Finite Group Databasebeta

← #22613577

Subgroups — #22613577

Order 9344.

1088 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 161 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×D4×D73C211yesmaximal, characteristic
2C2×#14556577C212yesmaximal, complemented
3C2×#14556569C211yesmaximal, characteristic, complemented
4#17988505C211yesmaximal, characteristic, complemented
5#17988504C211yesmaximal, characteristic, complemented
6#17988501C211yesmaximal, characteristic, complemented
7#17988487C212yesmaximal, complemented
8#17988442C212yesmaximal, complemented
9#17988442C212yesmaximal, complemented
10#17988434C211yesmaximal, characteristic, complemented
11#394×C73C211yesmaximal, characteristic, complemented
12C24×D73C2212yes—
13C22×Dic146C2211yescharacteristic, complemented
14C22×D292C2211yescharacteristic
15C22×C22⋊D73C2212yes—
16C2×D4×D73—28no—
17C2×D4×D73—24no—
18C22×C4×D73C2211yescharacteristic
19#14556577—28no—
20#14556569—24no—
21C2×#11924007C2211yescharacteristic, complemented
22C2×#11924007C2211yescharacteristic, complemented
23C2×C22⋊Dic73C2212yescomplemented
24C2×C22⋊Dic73C2212yescomplemented
25C2×#11924005C2212yes—
26C2×#11924005C2211yescharacteristic
27C2×#11924005C2211yescharacteristic
28C2×#11924005C2212yescomplemented
29C2×#11924005C2212yescomplemented
30C2×#11924005C2212yescomplemented
31C2×#11924005C2212yescomplemented
32C2×C4×Dic73C2212yescomplemented
33#14556498C2211yescharacteristic, complemented
34C22×D4×C73C2211yescharacteristic
35C2×C4⋊C4×C73C2211yescharacteristic, complemented
36C2×C22⋊C4×C73C2212yescomplemented
37C2×C22⋊C4×C73C2212yescomplemented
38#95×C73C2211yescharacteristic, complemented
39C23×D73—24no—
40C23×D73—24no—
41C23×D73—24no—
42C23×D73—24no—
43C23×D73—24no—
44C23×D73—42no—
45C23×D73—42no—
46C23×D73C2312yes—
47C23×D73C2311yescharacteristic
48C2×Dic146—22no—
49C2×Dic146—24no—
50C2×D292—24no—
51C2×D292—22no—
52C2×C22⋊D73—24no—
53C2×C22⋊D73—24no—
54C2×C22⋊D73D418yes—
55D4×D73—232no—
56C22×Dic73C2312yes—
57C22×Dic73C2311yescharacteristic
58C22×Dic73C2311yescharacteristic
59C22×Dic73C2311yescharacteristic
60C2×C4×D73—24no—
61C2×C4×D73D414yes—
62#11924007—22no—
63#11924007—22no—
64C22⋊Dic73—24no—
65C22⋊Dic73—42no—
66#11924005—22no—
67#11924005—22no—
68#11924005—24no—
69#11924005—24no—
70#11924005—24no—
71#11924005—42no—
72#11924005—42no—
73C4×Dic73—24no—
74C24×C73C2312yes—
75C2×D4×C73—24no—
76C2×D4×C73—22no—
77C22×C4×C73C2312yes—
78C22×C4×C73C2311yescharacteristic
79C22×C4×C73C2311yescharacteristic
80C22×C4×C73C2311yescharacteristic
81C4⋊C4×C73—22no—
82C22⋊C4×C73—24no—
83C22⋊C4×C73—42no—
84C23×C73—22no—
85C23×C73—22no—
86C23×C73—22no—
87C23×C73—22no—
88C23×C73—22no—
89C23×C73—22no—
90C23×C73C2×D414yes—
91C23×C73C2411yescharacteristic
92C22×D73—22no—
93C22×D73—21no—
94C22×D73—21no—
95C22×D73—216no—
96C22×D73—22no—
97C22×D73—22no—
98C22×D73—22no—
99C22×D73—22no—
100C22×D73—22no—
101C22×D73—22no—
102C22×D73—48no—
103C22×D73—48no—
104C22×D73—48no—
105C22×D73—48no—
106C22×D73—48no—
107C22×D73—48no—
108C22×D73C2×D414yes—
109C22×D73C2×D412yes—
110C22×D73#4114yes—
111D4×C73—28no—
112C2×C4×C73—22no—
113C2×C4×C73—22no—
114C2×C4×C73—22no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—22no—
118C2×C4×C73—21no—
119C2×C4×C73—22no—
120C2×C4×C73—21no—
121C2×C4×C73C2×D412yes—
122C22⋊D73—216no—
123C2×Dic73—22no—
124C2×Dic73—22no—
125C2×Dic73—21no—
126C2×Dic73—21no—
127C2×Dic73—22no—
128C2×Dic73—21no—
129C2×Dic73—22no—
130C2×Dic73—21no—
131C2×Dic73C2×D414yes—
132C2×Dic73C2×D412yes—
133D292—28no—
134C4×D73—28no—
135Dic146—44no—
136C22×C73—24no—
137C22×C73—24no—
138C22×C73—24no—
139C22×C73—42no—
140C22×C73—42no—
141C22×C73—42no—
142C22×C73—42no—
143C22×C73C22×D411yescharacteristic
144C22×C73C22×D412yes—
145C22×C73C2×#4112yes—
146C22×C73H(5,𝔽2)11yescharacteristic
147C22×C73H(5,𝔽2)11yescharacteristic
148C2×D73—22no—
149C2×D73—22no—
150C2×D73—24no—
151C2×D73—24no—
152C2×D73—24no—
153C2×D73—24no—
154C2×D73—24no—
155C2×D73—432no—
156C2×D73—42no—
157C2×D73—42no—
158C2×D73—42no—
159C2×D73—42no—
160C2×D73#12414yescomplemented
161C4×C73—22no—
162C4×C73—41no—
163C4×C73—41no—
164C4×C73—42no—
165Dic73—41no—
166Dic73—41no—
167Dic73—42no—
168Dic73#12014yes—
169C2×C73—44no—
170C2×C73C2×#12011yescharacteristic
171C2×C73C2×#12411yescharacteristic
172C2×C73#53511yescharacteristic
173C2×C73#54612yes—
174C2×C73#54612yes—
175D73—24no—
176D73—44no—
177#2435—731nomaximal, Sylow
178C73#243511yescharacteristic, complemented, Sylow
179C23×D4—731no—
180C2×#124—732no—
181C2×C22⋊Q8—731no—
182#394—731no—
183#394—731no—
184#394—731no—
185#394D7311yescharacteristic, complemented
186#390—732no—
187#379—732no—
188#379—732no—
189C4×C22⋊C4—731no—
190C25—732no—
191C22×Q8—731no—
192C22×D4—732no—
193C22×D4—731no—
194C22×D4—1464no—
195C22×D4—1468no—
196C22×D4C2×D7311yescharacteristic
197C23×C4—731no—
198#124—1468no—
199C22⋊Q8—1464no—
200C2×C4⋊C4—731no—
201C2×C4⋊C4—731no—
202C2×C4⋊C4C2×D7311yescharacteristic, complemented
203C2×C22⋊C4—732no—
204C2×C22⋊C4—732no—
205C2×C22⋊C4—732no—
206C2×C22⋊C4—732no—
207C2×C22⋊C4—731no—
208C2×C22⋊C4—731no—
209C2×C22⋊C4—732no—
210C2×C22⋊C4—732no—
211C2×C22⋊C4—732no—
212C2×C22⋊C4C2×D7312yescomplemented
213C2×C22⋊C4C2×D7312yescomplemented
214C2×C42—732no—
215#95—731no—
216#95C2×D7311yescharacteristic, complemented
217C24—2922no—
218C24—2922no—
219C24—731no—
220C24—732no—
221C24—1464no—
222C24—1464no—
223C24—1464no—
224C24—1464no—
225C24—1464no—
226C24C22×D7312yes—
227C2×Q8—1462no—
228C2×Q8—1464no—
229C2×D4—24no—
230C2×D4—22no—
231C2×D4—738no—
232C2×D4—1464no—
233C2×D4—1464no—
234C2×D4—1464no—
235C2×D4—14632no—
236C2×D4—1462no—
237C22×C4—731no—
238C22×C4—734no—
239C22×C4—732no—
240C22×C4—731no—
241C22×C4—731no—
242C22×C4—1464no—
243C22×C4C22×D7312yes—
244C22×C4C22×D7311yescharacteristic
245C22×C4C22×D7311yescharacteristic
246C22×C4C22×D7311yescharacteristic
247C4⋊C4—22no—
248C4⋊C4—1462no—
249C4⋊C4—1462no—
250C22⋊C4—24no—
251C22⋊C4—42no—
252C22⋊C4—2922no—
253C22⋊C4—2922no—
254C22⋊C4—2922no—
255C22⋊C4—1464no—
256C22⋊C4—1462no—
257C22⋊C4—1462no—
258C22⋊C4—1464no—
259C22⋊C4—1464no—
260C22⋊C4—1464no—
261C42—1464no—
262C23—22no—
263C23—22no—
264C23—22no—
265C23—22no—
266C23—22no—
267C23—22no—
268C23—2928no—
269C23—2928no—
270C23—2928no—
271C23—2928no—
272C23—2928no—
273C23—2928no—
274C23—732no—
275C23—734no—
276C23—734no—
277C23—14616no—
278C23—1462no—
279C23—1462no—
280C23—1462no—
281C23—1462no—
282C23—1462no—
283C23—1462no—
284C23—1462no—
285C23—1461no—
286C23—1461no—
287C23D4×D7314yes—
288C23C23×D7311yescharacteristic
289Q8—2924no—
290D4—28no—
291D4—1468no—
292D4—14616no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—22no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—21no—
302C2×C4—734no—
303C2×C4—732no—
304C2×C4—1468no—
305C2×C4—1462no—
306C2×C4—1462no—
307C2×C4—1461no—
308C2×C4—1461no—
309C2×C4—1462no—
310C2×C4—1461no—
311C2×C4—1461no—
312C2×C4—1462no—
313C2×C4D4×D7312yes—
314C22—24no—
315C22—24no—
316C22—24no—
317C22—42no—
318C22—42no—
319C22—42no—
320C22—42no—
321C22—29232no—
322C22—2922no—
323C22—2922no—
324C22—2922no—
325C22—2922no—
326C22—734no—
327C22—1464no—
328C22—1464no—
329C22—1464no—
330C22—1462no—
331C22—1464no—
332C22—1464no—
333C22—1462no—
334C22C2×D4×D7311yescharacteristic
335C22C2×D4×D7312yes—
336C22#41×D7312yes—
337C22#1455663611yescharacteristic
338C22#1455663711yescharacteristic
339C4—22no—
340C4—41no—
341C4—42no—
342C4—41no—
343C4—2921no—
344C4—2922no—
345C4—2921no—
346C4—734no—
347C2—44no—
348C2—2924no—
349C2—1464no—
350C2#120×D7311yescharacteristic
351C2#124×D7311yescharacteristic
352C2#1798915311yescharacteristic
353C2#1798922612yes—
354C2#1798922912yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#394×C73C2
hypercenter#394D73
hypocenterC73#2435
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#14556577C2semidirect
3. C2×#14556569C2semidirect
4. #17988505C2semidirect
5. #17988504C2semidirect
6. #17988501C2semidirect
7. #17988487C2semidirect
8. #17988442C2semidirect
9. #17988442C2semidirect
10. #17988434C2semidirect
11. #394×C73C2semidirect
13. C22×Dic146C22semidirect
21. C2×#11924007C22semidirect
22. C2×#11924007C22semidirect
23. C2×C22⋊Dic73C22semidirect
24. C2×C22⋊Dic73C22semidirect
28. C2×#11924005C22semidirect
29. C2×#11924005C22semidirect
30. C2×#11924005C22semidirect
31. C2×#11924005C22semidirect
32. C2×C4×Dic73C22semidirect
33. #14556498C22semidirect
35. C2×C4⋊C4×C73C22semidirect
36. C2×C22⋊C4×C73C22semidirect
37. C2×C22⋊C4×C73C22semidirect
38. #95×C73C22semidirect
160. C2×D73#124semidirect
178. C73#2435semidirect
185. #394D73semidirect
202. C2×C4⋊C4C2×D73semidirect
212. C2×C22⋊C4C2×D73semidirect
213. C2×C22⋊C4C2×D73semidirect
216. #95C2×D73semidirect