Finite Group Databasebeta

← #22619186

Subgroups — #22619186

Order 9344.

754 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 754 conjugacy classes of subgroups — too many to draw. Only its 141 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×#11924027C211yesmaximal, characteristic
2C2×#14556620C212yesmaximal, complemented
3C22⋊Q8×D73C211yesmaximal, characteristic, complemented
4#17988750C212yesmaximal, complemented
5#17988746C212yesmaximal, complemented
6#17988745C211yesmaximal, characteristic, complemented
7#17988742C211yesmaximal, characteristic, complemented
8#17988738C211yesmaximal, characteristic, complemented
9#17988585C212yesmaximal, complemented
10#17988549C211yesmaximal, characteristic, complemented
11#450×C73C211yesmaximal, characteristic, complemented
12C2×#11924027—28no—
13C2×#11924027—21no—
14C2×#11924027—21no—
15C2×#11924027C2212yes—
16C2×#11924027C2212yes—
17C22×Dic146C2211yescharacteristic
18C2×Q8×D73C2211yescharacteristic, complemented
19C22×C22⋊D73—21no—
20C23×Dic73—21no—
21C22×C4×D73C2211yescharacteristic
22#14556620—28no—
23C2×Dic292C2212yescomplemented
24C2×#11924018C2212yescomplemented
25C2×#11924016C2212yescomplemented
26C2×#11924011C2212yescomplemented
27#14556571C2211yescharacteristic, complemented
28#14556570C2211yescharacteristic
29#14556569—21no—
30#14556568—21no—
31#14556567C2211yescharacteristic, complemented
32C4⋊C4×D73—21no—
33C4⋊C4×D73C2211yescharacteristic, complemented
34C22⋊C4×D73—21no—
35#14556516C2212yescomplemented
36#14556514C2212yescomplemented
37#14556512C2212yescomplemented
38C22⋊#10596831C2211yescharacteristic
39#14556503C2212yescomplemented
40C22×D4×C73C2211yescharacteristic
41C2×SD16×C73C2212yescomplemented
42C22⋊Q8×C73C2211yescharacteristic
43#102×C73C2212yescomplemented
44C22⋊C8×C73C2211yescharacteristic
45C23×D73D411yescharacteristic
46#11924027—28no—
47#11924027—28no—
48#11924027—24no—
49#11924027—24no—
50#11924027—24no—
51#11924027D418yes—
52C2×Dic146—21no—
53C2×Dic146—24no—
54C2×Dic146—21no—
55C2×Dic146C2311yescharacteristic
56C2×Dic146C2312yes—
57Q8×D73—24no—
58C2×C22⋊D73—28no—
59C2×C22⋊D73—22no—
60C2×C22⋊D73—22no—
61C22×Dic73—28no—
62C22×Dic73—21no—
63C22×Dic73—22no—
64C22×Dic73—22no—
65C22×Dic73D411yescharacteristic
66C2×C4×D73—24no—
67C2×C4×D73—21no—
68C2×C4×D73—21no—
69C2×C4×D73D411yescharacteristic
70C2×C4×D73D411yescharacteristic
71C2×C4×D73C2311yescharacteristic
72C2×C4×D73C2311yescharacteristic
73Dic292—24no—
74#11924018—24no—
75#11924016—24no—
76#11924011—24no—
77C2×#10596831C2312yes—
78C4⋊Dic73—21no—
79C4⋊Dic73C2311yescharacteristic
80#11924007—21no—
81#11924007—21no—
82#11924007—21no—
83C22⋊Dic73—21no—
84#11924005—21no—
85#11924005—21no—
86C24×C73—21no—
87C2×Q8×C73C2311yescharacteristic
88C2×D4×C73—24no—
89C2×D4×C73—21no—
90C2×D4×C73C2312yes—
91C22×C4×C73C2311yescharacteristic
92SD16×C73—24no—
93C2×C8×C73C2312yes—
94C4⋊C4×C73—21no—
95C4⋊C4×C73C2311yescharacteristic
96C22⋊C4×C73—21no—
97C23×C73—24no—
98C23×C73—22no—
99C23×C73—42no—
100C23×C73—42no—
101C23×C73C2×D411yescharacteristic
102C22×D73—22no—
103C22×D73—22no—
104C22×D73—41no—
105C22×D73C2×D411yescharacteristic
106C22×D73C2×D411yescharacteristic
107Q8×C73—22no—
108D4×C73—24no—
109D4×C73—22no—
110D4×C73C2×D414yes—
111C2×C4×C73—22no—
112C2×C4×C73—21no—
113C2×C4×C73—21no—
114C2×C4×C73C2×D411yescharacteristic
115C2×C4×C73C2411yescharacteristic
116C22⋊D73—28no—
117C22⋊D73—28no—
118C2×Dic73—24no—
119C2×Dic73—28no—
120C2×Dic73—22no—
121C2×Dic73—22no—
122C2×Dic73—28no—
123C2×Dic73—21no—
124C2×Dic73—21no—
125C2×Dic73C2×D411yescharacteristic
126C2×Dic73C2×D411yescharacteristic
127C4×D73—22no—
128C4×D73—22no—
129C4×D73—22no—
130C4×D73—42no—
131C4×D73—42no—
132C4×D73C2×D414yes—
133Dic146—24no—
134Dic146—22no—
135Dic146—22no—
136Dic146—42no—
137Dic146C2×D414yes—
138C8×C73—22no—
139#10596831—22no—
140C22×C73—21no—
141C22×C73—21no—
142C22×C73—24no—
143C22×C73—48no—
144C22×C73—42no—
145C22×C73—42no—
146C22×C73#13712yescomplemented
147C22×C73C22×D411yescharacteristic
148C2×D73—21no—
149C2×D73—21no—
150C2×D73—21no—
151C2×D73—21no—
152C2×D73—21no—
153C2×D73—44no—
154C2×D73#12012yes—
155C4×C73—21no—
156C4×C73—41no—
157C4×C73—41no—
158C4×C73C22×D412yes—
159Dic73—24no—
160Dic73—21no—
161Dic73—41no—
162Dic73—41no—
163Dic73#12012yes—
164C2×C73—22no—
165C2×C73—44no—
166C2×C73C2×#12011yescharacteristic
167C2×C73C2×#13711yescharacteristic
168C2×C73#57511yescharacteristic
169D73—22no—
170D73—41no—
171#3007—731nomaximal, Sylow
172C73#300711yescharacteristic, complemented, Sylow
173C22×#41—731no—
174C2×#137—732no—
175C2×C22⋊Q8—731no—
176#452—732no—
177#452—732no—
178#451—731no—
179#451—731no—
180#450—731no—
181#450D7311yescharacteristic, complemented
182#417—732no—
183#407—731no—
184C2×#41—732no—
185C2×#41—732no—
186C2×#41—1461no—
187C2×#41—1461no—
188C2×#41—1468no—
189C22×Q8—731no—
190C22×Q8—731no—
191C22×D4—1461no—
192C22×D4C2×D7311yescharacteristic
193C23×C4—731no—
194C23×C4—1461no—
195#137—1468no—
196C2×Q16—732no—
197C2×Q16—732no—
198C2×SD16—732no—
199C2×SD16C2×D7312yescomplemented
200C2×M16—732no—
201C22⋊Q8—731no—
202C22⋊Q8—731no—
203C22⋊Q8—731no—
204C22⋊Q8—1461no—
205C22⋊Q8—1461no—
206C22⋊Q8C2×D7311yescharacteristic
207C2×C4⋊C4—731no—
208C2×C4⋊C4—1461no—
209C2×C22⋊C4—1461no—
210#103—732no—
211#103—732no—
212#102—732no—
213#102C2×D7312yescomplemented
214C22⋊C8—731no—
215C22⋊C8—732no—
216C22⋊C8C2×D7311yescharacteristic
217C24—21no—
218C24—731no—
219#41—738no—
220#41—1464no—
221#41—1464no—
222#41—1468no—
223#41—1468no—
224#41—1464no—
225C2×Q8—732no—
226C2×Q8—731no—
227C2×Q8—1461no—
228C2×Q8—1464no—
229C2×Q8—1464no—
230C2×Q8—1461no—
231C2×Q8C22×D7311yescharacteristic
232C2×D4—24no—
233C2×D4—21no—
234C2×D4—1462no—
235C2×D4—1462no—
236C2×D4—1468no—
237C2×D4C22×D7312yes—
238C22×C4—731no—
239C22×C4—731no—
240C22×C4—731no—
241C22×C4—731no—
242C22×C4—731no—
243C22×C4—1461no—
244C22×C4—1461no—
245C22×C4—1464no—
246C22×C4—1462no—
247C22×C4—1462no—
248C22×C4—1468no—
249C22×C4—1461no—
250C22×C4C22×D7311yescharacteristic
251Q16—1464no—
252Q16—1464no—
253SD16—24no—
254SD16—1464no—
255M16—1464no—
256C2×C8—732no—
257C2×C8C22×D7312yes—
258C4⋊C4—21no—
259C4⋊C4—731no—
260C4⋊C4—1461no—
261C4⋊C4—1461no—
262C4⋊C4—1461no—
263C4⋊C4—1461no—
264C4⋊C4C22×D7311yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—1461no—
267C22⋊C4—1461no—
268C22⋊C4—1461no—
269C23—24no—
270C23—22no—
271C23—42no—
272C23—42no—
273C23—2921no—
274C23—731no—
275C23—731no—
276C23—1462no—
277C23—1462no—
278C23D4×D7311yescharacteristic
279Q8—22no—
280Q8—2922no—
281Q8—734no—
282Q8—1464no—
283Q8—1462no—
284Q8—1462no—
285D4—24no—
286D4—22no—
287D4—1468no—
288D4—1468no—
289D4D4×D7314yes—
290C2×C4—22no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—2922no—
294C2×C4—2922no—
295C2×C4—731no—
296C2×C4—734no—
297C2×C4—731no—
298C2×C4—1462no—
299C2×C4—1462no—
300C2×C4—1461no—
301C2×C4—1461no—
302C2×C4—1462no—
303C2×C4—1468no—
304C2×C4—1464no—
305C2×C4—1468no—
306C2×C4—1462no—
307C2×C4—1462no—
308C2×C4D4×D7311yescharacteristic
309C2×C4C23×D7311yescharacteristic
310C8—22no—
311C8—1462no—
312C22—21no—
313C22—21no—
314C22—24no—
315C22—48no—
316C22—42no—
317C22—42no—
318C22—2924no—
319C22—732no—
320C22—1461no—
321C22—1461no—
322C22—1461no—
323C22—1461no—
324C22—1461no—
325C22#1455662012yescomplemented
326C22C2×D4×D7311yescharacteristic
327C4—21no—
328C4—41no—
329C4—41no—
330C4—2921no—
331C4—2921no—
332C4—732no—
333C4—1461no—
334C4—1464no—
335C4C2×D4×D7312yes—
336C2—22no—
337C2—44no—
338C2—2921no—
339C2—1462no—
340C2#120×D7311yescharacteristic
341C2C2×#1455662011yescharacteristic
342C2#1798938311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#450×C73C2
socleC22×C73C22×D4
hypercenter#450D73
hypocenterC73#3007
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
2. C2×#14556620C2semidirect
3. C22⋊Q8×D73C2semidirect
4. #17988750C2semidirect
5. #17988746C2semidirect
6. #17988745C2semidirect
7. #17988742C2semidirect
8. #17988738C2semidirect
9. #17988585C2semidirect
10. #17988549C2semidirect
11. #450×C73C2semidirect
18. C2×Q8×D73C22semidirect
23. C2×Dic292C22semidirect
24. C2×#11924018C22semidirect
25. C2×#11924016C22semidirect
26. C2×#11924011C22semidirect
27. #14556571C22semidirect
31. #14556567C22semidirect
33. C4⋊C4×D73C22semidirect
35. #14556516C22semidirect
36. #14556514C22semidirect
37. #14556512C22semidirect
39. #14556503C22semidirect
41. C2×SD16×C73C22semidirect
43. #102×C73C22semidirect
146. C22×C73#137semidirect
172. C73#3007semidirect
181. #450D73semidirect
199. C2×SD16C2×D73semidirect
213. #102C2×D73semidirect
325. C22#14556620semidirect