Finite Group Databasebeta

← #21457264

Subgroups — #21457264

Order 7808.

346 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840370C211yesmaximal, characteristic, complemented
2#16840368C211yesmaximal, characteristic
3#16840066C211yesmaximal, characteristic, complemented
4#16840065C211yesmaximal, characteristic, complemented
5#16840061C211yesmaximal, characteristic, complemented
6#16840011C211yesmaximal, characteristic, complemented
7#16840009C211yesmaximal, characteristic, complemented
8#16839994C211yesmaximal, characteristic, complemented
9#16839992C211yesmaximal, characteristic, complemented
10#16839966C211yesmaximal, characteristic, complemented
11#16839966C211yesmaximal, characteristic, complemented
12#16839963C211yesmaximal, characteristic, complemented
13#16839962C211yesmaximal, characteristic, complemented
14#16839787C211yesmaximal, characteristic, complemented
15C61×#479C211yesmaximal, characteristic, complemented
16C2×#11758190C2211yescharacteristic
17C2×#11758190C2211yescharacteristic
18C2×#11758201C2211yescharacteristic
19C2×#11758201C2211yescharacteristic
20C2×#11758189C2211yescharacteristic
21C2×C8×D61C2211yescharacteristic
22#14519775C2211yescharacteristic
23#14519774C2211yescharacteristic
24#14519772—21no—
25#14519771—21no—
26#14519769—21no—
27#14519768C2211yescharacteristic
28#14519767—21no—
29#14519762—21no—
30#14519762—21no—
31#14519757C2211yescharacteristic
32#14519753C2211yescharacteristic
33#14519752—21no—
34#14519752—21no—
35#14519752C2211yescharacteristic
36#14519752C2211yescharacteristic
37C4×Dic122C2211yescharacteristic
38#14519739C2211yescharacteristic
39#14519739C2211yescharacteristic
40#14519734C2211yescharacteristic
41#14519710C2211yescharacteristic
42#14519708C2211yescharacteristic
43C4⋊#92418C2211yescharacteristic
44#14519706C2211yescharacteristic
45#14519706C2211yescharacteristic
46#14519700C2211yescharacteristic
47#14519700C2211yescharacteristic
48#14519699C2211yescharacteristic
49#14519699C2211yescharacteristic
50#14519697C2211yescharacteristic
51#14519697C2211yescharacteristic
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×D244—21no—
63C2×D244—21no—
64C2×D244C2311yescharacteristic
65C2×D244C2311yescharacteristic
66C2×C4×D61—21no—
67C2×C4×D61—21no—
68C2×C4×D61C2311yescharacteristic
69C2×Dic122C2311yescharacteristic
70C2×C8×C61C2311yescharacteristic
71C2×C8×C61C2311yescharacteristic
72C4⋊C4×C61—21no—
73C4⋊C4×C61—21no—
74C4⋊C4×C61—21no—
75C4⋊C4×C61C2311yescharacteristic
76C4⋊C4×C61C2311yescharacteristic
77C4⋊C4×C61C2311yescharacteristic
78C42×C61—21no—
79C42×C61C2311yescharacteristic
80#11758201—41no—
81#11758201—41no—
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⋊Dic61—21no—
92C4⋊Dic61C2311yescharacteristic
93#11758196—21no—
94#11758196—21no—
95#11758196—21no—
96#11758196—21no—
97#11758196—21no—
98#11758196D411yescharacteristic
99#11758196D411yescharacteristic
100C4×Dic61—21no—
101C4×Dic61C2311yescharacteristic
102C2×#92418C2311yescharacteristic
103C2×#92418C2311yescharacteristic
104#11758190—41no—
105#11758190—41no—
106#11758189—41no—
107C8×D61—41no—
108C22×D61—21no—
109C22×D61—21no—
110C22×D61C2×D411yescharacteristic
111Q8×C61—21no—
112Q8×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61C2×D411yescharacteristic
118C2×C4×C61C2×D411yescharacteristic
119C2×C4×C61C2411yescharacteristic
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61C2×D411yescharacteristic
123C2×Dic61C2×D411yescharacteristic
124C2×Dic61C2×D411yescharacteristic
125D244—21no—
126D244—21no—
127D244—21no—
128D244—21no—
129D244—81no—
130D244—81no—
131D244—81no—
132D244—81no—
133C4×D61—21no—
134C4×D61—21no—
135C4×D61—81no—
136C4×D61—81no—
137Dic122—21no—
138Dic122—21no—
139C8×C61—21no—
140C8×C61—21no—
141#92418—21no—
142#92418—21no—
143C22×C61C22×D411yescharacteristic
144C2×D61—21no—
145C2×D61—21no—
146C2×D61—21no—
147C2×D61—41no—
148C2×D61—41no—
149C2×D61—41no—
150C2×D61—41no—
151C2×D61—41no—
152C2×D61—41no—
153C4×C61—21no—
154C4×C61—21no—
155C4×C61—41no—
156C4×C61—41no—
157C4×C61—41no—
158C4×C61—41no—
159C4×C61H(5,𝔽2)11yescharacteristic
160C4×C612−1+411yescharacteristic
161Dic61—21no—
162Dic61—21no—
163Dic61—21no—
164Dic61—41no—
165Dic61—41no—
166#3260—611nomaximal, Sylow
167C2×C61#53711yescharacteristic
168C2×C61#57711yescharacteristic
169C2×C61#57711yescharacteristic
170D61—41no—
171D61—81no—
172D61—81no—
173#541—611no—
174#540—611no—
175#479—611no—
176#479D6111yescharacteristic, complemented
177#478—611no—
178#478—611no—
179#468—611no—
180#468—611no—
181#465—611no—
182#465—611no—
183#461—611no—
184#461—611no—
185#460—611no—
186#460—611no—
187#424—611no—
188C61#326011yescharacteristic, complemented, Sylow
189C2×SD16—611no—
190C2×SD16—611no—
191C2×SD16—611no—
192C2×SD16—611no—
193C2×M16—611no—
194C22×C8—611no—
195C4⋊Q8—611no—
196#127—611no—
197#126—1221no—
198#126—1221no—
199#125—611no—
200#125—1221no—
201#125—1221no—
202#125C2×D6111yescharacteristic
203#123—1221no—
204#123—1221no—
205C22⋊Q8—611no—
206C22⋊Q8—611no—
207#121—611no—
208#121—611no—
209#121—1221no—
210#121—1221no—
211C4×Q8—611no—
212C4×Q8C2×D6111yescharacteristic
213C4×D4—611no—
214C4×D4—611no—
215#117—611no—
216#107—611no—
217#107C2×D6111yescharacteristic
218#106—611no—
219#106C2×D6111yescharacteristic
220C4⋊C8—611no—
221C4⋊C8—611no—
222C4⋊C8—611no—
223C4⋊C8C2×D6111yescharacteristic
224#103—611no—
225#103—611no—
226#103C2×D6111yescharacteristic
227#103C2×D6111yescharacteristic
228#102—611no—
229#102—611no—
230#102—611no—
231#102—611no—
232C2×Q8—611no—
233C2×Q8C22×D6111yescharacteristic
234C2×D4—611no—
235C2×D4—611no—
236C2×D4—1221no—
237C2×D4—1221no—
238C2×D4—1221no—
239C2×D4—1221no—
240C22×C4—611no—
241C22×C4—1221no—
242C22×C4—1221no—
243SD16—2441no—
244SD16—2441no—
245SD16—2441no—
246SD16—2441no—
247M16—2441no—
248C2×C8—611no—
249C2×C8—611no—
250C2×C8—2441no—
251C2×C8C22×D6111yescharacteristic
252C2×C8C22×D6111yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—611no—
257C4⋊C4—611no—
258C4⋊C4—611no—
259C4⋊C4—1221no—
260C4⋊C4—1221no—
261C4⋊C4—1221no—
262C4⋊C4—1221no—
263C4⋊C4—1221no—
264C4⋊C4—1221no—
265C4⋊C4—1221no—
266C4⋊C4C22×D6111yescharacteristic
267C4⋊C4C22×D6111yescharacteristic
268C4⋊C4C22×D6111yescharacteristic
269C22⋊C4—611no—
270C22⋊C4—611no—
271C22⋊C4—1221no—
272C22⋊C4—1221no—
273C22⋊C4—1221no—
274C22⋊C4—1221no—
275C22⋊C4—1221no—
276C22⋊C4—1221no—
277C42—21no—
278C42—611no—
279C42—1221no—
280C42C22×D6111yescharacteristic
281C23—611no—
282C23—1221no—
283C23—1221no—
284Q8—21no—
285Q8—21no—
286Q8—1221no—
287Q8—1221no—
288D4—1221no—
289D4—1221no—
290D4—1221no—
291D4—1221no—
292D4—4881no—
293D4—4881no—
294D4—4881no—
295D4—4881no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—611no—
301C2×C4—611no—
302C2×C4—611no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—4881no—
308C2×C4—4881no—
309C2×C4D4×D6111yescharacteristic
310C2×C4D4×D6111yescharacteristic
311C2×C4C23×D6111yescharacteristic
312C8—21no—
313C8—21no—
314C8—1221no—
315C8—1221no—
316C22—1221no—
317C22—1221no—
318C22—1221no—
319C22—2441no—
320C22—2441no—
321C22—2441no—
322C22—2441no—
323C22—2441no—
324C22—2441no—
325C22C2×D4×D6111yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—1221no—
333C4—1221no—
334C4—1221no—
335C4—2441no—
336C4—2441no—
337C4#1451982311yescharacteristic
338C4#1451982511yescharacteristic
339C2—4881no—
340C2—4881no—
341C2—2441no—
342C2#1684034211yescharacteristic
343C2#1684056911yescharacteristic
344C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#479C2
socleC22×C61C22×D4
hypercenter#479D61
hypocenterC61#3260
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. #16840370C2semidirect
3. #16840066C2semidirect
4. #16840065C2semidirect
5. #16840061C2semidirect
6. #16840011C2semidirect
7. #16840009C2semidirect
8. #16839994C2semidirect
9. #16839992C2semidirect
10. #16839966C2semidirect
11. #16839966C2semidirect
12. #16839963C2semidirect
13. #16839962C2semidirect
14. #16839787C2semidirect
15. C61×#479C2semidirect
176. #479D61semidirect
188. C61#3260semidirect