Finite Group Databasebeta

← #22615112

Subgroups — #22615112

Order 9344.

584 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 151 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×#14556567C211yesmaximal, characteristic, complemented
2C2×#14556553C211yesmaximal, characteristic
3#17988526C211yesmaximal, characteristic, complemented
4#17988524C211yesmaximal, characteristic, complemented
5#17988498C211yesmaximal, characteristic, complemented
6#17988470C212yesmaximal, complemented
7#17988465C212yesmaximal
8#17988458C212yesmaximal, complemented
9#17988444C212yesmaximal, complemented
10#95×D73C211yesmaximal, characteristic, complemented
11#395×C73C211yesmaximal, characteristic, complemented
12C22×D292C2211yescharacteristic
13C22×C4×D73C2212yes—
14C22×C4×D73C2211yescharacteristic
15C22×C4×D73C2211yescharacteristic
16#14556567—24no—
17#14556553—24no—
18C2×C4⋊Dic73C2212yes—
19C2×C4⋊Dic73C2211yescharacteristic
20C2×#11924007C2212yes—
21C2×#11924005C2211yescharacteristic
22C2×#11924005C2212yes—
23C2×#11924005C2212yes—
24C2×#11924005C2211yescharacteristic
25C2×#11924005C2212yes—
26C2×C4×Dic73C2211yescharacteristic
27#14556498C2212yes—
28#14556498C2211yescharacteristic
29#14556498C2212yes—
30#14556498C2212yes—
31#14556498C2212yes—
32C22×Q8×C73C2211yescharacteristic
33C2×C4⋊C4×C73C2211yescharacteristic
34C2×C4⋊C4×C73C2212yes—
35#95×C73C2211yescharacteristic
36#95×C73C2212yes—
37C23×D73C2311yescharacteristic
38C23×D73C2311yescharacteristic
39C2×D292—22no—
40C2×D292—22no—
41C2×D292Q814yescomplemented
42C22×Dic73C2312yes—
43C22×Dic73C2311yescharacteristic
44C22×Dic73C2312yes—
45C22×Dic73C2311yescharacteristic
46C2×C4×D73—24no—
47C2×C4×D73—24no—
48C2×C4×D73—22no—
49C2×C4×D73—42no—
50C2×C4×D73—42no—
51C2×C4×D73—42no—
52C2×C4×D73D414yes—
53C4⋊Dic73—22no—
54C4⋊Dic73—24no—
55#11924007—24no—
56#11924005—22no—
57#11924005—24no—
58#11924005—22no—
59#11924005—24no—
60#11924005—42no—
61C4×Dic73—22no—
62C2×Q8×C73—22no—
63C2×Q8×C73—42no—
64C22×C4×C73C2312yes—
65C22×C4×C73C2311yescharacteristic
66C22×C4×C73C2311yescharacteristic
67C22×C4×C73C2311yescharacteristic
68C22×C4×C73C2312yes—
69C4⋊C4×C73—22no—
70C4⋊C4×C73—42no—
71C23×C73C2411yescharacteristic
72C22×D73—22no—
73C22×D73—22no—
74C22×D73—21no—
75C22×D73—22no—
76C22×D73—21no—
77C22×D73—22no—
78C22×D73C2×D412yes—
79C22×D73C2×Q812yes—
80C22×D73C2×Q812yes—
81C22×D73#4112yes—
82Q8×C73—44no—
83C2×C4×C73—21no—
84C2×C4×C73—22no—
85C2×C4×C73—21no—
86C2×C4×C73—22no—
87C2×C4×C73—22no—
88C2×C4×C73—21no—
89C2×C4×C73—22no—
90C2×C4×C73—22no—
91C2×C4×C73—22no—
92C2×C4×C73—22no—
93C2×C4×C73C2×D412yes—
94C2×C4×C73C2×Q812yes—
95C2×C4×C73#4114yes—
96C2×Dic73—22no—
97C2×Dic73—21no—
98C2×Dic73—22no—
99C2×Dic73—22no—
100C2×Dic73—22no—
101C2×Dic73—22no—
102C2×Dic73—22no—
103C2×Dic73—22no—
104C2×Dic73—22no—
105C2×Dic73C2×D412yes—
106D292—28no—
107C4×D73—44no—
108C4×D73—44no—
109C4×D73—48no—
110C22×C73C22×D411yescharacteristic
111C22×C73C22×Q811yescharacteristic
112C22×C73C2×#4111yescharacteristic
113C22×C73C2×#4112yes—
114C22×C73H(5,𝔽2)12yes—
115C2×D73—22no—
116C2×D73—22no—
117C2×D73—24no—
118C2×D73—24no—
119C2×D73—22no—
120C2×D73—24no—
121C2×D73—41no—
122C2×D73—41no—
123C2×D73—42no—
124C2×D73C22⋊Q814yes—
125C4×C73—22no—
126C4×C73—22no—
127C4×C73—24no—
128C4×C73—41no—
129C4×C73—42no—
130Dic73—22no—
131Dic73—41no—
132Dic73—42no—
133Dic73—42no—
134C2×C73C2×C22⋊Q811yescharacteristic
135C2×C73#53211yescharacteristic
136C2×C73#53411yescharacteristic
137C2×C73#55112yes—
138C2×C73#55412yes—
139D73—24no—
140D73—42no—
141#2564—731nomaximal, Sylow
142C73#256411yescharacteristic, complemented, Sylow
143C2×C22⋊Q8—731no—
144C2×C4×D4—731no—
145#400—731no—
146#399—731no—
147#395D7311yescharacteristic, complemented
148#393—731no—
149#387—732no—
150#386—732no—
151#385—732no—
152#380—732no—
153C2×#95—731no—
154C22×Q8C2×D7311yescharacteristic
155C22×D4—731no—
156C23×C4—731no—
157C23×C4—731no—
158C23×C4—732no—
159C22⋊Q8—1464no—
160C4×D4—1464no—
161C2×C4⋊C4—732no—
162C2×C4⋊C4—731no—
163C2×C4⋊C4—732no—
164C2×C4⋊C4C2×D7311yescharacteristic
165C2×C4⋊C4C2×D7312yes—
166C2×C22⋊C4—732no—
167C2×C22⋊C4—731no—
168C2×C22⋊C4—731no—
169C2×C22⋊C4—732no—
170C2×C22⋊C4—732no—
171C2×C42—731no—
172#95—732no—
173#95—731no—
174#95—732no—
175#95—732no—
176#95—732no—
177#95C2×D7311yescharacteristic
178#95C2×D7312yes—
179C24—731no—
180C24—731no—
181C2×Q8—22no—
182C2×Q8—42no—
183C2×D4—734no—
184C2×D4—1462no—
185C2×D4—1462no—
186C22×C4—2922no—
187C22×C4—2922no—
188C22×C4—2922no—
189C22×C4—734no—
190C22×C4—731no—
191C22×C4—732no—
192C22×C4—731no—
193C22×C4—732no—
194C22×C4—1462no—
195C22×C4—1464no—
196C22×C4—1464no—
197C22×C4C22×D7311yescharacteristic
198C22×C4C22×D7312yes—
199C22×C4C22×D7311yescharacteristic
200C22×C4C22×D7311yescharacteristic
201C22×C4C22×D7312yes—
202C4⋊C4—22no—
203C4⋊C4—42no—
204C4⋊C4—1464no—
205C4⋊C4—1462no—
206C4⋊C4—1464no—
207C22⋊C4—2922no—
208C22⋊C4—1462no—
209C22⋊C4—1464no—
210C22⋊C4—1462no—
211C22⋊C4—1464no—
212C42—1462no—
213C23—732no—
214C23—732no—
215C23—732no—
216C23—732no—
217C23—1461no—
218C23—1461no—
219C23—1462no—
220C23—1462no—
221C23—1462no—
222C23—1462no—
223C23C23×D7311yescharacteristic
224Q8—44no—
225D4—1468no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—2928no—
237C2×C4—2924no—
238C2×C4—2924no—
239C2×C4—732no—
240C2×C4—1461no—
241C2×C4—1462no—
242C2×C4—1462no—
243C2×C4—1462no—
244C2×C4—1462no—
245C2×C4—1462no—
246C2×C4—1462no—
247C2×C4—1462no—
248C2×C4—1462no—
249C2×C4D4×D7312yes—
250C2×C4Q8×D7312yes—
251C2×C4#1192402914yes—
252C22—2921no—
253C22—2921no—
254C22—2922no—
255C22—734no—
256C22—1464no—
257C22—1462no—
258C22—1462no—
259C22—1462no—
260C22—1464no—
261C22—1464no—
262C22C2×D4×D7311yescharacteristic
263C22C2×Q8×D7311yescharacteristic
264C22#41×D7311yescharacteristic
265C22C2×#1192402912yes—
266C22#1455663612yes—
267C4—22no—
268C4—24no—
269C4—22no—
270C4—41no—
271C4—42no—
272C4—2921no—
273C4—2922no—
274C4—2922no—
275C4—1462no—
276C2—2922no—
277C2—1464no—
278C2C22⋊Q8×D7311yescharacteristic
279C2#1798913811yescharacteristic
280C2#1798914711yescharacteristic
281C2#1798926412yes—
282C2#1798929812yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#395×C73C2
hypercenter#395D73
hypocenterC73#2564
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. C2×#14556567C2semidirect
3. #17988526C2semidirect
4. #17988524C2semidirect
5. #17988498C2semidirect
6. #17988470C2semidirect
8. #17988458C2semidirect
9. #17988444C2semidirect
10. #95×D73C2semidirect
11. #395×C73C2semidirect
41. C2×D292Q8semidirect
142. C73#2564semidirect
147. #395D73semidirect