Finite Group Databasebeta

← #22616265

Subgroups — #22616265

Order 9344.

1000 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 1000 conjugacy classes of subgroups — too many to draw. Only its 157 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×#14556560C212yesmaximal, complemented
2C2×#14556559C212yesmaximal, complemented
3C2×#14556559C211yesmaximal, characteristic, complemented
4#17988503C212yesmaximal, complemented
5#17988502C212yesmaximal, complemented
6#17988501C212yesmaximal, complemented
7#17988490C211yesmaximal, characteristic, complemented
8#17988487C212yesmaximal, complemented
9C2×#120×C73C211yesmaximal, characteristic, complemented
10C24×D73C2211yescharacteristic, complemented
11C22×C22⋊D73C2212yes—
12C22×C22⋊D73C2212yes—
13C22×C22⋊D73C2212yes—
14#14556560—28no—
15#14556559—28no—
16#14556559—24no—
17C2×C4⋊Dic73C2211yescharacteristic, complemented
18C2×#11924007C2212yescomplemented
19C2×C22⋊Dic73C2212yescomplemented
20C2×C22⋊Dic73C2212yescomplemented
21C2×C22⋊Dic73C2212yescomplemented
22C2×C22⋊Dic73C2211yescharacteristic, complemented
23C2×C22⋊Dic73C2212yescomplemented
24C2×#11924005C2212yescomplemented
25C2×#11924005C2212yescomplemented
26C2×#11924005C2212yescomplemented
27C2×C4×Dic73C2211yescharacteristic, complemented
28#14556498C2212yescomplemented
29C25×C73C2211yescharacteristic, complemented
30C22×D4×C73C2212yes—
31C22×D4×C73C2211yescharacteristic
32#120×C73—24no—
33C2×C22⋊C4×C73C2212yescomplemented
34C2×C22⋊C4×C73C2211yescharacteristic, complemented
35C23×D73—22no—
36C23×D73—24no—
37C23×D73—41no—
38C23×D73—42no—
39C23×D73—41no—
40C23×D73C2312yes—
41C2×C22⋊D73—24no—
42C2×C22⋊D73—24no—
43C2×C22⋊D73—24no—
44C2×C22⋊D73—24no—
45C2×C22⋊D73—42no—
46C2×C22⋊D73—42no—
47C2×C22⋊D73—42no—
48C2×C22⋊D73—42no—
49C2×C22⋊D73D418yescomplemented
50C22×Dic73C2312yes—
51C22×Dic73C2312yes—
52C22×Dic73C2312yes—
53C4⋊Dic73—41no—
54#11924007—42no—
55C22⋊Dic73—22no—
56C22⋊Dic73—24no—
57C22⋊Dic73—24no—
58C22⋊Dic73—24no—
59C22⋊Dic73—24no—
60#11924005—24no—
61#11924005—24no—
62#11924005—24no—
63C4×Dic73—41no—
64C24×C73—22no—
65C24×C73—24no—
66C24×C73—41no—
67C24×C73—42no—
68C24×C73—41no—
69C24×C73C2312yes—
70C24×C73C2311yescharacteristic
71C24×C73C2311yescharacteristic
72C2×D4×C73—24no—
73C2×D4×C73—24no—
74C2×D4×C73—41no—
75C2×D4×C73—41no—
76C2×D4×C73—42no—
77C2×D4×C73D414yescomplemented
78C22×C4×C73C2312yes—
79C22×C4×C73C2311yescharacteristic
80C22⋊C4×C73—22no—
81C22⋊C4×C73—24no—
82C23×C73—22no—
83C23×C73—22no—
84C23×C73—22no—
85C23×C73—22no—
86C23×C73—21no—
87C23×C73—21no—
88C23×C73—22no—
89C23×C73—21no—
90C23×C73—21no—
91C23×C73—22no—
92C23×C73—22no—
93C23×C73—22no—
94C23×C73—22no—
95C23×C73—22no—
96C23×C73—44no—
97C23×C73—48no—
98C23×C73—48no—
99C23×C73—44no—
100C23×C73—44no—
101C23×C73C2×D414yes—
102C23×C73C2×D412yes—
103C23×C73C2×D412yes—
104C23×C73C2411yescharacteristic
105C22×D73—22no—
106C22×D73—22no—
107C22×D73—22no—
108C22×D73—22no—
109C22×D73—22no—
110C22×D73—22no—
111C22×D73—44no—
112C22×D73—48no—
113C22×D73—48no—
114C22×D73—44no—
115C22×D73—44no—
116C22×D73C2×D414yes—
117D4×C73—44no—
118D4×C73—48no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—22no—
122C2×C4×C73—22no—
123C2×C4×C73—22no—
124C2×C4×C73C2×D412yes—
125C22⋊D73—48no—
126C22⋊D73—48no—
127C22⋊D73—48no—
128C2×Dic73—22no—
129C2×Dic73—22no—
130C2×Dic73—22no—
131C2×Dic73—22no—
132C2×Dic73—22no—
133C2×Dic73—22no—
134C2×Dic73—22no—
135C2×Dic73—22no—
136C2×Dic73C2×D414yes—
137C22×C73—24no—
138C22×C73—22no—
139C22×C73—22no—
140C22×C73—24no—
141C22×C73—24no—
142C22×C73—24no—
143C22×C73—24no—
144C22×C73—416no—
145C22×C73—42no—
146C22×C73—42no—
147C22×C73—42no—
148C22×C73—42no—
149C22×C73—41no—
150C22×C73—41no—
151C22×C73—42no—
152C22×C73—41no—
153C22×C73—42no—
154C22×C73—41no—
155C22×C73C22×D412yes—
156C22×C73C22×D411yescharacteristic
157C22×C73H(5,𝔽2)11yescharacteristic
158C22×C73H(5,𝔽2)11yescharacteristic
159C22×C73H(5,𝔽2)12yes—
160C2×D73—24no—
161C2×D73—24no—
162C2×D73—24no—
163C2×D73—416no—
164C2×D73—42no—
165C2×D73—42no—
166C2×D73—42no—
167C2×D73—42no—
168C4×C73—22no—
169C4×C73—42no—
170Dic73—24no—
171Dic73—42no—
172Dic73—42no—
173C2×C73—42no—
174C2×C73—44no—
175C2×C73—42no—
176C2×C73#53411yescharacteristic
177C2×C73#53412yes—
178C2×C73D4211yescharacteristic
179C2×C73D4212yes—
180C2×C73H(3,𝔽4)11yescharacteristic
181D73—44no—
182#2679—731nomaximal, Sylow
183C73#267911yescharacteristic, complemented, Sylow
184C2×#120—732no—
185C2×#120—732no—
186C2×#120—731no—
187C2×#120D7311yescharacteristic, complemented
188#394—732no—
189#394—732no—
190#394—732no—
191#390—731no—
192#390—732no—
193C25—731no—
194C25C2×D7311yescharacteristic, complemented
195C22×D4—732no—
196C22×D4—732no—
197C22×D4—732no—
198C22×D4C2×D7312yes—
199C22×D4C2×D7311yescharacteristic
200#120—24no—
201#120—1468no—
202#120—1468no—
203#120—1464no—
204C2×C4⋊C4—732no—
205C2×C4⋊C4—731no—
206C2×C22⋊C4—732no—
207C2×C22⋊C4—732no—
208C2×C22⋊C4—732no—
209C2×C22⋊C4—732no—
210C2×C22⋊C4—731no—
211C2×C22⋊C4—732no—
212C2×C22⋊C4—732no—
213C2×C22⋊C4—732no—
214C2×C22⋊C4C2×D7312yescomplemented
215C2×C22⋊C4C2×D7311yescharacteristic, complemented
216C2×C42—731no—
217#95—732no—
218C24—24no—
219C24—22no—
220C24—41no—
221C24—42no—
222C24—41no—
223C24—2921no—
224C24—2921no—
225C24—2922no—
226C24—732no—
227C24—1464no—
228C24—1462no—
229C24C22×D7312yes—
230C24C22×D7311yescharacteristic
231C24C22×D7311yescharacteristic
232C2×D4—24no—
233C2×D4—24no—
234C2×D4—41no—
235C2×D4—41no—
236C2×D4—42no—
237C2×D4—2922no—
238C2×D4—2922no—
239C2×D4—2922no—
240C2×D4—2922no—
241C2×D4—738no—
242C2×D4—1464no—
243C2×D4—1464no—
244C2×D4—1464no—
245C2×D4—1464no—
246C2×D4C22⋊D7314yescomplemented
247C22×C4—732no—
248C22×C4—732no—
249C22×C4—732no—
250C22×C4C22×D7312yes—
251C22×C4C22×D7311yescharacteristic
252C4⋊C4—2922no—
253C4⋊C4—2921no—
254C22⋊C4—22no—
255C22⋊C4—24no—
256C22⋊C4—1464no—
257C22⋊C4—1464no—
258C22⋊C4—1464no—
259C22⋊C4—1464no—
260C22⋊C4—1464no—
261C22⋊C4—1464no—
262C22⋊C4—1462no—
263C22⋊C4—1464no—
264C42—2921no—
265C23—22no—
266C23—22no—
267C23—22no—
268C23—22no—
269C23—21no—
270C23—21no—
271C23—22no—
272C23—21no—
273C23—21no—
274C23—22no—
275C23—22no—
276C23—22no—
277C23—22no—
278C23—22no—
279C23—44no—
280C23—48no—
281C23—44no—
282C23—48no—
283C23—44no—
284C23—2924no—
285C23—2928no—
286C23—2924no—
287C23—2928no—
288C23—2924no—
289C23—734no—
290C23—1462no—
291C23—1462no—
292C23—1462no—
293C23—1462no—
294C23—1462no—
295C23—1462no—
296C23D4×D7314yes—
297C23C2×C22⋊D7312yes—
298C23C2×C22⋊D7312yes—
299C23C23×D7311yescharacteristic
300D4—44no—
301D4—48no—
302D4—2928no—
303D4—2928no—
304D4—2928no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—734no—
311C2×C4—1462no—
312C2×C4—1462no—
313C2×C4—1462no—
314C2×C4—1462no—
315C2×C4—1462no—
316C2×C4—1462no—
317C2×C4—1462no—
318C2×C4—1462no—
319C2×C4C2×C22⋊D7312yes—
320C22—22no—
321C22—22no—
322C22—24no—
323C22—24no—
324C22—24no—
325C22—24no—
326C22—24no—
327C22—416no—
328C22—42no—
329C22—42no—
330C22—42no—
331C22—42no—
332C22—41no—
333C22—41no—
334C22—42no—
335C22—41no—
336C22—42no—
337C22—41no—
338C22—29216no—
339C22—2922no—
340C22—2922no—
341C22—2922no—
342C22—2922no—
343C22—1464no—
344C22—1464no—
345C22—1464no—
346C22C2×D4×D7312yes—
347C22C22×C22⋊D7311yescharacteristic
348C22#1455663611yescharacteristic
349C22#1455663611yescharacteristic
350C22#1455663612yes—
351C4—22no—
352C4—42no—
353C4—2922no—
354C4—2922no—
355C4—1464no—
356C2—42no—
357C2—44no—
358C2—42no—
359C2—2924no—
360C2#1798914611yescharacteristic
361C2#1798914712yes—
362C2#1798921911yescharacteristic
363C2D4×C22⋊D7312yes—
364C2#1798933011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC2×#120×C73C2
hypercenterC2×#120D73
hypocenterC73#2679
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×#14556560C2semidirect
2. C2×#14556559C2semidirect
3. C2×#14556559C2semidirect
4. #17988503C2semidirect
5. #17988502C2semidirect
6. #17988501C2semidirect
7. #17988490C2semidirect
8. #17988487C2semidirect
9. C2×#120×C73C2semidirect
10. C24×D73C22semidirect
17. C2×C4⋊Dic73C22semidirect
18. C2×#11924007C22semidirect
19. C2×C22⋊Dic73C22semidirect
20. C2×C22⋊Dic73C22semidirect
21. C2×C22⋊Dic73C22semidirect
22. C2×C22⋊Dic73C22semidirect
23. C2×C22⋊Dic73C22semidirect
24. C2×#11924005C22semidirect
25. C2×#11924005C22semidirect
26. C2×#11924005C22semidirect
27. C2×C4×Dic73C22semidirect
28. #14556498C22semidirect
29. C25×C73C22semidirect
33. C2×C22⋊C4×C73C22semidirect
34. C2×C22⋊C4×C73C22semidirect
49. C2×C22⋊D73D4semidirect
77. C2×D4×C73D4semidirect
183. C73#2679semidirect
187. C2×#120D73semidirect
194. C25C2×D73semidirect
214. C2×C22⋊C4C2×D73semidirect
215. C2×C22⋊C4C2×D73semidirect
246. C2×D4C22⋊D73semidirect