Finite Group Databasebeta

← #22615856

Subgroups — #22615856

Order 9344.

520 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 131 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×#14556571C211yesmaximal, characteristic, complemented
2C2×#14556553C211yesmaximal, characteristic
3#17988516C212yesmaximal, complemented
4#17988513C211yesmaximal, characteristic, complemented
5#17988507C211yesmaximal, characteristic, complemented
6#17988504C212yesmaximal
7#17988500C211yesmaximal, characteristic, complemented
8#17988473C212yesmaximal, complemented
9#17988461C212yesmaximal, complemented
10#17988449C211yesmaximal, characteristic, complemented
11#398×C73C211yesmaximal, characteristic, complemented
12C22×Dic146C2211yescharacteristic
13C22×D292C2211yescharacteristic
14C22×C4×D73C2211yescharacteristic
15C22×C4×D73C2211yescharacteristic
16#14556571—24no—
17#14556553—24no—
18C2×C4⋊Dic73C2212yes—
19C2×#11924007C2212yes—
20C2×#11924005C2212yes—
21C2×#11924005C2211yescharacteristic
22C2×#11924005C2212yes—
23C2×#11924005C2211yescharacteristic
24C2×#11924005C2212yes—
25C2×#11924005C2212yes—
26C2×C4×Dic73C2211yescharacteristic
27#14556498C2212yes—
28#14556498C2211yescharacteristic
29#14556498C2212yes—
30#14556498C2212yes—
31#14556498C2212yes—
32C2×C4⋊C4×C73C2212yes—
33C2×C4⋊C4×C73C2211yescharacteristic
34C2×C4⋊C4×C73C2211yescharacteristic
35#95×C73C2211yescharacteristic
36#95×C73C2212yes—
37C23×D73C2311yescharacteristic
38C23×D73C2311yescharacteristic
39C2×Dic146—22no—
40C2×Dic146—42no—
41C2×D292—22no—
42C2×D292—22no—
43C2×D292—22no—
44C22×Dic73C2311yescharacteristic
45C22×Dic73C2312yes—
46C22×Dic73C2312yes—
47C22×Dic73C2311yescharacteristic
48C2×C4×D73—22no—
49C2×C4×D73—42no—
50C2×C4×D73—42no—
51C2×C4×D73D414yes—
52C4⋊Dic73—24no—
53#11924007—42no—
54#11924005—22no—
55#11924005—24no—
56#11924005—24no—
57#11924005—22no—
58#11924005—42no—
59#11924005—42no—
60C4×Dic73—22no—
61C22×C4×C73C2312yes—
62C22×C4×C73C2311yescharacteristic
63C22×C4×C73C2312yes—
64C22×C4×C73C2311yescharacteristic
65C22×C4×C73C2311yescharacteristic
66C4⋊C4×C73—22no—
67C4⋊C4×C73—22no—
68C4⋊C4×C73—24no—
69C23×C73C2411yescharacteristic
70C22×D73—21no—
71C22×D73—21no—
72C22×D73—21no—
73C22×D73—21no—
74C22×D73—22no—
75C22×D73—22no—
76C22×D73—22no—
77C22×D73—22no—
78C22×D73C2×D412yes—
79C22×D73#4112yes—
80C2×C4×C73—21no—
81C2×C4×C73—21no—
82C2×C4×C73—22no—
83C2×C4×C73—22no—
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×C73C2×D412yes—
92C2×C4×C73#4112yes—
93C2×Dic73—22no—
94C2×Dic73—21no—
95C2×Dic73—22no—
96C2×Dic73—22no—
97C2×Dic73—22no—
98C2×Dic73—22no—
99C2×Dic73—22no—
100C2×Dic73—22no—
101C2×Dic73—22no—
102C2×Dic73C2×D412yes—
103D292—28no—
104C4×D73—44no—
105C4×D73—44no—
106Dic146—44no—
107C22×C73C22×D411yescharacteristic
108C22×C73C2×#4111yescharacteristic
109C22×C73C2×#4111yescharacteristic
110C22×C73H(5,𝔽2)12yes—
111C22×C732−1+412yes—
112C2×D73—22no—
113C2×D73—22no—
114C2×D73—22no—
115C2×D73—22no—
116C2×D73—24no—
117C2×D73—41no—
118C2×D73—41no—
119C2×D73—42no—
120C2×D73—42no—
121C2×D73—42no—
122C4×C73—22no—
123C4×C73—22no—
124C4×C73—42no—
125C4×C73—41no—
126C4×C73—42no—
127Dic73—22no—
128Dic73—42no—
129Dic73—41no—
130Dic73—42no—
131C2×C73#52511yescharacteristic
132C2×C73#53411yescharacteristic
133C2×C73#53611yescharacteristic
134C2×C73#53912yes—
135C2×C73#54212yes—
136D73—42no—
137D73—42no—
138#2638—731nomaximal, Sylow
139C73#263811yescharacteristic, complemented, Sylow
140C2×C22⋊Q8—731no—
141C2×C4×D4—731no—
142#398D7311yescharacteristic, complemented
143#397—731no—
144#397—732no—
145#395—731no—
146#394—732no—
147#393—731no—
148#387—732no—
149#385—732no—
150#381—731no—
151C22×Q8—731no—
152C22×D4—731no—
153C23×C4—731no—
154C23×C4—731no—
155C22⋊Q8—1464no—
156C4×D4—1464no—
157C2×C4⋊C4—732no—
158C2×C4⋊C4—732no—
159C2×C4⋊C4C2×D7311yescharacteristic
160C2×C4⋊C4C2×D7311yescharacteristic
161C2×C4⋊C4C2×D7312yes—
162C2×C22⋊C4—732no—
163C2×C22⋊C4—732no—
164C2×C22⋊C4—731no—
165C2×C22⋊C4—731no—
166C2×C22⋊C4—732no—
167C2×C22⋊C4—732no—
168C2×C42—731no—
169#95—732no—
170#95—731no—
171#95—732no—
172#95—732no—
173#95—732no—
174#95C2×D7311yescharacteristic
175#95C2×D7312yes—
176C24—731no—
177C24—731no—
178C2×Q8—2922no—
179C2×Q8—1462no—
180C2×D4—1462no—
181C2×D4—1462no—
182C2×D4—1462no—
183C22×C4—2922no—
184C22×C4—2922no—
185C22×C4—734no—
186C22×C4—731no—
187C22×C4—731no—
188C22×C4—732no—
189C22×C4—732no—
190C22×C4—1462no—
191C22×C4C22×D7312yes—
192C22×C4C22×D7312yes—
193C22×C4C22×D7311yescharacteristic
194C22×C4C22×D7311yescharacteristic
195C22×C4C22×D7311yescharacteristic
196C4⋊C4—22no—
197C4⋊C4—22no—
198C4⋊C4—24no—
199C4⋊C4—2922no—
200C4⋊C4—1464no—
201C22⋊C4—2922no—
202C22⋊C4—2922no—
203C22⋊C4—1464no—
204C22⋊C4—1462no—
205C22⋊C4—1464no—
206C22⋊C4—1462no—
207C42—1462no—
208C23—732no—
209C23—732no—
210C23—1461no—
211C23—1461no—
212C23—1461no—
213C23—1461no—
214C23—1462no—
215C23—1462no—
216C23—1462no—
217C23—1462no—
218C23C23×D7311yescharacteristic
219Q8—2924no—
220D4—1468no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—2924no—
233C2×C4—2924no—
234C2×C4—732no—
235C2×C4—1461no—
236C2×C4—1462no—
237C2×C4—1462no—
238C2×C4—1462no—
239C2×C4—1462no—
240C2×C4—1462no—
241C2×C4—1462no—
242C2×C4—1462no—
243C2×C4—1462no—
244C2×C4D4×D7312yes—
245C2×C4#1192402712yes—
246C22—2921no—
247C22—2921no—
248C22—2922no—
249C22—2922no—
250C22—2922no—
251C22—1462no—
252C22—1462no—
253C22—1464no—
254C22—1462no—
255C22—1462no—
256C22C2×D4×D7311yescharacteristic
257C22#41×D7311yescharacteristic
258C22C2×#1192402711yescharacteristic
259C22#1455663712yes—
260C22#1455663912yes—
261C4—22no—
262C4—22no—
263C4—41no—
264C4—42no—
265C4—42no—
266C4—2922no—
267C4—2921no—
268C4—2922no—
269C4—1462no—
270C2—2922no—
271C2—2922no—
272C2#1798909711yescharacteristic
273C2#1798914811yescharacteristic
274C2#1798916211yescharacteristic
275C2#1798918512yes—
276C2#1798921012yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#398×C73C2
hypercenter#398D73
hypocenterC73#2638
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#14556571C2semidirect
3. #17988516C2semidirect
4. #17988513C2semidirect
5. #17988507C2semidirect
7. #17988500C2semidirect
8. #17988473C2semidirect
9. #17988461C2semidirect
10. #17988449C2semidirect
11. #398×C73C2semidirect
139. C73#2638semidirect
142. #398D73semidirect