Finite Group Databasebeta

← #22613587

Subgroups — #22613587

Order 9344.

852 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 852 conjugacy classes of subgroups — too many to draw. Only its 169 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
1C23×Dic146C211yesmaximal, characteristic, complemented
2C2×#14556577C212yesmaximal, complemented
3C2×#14556563C211yesmaximal, characteristic
4#17988500C212yesmaximal, complemented
5#17988499C212yesmaximal, complemented
6#17988491C212yesmaximal, complemented
7#17988467C211yesmaximal, characteristic, complemented
8#17988466C211yesmaximal, characteristic, complemented
9#17988464C211yesmaximal, characteristic, complemented
10C22⋊C4×Dic73C211yesmaximal, characteristic, complemented
11#386×C73C211yesmaximal, characteristic, complemented
12C22×Dic146—28no—
13C22×Dic146—24no—
14C22×Dic146C2212yes—
15C22×Dic146C2212yes—
16C22×C22⋊D73C2211yescharacteristic
17C22×C22⋊D73C2211yescharacteristic
18C23×Dic73C2211yescharacteristic
19C23×Dic73C2211yescharacteristic
20#14556577—28no—
21#14556563—24no—
22C2×#11924007C2211yescharacteristic
23C2×C22⋊Dic73C2211yescharacteristic
24C2×C22⋊Dic73C2212yes—
25C2×C22⋊Dic73C2211yescharacteristic
26C2×#11924005C2212yes—
27C2×#11924005C2212yes—
28C2×#11924005C2211yescharacteristic
29C2×C4×Dic73C2212yes—
30#14556498C2212yes—
31#14556498C2212yes—
32#14556498C2212yes—
33#14556498C2212yes—
34C22×D4×C73C2211yescharacteristic
35C23×C4×C73C2211yescharacteristic
36C2×C22⋊C4×C73C2211yescharacteristic
37C2×C22⋊C4×C73C2212yes—
38#95×C73C2212yes—
39C23×D73C2311yescharacteristic
40C2×Dic146—232no—
41C2×Dic146—24no—
42C2×Dic146—24no—
43C2×Dic146—24no—
44C2×Dic146—24no—
45C2×Dic146—24no—
46C2×Dic146D418yescomplemented
47C2×C22⋊D73—22no—
48C2×C22⋊D73—22no—
49C2×C22⋊D73—22no—
50C2×C22⋊D73—22no—
51C2×C22⋊D73—24no—
52C22×Dic73—22no—
53C22×Dic73—24no—
54C22×Dic73—24no—
55C22×Dic73D414yes—
56C22×Dic73C2311yescharacteristic
57C22×Dic73C2312yes—
58C22×Dic73C2312yes—
59C22×Dic73C2311yescharacteristic
60C22×Dic73C2311yescharacteristic
61#11924007—22no—
62C22⋊Dic73—22no—
63C22⋊Dic73—22no—
64C22⋊Dic73—24no—
65#11924005—24no—
66#11924005—22no—
67#11924005—24no—
68C4×Dic73—24no—
69C24×C73C2311yescharacteristic
70C24×C73C2311yescharacteristic
71C2×D4×C73—22no—
72C2×D4×C73—22no—
73C2×D4×C73—22no—
74C22×C4×C73—22no—
75C22×C4×C73—24no—
76C22×C4×C73C2311yescharacteristic
77C22×C4×C73C2312yes—
78C22×C4×C73C2312yes—
79C22⋊C4×C73—22no—
80C22⋊C4×C73—24no—
81C23×C73—22no—
82C23×C73—22no—
83C23×C73—22no—
84C23×C73—21no—
85C23×C73—21no—
86C23×C73—21no—
87C23×C73—22no—
88C23×C73C2×D412yes—
89C23×C73#4112yes—
90C23×C73#4112yes—
91C23×C73C2411yescharacteristic
92C22×D73—22no—
93C22×D73—21no—
94C22×D73—21no—
95C22×D73—21no—
96C22×D73—22no—
97D4×C73—44no—
98C2×C4×C73—28no—
99C2×C4×C73—22no—
100C2×C4×C73—22no—
101C2×C4×C73—22no—
102C2×C4×C73—21no—
103C2×C4×C73—22no—
104C2×C4×C73—21no—
105C2×C4×C73—21no—
106C2×C4×C73—22no—
107C2×C4×C73C2×D414yes—
108C22⋊D73—44no—
109C22⋊D73—44no—
110C2×Dic73—28no—
111C2×Dic73—22no—
112C2×Dic73—22no—
113C2×Dic73—22no—
114C2×Dic73—28no—
115C2×Dic73—22no—
116C2×Dic73—21no—
117C2×Dic73—22no—
118C2×Dic73—21no—
119C2×Dic73—21no—
120C2×Dic73—22no—
121C2×Dic73C2×D414yes—
122C2×Dic73C2×D412yes—
123C2×Dic73C2×D414yes—
124C2×Dic73C2×D412yes—
125Dic146—216no—
126Dic146—216no—
127C22×C73—22no—
128C22×C73—22no—
129C22×C73—24no—
130C22×C73—24no—
131C22×C73—41no—
132C22×C73—41no—
133C22×C73—41no—
134C22×C73—42no—
135C22×C73—42no—
136C22×C73#12414yescomplemented
137C22×C73C22×D411yescharacteristic
138C22×C73C22×D412yes—
139C22×C73C2×#4111yescharacteristic
140C22×C73C2×#4111yescharacteristic
141C22×C732−1+412yes—
142C2×D73—41no—
143C2×D73—41no—
144C2×D73—41no—
145C2×D73—42no—
146C2×D73—42no—
147C4×C73—24no—
148C4×C73—41no—
149C4×C73—42no—
150Dic73—22no—
151Dic73—24no—
152Dic73—41no—
153Dic73—42no—
154Dic73#12014yes—
155C2×C73—24no—
156C2×C73—81no—
157C2×C73C2×#12011yescharacteristic
158C2×C73C2×#12411yescharacteristic
159C2×C73#53611yescharacteristic
160C2×C73#54812yes—
161C2×C73#54812yes—
162D73—81no—
163#2436—731nomaximal, Sylow
164C73#243611yescharacteristic, complemented, Sylow
165C23×Q8—731no—
166C2×#124—732no—
167C2×#121—731no—
168#393—732no—
169#393—732no—
170#391—732no—
171#386—731no—
172#386—731no—
173#386—731no—
174#386D7311yescharacteristic, complemented
175C4×C22⋊C4—731no—
176C22×Q8—732no—
177C22×Q8—732no—
178C22×Q8—1464no—
179C22×Q8—1468no—
180C22×D4—731no—
181C22×D4—731no—
182C22×D4C2×D7311yescharacteristic
183C23×C4—731no—
184C23×C4—731no—
185C23×C4C2×D7311yescharacteristic
186#124—1468no—
187#121—1464no—
188C2×C4⋊C4—731no—
189C2×C22⋊C4—731no—
190C2×C22⋊C4—732no—
191C2×C22⋊C4—731no—
192C2×C22⋊C4—731no—
193C2×C22⋊C4—732no—
194C2×C22⋊C4—732no—
195C2×C22⋊C4C2×D7312yes—
196C2×C22⋊C4C2×D7311yescharacteristic
197C2×C42—732no—
198#95—732no—
199#95—732no—
200#95—732no—
201#95—732no—
202#95C2×D7312yes—
203C24—731no—
204C24C22×D7311yescharacteristic
205C24C22×D7311yescharacteristic
206C2×Q8—738no—
207C2×Q8—1464no—
208C2×Q8—1464no—
209C2×Q8—1464no—
210C2×Q8—1464no—
211C2×Q8—14632no—
212C2×Q8—1464no—
213C2×D4—22no—
214C2×D4—22no—
215C2×D4—22no—
216C2×D4—1462no—
217C2×D4—1464no—
218C2×D4—1462no—
219C2×D4—1462no—
220C2×D4—1462no—
221C22×C4—22no—
222C22×C4—24no—
223C22×C4—731no—
224C22×C4—734no—
225C22×C4—731no—
226C22×C4—732no—
227C22×C4—731no—
228C22×C4—732no—
229C22×C4—1464no—
230C22×C4—1464no—
231C22×C4—1462no—
232C22×C4C22×D7311yescharacteristic
233C22×C4C22×D7312yes—
234C22×C4C22×D7312yes—
235C4⋊C4—1462no—
236C22⋊C4—22no—
237C22⋊C4—24no—
238C22⋊C4—1462no—
239C22⋊C4—1464no—
240C22⋊C4—1462no—
241C22⋊C4—1464no—
242C22⋊C4—1462no—
243C22⋊C4—1464no—
244C42—1464no—
245C23—22no—
246C23—22no—
247C23—22no—
248C23—21no—
249C23—21no—
250C23—21no—
251C23—22no—
252C23—1462no—
253C23—1461no—
254C23—1461no—
255C23—1461no—
256C23—1462no—
257C23D4×D7312yes—
258C23#1192402712yes—
259C23#1192402812yes—
260C23C23×D7311yescharacteristic
261Q8—14616no—
262Q8—14616no—
263D4—44no—
264D4—2924no—
265D4—2924no—
266C2×C4—28no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—22no—
275C2×C4—734no—
276C2×C4—732no—
277C2×C4—732no—
278C2×C4—734no—
279C2×C4—1462no—
280C2×C4—1461no—
281C2×C4—1461no—
282C2×C4—1462no—
283C2×C4—1461no—
284C2×C4—1462no—
285C2×C4—1468no—
286C2×C4—1468no—
287C2×C4—1462no—
288C2×C4—1462no—
289C2×C4—1462no—
290C2×C4D4×D7314yes—
291C22—22no—
292C22—24no—
293C22—24no—
294C22—22no—
295C22—41no—
296C22—42no—
297C22—42no—
298C22—41no—
299C22—41no—
300C22—2921no—
301C22—2922no—
302C22—2922no—
303C22—2921no—
304C22—2921no—
305C22#1455657714yescomplemented
306C22C2×D4×D7311yescharacteristic
307C22C2×D4×D7312yes—
308C22C2×#1192402711yescharacteristic
309C22C2×#1192402811yescharacteristic
310C22#1455663812yes—
311C4—24no—
312C4—42no—
313C4—41no—
314C4—2922no—
315C4—2921no—
316C4—734no—
317C4—1462no—
318C4—1464no—
319C2—24no—
320C2—81no—
321C2—5841no—
322C2#120×D7311yescharacteristic
323C2C2×#1455657711yescharacteristic
324C2#1798915911yescharacteristic
325C2#1798924312yes—
326C2#1798924612yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#386×C73C2
hypercenter#386D73
hypocenterC73#2436
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C23×Dic146C2semidirect
2. C2×#14556577C2semidirect
4. #17988500C2semidirect
5. #17988499C2semidirect
6. #17988491C2semidirect
7. #17988467C2semidirect
8. #17988466C2semidirect
9. #17988464C2semidirect
10. C22⋊C4×Dic73C2semidirect
11. #386×C73C2semidirect
46. C2×Dic146D4semidirect
136. C22×C73#124semidirect
164. C73#2436semidirect
174. #386D73semidirect
305. C22#14556577semidirect