Finite Group Databasebeta

← #22613541

Subgroups — #22613541

Order 9344.

914 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 914 conjugacy classes of subgroups — too many to draw. Only its 173 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×#11924028C211yesmaximal, characteristic, complemented
2C2×#14556574C211yesmaximal, characteristic, complemented
3C2×#14556565C212yesmaximal, complemented
4#17988508C211yesmaximal, characteristic, complemented
5#17988505C211yesmaximal, characteristic, complemented
6#17988500C211yesmaximal, characteristic, complemented
7#17988497C211yesmaximal, characteristic, complemented
8#17988466C212yesmaximal, complemented
9#17988465C212yesmaximal, complemented
10#17988461C212yesmaximal, complemented
11C2×#95×C73C211yesmaximal, characteristic, complemented
12C2×#11924028—28no—
13C2×#11924028—24no—
14C22×Dic146C2211yescharacteristic
15C22×D292C2211yescharacteristic
16C22×D292C2212yes—
17C22×C22⋊D73C2211yescharacteristic
18C22×C22⋊D73C2212yes—
19C22×C4×D73C2212yes—
20#14556574—24no—
21#14556565—28no—
22C2×C4⋊Dic73C2212yes—
23C2×#11924007C2211yescharacteristic
24C2×#11924007C2211yescharacteristic
25C2×C22⋊Dic73C2211yescharacteristic
26C2×#11924005C2212yes—
27C2×#11924005C2212yes—
28C2×#11924005C2211yescharacteristic
29C2×#11924005C2212yes—
30C2×#11924005C2211yescharacteristic
31C2×#11924005C2212yes—
32#14556498C2212yes—
33#14556498C2212yes—
34C23×C4×C73C2212yes—
35C23×C4×C73C2211yescharacteristic
36#95×C73C2212yes—
37#95×C73C2211yescharacteristic
38#95×C73C2211yescharacteristic
39C23×D73C2311yescharacteristic
40C23×D73C2312yes—
41#11924028—232no—
42C2×Dic146—22no—
43C2×Dic146—24no—
44C2×D292—24no—
45C2×D292—22no—
46C2×D292—24no—
47C2×D292—24no—
48C2×D292—42no—
49C2×C22⋊D73—24no—
50C2×C22⋊D73—24no—
51C2×C22⋊D73—24no—
52C2×C22⋊D73—22no—
53C2×C22⋊D73D418yescomplemented
54C22×Dic73C2311yescharacteristic
55C22×Dic73C2311yescharacteristic
56C22×Dic73C2311yescharacteristic
57C22×Dic73C2312yes—
58C2×C4×D73—24no—
59C2×C4×D73—24no—
60C2×C4×D73—24no—
61C4⋊Dic73—24no—
62#11924007—22no—
63#11924007—22no—
64C22⋊Dic73—22no—
65#11924005—24no—
66#11924005—22no—
67#11924005—22no—
68#11924005—24no—
69#11924005—24no—
70#11924005—42no—
71C24×C73C2311yescharacteristic
72C22×C4×C73—24no—
73C22×C4×C73—24no—
74C22×C4×C73—24no—
75C22×C4×C73—42no—
76C22×C4×C73D414yescomplemented
77C22×C4×C73C2312yes—
78C22×C4×C73C2311yescharacteristic
79C22×C4×C73C2311yescharacteristic
80C22×C4×C73C2312yes—
81C23×C73—22no—
82C23×C73—21no—
83C23×C73—21no—
84C23×C73C2×D414yes—
85C23×C73C2×D412yes—
86C23×C73C2411yescharacteristic
87C22×D73—22no—
88C22×D73—22no—
89C22×D73—22no—
90C22×D73—22no—
91C22×D73—22no—
92C22×D73—22no—
93C22×D73—21no—
94C22×D73—22no—
95C22×D73—22no—
96C22×D73—21no—
97C22×D73—21no—
98C22×D73C2×D414yes—
99C2×C4×C73—28no—
100C2×C4×C73—22no—
101C2×C4×C73—22no—
102C2×C4×C73—22no—
103C2×C4×C73—22no—
104C2×C4×C73—22no—
105C2×C4×C73—22no—
106C2×C4×C73—22no—
107C2×C4×C73—48no—
108C2×C4×C73C2×D412yes—
109C2×C4×C73C2×D412yes—
110C2×C4×C73#4114yescomplemented
111C22⋊D73—216no—
112C22⋊D73—44no—
113C2×Dic73—22no—
114C2×Dic73—22no—
115C2×Dic73—21no—
116C2×Dic73—21no—
117C2×Dic73—22no—
118C2×Dic73—21no—
119C2×Dic73—22no—
120C2×Dic73—21no—
121C2×Dic73—21no—
122C2×Dic73C2×D414yes—
123D292—28no—
124D292—48no—
125C4×D73—216no—
126Dic146—28no—
127C22×C73—22no—
128C22×C73—22no—
129C22×C73—24no—
130C22×C73—24no—
131C22×C73#12014yes—
132C22×C73C22×D412yes—
133C22×C73C22×D411yescharacteristic
134C22×C73C2×#4112yes—
135C22×C73H(5,𝔽2)11yescharacteristic
136C22×C732−1+411yescharacteristic
137C2×D73—24no—
138C2×D73—24no—
139C2×D73—24no—
140C2×D73—42no—
141C2×D73—42no—
142C2×D73—42no—
143C2×D73—42no—
144C2×D73—41no—
145C2×D73—41no—
146C2×D73—41no—
147C2×D73—42no—
148C2×D73—42no—
149C4×C73—22no—
150C4×C73—22no—
151C4×C73—24no—
152C4×C73—42no—
153Dic73—24no—
154Dic73—41no—
155Dic73—41no—
156Dic73—41no—
157C2×C73—24no—
158C2×C73C2×#12011yescharacteristic
159C2×C73#53211yescharacteristic
160C2×C73#53711yescharacteristic
161C2×C73#54612yes—
162C2×C73#54712yes—
163D73—44no—
164D73—81no—
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#392—731no—
174#386—732no—
175#386—732no—
176#385—732no—
177C2×#95D7311yescharacteristic, complemented
178C2×#41—1468no—
179C2×#41—1464no—
180C22×Q8—731no—
181C22×D4—732no—
182C22×D4—731no—
183C22×D4—732no—
184C22×D4—731no—
185C23×C4—732no—
186C23×C4C2×D7312yes—
187C23×C4C2×D7311yescharacteristic
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—731no—
195C2×C22⋊C4—732no—
196C2×C22⋊C4—732no—
197C2×C22⋊C4—731no—
198C2×C22⋊C4—731no—
199C2×C22⋊C4—732no—
200#95—732no—
201#95—732no—
202#95C2×D7312yes—
203#95C2×D7311yescharacteristic
204#95C2×D7311yescharacteristic
205C24—732no—
206C24—731no—
207C24C22×D7311yescharacteristic
208#41—14632no—
209C2×Q8—1464no—
210C2×Q8—1462no—
211C2×D4—2922no—
212C2×D4—738no—
213C2×D4—1464no—
214C2×D4—1464no—
215C2×D4—1464no—
216C2×D4—1462no—
217C2×D4—1464no—
218C2×D4—1464no—
219C2×D4—1462no—
220C2×D4—1464no—
221C22×C4—24no—
222C22×C4—24no—
223C22×C4—24no—
224C22×C4—42no—
225C22×C4—732no—
226C22×C4—731no—
227C22×C4—731no—
228C22×C4—731no—
229C22×C4—1464no—
230C22×C4—1464no—
231C22×C4—1464no—
232C22×C4D29214yescomplemented
233C22×C4C22×D7312yes—
234C22×C4C22×D7311yescharacteristic
235C22×C4C22×D7311yescharacteristic
236C22×C4C22×D7312yes—
237C4⋊C4—1464no—
238C4⋊C4—1462no—
239C4⋊C4—1462no—
240C22⋊C4—2922no—
241C22⋊C4—1464no—
242C22⋊C4—1464no—
243C22⋊C4—1462no—
244C22⋊C4—1462no—
245C22⋊C4—1462no—
246C22⋊C4—1464no—
247C23—22no—
248C23—21no—
249C23—21no—
250C23—734no—
251C23—1462no—
252C23—1461no—
253C23—1462no—
254C23—1461no—
255C23—1461no—
256C23—1462no—
257C23—1462no—
258C23—1462no—
259C23—1462no—
260C23—1462no—
261C23—1462no—
262C23D4×D7314yes—
263C23C2×D29212yes—
264C23C23×D7311yescharacteristic
265Q8—1468no—
266D4—2928no—
267D4—2924no—
268D4—1468no—
269D4—14616no—
270C2×C4—28no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—48no—
279C2×C4—734no—
280C2×C4—14616no—
281C2×C4—1462no—
282C2×C4—1461no—
283C2×C4—1461no—
284C2×C4—1461no—
285C2×C4—1462no—
286C2×C4—1461no—
287C2×C4—1461no—
288C2×C4—1462no—
289C2×C4—1462no—
290C2×C4C2×D29212yes—
291C2×C4C2×D29212yes—
292C2×C4#1192402814yescomplemented
293C22—22no—
294C22—22no—
295C22—24no—
296C22—24no—
297C22—2922no—
298C22—2922no—
299C22—2922no—
300C22—2922no—
301C22—2921no—
302C22—2921no—
303C22—2922no—
304C22—2922no—
305C22—2921no—
306C22—1464no—
307C22—1464no—
308C22—1464no—
309C22#1455656114yes—
310C22C2×D4×D7312yes—
311C22C22×D29211yescharacteristic
312C22C2×#1192402812yes—
313C22#1455663611yescharacteristic
314C22#1455663911yescharacteristic
315C4—24no—
316C4—22no—
317C4—22no—
318C4—42no—
319C4—2921no—
320C4—2921no—
321C4—2921no—
322C4—1464no—
323C2—24no—
324C2—2924no—
325C2—5841no—
326C2C2×#1455656111yescharacteristic
327C2#1798913711yescharacteristic
328C2#1798916811yescharacteristic
329C2#1798922712yes—
330C2#1798923812yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC2×#95×C73C2
hypercenterC2×#95D73
hypocenterC73#2430
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
1. C22×#11924028C2semidirect
2. C2×#14556574C2semidirect
3. C2×#14556565C2semidirect
4. #17988508C2semidirect
5. #17988505C2semidirect
6. #17988500C2semidirect
7. #17988497C2semidirect
8. #17988466C2semidirect
9. #17988465C2semidirect
10. #17988461C2semidirect
11. C2×#95×C73C2semidirect
53. C2×C22⋊D73D4semidirect
76. C22×C4×C73D4semidirect
110. C2×C4×C73#41semidirect
166. C73#2430semidirect
177. C2×#95D73semidirect
232. C22×C4D292semidirect
292. C2×C4#11924028semidirect