Finite Group Databasebeta

← #21455074

Subgroups — #21455074

Order 7808.

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×#11758224C211yesmaximal, characteristic
2C2×#14519806C212yesmaximal, complemented
3C22⋊Q8×D61C211yesmaximal, characteristic, complemented
4#16839925C212yesmaximal, complemented
5#16839921C212yesmaximal, complemented
6#16839920C211yesmaximal, characteristic, complemented
7#16839917C211yesmaximal, characteristic, complemented
8#16839913C211yesmaximal, characteristic, complemented
9#16839760C212yesmaximal, complemented
10#16839724C211yesmaximal, characteristic, complemented
11C61×#450C211yesmaximal, characteristic, complemented
12C2×#11758224—28no—
13C2×#11758224—21no—
14C2×#11758224—21no—
15C2×#11758224C2212yes—
16C2×#11758224C2212yes—
17C22×Dic122C2211yescharacteristic
18C2×Q8×D61C2211yescharacteristic, complemented
19C22×C22⋊D61—21no—
20C23×Dic61—21no—
21C22×C4×D61C2211yescharacteristic
22#14519806—28no—
23C2×Dic244C2212yescomplemented
24C2×#11758202C2212yescomplemented
25C2×#11758200C2212yescomplemented
26C2×#11758189C2212yescomplemented
27#14519757C2211yescharacteristic, complemented
28#14519756C2211yescharacteristic
29#14519755—21no—
30#14519754—21no—
31#14519753C2211yescharacteristic, complemented
32C4⋊C4×D61—21no—
33C4⋊C4×D61C2211yescharacteristic, complemented
34C22⋊C4×D61—21no—
35#14519702C2212yescomplemented
36#14519700C2212yescomplemented
37#14519698C2212yescomplemented
38C22⋊#92418C2211yescharacteristic
39#14519689C2212yescomplemented
40C22×D4×C61C2211yescharacteristic
41C2×SD16×C61C2212yescomplemented
42C22⋊Q8×C61C2211yescharacteristic
43#102×C61C2212yescomplemented
44C22⋊C8×C61C2211yescharacteristic
45C24×C61—21no—
46C23×D61D411yescharacteristic
47C2×Q8×C61C2311yescharacteristic
48C2×D4×C61—24no—
49C2×D4×C61—21no—
50C2×D4×C61C2312yes—
51C22×C4×C61C2311yescharacteristic
52C2×C22⋊D61—28no—
53C2×C22⋊D61—22no—
54C2×C22⋊D61—22no—
55C22×Dic61—28no—
56C22×Dic61—21no—
57C22×Dic61—22no—
58C22×Dic61—22no—
59C22×Dic61D411yescharacteristic
60Q8×D61—24no—
61#11758224—28no—
62#11758224—28no—
63#11758224—24no—
64#11758224—24no—
65#11758224—24no—
66#11758224D418yes—
67C2×C4×D61—24no—
68C2×C4×D61—21no—
69C2×C4×D61—21no—
70C2×C4×D61D411yescharacteristic
71C2×C4×D61D411yescharacteristic
72C2×C4×D61C2311yescharacteristic
73C2×C4×D61C2311yescharacteristic
74C2×Dic122—21no—
75C2×Dic122—24no—
76C2×Dic122—21no—
77C2×Dic122C2311yescharacteristic
78C2×Dic122C2312yes—
79SD16×C61—24no—
80C2×C8×C61C2312yes—
81C4⋊C4×C61—21no—
82C4⋊C4×C61C2311yescharacteristic
83C22⋊C4×C61—21no—
84C22⋊Dic61—21no—
85#11758202—24no—
86#11758200—24no—
87#11758198—21no—
88#11758198—21no—
89C4⋊Dic61—21no—
90C4⋊Dic61C2311yescharacteristic
91#11758196—21no—
92#11758196—21no—
93#11758196—21no—
94C2×#92418C2312yes—
95Dic244—24no—
96#11758189—24no—
97C23×C61—24no—
98C23×C61—22no—
99C23×C61—42no—
100C23×C61—42no—
101C23×C61C2×D411yescharacteristic
102C22×D61—22no—
103C22×D61—22no—
104C22×D61—41no—
105C22×D61C2×D411yescharacteristic
106C22×D61C2×D411yescharacteristic
107Q8×C61—22no—
108D4×C61—24no—
109D4×C61—22no—
110D4×C61C2×D414yes—
111C2×C4×C61—22no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61C2×D411yescharacteristic
115C2×C4×C61C2411yescharacteristic
116C22⋊D61—28no—
117C22⋊D61—28no—
118C2×Dic61—24no—
119C2×Dic61—28no—
120C2×Dic61—22no—
121C2×Dic61—22no—
122C2×Dic61—28no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61C2×D411yescharacteristic
126C2×Dic61C2×D411yescharacteristic
127C4×D61—22no—
128C4×D61—22no—
129C4×D61—22no—
130C4×D61—42no—
131C4×D61—42no—
132C4×D61C2×D414yes—
133Dic122—24no—
134Dic122—22no—
135Dic122—22no—
136Dic122—42no—
137Dic122C2×D414yes—
138C8×C61—22no—
139#92418—22no—
140C22×C61—21no—
141C22×C61—21no—
142C22×C61—24no—
143C22×C61—48no—
144C22×C61—42no—
145C22×C61—42no—
146C22×C61#13712yescomplemented
147C22×C61C22×D411yescharacteristic
148C2×D61—21no—
149C2×D61—21no—
150C2×D61—21no—
151C2×D61—21no—
152C2×D61—21no—
153C2×D61—44no—
154C2×D61#12012yes—
155C4×C61—21no—
156C4×C61—41no—
157C4×C61—41no—
158C4×C61C22×D412yes—
159Dic61—24no—
160Dic61—21no—
161Dic61—41no—
162Dic61—41no—
163Dic61#12012yes—
164#3007—611nomaximal, Sylow
165C2×C61—22no—
166C2×C61—44no—
167C2×C61C2×#12011yescharacteristic
168C2×C61C2×#13711yescharacteristic
169C2×C61#57511yescharacteristic
170D61—22no—
171D61—41no—
172C22×#41—611no—
173C2×#137—612no—
174C2×C22⋊Q8—611no—
175#452—612no—
176#452—612no—
177#451—611no—
178#451—611no—
179#450—611no—
180#450D6111yescharacteristic, complemented
181#417—612no—
182#407—611no—
183C61#300711yescharacteristic, complemented, Sylow
184C2×#41—612no—
185C2×#41—612no—
186C2×#41—1221no—
187C2×#41—1221no—
188C2×#41—1228no—
189C22×Q8—611no—
190C22×Q8—611no—
191C22×D4—1221no—
192C22×D4C2×D6111yescharacteristic
193C23×C4—611no—
194C23×C4—1221no—
195#137—1228no—
196C2×Q16—612no—
197C2×Q16—612no—
198C2×SD16—612no—
199C2×SD16C2×D6112yescomplemented
200C2×M16—612no—
201C22⋊Q8—611no—
202C22⋊Q8—611no—
203C22⋊Q8—611no—
204C22⋊Q8—1221no—
205C22⋊Q8—1221no—
206C22⋊Q8C2×D6111yescharacteristic
207C2×C4⋊C4—611no—
208C2×C4⋊C4—1221no—
209C2×C22⋊C4—1221no—
210#103—612no—
211#103—612no—
212#102—612no—
213#102C2×D6112yescomplemented
214C22⋊C8—611no—
215C22⋊C8—612no—
216C22⋊C8C2×D6111yescharacteristic
217C24—21no—
218C24—611no—
219#41—618no—
220#41—1224no—
221#41—1224no—
222#41—1228no—
223#41—1228no—
224#41—1224no—
225C2×Q8—612no—
226C2×Q8—611no—
227C2×Q8—1221no—
228C2×Q8—1224no—
229C2×Q8—1224no—
230C2×Q8—1221no—
231C2×Q8C22×D6111yescharacteristic
232C2×D4—24no—
233C2×D4—21no—
234C2×D4—1222no—
235C2×D4—1222no—
236C2×D4—1228no—
237C2×D4C22×D6112yes—
238C22×C4—611no—
239C22×C4—611no—
240C22×C4—611no—
241C22×C4—611no—
242C22×C4—611no—
243C22×C4—1224no—
244C22×C4—1221no—
245C22×C4—1221no—
246C22×C4—1222no—
247C22×C4—1222no—
248C22×C4—1228no—
249C22×C4—1221no—
250C22×C4C22×D6111yescharacteristic
251Q16—1224no—
252Q16—1224no—
253SD16—24no—
254SD16—1224no—
255M16—1224no—
256C2×C8—612no—
257C2×C8C22×D6112yes—
258C4⋊C4—21no—
259C4⋊C4—611no—
260C4⋊C4—1221no—
261C4⋊C4—1221no—
262C4⋊C4—1221no—
263C4⋊C4—1221no—
264C4⋊C4C22×D6111yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—1221no—
267C22⋊C4—1221no—
268C22⋊C4—1221no—
269C23—24no—
270C23—22no—
271C23—42no—
272C23—42no—
273C23—611no—
274C23—611no—
275C23—1222no—
276C23—1222no—
277C23—2441no—
278C23D4×D6111yescharacteristic
279Q8—22no—
280Q8—614no—
281Q8—1224no—
282Q8—1222no—
283Q8—1222no—
284Q8—2442no—
285D4—24no—
286D4—22no—
287D4—1228no—
288D4—1228no—
289D4D4×D6114yes—
290C2×C4—22no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—611no—
294C2×C4—614no—
295C2×C4—611no—
296C2×C4—1222no—
297C2×C4—1222no—
298C2×C4—1222no—
299C2×C4—1228no—
300C2×C4—1224no—
301C2×C4—1228no—
302C2×C4—1222no—
303C2×C4—1222no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—2442no—
307C2×C4—2442no—
308C2×C4D4×D6111yescharacteristic
309C2×C4C23×D6111yescharacteristic
310C8—22no—
311C8—1222no—
312C22—21no—
313C22—21no—
314C22—24no—
315C22—48no—
316C22—42no—
317C22—42no—
318C22—612no—
319C22—1221no—
320C22—1221no—
321C22—1221no—
322C22—1221no—
323C22—1221no—
324C22—2444no—
325C22#1451980612yescomplemented
326C22C2×D4×D6111yescharacteristic
327C4—21no—
328C4—41no—
329C4—41no—
330C4—612no—
331C4—1221no—
332C4—1224no—
333C4—2441no—
334C4—2441no—
335C4C2×D4×D6112yes—
336C2—22no—
337C2—44no—
338C2—1222no—
339C2—2441no—
340C2#120×D6111yescharacteristic
341C2C2×#1451980611yescharacteristic
342C2#1684055811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#450C2
socleC22×C61C22×D4
hypercenter#450D61
hypocenterC61#3007
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
2. C2×#14519806C2semidirect
3. C22⋊Q8×D61C2semidirect
4. #16839925C2semidirect
5. #16839921C2semidirect
6. #16839920C2semidirect
7. #16839917C2semidirect
8. #16839913C2semidirect
9. #16839760C2semidirect
10. #16839724C2semidirect
11. C61×#450C2semidirect
18. C2×Q8×D61C22semidirect
23. C2×Dic244C22semidirect
24. C2×#11758202C22semidirect
25. C2×#11758200C22semidirect
26. C2×#11758189C22semidirect
27. #14519757C22semidirect
31. #14519753C22semidirect
33. C4⋊C4×D61C22semidirect
35. #14519702C22semidirect
36. #14519700C22semidirect
37. #14519698C22semidirect
39. #14519689C22semidirect
41. C2×SD16×C61C22semidirect
43. #102×C61C22semidirect
146. C22×C61#137semidirect
180. #450D61semidirect
183. C61#3007semidirect
199. C2×SD16C2×D61semidirect
213. #102C2×D61semidirect
325. C22#14519806semidirect