Finite Group Databasebeta

← #22615788

Subgroups — #22615788

Order 9344.

628 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 131 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×#14556578C211yesmaximal, characteristic, complemented
2C2×#14556551C211yesmaximal, characteristic, complemented
3#17988515C212yesmaximal, complemented
4#17988500C211yesmaximal, characteristic, complemented
5#17988499C211yesmaximal, characteristic, complemented
6#17988495C212yesmaximal, complemented
7#17988495C211yesmaximal, characteristic, complemented
8#17988467C212yesmaximal, complemented
9#17988463C212yesmaximal, complemented
10#17988454C211yesmaximal, characteristic, complemented
11#392×C73C211yesmaximal, characteristic, complemented
12C22×Dic146C2211yescharacteristic
13C22×C22⋊D73C2211yescharacteristic
14C22×C22⋊D73C2212yes—
15C23×Dic73C2211yescharacteristic
16C22×C4×D73C2211yescharacteristic
17#14556578—24no—
18#14556551—24no—
19C2×#11924007C2211yescharacteristic
20C2×C22⋊Dic73C2212yes—
21C2×C22⋊Dic73C2212yes—
22C2×C22⋊Dic73C2212yes—
23C2×C22⋊Dic73C2212yes—
24C2×#11924005C2211yescharacteristic
25C2×#11924005C2212yes—
26C2×C4×Dic73C2211yescharacteristic
27#14556498C2212yes—
28#14556498C2211yescharacteristic
29#14556498C2212yes—
30#14556498C2212yes—
31#14556498C2212yes—
32C22×D4×C73C2212yes—
33C22×D4×C73C2211yescharacteristic
34C2×C22⋊C4×C73C2211yescharacteristic
35C2×C22⋊C4×C73C2212yes—
36#95×C73C2211yescharacteristic
37C23×D73C2311yescharacteristic
38C2×Dic146—22no—
39C2×Dic146—42no—
40C2×C22⋊D73—22no—
41C2×C22⋊D73—22no—
42C2×C22⋊D73—24no—
43C2×C22⋊D73—22no—
44C2×C22⋊D73—42no—
45C2×C22⋊D73—42no—
46C22×Dic73—22no—
47C22×Dic73—42no—
48C22×Dic73C2312yes—
49C22×Dic73C2312yes—
50C22×Dic73C2311yescharacteristic
51C22×Dic73C2311yescharacteristic
52C22×Dic73C2311yescharacteristic
53C2×C4×D73—22no—
54C2×C4×D73—42no—
55#11924007—22no—
56C22⋊Dic73—24no—
57C22⋊Dic73—24no—
58C22⋊Dic73—42no—
59C22⋊Dic73—42no—
60#11924005—22no—
61#11924005—42no—
62C4×Dic73D414yescomplemented
63C24×C73C2312yes—
64C24×C73C2311yescharacteristic
65C2×D4×C73—24no—
66C2×D4×C73—22no—
67C2×D4×C73—42no—
68C2×D4×C73—42no—
69C2×D4×C73—42no—
70C22×C4×C73C2312yes—
71C22×C4×C73C2311yescharacteristic
72C22×C4×C73C2311yescharacteristic
73C22⋊C4×C73—22no—
74C22⋊C4×C73—42no—
75C23×C73—21no—
76C23×C73—21no—
77C23×C73—22no—
78C23×C73—22no—
79C23×C73—22no—
80C23×C73—22no—
81C23×C73—22no—
82C23×C73—22no—
83C23×C73—22no—
84C23×C73—22no—
85C23×C73—22no—
86C23×C73#4112yes—
87C23×C73C2411yescharacteristic
88C22×D73—21no—
89C22×D73—21no—
90C22×D73—22no—
91C22×D73—22no—
92C22×D73#4112yes—
93D4×C73—44no—
94D4×C73—48no—
95C2×C4×C73—22no—
96C2×C4×C73—21no—
97C2×C4×C73—22no—
98C2×C4×C73—22no—
99C2×C4×C73—22no—
100C2×C4×C73—22no—
101C2×C4×C73C2×D412yes—
102C22⋊D73—28no—
103C22⋊D73—48no—
104C2×Dic73—21no—
105C2×Dic73—21no—
106C2×Dic73—22no—
107C2×Dic73—21no—
108C2×Dic73—22no—
109C2×Dic73—22no—
110C2×Dic73—22no—
111C2×Dic73—22no—
112C2×Dic73—22no—
113C2×Dic73—22no—
114C2×Dic73—22no—
115C2×Dic73—44no—
116C2×Dic73C2×D412yes—
117C2×Dic73C2×D412yes—
118C4×D73—44no—
119Dic146—44no—
120C22×C73—22no—
121C22×C73—24no—
122C22×C73—41no—
123C22×C73—41no—
124C22×C73—42no—
125C22×C73—42no—
126C22×C73—42no—
127C22×C73—42no—
128C22×C73—42no—
129C22×C73—42no—
130C22×C73—42no—
131C22×C73—42no—
132C22×C73C22×D411yescharacteristic
133C22×C73C2×#4111yescharacteristic
134C22×C73C2×#4111yescharacteristic
135C22×C73H(5,𝔽2)12yes—
136C22×C73H(5,𝔽2)12yes—
137C2×D73—22no—
138C2×D73—24no—
139C2×D73—41no—
140C2×D73—41no—
141C2×D73—42no—
142C4×C73—22no—
143C4×C73—41no—
144C4×C73—42no—
145Dic73—22no—
146Dic73—22no—
147Dic73—42no—
148Dic73—41no—
149Dic73—42no—
150C2×C73—42no—
151C2×C73—82no—
152C2×C73#52511yescharacteristic
153C2×C73#53511yescharacteristic
154C2×C73#53511yescharacteristic
155C2×C73#53812yes—
156C2×C73#53812yes—
157D73—42no—
158#2631—731nomaximal, Sylow
159C73#263111yescharacteristic, complemented, Sylow
160C2×#124—731no—
161C2×C4×D4—731no—
162#397—732no—
163#393—731no—
164#393—731no—
165#392—731no—
166#392—732no—
167#392D7311yescharacteristic, complemented
168#386—732no—
169#386—732no—
170#383—731no—
171C22×Q8—731no—
172C22×D4—732no—
173C22×D4—731no—
174C22×D4C2×D7311yescharacteristic
175C22×D4C2×D7312yes—
176C23×C4—731no—
177C23×C4—731no—
178#124—1464no—
179C4×D4—1464no—
180C2×C4⋊C4—731no—
181C2×C22⋊C4—732no—
182C2×C22⋊C4—732no—
183C2×C22⋊C4—732no—
184C2×C22⋊C4—732no—
185C2×C22⋊C4—732no—
186C2×C22⋊C4—731no—
187C2×C22⋊C4C2×D7311yescharacteristic
188C2×C22⋊C4C2×D7312yes—
189C2×C42—731no—
190#95—732no—
191#95—731no—
192#95—732no—
193#95—732no—
194#95—732no—
195#95C2×D7311yescharacteristic
196C24—731no—
197C24C22×D7312yes—
198C24C22×D7311yescharacteristic
199C2×Q8—2922no—
200C2×Q8—1462no—
201C2×D4—24no—
202C2×D4—22no—
203C2×D4—42no—
204C2×D4—42no—
205C2×D4—42no—
206C2×D4—2922no—
207C2×D4—2922no—
208C2×D4—1462no—
209C2×D4—1464no—
210C2×D4—1462no—
211C2×D4—1462no—
212C22×C4—2922no—
213C22×C4—2922no—
214C22×C4—731no—
215C22×C4—731no—
216C22×C4—732no—
217C22×C4—732no—
218C22×C4—731no—
219C22×C4—1462no—
220C22×C4—1462no—
221C22×C4C22×D7312yes—
222C22×C4C22×D7311yescharacteristic
223C22×C4C22×D7311yescharacteristic
224C4⋊C4—1462no—
225C22⋊C4—22no—
226C22⋊C4—42no—
227C22⋊C4—2922no—
228C22⋊C4—2922no—
229C22⋊C4—2922no—
230C22⋊C4—1464no—
231C22⋊C4—1464no—
232C22⋊C4—1462no—
233C42—734no—
234C23—21no—
235C23—21no—
236C23—22no—
237C23—22no—
238C23—22no—
239C23—22no—
240C23—22no—
241C23—22no—
242C23—22no—
243C23—22no—
244C23—22no—
245C23—732no—
246C23—1461no—
247C23—1461no—
248C23—1462no—
249C23—1462no—
250C23#1192402712yes—
251C23C23×D7311yescharacteristic
252Q8—2924no—
253D4—44no—
254D4—48no—
255D4—2928no—
256D4—1468no—
257C2×C4—22no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—2924no—
264C2×C4—2924no—
265C2×C4—732no—
266C2×C4—732no—
267C2×C4—1462no—
268C2×C4—1461no—
269C2×C4—1462no—
270C2×C4—1462no—
271C2×C4—1462no—
272C2×C4—1462no—
273C2×C4—1462no—
274C2×C4—1462no—
275C2×C4—1461no—
276C2×C4—1461no—
277C2×C4—1462no—
278C2×C4D4×D7312yes—
279C22—24no—
280C22—22no—
281C22—41no—
282C22—41no—
283C22—42no—
284C22—42no—
285C22—42no—
286C22—42no—
287C22—42no—
288C22—42no—
289C22—42no—
290C22—42no—
291C22—2921no—
292C22—2921no—
293C22—2922no—
294C22—1464no—
295C22—1462no—
296C22C2×D4×D7311yescharacteristic
297C22#41×D7311yescharacteristic
298C22C2×#1192402711yescharacteristic
299C22#1455663612yes—
300C22#1455663612yes—
301C4—22no—
302C4—41no—
303C4—42no—
304C4—2921no—
305C4—2922no—
306C4—2922no—
307C4—1462no—
308C4—1462no—
309C2—42no—
310C2—82no—
311C2—2922no—
312C2#1798909711yescharacteristic
313C2#1798915011yescharacteristic
314C2#1798915211yescharacteristic
315C2#1798916912yes—
316C2#1798917212yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#392×C73C2
hypercenter#392D73
hypocenterC73#2631
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#14556578C2semidirect
2. C2×#14556551C2semidirect
3. #17988515C2semidirect
4. #17988500C2semidirect
5. #17988499C2semidirect
6. #17988495C2semidirect
7. #17988495C2semidirect
8. #17988467C2semidirect
9. #17988463C2semidirect
10. #17988454C2semidirect
11. #392×C73C2semidirect
62. C4×Dic73D4semidirect
159. C73#2631semidirect
167. #392D73semidirect