Finite Group Databasebeta

← #22614211

Subgroups — #22614211

Order 9344.

700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11924005C211yesmaximal, characteristic
2C2×C22⋊C4×D73C211yesmaximal, characteristic
3#17988516C212yesmaximal, complemented
4#17988513C212yesmaximal, complemented
5#17988460C211yesmaximal, characteristic, complemented
6#17988458C212yesmaximal, complemented
7#17988449C212yesmaximal, complemented
8#17988448C211yesmaximal, characteristic, complemented
9#17988448C211yesmaximal, characteristic, complemented
10#17988442C211yesmaximal, characteristic
11#385×C73C211yesmaximal, characteristic, complemented
12C24×D73C2211yescharacteristic
13C23×Dic73C2211yescharacteristic
14C22×C4×D73C2211yescharacteristic
15C22×C4×D73C2211yescharacteristic
16C2×#11924007C2212yescomplemented
17C2×C22⋊Dic73C2211yescharacteristic
18C2×C22⋊Dic73C2211yescharacteristic
19C2×#11924005—24no—
20C2×#11924005C2212yes—
21C2×#11924005C2212yes—
22C2×#11924005C2211yescharacteristic
23C2×#11924005C2212yes—
24C2×#11924005C2211yescharacteristic
25C2×#11924005C2212yes—
26C22⋊C4×D73—24no—
27#14556498C2212yescomplemented
28#14556498C2212yescomplemented
29#14556498C2212yescomplemented
30#14556498C2212yescomplemented
31#14556498C2212yescomplemented
32C23×C4×C73C2211yescharacteristic
33C2×C4⋊C4×C73C2212yescomplemented
34C2×C22⋊C4×C73C2211yescharacteristic
35C2×C22⋊C4×C73C2211yescharacteristic
36#95×C73C2212yescomplemented
37C23×D73—22no—
38C23×D73—22no—
39C23×D73—24no—
40C23×D73—42no—
41C23×D73D414yes—
42C23×D73C2311yescharacteristic
43C23×D73C2311yescharacteristic
44C22×Dic73—22no—
45C22×Dic73—22no—
46C22×Dic73—22no—
47C22×Dic73C2312yes—
48C22×Dic73C2311yescharacteristic
49C22×Dic73C2312yes—
50C22×Dic73C2311yescharacteristic
51C2×C4×D73—22no—
52C2×C4×D73—22no—
53C2×C4×D73—24no—
54C2×C4×D73—42no—
55#11924007—42no—
56C22⋊Dic73—22no—
57C22⋊Dic73—22no—
58#11924005—22no—
59#11924005—22no—
60#11924005—24no—
61#11924005—24no—
62#11924005—24no—
63#11924005—42no—
64C24×C73C2311yescharacteristic
65C22×C4×C73—22no—
66C22×C4×C73—42no—
67C22×C4×C73C2311yescharacteristic
68C22×C4×C73C2312yes—
69C22×C4×C73C2312yes—
70C22×C4×C73C2311yescharacteristic
71C4⋊C4×C73—42no—
72C22⋊C4×C73—22no—
73C22⋊C4×C73—22no—
74C23×C73—22no—
75C23×C73—22no—
76C23×C73C2×D412yes—
77C23×C73#4112yes—
78C23×C73#4112yes—
79C23×C73C2411yescharacteristic
80C22×D73—21no—
81C22×D73—21no—
82C22×D73—22no—
83C22×D73—28no—
84C22×D73—22no—
85C22×D73—21no—
86C22×D73—21no—
87C22×D73—22no—
88C22×D73—28no—
89C22×D73—44no—
90C22×D73—48no—
91C22×D73—48no—
92C22×D73C2×D412yes—
93C22×D73C2×D412yes—
94C22×D73#4114yes—
95C2×C4×C73—21no—
96C2×C4×C73—21no—
97C2×C4×C73—22no—
98C2×C4×C73—22no—
99C2×C4×C73—22no—
100C2×C4×C73—22no—
101C2×C4×C73—22no—
102C2×C4×C73—22no—
103C2×C4×C73—22no—
104C2×C4×C73—22no—
105C2×C4×C73—44no—
106C2×Dic73—22no—
107C2×Dic73—21no—
108C2×Dic73—21no—
109C2×Dic73—22no—
110C2×Dic73—22no—
111C2×Dic73—22no—
112C2×Dic73—22no—
113C2×Dic73—22no—
114C2×Dic73—22no—
115C2×Dic73—22no—
116C2×Dic73—44no—
117C4×D73—44no—
118C4×D73—44no—
119C22×C73—22no—
120C22×C73—22no—
121C22×C73—24no—
122C22×C73—24no—
123C22×C73#12314yes—
124C22×C73C22×D411yescharacteristic
125C22×C73C2×#4112yes—
126C22×C73C2×#4111yescharacteristic
127C22×C73C2×#4111yescharacteristic
128C22×C73H(5,𝔽2)12yes—
129C2×D73—22no—
130C2×D73—22no—
131C2×D73—24no—
132C2×D73—24no—
133C2×D73—22no—
134C2×D73—22no—
135C2×D73—22no—
136C2×D73—416no—
137C2×D73—42no—
138C2×D73—42no—
139C2×D73#12314yes—
140C4×C73—41no—
141C4×C73—41no—
142C4×C73—42no—
143C4×C73—42no—
144Dic73—41no—
145Dic73—42no—
146Dic73—41no—
147Dic73—42no—
148C2×C73—24no—
149C2×C73C2×#12311yescharacteristic
150C2×C73C2×#12311yescharacteristic
151C2×C73#53411yescharacteristic
152C2×C73#55112yes—
153C2×C73#55112yes—
154D73—24no—
155D73—42no—
156#2483—731nomaximal, Sylow
157C73#248311yescharacteristic, complemented, Sylow
158C22×C22⋊C4—731no—
159C22×C22⋊C4—731no—
160#397—732no—
161#397—732no—
162#385—731no—
163#385—732no—
164#385D7311yescharacteristic, complemented
165#381—731no—
166#381—731no—
167#381—732no—
168#379—731no—
169C25—731no—
170C23×C4—731no—
171C23×C4—731no—
172C23×C4—731no—
173C23×C4C2×D7311yescharacteristic
174C2×C4⋊C4—732no—
175C2×C4⋊C4C2×D7312yescomplemented
176C2×C22⋊C4—732no—
177C2×C22⋊C4—731no—
178C2×C22⋊C4—731no—
179C2×C22⋊C4—732no—
180C2×C22⋊C4—731no—
181C2×C22⋊C4—732no—
182C2×C22⋊C4—731no—
183C2×C22⋊C4—732no—
184C2×C22⋊C4—1464no—
185C2×C22⋊C4—1464no—
186C2×C22⋊C4C2×D7311yescharacteristic
187C2×C22⋊C4C2×D7311yescharacteristic
188#95—732no—
189#95—732no—
190#95—732no—
191#95—732no—
192#95—732no—
193#95C2×D7312yescomplemented
194C24—2922no—
195C24—734no—
196C24—731no—
197C24—731no—
198C24—1464no—
199C24—1462no—
200C24—1462no—
201C24C22×D7311yescharacteristic
202C22×C4—22no—
203C22×C4—42no—
204C22×C4—2922no—
205C22×C4—731no—
206C22×C4—732no—
207C22×C4—732no—
208C22×C4—731no—
209C22×C4—1462no—
210C22×C4—1462no—
211C22×C4—1464no—
212C22×C4—1462no—
213C22×C4—1462no—
214C22×C4—1462no—
215C22×C4C22×D7311yescharacteristic
216C22×C4C22×D7312yes—
217C22×C4C22×D7311yescharacteristic
218C22×C4C22×D7312yes—
219C4⋊C4—42no—
220C4⋊C4—2922no—
221C22⋊C4—22no—
222C22⋊C4—22no—
223C22⋊C4—2922no—
224C22⋊C4—1464no—
225C22⋊C4—1462no—
226C22⋊C4—1462no—
227C22⋊C4—1464no—
228C22⋊C4—1464no—
229C22⋊C4—1462no—
230C22⋊C4—1462no—
231C23—22no—
232C23—22no—
233C23—2928no—
234C23—2928no—
235C23—2924no—
236C23—732no—
237C23—734no—
238C23—732no—
239C23—1468no—
240C23—1468no—
241C23—1462no—
242C23—1461no—
243C23—1461no—
244C23—1462no—
245C23—1461no—
246C23—1461no—
247C23—1462no—
248C23D4×D7312yes—
249C23#1192402812yes—
250C23#1192402912yes—
251C23C23×D7311yescharacteristic
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—44no—
263C2×C4—2924no—
264C2×C4—2924no—
265C2×C4—2924no—
266C2×C4—1461no—
267C2×C4—1461no—
268C2×C4—1462no—
269C2×C4—1462no—
270C2×C4—1462no—
271C2×C4—1462no—
272C2×C4—1462no—
273C2×C4—1462no—
274C2×C4—1462no—
275C2×C4—1462no—
276C22—22no—
277C22—24no—
278C22—24no—
279C22—22no—
280C22—29216no—
281C22—2922no—
282C22—2922no—
283C22—734no—
284C22—1462no—
285C22—1462no—
286C22—1462no—
287C22—1462no—
288C22—1464no—
289C22—1464no—
290C22—1462no—
291C22#1455657614yes—
292C22C2×D4×D7311yescharacteristic
293C22#41×D7312yes—
294C22C2×#1192402811yescharacteristic
295C22C2×#1192402911yescharacteristic
296C22#1455663612yes—
297C4—42no—
298C4—41no—
299C4—42no—
300C4—41no—
301C4—2921no—
302C4—2922no—
303C4—2921no—
304C4—2922no—
305C2—24no—
306C2—2922no—
307C2—1464no—
308C2#123×D7311yescharacteristic
309C2C2×#1455657611yescharacteristic
310C2#1798914711yescharacteristic
311C2#1798926412yes—
312C2#1798926612yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#385×C73C2
hypercenter#385D73
hypocenterC73#2483
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
3. #17988516C2semidirect
4. #17988513C2semidirect
5. #17988460C2semidirect
6. #17988458C2semidirect
7. #17988449C2semidirect
8. #17988448C2semidirect
9. #17988448C2semidirect
11. #385×C73C2semidirect
16. C2×#11924007C22semidirect
27. #14556498C22semidirect
28. #14556498C22semidirect
29. #14556498C22semidirect
30. #14556498C22semidirect
31. #14556498C22semidirect
33. C2×C4⋊C4×C73C22semidirect
36. #95×C73C22semidirect
157. C73#2483semidirect
164. #385D73semidirect
175. C2×C4⋊C4C2×D73semidirect
193. #95C2×D73semidirect