Finite Group Databasebeta

← #22620714

Subgroups — #22620714

Order 9344.

420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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#17989098C211yesmaximal, characteristic
2C2×#14556570C211yesmaximal, characteristic, complemented
3#17988929C212yesmaximal, complemented
4#17988918C211yesmaximal, characteristic, complemented
5#17988901C211yesmaximal, characteristic, complemented
6#17988828C212yesmaximal, complemented
7#17988816C212yesmaximal, complemented
8#17988751C212yesmaximal, complemented
9#17988745C211yesmaximal, characteristic, complemented
10#17988728C211yesmaximal, characteristic, complemented
11C2×C22⋊C8×C73C211yesmaximal, characteristic, complemented
12C2×#11924028C2211yescharacteristic
13C22×Dic146C2211yescharacteristic
14C2×Dic292C2212yescomplemented
15C2×#11924017C2212yescomplemented
16#14556574—21no—
17#14556570—21no—
18#14556570—21no—
19#14556570C2211yescharacteristic
20#14556570C2212yes—
21#14556570C2212yes—
22#14556570C2211yescharacteristic
23#14556565C2211yescharacteristic
24#14556565C2211yescharacteristic
25#14556560—21no—
26C4×C22⋊D73—21no—
27C4×C22⋊D73—21no—
28#14556550C2211yescharacteristic
29C2×C4⋊Dic73C2211yescharacteristic
30C2×#11924007—21no—
31C2×C22⋊Dic73—21no—
32#14556525C2212yescomplemented
33#14556523C2212yescomplemented
34#14556516C2212yescomplemented
35#14556516C2212yescomplemented
36#14556516C2212yescomplemented
37#14556513C2212yescomplemented
38C23×C4×C73C2211yescharacteristic
39C22×C8×C73C2212yes—
40C22⋊C8×C73C2211yescharacteristic
41C22⋊C8×C73C2211yescharacteristic
42C22⋊C8×C73C2212yes—
43#11924028—42no—
44C2×Dic146—21no—
45C2×Dic146—42no—
46C2×Dic146C2312yes—
47C2×Dic146C2311yescharacteristic
48C2×D292C2311yescharacteristic
49C2×C22⋊D73—21no—
50C2×C22⋊D73—21no—
51C2×C22⋊D73—21no—
52C22×Dic73—21no—
53C22×Dic73—21no—
54C2×C4×D73—21no—
55Dic292—42no—
56#11924017—42no—
57C4⋊Dic73—21no—
58C4⋊Dic73C2312yes—
59C4⋊Dic73C2311yescharacteristic
60C4⋊Dic73C2311yescharacteristic
61#11924007—22no—
62#11924007—22no—
63#11924007—21no—
64#11924007—21no—
65C22⋊Dic73—22no—
66C22⋊Dic73—22no—
67C22⋊Dic73—21no—
68C22⋊Dic73—21no—
69C22⋊Dic73—21no—
70#11924005—21no—
71#11924005—21no—
72C4×Dic73—21no—
73C24×C73D411yescharacteristic
74C22×C4×C73—42no—
75C22×C4×C73D411yescharacteristic
76C22×C4×C73D411yescharacteristic
77C22×C4×C73D411yescharacteristic
78C22×C4×C73C2311yescharacteristic
79C22×C4×C73C2311yescharacteristic
80C22×C4×C73C2311yescharacteristic
81C2×C8×C73—42no—
82C2×C8×C73C2312yes—
83C2×C8×C73C2312yes—
84C23×C73—22no—
85C23×C73—22no—
86C23×C73—41no—
87C23×C73C2×D411yescharacteristic
88C23×C73C2×D411yescharacteristic
89C23×C73C2×D411yescharacteristic
90C22×D73—21no—
91C2×C4×C73—22no—
92C2×C4×C73—22no—
93C2×C4×C73—22no—
94C2×C4×C73—41no—
95C2×C4×C73—41no—
96C2×C4×C73—41no—
97C2×C4×C73C2×D411yescharacteristic
98C2×C4×C73C2×D411yescharacteristic
99C2×C4×C73C2×D411yescharacteristic
100C2×C4×C73C2411yescharacteristic
101C22⋊D73—42no—
102C22⋊D73—42no—
103C22⋊D73—42no—
104C2×Dic73—21no—
105C2×Dic73—21no—
106C2×Dic73—22no—
107C2×Dic73—21no—
108C2×Dic73—22no—
109C2×Dic73—42no—
110C2×Dic73—42no—
111D292—22no—
112C4×D73—42no—
113Dic146—22no—
114Dic146—22no—
115Dic146—22no—
116Dic146—42no—
117C8×C73—22no—
118C8×C73—22no—
119C22×C73—21no—
120C22×C73—21no—
121C22×C73—21no—
122C22×C73—21no—
123C22×C73—21no—
124C22×C73—21no—
125C22×C73—21no—
126C22×C73—44no—
127C22×C73#13512yes—
128C22×C73#13712yes—
129C22×C73C22×D411yescharacteristic
130C2×D73—41no—
131C2×D73—41no—
132C2×D73—41no—
133C4×C73—21no—
134C4×C73—21no—
135C4×C73—21no—
136C4×C73H(5,𝔽2)12yes—
137Dic73—42no—
138Dic73—41no—
139Dic73—42no—
140Dic73—41no—
141Dic73—41no—
142C2×C73—22no—
143C2×C73—22no—
144C2×C73—41no—
145C2×C73#53411yescharacteristic
146C2×C73C2×#13511yescharacteristic
147C2×C73C2×#13711yescharacteristic
148D73—81no—
149#3190—731nomaximal, Sylow
150C73#319011yescharacteristic, complemented, Sylow
151#525—731no—
152C2×C22⋊Q8—731no—
153#485—732no—
154#483—731no—
155#480—731no—
156#467—732no—
157#465—732no—
158#452—732no—
159#451—731no—
160#448—731no—
161C2×C22⋊C8D7311yescharacteristic, complemented
162C2×#41—731no—
163C22×Q8—731no—
164C23×C4C2×D7311yescharacteristic
165C2×Q16—732no—
166C2×SD16—732no—
167C22×C8C2×D7312yes—
168#123—1461no—
169C22⋊Q8—732no—
170C22⋊Q8—732no—
171C22⋊Q8—731no—
172C22⋊Q8—731no—
173C22⋊Q8—1461no—
174C22⋊Q8—1461no—
175#121—731no—
176#121—731no—
177#120—1461no—
178C4×D4—1461no—
179C4×D4—1461no—
180#117—731no—
181C2×C4⋊C4—731no—
182C2×C4⋊C4—1461no—
183C2×C22⋊C4—1461no—
184#107—732no—
185#106—732no—
186#103—732no—
187#103—732no—
188#103—732no—
189#102—732no—
190C22⋊C8C2×D7311yescharacteristic
191C22⋊C8C2×D7311yescharacteristic
192C22⋊C8C2×D7312yes—
193C24D29211yescharacteristic
194#41—2922no—
195C2×Q8—2922no—
196C2×Q8—732no—
197C2×Q8—731no—
198C2×Q8—1461no—
199C2×D4—731no—
200C2×D4—1461no—
201C2×D4—1461no—
202C2×D4—1461no—
203C22×C4—42no—
204C22×C4—1461no—
205C22×C4—1461no—
206C22×C4—1461no—
207C22×C4D29211yescharacteristic
208C22×C4D29211yescharacteristic
209C22×C4D29211yescharacteristic
210C22×C4C22×D7311yescharacteristic
211C22×C4C22×D7311yescharacteristic
212C22×C4C22×D7311yescharacteristic
213Q16—2922no—
214SD16—2922no—
215C2×C8—42no—
216C2×C8C22×D7312yes—
217C2×C8C22×D7312yes—
218C4⋊C4—732no—
219C4⋊C4—731no—
220C4⋊C4—731no—
221C4⋊C4—1462no—
222C4⋊C4—1462no—
223C4⋊C4—1461no—
224C4⋊C4—1461no—
225C4⋊C4—1461no—
226C22⋊C4—1462no—
227C22⋊C4—1462no—
228C22⋊C4—1461no—
229C22⋊C4—1461no—
230C22⋊C4—1461no—
231C22⋊C4—1461no—
232C22⋊C4—1461no—
233C42—1461no—
234C23—22no—
235C23—22no—
236C23—41no—
237C23—1461no—
238C23C2×D29211yescharacteristic
239C23C2×D29211yescharacteristic
240C23C2×D29211yescharacteristic
241Q8—2922no—
242Q8—1462no—
243Q8—1462no—
244Q8—1462no—
245D4—2922no—
246D4—2922no—
247D4—2922no—
248D4—1462no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—2922no—
256C2×C4—2922no—
257C2×C4—2922no—
258C2×C4—1461no—
259C2×C4—1461no—
260C2×C4—1462no—
261C2×C4—1461no—
262C2×C4—1462no—
263C2×C4C2×D29211yescharacteristic
264C2×C4C2×D29211yescharacteristic
265C2×C4C2×D29211yescharacteristic
266C2×C4C23×D7311yescharacteristic
267C8—22no—
268C8—22no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—44no—
277C22—2921no—
278C22—2921no—
279C22—2921no—
280C22#1455661312yes—
281C22#1455662412yes—
282C22C22×D29211yescharacteristic
283C4—21no—
284C4—21no—
285C4—21no—
286C4—2921no—
287C4—2921no—
288C4—2922no—
289C4—2922no—
290C4—2921no—
291C4#1455663612yes—
292C2—22no—
293C2—22no—
294C2—41no—
295C2—5841no—
296C2#1798914911yescharacteristic
297C2C2×#1455661311yescharacteristic
298C2C2×#1455662411yescharacteristic
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC2×C22⋊C8×C73C2
socleC22×C73C22×D4
hypercenterC2×C22⋊C8D73
hypocenterC73#3190
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#14556570C2semidirect
3. #17988929C2semidirect
4. #17988918C2semidirect
5. #17988901C2semidirect
6. #17988828C2semidirect
7. #17988816C2semidirect
8. #17988751C2semidirect
9. #17988745C2semidirect
10. #17988728C2semidirect
11. C2×C22⋊C8×C73C2semidirect
14. C2×Dic292C22semidirect
15. C2×#11924017C22semidirect
32. #14556525C22semidirect
33. #14556523C22semidirect
34. #14556516C22semidirect
35. #14556516C22semidirect
36. #14556516C22semidirect
37. #14556513C22semidirect
150. C73#3190semidirect
161. C2×C22⋊C8D73semidirect