Finite Group Databasebeta

← #21458355

Subgroups — #21458355

Order 7808.

336 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840483C211yesmaximal, characteristic
2#16840446C211yesmaximal, characteristic
3#16840170C211yesmaximal, characteristic, complemented
4#16840102C211yesmaximal, characteristic, complemented
5#16840100C211yesmaximal, characteristic, complemented
6#16840100C211yesmaximal, characteristic, complemented
7#16840096C211yesmaximal, characteristic, complemented
8#16840071C211yesmaximal, characteristic, complemented
9#16840055C211yesmaximal, characteristic, complemented
10#16840017C211yesmaximal, characteristic, complemented
11#16839869C211yesmaximal, characteristic, complemented
12#16839833C211yesmaximal, characteristic
13#16839803C211yesmaximal, characteristic, complemented
14#16839800C211yesmaximal, characteristic, complemented
15C61×#467C211yesmaximal, characteristic, complemented
16C2×#11758189C2211yescharacteristic
17#14519776C2211yescharacteristic
18#14519772—21no—
19#14519770—21no—
20#14519770—21no—
21#14519768C2211yescharacteristic
22#14519767—21no—
23#14519763—21no—
24#14519759—21no—
25#14519753C2211yescharacteristic
26#14519753C2211yescharacteristic
27Q8×Dic61C2211yescharacteristic
28Q8×Dic61C2211yescharacteristic
29#14519742—21no—
30C4×C22⋊D61C2211yescharacteristic
31#14519736C2211yescharacteristic
32#14519736C2211yescharacteristic
33#14519735—21no—
34#14519735C2211yescharacteristic
35C4⋊C4×D61C2211yescharacteristic
36#14519711C2211yescharacteristic
37#14519711C2211yescharacteristic
38#14519710C2211yescharacteristic
39#14519710C2211yescharacteristic
40#14519709C2211yescharacteristic
41#14519709C2211yescharacteristic
42#14519708C2211yescharacteristic
43#14519708C2211yescharacteristic
44#14519706C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519701C2211yescharacteristic
47#14519701C2211yescharacteristic
48#14519701C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519687C2211yescharacteristic
52C2×Q16×C61C2211yescharacteristic
53C22×C8×C61C2211yescharacteristic
54C22⋊Q8×C61C2211yescharacteristic
55C22⋊Q8×C61C2211yescharacteristic
56#107×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#103×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×Q8×C61C2311yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C2×C22⋊D61D411yescharacteristic
63C2×C4×D61—21no—
64C2×C4×D61C2311yescharacteristic
65C2×Dic122—21no—
66Q16×C61—22no—
67C2×C8×C61—22no—
68C2×C8×C61C2311yescharacteristic
69C2×C8×C61C2311yescharacteristic
70C4⋊C4×C61—21no—
71C4⋊C4×C61—21no—
72C4⋊C4×C61C2311yescharacteristic
73C4⋊C4×C61C2311yescharacteristic
74C22⋊C4×C61—21no—
75C22⋊C4×C61—21no—
76C22⋊Dic61—21no—
77C22⋊Dic61—21no—
78C22⋊Dic61D411yescharacteristic
79#11758198—21no—
80#11758198—21no—
81#11758198—21no—
82#11758198D411yescharacteristic
83C4⋊Dic61—21no—
84C4⋊Dic61—21no—
85C4⋊Dic61—21no—
86C4⋊Dic61C2311yescharacteristic
87C4⋊Dic61C2311yescharacteristic
88C4⋊Dic61C2311yescharacteristic
89C4⋊Dic61C2311yescharacteristic
90#11758196—21no—
91#11758196—21no—
92#11758196—21no—
93#11758196—21no—
94#11758196—21no—
95#11758196D411yescharacteristic
96C4×Dic61—21no—
97C4×Dic61—21no—
98C4×Dic61—21no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61C2311yescharacteristic
102C2×#92418C2311yescharacteristic
103C2×#92418C2311yescharacteristic
104#11758189—22no—
105C23×C61C2×D411yescharacteristic
106C22×D61C2×D411yescharacteristic
107Q8×C61—21no—
108Q8×C61—21no—
109Q8×C61—21no—
110Q8×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61C2×D411yescharacteristic
118C2×C4×C61C2411yescharacteristic
119C22⋊D61—41no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61C2×D411yescharacteristic
125C2×Dic61C2×D411yescharacteristic
126C2×Dic61C2×D411yescharacteristic
127C4×D61—21no—
128C4×D61—21no—
129C4×D61—42no—
130Dic122—42no—
131C8×C61—21no—
132C8×C61#4112yes—
133#92418—21no—
134#92418—21no—
135C22×C61—21no—
136C22×C61—21no—
137C22×C61—21no—
138C22×C61C22×D411yescharacteristic
139C2×D61—21no—
140C2×D61—21no—
141C2×D61—21no—
142C4×C61—21no—
143C4×C61—41no—
144C4×C61—41no—
145C4×C61—41no—
146C4×C61—41no—
147C4×C61C2×#4111yescharacteristic
148C4×C612−1+411yescharacteristic
149Dic61—21no—
150Dic61—21no—
151Dic61—21no—
152Dic61—41no—
153Dic61—41no—
154Dic61—41no—
155Dic61—41no—
156#3349—611nomaximal, Sylow
157C2×C61—41no—
158C2×C61#54711yescharacteristic
159C2×C61#57511yescharacteristic
160C2×C61#57811yescharacteristic
161D61—41no—
162#556—611no—
163#552—611no—
164#501—611no—
165#485—611no—
166#485—611no—
167#485—611no—
168#484—611no—
169#479—611no—
170#477—611no—
171#470—611no—
172#467D6111yescharacteristic, complemented
173#441—611no—
174#435—611no—
175#428—611no—
176#427—611no—
177C61#334911yescharacteristic, complemented, Sylow
178C2×Q16C2×D6111yescharacteristic
179C2×M16—611no—
180C22×C8C2×D6111yescharacteristic
181C4⋊Q8—611no—
182#126—1221no—
183#126—1221no—
184#126—1221no—
185#125—611no—
186#125—1221no—
187#124—1221no—
188#123—1221no—
189C22⋊Q8—611no—
190C22⋊Q8—611no—
191C22⋊Q8C2×D6111yescharacteristic
192C22⋊Q8C2×D6111yescharacteristic
193C4×Q8—611no—
194C4×Q8—611no—
195C4×Q8—1221no—
196C4×D4—611no—
197#117—611no—
198#117—611no—
199#117—611no—
200#117—1221no—
201C2×C4⋊C4—611no—
202#107—611no—
203#107—611no—
204#107—611no—
205#107—611no—
206#107C2×D6111yescharacteristic
207#106—611no—
208#106—611no—
209#106—611no—
210#106—611no—
211C4⋊C8—611no—
212#103—611no—
213#103—611no—
214#103—611no—
215#103—611no—
216#103C2×D6111yescharacteristic
217#103C2×D6111yescharacteristic
218C22⋊C8—611no—
219C22⋊C8—611no—
220#97—611no—
221C2×Q8—1221no—
222C2×Q8C22×D6111yescharacteristic
223C2×Q8C22×D6111yescharacteristic
224C2×D4—611no—
225C22×C4—611no—
226C22×C4—1221no—
227C22×C4C22×D6111yescharacteristic
228Q16—22no—
229M16—1222no—
230C2×C8—22no—
231C2×C8—611no—
232C2×C8—611no—
233C2×C8C22×D6111yescharacteristic
234C2×C8C22×D6111yescharacteristic
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—611no—
238C4⋊C4—611no—
239C4⋊C4—611no—
240C4⋊C4—611no—
241C4⋊C4—611no—
242C4⋊C4—1221no—
243C4⋊C4—1221no—
244C4⋊C4—1221no—
245C4⋊C4—1221no—
246C4⋊C4—1221no—
247C4⋊C4—1221no—
248C4⋊C4—1221no—
249C4⋊C4—1221no—
250C4⋊C4C22×D6111yescharacteristic
251C4⋊C4C22×D6111yescharacteristic
252C22⋊C4—21no—
253C22⋊C4—21no—
254C22⋊C4—611no—
255C22⋊C4—611no—
256C22⋊C4—1221no—
257C22⋊C4—1221no—
258C22⋊C4—1221no—
259C22⋊C4—1221no—
260C22⋊C4—1221no—
261C42—611no—
262C42—1221no—
263C42—1221no—
264C42—1221no—
265C42—1221no—
266C42—1221no—
267C23—611no—
268C23D4×D6111yescharacteristic
269Q8—21no—
270Q8—21no—
271Q8—21no—
272Q8—21no—
273Q8—2442no—
274D4—2441no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—611no—
282C2×C4—611no—
283C2×C4—611no—
284C2×C4—1221no—
285C2×C4—1221no—
286C2×C4—1221no—
287C2×C4—1221no—
288C2×C4—1221no—
289C2×C4—1221no—
290C2×C4—2442no—
291C2×C4D4×D6111yescharacteristic
292C2×C4C23×D6111yescharacteristic
293C8—21no—
294C8—1221no—
295C8—1221no—
296C8#1175822412yes—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—1221no—
301C22—1221no—
302C22—1221no—
303C22C2×D4×D6111yescharacteristic
304C4—21no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—1221no—
310C4—1221no—
311C4—1221no—
312C4—2441no—
313C4—2441no—
314C4—2441no—
315C4—2441no—
316C4C2×#1175822411yescharacteristic
317C4#1451982411yescharacteristic
318C2—41no—
319C2—2441no—
320C2#1684041211yescharacteristic
321C2#1684055911yescharacteristic
322C2#1684057511yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#467C2
socleC22×C61C22×D4
hypercenter#467D61
hypocenterC61#3349
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
3. #16840170C2semidirect
4. #16840102C2semidirect
5. #16840100C2semidirect
6. #16840100C2semidirect
7. #16840096C2semidirect
8. #16840071C2semidirect
9. #16840055C2semidirect
10. #16840017C2semidirect
11. #16839869C2semidirect
13. #16839803C2semidirect
14. #16839800C2semidirect
15. C61×#467C2semidirect
172. #467D61semidirect
177. C61#3349semidirect