Finite Group Databasebeta

← #22615410

Subgroups — #22615410

Order 9344.

596 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 145 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×#14556563C211yesmaximal, characteristic
2C22×#11924007C211yesmaximal, characteristic, complemented
3#17988528C212yesmaximal, complemented
4#17988502C212yesmaximal, complemented
5#17988476C212yesmaximal, complemented
6#17988475C212yesmaximal, complemented
7#17988467C211yesmaximal, characteristic, complemented
8#17988466C211yesmaximal, characteristic, complemented
9#17988464C211yesmaximal, characteristic, complemented
10C22⋊C4×Dic73C211yesmaximal, characteristic, complemented
11#386×C73C211yesmaximal, characteristic, complemented
12C22×C22⋊D73C2211yescharacteristic
13C22×C22⋊D73C2211yescharacteristic
14C23×Dic73C2211yescharacteristic
15C23×Dic73C2211yescharacteristic
16#14556563—24no—
17C2×#11924007—24no—
18C2×#11924007C2212yes—
19C2×#11924007C2212yes—
20C2×#11924007C2211yescharacteristic
21C2×C22⋊Dic73C2211yescharacteristic
22C2×C22⋊Dic73C2212yes—
23C2×C22⋊Dic73C2211yescharacteristic
24C2×#11924005C2212yes—
25C2×#11924005C2211yescharacteristic
26C2×#11924005C2212yes—
27C2×C4×Dic73C2212yes—
28#14556498C2212yes—
29#14556498C2212yes—
30#14556498C2212yes—
31#14556498C2212yes—
32C22×D4×C73C2211yescharacteristic
33C23×C4×C73C2211yescharacteristic
34C2×C22⋊C4×C73C2211yescharacteristic
35C2×C22⋊C4×C73C2212yes—
36#95×C73C2212yes—
37C23×D73C2311yescharacteristic
38C2×C22⋊D73—22no—
39C2×C22⋊D73—22no—
40C2×C22⋊D73—22no—
41C2×C22⋊D73—22no—
42C2×C22⋊D73—42no—
43C22×Dic73—22no—
44C22×Dic73—24no—
45C22×Dic73—42no—
46C22×Dic73D414yes—
47C22×Dic73C2311yescharacteristic
48C22×Dic73C2312yes—
49C22×Dic73C2311yescharacteristic
50C22×Dic73C2311yescharacteristic
51C22×Dic73C2312yes—
52#11924007—24no—
53#11924007—24no—
54#11924007—22no—
55C22⋊Dic73—22no—
56C22⋊Dic73—22no—
57C22⋊Dic73—24no—
58#11924005—22no—
59#11924005—24no—
60#11924005—42no—
61C4×Dic73—42no—
62C24×C73C2311yescharacteristic
63C24×C73C2311yescharacteristic
64C2×D4×C73—22no—
65C2×D4×C73—22no—
66C2×D4×C73—22no—
67C22×C4×C73—22no—
68C22×C4×C73—42no—
69C22×C4×C73C2311yescharacteristic
70C22×C4×C73C2312yes—
71C22×C4×C73C2312yes—
72C22⋊C4×C73—22no—
73C22⋊C4×C73—42no—
74C23×C73—22no—
75C23×C73—22no—
76C23×C73—21no—
77C23×C73—21no—
78C23×C73—21no—
79C23×C73—22no—
80C23×C73—22no—
81C23×C73C2×D412yes—
82C23×C73#4112yes—
83C23×C73#4112yes—
84C23×C73C2411yescharacteristic
85C22×D73—21no—
86C22×D73—22no—
87C22×D73—21no—
88C22×D73—21no—
89C22×D73—22no—
90D4×C73—44no—
91C2×C4×C73—22no—
92C2×C4×C73—21no—
93C2×C4×C73—22no—
94C2×C4×C73—21no—
95C2×C4×C73—21no—
96C2×C4×C73—22no—
97C2×C4×C73—22no—
98C2×C4×C73—22no—
99C2×C4×C73—22no—
100C2×C4×C73—44no—
101C22⋊D73—44no—
102C22⋊D73—44no—
103C2×Dic73—28no—
104C2×Dic73—22no—
105C2×Dic73—22no—
106C2×Dic73—22no—
107C2×Dic73—22no—
108C2×Dic73—21no—
109C2×Dic73—22no—
110C2×Dic73—22no—
111C2×Dic73—21no—
112C2×Dic73—21no—
113C2×Dic73—22no—
114C2×Dic73—44no—
115C2×Dic73C2×D412yes—
116C2×Dic73C2×D412yes—
117C2×Dic73#4114yes—
118C22×C73—22no—
119C22×C73—22no—
120C22×C73—24no—
121C22×C73—24no—
122C22×C73—41no—
123C22×C73—41no—
124C22×C73—41no—
125C22×C73—42no—
126C22×C73—42no—
127C22×C73#12414yes—
128C22×C73C22×D411yescharacteristic
129C22×C73C2×#4112yes—
130C22×C73C2×#4111yescharacteristic
131C22×C73C2×#4111yescharacteristic
132C22×C73H(5,𝔽2)12yes—
133C2×D73—41no—
134C2×D73—41no—
135C2×D73—41no—
136C2×D73—42no—
137C2×D73—42no—
138C4×C73—41no—
139C4×C73—42no—
140C4×C73—42no—
141Dic73—24no—
142Dic73—22no—
143Dic73—22no—
144Dic73—41no—
145Dic73—42no—
146C2×C73—24no—
147C2×C73—81no—
148C2×C73#52511yescharacteristic
149C2×C73C2×#12411yescharacteristic
150C2×C73#53411yescharacteristic
151C2×C73#55312yes—
152C2×C73#55312yes—
153D73—81no—
154#2591—731nomaximal, Sylow
155C73#259111yescharacteristic, complemented, Sylow
156C2×#121—731no—
157C22×C4⋊C4—731no—
158#400—732no—
159#394—732no—
160#388—732no—
161#388—732no—
162#386—731no—
163#386—731no—
164#386—731no—
165#386D7311yescharacteristic, complemented
166C4×C22⋊C4—731no—
167C22×D4—731no—
168C22×D4—731no—
169C22×D4C2×D7311yescharacteristic
170C23×C4—731no—
171C23×C4—731no—
172C23×C4C2×D7311yescharacteristic
173#121—1464no—
174C2×C4⋊C4—732no—
175C2×C4⋊C4—732no—
176C2×C4⋊C4—731no—
177C2×C4⋊C4—1464no—
178C2×C22⋊C4—732no—
179C2×C22⋊C4—731no—
180C2×C22⋊C4—731no—
181C2×C22⋊C4—732no—
182C2×C22⋊C4—731no—
183C2×C22⋊C4—732no—
184C2×C22⋊C4C2×D7311yescharacteristic
185C2×C22⋊C4C2×D7312yes—
186C2×C42—732no—
187#95—732no—
188#95—732no—
189#95—732no—
190#95—732no—
191#95C2×D7312yes—
192C24—731no—
193C24C22×D7311yescharacteristic
194C24C22×D7311yescharacteristic
195C2×D4—22no—
196C2×D4—22no—
197C2×D4—22no—
198C2×D4—2922no—
199C2×D4—1462no—
200C2×D4—1462no—
201C2×D4—1462no—
202C2×D4—1462no—
203C22×C4—22no—
204C22×C4—42no—
205C22×C4—2922no—
206C22×C4—734no—
207C22×C4—732no—
208C22×C4—731no—
209C22×C4—731no—
210C22×C4—731no—
211C22×C4—732no—
212C22×C4—1464no—
213C22×C4—1462no—
214C22×C4C22×D7311yescharacteristic
215C22×C4C22×D7312yes—
216C22×C4C22×D7312yes—
217C4⋊C4—1464no—
218C4⋊C4—1464no—
219C4⋊C4—1462no—
220C22⋊C4—22no—
221C22⋊C4—42no—
222C22⋊C4—2922no—
223C22⋊C4—1464no—
224C22⋊C4—1462no—
225C22⋊C4—1464no—
226C22⋊C4—1462no—
227C22⋊C4—1462no—
228C42—2922no—
229C23—22no—
230C23—22no—
231C23—21no—
232C23—22no—
233C23—21no—
234C23—21no—
235C23—22no—
236C23—1461no—
237C23—1462no—
238C23—1461no—
239C23—1461no—
240C23—1462no—
241C23D4×D7312yes—
242C23#1192402712yes—
243C23#1192402812yes—
244C23C23×D7311yescharacteristic
245D4—44no—
246D4—2924no—
247D4—2924no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—44no—
258C2×C4—2924no—
259C2×C4—732no—
260C2×C4—732no—
261C2×C4—734no—
262C2×C4—1461no—
263C2×C4—1462no—
264C2×C4—1461no—
265C2×C4—1462no—
266C2×C4—1461no—
267C2×C4—1462no—
268C2×C4—1468no—
269C2×C4—1462no—
270C2×C4—1462no—
271C2×C4—1462no—
272C2×C4—1462no—
273C22—22no—
274C22—24no—
275C22—24no—
276C22—22no—
277C22—41no—
278C22—42no—
279C22—42no—
280C22—41no—
281C22—41no—
282C22—2921no—
283C22—2922no—
284C22—2922no—
285C22—2921no—
286C22—2921no—
287C22#1455657714yes—
288C22C2×D4×D7311yescharacteristic
289C22#41×D7312yes—
290C22C2×#1192402711yescharacteristic
291C22C2×#1192402811yescharacteristic
292C22#1455663612yes—
293C4—42no—
294C4—42no—
295C4—41no—
296C4—2922no—
297C4—2921no—
298C4—1462no—
299C4—1462no—
300C4—1464no—
301C2—24no—
302C2—81no—
303C2—5841no—
304C2#1798909511yescharacteristic
305C2C2×#1455657711yescharacteristic
306C2#1798914711yescharacteristic
307C2#1798928012yes—
308C2#1798928612yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#386×C73C2
hypercenter#386D73
hypocenterC73#2591
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C22×#11924007C2semidirect
3. #17988528C2semidirect
4. #17988502C2semidirect
5. #17988476C2semidirect
6. #17988475C2semidirect
7. #17988467C2semidirect
8. #17988466C2semidirect
9. #17988464C2semidirect
10. C22⋊C4×Dic73C2semidirect
11. #386×C73C2semidirect
155. C73#2591semidirect
165. #386D73semidirect