Finite Group Databasebeta

← #21456688

Subgroups — #21456688

Order 7808.

410 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840335C211yesmaximal, characteristic, complemented
2#16840329C211yesmaximal, characteristic
3#16840104C211yesmaximal, characteristic, complemented
4#16840100C211yesmaximal, characteristic, complemented
5#16840085C211yesmaximal, characteristic, complemented
6#16840084C211yesmaximal, characteristic, complemented
7#16840007C211yesmaximal, characteristic, complemented
8#16840005C211yesmaximal, characteristic, complemented
9#16839990C211yesmaximal, characteristic, complemented
10#16839988C211yesmaximal, characteristic, complemented
11#16839913C211yesmaximal, characteristic, complemented
12#16839899C211yesmaximal, characteristic, complemented
13#16839899C211yesmaximal, characteristic, complemented
14#16839727C211yesmaximal, characteristic, complemented
15C61×#450C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×Q8×D61C2211yescharacteristic, complemented
18C2×#11758200C2211yescharacteristic
19C2×#11758200C2211yescharacteristic
20C2×#11758189C2211yescharacteristic, complemented
21C2×C8×D61C2211yescharacteristic, complemented
22#14519776—21no—
23#14519773—21no—
24#14519764—21no—
25#14519763—21no—
26#14519762—21no—
27#14519759—21no—
28#14519757C2211yescharacteristic, complemented
29#14519756C2211yescharacteristic
30#14519753C2211yescharacteristic, complemented
31#14519748C2211yescharacteristic
32#14519748C2211yescharacteristic
33#14519748C2211yescharacteristic
34#14519748C2211yescharacteristic
35#14519746—21no—
36#14519746—21no—
37#14519736C2211yescharacteristic
38#14519735C2211yescharacteristic, complemented
39#14519711C2211yescharacteristic, complemented
40#14519710C2211yescharacteristic, complemented
41#14519709C2211yescharacteristic, complemented
42#14519708C2211yescharacteristic, complemented
43#14519702C2211yescharacteristic, complemented
44#14519702C2211yescharacteristic, complemented
45#14519701C2211yescharacteristic, complemented
46#14519701C2211yescharacteristic, complemented
47#14519698C2211yescharacteristic
48#14519698C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519689C2211yescharacteristic, complemented
51#14519689C2211yescharacteristic, complemented
52C22×D4×C61C2211yescharacteristic
53C2×SD16×C61C2211yescharacteristic
54C2×SD16×C61C2211yescharacteristic
55C22⋊Q8×C61C2211yescharacteristic
56#102×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59C24×C61—21no—
60C2×Q8×C61C2311yescharacteristic
61C2×D4×C61—21no—
62C2×D4×C61—41no—
63C2×D4×C61—41no—
64C2×D4×C61C2311yescharacteristic
65C2×D4×C61C2311yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C2×C22⋊D61D411yescharacteristic
72C2×C22⋊D61D411yescharacteristic
73Q8×D61—41no—
74Q8×D61—41no—
75#11758222—41no—
76#11758222—41no—
77C2×D244D411yescharacteristic
78C2×C4×D61—21no—
79C2×C4×D61C2311yescharacteristic
80C2×C4×D61C2311yescharacteristic
81C2×Dic122—21no—
82C2×Dic122D411yescharacteristic
83C2×Dic122C2311yescharacteristic
84SD16×C61—41no—
85SD16×C61—41no—
86C2×C8×C61C2311yescharacteristic
87C2×C8×C61C2311yescharacteristic
88C4⋊C4×C61—21no—
89C4⋊C4×C61C2311yescharacteristic
90C22⋊C4×C61—21no—
91C22⋊Dic61—21no—
92C22⋊Dic61—21no—
93C22⋊Dic61—21no—
94C22⋊Dic61—21no—
95C22⋊Dic61—21no—
96C22⋊Dic61—21no—
97#11758200—41no—
98#11758200—41no—
99#11758198—21no—
100#11758198—21no—
101#11758198—21no—
102C4⋊Dic61—21no—
103C4⋊Dic61C2311yescharacteristic
104C4⋊Dic61C2311yescharacteristic
105C4⋊Dic61C2311yescharacteristic
106#11758196—21no—
107#11758196—21no—
108C4×Dic61—21no—
109C4×Dic61—21no—
110C2×#92418C2311yescharacteristic
111C2×#92418C2311yescharacteristic
112#11758189—41no—
113C8×D61—41no—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61—42no—
117C23×C61—81no—
118C23×C61—81no—
119C23×C61C2×D411yescharacteristic
120C22×D61C2×D411yescharacteristic
121C22×D61C2×D411yescharacteristic
122Q8×C61—21no—
123Q8×C61—21no—
124D4×C61—21no—
125D4×C61—21no—
126D4×C61—21no—
127D4×C61—21no—
128D4×C61—42no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61C2×D411yescharacteristic
134C2×C4×C61C2411yescharacteristic
135C22⋊D61—41no—
136C22⋊D61—41no—
137C22⋊D61—81no—
138C22⋊D61—81no—
139C22⋊D61—81no—
140C22⋊D61—81no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61C2×D411yescharacteristic
146C2×Dic61C2×D411yescharacteristic
147D244—41no—
148C4×D61—21no—
149C4×D61—21no—
150C4×D61—21no—
151C4×D61—21no—
152C4×D61—42no—
153Dic122—21no—
154Dic122—21no—
155Dic122—41no—
156Dic122—42no—
157C8×C61—21no—
158C8×C61—21no—
159#92418—21no—
160#92418—21no—
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61—84no—
171C22×C61C22×D411yescharacteristic
172C2×D61—21no—
173C2×D61—21no—
174C2×D61—21no—
175C2×D61—21no—
176C2×D61—21no—
177C2×D61—21no—
178C4×C61—21no—
179C4×C61—41no—
180C4×C61—41no—
181C4×C61H(5,𝔽2)11yescharacteristic
182C4×C61H(5,𝔽2)11yescharacteristic
183Dic61—21no—
184Dic61—21no—
185Dic61—41no—
186Dic61—41no—
187Dic61—41no—
188Dic61—41no—
189#3200—611nomaximal, Sylow
190C2×C61—41no—
191C2×C61—81no—
192C2×C61—81no—
193C2×C61#53411yescharacteristic
194C2×C61#57711yescharacteristic
195C2×C61#57711yescharacteristic
196D61—41no—
197D61—41no—
198#536—611no—
199#535—611no—
200#485—611no—
201#485—611no—
202#482—611no—
203#482—611no—
204#468—611no—
205#468—611no—
206#465—611no—
207#465—611no—
208#450—611no—
209#450D6111yescharacteristic, complemented
210#448—611no—
211#448—611no—
212#408—611no—
213C61#320011yescharacteristic, complemented, Sylow
214C2×#41—611no—
215C22×Q8—611no—
216C22×D4C2×D6111yescharacteristic
217C2×SD16—611no—
218C2×SD16—611no—
219C2×SD16C2×D6111yescharacteristic
220C2×SD16C2×D6111yescharacteristic
221C2×M16—611no—
222C22×C8—611no—
223C4⋊Q8—1221no—
224#127—1221no—
225#124—1221no—
226#124—1221no—
227#123—1221no—
228#123—1221no—
229C22⋊Q8—611no—
230C22⋊Q8—611no—
231C22⋊Q8—611no—
232C22⋊Q8C2×D6111yescharacteristic
233#121—611no—
234#121—611no—
235#121—611no—
236#121—611no—
237#120—1221no—
238#120—1221no—
239#117—611no—
240#117—611no—
241#107—611no—
242#107—611no—
243#106—611no—
244#106—611no—
245#103—611no—
246#103—611no—
247#103—611no—
248#103—611no—
249#102—611no—
250#102—611no—
251#102C2×D6111yescharacteristic
252#102C2×D6111yescharacteristic
253C22⋊C8—611no—
254C22⋊C8—611no—
255C22⋊C8—611no—
256C22⋊C8C2×D6111yescharacteristic
257C24—21no—
258#41—2441no—
259#41—2441no—
260C2×Q8—611no—
261C2×Q8—611no—
262C2×Q8—1221no—
263C2×Q8—2441no—
264C2×Q8—2441no—
265C2×Q8C22×D6111yescharacteristic
266C2×D4—21no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—611no—
270C2×D4—611no—
271C2×D4—611no—
272C2×D4—1221no—
273C2×D4—1221no—
274C2×D4—1221no—
275C2×D4—1221no—
276C2×D4C22×D6111yescharacteristic
277C2×D4C22×D6111yescharacteristic
278C22×C4—611no—
279C22×C4—611no—
280C22×C4—1221no—
281C22×C4C22×D6111yescharacteristic
282SD16—41no—
283SD16—41no—
284SD16—2441no—
285SD16—2441no—
286M16—2441no—
287C2×C8—611no—
288C2×C8—611no—
289C2×C8—2441no—
290C2×C8C22×D6111yescharacteristic
291C2×C8C22×D6111yescharacteristic
292C4⋊C4—21no—
293C4⋊C4—611no—
294C4⋊C4—611no—
295C4⋊C4—611no—
296C4⋊C4—1221no—
297C4⋊C4—1221no—
298C4⋊C4—1221no—
299C4⋊C4C22×D6111yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—1221no—
302C22⋊C4—1221no—
303C22⋊C4—1221no—
304C22⋊C4—1221no—
305C22⋊C4—1221no—
306C22⋊C4—1221no—
307C22⋊C4—1221no—
308C22⋊C4—1221no—
309C22⋊C4—1221no—
310C42—1221no—
311C42—1221no—
312C23—21no—
313C23—21no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23—611no—
318C23—611no—
319C23D4×D6111yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—1221no—
323Q8—1221no—
324Q8—2441no—
325Q8—2442no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—4881no—
332D4—4881no—
333D4—4881no—
334D4—4881no—
335D4—2441no—
336D4—2441no—
337D4—2441no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—611no—
343C2×C4—611no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—2442no—
353C2×C4D4×D6111yescharacteristic
354C2×C4C23×D6111yescharacteristic
355C8—21no—
356C8—21no—
357C8—1221no—
358C8—1221no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—84no—
369C22—1221no—
370C22—1221no—
371C22—1221no—
372C22—1221no—
373C22—1221no—
374C22—1221no—
375C22C2×D4×D6111yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—1221no—
380C4—1221no—
381C4—2441no—
382C4—2441no—
383C4—2441no—
384C4—2441no—
385C4#1451982211yescharacteristic
386C4#1451982211yescharacteristic
387C2—41no—
388C2—81no—
389C2—81no—
390C2—2441no—
391C2—2441no—
392C2#1684032211yescharacteristic
393C2#1684056811yescharacteristic
394C2#1684057211yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#450C2
socleC22×C61C22×D4
hypercenter#450D61
hypocenterC61#3200
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #16840335C2semidirect
3. #16840104C2semidirect
4. #16840100C2semidirect
5. #16840085C2semidirect
6. #16840084C2semidirect
7. #16840007C2semidirect
8. #16840005C2semidirect
9. #16839990C2semidirect
10. #16839988C2semidirect
11. #16839913C2semidirect
12. #16839899C2semidirect
13. #16839899C2semidirect
14. #16839727C2semidirect
15. C61×#450C2semidirect
17. C2×Q8×D61C22semidirect
20. C2×#11758189C22semidirect
21. C2×C8×D61C22semidirect
28. #14519757C22semidirect
30. #14519753C22semidirect
38. #14519735C22semidirect
39. #14519711C22semidirect
40. #14519710C22semidirect
41. #14519709C22semidirect
42. #14519708C22semidirect
43. #14519702C22semidirect
44. #14519702C22semidirect
45. #14519701C22semidirect
46. #14519701C22semidirect
50. #14519689C22semidirect
51. #14519689C22semidirect
209. #450D61semidirect
213. C61#3200semidirect