—
97C2×C4×C73—22no—
98C2×C4×C73—22no—
99C2×C4×C73—22no—
100C2×C4×C73C2×D412yes—
101C22⋊D73—44no—
102C22⋊D73—48no—
103C2×Dic73—22no—
104C2×Dic73—21no—
105C2×Dic73—22no—
106C2×Dic73—21no—
107C2×Dic73—22no—
108C2×Dic73—21no—
109C2×Dic73—22no—
110C2×Dic73—22no—
111C2×Dic73—22no—
112C2×Dic73—22no—
113C2×Dic73—22no—
114C2×Dic73—21no—
115C2×Dic73C2×D412yes—
116C4×D73—44no—
117C22×C73—41no—
118C22×C73—42no—
119C22×C73—42no—
120C22×C73—41no—
121C22×C73—41no—
122C22×C73—42no—
123C22×C73—42no—
124C22×C73—42no—
125C22×C73—42no—
126C22×C73—42no—
127C22×C73—42no—
128C22×C73—42no—
129C22×C73C22×D411yescharacteristic
130C22×C73H(5,𝔽2)12yes—
131C22×C73H(5,𝔽2)12yes—
132C22×C73H(5,𝔽2)11yescharacteristic
133C22×C732−1+411yescharacteristic
134C2×D73—22no—
135C2×D73—22no—
136C2×D73—22no—
137C2×D73—42no—
138C2×D73—42no—
139C4×C73—22no—
140C4×C73—41no—
141C4×C73—42no—
142Dic73—22no—
143Dic73—41no—
144Dic73—42no—
145Dic73—41no—
146Dic73—42no—
147C2×C73—81no—
148C2×C73—82no—
149C2×C73#53411yescharacteristic
150C2×C73#53511yescharacteristic
151C2×C73#53711yescharacteristic
152C2×C73#56012yes—
153C2×C73#56212yes—
154D73—42no—
155#2813—731nomaximal, Sylow
156C73#281311yescharacteristic, complemented, Sylow
157C2×#123—731no—
158C2×#121—731no—
159#400—731no—
160#399—731no—
161#396—732no—
162#394—731no—
163#394—732no—
164#394—732no—
165#392—732no—
166#392D7311yescharacteristic, complemented
167#380—731no—
168C22×D4—732no—
169C22×D4—731no—
170C22×D4C2×D7311yescharacteristic
171C22×D4C2×D7312yes—
172C23×C4—731no—
173#123—1464no—
174#121—1464no—
175C2×C4⋊C4—732no—
176C2×C4⋊C4—732no—
177C2×C4⋊C4—731no—
178C2×C4⋊C4—731no—
179C2×C4⋊C4—731no—
180C2×C22⋊C4—732no—
181C2×C22⋊C4—732no—
182C2×C22⋊C4—732no—
183C2×C22⋊C4—732no—
184C2×C22⋊C4—732no—
185C2×C22⋊C4—731no—
186C2×C22⋊C4—731no—
187C2×C22⋊C4C2×D7311yescharacteristic
188C2×C22⋊C4C2×D7312yes—
189#95—731no—
190#95—732no—
191#95—732no—
192#95C2×D7311yescharacteristic
193C24—731no—
194C24C22×D7311yescharacteristic
195C24C22×D7312yes—
196C2×D4—22no—
197C2×D4—42no—
198C2×D4—42no—
199C2×D4—42no—
200C2×D4—42no—
201C2×D4—2922no—
202C2×D4—2922no—
203C2×D4—2922no—
204C2×D4—1464no—
205C2×D4—1462no—
206C22×C4—2922no—
207C22×C4—734no—
208C22×C4—731no—
209C22×C4—731no—
210C22×C4—732no—
211C22×C4—731no—
212C22×C4—732no—
213C22×C4C22×D7312yes—
214C22×C4C22×D7311yescharacteristic
215C22×C4C22×D7311yescharacteristic
216C4⋊C4—2922no—
217C4⋊C4—2922no—
218C4⋊C4—1462no—
219C4⋊C4—1462no—
220C4⋊C4—1462no—
221C22⋊C4—22no—
222C22⋊C4—42no—
223C22⋊C4—2922no—
224C22⋊C4—2922no—
225C22⋊C4—2922no—
226C22⋊C4—2922no—
227C22⋊C4—1462no—
228C22⋊C4—1464no—
229C22⋊C4—1462no—
230C23—21no—
231C23—22no—
232C23—22no—
233C23—22no—
234C23—22no—
235C23—22no—
236C23—22no—
237C23—21no—
238C23—22no—
239C23—22no—
240C23—21no—
241C23—22no—
242C23—732no—
243C23—1461no—
244C23—1462no—
245C23—1462no—
246C23—1461no—
247C23C23×D7311yescharacteristic
248D4—44no—
249D4—48no—
250D4—2924no—
251D4—2928no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—2924no—
259C2×C4—732no—
260C2×C4—1461no—
261C2×C4—1462no—
262C2×C4—1461no—
263C2×C4—1461no—
264C2×C4—1462no—
265C2×C4—1462no—
266C2×C4—1462no—
267C2×C4—1462no—
268C2×C4—1462no—
269C2×C4—1462no—
270C2×C4—1461no—
271C2×C4—1462no—
272C2×C4D4×D7312yes—
273C22—42no—
274C22—41no—
275C22—42no—
276C22—41no—
277C22—41no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—42no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—2922no—
286C22—2922no—
287C22—1462no—
288C22—1462no—
289C22—1462no—
290C22C2×D4×D7311yescharacteristic
291C22#1455663612yes—
292C22#1455663612yes—
293C22#1455663611yescharacteristic
294C22#1455663811yescharacteristic
295C4—22no—
296C4—41no—
297C4—42no—
298C4—2921no—
299C4—2922no—
300C4—2921no—
301C4—2922no—
302C4—1462no—
303C2—82no—
304C2—81no—
305C2—2922no—
306C2#1798914711yescharacteristic
307C2#1798915011yescharacteristic
308C2#1798916611yescharacteristic
309C2#1798932612yes—
310C2#1798933212yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#392×C73C2
hypercenter#392D73
hypocenterC73#2813
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#14556573C2semidirect
2. C2×#14556562C2semidirect
3. #17988527C2semidirect
4. #17988523C2semidirect
5. #17988510C2semidirect
6. #17988502C2semidirect
7. #17988501C2semidirect
8. #17988501C2semidirect
9. #17988495C2semidirect
10. #17988446C2semidirect
11. #392×C73C2semidirect
49. C2×C4×D73D4semidirect
156. C73#2813semidirect
166. #392D73semidirect