Finite Group Databasebeta

← #22613534

Subgroups — #22613534

Order 9344.

914 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 914 conjugacy classes of subgroups — too many to draw. Only its 161 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
1C22×#11924027C211yesmaximal, characteristic, complemented
2C2×#14556573C211yesmaximal, characteristic, complemented
3C2×#14556562C212yesmaximal, complemented
4#17988508C211yesmaximal, characteristic, complemented
5#17988501C211yesmaximal, characteristic, complemented
6#17988499C211yesmaximal, characteristic, complemented
7#17988467C212yesmaximal, complemented
8#17988463C212yesmaximal, complemented
9#17988462C212yesmaximal, complemented
10#95×D73C211yesmaximal, characteristic, complemented
11#392×C73C211yesmaximal, characteristic, complemented
12C2×#11924027—28no—
13C2×#11924027—24no—
14C22×Dic146C2211yescharacteristic
15C22×C22⋊D73C2211yescharacteristic
16C22×C22⋊D73C2212yes—
17C23×Dic73C2212yes—
18C22×C4×D73C2212yes—
19C22×C4×D73C2211yescharacteristic
20#14556573—24no—
21#14556562—28no—
22C2×C4⋊Dic73C2211yescharacteristic
23C2×C4⋊Dic73C2212yes—
24C2×#11924007C2211yescharacteristic
25C2×C22⋊Dic73C2212yes—
26C2×C22⋊Dic73C2211yescharacteristic
27C2×C22⋊Dic73C2212yes—
28C2×C22⋊Dic73C2212yes—
29C2×#11924005C2211yescharacteristic
30#14556498C2212yes—
31#14556498C2211yescharacteristic
32#14556498C2212yes—
33#14556498C2212yes—
34C22×D4×C73C2211yescharacteristic
35C22×D4×C73C2212yes—
36C2×C22⋊C4×C73C2212yes—
37C2×C22⋊C4×C73C2211yescharacteristic
38#95×C73C2211yescharacteristic
39C23×D73C2311yescharacteristic
40#11924027—232no—
41C2×Dic146—22no—
42C2×Dic146—24no—
43C2×C22⋊D73—24no—
44C2×C22⋊D73—24no—
45C2×C22⋊D73—24no—
46C2×C22⋊D73—22no—
47C2×C22⋊D73D418yescomplemented
48C22×Dic73—24no—
49C22×Dic73—24no—
50C22×Dic73—24no—
51C22×Dic73C2312yes—
52C22×Dic73C2311yescharacteristic
53C22×Dic73C2311yescharacteristic
54C22×Dic73C2311yescharacteristic
55C22×Dic73C2312yes—
56C2×C4×D73—24no—
57C2×C4×D73—24no—
58C2×C4×D73—24no—
59C2×C4×D73—42no—
60C2×C4×D73D414yescomplemented
61C4⋊Dic73—24no—
62C4⋊Dic73—22no—
63#11924007—22no—
64C22⋊Dic73—24no—
65C22⋊Dic73—24no—
66C22⋊Dic73—22no—
67C22⋊Dic73—42no—
68#11924005—22no—
69C24×C73C2311yescharacteristic
70C24×C73C2312yes—
71C2×D4×C73—24no—
72C2×D4×C73—24no—
73C2×D4×C73—22no—
74C2×D4×C73—24no—
75C2×D4×C73—42no—
76C22×C4×C73C2311yescharacteristic
77C22×C4×C73C2311yescharacteristic
78C22×C4×C73C2312yes—
79C22⋊C4×C73—22no—
80C22⋊C4×C73—24no—
81C23×C73—22no—
82C23×C73—22no—
83C23×C73—22no—
84C23×C73—22no—
85C23×C73—22no—
86C23×C73—22no—
87C23×C73—21no—
88C23×C73—22no—
89C23×C73—22no—
90C23×C73—21no—
91C23×C73—21no—
92C23×C73C2×D414yes—
93C23×C73C2411yescharacteristic
94C22×D73—22no—
95C22×D73—21no—
96C22×D73—21no—
97C22×D73C2×D412yes—
98C22×D73C2×D414yes—
99D4×C73—28no—
100D4×C73—48no—
101C2×C4×C73—22no—
102C2×C4×C73—22no—
103C2×C4×C73—22no—
104C2×C4×C73—21no—
105C2×C4×C73—22no—
106C2×C4×C73C2×D412yes—
107C2×C4×C73#4114yescomplemented
108C22⋊D73—216no—
109C22⋊D73—44no—
110C2×Dic73—216no—
111C2×Dic73—22no—
112C2×Dic73—22no—
113C2×Dic73—22no—
114C2×Dic73—21no—
115C2×Dic73—22no—
116C2×Dic73—22no—
117C2×Dic73—21no—
118C2×Dic73—22no—
119C2×Dic73—21no—
120C2×Dic73—22no—
121C2×Dic73—21no—
122C2×Dic73C2×D412yes—
123C2×Dic73C2×D414yes—
124C4×D73—28no—
125C4×D73—48no—
126Dic146—28no—
127C22×C73—24no—
128C22×C73—24no—
129C22×C73—24no—
130C22×C73—42no—
131C22×C73—42no—
132C22×C73—42no—
133C22×C73—42no—
134C22×C73—41no—
135C22×C73—41no—
136C22×C73—41no—
137C22×C73—42no—
138C22×C73—42no—
139C22×C73C22×D411yescharacteristic
140C22×C73C22×D412yes—
141C22×C73C2×#4112yes—
142C22×C73H(5,𝔽2)11yescharacteristic
143C22×C732−1+411yescharacteristic
144C2×D73—22no—
145C2×D73—22no—
146C2×D73—24no—
147C2×D73—24no—
148C2×D73#12014yes—
149C4×C73—22no—
150C4×C73—24no—
151C4×C73—41no—
152Dic73—24no—
153Dic73—22no—
154Dic73—41no—
155Dic73—41no—
156Dic73—42no—
157C2×C73—44no—
158C2×C73—81no—
159C2×C73C2×#12011yescharacteristic
160C2×C73#53211yescharacteristic
161C2×C73#53711yescharacteristic
162C2×C73#54612yes—
163C2×C73#54712yes—
164D73—24no—
165#2430—731nomaximal, Sylow
166C73#243011yescharacteristic, complemented, Sylow
167C22×#41—731no—
168C2×#123—731no—
169C2×#121—732no—
170#395—731no—
171#394—731no—
172#393—731no—
173#392D7311yescharacteristic, complemented
174#386—732no—
175#386—732no—
176#385—732no—
177C2×#95—731no—
178C2×#41—1464no—
179C2×#41—1468no—
180C22×Q8—731no—
181C22×D4—732no—
182C22×D4—731no—
183C22×D4C2×D7311yescharacteristic
184C22×D4C2×D7312yes—
185C23×C4—732no—
186C23×C4—731no—
187C23×C4—732no—
188#123—1464no—
189#121—1468no—
190C2×C4⋊C4—732no—
191C2×C4⋊C4—731no—
192C2×C4⋊C4—731no—
193C2×C22⋊C4—732no—
194C2×C22⋊C4—732no—
195C2×C22⋊C4—732no—
196C2×C22⋊C4—731no—
197C2×C22⋊C4—731no—
198C2×C22⋊C4C2×D7311yescharacteristic
199C2×C22⋊C4C2×D7312yes—
200#95—732no—
201#95—731no—
202#95—732no—
203#95—732no—
204#95C2×D7311yescharacteristic
205C24—731no—
206C24C22×D7311yescharacteristic
207C24C22×D7312yes—
208#41—14632no—
209C2×Q8—1464no—
210C2×Q8—1462no—
211C2×D4—24no—
212C2×D4—24no—
213C2×D4—22no—
214C2×D4—24no—
215C2×D4—42no—
216C2×D4—738no—
217C2×D4—1464no—
218C2×D4—1462no—
219C2×D4—1464no—
220C2×D4—1464no—
221C22×C4—2922no—
222C22×C4—731no—
223C22×C4—732no—
224C22×C4—734no—
225C22×C4—732no—
226C22×C4—731no—
227C22×C4—731no—
228C22×C4—1464no—
229C22×C4—1464no—
230C22×C4—1464no—
231C22×C4—1464no—
232C22×C4—1464no—
233C22×C4—1464no—
234C22×C4C22×D7311yescharacteristic
235C22×C4C22×D7311yescharacteristic
236C22×C4C22×D7312yes—
237C4⋊C4—1464no—
238C4⋊C4—1462no—
239C4⋊C4—1462no—
240C22⋊C4—22no—
241C22⋊C4—24no—
242C22⋊C4—2922no—
243C22⋊C4—1462no—
244C22⋊C4—1464no—
245C22⋊C4—1462no—
246C22⋊C4—1464no—
247C23—22no—
248C23—22no—
249C23—22no—
250C23—22no—
251C23—22no—
252C23—22no—
253C23—21no—
254C23—22no—
255C23—22no—
256C23—21no—
257C23—21no—
258C23—732no—
259C23—734no—
260C23—1462no—
261C23—1461no—
262C23—1461no—
263C23D4×D7314yes—
264C23C23×D7311yescharacteristic
265Q8—1468no—
266D4—28no—
267D4—48no—
268D4—2924no—
269D4—14616no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—21no—
274C2×C4—22no—
275C2×C4—2928no—
276C2×C4—732no—
277C2×C4—734no—
278C2×C4—1468no—
279C2×C4—1461no—
280C2×C4—1462no—
281C2×C4—1462no—
282C2×C4—1461no—
283C2×C4—1462no—
284C2×C4—1461no—
285C2×C4—1462no—
286C2×C4—1461no—
287C2×C4—14616no—
288C2×C4—1462no—
289C2×C4—1462no—
290C2×C4—1462no—
291C2×C4D4×D7312yes—
292C2×C4#1192402714yescomplemented
293C22—24no—
294C22—24no—
295C22—24no—
296C22—42no—
297C22—42no—
298C22—42no—
299C22—42no—
300C22—41no—
301C22—41no—
302C22—42no—
303C22—42no—
304C22—41no—
305C22—734no—
306C22—1462no—
307C22—1462no—
308C22—1464no—
309C22—1464no—
310C22C2×D4×D7311yescharacteristic
311C22C2×D4×D7312yes—
312C22C2×#1192402712yes—
313C22#1455663611yescharacteristic
314C22#1455663811yescharacteristic
315C4—24no—
316C4—22no—
317C4—41no—
318C4—2921no—
319C4—2922no—
320C4—2921no—
321C4—1462no—
322C4—1464no—
323C2—44no—
324C2—81no—
325C2—1464no—
326C2#120×D7311yescharacteristic
327C2#1798913511yescharacteristic
328C2#1798916611yescharacteristic
329C2#1798922412yes—
330C2#1798923712yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#392×C73C2
hypercenter#392D73
hypocenterC73#2430
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×#11924027C2semidirect
2. C2×#14556573C2semidirect
3. C2×#14556562C2semidirect
4. #17988508C2semidirect
5. #17988501C2semidirect
6. #17988499C2semidirect
7. #17988467C2semidirect
8. #17988463C2semidirect
9. #17988462C2semidirect
10. #95×D73C2semidirect
11. #392×C73C2semidirect
47. C2×C22⋊D73D4semidirect
60. C2×C4×D73D4semidirect
107. C2×C4×C73#41semidirect
166. C73#2430semidirect
173. #392D73semidirect
292. C2×C4#11924027semidirect