Finite Group Databasebeta

← #22615500

Subgroups — #22615500

Order 9344.

604 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 135 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×#14556553C211yesmaximal, characteristic, complemented
2C2×#14556549C211yesmaximal, characteristic, complemented
3#17988522C211yesmaximal, characteristic, complemented
4#17988504C211yesmaximal, characteristic, complemented
5#17988497C211yesmaximal, characteristic
6#17988476C212yesmaximal, complemented
7#17988465C212yesmaximal, complemented
8#17988465C212yesmaximal, complemented
9#17988461C212yesmaximal, complemented
10#17988454C211yesmaximal, characteristic, complemented
11#400×C73C211yesmaximal, characteristic, complemented
12C22×D292C2211yescharacteristic
13C22×D292C2212yes—
14C22×C4×D73C2211yescharacteristic
15C22×C4×D73C2212yes—
16#14556553—24no—
17#14556549—24no—
18C2×C4⋊Dic73C2211yescharacteristic
19C2×#11924007C2212yes—
20C2×#11924005C2212yes—
21C2×#11924005C2211yescharacteristic
22C2×#11924005C2212yes—
23C2×#11924005C2212yes—
24C2×#11924005C2211yescharacteristic
25C2×#11924005C2212yes—
26C2×#11924005C2212yes—
27C2×C4×Dic73C2211yescharacteristic
28C2×C4×Dic73C2211yescharacteristic
29#14556498C2212yes—
30#14556498C2212yes—
31#14556498C2211yescharacteristic
32C2×C4⋊C4×C73C2211yescharacteristic
33C2×C4⋊C4×C73C2211yescharacteristic
34#95×C73C2211yescharacteristic
35#95×C73C2212yes—
36#95×C73C2212yes—
37C23×D73C2311yescharacteristic
38C23×D73C2312yes—
39C2×D292—24no—
40C2×D292—22no—
41C2×D292—24no—
42C2×D292—24no—
43C2×D292—42no—
44C22×Dic73C2312yes—
45C22×Dic73C2311yescharacteristic
46C22×Dic73C2311yescharacteristic
47C22×Dic73C2311yescharacteristic
48C2×C4×D73—22no—
49C2×C4×D73—22no—
50C2×C4×D73—22no—
51C2×C4×D73—24no—
52C2×C4×D73—42no—
53C2×C4×D73—42no—
54C4⋊Dic73—22no—
55#11924007—42no—
56#11924005—24no—
57#11924005—22no—
58#11924005—24no—
59#11924005—22no—
60#11924005—24no—
61#11924005—42no—
62#11924005—42no—
63C4×Dic73—22no—
64C4×Dic73D414yescomplemented
65C22×C4×C73C2312yes—
66C22×C4×C73C2311yescharacteristic
67C22×C4×C73C2312yes—
68C22×C4×C73C2311yescharacteristic
69C22×C4×C73C2311yescharacteristic
70C4⋊C4×C73—22no—
71C4⋊C4×C73—22no—
72C23×C73C2411yescharacteristic
73C22×D73—21no—
74C22×D73—22no—
75C22×D73—22no—
76C22×D73—21no—
77C22×D73—22no—
78C22×D73—22no—
79C22×D73—22no—
80C22×D73—22no—
81C22×D73—22no—
82C22×D73—22no—
83C22×D73#4114yes—
84C22×D73#4112yes—
85C2×C4×C73—21no—
86C2×C4×C73—21no—
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×C73—22no—
94C2×C4×C73—22no—
95C2×C4×C73—22no—
96C2×C4×C73C2×D412yes—
97C2×C4×C73#4112yes—
98C2×Dic73—21no—
99C2×Dic73—21no—
100C2×Dic73—22no—
101C2×Dic73—21no—
102C2×Dic73—22no—
103C2×Dic73—22no—
104C2×Dic73—22no—
105C2×Dic73—22no—
106C2×Dic73C2×D412yes—
107C2×Dic73C2×D412yes—
108D292—28no—
109D292—48no—
110C4×D73—28no—
111C4×D73—48no—
112C22×C73C22×D411yescharacteristic
113C22×C73C2×#4111yescharacteristic
114C22×C73C2×#4112yes—
115C22×C73C2×#4111yescharacteristic
116C22×C73H(5,𝔽2)12yes—
117C2×D73—22no—
118C2×D73—24no—
119C2×D73—24no—
120C2×D73—24no—
121C2×D73—24no—
122C2×D73—41no—
123C2×D73—42no—
124C2×D73—42no—
125C2×D73—41no—
126C2×D73—42no—
127C2×D73—42no—
128C2×D73—42no—
129C4×C73—22no—
130C4×C73—22no—
131C4×C73—41no—
132C4×C73—42no—
133C4×C73—42no—
134Dic73—22no—
135Dic73—22no—
136Dic73—41no—
137Dic73—42no—
138C2×C73#52511yescharacteristic
139C2×C73#52511yescharacteristic
140C2×C73#53511yescharacteristic
141C2×C73#55112yes—
142C2×C73#55312yes—
143D73—42no—
144D73—44no—
145#2598—731nomaximal, Sylow
146C73#259811yescharacteristic, complemented, Sylow
147C2×C4×D4—731no—
148C2×#117—731no—
149#400D7311yescharacteristic, complemented
150#399—731no—
151#394—731no—
152#392—731no—
153#388—732no—
154#386—732no—
155#386—732no—
156#385—732no—
157#383—731no—
158C22×D4—732no—
159C22×D4—731no—
160C23×C4—732no—
161C23×C4—731no—
162C4×D4—1464no—
163#117—1464no—
164C2×C4⋊C4—732no—
165C2×C4⋊C4—731no—
166C2×C4⋊C4C2×D7311yescharacteristic
167C2×C4⋊C4C2×D7311yescharacteristic
168C2×C22⋊C4—732no—
169C2×C22⋊C4—732no—
170C2×C22⋊C4—731no—
171C2×C22⋊C4—731no—
172C2×C22⋊C4—732no—
173C2×C22⋊C4—732no—
174C2×C22⋊C4—732no—
175C2×C42—731no—
176C2×C42—731no—
177#95—732no—
178#95—732no—
179#95—731no—
180#95C2×D7311yescharacteristic
181#95C2×D7312yes—
182#95C2×D7312yes—
183C24—732no—
184C24—731no—
185C2×D4—2922no—
186C2×D4—1464no—
187C2×D4—1464no—
188C2×D4—1464no—
189C2×D4—1462no—
190C22×C4—2922no—
191C22×C4—2922no—
192C22×C4—731no—
193C22×C4—731no—
194C22×C4—732no—
195C22×C4—731no—
196C22×C4—1464no—
197C22×C4—1462no—
198C22×C4—1462no—
199C22×C4—1462no—
200C22×C4C22×D7312yes—
201C22×C4C22×D7311yescharacteristic
202C22×C4C22×D7312yes—
203C22×C4C22×D7311yescharacteristic
204C22×C4C22×D7311yescharacteristic
205C4⋊C4—22no—
206C4⋊C4—22no—
207C4⋊C4—2922no—
208C4⋊C4—1462no—
209C22⋊C4—2922no—
210C22⋊C4—2922no—
211C22⋊C4—1462no—
212C22⋊C4—1464no—
213C22⋊C4—1464no—
214C22⋊C4—1462no—
215C22⋊C4—1464no—
216C42—734no—
217C42—1462no—
218C23—734no—
219C23—732no—
220C23—1461no—
221C23—1462no—
222C23—1462no—
223C23—1462no—
224C23—1462no—
225C23—1462no—
226C23—1461no—
227C23—1462no—
228C23—1462no—
229C23—1462no—
230C23C23×D7311yescharacteristic
231D4—2928no—
232D4—1468no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—2928no—
245C2×C4—732no—
246C2×C4—732no—
247C2×C4—1468no—
248C2×C4—1461no—
249C2×C4—1462no—
250C2×C4—1462no—
251C2×C4—1462no—
252C2×C4—1462no—
253C2×C4—1461no—
254C2×C4—1461no—
255C2×C4—1462no—
256C2×C4D4×D7312yes—
257C2×C4#1192402912yes—
258C22—2922no—
259C22—2921no—
260C22—2922no—
261C22—2922no—
262C22—2922no—
263C22—2921no—
264C22—2922no—
265C22—1464no—
266C22—1464no—
267C22—1464no—
268C22—1464no—
269C22—1462no—
270C22C2×D4×D7311yescharacteristic
271C22#41×D7311yescharacteristic
272C22#41×D7312yes—
273C22C2×#1192402911yescharacteristic
274C22#1455663712yes—
275C4—22no—
276C4—22no—
277C4—42no—
278C4—42no—
279C4—41no—
280C4—2921no—
281C4—2922no—
282C4—1462no—
283C4—1462no—
284C2—2924no—
285C2—2922no—
286C2#1798909511yescharacteristic
287C2#1798910011yescharacteristic
288C2#1798915511yescharacteristic
289C2#1798926212yes—
290C2#1798929012yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#400×C73C2
hypercenter#400D73
hypocenterC73#2598
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C2×#14556553C2semidirect
2. C2×#14556549C2semidirect
3. #17988522C2semidirect
4. #17988504C2semidirect
6. #17988476C2semidirect
7. #17988465C2semidirect
8. #17988465C2semidirect
9. #17988461C2semidirect
10. #17988454C2semidirect
11. #400×C73C2semidirect
64. C4×Dic73D4semidirect
146. C73#2598semidirect
149. #400D73semidirect