Finite Group Databasebeta

← #21456868

Subgroups — #21456868

Order 7808.

420 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840363C211yesmaximal, characteristic, complemented
2#16840325C211yesmaximal, characteristic, complemented
3#16840150C211yesmaximal, characteristic, complemented
4#16840137C211yesmaximal, characteristic, complemented
5#16840125C211yesmaximal, characteristic, complemented
6#16840115C211yesmaximal, characteristic, complemented
7#16839978C211yesmaximal, characteristic, complemented
8#16839977C211yesmaximal, characteristic, complemented
9#16839954C211yesmaximal, characteristic, complemented
10#16839908C211yesmaximal, characteristic, complemented
11#16839904C211yesmaximal, characteristic, complemented
12#16839897C211yesmaximal, characteristic, complemented
13#16839894C211yesmaximal, characteristic, complemented
14#16839822C211yesmaximal, characteristic, complemented
15C61×#459C211yesmaximal, characteristic, complemented
16C2×#11758224C2211yescharacteristic
17C2×D4×D61C2211yescharacteristic
18C2×#11758190C2211yescharacteristic, complemented
19C2×#11758200C2211yescharacteristic, complemented
20C2×D488C2211yescharacteristic
21C2×#11758199C2211yescharacteristic
22C2×#11758199C2211yescharacteristic
23C2×#11758199C2211yescharacteristic, complemented
24#14519773C2211yescharacteristic
25#14519773C2211yescharacteristic, complemented
26#14519768C2211yescharacteristic, complemented
27#14519765C2211yescharacteristic
28#14519764C2211yescharacteristic
29#14519760—21no—
30#14519759—21no—
31#14519752C2211yescharacteristic
32#14519751—21no—
33#14519750—21no—
34#14519749—21no—
35#14519749—21no—
36#14519748C2211yescharacteristic
37#14519745—21no—
38#14519745—21no—
39C4×D244C2211yescharacteristic, complemented
40#14519734C2211yescharacteristic
41C4⋊#92418C2211yescharacteristic, complemented
42#14519702C2211yescharacteristic, complemented
43#14519700C2211yescharacteristic, complemented
44#14519699C2211yescharacteristic
45#14519698C2211yescharacteristic
46#14519698C2211yescharacteristic, complemented
47#14519697C2211yescharacteristic
48#14519689C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519687C2211yescharacteristic, complemented
51C8×Dic61C2211yescharacteristic, complemented
52C2×D8×C61C2211yescharacteristic
53C2×D8×C61C2211yescharacteristic, complemented
54#127×C61C2211yescharacteristic
55C4×D4×C61C2211yescharacteristic, complemented
56C4⋊C8×C61C2211yescharacteristic, complemented
57#102×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C2×D4×C61—21no—
61C2×D4×C61—21no—
62C2×D4×C61C2311yescharacteristic
63C2×D4×C61C2311yescharacteristic
64C2×D4×C61C2311yescharacteristic
65C22×C4×C61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C2×C22⋊D61—21no—
72C2×C22⋊D61—21no—
73C22×Dic61—21no—
74#11758224—41no—
75#11758224—41no—
76D4×D61—41no—
77D4×D61—41no—
78C2×D244—21no—
79C2×D244C2311yescharacteristic
80C2×D244C2311yescharacteristic
81C2×C4×D61—21no—
82C2×C4×D61C2311yescharacteristic
83C2×Dic122C2311yescharacteristic
84D8×C61—41no—
85D8×C61—41no—
86C2×C8×C61C2311yescharacteristic
87C2×C8×C61C2311yescharacteristic
88C4⋊C4×C61C2311yescharacteristic
89C22⋊C4×C61—21no—
90C42×C61C2311yescharacteristic
91C22⋊Dic61—21no—
92C22⋊Dic61—21no—
93C22⋊Dic61—21no—
94#11758200—41no—
95#11758199—41no—
96#11758199—41no—
97#11758199—41no—
98#11758198—21no—
99#11758198—21no—
100#11758198—21no—
101#11758198—21no—
102#11758198D411yescharacteristic
103#11758198D411yescharacteristic
104C4⋊Dic61—21no—
105C4⋊Dic61C2311yescharacteristic
106#11758196—21no—
107#11758196D411yescharacteristic
108#11758196D411yescharacteristic
109C4×Dic61C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111C2×#92418C2311yescharacteristic
112D488—41no—
113#11758190—41no—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61—21no—
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—42no—
120C22×D61—81no—
121C22×D61—81no—
122C22×D61C2×D411yescharacteristic
123D4×C61—21no—
124D4×C61—21no—
125D4×C61—21no—
126D4×C61—21no—
127D4×C61—21no—
128D4×C61—21no—
129D4×C61—81no—
130D4×C61—81no—
131C2×C4×C61—21no—
132C2×C4×C61—81no—
133C2×C4×C61C2×D411yescharacteristic
134C2×C4×C61C2×D411yescharacteristic
135C2×C4×C61C2411yescharacteristic
136C22⋊D61—42no—
137C22⋊D61—42no—
138C22⋊D61—81no—
139C22⋊D61—81no—
140C22⋊D61—81no—
141C22⋊D61—81no—
142C22⋊D61—81no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—42no—
146C2×Dic61C2×D411yescharacteristic
147C2×Dic61C2×D411yescharacteristic
148C2×Dic61C2×D411yescharacteristic
149D244—21no—
150D244—21no—
151D244—21no—
152D244—21no—
153D244—81no—
154C4×D61—21no—
155C4×D61—21no—
156C4×D61—81no—
157Dic122—21no—
158Dic122—21no—
159C8×C61—21no—
160C8×C61—21no—
161#92418—21no—
162#92418—21no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61—41no—
171C22×C61—41no—
172C22×C61C22×D411yescharacteristic
173C2×D61—21no—
174C2×D61—21no—
175C2×D61—21no—
176C2×D61—41no—
177C2×D61—41no—
178C2×D61—41no—
179C2×D61—41no—
180C2×D61—41no—
181C2×D61—41no—
182C2×D61—84no—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—41no—
186C4×C61H(5,𝔽2)11yescharacteristic
187C4×C61H(5,𝔽2)11yescharacteristic
188Dic61—21no—
189Dic61—21no—
190Dic61—21no—
191Dic61—41no—
192Dic61—41no—
193#3220—611nomaximal, Sylow
194C2×C61—81no—
195C2×C61—81no—
196C2×C61—81no—
197C2×C61#53511yescharacteristic
198C2×C61#57611yescharacteristic
199C2×C61#57611yescharacteristic
200D61—41no—
201D61—81no—
202D61—81no—
203#540—611no—
204#535—611no—
205#496—611no—
206#493—611no—
207#490—611no—
208#488—611no—
209#463—611no—
210#463—611no—
211#459—611no—
212#459D6111yescharacteristic, complemented
213#449—611no—
214#449—611no—
215#447—611no—
216#447—611no—
217#433—611no—
218C61#322011yescharacteristic, complemented, Sylow
219C2×#41—611no—
220C22×D4—611no—
221C2×SD16—611no—
222C2×SD16—611no—
223C2×D8—611no—
224C2×D8—611no—
225C2×D8—611no—
226C2×D8—611no—
227C2×D8C2×D6111yescharacteristic
228C2×D8C2×D6111yescharacteristic, complemented
229#127—611no—
230#127—611no—
231#127C2×D6111yescharacteristic
232#125—611no—
233#124—611no—
234#124—611no—
235#123—1221no—
236#123—1221no—
237#121—611no—
238#121—611no—
239#121—1221no—
240#121—1221no—
241#121—1221no—
242#121—1221no—
243#120—1221no—
244#120—1221no—
245C4×D4—611no—
246C4×D4C2×D6111yescharacteristic, complemented
247#117—611no—
248C4⋊C8—611no—
249C4⋊C8C2×D6111yescharacteristic, complemented
250#103—611no—
251#103—611no—
252#102—611no—
253#102—611no—
254#102—611no—
255#102—611no—
256#102C2×D6111yescharacteristic
257#102C2×D6111yescharacteristic, complemented
258C22⋊C8—611no—
259C22⋊C8—611no—
260#97—611no—
261C4×C8—611no—
262C24—1221no—
263#41—2441no—
264#41—2441no—
265C2×Q8—611no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—611no—
269C2×D4—611no—
270C2×D4—1221no—
271C2×D4—1221no—
272C2×D4—1221no—
273C2×D4—1221no—
274C2×D4—1221no—
275C2×D4—1221no—
276C2×D4—1221no—
277C2×D4—1221no—
278C2×D4—2441no—
279C2×D4—2441no—
280C2×D4C22×D6111yescharacteristic
281C2×D4C22×D6111yescharacteristic
282C2×D4C22×D6111yescharacteristic
283C22×C4—21no—
284C22×C4—611no—
285C22×C4—1221no—
286C22×C4—1221no—
287SD16—2441no—
288SD16—2441no—
289D8—41no—
290D8—41no—
291D8—2441no—
292D8—2441no—
293D8—2441no—
294D8—2441no—
295C2×C8—611no—
296C2×C8—611no—
297C2×C8C22×D6111yescharacteristic
298C2×C8C22×D6111yescharacteristic
299C4⋊C4—611no—
300C4⋊C4—611no—
301C4⋊C4—611no—
302C4⋊C4—1221no—
303C4⋊C4—1221no—
304C4⋊C4C22×D6111yescharacteristic
305C22⋊C4—21no—
306C22⋊C4—611no—
307C22⋊C4—611no—
308C22⋊C4—1221no—
309C22⋊C4—1221no—
310C22⋊C4—1221no—
311C22⋊C4—1221no—
312C22⋊C4—1221no—
313C22⋊C4—1221no—
314C22⋊C4—1221no—
315C42—611no—
316C42C22×D6111yescharacteristic
317C23—21no—
318C23—21no—
319C23—21no—
320C23—611no—
321C23—1221no—
322C23—1221no—
323C23—4881no—
324C23—4881no—
325C23—2442no—
326Q8—1221no—
327Q8—1221no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—81no—
335D4—81no—
336D4—1221no—
337D4—1221no—
338D4—1221no—
339D4—1221no—
340D4—4881no—
341D4—4881no—
342D4—4881no—
343D4—4881no—
344D4—4881no—
345D4—4881no—
346D4—2442no—
347D4—2442no—
348C2×C4—21no—
349C2×C4—81no—
350C2×C4—611no—
351C2×C4—611no—
352C2×C4—611no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—4881no—
358C2×C4—2442no—
359C2×C4D4×D6111yescharacteristic
360C2×C4D4×D6111yescharacteristic
361C2×C4C23×D6111yescharacteristic
362C8—21no—
363C8—21no—
364C8—1221no—
365C8—1221no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—1221no—
376C22—1221no—
377C22—1221no—
378C22—4884no—
379C22—2441no—
380C22—2441no—
381C22—2441no—
382C22—2441no—
383C22—2441no—
384C22—2441no—
385C22C2×D4×D6111yescharacteristic
386C4—21no—
387C4—21no—
388C4—41no—
389C4—1221no—
390C4—1221no—
391C4—1221no—
392C4—2441no—
393C4—2441no—
394C4#1451982211yescharacteristic
395C4#1451982311yescharacteristic
396C2—81no—
397C2—81no—
398C2—81no—
399C2—4881no—
400C2—4881no—
401C2—2441no—
402C2#1684032811yescharacteristic
403C2#1684056311yescharacteristic
404C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#459C2
socleC22×C61C22×D4
hypercenter#459D61
hypocenterC61#3220
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #16840363C2semidirect
2. #16840325C2semidirect
3. #16840150C2semidirect
4. #16840137C2semidirect
5. #16840125C2semidirect
6. #16840115C2semidirect
7. #16839978C2semidirect
8. #16839977C2semidirect
9. #16839954C2semidirect
10. #16839908C2semidirect
11. #16839904C2semidirect
12. #16839897C2semidirect
13. #16839894C2semidirect
14. #16839822C2semidirect
15. C61×#459C2semidirect
18. C2×#11758190C22semidirect
19. C2×#11758200C22semidirect
23. C2×#11758199C22semidirect
25. #14519773C22semidirect
26. #14519768C22semidirect
39. C4×D244C22semidirect
41. C4⋊#92418C22semidirect
42. #14519702C22semidirect
43. #14519700C22semidirect
46. #14519698C22semidirect
50. #14519687C22semidirect
51. C8×Dic61C22semidirect
53. C2×D8×C61C22semidirect
55. C4×D4×C61C22semidirect
56. C4⋊C8×C61C22semidirect
58. #102×C61C22semidirect
212. #459D61semidirect
218. C61#3220semidirect
228. C2×D8C2×D61semidirect
246. C4×D4C2×D61semidirect
249. C4⋊C8C2×D61semidirect
257. #102C2×D61semidirect