Finite Group Databasebeta

← #22615708

Subgroups — #22615708

Order 9344.

702 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 702 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14556559C211yesmaximal, characteristic
2C22×#11924005C211yesmaximal, characteristic, complemented
3#17988516C212yesmaximal, complemented
4#17988514C212yesmaximal, complemented
5#17988503C212yesmaximal, complemented
6#17988502C212yesmaximal, complemented
7#17988467C211yesmaximal, characteristic, complemented
8#17988462C211yesmaximal, characteristic, complemented
9#17988460C211yesmaximal, characteristic, complemented
10#17988442C211yesmaximal, characteristic, complemented
11#386×C73C211yesmaximal, characteristic, complemented
12C24×D73C2211yescharacteristic
13C22×C22⋊D73C2211yescharacteristic
14C22×C22⋊D73C2211yescharacteristic
15C23×Dic73C2211yescharacteristic
16#14556559—24no—
17C2×C4⋊Dic73C2212yescomplemented
18C2×#11924007C2212yescomplemented
19C2×C22⋊Dic73C2211yescharacteristic
20C2×C22⋊Dic73C2211yescharacteristic
21C2×C22⋊Dic73C2212yescomplemented
22C2×#11924005—24no—
23C2×#11924005C2212yes—
24C2×#11924005C2212yes—
25C2×#11924005C2211yescharacteristic
26C2×#11924005C2211yescharacteristic
27C2×#11924005C2212yes—
28C2×#11924005C2212yes—
29#14556498C2212yescomplemented
30#14556498C2212yescomplemented
31#14556498C2212yescomplemented
32C22×D4×C73C2211yescharacteristic
33C23×C4×C73C2211yescharacteristic
34C2×C22⋊C4×C73C2211yescharacteristic
35C2×C22⋊C4×C73C2212yescomplemented
36#95×C73C2212yescomplemented
37C23×D73—22no—
38C23×D73—22no—
39C23×D73—42no—
40C23×D73—42no—
41C23×D73D414yes—
42C23×D73C2311yescharacteristic
43C23×D73C2311yescharacteristic
44C2×C22⋊D73—22no—
45C2×C22⋊D73—22no—
46C2×C22⋊D73—42no—
47C2×C22⋊D73—42no—
48C22×Dic73—22no—
49C22×Dic73—42no—
50C22×Dic73C2312yes—
51C22×Dic73C2312yes—
52C22×Dic73C2311yescharacteristic
53C22×Dic73C2311yescharacteristic
54C4⋊Dic73—42no—
55#11924007—42no—
56C22⋊Dic73—22no—
57C22⋊Dic73—22no—
58C22⋊Dic73—42no—
59#11924005—24no—
60#11924005—24no—
61#11924005—22no—
62#11924005—22no—
63#11924005—42no—
64#11924005—42no—
65C24×C73C2311yescharacteristic
66C24×C73C2311yescharacteristic
67C2×D4×C73—22no—
68C2×D4×C73—22no—
69C2×D4×C73—22no—
70C22×C4×C73—22no—
71C22×C4×C73—42no—
72C22×C4×C73C2311yescharacteristic
73C22×C4×C73C2312yes—
74C22×C4×C73C2312yes—
75C22⋊C4×C73—22no—
76C22⋊C4×C73—42no—
77C23×C73—22no—
78C23×C73—22no—
79C23×C73—21no—
80C23×C73—21no—
81C23×C73—21no—
82C23×C73—22no—
83C23×C73—22no—
84C23×C73C2×D412yes—
85C23×C73#4112yes—
86C23×C73#4112yes—
87C23×C73C2411yescharacteristic
88C22×D73—28no—
89C22×D73—21no—
90C22×D73—21no—
91C22×D73—21no—
92C22×D73—21no—
93C22×D73—22no—
94C22×D73—22no—
95C22×D73—22no—
96C22×D73—22no—
97C22×D73—44no—
98C22×D73—44no—
99C22×D73—48no—
100C22×D73—48no—
101C22×D73C2×D412yes—
102C22×D73C2×D412yes—
103D4×C73—44no—
104C2×C4×C73—22no—
105C2×C4×C73—21no—
106C2×C4×C73—22no—
107C2×C4×C73—21no—
108C2×C4×C73—21no—
109C2×C4×C73—22no—
110C2×C4×C73—22no—
111C2×C4×C73—22no—
112C2×C4×C73—22no—
113C2×C4×C73—44no—
114C22⋊D73—44no—
115C22⋊D73—44no—
116C2×Dic73—22no—
117C2×Dic73—21no—
118C2×Dic73—21no—
119C2×Dic73—22no—
120C2×Dic73—22no—
121C2×Dic73—22no—
122C2×Dic73—22no—
123C2×Dic73—22no—
124C2×Dic73—22no—
125C2×Dic73—22no—
126C2×Dic73—44no—
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#12314yes—
137C22×C73C22×D411yescharacteristic
138C22×C73C2×#4111yescharacteristic
139C22×C73C2×#4111yescharacteristic
140C22×C73H(5,𝔽2)12yes—
141C22×C73H(5,𝔽2)12yes—
142C2×D73—22no—
143C2×D73—22no—
144C2×D73—22no—
145C2×D73—22no—
146C2×D73—22no—
147C2×D73—22no—
148C2×D73—416no—
149C2×D73—42no—
150C2×D73—42no—
151C2×D73—42no—
152C2×D73—42no—
153C4×C73—41no—
154C4×C73—42no—
155C4×C73—42no—
156Dic73—42no—
157Dic73—41no—
158Dic73—41no—
159Dic73—42no—
160C2×C73—24no—
161C2×C73—81no—
162C2×C73C2×#12311yescharacteristic
163C2×C73#53411yescharacteristic
164C2×C73#53411yescharacteristic
165C2×C73#53812yes—
166C2×C73#53812yes—
167D73—42no—
168D73—42no—
169#2622—731nomaximal, Sylow
170C73#262211yescharacteristic, complemented, Sylow
171C2×#120—731no—
172C22×C22⋊C4—731no—
173#397—732no—
174#397—732no—
175#394—732no—
176#394—732no—
177#386—731no—
178#386D7311yescharacteristic, complemented
179#385—731no—
180#385—731no—
181#379—731no—
182C25—731no—
183C22×D4—731no—
184C22×D4—731no—
185C22×D4C2×D7311yescharacteristic
186C23×C4—731no—
187C23×C4C2×D7311yescharacteristic
188#120—1464no—
189C2×C4⋊C4—732no—
190C2×C4⋊C4—732no—
191C2×C22⋊C4—732no—
192C2×C22⋊C4—732no—
193C2×C22⋊C4—732no—
194C2×C22⋊C4—731no—
195C2×C22⋊C4—731no—
196C2×C22⋊C4—732no—
197C2×C22⋊C4—732no—
198C2×C22⋊C4—731no—
199C2×C22⋊C4—731no—
200C2×C22⋊C4—1464no—
201C2×C22⋊C4C2×D7311yescharacteristic
202C2×C22⋊C4C2×D7312yescomplemented
203#95—732no—
204#95—732no—
205#95—732no—
206#95C2×D7312yescomplemented
207C24—2922no—
208C24—2922no—
209C24—734no—
210C24—731no—
211C24—731no—
212C24—1462no—
213C24—1462no—
214C24C22×D7311yescharacteristic
215C24C22×D7311yescharacteristic
216C2×D4—22no—
217C2×D4—22no—
218C2×D4—22no—
219C2×D4—2922no—
220C2×D4—2922no—
221C2×D4—1462no—
222C2×D4—1462no—
223C22×C4—22no—
224C22×C4—42no—
225C22×C4—2922no—
226C22×C4—732no—
227C22×C4—732no—
228C22×C4—731no—
229C22×C4—731no—
230C22×C4—1462no—
231C22×C4C22×D7311yescharacteristic
232C22×C4C22×D7312yes—
233C22×C4C22×D7312yes—
234C4⋊C4—2922no—
235C4⋊C4—2922no—
236C22⋊C4—22no—
237C22⋊C4—42no—
238C22⋊C4—2922no—
239C22⋊C4—2922no—
240C22⋊C4—2922no—
241C22⋊C4—1464no—
242C22⋊C4—1464no—
243C22⋊C4—1462no—
244C22⋊C4—1462no—
245C22⋊C4—1462no—
246C22⋊C4—1462no—
247C23—22no—
248C23—22no—
249C23—21no—
250C23—21no—
251C23—21no—
252C23—22no—
253C23—22no—
254C23—2928no—
255C23—2928no—
256C23—2924no—
257C23—2924no—
258C23—732no—
259C23—732no—
260C23—1468no—
261C23—1461no—
262C23—1461no—
263C23—1461no—
264C23—1461no—
265C23—1462no—
266C23—1462no—
267C23—1462no—
268C23—1462no—
269C23D4×D7312yes—
270C23#1192402712yes—
271C23#1192402812yes—
272C23C23×D7311yescharacteristic
273D4—44no—
274D4—2924no—
275D4—2924no—
276C2×C4—22no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—44no—
286C2×C4—2924no—
287C2×C4—1462no—
288C2×C4—1461no—
289C2×C4—1461no—
290C2×C4—1462no—
291C2×C4—1462no—
292C2×C4—1462no—
293C2×C4—1462no—
294C2×C4—1462no—
295C2×C4—1462no—
296C2×C4—1462no—
297C22—22no—
298C22—22no—
299C22—24no—
300C22—24no—
301C22—41no—
302C22—41no—
303C22—42no—
304C22—42no—
305C22—41no—
306C22—29216no—
307C22—2922no—
308C22—2922no—
309C22—2922no—
310C22—2922no—
311C22—1462no—
312C22—1462no—
313C22—1462no—
314C22—1462no—
315C22—1462no—
316C22—1462no—
317C22#1455657314yes—
318C22C2×D4×D7311yescharacteristic
319C22C2×#1192402711yescharacteristic
320C22C2×#1192402811yescharacteristic
321C22#1455663612yes—
322C22#1455663712yes—
323C4—42no—
324C4—42no—
325C4—41no—
326C4—2921no—
327C4—2922no—
328C4—2921no—
329C4—2922no—
330C2—24no—
331C2—81no—
332C2—2922no—
333C2—2922no—
334C2C2×#1455657311yescharacteristic
335C2#1798914711yescharacteristic
336C2#1798914811yescharacteristic
337C2#1798917012yes—
338C2#1798917412yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#386×C73C2
hypercenter#386D73
hypocenterC73#2622
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C22×#11924005C2semidirect
3. #17988516C2semidirect
4. #17988514C2semidirect
5. #17988503C2semidirect
6. #17988502C2semidirect
7. #17988467C2semidirect
8. #17988462C2semidirect
9. #17988460C2semidirect
10. #17988442C2semidirect
11. #386×C73C2semidirect
17. C2×C4⋊Dic73C22semidirect
18. C2×#11924007C22semidirect
21. C2×C22⋊Dic73C22semidirect
29. #14556498C22semidirect
30. #14556498C22semidirect
31. #14556498C22semidirect
35. C2×C22⋊C4×C73C22semidirect
36. #95×C73C22semidirect
170. C73#2622semidirect
178. #386D73semidirect
202. C2×C22⋊C4C2×D73semidirect
206. #95C2×D73semidirect