Finite Group Databasebeta

← #21456671

Subgroups — #21456671

Order 7808.

422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840340C211yesmaximal, characteristic, complemented
2#16840103C211yesmaximal, characteristic, complemented
3#16840086C211yesmaximal, characteristic, complemented
4#16840078C211yesmaximal, characteristic, complemented
5#16840073C211yesmaximal, characteristic, complemented
6#16840013C211yesmaximal, characteristic, complemented
7#16840006C211yesmaximal, characteristic, complemented
8#16839996C211yesmaximal, characteristic, complemented
9#16839989C211yesmaximal, characteristic, complemented
10#16839913C211yesmaximal, characteristic, complemented
11#16839905C211yesmaximal, characteristic, complemented
12#16839905C211yesmaximal, characteristic, complemented
13#16839896C211yesmaximal, characteristic, complemented
14#16839729C211yesmaximal, characteristic, complemented
15C61×#535C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic, complemented
17C2×#11758200C2211yescharacteristic
18C2×#11758200C2211yescharacteristic
19C2×#11758199C2211yescharacteristic
20C2×#11758199C2211yescharacteristic
21C2×#11758194C2211yescharacteristic, complemented
22C22×#92418C2211yescharacteristic, complemented
23#14519756C2211yescharacteristic
24#14519756C2211yescharacteristic, complemented
25#14519753—21no—
26#14519751C2211yescharacteristic
27#14519751C2211yescharacteristic, complemented
28#14519749—21no—
29#14519749—21no—
30#14519748—21no—
31C2×C4⋊Dic61C2211yescharacteristic, complemented
32#14519710C2211yescharacteristic, complemented
33#14519710C2211yescharacteristic, complemented
34#14519708C2211yescharacteristic, complemented
35#14519708C2211yescharacteristic, complemented
36#14519700C2211yescharacteristic, complemented
37#14519700C2211yescharacteristic, complemented
38#14519698C2211yescharacteristic
39#14519698C2211yescharacteristic
40#14519698C2211yescharacteristic
41#14519698C2211yescharacteristic
42#14519697C2211yescharacteristic, complemented
43#14519697C2211yescharacteristic, complemented
44C22⋊#92418C2211yescharacteristic
45C22⋊#92418C2211yescharacteristic
46C22⋊#92418C2211yescharacteristic, complemented
47C22⋊#92418C2211yescharacteristic, complemented
48C2×#41×C61C2211yescharacteristic
49C22×D4×C61C2211yescharacteristic
50#127×C61—21no—
51#124×C61—21no—
52#121×C61C2211yescharacteristic
53#121×C61C2211yescharacteristic
54#121×C61C2211yescharacteristic
55#121×C61C2211yescharacteristic
56#120×C61—21no—
57#120×C61—21no—
58#117×C61C2211yescharacteristic
59C24×C61—21no—
60#41×C61—41no—
61#41×C61—41no—
62C2×Q8×C61D411yescharacteristic
63C2×D4×C61—21no—
64C2×D4×C61—21no—
65C2×D4×C61—21no—
66C2×D4×C61—21no—
67C2×D4×C61—21no—
68C2×D4×C61—41no—
69C2×D4×C61—41no—
70C2×D4×C61D411yescharacteristic
71C2×D4×C61D411yescharacteristic
72C2×D4×C61D411yescharacteristic
73C2×D4×C61C2311yescharacteristic
74C2×D4×C61C2311yescharacteristic
75C22×C4×C61C2311yescharacteristic
76C22×C4×C61C2311yescharacteristic
77C22×C4×C61C2311yescharacteristic
78C2×C22⋊D61—21no—
79C2×C22⋊D61—21no—
80C2×C22⋊D61—21no—
81C22×Dic61—21no—
82#11758222—41no—
83#11758222—41no—
84C2×D244C2311yescharacteristic
85C2×C4×D61—21no—
86C2×Dic122C2311yescharacteristic
87C4⋊C4×C61C2311yescharacteristic
88C4⋊C4×C61C2311yescharacteristic
89C22⋊C4×C61—21no—
90C22⋊C4×C61—21no—
91C22⋊C4×C61—21no—
92C22⋊C4×C61—21no—
93C22⋊C4×C61—21no—
94C42×C61—21no—
95C22⋊Dic61—21no—
96C22⋊Dic61—21no—
97#11758200—41no—
98#11758200—41no—
99#11758199—41no—
100#11758199—41no—
101#11758198—21no—
102#11758198—21no—
103C4⋊Dic61—21no—
104C4⋊Dic61C2311yescharacteristic
105C4⋊Dic61C2311yescharacteristic
106#11758196—21no—
107#11758196—21no—
108#11758194—41no—
109C2×#92418—41no—
110C2×#92418C2311yescharacteristic
111C2×#92418C2311yescharacteristic
112C2×#92418C2311yescharacteristic
113C2×#92418C2311yescharacteristic
114C23×C61—21no—
115C23×C61—21no—
116C23×C61—42no—
117C23×C61—81no—
118C23×C61—81no—
119C23×C61C2×D411yescharacteristic
120C23×C61C2×D411yescharacteristic
121C23×C61C2×D411yescharacteristic
122C22×D61—21no—
123Q8×C61—41no—
124D4×C61—21no—
125D4×C61—21no—
126D4×C61—21no—
127D4×C61—21no—
128D4×C61—41no—
129D4×C61—41no—
130D4×C61—41no—
131D4×C61—42no—
132D4×C61—81no—
133D4×C61—81no—
134D4×C61—81no—
135D4×C61—81no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61C2×D411yescharacteristic
145C2×C4×C61C2×D411yescharacteristic
146C2×C4×C61C2×D411yescharacteristic
147C2×C4×C61C2411yescharacteristic
148C22⋊D61—42no—
149C22⋊D61—81no—
150C22⋊D61—81no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—81no—
155D244—21no—
156D244—21no—
157C4×D61—42no—
158Dic122—21no—
159Dic122—21no—
160#92418—21no—
161#92418—21no—
162#92418—21no—
163#92418—21no—
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—21no—
167C22×C61—21no—
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—21no—
173C22×C61—41no—
174C22×C61—41no—
175C22×C61—41no—
176C22×C61—41no—
177C22×C61—41no—
178C22×C61—41no—
179C22×C61—84no—
180C22×C61C22×D411yescharacteristic
181C2×D61—41no—
182C2×D61—41no—
183C2×D61—41no—
184C4×C61—21no—
185C4×C61—21no—
186C4×C61—21no—
187C4×C61—41no—
188C4×C61—41no—
189C4×C61H(5,𝔽2)11yescharacteristic
190C4×C61H(5,𝔽2)11yescharacteristic
191Dic61—41no—
192Dic61—41no—
193Dic61—41no—
194#3198—611nomaximal, Sylow
195C2×C61—41no—
196C2×C61—41no—
197C2×C61—41no—
198C2×C61—81no—
199C2×C61—81no—
200C2×C61#53411yescharacteristic
201C2×C61#57611yescharacteristic
202C2×C61#57711yescharacteristic
203D61—81no—
204#537—611no—
205#535D6111yescharacteristic, complemented
206#485—611no—
207#482—611no—
208#481—611no—
209#480—611no—
210#469—611no—
211#468—611no—
212#466—611no—
213#465—611no—
214#450—611no—
215#449—611no—
216#449—611no—
217#447—611no—
218#408—611no—
219C61#319811yescharacteristic, complemented, Sylow
220C2×#41—611no—
221C2×#41C2×D6111yescharacteristic
222C22×D4C2×D6111yescharacteristic
223C2×SD16—611no—
224C2×SD16—611no—
225C2×D8—611no—
226C2×D8—611no—
227C2×M16—611no—
228C22×C8—611no—
229#127—21no—
230#124—21no—
231C22⋊Q8—611no—
232C22⋊Q8—611no—
233C22⋊Q8—1221no—
234#121—611no—
235#121—611no—
236#121—1221no—
237#121—1221no—
238#121—1221no—
239#121C2×D6111yescharacteristic
240#121C2×D6111yescharacteristic
241#121C2×D6111yescharacteristic
242#121C2×D6111yescharacteristic
243#120—21no—
244#120—21no—
245#117C2×D6111yescharacteristic
246C2×C4⋊C4—611no—
247#107—611no—
248#107—611no—
249#106—611no—
250#106—611no—
251#103—611no—
252#103—611no—
253#102—611no—
254#102—611no—
255#102—611no—
256#102—611no—
257#102—611no—
258#102—611no—
259C22⋊C8—611no—
260C22⋊C8—611no—
261C22⋊C8—611no—
262C22⋊C8—611no—
263C24—21no—
264#41—41no—
265#41—41no—
266#41—2441no—
267#41—2441no—
268C2×Q8—611no—
269C2×Q8C22⋊D6111yescharacteristic
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—611no—
278C2×D4—1221no—
279C2×D4—1221no—
280C2×D4—1221no—
281C2×D4C22⋊D6111yescharacteristic
282C2×D4C22⋊D6111yescharacteristic
283C2×D4C22⋊D6111yescharacteristic
284C2×D4C22×D6111yescharacteristic
285C2×D4C22×D6111yescharacteristic
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4C22×D6111yescharacteristic
289C22×C4C22×D6111yescharacteristic
290C22×C4C22×D6111yescharacteristic
291SD16—2441no—
292SD16—2441no—
293D8—2441no—
294D8—2441no—
295M16—2441no—
296C2×C8—611no—
297C2×C8—611no—
298C2×C8—611no—
299C2×C8—611no—
300C2×C8—2441no—
301C4⋊C4—611no—
302C4⋊C4—611no—
303C4⋊C4—1221no—
304C4⋊C4—1221no—
305C4⋊C4—1221no—
306C4⋊C4C22×D6111yescharacteristic
307C4⋊C4C22×D6111yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—21no—
313C22⋊C4—1221no—
314C22⋊C4—1221no—
315C22⋊C4—1221no—
316C22⋊C4—1221no—
317C42—21no—
318C23—21no—
319C23—21no—
320C23—42no—
321C23—81no—
322C23—81no—
323C23—1221no—
324C23C2×C22⋊D6111yescharacteristic
325C23C2×C22⋊D6111yescharacteristic
326C23C2×C22⋊D6111yescharacteristic
327Q8—41no—
328Q8—1221no—
329Q8—1221no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—41no—
335D4—41no—
336D4—41no—
337D4—42no—
338D4—81no—
339D4—81no—
340D4—81no—
341D4—81no—
342D4—1221no—
343D4—1221no—
344D4—4881no—
345D4—4881no—
346D4—2442no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—1221no—
358C2×C4—4881no—
359C2×C4—2442no—
360C2×C4C2×C22⋊D6111yescharacteristic
361C2×C4C2×C22⋊D6111yescharacteristic
362C2×C4C2×C22⋊D6111yescharacteristic
363C2×C4C23×D6111yescharacteristic
364C8—1221no—
365C8—1221no—
366C8—1221no—
367C8—1221no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—84no—
384C22—2441no—
385C22—2441no—
386C22—2441no—
387C22C22×C22⋊D6111yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—41no—
392C4—41no—
393C4—2441no—
394C4—2441no—
395C4—2441no—
396C4#1451982211yescharacteristic
397C4#1451982211yescharacteristic
398C2—41no—
399C2—41no—
400C2—41no—
401C2—81no—
402C2—81no—
403C2—4881no—
404C2#1684032111yescharacteristic
405C2#1684056511yescharacteristic
406C2#1684057311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#535C2
socleC22×C61C22×D4
hypercenter#535D61
hypocenterC61#3198
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #16840340C2semidirect
2. #16840103C2semidirect
3. #16840086C2semidirect
4. #16840078C2semidirect
5. #16840073C2semidirect
6. #16840013C2semidirect
7. #16840006C2semidirect
8. #16839996C2semidirect
9. #16839989C2semidirect
10. #16839913C2semidirect
11. #16839905C2semidirect
12. #16839905C2semidirect
13. #16839896C2semidirect
14. #16839729C2semidirect
15. C61×#535C2semidirect
16. C2×#11758222C22semidirect
21. C2×#11758194C22semidirect
22. C22×#92418C22semidirect
24. #14519756C22semidirect
27. #14519751C22semidirect
31. C2×C4⋊Dic61C22semidirect
32. #14519710C22semidirect
33. #14519710C22semidirect
34. #14519708C22semidirect
35. #14519708C22semidirect
36. #14519700C22semidirect
37. #14519700C22semidirect
42. #14519697C22semidirect
43. #14519697C22semidirect
46. C22⋊#92418C22semidirect
47. C22⋊#92418C22semidirect
205. #535D61semidirect
219. C61#3198semidirect