Finite Group Databasebeta

← #22613172

Subgroups — #22613172

Order 9344.

696 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 696 conjugacy classes of subgroups — too many to draw. Only its 155 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×#14556553C212yesmaximal, complemented
2C2×#14556553C211yesmaximal, characteristic, complemented
3C2×#14556549C211yesmaximal, characteristic, complemented
4#17988513C211yesmaximal, characteristic, complemented
5#17988509C212yesmaximal, complemented
6#17988505C212yesmaximal, complemented
7#17988504C211yesmaximal, characteristic, complemented
8#17988497C211yesmaximal, characteristic
9#17988438C211yesmaximal, characteristic, complemented
10#17988434C212yesmaximal, complemented
11#398×C73C211yesmaximal, characteristic, complemented
12C22×D292C2211yescharacteristic
13C22×D292C2212yes—
14C22×C4×D73C2212yes—
15C22×C4×D73C2211yescharacteristic
16#14556553—28no—
17#14556553—24no—
18#14556549—24no—
19C2×C4⋊Dic73C2211yescharacteristic
20C2×#11924007C2212yes—
21C2×#11924005C2212yes—
22C2×#11924005C2212yes—
23C2×#11924005C2211yescharacteristic
24C2×#11924005C2212yes—
25C2×#11924005C2211yescharacteristic
26C2×#11924005C2212yes—
27C2×#11924005C2212yes—
28C2×C4×Dic73C2211yescharacteristic
29C2×C4×Dic73C2212yes—
30C2×C4×Dic73C2211yescharacteristic
31#14556498C2212yes—
32#14556498C2211yescharacteristic
33C2×C4⋊C4×C73C2211yescharacteristic
34C2×C4⋊C4×C73C2212yes—
35C2×C4⋊C4×C73C2211yescharacteristic
36#95×C73C2212yes—
37#95×C73C2211yescharacteristic
38C23×D73C2311yescharacteristic
39C23×D73C2312yes—
40C2×D292—24no—
41C2×D292—24no—
42C2×D292—24no—
43C2×D292—22no—
44C2×D292—24no—
45C22×Dic73C2312yes—
46C22×Dic73C2311yescharacteristic
47C22×Dic73C2311yescharacteristic
48C22×Dic73C2311yescharacteristic
49C2×C4×D73—22no—
50C2×C4×D73—22no—
51C2×C4×D73—24no—
52C2×C4×D73—24no—
53C2×C4×D73—24no—
54C2×C4×D73D414yescomplemented
55C4⋊Dic73—22no—
56#11924007—24no—
57#11924005—24no—
58#11924005—24no—
59#11924005—22no—
60#11924005—24no—
61#11924005—24no—
62#11924005—22no—
63#11924005—24no—
64C4×Dic73—22no—
65C4×Dic73—24no—
66C4×Dic73D414yescomplemented
67C22×C4×C73C2311yescharacteristic
68C22×C4×C73C2312yes—
69C22×C4×C73C2311yescharacteristic
70C22×C4×C73C2311yescharacteristic
71C22×C4×C73C2312yes—
72C4⋊C4×C73—22no—
73C4⋊C4×C73—24no—
74C4⋊C4×C73—22no—
75C23×C73C2411yescharacteristic
76C22×D73—21no—
77C22×D73—22no—
78C22×D73—22no—
79C22×D73—22no—
80C22×D73—21no—
81C22×D73—22no—
82C22×D73—22no—
83C22×D73—22no—
84C22×D73—22no—
85C22×D73—22no—
86C22×D73C2×D412yes—
87C22×D73#4114yes—
88C2×C4×C73—22no—
89C2×C4×C73—21no—
90C2×C4×C73—21no—
91C2×C4×C73—22no—
92C2×C4×C73—22no—
93C2×C4×C73—21no—
94C2×C4×C73—22no—
95C2×C4×C73—22no—
96C2×C4×C73—22no—
97C2×C4×C73—22no—
98C2×C4×C73C2×D412yes—
99C2×C4×C73C2×D412yes—
100C2×C4×C73#4114yes—
101C2×Dic73—22no—
102C2×Dic73—22no—
103C2×Dic73—21no—
104C2×Dic73—22no—
105C2×Dic73—22no—
106C2×Dic73—22no—
107C2×Dic73C2×D412yes—
108C2×Dic73C2×D412yes—
109C2×Dic73C2×D412yes—
110C2×Dic73#4112yes—
111D292—28no—
112D292—216no—
113C4×D73—28no—
114C4×D73—48no—
115C22×C73C22×D411yescharacteristic
116C22×C73C22×D411yescharacteristic
117C22×C73C2×#4111yescharacteristic
118C22×C73C2×#4112yes—
119C22×C73C2×#4112yes—
120C2×D73—22no—
121C2×D73—24no—
122C2×D73—24no—
123C2×D73—24no—
124C2×D73—24no—
125C2×D73—42no—
126C2×D73—41no—
127C2×D73—42no—
128C2×D73—42no—
129C2×D73—42no—
130C2×D73—41no—
131C2×D73—42no—
132C4×C73—22no—
133C4×C73—22no—
134C4×C73—24no—
135C4×C73—42no—
136C4×C73—41no—
137Dic73—22no—
138Dic73—42no—
139Dic73—41no—
140Dic73#12114yes—
141C2×C73C2×#12111yescharacteristic
142C2×C73#52511yescharacteristic
143C2×C73#52512yes—
144C2×C73#52912yes—
145C2×C73#53211yescharacteristic
146D73—42no—
147D73—44no—
148#2392—731nomaximal, Sylow
149C73#239211yescharacteristic, complemented, Sylow
150C2×C4×D4—731no—
151C2×C4×D4—732no—
152C2×#117—731no—
153#398D7311yescharacteristic, complemented
154#397—731no—
155#396—732no—
156#394—731no—
157#394—732no—
158#392—731no—
159C4×C4⋊C4—731no—
160C4×C22⋊C4—732no—
161C22×D4—731no—
162C22×D4—732no—
163C23×C4—731no—
164C23×C4—732no—
165C4×D4—1464no—
166C4×D4—1468no—
167#117—1464no—
168C2×C4⋊C4—731no—
169C2×C4⋊C4—732no—
170C2×C4⋊C4C2×D7311yescharacteristic
171C2×C4⋊C4C2×D7312yes—
172C2×C4⋊C4C2×D7311yescharacteristic
173C2×C22⋊C4—731no—
174C2×C22⋊C4—731no—
175C2×C22⋊C4—732no—
176C2×C22⋊C4—732no—
177C2×C22⋊C4—732no—
178C2×C22⋊C4—732no—
179C2×C22⋊C4—732no—
180C2×C42—731no—
181C2×C42—731no—
182C2×C42—732no—
183#95—732no—
184#95—731no—
185#95C2×D7312yes—
186#95C2×D7311yescharacteristic
187C24—731no—
188C24—732no—
189C2×D4—1464no—
190C2×D4—1464no—
191C2×D4—1464no—
192C2×D4—1462no—
193C2×D4—1464no—
194C22×C4—731no—
195C22×C4—731no—
196C22×C4—734no—
197C22×C4—732no—
198C22×C4—731no—
199C22×C4—1464no—
200C22×C4—1464no—
201C22×C4—1464no—
202C22×C4—1462no—
203C22×C4—1462no—
204C22×C4C22×D7312yes—
205C22×C4C22×D7311yescharacteristic
206C22×C4C22×D7311yescharacteristic
207C22×C4C22×D7311yescharacteristic
208C22×C4C22×D7312yes—
209C4⋊C4—22no—
210C4⋊C4—24no—
211C4⋊C4—22no—
212C4⋊C4—1462no—
213C4⋊C4—1464no—
214C22⋊C4—1462no—
215C22⋊C4—1464no—
216C22⋊C4—1464no—
217C22⋊C4—1464no—
218C22⋊C4—1462no—
219C22⋊C4—1464no—
220C22⋊C4—1464no—
221C42—734no—
222C42—1462no—
223C42—1464no—
224C23—732no—
225C23—734no—
226C23—1461no—
227C23—1462no—
228C23—1462no—
229C23—1461no—
230C23—1462no—
231C23—1462no—
232C23—1462no—
233C23—1462no—
234C23—1462no—
235C23—1462no—
236C23C23×D7311yescharacteristic
237D4—1468no—
238D4—14616no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—2928no—
250C2×C4—732no—
251C2×C4—732no—
252C2×C4—732no—
253C2×C4—732no—
254C2×C4—1468no—
255C2×C4—1462no—
256C2×C4—1461no—
257C2×C4—1462no—
258C2×C4—1462no—
259C2×C4—1462no—
260C2×C4—1462no—
261C2×C4D4×D7312yes—
262C2×C4D4×D7312yes—
263C2×C4#1192402914yes—
264C22—2922no—
265C22—2922no—
266C22—2921no—
267C22—2922no—
268C22—2922no—
269C22—2921no—
270C22—2922no—
271C22—1464no—
272C22—1462no—
273C22—1464no—
274C22—1464no—
275C22—1464no—
276C22C2×D4×D7311yescharacteristic
277C22C2×D4×D7311yescharacteristic
278C22#41×D7311yescharacteristic
279C22#41×D7312yes—
280C22C2×#1192402912yes—
281C4—22no—
282C4—22no—
283C4—24no—
284C4—42no—
285C4—41no—
286C4—2921no—
287C4—2922no—
288C4—734no—
289C4—1462no—
290C2—2922no—
291C2—2924no—
292C2#121×D7311yescharacteristic
293C2#1798909511yescharacteristic
294C2#1798910012yes—
295C2#1798912212yes—
296C2#1798913811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#398×C73C2
hypercenter#398D73
hypocenterC73#2392
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#14556553C2semidirect
2. C2×#14556553C2semidirect
3. C2×#14556549C2semidirect
4. #17988513C2semidirect
5. #17988509C2semidirect
6. #17988505C2semidirect
7. #17988504C2semidirect
9. #17988438C2semidirect
10. #17988434C2semidirect
11. #398×C73C2semidirect
54. C2×C4×D73D4semidirect
66. C4×Dic73D4semidirect
149. C73#2392semidirect
153. #398D73semidirect