Finite Group Databasebeta

← #21458649

Subgroups — #21458649

Order 7808.

346 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840482C211yesmaximal, characteristic, complemented
2#16840468C211yesmaximal, characteristic, complemented
3#16840132C211yesmaximal, characteristic, complemented
4#16840120C211yesmaximal, characteristic, complemented
5#16840115C211yesmaximal, characteristic, complemented
6#16840068C211yesmaximal, characteristic, complemented
7#16840046C211yesmaximal, characteristic, complemented
8#16839976C211yesmaximal, characteristic
9#16839976C211yesmaximal, characteristic
10#16839968C211yesmaximal, characteristic, complemented
11#16839891C211yesmaximal, characteristic, complemented
12#16839872C211yesmaximal, characteristic
13#16839861C211yesmaximal, characteristic, complemented
14#16839849C211yesmaximal, characteristic, complemented
15C61×#478C211yesmaximal, characteristic, complemented
16C2×#11758190C2211yescharacteristic
17C2×#11758190C2211yescharacteristic
18C2×#11758199C2211yescharacteristic
19#14519777C2211yescharacteristic
20#14519776C2211yescharacteristic
21#14519770—21no—
22#14519770—21no—
23#14519768C2211yescharacteristic
24#14519764C2211yescharacteristic
25#14519764C2211yescharacteristic
26#14519757—21no—
27#14519756—21no—
28#14519755—21no—
29#14519755—21no—
30C4×Dic122C2211yescharacteristic
31#14519742C2211yescharacteristic
32#14519742C2211yescharacteristic
33C4×D244C2211yescharacteristic
34#14519739C2211yescharacteristic
35#14519739C2211yescharacteristic
36#14519736—21no—
37C4⋊C4×D61—21no—
38#14519708C2211yescharacteristic
39#14519706C2211yescharacteristic
40#14519706C2211yescharacteristic
41#14519702C2211yescharacteristic
42#14519702C2211yescharacteristic
43#14519700C2211yescharacteristic
44#14519700C2211yescharacteristic
45#14519700C2211yescharacteristic
46#14519700C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519697C2211yescharacteristic
49#14519688C2211yescharacteristic
50#14519687C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52#125×C61C2211yescharacteristic
53C4×D4×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic
55#106×C61C2211yescharacteristic
56C4⋊C8×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic
59C2×D4×C61C2311yescharacteristic
60C22×C4×C61—21no—
61C2×D244C2311yescharacteristic
62C2×C4×D61—21no—
63C2×C4×D61—21no—
64C2×C4×D61—21no—
65C2×Dic122—21no—
66C2×Dic122D411yescharacteristic
67C2×Dic122C2311yescharacteristic
68C2×Dic122C2311yescharacteristic
69C2×C8×C61C2311yescharacteristic
70C2×C8×C61C2311yescharacteristic
71C4⋊C4×C61—21no—
72C4⋊C4×C61—21no—
73C4⋊C4×C61C2311yescharacteristic
74C4⋊C4×C61C2311yescharacteristic
75C4⋊C4×C61C2311yescharacteristic
76C22⋊C4×C61—21no—
77C42×C61C2311yescharacteristic
78C22⋊Dic61—21no—
79C22⋊Dic61—21no—
80C22⋊Dic61—21no—
81C22⋊Dic61—21no—
82#11758199—22no—
83#11758198—21no—
84#11758198—21no—
85#11758198—21no—
86C4⋊Dic61—21no—
87C4⋊Dic61—21no—
88C4⋊Dic61—21no—
89C4⋊Dic61D411yescharacteristic
90C4⋊Dic61C2311yescharacteristic
91#11758196—21no—
92#11758196—21no—
93#11758196—21no—
94#11758196—21no—
95#11758196D411yescharacteristic
96#11758196D411yescharacteristic
97C4×Dic61—21no—
98C4×Dic61—21no—
99C4×Dic61C2311yescharacteristic
100C4×Dic61C2311yescharacteristic
101C2×#92418C2311yescharacteristic
102C2×#92418C2311yescharacteristic
103#11758190—22no—
104#11758190—22no—
105C23×C61—21no—
106C22×D61—21no—
107D4×C61—21no—
108D4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—42no—
113C2×C4×C61C2×D411yescharacteristic
114C2×C4×C61C2×D411yescharacteristic
115C2×C4×C61C2411yescharacteristic
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61C2×D411yescharacteristic
120C2×Dic61C2×D411yescharacteristic
121C2×Dic61C2×D411yescharacteristic
122C2×Dic61C2×D411yescharacteristic
123D244—21no—
124D244#4112yes—
125C4×D61—42no—
126C4×D61—81no—
127C4×D61—81no—
128Dic122—21no—
129Dic122—21no—
130Dic122—21no—
131Dic122—21no—
132Dic122—41no—
133Dic122—81no—
134C8×C61—21no—
135C8×C61—21no—
136#92418—21no—
137#92418—21no—
138C22×C61—41no—
139C22×C61—41no—
140C22×C61—41no—
141C22×C61C22×D411yescharacteristic
142C2×D61—22no—
143C2×D61—41no—
144C2×D61—41no—
145C4×C61—21no—
146C4×C61—21no—
147C4×C61—41no—
148C4×C61—41no—
149C4×C61—41no—
150C4×C61C2×#4111yescharacteristic
151C4×C612−1+411yescharacteristic
152Dic61—21no—
153Dic61—21no—
154Dic61—21no—
155Dic61—21no—
156Dic61—41no—
157Dic61—41no—
158Dic61—41no—
159#3376—611nomaximal, Sylow
160C2×C61—81no—
161C2×C61#54811yescharacteristic
162C2×C61#57511yescharacteristic
163C2×C61#57711yescharacteristic
164D61—42no—
165#556—611no—
166#554—611no—
167#491—611no—
168#489—611no—
169#488—611no—
170#479—611no—
171#478D6111yescharacteristic, complemented
172#475—611no—
173#463—611no—
174#463—611no—
175#461—611no—
176#446—611no—
177#442—611no—
178#440—611no—
179C4×SD16—611no—
180C61#337611yescharacteristic, complemented, Sylow
181C2×SD16—611no—
182C2×SD16—611no—
183C2×D8—611no—
184C4⋊Q8—611no—
185C4⋊Q8—611no—
186#126—1221no—
187#126—1221no—
188#125—611no—
189#125C2×D6111yescharacteristic
190#124—611no—
191#124—611no—
192C22⋊Q8—1221no—
193C22⋊Q8—1221no—
194C22⋊Q8—1221no—
195C22⋊Q8—1221no—
196C4×Q8—611no—
197C4×Q8—611no—
198C4×Q8—611no—
199C4×D4—611no—
200C4×D4—611no—
201C4×D4—611no—
202C4×D4C2×D6111yescharacteristic
203#117—1221no—
204C2×C4⋊C4—1221no—
205#107C2×D6111yescharacteristic
206#106—611no—
207#106C2×D6111yescharacteristic
208C4⋊C8—611no—
209C4⋊C8—611no—
210C4⋊C8C2×D6111yescharacteristic
211#103—611no—
212#103—611no—
213#103—611no—
214#103—611no—
215#103—611no—
216#103—611no—
217#102—611no—
218#102—611no—
219#102C2×D6111yescharacteristic
220#102C2×D6111yescharacteristic
221#97—611no—
222#97—611no—
223C4×C8—611no—
224C2×Q8—611no—
225C2×Q8—611no—
226C2×Q8—611no—
227C2×Q8—1221no—
228C2×D4—611no—
229C2×D4C22×D6111yescharacteristic
230C22×C4—21no—
231C22×C4—1221no—
232C22×C4—1221no—
233C22×C4—1221no—
234SD16—1222no—
235SD16—1222no—
236D8—1222no—
237C2×C8—611no—
238C2×C8—611no—
239C2×C8C22×D6111yescharacteristic
240C2×C8C22×D6111yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—611no—
244C4⋊C4—611no—
245C4⋊C4—611no—
246C4⋊C4—611no—
247C4⋊C4—1221no—
248C4⋊C4—1221no—
249C4⋊C4—1221no—
250C4⋊C4—1221no—
251C4⋊C4—1221no—
252C4⋊C4—1221no—
253C4⋊C4—1221no—
254C4⋊C4C22×D6111yescharacteristic
255C4⋊C4C22×D6111yescharacteristic
256C4⋊C4C22×D6111yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—1221no—
259C22⋊C4—1221no—
260C22⋊C4—1221no—
261C22⋊C4—1221no—
262C22⋊C4—1221no—
263C22⋊C4—1221no—
264C22⋊C4—1221no—
265C42—611no—
266C42—611no—
267C42—1221no—
268C42—1221no—
269C42C22×D6111yescharacteristic
270C23—21no—
271C23—1221no—
272Q8—1221no—
273Q8—1221no—
274Q8—1221no—
275Q8—1221no—
276Q8—4881no—
277Q8—2441no—
278D4—21no—
279D4—21no—
280D4—612no—
281D4—1221no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—42no—
286C2×C4—611no—
287C2×C4—611no—
288C2×C4—611no—
289C2×C4—611no—
290C2×C4—1221no—
291C2×C4—1221no—
292C2×C4—1221no—
293C2×C4—4881no—
294C2×C4—4881no—
295C2×C4—2442no—
296C2×C4D4×D6111yescharacteristic
297C2×C4D4×D6111yescharacteristic
298C2×C4C23×D6111yescharacteristic
299C8—21no—
300C8—21no—
301C8—1221no—
302C8—1221no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—1222no—
307C22—2441no—
308C22—2441no—
309C22C2×D4×D6111yescharacteristic
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—1221no—
316C4—1221no—
317C4—1221no—
318C4—1221no—
319C4—2441no—
320C4—2441no—
321C4—2441no—
322C4#41×D6111yescharacteristic
323C4#1451982511yescharacteristic
324C2—81no—
325C2—2442no—
326C2#1684042211yescharacteristic
327C2#1684055811yescharacteristic
328C2#1684056911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#478C2
socleC22×C61C22×D4
hypercenter#478D61
hypocenterC61#3376
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #16840482C2semidirect
2. #16840468C2semidirect
3. #16840132C2semidirect
4. #16840120C2semidirect
5. #16840115C2semidirect
6. #16840068C2semidirect
7. #16840046C2semidirect
10. #16839968C2semidirect
11. #16839891C2semidirect
13. #16839861C2semidirect
14. #16839849C2semidirect
15. C61×#478C2semidirect
171. #478D61semidirect
180. C61#3376semidirect