Finite Group Databasebeta

← #21458266

Subgroups — #21458266

Order 7808.

376 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840450C211yesmaximal, characteristic, complemented
2#16840417C211yesmaximal, characteristic
3#16840172C211yesmaximal, characteristic, complemented
4#16840099C211yesmaximal, characteristic, complemented
5#16840094C211yesmaximal, characteristic, complemented
6#16840084C211yesmaximal, characteristic, complemented
7#16840074C211yesmaximal, characteristic, complemented
8#16840058C211yesmaximal, characteristic, complemented
9#16840007C211yesmaximal, characteristic, complemented
10#16839990C211yesmaximal, characteristic, complemented
11#16839862C211yesmaximal, characteristic, complemented
12#16839832C211yesmaximal, characteristic, complemented
13#16839801C211yesmaximal, characteristic, complemented
14#107×D61C211yesmaximal, characteristic, complemented
15C61×#478C211yesmaximal, characteristic, complemented
16C2×#11758222—21no—
17C2×#11758200C2211yescharacteristic
18C2×#11758189C2211yescharacteristic
19C2×C8×D61C2211yescharacteristic
20#14519777C2211yescharacteristic
21#14519772—21no—
22#14519768—21no—
23#14519762—21no—
24#14519759—21no—
25#14519759—21no—
26#14519757C2211yescharacteristic
27#14519757C2211yescharacteristic
28#14519756—21no—
29#14519748C2211yescharacteristic
30#14519748C2211yescharacteristic
31C4×Dic122C2211yescharacteristic
32C4×D244C2211yescharacteristic
33#14519735—21no—
34#14519735C2211yescharacteristic
35C4⋊C4×D61C2211yescharacteristic
36C4⋊C4×D61C2211yescharacteristic
37C4⋊C4×D61C2211yescharacteristic
38#14519711C2211yescharacteristic
39#14519711C2211yescharacteristic
40#14519710C2211yescharacteristic
41#14519710C2211yescharacteristic
42#14519710C2211yescharacteristic
43#14519708C2211yescharacteristic
44#14519708C2211yescharacteristic
45#14519702C2211yescharacteristic
46#14519702C2211yescharacteristic
47#14519700C2211yescharacteristic
48#14519698C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519688C2211yescharacteristic
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×C22⋊D61—21no—
62C2×C22⋊D61—21no—
63#11758222—44no—
64C2×D244D411yescharacteristic
65C2×C4×D61—21no—
66C2×C4×D61—21no—
67C2×C4×D61—21no—
68C2×C4×D61C2311yescharacteristic
69C2×C4×D61C2311yescharacteristic
70C2×Dic122—21no—
71C2×Dic122C2311yescharacteristic
72C2×C8×C61C2311yescharacteristic
73C2×C8×C61C2311yescharacteristic
74C4⋊C4×C61—21no—
75C4⋊C4×C61—21no—
76C4⋊C4×C61C2311yescharacteristic
77C4⋊C4×C61C2311yescharacteristic
78C4⋊C4×C61C2311yescharacteristic
79C22⋊C4×C61—21no—
80C42×C61C2311yescharacteristic
81C22⋊Dic61—21no—
82C22⋊Dic61—21no—
83#11758200—22no—
84#11758198—21no—
85#11758198—21no—
86#11758198—21no—
87#11758198D411yescharacteristic
88#11758198D411yescharacteristic
89C4⋊Dic61—21no—
90C4⋊Dic61—21no—
91C4⋊Dic61—21no—
92C4⋊Dic61D411yescharacteristic
93C4⋊Dic61C2311yescharacteristic
94C4⋊Dic61C2311yescharacteristic
95C4⋊Dic61C2311yescharacteristic
96#11758196—21no—
97#11758196—21no—
98#11758196—21no—
99#11758196—21no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102C2×#92418C2311yescharacteristic
103C2×#92418C2311yescharacteristic
104#11758189—22no—
105C8×D61—22no—
106C23×C61—21no—
107C22×D61C2×D411yescharacteristic
108C22×D61C2×D411yescharacteristic
109D4×C61—21no—
110D4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—42no—
115C2×C4×C61C2×D411yescharacteristic
116C2×C4×C61C2×D411yescharacteristic
117C2×C4×C61C2411yescharacteristic
118C22⋊D61—42no—
119C22⋊D61—42no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61C2×D411yescharacteristic
125C2×Dic61C2×D411yescharacteristic
126D244—22no—
127C4×D61—21no—
128C4×D61—21no—
129C4×D61—21no—
130C4×D61—21no—
131C4×D61—42no—
132C4×D61—42no—
133C4×D61—42no—
134Dic122—21no—
135Dic122—21no—
136Dic122—42no—
137C8×C61—21no—
138C8×C61—21no—
139#92418—21no—
140#92418#4112yescomplemented
141C22×C61—41no—
142C22×C61—41no—
143C22×C61—41no—
144C22×C61C22×D411yescharacteristic
145C2×D61—21no—
146C2×D61—21no—
147C2×D61—21no—
148C2×D61—21no—
149C2×D61—21no—
150C2×D61AGL(1,ℤ/8)12yes—
151C4×C61—21no—
152C4×C61—21no—
153C4×C61—41no—
154C4×C61—41no—
155C4×C61—41no—
156C4×C61C2×#4111yescharacteristic
157C4×C612−1+411yescharacteristic
158Dic61—21no—
159Dic61—21no—
160Dic61—41no—
161Dic61—41no—
162Dic61—41no—
163Dic61—41no—
164#3343—611nomaximal, Sylow
165C2×C61—81no—
166C2×C61#54711yescharacteristic
167C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
168C2×C61#57811yescharacteristic
169D61—22no—
170D61—41no—
171#552—611no—
172#547—611no—
173#501—611no—
174#484—611no—
175#483—611no—
176#482—611no—
177#480—611no—
178#478D6111yescharacteristic, complemented
179#477—611no—
180#468—611no—
181#465—611no—
182#440—611no—
183#435—611no—
184#428—611no—
185C2×#107—611no—
186C61#334311yescharacteristic, complemented, Sylow
187C2×#41—1221no—
188C2×SD16—611no—
189C2×M16—611no—
190C22×C8—611no—
191C4⋊Q8—611no—
192#126—1221no—
193#125—1221no—
194#125C2×D6111yescharacteristic
195#123—1221no—
196#123—1221no—
197#123—1221no—
198C22⋊Q8—611no—
199C22⋊Q8—611no—
200C22⋊Q8—1221no—
201#121—611no—
202#121—611no—
203C4×Q8—611no—
204C4×D4—611no—
205C4×D4C2×D6111yescharacteristic
206#117—611no—
207#117—1221no—
208C2×C4⋊C4—611no—
209C2×C4⋊C4—611no—
210C2×C4⋊C4—611no—
211#107—611no—
212#107—611no—
213#107—611no—
214#107—611no—
215#107—611no—
216#107C2×D6111yescharacteristic
217#106—611no—
218#106—611no—
219#106C2×D6111yescharacteristic
220C4⋊C8C2×D6111yescharacteristic
221#103—611no—
222#103—611no—
223#103—611no—
224#102—611no—
225#102C2×D6111yescharacteristic
226#102C2×D6111yescharacteristic
227C22⋊C8—611no—
228C22⋊C8—611no—
229#97—611no—
230#41—2444no—
231C2×Q8—611no—
232C2×Q8—1221no—
233C2×D4—611no—
234C2×D4—1221no—
235C2×D4—1221no—
236C2×D4C22×D6111yescharacteristic
237C22×C4—21no—
238C22×C4—611no—
239C22×C4—611no—
240C22×C4—1221no—
241C22×C4—1221no—
242C22×C4—1221no—
243SD16—1222no—
244M16—1222no—
245C2×C8—611no—
246C2×C8—611no—
247C2×C8—1222no—
248C2×C8C22×D6111yescharacteristic
249C2×C8C22×D6111yescharacteristic
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—611no—
253C4⋊C4—611no—
254C4⋊C4—611no—
255C4⋊C4—611no—
256C4⋊C4—1221no—
257C4⋊C4—1221no—
258C4⋊C4—1221no—
259C4⋊C4—1221no—
260C4⋊C4—1221no—
261C4⋊C4—1221no—
262C4⋊C4—1221no—
263C4⋊C4C22×D6111yescharacteristic
264C4⋊C4C22×D6111yescharacteristic
265C4⋊C4C22×D6111yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—611no—
268C22⋊C4—611no—
269C22⋊C4—1221no—
270C22⋊C4—1221no—
271C22⋊C4—1221no—
272C22⋊C4—1221no—
273C22⋊C4—1221no—
274C42—1221no—
275C42—1221no—
276C42C22×D6111yescharacteristic
277C23—21no—
278C23—611no—
279C23—611no—
280Q8—1221no—
281Q8—1221no—
282Q8—2442no—
283D4—21no—
284D4—21no—
285D4—1222no—
286D4—2442no—
287D4—2442no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—42no—
292C2×C4—611no—
293C2×C4—611no—
294C2×C4—1221no—
295C2×C4—1221no—
296C2×C4—1221no—
297C2×C4—1221no—
298C2×C4—1221no—
299C2×C4—1221no—
300C2×C4—1221no—
301C2×C4—1221no—
302C2×C4—2442no—
303C2×C4—2442no—
304C2×C4—2442no—
305C2×C4D4×D6111yescharacteristic
306C2×C4D4×D6111yescharacteristic
307C2×C4C23×D6111yescharacteristic
308C8—21no—
309C8—21no—
310C8—612no—
311C8—1221no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—612no—
316C22—1221no—
317C22—1221no—
318C22—1221no—
319C22—1221no—
320C22—1221no—
321C22C2×D4×D6111yescharacteristic
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—1221no—
328C4—1221no—
329C4—2441no—
330C4—2441no—
331C4—2441no—
332C4—2441no—
333C4#41×D6111yescharacteristic
334C4#1451982511yescharacteristic
335C2—81no—
336C2—1222no—
337C2—2441no—
338C2#1684041411yescharacteristic
339C2AGL(1,ℤ/8)×D6111yescharacteristic
340C2#1684057611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#478C2
socleC22×C61C22×D4
hypercenter#478D61
hypocenterC61#3343
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. #16840450C2semidirect
3. #16840172C2semidirect
4. #16840099C2semidirect
5. #16840094C2semidirect
6. #16840084C2semidirect
7. #16840074C2semidirect
8. #16840058C2semidirect
9. #16840007C2semidirect
10. #16839990C2semidirect
11. #16839862C2semidirect
12. #16839832C2semidirect
13. #16839801C2semidirect
14. #107×D61C2semidirect
15. C61×#478C2semidirect
140. #92418#41semidirect
178. #478D61semidirect
186. C61#3343semidirect