Finite Group Databasebeta

← #21455038

Subgroups — #21455038

Order 7808.

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

normal subgroups only

This group has 764 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, complemented
2C2×#14519798C212yesmaximal, complemented
3#16840275C211yesmaximal, characteristic, complemented
4#16839921C212yesmaximal, complemented
5#16839917C211yesmaximal, characteristic, complemented
6#16839908C212yesmaximal, complemented
7#16839903C211yesmaximal, characteristic, complemented
8#16839896C211yesmaximal, characteristic, complemented
9#16839755C212yesmaximal, complemented
10C22⋊C8×D61C211yesmaximal, characteristic, complemented
11C61×#450C211yesmaximal, characteristic, complemented
12C2×#11758226C2211yescharacteristic, complemented
13C2×#11758224—28no—
14C2×#11758224—21no—
15C2×#11758224—21no—
16C2×#11758224C2212yes—
17C2×#11758224C2212yes—
18C22×Dic122C2211yescharacteristic
19C22×C22⋊D61—21no—
20C23×Dic61—21no—
21C22×C4×D61C2211yescharacteristic
22#14519798—28no—
23C2×#11758202C2212yescomplemented
24C2×#11758190C2212yescomplemented
25C2×#11758199C2212yescomplemented
26C2×C8×D61C2212yescomplemented
27#14519762—21no—
28#14519753C2211yescharacteristic, complemented
29#14519752C2211yescharacteristic, complemented
30#14519751C2211yescharacteristic
31#14519747—21no—
32#14519739—21no—
33#14519737—21no—
34#14519735C2211yescharacteristic, complemented
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—
55C2×C22⋊D61—21no—
56C22×Dic61—28no—
57C22×Dic61—21no—
58C22×Dic61—22no—
59C22×Dic61—22no—
60C22×Dic61D411yescharacteristic
61#11758226—24no—
62#11758224—28no—
63#11758224—28no—
64#11758224—24no—
65#11758224—24no—
66#11758224—24no—
67#11758224D418yescomplemented
68C2×D244—21no—
69C2×D244—21no—
70C2×D244C2311yescharacteristic
71C2×C4×D61—24no—
72C2×C4×D61—21no—
73C2×C4×D61D411yescharacteristic
74C2×C4×D61D411yescharacteristic
75C2×C4×D61C2311yescharacteristic
76C2×C4×D61C2311yescharacteristic
77C2×Dic122—21no—
78C2×Dic122—24no—
79C2×Dic122C2312yes—
80SD16×C61—24no—
81C2×C8×C61C2312yes—
82C4⋊C4×C61—21no—
83C4⋊C4×C61C2311yescharacteristic
84C22⋊C4×C61—21no—
85#11758202—24no—
86#11758199—24no—
87#11758198—21no—
88#11758198—21no—
89#11758198—21no—
90#11758198—21no—
91C4⋊Dic61C2311yescharacteristic
92#11758196—21no—
93C4×Dic61—21no—
94C2×#92418C2312yes—
95#11758190—24no—
96C8×D61—24no—
97C23×C61—24no—
98C23×C61—22no—
99C23×C61—42no—
100C23×C61—42no—
101C23×C61C2×D411yescharacteristic
102C22×D61—22no—
103C22×D61—22no—
104C22×D61—21no—
105C22×D61—41no—
106C22×D61C2×D411yescharacteristic
107C22×D61C2×D411yescharacteristic
108Q8×C61—22no—
109D4×C61—24no—
110D4×C61—22no—
111D4×C61C2×D414yes—
112C2×C4×C61—22no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61C2×D411yescharacteristic
116C2×C4×C61C2411yescharacteristic
117C22⋊D61—28no—
118C22⋊D61—28no—
119C22⋊D61—42no—
120C2×Dic61—24no—
121C2×Dic61—28no—
122C2×Dic61—22no—
123C2×Dic61—22no—
124C2×Dic61—28no—
125C2×Dic61—21no—
126C2×Dic61C2×D411yescharacteristic
127C2×Dic61C2×D411yescharacteristic
128D244—22no—
129D244—42no—
130D244—42no—
131C4×D61—22no—
132C4×D61—22no—
133C4×D61—22no—
134C4×D61—42no—
135C4×D61C2×D414yes—
136Dic122—24no—
137Dic122—22no—
138Dic122C2×D414yes—
139C8×C61—22no—
140#92418—22no—
141C22×C61—21no—
142C22×C61—21no—
143C22×C61—24no—
144C22×C61—48no—
145C22×C61—42no—
146C22×C61—42no—
147C22×C61#13512yescomplemented
148C22×C61C22×D411yescharacteristic
149C2×D61—21no—
150C2×D61—21no—
151C2×D61—21no—
152C2×D61—21no—
153C2×D61—21no—
154C2×D61—44no—
155C2×D61—41no—
156C2×D61—41no—
157C2×D61—41no—
158C2×D61#12012yes—
159C4×C61—21no—
160C4×C61—41no—
161C4×C61—41no—
162C4×C61C22×D412yes—
163Dic61—24no—
164Dic61—21no—
165Dic61—41no—
166Dic61#12012yes—
167#3002—611nomaximal, Sylow
168C2×C61—22no—
169C2×C61—44no—
170C2×C61C2×#12011yescharacteristic
171C2×C61C2×#13511yescharacteristic
172C2×C61#57511yescharacteristic
173D61—22no—
174D61—41no—
175D61—81no—
176C22×#41—611no—
177C2×#135—612no—
178#525—611no—
179#452—612no—
180#451—611no—
181#450D6111yescharacteristic, complemented
182#449—612no—
183#448—611no—
184#447—611no—
185#416—612no—
186C2×C22⋊C8—611no—
187C61#300211yescharacteristic, complemented, Sylow
188C2×#41—611no—
189C2×#41—612no—
190C2×#41—612no—
191C2×#41—1221no—
192C2×#41—1221no—
193C2×#41—1228no—
194C22×Q8—611no—
195C22×D4—1221no—
196C22×D4C2×D6111yescharacteristic
197C23×C4—611no—
198C23×C4—1221no—
199#135—1228no—
200C2×Q16—612no—
201C2×SD16—612no—
202C2×SD16C2×D6112yescomplemented
203C2×D8—612no—
204C22×C8—612no—
205#123—1221no—
206C22⋊Q8—611no—
207C22⋊Q8C2×D6111yescharacteristic
208#121—611no—
209#121—611no—
210#120—1221no—
211C4×D4—1221no—
212C4×D4—1221no—
213#117—611no—
214#103—612no—
215#103—612no—
216#102—612no—
217#102C2×D6112yescomplemented
218C22⋊C8—611no—
219C22⋊C8—612no—
220C22⋊C8C2×D6111yescharacteristic
221C24—21no—
222C24—611no—
223#41—618no—
224#41—1224no—
225#41—1224no—
226#41—1224no—
227#41—1228no—
228#41—1228no—
229#41—1224no—
230C2×Q8—612no—
231C2×Q8—1224no—
232C2×Q8—1221no—
233C2×Q8C22×D6111yescharacteristic
234C2×D4—24no—
235C2×D4—21no—
236C2×D4—611no—
237C2×D4—1221no—
238C2×D4—1221no—
239C2×D4—1222no—
240C2×D4—1222no—
241C2×D4—1228no—
242C2×D4—1221no—
243C2×D4C22×D6112yes—
244C22×C4—611no—
245C22×C4—611no—
246C22×C4—611no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—1224no—
250C22×C4—1221no—
251C22×C4—1222no—
252C22×C4—1222no—
253C22×C4—1228no—
254C22×C4—1221no—
255C22×C4C22×D6111yescharacteristic
256Q16—1224no—
257SD16—24no—
258SD16—1224no—
259D8—1224no—
260C2×C8—612no—
261C2×C8—1224no—
262C2×C8C22×D6112yes—
263C4⋊C4—21no—
264C4⋊C4—611no—
265C4⋊C4—1221no—
266C4⋊C4C22×D6111yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—1221no—
269C22⋊C4—1221no—
270C22⋊C4—1221no—
271C22⋊C4—1221no—
272C42—1221no—
273C23—24no—
274C23—22no—
275C23—42no—
276C23—42no—
277C23—611no—
278C23—611no—
279C23—1222no—
280C23—1222no—
281C23—1221no—
282C23—2441no—
283C23D4×D6111yescharacteristic
284Q8—22no—
285Q8—614no—
286Q8—1224no—
287Q8—1222no—
288D4—24no—
289D4—22no—
290D4—1228no—
291D4—1228no—
292D4—1222no—
293D4—2442no—
294D4—2442no—
295D4—2442no—
296D4D4×D6114yes—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—611no—
301C2×C4—614no—
302C2×C4—611no—
303C2×C4—1222no—
304C2×C4—1222no—
305C2×C4—1222no—
306C2×C4—1228no—
307C2×C4—1224no—
308C2×C4—1228no—
309C2×C4—1222no—
310C2×C4—1222no—
311C2×C4—1221no—
312C2×C4—2442no—
313C2×C4D4×D6111yescharacteristic
314C2×C4C23×D6111yescharacteristic
315C8—22no—
316C8—1222no—
317C22—21no—
318C22—21no—
319C22—24no—
320C22—48no—
321C22—42no—
322C22—42no—
323C22—612no—
324C22—1221no—
325C22—1221no—
326C22—1221no—
327C22—1221no—
328C22—1221no—
329C22—2444no—
330C22—2441no—
331C22—2441no—
332C22—2441no—
333C22#1451979812yescomplemented
334C22C2×D4×D6111yescharacteristic
335C4—21no—
336C4—41no—
337C4—41no—
338C4—612no—
339C4—1221no—
340C4—1224no—
341C4—2441no—
342C4C2×D4×D6112yes—
343C2—22no—
344C2—44no—
345C2—1222no—
346C2—4881no—
347C2—2441no—
348C2#120×D6111yescharacteristic
349C2C2×#1451979811yescharacteristic
350C2#1684055811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#450C2
socleC22×C61C22×D4
hypercenter#450D61
hypocenterC61#3002
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
1. C22×#11758224C2semidirect
2. C2×#14519798C2semidirect
3. #16840275C2semidirect
4. #16839921C2semidirect
5. #16839917C2semidirect
6. #16839908C2semidirect
7. #16839903C2semidirect
8. #16839896C2semidirect
9. #16839755C2semidirect
10. C22⋊C8×D61C2semidirect
11. C61×#450C2semidirect
12. C2×#11758226C22semidirect
23. C2×#11758202C22semidirect
24. C2×#11758190C22semidirect
25. C2×#11758199C22semidirect
26. C2×C8×D61C22semidirect
28. #14519753C22semidirect
29. #14519752C22semidirect
34. #14519735C22semidirect
35. #14519702C22semidirect
36. #14519700C22semidirect
37. #14519698C22semidirect
39. #14519689C22semidirect
41. C2×SD16×C61C22semidirect
43. #102×C61C22semidirect
67. #11758224D4semidirect
147. C22×C61#135semidirect
181. #450D61semidirect
187. C61#3002semidirect
202. C2×SD16C2×D61semidirect
217. #102C2×D61semidirect
333. C22#14519798semidirect