Finite Group Databasebeta

← #21455078

Subgroups — #21455078

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×#11758226C211yesmaximal, characteristic
2C2×#14519809C212yesmaximal, complemented
3C22⋊Q8×D61C211yesmaximal, characteristic, complemented
4#16839927C212yesmaximal, complemented
5#16839923C212yesmaximal, complemented
6#16839918C211yesmaximal, characteristic, complemented
7#16839915C211yesmaximal, characteristic, complemented
8#16839912C211yesmaximal, characteristic, complemented
9#16839762C212yesmaximal, complemented
10#16839724C211yesmaximal, characteristic, complemented
11C61×#451C211yesmaximal, characteristic, complemented
12C2×#11758226—28no—
13C2×#11758226—21no—
14C2×#11758226—21no—
15C2×#11758226C2212yes—
16C2×#11758226C2212yes—
17C2×Q8×D61C2211yescharacteristic, complemented
18C22×D244—21no—
19C22×D244C2211yescharacteristic
20C22×C4×D61—21no—
21C22×C4×D61C2211yescharacteristic
22#14519809—28no—
23C2×#11758202C2212yescomplemented
24C2×#11758190C2212yescomplemented
25C2×#11758201C2212yescomplemented
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#14519701C2212yescomplemented
36#14519699C2212yescomplemented
37#14519697C2212yescomplemented
38C22⋊#92418C2211yescharacteristic
39#14519689C2212yescomplemented
40C22×Q8×C61C2211yescharacteristic
41C2×Q16×C61C2212yescomplemented
42C22⋊Q8×C61C2211yescharacteristic
43#103×C61C2212yescomplemented
44C22⋊C8×C61C2211yescharacteristic
45C23×D61—21no—
46C23×D61D411yescharacteristic
47C2×Q8×C61—24no—
48C2×Q8×C61—21no—
49C2×Q8×C61C2311yescharacteristic
50C2×Q8×C61C2312yes—
51C22×C4×C61—21no—
52C22×C4×C61C2311yescharacteristic
53C22×Dic61D411yescharacteristic
54#11758226—28no—
55#11758226—28no—
56#11758226—24no—
57#11758226—24no—
58#11758226—24no—
59#11758226D418yes—
60Q8×D61—24no—
61C2×D244—28no—
62C2×D244—22no—
63C2×D244—22no—
64C2×D244—21no—
65C2×D244—24no—
66C2×D244C2312yes—
67C2×C4×D61—28no—
68C2×C4×D61—22no—
69C2×C4×D61—22no—
70C2×C4×D61—24no—
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×C4×D61D411yescharacteristic
74C2×C4×D61D411yescharacteristic
75C2×C4×D61C2311yescharacteristic
76C2×C4×D61C2311yescharacteristic
77C2×Dic122—21no—
78C2×Dic122C2311yescharacteristic
79Q16×C61—24no—
80C2×C8×C61C2312yes—
81C4⋊C4×C61—21no—
82C4⋊C4×C61C2311yescharacteristic
83C22⋊C4×C61—21no—
84C22⋊Dic61—21no—
85#11758202—24no—
86#11758201—24no—
87#11758198—21no—
88#11758198—21no—
89C4⋊Dic61—21no—
90C4⋊Dic61C2311yescharacteristic
91#11758196—21no—
92#11758196—21no—
93#11758196—21no—
94C2×#92418C2312yes—
95#11758190—24no—
96#11758189—24no—
97C23×C61C2×D411yescharacteristic
98C22×D61—24no—
99C22×D61—22no—
100C22×D61—22no—
101C22×D61—22no—
102C22×D61—41no—
103C22×D61—42no—
104C22×D61—42no—
105C22×D61C2×D411yescharacteristic
106C22×D61C2×D411yescharacteristic
107Q8×C61—24no—
108Q8×C61—22no—
109Q8×C61—22no—
110Q8×C61C2×D414yes—
111C2×C4×C61—24no—
112C2×C4×C61—22no—
113C2×C4×C61—22no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61C2×D411yescharacteristic
117C2×C4×C61C2411yescharacteristic
118C2×Dic61—22no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61C2×D411yescharacteristic
122C2×Dic61C2×D411yescharacteristic
123D244—28no—
124D244—24no—
125D244—28no—
126D244—22no—
127D244C2×D414yes—
128C4×D61—28no—
129C4×D61—22no—
130C4×D61—22no—
131C4×D61—28no—
132C4×D61—22no—
133C4×D61—42no—
134C4×D61—42no—
135C4×D61C2×D414yes—
136Dic122—22no—
137Dic122—42no—
138C8×C61—22no—
139#92418—22no—
140C22×C61—21no—
141C22×C61—21no—
142C22×C61#13712yescomplemented
143C22×C61C22×D411yescharacteristic
144C2×D61—21no—
145C2×D61—21no—
146C2×D61—21no—
147C2×D61—24no—
148C2×D61—21no—
149C2×D61—21no—
150C2×D61—44no—
151C2×D61—48no—
152C2×D61—42no—
153C2×D61—42no—
154C2×D61#12012yes—
155C4×C61—24no—
156C4×C61—21no—
157C4×C61—41no—
158C4×C61—41no—
159C4×C61C22×D412yes—
160Dic61—21no—
161Dic61—41no—
162Dic61—41no—
163Dic61#12012yes—
164#3007—611nomaximal, Sylow
165C2×C61—22no—
166C2×C61C2×#12011yescharacteristic
167C2×C61C2×#13711yescharacteristic
168C2×C61#57511yescharacteristic
169D61—22no—
170D61—41no—
171D61—44no—
172C22×#41—611no—
173C2×#137—612no—
174C2×C22⋊Q8—611no—
175#452—612no—
176#452—612no—
177#451—611no—
178#451D6111yescharacteristic, complemented
179#450—611no—
180#450—611no—
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×Q8C2×D6111yescharacteristic
191C22×D4—611no—
192C22×D4—1221no—
193C23×C4—611no—
194C23×C4—1221no—
195#137—1228no—
196C2×Q16—612no—
197C2×Q16C2×D6112yescomplemented
198C2×SD16—612no—
199C2×SD16—612no—
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#103C2×D6112yescomplemented
212#102—612no—
213#102—612no—
214C22⋊C8—611no—
215C22⋊C8—612no—
216C22⋊C8C2×D6111yescharacteristic
217C24—611no—
218C24—1221no—
219#41—618no—
220#41—1224no—
221#41—1224no—
222#41—1228no—
223#41—1228no—
224#41—1224no—
225C2×Q8—24no—
226C2×Q8—21no—
227C2×Q8—611no—
228C2×Q8—1221no—
229C2×Q8—1224no—
230C2×Q8C22×D6111yescharacteristic
231C2×Q8C22×D6112yes—
232C2×D4—612no—
233C2×D4—1224no—
234C2×D4—1222no—
235C2×D4—1222no—
236C2×D4—1228no—
237C2×D4—1221no—
238C22×C4—21no—
239C22×C4—611no—
240C22×C4—611no—
241C22×C4—611no—
242C22×C4—611no—
243C22×C4—611no—
244C22×C4—1224no—
245C22×C4—1222no—
246C22×C4—1222no—
247C22×C4—1228no—
248C22×C4—1221no—
249C22×C4—1221no—
250C22×C4C22×D6111yescharacteristic
251Q16—24no—
252Q16—1224no—
253SD16—1224no—
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—611no—
270C23—611no—
271C23—1222no—
272C23—1224no—
273C23—1222no—
274C23—1222no—
275C23—2441no—
276C23—2442no—
277C23—2442no—
278C23D4×D6111yescharacteristic
279Q8—24no—
280Q8—22no—
281Q8—22no—
282Q8—1222no—
283Q8—2442no—
284Q8D4×D6114yes—
285D4—614no—
286D4—1228no—
287D4—1228no—
288D4—1224no—
289D4—1222no—
290C2×C4—24no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—611no—
296C2×C4—614no—
297C2×C4—611no—
298C2×C4—1222no—
299C2×C4—1228no—
300C2×C4—1222no—
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—612no—
315C22—1221no—
316C22—1221no—
317C22—1224no—
318C22—1221no—
319C22—1221no—
320C22—1221no—
321C22—2444no—
322C22—2448no—
323C22—2442no—
324C22—2442no—
325C22#1451980912yescomplemented
326C22C2×D4×D6111yescharacteristic
327C4—24no—
328C4—21no—
329C4—41no—
330C4—41no—
331C4—612no—
332C4—1221no—
333C4—2441no—
334C4—2441no—
335C4C2×D4×D6112yes—
336C2—22no—
337C2—1222no—
338C2—2441no—
339C2—2444no—
340C2#120×D6111yescharacteristic
341C2C2×#1451980911yescharacteristic
342C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#451C2
socleC22×C61C22×D4
hypercenter#451D61
hypocenterC61#3007
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
2. C2×#14519809C2semidirect
3. C22⋊Q8×D61C2semidirect
4. #16839927C2semidirect
5. #16839923C2semidirect
6. #16839918C2semidirect
7. #16839915C2semidirect
8. #16839912C2semidirect
9. #16839762C2semidirect
10. #16839724C2semidirect
11. C61×#451C2semidirect
17. C2×Q8×D61C22semidirect
23. C2×#11758202C22semidirect
24. C2×#11758190C22semidirect
25. C2×#11758201C22semidirect
26. C2×#11758189C22semidirect
27. #14519757C22semidirect
31. #14519753C22semidirect
33. C4⋊C4×D61C22semidirect
35. #14519701C22semidirect
36. #14519699C22semidirect
37. #14519697C22semidirect
39. #14519689C22semidirect
41. C2×Q16×C61C22semidirect
43. #103×C61C22semidirect
142. C22×C61#137semidirect
178. #451D61semidirect
183. C61#3007semidirect
197. C2×Q16C2×D61semidirect
211. #103C2×D61semidirect
325. C22#14519809semidirect