Finite Group Databasebeta

← #21456867

Subgroups — #21456867

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#16840365C211yesmaximal, characteristic, complemented
2#16840326C211yesmaximal, characteristic, complemented
3#16840148C211yesmaximal, characteristic, complemented
4#16840137C211yesmaximal, characteristic, complemented
5#16840125C211yesmaximal, characteristic, complemented
6#16840118C211yesmaximal, characteristic, complemented
7#16839980C211yesmaximal, characteristic, complemented
8#16839979C211yesmaximal, characteristic, complemented
9#16839956C211yesmaximal, characteristic, complemented
10#16839955C211yesmaximal, characteristic, complemented
11#16839907C211yesmaximal, characteristic, complemented
12#16839898C211yesmaximal, characteristic, complemented
13#16839895C211yesmaximal, characteristic, complemented
14#16839820C211yesmaximal, characteristic, complemented
15C61×#449C211yesmaximal, characteristic, complemented
16C22×D244C2211yescharacteristic
17C2×#11758201C2211yescharacteristic, complemented
18C2×D488C2211yescharacteristic
19C2×D488C2211yescharacteristic
20C2×#11758199C2211yescharacteristic
21C2×#11758199C2211yescharacteristic
22C2×#11758199C2211yescharacteristic, complemented
23#14519773C2211yescharacteristic
24#14519773C2211yescharacteristic
25#14519773C2211yescharacteristic, complemented
26#14519768C2211yescharacteristic, complemented
27#14519766C2211yescharacteristic
28#14519766C2211yescharacteristic
29#14519761—21no—
30#14519759—21no—
31#14519751—21no—
32#14519751—21no—
33#14519751C2211yescharacteristic
34#14519749—21no—
35#14519748—21no—
36#14519745—21no—
37#14519745—21no—
38D4×Dic61C2211yescharacteristic, complemented
39#14519739C2211yescharacteristic, complemented
40#14519736C2211yescharacteristic
41#14519706C2211yescharacteristic, complemented
42#14519706C2211yescharacteristic, complemented
43#14519701C2211yescharacteristic, complemented
44#14519699C2211yescharacteristic
45#14519699C2211yescharacteristic
46#14519698C2211yescharacteristic, complemented
47#14519697C2211yescharacteristic
48#14519697C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519687C2211yescharacteristic, complemented
51C8×Dic61C2211yescharacteristic, complemented
52C2×#41×C61C2211yescharacteristic
53C2×SD16×C61C2211yescharacteristic, complemented
54C2×D8×C61C2211yescharacteristic, complemented
55#121×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic, complemented
57#102×C61C2211yescharacteristic, complemented
58C22⋊C8×C61C2211yescharacteristic
59C23×D61—21no—
60#41×C61—41no—
61#41×C61—41no—
62C2×Q8×C61C2311yescharacteristic
63C2×D4×C61—21no—
64C2×D4×C61—21no—
65C2×D4×C61C2311yescharacteristic
66C2×D4×C61C2311yescharacteristic
67C22×C4×C61—21no—
68C22×C4×C61C2311yescharacteristic
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C2×C22⋊D61—21no—
72C2×C22⋊D61—21no—
73C2×C22⋊D61—21no—
74C2×C22⋊D61—21no—
75C2×C22⋊D61—21no—
76C22×Dic61—21no—
77C2×D244—21no—
78C2×D244—41no—
79C2×D244—41no—
80C2×D244C2311yescharacteristic
81C2×D244C2311yescharacteristic
82C2×D244C2311yescharacteristic
83C2×C4×D61—21no—
84SD16×C61—41no—
85D8×C61—41no—
86C2×C8×C61C2311yescharacteristic
87C2×C8×C61C2311yescharacteristic
88C4⋊C4×C61C2311yescharacteristic
89C22⋊C4×C61—21no—
90C22⋊Dic61—21no—
91C22⋊Dic61D411yescharacteristic
92C22⋊Dic61D411yescharacteristic
93#11758201—41no—
94#11758199—41no—
95#11758199—41no—
96#11758199—41no—
97#11758198—21no—
98#11758198—21no—
99#11758198—21no—
100#11758198—21no—
101#11758198—21no—
102#11758198—21no—
103C4⋊Dic61—21no—
104C4⋊Dic61D411yescharacteristic
105C4⋊Dic61D411yescharacteristic
106C4⋊Dic61C2311yescharacteristic
107#11758196—21no—
108C4×Dic61C2311yescharacteristic
109C4×Dic61C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111C2×#92418C2311yescharacteristic
112D488—41no—
113D488—41no—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61C2×D411yescharacteristic
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—42no—
121C22×D61—81no—
122C22×D61—81no—
123Q8×C61—21no—
124Q8×C61—21no—
125D4×C61—21no—
126D4×C61—21no—
127D4×C61—21no—
128D4×C61—21no—
129D4×C61—42no—
130D4×C61—81no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—42no—
136C2×C4×C61C2×D411yescharacteristic
137C2×C4×C61C2411yescharacteristic
138C22⋊D61—81no—
139C22⋊D61—81no—
140C22⋊D61—81no—
141C22⋊D61—81no—
142C22⋊D61—81no—
143C22⋊D61—81no—
144C22⋊D61—81no—
145C2×Dic61—21no—
146C2×Dic61—81no—
147C2×Dic61C2×D411yescharacteristic
148C2×Dic61C2×D411yescharacteristic
149C2×Dic61C2×D411yescharacteristic
150C2×Dic61C2×D411yescharacteristic
151D244—21no—
152D244—21no—
153D244—21no—
154D244—21no—
155D244—21no—
156D244—21no—
157D244—42no—
158C4×D61—81no—
159C8×C61—21no—
160C8×C61—21no—
161#92418—21no—
162#92418—21no—
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61—41no—
171C22×C61—41no—
172C22×C61C22×D411yescharacteristic
173C2×D61—41no—
174C2×D61—41no—
175C2×D61—41no—
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—41no—
185C4×C61—41no—
186C4×C61H(5,𝔽2)11yescharacteristic
187C4×C61H(5,𝔽2)11yescharacteristic
188Dic61—21no—
189Dic61—21no—
190Dic61—21no—
191Dic61—21no—
192Dic61—41no—
193#3220—611nomaximal, Sylow
194C2×C61—41no—
195C2×C61—81no—
196C2×C61—81no—
197C2×C61#53511yescharacteristic
198C2×C61#57611yescharacteristic
199C2×C61#57611yescharacteristic
200D61—81no—
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#459—611no—
213#449—611no—
214#449D6111yescharacteristic, complemented
215#447—611no—
216#447—611no—
217#433—611no—
218C61#322011yescharacteristic, complemented, Sylow
219C2×#41C2×D6111yescharacteristic
220C22×D4—611no—
221C2×SD16—611no—
222C2×SD16C2×D6111yescharacteristic, complemented
223C2×D8—611no—
224C2×D8—611no—
225C2×D8—611no—
226C2×D8—611no—
227C2×D8—611no—
228C2×D8C2×D6111yescharacteristic, complemented
229#127—611no—
230#127—611no—
231#127—611no—
232#125—611no—
233#124—611no—
234#124—611no—
235#123—1221no—
236#123—1221no—
237#121—611no—
238#121—1221no—
239#121—1221no—
240#121—1221no—
241#121—1221no—
242#121C2×D6111yescharacteristic
243#120—1221no—
244#120—1221no—
245C4×D4—611no—
246C4×D4—611no—
247#117—611no—
248C4⋊C8—611no—
249C4⋊C8—611no—
250#103—611no—
251#103C2×D6111yescharacteristic, complemented
252#102—611no—
253#102—611no—
254#102—611no—
255#102—611no—
256#102—611no—
257#102C2×D6111yescharacteristic, complemented
258C22⋊C8—611no—
259C22⋊C8C2×D6111yescharacteristic
260#97—611no—
261C4×C8—611no—
262C24—1221no—
263#41—41no—
264#41—41no—
265C2×Q8C22×D6111yescharacteristic
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—611no—
269C2×D4—611no—
270C2×D4—611no—
271C2×D4—1221no—
272C2×D4—1221no—
273C2×D4—1221no—
274C2×D4—1221no—
275C2×D4—1221no—
276C2×D4—1221no—
277C2×D4—1221no—
278C2×D4—1221no—
279C2×D4—2441no—
280C2×D4—2441no—
281C2×D4C22×D6111yescharacteristic
282C2×D4C22×D6111yescharacteristic
283C22×C4—21no—
284C22×C4—1221no—
285C22×C4—1221no—
286C22×C4C22×D6111yescharacteristic
287SD16—41no—
288SD16—2441no—
289D8—41no—
290D8—2441no—
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—
316C42—611no—
317C23—21no—
318C23—21no—
319C23—1221no—
320C23—1221no—
321C23—1221no—
322C23—4881no—
323C23—4881no—
324C23—2442no—
325C23D4×D6111yescharacteristic
326Q8—21no—
327Q8—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—42no—
333D4—81no—
334D4—1221no—
335D4—1221no—
336D4—1221no—
337D4—1221no—
338D4—1221no—
339D4—1221no—
340D4—4881no—
341D4—4881no—
342D4—4881no—
343D4—4881no—
344D4—4881no—
345D4—4881no—
346D4—4881no—
347D4—2442no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—42no—
353C2×C4—611no—
354C2×C4—611no—
355C2×C4—611no—
356C2×C4—611no—
357C2×C4—1221no—
358C2×C4—4881no—
359C2×C4—4881no—
360C2×C4D4×D6111yescharacteristic
361C2×C4C23×D6111yescharacteristic
362C8—21no—
363C8—21no—
364C8—1221no—
365C8—1221no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—4884no—
376C22—2441no—
377C22—2441no—
378C22—2441no—
379C22—2441no—
380C22—2441no—
381C22—2441no—
382C22—2441no—
383C22—2441no—
384C22—2441no—
385C22C2×D4×D6111yescharacteristic
386C4—21no—
387C4—41no—
388C4—41no—
389C4—1221no—
390C4—1221no—
391C4—1221no—
392C4—1221no—
393C4—2441no—
394C4#1451982211yescharacteristic
395C4#1451982211yescharacteristic
396C2—41no—
397C2—81no—
398C2—81no—
399C2—4881no—
400C2—4881no—
401C2—4881no—
402C2#1684032711yescharacteristic
403C2#1684056411yescharacteristic
404C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#449C2
socleC22×C61C22×D4
hypercenter#449D61
hypocenterC61#3220
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #16840365C2semidirect
2. #16840326C2semidirect
3. #16840148C2semidirect
4. #16840137C2semidirect
5. #16840125C2semidirect
6. #16840118C2semidirect
7. #16839980C2semidirect
8. #16839979C2semidirect
9. #16839956C2semidirect
10. #16839955C2semidirect
11. #16839907C2semidirect
12. #16839898C2semidirect
13. #16839895C2semidirect
14. #16839820C2semidirect
15. C61×#449C2semidirect
17. C2×#11758201C22semidirect
22. C2×#11758199C22semidirect
25. #14519773C22semidirect
26. #14519768C22semidirect
38. D4×Dic61C22semidirect
39. #14519739C22semidirect
41. #14519706C22semidirect
42. #14519706C22semidirect
43. #14519701C22semidirect
46. #14519698C22semidirect
50. #14519687C22semidirect
51. C8×Dic61C22semidirect
53. C2×SD16×C61C22semidirect
54. C2×D8×C61C22semidirect
56. #103×C61C22semidirect
57. #102×C61C22semidirect
214. #449D61semidirect
218. C61#3220semidirect
222. C2×SD16C2×D61semidirect
228. C2×D8C2×D61semidirect
251. #103C2×D61semidirect
257. #102C2×D61semidirect