Finite Group Databasebeta

← #21456917

Subgroups — #21456917

Order 7808.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840385C211yesmaximal, characteristic, complemented
2#16840329C211yesmaximal, characteristic, complemented
3#16840148C211yesmaximal, characteristic, complemented
4#16840143C211yesmaximal, characteristic, complemented
5#16840120C211yesmaximal, characteristic, complemented
6#16840107C211yesmaximal, characteristic, complemented
7#16839982C211yesmaximal, characteristic, complemented
8#16839976C211yesmaximal, characteristic, complemented
9#16839960C211yesmaximal, characteristic, complemented
10#16839956C211yesmaximal, characteristic, complemented
11#16839922C211yesmaximal, characteristic, complemented
12#16839909C211yesmaximal, characteristic, complemented
13#16839896C211yesmaximal, characteristic, complemented
14#16839820C211yesmaximal, characteristic, complemented
15C61×#450C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×#11758202C2211yescharacteristic, complemented
18C2×#11758190C2211yescharacteristic, complemented
19C2×#11758201C2211yescharacteristic, complemented
20C2×D488C2211yescharacteristic, complemented
21C2×#11758199C2211yescharacteristic
22C2×#11758199C2211yescharacteristic
23#14519776C2211yescharacteristic, complemented
24#14519773C2211yescharacteristic
25#14519773C2211yescharacteristic
26#14519772—21no—
27#14519766C2211yescharacteristic, complemented
28#14519764C2211yescharacteristic
29#14519764C2211yescharacteristic
30#14519763—21no—
31#14519759—21no—
32#14519757—21no—
33#14519751C2211yescharacteristic
34#14519748—21no—
35#14519748—21no—
36#14519746—21no—
37#14519746—21no—
38Q8×Dic61C2211yescharacteristic, complemented
39#14519739C2211yescharacteristic, complemented
40#14519736C2211yescharacteristic
41#14519706C2211yescharacteristic, complemented
42#14519706C2211yescharacteristic, complemented
43#14519702C2211yescharacteristic, complemented
44#14519700C2211yescharacteristic, complemented
45#14519699C2211yescharacteristic, complemented
46#14519698C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519697C2211yescharacteristic, complemented
49C22⋊#92418C2211yescharacteristic
50#14519687C2211yescharacteristic, complemented
51C8×Dic61C2211yescharacteristic, 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⋊D61—21no—
72C2×C22⋊D61—21no—
73#11758222—41no—
74#11758222—41no—
75C2×D244C2311yescharacteristic
76C2×D244C2311yescharacteristic
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×Dic122—21no—
80C2×Dic122C2311yescharacteristic
81SD16×C61—41no—
82SD16×C61—41no—
83C2×C8×C61C2311yescharacteristic
84C2×C8×C61C2311yescharacteristic
85C4⋊C4×C61—21no—
86C4⋊C4×C61C2311yescharacteristic
87C22⋊C4×C61—21no—
88C22⋊Dic61—21no—
89C22⋊Dic61—21no—
90C22⋊Dic61—21no—
91C22⋊Dic61—21no—
92C22⋊Dic61D411yescharacteristic
93C22⋊Dic61D411yescharacteristic
94#11758202—41no—
95#11758201—41no—
96#11758199—41no—
97#11758199—41no—
98#11758198—21no—
99#11758198—21no—
100#11758198—21no—
101#11758198—21no—
102C4⋊Dic61—21no—
103C4⋊Dic61D411yescharacteristic
104C4⋊Dic61D411yescharacteristic
105C4⋊Dic61C2311yescharacteristic
106#11758196—21no—
107C4×Dic61—21no—
108C4×Dic61C2311yescharacteristic
109C4×Dic61C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111C2×#92418C2311yescharacteristic
112D488—41no—
113#11758190—41no—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61—42no—
117C23×C61—81no—
118C23×C61—81no—
119C23×C61C2×D411yescharacteristic
120C22×D61—21no—
121C22×D61—21no—
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—42no—
136C22⋊D61—81no—
137C22⋊D61—81no—
138C22⋊D61—81no—
139C22⋊D61—81no—
140C22⋊D61—81no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61C2×D411yescharacteristic
144C2×Dic61C2×D411yescharacteristic
145C2×Dic61C2×D411yescharacteristic
146C2×Dic61C2×D411yescharacteristic
147D244—21no—
148D244—21no—
149D244—21no—
150D244—21no—
151C4×D61—42no—
152C4×D61—81no—
153Dic122—21no—
154Dic122—21no—
155Dic122—81no—
156C8×C61—21no—
157C8×C61—21no—
158#92418—21no—
159#92418—21no—
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—84no—
170C22×C61C22×D411yescharacteristic
171C2×D61—41no—
172C2×D61—41no—
173C2×D61—41no—
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—41no—
177C4×C61—21no—
178C4×C61—41no—
179C4×C61—41no—
180C4×C61H(5,𝔽2)11yescharacteristic
181C4×C61H(5,𝔽2)11yescharacteristic
182Dic61—21no—
183Dic61—21no—
184Dic61—21no—
185Dic61—21no—
186Dic61—41no—
187Dic61—41no—
188#3224—611nomaximal, Sylow
189C2×C61—41no—
190C2×C61—81no—
191C2×C61—81no—
192C2×C61#53511yescharacteristic
193C2×C61#57611yescharacteristic
194C2×C61#57711yescharacteristic
195D61—81no—
196D61—81no—
197#542—611no—
198#535—611no—
199#496—611no—
200#495—611no—
201#489—611no—
202#486—611no—
203#464—611no—
204#463—611no—
205#460—611no—
206#459—611no—
207#452—611no—
208#450D6111yescharacteristic, complemented
209#449—611no—
210#447—611no—
211#433—611no—
212C61#322411yescharacteristic, complemented, Sylow
213C2×#41—611no—
214C22×D4C2×D6111yescharacteristic
215C2×Q16—611no—
216C2×SD16—611no—
217C2×SD16—611no—
218C2×SD16C2×D6111yescharacteristic
219C2×SD16C2×D6111yescharacteristic
220C2×D8—611no—
221C2×D8—611no—
222C2×D8—611no—
223C4⋊Q8—611no—
224#127—611no—
225#127—611no—
226#126—1221no—
227#124—611no—
228#124—611no—
229#124—611no—
230#124—1221no—
231#123—1221no—
232C22⋊Q8—1221no—
233C22⋊Q8C2×D6111yescharacteristic
234#121—611no—
235#121—1221no—
236#121—1221no—
237#120—1221no—
238#120—1221no—
239C4×Q8—611no—
240C4×D4—611no—
241#117—611no—
242C4⋊C8—611no—
243C4⋊C8—611no—
244#103—611no—
245#103—611no—
246#102—611no—
247#102—611no—
248#102—611no—
249#102—611no—
250#102C2×D6111yescharacteristic
251#102C2×D6111yescharacteristic
252C22⋊C8—611no—
253C22⋊C8C2×D6111yescharacteristic
254#97—611no—
255C4×C8—611no—
256C24—21no—
257#41—2441no—
258#41—2441no—
259C2×Q8—611no—
260C2×Q8—1221no—
261C2×Q8C22×D6111yescharacteristic
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—611no—
266C2×D4—611no—
267C2×D4—1221no—
268C2×D4—1221no—
269C2×D4—1221no—
270C2×D4—1221no—
271C2×D4—1221no—
272C2×D4—1221no—
273C2×D4C22×D6111yescharacteristic
274C2×D4C22×D6111yescharacteristic
275C22×C4—1221no—
276C22×C4—1221no—
277C22×C4C22×D6111yescharacteristic
278Q16—2441no—
279SD16—41no—
280SD16—41no—
281SD16—2441no—
282SD16—2441no—
283D8—2441no—
284D8—2441no—
285D8—2441no—
286C2×C8—611no—
287C2×C8—611no—
288C2×C8C22×D6111yescharacteristic
289C2×C8C22×D6111yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—611no—
292C4⋊C4—611no—
293C4⋊C4—611no—
294C4⋊C4—1221no—
295C4⋊C4—1221no—
296C4⋊C4C22×D6111yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—611no—
299C22⋊C4—611no—
300C22⋊C4—1221no—
301C22⋊C4—1221no—
302C22⋊C4—1221no—
303C22⋊C4—1221no—
304C22⋊C4—1221no—
305C22⋊C4—1221no—
306C22⋊C4—1221no—
307C22⋊C4—1221no—
308C42—611no—
309C42—611no—
310C42—1221no—
311C23—21no—
312C23—21no—
313C23—42no—
314C23—81no—
315C23—81no—
316C23—1221no—
317C23—1221no—
318C23D4×D6111yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—1221no—
322Q8—1221no—
323Q8—4881no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—42no—
329D4—1221no—
330D4—1221no—
331D4—1221no—
332D4—1221no—
333D4—4881no—
334D4—4881no—
335D4—4881no—
336D4—4881no—
337D4—4881no—
338D4—2442no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—611no—
344C2×C4—611no—
345C2×C4—611no—
346C2×C4—611no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—4881no—
350C2×C4—2442no—
351C2×C4D4×D6111yescharacteristic
352C2×C4C23×D6111yescharacteristic
353C8—21no—
354C8—21no—
355C8—1221no—
356C8—1221no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—84no—
367C22—2441no—
368C22—2441no—
369C22—2441no—
370C22—2441no—
371C22—2441no—
372C22—2441no—
373C22C2×D4×D6111yescharacteristic
374C4—21no—
375C4—41no—
376C4—41no—
377C4—1221no—
378C4—1221no—
379C4—1221no—
380C4—1221no—
381C4—2441no—
382C4—2441no—
383C4#1451982211yescharacteristic
384C4#1451982211yescharacteristic
385C2—41no—
386C2—81no—
387C2—81no—
388C2—4881no—
389C2—4881no—
390C2#1684032711yescharacteristic
391C2#1684056611yescharacteristic
392C2#1684056811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#450C2
socleC22×C61C22×D4
hypercenter#450D61
hypocenterC61#3224
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. #16840385C2semidirect
2. #16840329C2semidirect
3. #16840148C2semidirect
4. #16840143C2semidirect
5. #16840120C2semidirect
6. #16840107C2semidirect
7. #16839982C2semidirect
8. #16839976C2semidirect
9. #16839960C2semidirect
10. #16839956C2semidirect
11. #16839922C2semidirect
12. #16839909C2semidirect
13. #16839896C2semidirect
14. #16839820C2semidirect
15. C61×#450C2semidirect
17. C2×#11758202C22semidirect
18. C2×#11758190C22semidirect
19. C2×#11758201C22semidirect
20. C2×D488C22semidirect
23. #14519776C22semidirect
27. #14519766C22semidirect
38. Q8×Dic61C22semidirect
39. #14519739C22semidirect
41. #14519706C22semidirect
42. #14519706C22semidirect
43. #14519702C22semidirect
44. #14519700C22semidirect
45. #14519699C22semidirect
48. #14519697C22semidirect
50. #14519687C22semidirect
51. C8×Dic61C22semidirect
208. #450D61semidirect
212. C61#3224semidirect