Finite Group Databasebeta

← #22615664

Subgroups — #22615664

Order 9344.

824 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 824 conjugacy classes of subgroups — too many to draw. Only its 143 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×#14556562C211yesmaximal, characteristic, complemented
2C2×#14556559C212yesmaximal, complemented
3C2×C22⋊C4×D73C211yesmaximal, characteristic, complemented
4#17988514C211yesmaximal, characteristic, complemented
5#17988512C211yesmaximal, characteristic, complemented
6#17988502C212yesmaximal, complemented
7#17988501C212yesmaximal, complemented
8#17988495C211yesmaximal, characteristic, complemented
9#17988463C212yesmaximal, complemented
10#17988446C211yesmaximal, characteristic, complemented
11#392×C73C211yesmaximal, characteristic, complemented
12C24×D73C2211yescharacteristic
13C22×C22⋊D73C2212yes—
14C22×C22⋊D73C2212yes—
15C22×C4×D73C2211yescharacteristic
16C22×C4×D73C2211yescharacteristic
17#14556562—24no—
18#14556559—28no—
19C2×C4⋊Dic73C2211yescharacteristic, complemented
20C2×#11924007C2212yescomplemented
21C2×C22⋊Dic73C2211yescharacteristic
22C2×C22⋊Dic73C2212yes—
23C2×C22⋊Dic73C2212yescomplemented
24C2×C22⋊Dic73C2212yescomplemented
25C2×#11924005C2212yes—
26C2×#11924005C2211yescharacteristic
27C2×#11924005C2211yescharacteristic
28C2×#11924005C2212yes—
29C22⋊C4×D73—24no—
30#14556498C2211yescharacteristic, complemented
31#14556498C2212yescomplemented
32#14556498C2212yescomplemented
33C22×D4×C73C2212yes—
34C22×D4×C73C2211yescharacteristic, complemented
35C2×C22⋊C4×C73C2211yescharacteristic
36C2×C22⋊C4×C73C2212yescomplemented
37#95×C73C2211yescharacteristic, complemented
38C23×D73—22no—
39C23×D73—22no—
40C23×D73—42no—
41C23×D73—42no—
42C23×D73D414yescomplemented
43C23×D73C2311yescharacteristic
44C23×D73C2311yescharacteristic
45C2×C22⋊D73—24no—
46C2×C22⋊D73—24no—
47C2×C22⋊D73—24no—
48C2×C22⋊D73—24no—
49C2×C22⋊D73—42no—
50C2×C22⋊D73—42no—
51C22×Dic73C2311yescharacteristic
52C22×Dic73C2312yes—
53C22×Dic73C2312yes—
54C22×Dic73C2311yescharacteristic
55C2×C4×D73—22no—
56C2×C4×D73—42no—
57C2×C4×D73—42no—
58C2×C4×D73D414yescomplemented
59C4⋊Dic73—22no—
60#11924007—42no—
61C22⋊Dic73—24no—
62C22⋊Dic73—22no—
63C22⋊Dic73—24no—
64C22⋊Dic73—42no—
65#11924005—24no—
66#11924005—24no—
67#11924005—22no—
68#11924005—22no—
69C24×C73C2312yes—
70C24×C73C2311yescharacteristic
71C2×D4×C73—24no—
72C2×D4×C73—22no—
73C2×D4×C73—42no—
74C2×D4×C73—42no—
75C2×D4×C73—42no—
76C22×C4×C73C2312yes—
77C22×C4×C73C2311yescharacteristic
78C22×C4×C73C2311yescharacteristic
79C22⋊C4×C73—22no—
80C22⋊C4×C73—42no—
81C23×C73—21no—
82C23×C73—21no—
83C23×C73—22no—
84C23×C73—22no—
85C23×C73—22no—
86C23×C73—22no—
87C23×C73—22no—
88C23×C73—22no—
89C23×C73—22no—
90C23×C73—22no—
91C23×C73—22no—
92C23×C73C2×D412yes—
93C23×C73C2411yescharacteristic
94C22×D73—22no—
95C22×D73—22no—
96C22×D73—21no—
97C22×D73—21no—
98C22×D73—22no—
99C22×D73—22no—
100C22×D73—28no—
101C22×D73—48no—
102C22×D73—44no—
103C22×D73—44no—
104C22×D73—48no—
105C22×D73C2×D412yes—
106C22×D73C2×D412yes—
107C22×D73C2×D412yes—
108C22×D73#4112yes—
109D4×C73—44no—
110D4×C73—48no—
111C2×C4×C73—22no—
112C2×C4×C73—21no—
113C2×C4×C73—22no—
114C2×C4×C73—22no—
115C2×C4×C73—22no—
116C2×C4×C73—22no—
117C2×C4×C73C2×D412yes—
118C22⋊D73—48no—
119C22⋊D73—48no—
120C2×Dic73—22no—
121C2×Dic73—21no—
122C2×Dic73—22no—
123C2×Dic73—22no—
124C2×Dic73—22no—
125C2×Dic73—22no—
126C2×Dic73—22no—
127C2×Dic73—22no—
128C2×Dic73—22no—
129C2×Dic73C2×D412yes—
130C4×D73—44no—
131C4×D73—44no—
132C22×C73—22no—
133C22×C73—24no—
134C22×C73—41no—
135C22×C73—41no—
136C22×C73—42no—
137C22×C73—42no—
138C22×C73—42no—
139C22×C73—42no—
140C22×C73—42no—
141C22×C73—42no—
142C22×C73—42no—
143C22×C73—42no—
144C22×C73C22×D411yescharacteristic
145C22×C73C22×D411yescharacteristic
146C22×C73C2×#4111yescharacteristic
147C22×C73H(5,𝔽2)12yes—
148C22×C73H(5,𝔽2)12yes—
149C2×D73—22no—
150C2×D73—24no—
151C2×D73—22no—
152C2×D73—24no—
153C2×D73—22no—
154C2×D73—24no—
155C2×D73—416no—
156C2×D73—41no—
157C2×D73—41no—
158C2×D73—42no—
159C2×D73#12114yes—
160C4×C73—22no—
161C4×C73—42no—
162C4×C73—41no—
163Dic73—22no—
164Dic73—42no—
165Dic73—42no—
166Dic73—41no—
167C2×C73—42no—
168C2×C73—82no—
169C2×C73C2×#12111yescharacteristic
170C2×C73#53411yescharacteristic
171C2×C73#53412yes—
172C2×C73#53511yescharacteristic
173C2×C73#53812yes—
174D73—24no—
175D73—42no—
176#2617—731nomaximal, Sylow
177C73#261711yescharacteristic, complemented, Sylow
178C2×#121—731no—
179C2×#120—732no—
180C22×C22⋊C4—731no—
181#397—731no—
182#397—731no—
183#394—732no—
184#394—732no—
185#392—731no—
186#392D7311yescharacteristic, complemented
187#386—732no—
188#380—731no—
189C25—731no—
190C22×D4—732no—
191C22×D4—732no—
192C22×D4C2×D7312yes—
193C22×D4C2×D7311yescharacteristic, complemented
194C23×C4—731no—
195C23×C4—731no—
196#121—1464no—
197#120—1468no—
198C2×C4⋊C4—732no—
199C2×C4⋊C4—731no—
200C2×C22⋊C4—732no—
201C2×C22⋊C4—731no—
202C2×C22⋊C4—732no—
203C2×C22⋊C4—732no—
204C2×C22⋊C4—731no—
205C2×C22⋊C4—731no—
206C2×C22⋊C4—732no—
207C2×C22⋊C4—732no—
208C2×C22⋊C4—1464no—
209C2×C22⋊C4C2×D7311yescharacteristic
210C2×C22⋊C4C2×D7312yescomplemented
211#95—731no—
212#95—732no—
213#95—732no—
214#95C2×D7311yescharacteristic, complemented
215C24—2922no—
216C24—2922no—
217C24—734no—
218C24—731no—
219C24—731no—
220C24—1462no—
221C24—1462no—
222C24C22×D7312yes—
223C24C22×D7311yescharacteristic
224C2×D4—24no—
225C2×D4—22no—
226C2×D4—42no—
227C2×D4—42no—
228C2×D4—42no—
229C2×D4—2922no—
230C2×D4—2922no—
231C2×D4—1464no—
232C2×D4—1464no—
233C2×D4—1464no—
234C2×D4—1464no—
235C22×C4—2922no—
236C22×C4—2922no—
237C22×C4—734no—
238C22×C4—731no—
239C22×C4—731no—
240C22×C4—732no—
241C22×C4—732no—
242C22×C4—1462no—
243C22×C4C22×D7311yescharacteristic
244C22×C4C22×D7312yes—
245C22×C4C22×D7311yescharacteristic
246C4⋊C4—2922no—
247C4⋊C4—1462no—
248C22⋊C4—22no—
249C22⋊C4—42no—
250C22⋊C4—2922no—
251C22⋊C4—1462no—
252C22⋊C4—1464no—
253C22⋊C4—1464no—
254C22⋊C4—1462no—
255C22⋊C4—1464no—
256C22⋊C4—1464no—
257C22⋊C4—1462no—
258C23—21no—
259C23—21no—
260C23—22no—
261C23—22no—
262C23—22no—
263C23—22no—
264C23—22no—
265C23—22no—
266C23—22no—
267C23—22no—
268C23—22no—
269C23—2928no—
270C23—2924no—
271C23—2924no—
272C23—2928no—
273C23—732no—
274C23—732no—
275C23—732no—
276C23—732no—
277C23—1468no—
278C23—1461no—
279C23—1461no—
280C23—1462no—
281C23—1462no—
282C23—1462no—
283C23—1462no—
284C23D4×D7312yes—
285C23C23×D7311yescharacteristic
286D4—44no—
287D4—48no—
288D4—2928no—
289D4—2928no—
290C2×C4—22no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—2924no—
297C2×C4—2924no—
298C2×C4—732no—
299C2×C4—1461no—
300C2×C4—1462no—
301C2×C4—1462no—
302C2×C4—1462no—
303C2×C4—1462no—
304C2×C4—1462no—
305C2×C4—1462no—
306C2×C4—1462no—
307C2×C4—1462no—
308C2×C4D4×D7312yes—
309C22—24no—
310C22—22no—
311C22—41no—
312C22—41no—
313C22—42no—
314C22—42no—
315C22—42no—
316C22—42no—
317C22—42no—
318C22—42no—
319C22—42no—
320C22—42no—
321C22—29216no—
322C22—2921no—
323C22—2921no—
324C22—2922no—
325C22—734no—
326C22—1464no—
327C22—1462no—
328C22—1462no—
329C22—1464no—
330C22—1462no—
331C22—1464no—
332C22C2×D4×D7311yescharacteristic
333C22C2×D4×D7311yescharacteristic
334C22#41×D7311yescharacteristic
335C22#1455663612yes—
336C22#1455663612yes—
337C4—22no—
338C4—42no—
339C4—41no—
340C4—2922no—
341C4—2921no—
342C4—2922no—
343C4—1462no—
344C2—42no—
345C2—82no—
346C2—2922no—
347C2—1464no—
348C2#121×D7311yescharacteristic
349C2#1798914711yescharacteristic
350C2#1798914712yes—
351C2#1798915011yescharacteristic
352C2#1798916912yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#392×C73C2
hypercenter#392D73
hypocenterC73#2617
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#14556562C2semidirect
2. C2×#14556559C2semidirect
3. C2×C22⋊C4×D73C2semidirect
4. #17988514C2semidirect
5. #17988512C2semidirect
6. #17988502C2semidirect
7. #17988501C2semidirect
8. #17988495C2semidirect
9. #17988463C2semidirect
10. #17988446C2semidirect
11. #392×C73C2semidirect
19. C2×C4⋊Dic73C22semidirect
20. C2×#11924007C22semidirect
23. C2×C22⋊Dic73C22semidirect
24. C2×C22⋊Dic73C22semidirect
30. #14556498C22semidirect
31. #14556498C22semidirect
32. #14556498C22semidirect
34. C22×D4×C73C22semidirect
36. C2×C22⋊C4×C73C22semidirect
37. #95×C73C22semidirect
42. C23×D73D4semidirect
58. C2×C4×D73D4semidirect
177. C73#2617semidirect
186. #392D73semidirect
193. C22×D4C2×D73semidirect
210. C2×C22⋊C4C2×D73semidirect
214. #95C2×D73semidirect