Finite Group Databasebeta

← #22619562

Subgroups — #22619562

Order 9344.

496 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 143 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×#14556624C211yesmaximal, characteristic, complemented
2C2×M16×D73C211yesmaximal, characteristic, complemented
3#17989099C211yesmaximal, characteristic
4C2×#14556571C211yesmaximal, characteristic, complemented
5#17988846C212yesmaximal, complemented
6#17988834C212yesmaximal, complemented
7#17988829C212yesmaximal, complemented
8#17988817C212yesmaximal, complemented
9#17988595C211yesmaximal, characteristic, complemented
10#17988586C211yesmaximal, characteristic, complemented
11#428×C73C211yesmaximal, characteristic, complemented
12C2×#11924028C2211yescharacteristic
13C22×Dic146C2211yescharacteristic
14C22×C4×D73C2211yescharacteristic
15#14556624—24no—
16C2×Dic292C2212yescomplemented
17C2×#11924017C2212yescomplemented
18C2×#11924012C2211yescharacteristic
19C2×#11924011C2212yes—
20M16×D73—24no—
21C2×C8×D73C2212yes—
22#14556575—21no—
23#14556571—21no—
24#14556571—21no—
25#14556571C2212yes—
26#14556571C2211yescharacteristic
27#14556571C2212yes—
28#14556571C2211yescharacteristic
29#14556566C2211yescharacteristic
30#14556566C2211yescharacteristic
31#14556561—21no—
32C4×D292—21no—
33C4×D292—21no—
34C2×C4⋊Dic73—21no—
35C2×#11924005—21no—
36#14556514C2212yescomplemented
37#14556514C2212yescomplemented
38#14556514C2212yescomplemented
39#14556511C2212yescomplemented
40C2×M16×C73C2211yescharacteristic
41#117×C73C2211yescharacteristic
42C2×C4⋊C4×C73C2211yescharacteristic
43#107×C73C2212yescomplemented
44#106×C73C2212yescomplemented
45C23×D73D411yescharacteristic
46#11924028—22no—
47#11924028—22no—
48C2×Dic146—22no—
49C2×Dic146—22no—
50C2×Dic146—21no—
51C2×Dic146C2312yes—
52C2×Dic146C2311yescharacteristic
53C2×D292—21no—
54C2×D292—21no—
55C2×D292C2311yescharacteristic
56C2×C22⋊D73—21no—
57C22×Dic73—21no—
58C22×Dic73D411yescharacteristic
59C2×C4×D73—22no—
60C2×C4×D73—22no—
61C2×C4×D73—21no—
62C2×C4×D73D411yescharacteristic
63C2×C4×D73D411yescharacteristic
64C2×C4×D73C2311yescharacteristic
65C2×C4×D73C2311yescharacteristic
66Dic292—24no—
67#11924017—24no—
68#11924012—22no—
69#11924011—24no—
70C2×#10596831C2312yes—
71C8×D73—24no—
72C4⋊Dic73—22no—
73C4⋊Dic73—22no—
74C4⋊Dic73—21no—
75C4⋊Dic73—21no—
76#11924005—22no—
77#11924005—22no—
78#11924005—21no—
79#11924005—21no—
80#11924005—21no—
81#11924005—21no—
82C22×C4×C73—21no—
83C22×C4×C73C2311yescharacteristic
84M16×C73D414yescomplemented
85C2×C8×C73C2312yes—
86C4⋊C4×C73—21no—
87C4⋊C4×C73C2311yescharacteristic
88C4⋊C4×C73C2312yes—
89C4⋊C4×C73C2311yescharacteristic
90C22⋊C4×C73—21no—
91C42×C73—21no—
92C23×C73C2×D411yescharacteristic
93C22×D73—22no—
94C22×D73—22no—
95C22×D73—21no—
96C22×D73—41no—
97C22×D73C2×D411yescharacteristic
98C22×D73C2×D411yescharacteristic
99C2×C4×C73—21no—
100C2×C4×C73—21no—
101C2×C4×C73—22no—
102C2×C4×C73—42no—
103C2×C4×C73C2×D411yescharacteristic
104C2×C4×C73C2×D412yes—
105C2×C4×C73#4112yes—
106C2×C4×C73C2411yescharacteristic
107C22⋊D73—42no—
108C2×Dic73—22no—
109C2×Dic73—21no—
110C2×Dic73—22no—
111C2×Dic73—42no—
112C2×Dic73C2×D411yescharacteristic
113C2×Dic73C2×D411yescharacteristic
114D292—21no—
115D292—21no—
116D292—42no—
117D292—42no—
118C4×D73—22no—
119C4×D73—22no—
120C4×D73—21no—
121C4×D73—21no—
122C4×D73—21no—
123C4×D73—21no—
124C4×D73—42no—
125Dic146—22no—
126Dic146—21no—
127Dic146—22no—
128Dic146—21no—
129Dic146—42no—
130C8×C73C2×D414yes—
131#10596831—22no—
132C22×C73—21no—
133C22×C73—21no—
134C22×C73#12112yes—
135C22×C73C22×D411yescharacteristic
136C2×D73—21no—
137C2×D73—21no—
138C2×D73—21no—
139C2×D73—21no—
140C2×D73—21no—
141C2×D73—44no—
142C2×D73—41no—
143C2×D73—41no—
144C2×D73—41no—
145C2×D73#13712yescomplemented
146C4×C73—41no—
147C4×C73—41no—
148C4×C73—42no—
149C4×C73#12112yes—
150C4×C73C22×D411yescharacteristic
151C4×C73C2×#4111yescharacteristic
152Dic73—21no—
153Dic73—21no—
154Dic73—42no—
155Dic73—41no—
156C2×C73—22no—
157C2×C73C2×#12111yescharacteristic
158C2×C73C2×#13711yescharacteristic
159C2×C73#57511yescharacteristic
160D73—22no—
161D73—41no—
162D73—81no—
163#3056—731nomaximal, Sylow
164C73#305611yescharacteristic, complemented, Sylow
165C2×#137—731no—
166C22×M16—731no—
167#525—731no—
168C2×C22⋊Q8—731no—
169#470—732no—
170#468—732no—
171#467—732no—
172#465—732no—
173#428D7311yescharacteristic, complemented
174#419—731no—
175#417—731no—
176C2×#41—731no—
177C22×Q8—731no—
178C23×C4—731no—
179#137—1464no—
180C2×Q16—732no—
181C2×SD16—732no—
182C2×M16—731no—
183C2×M16—732no—
184C2×M16—1464no—
185C2×M16C2×D7311yescharacteristic
186C22×C8—732no—
187#123—1461no—
188C22⋊Q8—732no—
189C22⋊Q8—732no—
190C22⋊Q8—731no—
191C22⋊Q8—731no—
192C22⋊Q8—1461no—
193C22⋊Q8—1461no—
194#121—731no—
195#121—731no—
196#120—1461no—
197C4×D4—1461no—
198C4×D4—1461no—
199#117C2×D7311yescharacteristic
200C2×C4⋊C4—1461no—
201C2×C4⋊C4C2×D7311yescharacteristic
202C2×C22⋊C4—1461no—
203#107C2×D7312yescomplemented
204#106C2×D7312yescomplemented
205#103—732no—
206#103—732no—
207#103—732no—
208#102—732no—
209C24—731no—
210#41—1462no—
211#41—1462no—
212C2×Q8—732no—
213C2×Q8—731no—
214C2×Q8—1462no—
215C2×Q8—1462no—
216C2×Q8—1461no—
217C2×D4—731no—
218C2×D4—1461no—
219C2×D4—1461no—
220C2×D4—1461no—
221C22×C4—21no—
222C22×C4—731no—
223C22×C4—731no—
224C22×C4—731no—
225C22×C4—731no—
226C22×C4—731no—
227C22×C4—1461no—
228C22×C4—1461no—
229C22×C4—1462no—
230C22×C4—1462no—
231C22×C4C22×D7311yescharacteristic
232Q16—1464no—
233SD16—1464no—
234M16—1462no—
235M16—1464no—
236M16D29214yescomplemented
237C2×C8—732no—
238C2×C8—1464no—
239C2×C8C22×D7312yes—
240C4⋊C4—21no—
241C4⋊C4—1462no—
242C4⋊C4—1462no—
243C4⋊C4—1461no—
244C4⋊C4—1461no—
245C4⋊C4C22×D7312yes—
246C4⋊C4C22×D7311yescharacteristic
247C4⋊C4C22×D7311yescharacteristic
248C22⋊C4—21no—
249C22⋊C4—1461no—
250C22⋊C4—1461no—
251C22⋊C4—1462no—
252C22⋊C4—1462no—
253C22⋊C4—1461no—
254C22⋊C4—1461no—
255C42—21no—
256C23—2921no—
257C23—731no—
258C23—731no—
259C23—1462no—
260C23—1461no—
261C23—1462no—
262C23D4×D7311yescharacteristic
263Q8—2922no—
264Q8—1462no—
265Q8—1461no—
266Q8—1462no—
267Q8—1461no—
268D4—2922no—
269D4—2922no—
270D4—2922no—
271D4—1461no—
272D4—1461no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—22no—
276C2×C4—42no—
277C2×C4—2922no—
278C2×C4—2922no—
279C2×C4—731no—
280C2×C4—731no—
281C2×C4—1461no—
282C2×C4—1462no—
283C2×C4—1462no—
284C2×C4—1462no—
285C2×C4—1462no—
286C2×C4—1461no—
287C2×C4—1461no—
288C2×C4—1461no—
289C2×C4—1461no—
290C2×C4D4×D7311yescharacteristic
291C2×C4C2×D29212yes—
292C2×C4#1192402912yes—
293C2×C4C23×D7311yescharacteristic
294C8—1462no—
295C8C2×D29214yes—
296C22—21no—
297C22—21no—
298C22—2924no—
299C22—2921no—
300C22—2921no—
301C22—2921no—
302C22—732no—
303C22—1461no—
304C22—1461no—
305C22—1461no—
306C22—1461no—
307C22—1461no—
308C22#1455656612yes—
309C22C2×D4×D7311yescharacteristic
310C4—41no—
311C4—42no—
312C4—41no—
313C4—2921no—
314C4—2922no—
315C4—1461no—
316C4—1461no—
317C4#1455656612yes—
318C4C22×D29211yescharacteristic
319C4C2×#1192402911yescharacteristic
320C2—22no—
321C2—2921no—
322C2—5841no—
323C2—1462no—
324C2C2×#1455656611yescharacteristic
325C2#137×D7311yescharacteristic
326C2#1798938311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#428×C73C2
socleC22×C73C22×D4
hypercenter#428D73
hypocenterC73#3056
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. C2×#14556624C2semidirect
2. C2×M16×D73C2semidirect
4. C2×#14556571C2semidirect
5. #17988846C2semidirect
6. #17988834C2semidirect
7. #17988829C2semidirect
8. #17988817C2semidirect
9. #17988595C2semidirect
10. #17988586C2semidirect
11. #428×C73C2semidirect
16. C2×Dic292C22semidirect
17. C2×#11924017C22semidirect
36. #14556514C22semidirect
37. #14556514C22semidirect
38. #14556514C22semidirect
39. #14556511C22semidirect
43. #107×C73C22semidirect
44. #106×C73C22semidirect
84. M16×C73D4semidirect
145. C2×D73#137semidirect
164. C73#3056semidirect
173. #428D73semidirect
203. #107C2×D73semidirect
204. #106C2×D73semidirect
236. M16D292semidirect