Finite Group Databasebeta

← #22620693

Subgroups — #22620693

Order 9344.

472 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 115 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
1#17989097C211yesmaximal, characteristic, complemented
2C2×#14556562C211yesmaximal, characteristic, complemented
3#17988923C211yesmaximal, characteristic, complemented
4#17988909C212yesmaximal, complemented
5#17988903C211yesmaximal, characteristic, complemented
6#17988820C212yesmaximal, complemented
7#17988815C212yesmaximal, complemented
8#17988738C211yesmaximal, characteristic, complemented
9#17988729C212yesmaximal, complemented
10C22⋊C8×D73C211yesmaximal, characteristic, complemented
11#447×C73C211yesmaximal, characteristic, complemented
12C2×#11924027C2211yescharacteristic, complemented
13C22×C22⋊D73—21no—
14C22×C4×D73C2211yescharacteristic
15C2×#11924016C2212yescomplemented
16C2×C8×D73C2212yescomplemented
17#14556573—21no—
18#14556571C2211yescharacteristic, complemented
19#14556570C2211yescharacteristic
20#14556562—21no—
21#14556562—21no—
22#14556562C2212yes—
23#14556562C2212yes—
24#14556562C2211yescharacteristic, complemented
25#14556559—21no—
26D4×Dic73—21no—
27#14556551—21no—
28#14556549C2211yescharacteristic, complemented
29C2×C4⋊Dic73C2211yescharacteristic
30C2×C22⋊Dic73—21no—
31#14556525C2212yescomplemented
32#14556522C2212yescomplemented
33#14556516C2212yescomplemented
34#14556512C2212yescomplemented
35#14556512C2212yescomplemented
36C22⋊#10596831C2211yescharacteristic
37#14556503C2212yescomplemented
38C22×D4×C73C2211yescharacteristic
39C2×D8×C73C2212yescomplemented
40#121×C73C2211yescharacteristic
41#102×C73C2212yescomplemented
42C22⋊C8×C73C2211yescharacteristic
43C23×D73D411yescharacteristic
44#11924027—42no—
45C2×Dic146C2311yescharacteristic
46C2×C22⋊D73—21no—
47C2×C22⋊D73—21no—
48C2×C22⋊D73—22no—
49C2×C22⋊D73—22no—
50C2×C22⋊D73—44no—
51C22×Dic73—21no—
52C22×Dic73—21no—
53C22×Dic73D411yescharacteristic
54C2×C4×D73—42no—
55C2×C4×D73D411yescharacteristic
56C2×C4×D73D411yescharacteristic
57C2×C4×D73C2311yescharacteristic
58C2×C4×D73C2311yescharacteristic
59#11924016—42no—
60C2×#10596831C2312yes—
61C8×D73—42no—
62C4⋊Dic73—21no—
63C4⋊Dic73—21no—
64C4⋊Dic73C2311yescharacteristic
65C4⋊Dic73C2312yes—
66#11924007—21no—
67C22⋊Dic73—21no—
68C22⋊Dic73—22no—
69C22⋊Dic73—22no—
70C22⋊Dic73—21no—
71#11924005—21no—
72#11924005—21no—
73C4×Dic73—21no—
74C24×C73—21no—
75C2×D4×C73—21no—
76C2×D4×C73—21no—
77C2×D4×C73—42no—
78C2×D4×C73C2312yes—
79C2×D4×C73C2311yescharacteristic
80C22×C4×C73C2311yescharacteristic
81D8×C73—42no—
82C2×C8×C73C2312yes—
83C4⋊C4×C73C2311yescharacteristic
84C22⋊C4×C73—21no—
85C23×C73—21no—
86C23×C73—22no—
87C23×C73—42no—
88C23×C73—42no—
89C23×C73—42no—
90C23×C73C2×D411yescharacteristic
91C22×D73—22no—
92C22×D73—22no—
93C22×D73—41no—
94C22×D73C2×D411yescharacteristic
95C22×D73C2×D411yescharacteristic
96D4×C73—22no—
97D4×C73—22no—
98D4×C73—22no—
99D4×C73—42no—
100D4×C73—42no—
101C2×C4×C73—22no—
102C2×C4×C73—21no—
103C2×C4×C73C2×D411yescharacteristic
104C2×C4×C73C2411yescharacteristic
105C22⋊D73—44no—
106C22⋊D73—42no—
107C22⋊D73—42no—
108C22⋊D73—44no—
109C2×Dic73—21no—
110C2×Dic73—21no—
111C2×Dic73—22no—
112C2×Dic73—41no—
113C2×Dic73—42no—
114C2×Dic73—42no—
115C2×Dic73C2×D411yescharacteristic
116C2×Dic73C2×D411yescharacteristic
117C4×D73—22no—
118C4×D73—22no—
119C4×D73—41no—
120C4×D73—41no—
121Dic146—22no—
122C8×C73—22no—
123#10596831—22no—
124C22×C73—21no—
125C22×C73—21no—
126C22×C73—41no—
127C22×C73—42no—
128C22×C73—41no—
129C22×C73—42no—
130C22×C73—42no—
131C22×C73—41no—
132C22×C73—84no—
133C22×C73#13512yes—
134C22×C73C22×D411yescharacteristic
135C2×D73—21no—
136C2×D73—21no—
137C2×D73—21no—
138C2×D73—21no—
139C2×D73—21no—
140C2×D73—44no—
141C2×D73AGL(1,ℤ/8)12yes—
142C4×C73—21no—
143C4×C73—41no—
144C4×C73H(5,𝔽2)12yes—
145Dic73—21no—
146Dic73—21no—
147Dic73—41no—
148Dic73—42no—
149Dic73—41no—
150C2×C73—22no—
151C2×C73—81no—
152C2×C73—82no—
153C2×C73#53411yescharacteristic
154C2×C73C2×#13511yescharacteristic
155C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
156D73—22no—
157D73—41no—
158#3188—731nomaximal, Sylow
159C73#318811yescharacteristic, complemented, Sylow
160#525—731no—
161C2×#121—731no—
162#484—731no—
163#482—732no—
164#481—731no—
165#466—732no—
166#465—732no—
167#450—731no—
168#449—732no—
169#447D7311yescharacteristic, complemented
170C2×C22⋊C8—731no—
171C2×#41—731no—
172C22×D4—1461no—
173C22×D4C2×D7311yescharacteristic
174C23×C4—731no—
175C2×SD16—732no—
176C2×D8C2×D7312yescomplemented
177C22×C8—732no—
178#123—1461no—
179C22⋊Q8—731no—
180C22⋊Q8—731no—
181#121—732no—
182#121—732no—
183#121—731no—
184#121—1461no—
185#121—1461no—
186#121C2×D7311yescharacteristic
187#120—1461no—
188C4×D4—1461no—
189C4×D4—1461no—
190#117—731no—
191C2×C4⋊C4—731no—
192C2×C22⋊C4—1461no—
193#107—732no—
194#106—732no—
195#103—732no—
196#102—732no—
197#102—732no—
198#102C2×D7312yescomplemented
199C22⋊C8—731no—
200C22⋊C8—732no—
201C22⋊C8C2×D7311yescharacteristic
202C24—21no—
203C24—731no—
204#41—2922no—
205C2×Q8—731no—
206C2×D4—21no—
207C2×D4—21no—
208C2×D4—42no—
209C2×D4—2924no—
210C2×D4—1461no—
211C2×D4—1461no—
212C2×D4—1462no—
213C2×D4—1462no—
214C2×D4C22×D7311yescharacteristic
215C2×D4C22×D7312yes—
216C22×C4—2922no—
217C22×C4—731no—
218C22×C4—731no—
219C22×C4—731no—
220C22×C4—731no—
221C22×C4—731no—
222C22×C4—1461no—
223C22×C4—1461no—
224C22×C4C22×D7311yescharacteristic
225SD16—2922no—
226D8—42no—
227C2×C8—2922no—
228C2×C8—732no—
229C2×C8C22×D7312yes—
230C4⋊C4—731no—
231C4⋊C4—732no—
232C4⋊C4—1461no—
233C4⋊C4—1461no—
234C4⋊C4—1461no—
235C4⋊C4C22×D7311yescharacteristic
236C22⋊C4—21no—
237C22⋊C4—1461no—
238C22⋊C4—1461no—
239C22⋊C4—1462no—
240C22⋊C4—1462no—
241C22⋊C4—1461no—
242C22⋊C4—1461no—
243C42—1461no—
244C23—21no—
245C23—22no—
246C23—42no—
247C23—42no—
248C23—42no—
249C23—2921no—
250C23—731no—
251C23—731no—
252C23—1462no—
253C23—1462no—
254C23D4×D7311yescharacteristic
255Q8—1462no—
256D4—22no—
257D4—22no—
258D4—22no—
259D4—42no—
260D4—42no—
261D4—2924no—
262D4—2922no—
263D4—2924no—
264D4—2922no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—2921no—
268C2×C4—2921no—
269C2×C4—2922no—
270C2×C4—2922no—
271C2×C4—2921no—
272C2×C4—731no—
273C2×C4—731no—
274C2×C4—1461no—
275C2×C4—1462no—
276C2×C4—1461no—
277C2×C4—1462no—
278C2×C4—1462no—
279C2×C4D4×D7311yescharacteristic
280C2×C4C23×D7311yescharacteristic
281C8—22no—
282C8—1462no—
283C22—21no—
284C22—21no—
285C22—41no—
286C22—42no—
287C22—41no—
288C22—42no—
289C22—42no—
290C22—41no—
291C22—84no—
292C22—2924no—
293C22—732no—
294C22—1461no—
295C22—1461no—
296C22—1461no—
297C22—1461no—
298C22—1461no—
299C22#1455661012yes—
300C22C2×D4×D7311yescharacteristic
301C4—21no—
302C4—41no—
303C4—2921no—
304C4—2922no—
305C4—2921no—
306C4—1461no—
307C4—1461no—
308C4#1455663612yes—
309C2—22no—
310C2—82no—
311C2—81no—
312C2—2921no—
313C2—1462no—
314C2#1798914711yescharacteristic
315C2C2×#1455661011yescharacteristic
316C2AGL(1,ℤ/8)×D7311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#447×C73C2
socleC22×C73C22×D4
hypercenter#447D73
hypocenterC73#3188
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #17989097C2semidirect
2. C2×#14556562C2semidirect
3. #17988923C2semidirect
4. #17988909C2semidirect
5. #17988903C2semidirect
6. #17988820C2semidirect
7. #17988815C2semidirect
8. #17988738C2semidirect
9. #17988729C2semidirect
10. C22⋊C8×D73C2semidirect
11. #447×C73C2semidirect
12. C2×#11924027C22semidirect
15. C2×#11924016C22semidirect
16. C2×C8×D73C22semidirect
18. #14556571C22semidirect
24. #14556562C22semidirect
28. #14556549C22semidirect
31. #14556525C22semidirect
32. #14556522C22semidirect
33. #14556516C22semidirect
34. #14556512C22semidirect
35. #14556512C22semidirect
37. #14556503C22semidirect
39. C2×D8×C73C22semidirect
41. #102×C73C22semidirect
159. C73#3188semidirect
169. #447D73semidirect
176. C2×D8C2×D73semidirect
198. #102C2×D73semidirect