Finite Group Databasebeta

← #21455541

Subgroups — #21455541

Order 7808.

452 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 123 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
1#16840561C212yesmaximal, complemented
2C2×#14519800C211yesmaximal, characteristic, complemented
3#131×D61C211yesmaximal, characteristic, complemented
4#16840034C211yesmaximal, characteristic, complemented
5#16840033C211yesmaximal, characteristic, complemented
6#16840032C211yesmaximal, characteristic, complemented
7#16840028C212yesmaximal, complemented
8#16840027C212yesmaximal, complemented
9#108×D61C211yesmaximal, characteristic, complemented
10#16839745C212yesmaximal, complemented
11C61×#473C211yesmaximal, characteristic, complemented
12C2×#11758226C2212yes—
13#41×D61C2211yescharacteristic
14#14519809—22no—
15#14519808C2212yes—
16#14519805C2212yes—
17#14519804—22no—
18#14519802C2212yes—
19#14519800—22no—
20#14519800—21no—
21#14519800—21no—
22#14519800—21no—
23#14519800—21no—
24#14519798—22no—
25C2×#11758201C2212yescomplemented
26C2×D488C2211yescharacteristic, complemented
27#14519785—21no—
28#14519785C2211yescharacteristic
29#14519784C2211yescharacteristic
30#14519783—21no—
31#14519783C2211yescharacteristic
32M16×D61—21no—
33M16×D61C2211yescharacteristic
34M16×D61C2212yes—
35C2×C8×D61—21no—
36C2×C8×D61C2211yescharacteristic
37#14519713C2211yescharacteristic, complemented
38#14519712C2212yescomplemented
39#14519696C2212yescomplemented
40#14519693C2212yescomplemented
41#14519693C2212yescomplemented
42#137×C61C2212yes—
43C2×Q16×C61C2211yescharacteristic, complemented
44#131×C61C2211yescharacteristic
45#108×C61C2211yescharacteristic, complemented
46#101×C61C2212yescomplemented
47#41×C61C2311yescharacteristic
48C2×Q8×C61C2312yes—
49#11758226—22no—
50#11758226—22no—
51#11758226—22no—
52#11758226—22no—
53#11758226D411yescharacteristic
54Q8×D61D411yescharacteristic
55#11758224—21no—
56#11758224D411yescharacteristic
57D4×D61—21no—
58D4×D61D411yescharacteristic
59#11758222—21no—
60#11758222C2311yescharacteristic
61C2×D244—22no—
62C2×D244C2312yes—
63C2×C4×D61—21no—
64C2×C4×D61—22no—
65C2×C4×D61C2311yescharacteristic
66Q16×C61—22no—
67Q16×C61—21no—
68Q16×C61—21no—
69SD16×C61—22no—
70M16×C61—21no—
71M16×C61C2311yescharacteristic
72M16×C61C2312yes—
73C2×C8×C61—21no—
74C2×C8×C61C2311yescharacteristic
75#11758202—22no—
76#11758201—22no—
77#11758201—22no—
78#11758201—22no—
79#11758201—22no—
80#11758199—22no—
81#11758194—21no—
82#11758194C2312yes—
83#11758194C2311yescharacteristic
84C2×#92418—21no—
85C2×#92418C2311yescharacteristic
86D488—22no—
87D488—21no—
88D488—21no—
89#11758190—22no—
90#11758189—22no—
91#11758189—21no—
92#11758189—21no—
93#11758189—21no—
94C8×D61—21no—
95C8×D61—22no—
96C8×D61—21no—
97C8×D61—21no—
98C8×D61D411yescharacteristic
99C8×D61D411yescharacteristic
100C8×D61D411yescharacteristic
101C8×D61D411yescharacteristic
102C22×D61—21no—
103C22×D61—22no—
104C22×D61#4111yescharacteristic
105Q8×C61—22no—
106Q8×C61—22no—
107Q8×C61C2×D411yescharacteristic
108D4×C61—21no—
109D4×C61C2×D411yescharacteristic
110C2×C4×C61—21no—
111C2×C4×C61—22no—
112C2×C4×C61C2411yescharacteristic
113C22⋊D61—21no—
114C22⋊D61—21no—
115C22⋊D61—21no—
116C2×Dic61—21no—
117C2×Dic61#4111yescharacteristic
118D244—21no—
119D244—22no—
120D244—22no—
121D244—42no—
122D244—42no—
123D244C2×D411yescharacteristic
124C4×D61—21no—
125C4×D61—21no—
126C4×D61—21no—
127C4×D61—42no—
128C4×D61—42no—
129C4×D61C2×D411yescharacteristic
130C4×D61C2×D411yescharacteristic
131C4×D61C2×D411yescharacteristic
132C4×D61C2×D411yescharacteristic
133Dic122—21no—
134Dic122C2×D411yescharacteristic
135C8×C61—21no—
136C8×C61—22no—
137C8×C61C2×D411yescharacteristic
138C8×C61C2×D411yescharacteristic
139#92418—21no—
140#92418—22no—
141#92418C2×D411yescharacteristic
142#92418C2×D411yescharacteristic
143C22×C61—21no—
144C22×C61C2×#4111yescharacteristic
145C2×D61—21no—
146C2×D61—41no—
147C2×D61—42no—
148C2×D61—42no—
149C2×D61—82no—
150C2×D61#12111yescharacteristic
151C2×D61#12111yescharacteristic
152C4×C61—21no—
153C4×C61—42no—
154C4×C61C22×D411yescharacteristic
155C4×C61C22×D411yescharacteristic
156Dic61—21no—
157Dic61#12111yescharacteristic
158Dic61#12111yescharacteristic
159#3067—611nomaximal, Sylow
160C2×C61—21no—
161C2×C61—41no—
162C2×C61C2×#12111yescharacteristic
163D61—21no—
164D61—21no—
165D61—41no—
166D61—82no—
167#575—612no—
168C2×#135—611no—
169C2×#131—611no—
170#473—611no—
171#473D6111yescharacteristic, complemented
172#472—611no—
173#472—611no—
174#471—612no—
175#471—612no—
176C2×#108—611no—
177#413—612no—
178C61#306711yescharacteristic, complemented, Sylow
179C2×#41—611no—
180C2×#41—612no—
181#137—612no—
182#137—1222no—
183#137C2×D6112yes—
184AGL(1,ℤ/8)—612no—
185AGL(1,ℤ/8)—612no—
186AGL(1,ℤ/8)—1222no—
187#135—1221no—
188#135—1221no—
189#135—1221no—
190#135—1221no—
191#135—1222no—
192#135—1222no—
193C2×Q16C2×D6111yescharacteristic, complemented
194C2×SD16—612no—
195C2×D8—611no—
196#131—611no—
197#131—611no—
198#131—611no—
199#131—1221no—
200#131—1221no—
201#131C2×D6111yescharacteristic
202C2×M16—611no—
203C2×M16—612no—
204C2×M16—1221no—
205C22×C8—611no—
206C22×C8—1221no—
207#108—612no—
208#108—611no—
209#108C2×D6111yescharacteristic, complemented
210#101—612no—
211#101C2×D6112yescomplemented
212#100—612no—
213#100—612no—
214#41—611no—
215#41—611no—
216#41—611no—
217#41—1221no—
218#41—1221no—
219#41—1222no—
220#41—1222no—
221#41—1222no—
222#41—1222no—
223#41C22×D6111yescharacteristic
224C2×Q8—611no—
225C2×Q8C22×D6112yes—
226C2×D4—611no—
227C2×D4—612no—
228C2×D4—1222no—
229C2×D4—1221no—
230C22×C4—611no—
231C22×C4—1221no—
232C22×C4—1222no—
233Q16—22no—
234Q16—21no—
235Q16—21no—
236Q16—1222no—
237SD16—22no—
238SD16—1222no—
239SD16—1222no—
240SD16—1222no—
241SD16—1222no—
242SD16—1222no—
243D8—1222no—
244D8—1222no—
245D8—1221no—
246D8—1221no—
247M16—21no—
248M16—611no—
249M16—612no—
250M16—1221no—
251M16—1221no—
252M16—1222no—
253M16—1221no—
254M16—1221no—
255M16C22×D6111yescharacteristic
256M16C22×D6112yes—
257C2×C8—21no—
258C2×C8—611no—
259C2×C8—611no—
260C2×C8—611no—
261C2×C8—611no—
262C2×C8—611no—
263C2×C8—1221no—
264C2×C8—1221no—
265C2×C8—1222no—
266C2×C8—1221no—
267C2×C8—1221no—
268C2×C8C22×D6111yescharacteristic
269C23—611no—
270C23—1221no—
271C23—1222no—
272Q8—22no—
273Q8—22no—
274Q8—611no—
275Q8—1221no—
276Q8D4×D6111yescharacteristic
277D4—21no—
278D4—611no—
279D4—1221no—
280D4—1221no—
281D4—1221no—
282D4—1221no—
283D4—1222no—
284D4—1222no—
285D4—2442no—
286D4—2442no—
287D4D4×D6111yescharacteristic
288C2×C4—21no—
289C2×C4—22no—
290C2×C4—611no—
291C2×C4—611no—
292C2×C4—611no—
293C2×C4—611no—
294C2×C4—611no—
295C2×C4—1221no—
296C2×C4—1221no—
297C2×C4—1221no—
298C2×C4—1221no—
299C2×C4—2442no—
300C2×C4—2442no—
301C2×C4C23×D6111yescharacteristic
302C8—21no—
303C8—22no—
304C8—611no—
305C8—611no—
306C8—1221no—
307C8—1222no—
308C8D4×D6111yescharacteristic
309C8D4×D6111yescharacteristic
310C22—21no—
311C22—611no—
312C22—611no—
313C22—1221no—
314C22—4882no—
315C22—2441no—
316C22—2442no—
317C22—2442no—
318C22#41×D6111yescharacteristic
319C4—21no—
320C4—42no—
321C4—611no—
322C4—611no—
323C4—1221no—
324C4C2×D4×D6111yescharacteristic
325C4C2×D4×D6111yescharacteristic
326C2—21no—
327C2—41no—
328C2—1221no—
329C2—1221no—
330C2—4882no—
331C2—2441no—
332C2#121×D6111yescharacteristic
subgroupG/H
centerC2#121×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#473C2
socleC2×C61C2×#121
hypercenter#473D61
hypocenterC61#3067
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #473

Complements

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

NH ≅ G/Ntype
1. #16840561C2semidirect
2. C2×#14519800C2semidirect
3. #131×D61C2semidirect
4. #16840034C2semidirect
5. #16840033C2semidirect
6. #16840032C2semidirect
7. #16840028C2semidirect
8. #16840027C2semidirect
9. #108×D61C2semidirect
10. #16839745C2semidirect
11. C61×#473C2semidirect
25. C2×#11758201C22semidirect
26. C2×D488C22semidirect
37. #14519713C22semidirect
38. #14519712C22semidirect
39. #14519696C22semidirect
40. #14519693C22semidirect
41. #14519693C22semidirect
43. C2×Q16×C61C22semidirect
45. #108×C61C22semidirect
46. #101×C61C22semidirect
171. #473D61semidirect
178. C61#3067semidirect
193. C2×Q16C2×D61semidirect
209. #108C2×D61semidirect
211. #101C2×D61semidirect