Finite Group Databasebeta

← #21458361

Subgroups — #21458361

Order 7808.

348 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#16840485C211yesmaximal, characteristic, complemented
2#16840465C211yesmaximal, characteristic
3#16840172C211yesmaximal, characteristic, complemented
4#16840101C211yesmaximal, characteristic, complemented
5#16840091C211yesmaximal, characteristic, complemented
6#16840089C211yesmaximal, characteristic, complemented
7#16840088C211yesmaximal, characteristic, complemented
8#16840053C211yesmaximal, characteristic, complemented
9#16840011C211yesmaximal, characteristic, complemented
10#16839994C211yesmaximal, characteristic, complemented
11#16839860C211yesmaximal, characteristic, complemented
12#16839832C211yesmaximal, characteristic, complemented
13#16839803C211yesmaximal, characteristic, complemented
14#16839797C211yesmaximal, characteristic, complemented
15C61×#479C211yesmaximal, characteristic, complemented
16C2×#11758201C2211yescharacteristic
17C2×#11758189C2211yescharacteristic
18C2×C8×D61C2211yescharacteristic
19#14519777C2211yescharacteristic
20#14519772—21no—
21#14519772—21no—
22#14519772—21no—
23#14519765—21no—
24#14519762—21no—
25#14519753C2211yescharacteristic
26#14519753C2211yescharacteristic
27#14519752—21no—
28#14519752C2211yescharacteristic
29#14519752C2211yescharacteristic
30C4×Dic122—21no—
31C4×D244C2211yescharacteristic
32C4×D244C2211yescharacteristic
33#14519739—21no—
34#14519735C2211yescharacteristic
35#14519735C2211yescharacteristic
36#14519735C2211yescharacteristic
37C4⋊C4×D61C2211yescharacteristic
38#14519710C2211yescharacteristic
39#14519710C2211yescharacteristic
40#14519710C2211yescharacteristic
41#14519709C2211yescharacteristic
42#14519709C2211yescharacteristic
43#14519708C2211yescharacteristic
44#14519708C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519699C2211yescharacteristic
48#14519697C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519688C2211yescharacteristic
52#125×C61C2211yescharacteristic
53C4×Q8×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic
55#106×C61C2211yescharacteristic
56C4⋊C8×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#103×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×D244—21no—
61C2×D244—21no—
62C2×D244D411yescharacteristic
63C2×D244C2311yescharacteristic
64C2×C4×D61—21no—
65C2×C4×D61—21no—
66C2×C4×D61C2311yescharacteristic
67C2×C4×D61C2311yescharacteristic
68C2×Dic122—21no—
69C2×C8×C61C2311yescharacteristic
70C2×C8×C61C2311yescharacteristic
71C4⋊C4×C61—21no—
72C4⋊C4×C61—21no—
73C4⋊C4×C61—21no—
74C4⋊C4×C61C2311yescharacteristic
75C4⋊C4×C61C2311yescharacteristic
76C4⋊C4×C61C2311yescharacteristic
77C42×C61—21no—
78C42×C61C2311yescharacteristic
79#11758201—22no—
80#11758198—21no—
81#11758198—21no—
82#11758198—21no—
83#11758198—21no—
84#11758198—21no—
85#11758198—21no—
86#11758198—21no—
87#11758198—21no—
88#11758198D411yescharacteristic
89#11758198D411yescharacteristic
90C4⋊Dic61—21no—
91C4⋊Dic61D411yescharacteristic
92C4⋊Dic61C2311yescharacteristic
93C4⋊Dic61C2311yescharacteristic
94C4⋊Dic61C2311yescharacteristic
95#11758196—21no—
96#11758196—21no—
97#11758196—21no—
98C4×Dic61—21no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C2×#92418C2311yescharacteristic
102C2×#92418C2311yescharacteristic
103#11758189—22no—
104C8×D61—22no—
105C22×D61—21no—
106C22×D61C2×D411yescharacteristic
107C22×D61C2×D411yescharacteristic
108Q8×C61—21no—
109Q8×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61C2×D411yescharacteristic
115C2×C4×C61C2×D411yescharacteristic
116C2×C4×C61C2411yescharacteristic
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61C2×D411yescharacteristic
121C2×Dic61C2×D411yescharacteristic
122D244—21no—
123D244—21no—
124D244—41no—
125D244—42no—
126D244—81no—
127C4×D61—21no—
128C4×D61—21no—
129C4×D61—21no—
130C4×D61—21no—
131C4×D61—81no—
132C4×D61—81no—
133Dic122—42no—
134C8×C61—21no—
135C8×C61—21no—
136#92418—21no—
137#92418#4112yes—
138C22×C61C22×D411yescharacteristic
139C2×D61—21no—
140C2×D61—21no—
141C2×D61—21no—
142C2×D61—21no—
143C2×D61—21no—
144C2×D61—21no—
145C2×D61—41no—
146C2×D61—41no—
147C2×D61—41no—
148C4×C61—21no—
149C4×C61—21no—
150C4×C61—41no—
151C4×C61—41no—
152C4×C61—41no—
153C4×C61—41no—
154C4×C61C2×#4111yescharacteristic
155C4×C612−1+411yescharacteristic
156Dic61—21no—
157Dic61—21no—
158Dic61—41no—
159Dic61—41no—
160Dic61—41no—
161#3350—611nomaximal, Sylow
162C2×C61#54711yescharacteristic
163C2×C61#57511yescharacteristic
164C2×C61#57711yescharacteristic
165D61—41no—
166D61—41no—
167D61—81no—
168#556—611no—
169#553—611no—
170#501—611no—
171#485—611no—
172#483—611no—
173#482—611no—
174#482—611no—
175#479D6111yescharacteristic, complemented
176#476—611no—
177#468—611no—
178#465—611no—
179#440—611no—
180#435—611no—
181#428—611no—
182#427—611no—
183C61#335011yescharacteristic, complemented, Sylow
184C2×SD16—611no—
185C2×M16—611no—
186C22×C8—611no—
187C4⋊Q8—611no—
188#126—1221no—
189#126—1221no—
190#126—1221no—
191#125C2×D6111yescharacteristic
192#124—1221no—
193#123—1221no—
194C22⋊Q8—611no—
195C22⋊Q8—611no—
196#121—611no—
197#121—611no—
198#121—1221no—
199C4×Q8—1221no—
200C4×Q8C2×D6111yescharacteristic
201C4×D4—611no—
202C4×D4—611no—
203C4×D4—1221no—
204#117—611no—
205#117—611no—
206#117—611no—
207C2×C4⋊C4—611no—
208#107—611no—
209#107—611no—
210#107—611no—
211#107C2×D6111yescharacteristic
212#106—611no—
213#106—611no—
214#106—611no—
215#106—611no—
216#106C2×D6111yescharacteristic
217C4⋊C8C2×D6111yescharacteristic
218#103—611no—
219#103C2×D6111yescharacteristic
220#103C2×D6111yescharacteristic
221#102—611no—
222#102—611no—
223#102—611no—
224C22⋊C8—611no—
225C22⋊C8—611no—
226#97—611no—
227C2×Q8—1221no—
228C2×Q8C22×D6111yescharacteristic
229C2×D4—611no—
230C2×D4—611no—
231C2×D4—1221no—
232C2×D4—1221no—
233C22×C4—611no—
234C22×C4—611no—
235C22×C4—1221no—
236C22×C4—1221no—
237SD16—1222no—
238M16—1222no—
239C2×C8—611no—
240C2×C8—611no—
241C2×C8—1222no—
242C2×C8C22×D6111yescharacteristic
243C2×C8C22×D6111yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—611no—
248C4⋊C4—611no—
249C4⋊C4—611no—
250C4⋊C4—611no—
251C4⋊C4—1221no—
252C4⋊C4—1221no—
253C4⋊C4—1221no—
254C4⋊C4—1221no—
255C4⋊C4C22×D6111yescharacteristic
256C4⋊C4C22×D6111yescharacteristic
257C4⋊C4C22×D6111yescharacteristic
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—
267C22⋊C4—1221no—
268C42—21no—
269C42—1221no—
270C42—1221no—
271C42—1221no—
272C42C22×D6111yescharacteristic
273C23—611no—
274C23—611no—
275C23—1221no—
276Q8—21no—
277Q8—21no—
278Q8—2442no—
279D4—1221no—
280D4—1221no—
281D4—4881no—
282D4—2441no—
283D4—2442no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—611no—
289C2×C4—611no—
290C2×C4—1221no—
291C2×C4—1221no—
292C2×C4—1221no—
293C2×C4—1221no—
294C2×C4—1221no—
295C2×C4—1221no—
296C2×C4—1221no—
297C2×C4—4881no—
298C2×C4—4881no—
299C2×C4D4×D6111yescharacteristic
300C2×C4D4×D6111yescharacteristic
301C2×C4C23×D6111yescharacteristic
302C8—21no—
303C8—21no—
304C8—612no—
305C8—1221no—
306C22—1221no—
307C22—1221no—
308C22—1221no—
309C22—1221no—
310C22—1221no—
311C22—1221no—
312C22—2441no—
313C22—2441no—
314C22—2441no—
315C22C2×D4×D6111yescharacteristic
316C4—21no—
317C4—21no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—1221no—
323C4—1221no—
324C4—2441no—
325C4—2441no—
326C4—2441no—
327C4#41×D6111yescharacteristic
328C4#1451982511yescharacteristic
329C2—4881no—
330C2—2441no—
331C2—2441no—
332C2#1684041411yescharacteristic
333C2#1684056111yescharacteristic
334C2#1684056911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#479C2
socleC22×C61C22×D4
hypercenter#479D61
hypocenterC61#3350
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #16840485C2semidirect
3. #16840172C2semidirect
4. #16840101C2semidirect
5. #16840091C2semidirect
6. #16840089C2semidirect
7. #16840088C2semidirect
8. #16840053C2semidirect
9. #16840011C2semidirect
10. #16839994C2semidirect
11. #16839860C2semidirect
12. #16839832C2semidirect
13. #16839803C2semidirect
14. #16839797C2semidirect
15. C61×#479C2semidirect
175. #479D61semidirect
183. C61#3350semidirect