Finite Group Databasebeta

← #21458228

Subgroups — #21458228

Order 7808.

352 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840480C211yesmaximal, characteristic, complemented
2#16840475C211yesmaximal, characteristic
3#16840159C211yesmaximal, characteristic, complemented
4#16840105C211yesmaximal, characteristic, complemented
5#16840103C211yesmaximal, characteristic, complemented
6#16840089C211yesmaximal, characteristic, complemented
7#16840086C211yesmaximal, characteristic, complemented
8#16840056C211yesmaximal, characteristic, complemented
9#16840041C211yesmaximal, characteristic, complemented
10#16839992C211yesmaximal, characteristic, complemented
11#16839991C211yesmaximal, characteristic, complemented
12#16839849C211yesmaximal, characteristic, complemented
13C8×C22⋊D61C211yesmaximal, characteristic, complemented
14#16839797C211yesmaximal, characteristic, complemented
15C61×#427C211yesmaximal, characteristic, complemented
16C2×#11758190C2211yescharacteristic
17C2×C8×D61C2211yescharacteristic
18#14519776C2211yescharacteristic
19#14519776C2211yescharacteristic
20#14519771—21no—
21#14519770—21no—
22#14519765—21no—
23#14519763—21no—
24#14519763—21no—
25#14519757C2211yescharacteristic
26#14519756C2211yescharacteristic
27#14519752C2211yescharacteristic
28#14519751C2211yescharacteristic
29#14519750—21no—
30C4×Dic122—21no—
31#14519742C2211yescharacteristic
32#14519739C2211yescharacteristic
33C4×C22⋊D61C2211yescharacteristic
34#14519735C2211yescharacteristic
35#14519735C2211yescharacteristic
36#14519734—21no—
37#14519710C2211yescharacteristic
38#14519710C2211yescharacteristic
39#14519709C2211yescharacteristic
40#14519708C2211yescharacteristic
41#14519708C2211yescharacteristic
42#14519706C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519700C2211yescharacteristic
45#14519700C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519697C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519689C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C22×C8×C61C2211yescharacteristic
53#117×C61C2211yescharacteristic
54#117×C61C2211yescharacteristic
55#107×C61C2211yescharacteristic
56#107×C61C2211yescharacteristic
57#106×C61C2211yescharacteristic
58#106×C61C2211yescharacteristic
59C22×C4×C61C2311yescharacteristic
60C2×C22⋊D61—21no—
61C2×C22⋊D61D411yescharacteristic
62C2×D244—21no—
63C2×D244C2311yescharacteristic
64C2×C4×D61—21no—
65C2×C4×D61C2311yescharacteristic
66C2×Dic122—21no—
67C2×Dic122—21no—
68C2×Dic122C2311yescharacteristic
69C2×C8×C61—22no—
70C2×C8×C61C2311yescharacteristic
71C2×C8×C61C2311yescharacteristic
72C4⋊C4×C61C2311yescharacteristic
73C4⋊C4×C61C2311yescharacteristic
74C4⋊C4×C61C2311yescharacteristic
75C4⋊C4×C61C2311yescharacteristic
76C22⋊C4×C61—21no—
77C22⋊C4×C61—21no—
78C42×C61—21no—
79C42×C61—21no—
80C22⋊Dic61—21no—
81C22⋊Dic61D411yescharacteristic
82#11758198—21no—
83#11758198—21no—
84#11758198—21no—
85#11758198—21no—
86#11758198—21no—
87#11758198—21no—
88#11758198D411yescharacteristic
89C4⋊Dic61—21no—
90C4⋊Dic61C2311yescharacteristic
91C4⋊Dic61C2311yescharacteristic
92#11758196—21no—
93#11758196—21no—
94#11758196—21no—
95#11758196—21no—
96#11758196D411yescharacteristic
97C4×Dic61—21no—
98C4×Dic61—21no—
99C4×Dic61—21no—
100C4×Dic61C2311yescharacteristic
101C2×#92418C2311yescharacteristic
102C2×#92418C2311yescharacteristic
103#11758190—22no—
104C8×D61—22no—
105C23×C61C2×D411yescharacteristic
106C22×D61—21no—
107C22×D61C2×D411yescharacteristic
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61C2×D411yescharacteristic
115C2×C4×C61C2411yescharacteristic
116C22⋊D61—22no—
117C22⋊D61—81no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61C2×D411yescharacteristic
122C2×Dic61C2×D411yescharacteristic
123C2×Dic61C2×D411yescharacteristic
124D244—21no—
125D244—21no—
126D244—81no—
127C4×D61—21no—
128C4×D61—21no—
129C4×D61—42no—
130Dic122—21no—
131Dic122—21no—
132Dic122—42no—
133Dic122—81no—
134C8×C61—21no—
135C8×C61#4112yes—
136#92418—21no—
137#92418—21no—
138C22×C61—21no—
139C22×C61—21no—
140C22×C61—21no—
141C22×C61C22×D411yescharacteristic
142C2×D61—21no—
143C2×D61—21no—
144C2×D61—21no—
145C2×D61—41no—
146C2×D61—41no—
147C2×D61—41no—
148C4×C61—21no—
149C4×C61—41no—
150C4×C61—41no—
151C4×C61—41no—
152C4×C61—41no—
153C4×C61C2×#4111yescharacteristic
154C4×C612−1+411yescharacteristic
155Dic61—21no—
156Dic61—21no—
157Dic61—41no—
158Dic61—41no—
159Dic61—41no—
160Dic61#13512yes—
161#3340—611nomaximal, Sylow
162C2×C61—41no—
163C2×C61#54711yescharacteristic
164C2×C61C2×#13511yescharacteristic
165C2×C61#57711yescharacteristic
166D61—41no—
167D61—81no—
168#556—611no—
169#555—611no—
170#498—611no—
171#485—611no—
172#485—611no—
173#482—611no—
174#482—611no—
175#477—611no—
176#474—611no—
177#465—611no—
178#465—611no—
179C4×SD16—611no—
180C8×D4—611no—
181#427—611no—
182#427D6111yescharacteristic, complemented
183C61#334011yescharacteristic, complemented, Sylow
184C2×SD16—611no—
185C22×C8—611no—
186C22×C8C2×D6111yescharacteristic
187C4⋊Q8—611no—
188C4⋊Q8—611no—
189#126—1221no—
190#126—1221no—
191#124—1221no—
192#124—1221no—
193#124—1221no—
194C22⋊Q8—611no—
195C22⋊Q8—611no—
196#121—611no—
197#121—611no—
198#121—1221no—
199C4×Q8—611no—
200C4×Q8—1221no—
201C4×D4—611no—
202C4×D4—611no—
203#117—611no—
204#117—611no—
205#117—1221no—
206#117C2×D6111yescharacteristic
207#117C2×D6111yescharacteristic
208#107—611no—
209#107—611no—
210#107C2×D6111yescharacteristic
211#107C2×D6111yescharacteristic
212#106—611no—
213#106—611no—
214#106—611no—
215#106C2×D6111yescharacteristic
216#106C2×D6111yescharacteristic
217C4⋊C8—611no—
218#103—611no—
219#103—611no—
220#103—611no—
221#102—611no—
222#102—611no—
223#102—611no—
224C22⋊C8—611no—
225C22⋊C8—611no—
226C4×C8—611no—
227C2×Q8—611no—
228C2×Q8—1221no—
229C2×Q8—1221no—
230C2×D4—611no—
231C2×D4—611no—
232C2×D4—1221no—
233C2×D4—1221no—
234C22×C4—611no—
235C22×C4—1221no—
236C22×C4C22×D6111yescharacteristic
237SD16—1222no—
238C2×C8—22no—
239C2×C8—611no—
240C2×C8—611no—
241C2×C8—1222no—
242C2×C8C22×D6111yescharacteristic
243C2×C8C22×D6111yescharacteristic
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⋊C4C22×D6111yescharacteristic
253C4⋊C4C22×D6111yescharacteristic
254C4⋊C4C22×D6111yescharacteristic
255C4⋊C4C22×D6111yescharacteristic
256C22⋊C4—21no—
257C22⋊C4—21no—
258C22⋊C4—611no—
259C22⋊C4—611no—
260C22⋊C4—1221no—
261C22⋊C4—1221no—
262C22⋊C4—1221no—
263C22⋊C4—1221no—
264C22⋊C4—1221no—
265C22⋊C4—1221no—
266C22⋊C4—1221no—
267C42—21no—
268C42—21no—
269C42—611no—
270C42—1221no—
271C42—1221no—
272C42—1221no—
273C23—611no—
274C23—1221no—
275C23D4×D6111yescharacteristic
276Q8—1221no—
277Q8—1221no—
278Q8—4881no—
279Q8—2442no—
280D4—1222no—
281D4—1221no—
282D4—1221no—
283D4—4881no—
284D4—4881no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—611no—
292C2×C4—611no—
293C2×C4—611no—
294C2×C4—1221no—
295C2×C4—1221no—
296C2×C4—1221no—
297C2×C4—1221no—
298C2×C4—1221no—
299C2×C4—2442no—
300C2×C4D4×D6111yescharacteristic
301C2×C4C23×D6111yescharacteristic
302C8—21no—
303C8—1221no—
304C8—1221no—
305C8#1175822212yes—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—1221no—
310C22—1221no—
311C22—1221no—
312C22—2441no—
313C22—2441no—
314C22—2441no—
315C22C2×D4×D6111yescharacteristic
316C4—21no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—612no—
322C4—1221no—
323C4—1221no—
324C4—2441no—
325C4—2441no—
326C4—2441no—
327C4C2×#1175822211yescharacteristic
328C4#1451982511yescharacteristic
329C2—41no—
330C2—4881no—
331C2—2441no—
332C2#1684041311yescharacteristic
333C2#135×D6111yescharacteristic
334C2#1684056911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#427C2
socleC22×C61C22×D4
hypercenter#427D61
hypocenterC61#3340
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
1. #16840480C2semidirect
3. #16840159C2semidirect
4. #16840105C2semidirect
5. #16840103C2semidirect
6. #16840089C2semidirect
7. #16840086C2semidirect
8. #16840056C2semidirect
9. #16840041C2semidirect
10. #16839992C2semidirect
11. #16839991C2semidirect
12. #16839849C2semidirect
13. C8×C22⋊D61C2semidirect
14. #16839797C2semidirect
15. C61×#427C2semidirect
182. #427D61semidirect
183. C61#3340semidirect