Finite Group Databasebeta

← #21456665

Subgroups — #21456665

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#16840326C211yesmaximal, characteristic, complemented
2#16840100C211yesmaximal, characteristic, complemented
3#16840083C211yesmaximal, characteristic, complemented
4#16840080C211yesmaximal, characteristic, complemented
5#16840075C211yesmaximal, characteristic, complemented
6#16840013C211yesmaximal, characteristic, complemented
7#16840010C211yesmaximal, characteristic, complemented
8#16839996C211yesmaximal, characteristic, complemented
9#16839993C211yesmaximal, characteristic, complemented
10#16839912C211yesmaximal, characteristic, complemented
11#16839907C211yesmaximal, characteristic, complemented
12#16839907C211yesmaximal, characteristic, complemented
13#16839895C211yesmaximal, characteristic, complemented
14#16839729C211yesmaximal, characteristic, complemented
15C61×#537C211yesmaximal, characteristic, complemented
16C22×D244C2211yescharacteristic
17C2×#11758201C2211yescharacteristic
18C2×#11758201C2211yescharacteristic
19C2×#11758199C2211yescharacteristic
20C2×#11758199C2211yescharacteristic
21C2×#11758194C2211yescharacteristic, complemented
22C22×#92418C2211yescharacteristic, complemented
23#14519773—21no—
24#14519766—21no—
25#14519751C2211yescharacteristic
26#14519751C2211yescharacteristic
27#14519751C2211yescharacteristic
28#14519751C2211yescharacteristic
29#14519745—21no—
30#14519745—21no—
31#14519736C2211yescharacteristic
32#14519710C2211yescharacteristic, complemented
33#14519710C2211yescharacteristic, complemented
34#14519708C2211yescharacteristic, complemented
35#14519708C2211yescharacteristic, complemented
36#14519701C2211yescharacteristic, complemented
37#14519701C2211yescharacteristic, complemented
38#14519698C2211yescharacteristic, complemented
39#14519698C2211yescharacteristic, complemented
40#14519697C2211yescharacteristic
41#14519697C2211yescharacteristic
42#14519697C2211yescharacteristic
43#14519697C2211yescharacteristic
44C22⋊#92418C2211yescharacteristic
45C22⋊#92418C2211yescharacteristic
46C22⋊#92418C2211yescharacteristic, complemented
47C22⋊#92418C2211yescharacteristic, complemented
48C2×#41×C61C2211yescharacteristic
49C2×#41×C61C2211yescharacteristic, complemented
50C22⋊Q8×C61—21no—
51C22⋊Q8×C61C2211yescharacteristic
52C22⋊Q8×C61C2211yescharacteristic, complemented
53#121×C61—21no—
54#121×C61—21no—
55#121×C61—21no—
56#121×C61C2211yescharacteristic
57#121×C61C2211yescharacteristic, complemented
58C2×C4⋊C4×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60#41×C61—41no—
61#41×C61—41no—
62#41×C61—41no—
63#41×C61—41no—
64C2×Q8×C61D411yescharacteristic
65C2×Q8×C61C2311yescharacteristic
66C2×D4×C61—21no—
67C2×D4×C61—21no—
68C2×D4×C61—21no—
69C2×D4×C61D411yescharacteristic
70C2×D4×C61D411yescharacteristic
71C2×D4×C61D411yescharacteristic
72C2×D4×C61C2311yescharacteristic
73C22×C4×C61—21no—
74C22×C4×C61—21no—
75C22×C4×C61C2311yescharacteristic
76C22×C4×C61C2311yescharacteristic
77C22×C4×C61C2311yescharacteristic
78C2×C22⋊D61—21no—
79C2×C22⋊D61—21no—
80C2×C22⋊D61—21no—
81C2×C22⋊D61—21no—
82C2×D244—21no—
83C2×D244—41no—
84C2×D244—41no—
85C2×D244C2311yescharacteristic
86C2×D244C2311yescharacteristic
87C4⋊C4×C61—21no—
88C4⋊C4×C61—21no—
89C4⋊C4×C61—21no—
90C4⋊C4×C61C2311yescharacteristic
91C4⋊C4×C61C2311yescharacteristic
92C22⋊C4×C61—21no—
93C22⋊C4×C61—21no—
94C22⋊C4×C61—21no—
95C22⋊C4×C61—21no—
96C22⋊Dic61—21no—
97#11758201—41no—
98#11758201—41no—
99#11758199—41no—
100#11758199—41no—
101#11758198—21no—
102#11758198—21no—
103#11758198—21no—
104#11758198—21no—
105C4⋊Dic61C2311yescharacteristic
106C4⋊Dic61C2311yescharacteristic
107C4×Dic61—21no—
108#11758194—41no—
109C2×#92418—41no—
110C2×#92418C2311yescharacteristic
111C2×#92418C2311yescharacteristic
112C2×#92418C2311yescharacteristic
113C2×#92418C2311yescharacteristic
114C23×C61—21no—
115C23×C61C2×D411yescharacteristic
116C23×C61C2×D411yescharacteristic
117C23×C61C2×D411yescharacteristic
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—42no—
121C22×D61—81no—
122C22×D61—81no—
123Q8×C61—21no—
124Q8×C61—21no—
125Q8×C61—41no—
126D4×C61—21no—
127D4×C61—21no—
128D4×C61—41no—
129D4×C61—41no—
130D4×C61—41no—
131D4×C61—42no—
132D4×C61—81no—
133D4×C61—81no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
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—42no—
144C2×C4×C61—81no—
145C2×C4×C61C2×D411yescharacteristic
146C2×C4×C61C2×D411yescharacteristic
147C2×C4×C61C2×D411yescharacteristic
148C2×C4×C61C2411yescharacteristic
149C22⋊D61—81no—
150C22⋊D61—81no—
151C22⋊D61—81no—
152C22⋊D61—81no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155D244—21no—
156D244—21no—
157D244—21no—
158D244—21no—
159D244—42no—
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×C61C22×D411yescharacteristic
177C2×D61—41no—
178C2×D61—41no—
179C2×D61—41no—
180C2×D61—41no—
181C2×D61—41no—
182C2×D61—41no—
183C2×D61—84no—
184C4×C61—21no—
185C4×C61—21no—
186C4×C61—21no—
187C4×C61—41no—
188C4×C61—41no—
189C4×C61—41no—
190C4×C61H(5,𝔽2)11yescharacteristic
191C4×C61H(5,𝔽2)11yescharacteristic
192Dic61—41no—
193Dic61—41no—
194#3198—611nomaximal, Sylow
195C2×C61—41no—
196C2×C61—41no—
197C2×C61—41no—
198C2×C61—81no—
199C2×C61#53411yescharacteristic
200C2×C61#57611yescharacteristic
201C2×C61#57711yescharacteristic
202D61—81no—
203D61—81no—
204#537D6111yescharacteristic, complemented
205#535—611no—
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×#41C2×D6111yescharacteristic
221C2×#41C2×D6111yescharacteristic, complemented
222C22×D4—611no—
223C2×SD16—611no—
224C2×SD16—611no—
225C2×D8—611no—
226C2×D8—611no—
227C2×M16—611no—
228C22×C8—611no—
229#127—1221no—
230#124—1221no—
231C22⋊Q8—21no—
232C22⋊Q8C2×D6111yescharacteristic
233C22⋊Q8C2×D6111yescharacteristic, complemented
234#121—21no—
235#121—21no—
236#121—21no—
237#121—611no—
238#121—611no—
239#121—611no—
240#121—611no—
241#121C2×D6111yescharacteristic
242#121C2×D6111yescharacteristic, complemented
243#120—1221no—
244#120—1221no—
245#117—611no—
246C2×C4⋊C4C2×D6111yescharacteristic, complemented
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—1221no—
264#41—41no—
265#41—41no—
266#41—41no—
267#41—41no—
268C2×Q8C22⋊D6111yescharacteristic
269C2×Q8C22×D6111yescharacteristic
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—611no—
274C2×D4—611no—
275C2×D4—1221no—
276C2×D4—1221no—
277C2×D4—1221no—
278C2×D4—1221no—
279C2×D4—1221no—
280C2×D4—2441no—
281C2×D4—2441no—
282C2×D4C22⋊D6111yescharacteristic
283C2×D4C22⋊D6111yescharacteristic
284C2×D4C22⋊D6111yescharacteristic
285C2×D4C22×D6111yescharacteristic
286C22×C4—21no—
287C22×C4—21no—
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—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—611no—
305C4⋊C4—611no—
306C4⋊C4C22×D6111yescharacteristic
307C4⋊C4C22×D6111yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—1221no—
313C22⋊C4—1221no—
314C22⋊C4—1221no—
315C22⋊C4—1221no—
316C22⋊C4—1221no—
317C42—1221no—
318C23—21no—
319C23—1221no—
320C23—1221no—
321C23—4881no—
322C23—4881no—
323C23—2442no—
324C23C2×C22⋊D6111yescharacteristic
325C23C2×C22⋊D6111yescharacteristic
326C23C2×C22⋊D6111yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—41no—
330D4—21no—
331D4—21no—
332D4—41no—
333D4—41no—
334D4—41no—
335D4—42no—
336D4—81no—
337D4—81no—
338D4—1221no—
339D4—1221no—
340D4—1221no—
341D4—1221no—
342D4—4881no—
343D4—4881no—
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—21no—
356C2×C4—42no—
357C2×C4—81no—
358C2×C4—1221no—
359C2×C4—1221no—
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—4884no—
381C22—2441no—
382C22—2441no—
383C22—2441no—
384C22—2441no—
385C22—2441no—
386C22—2441no—
387C22C22×C22⋊D6111yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—2441no—
395C4—2441no—
396C4#1451982211yescharacteristic
397C4#1451982211yescharacteristic
398C2—41no—
399C2—41no—
400C2—41no—
401C2—81no—
402C2—4881no—
403C2—4881no—
404C2#1684032111yescharacteristic
405C2#1684056511yescharacteristic
406C2#1684057011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#537C2
socleC22×C61C22×D4
hypercenter#537D61
hypocenterC61#3198
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #16840326C2semidirect
2. #16840100C2semidirect
3. #16840083C2semidirect
4. #16840080C2semidirect
5. #16840075C2semidirect
6. #16840013C2semidirect
7. #16840010C2semidirect
8. #16839996C2semidirect
9. #16839993C2semidirect
10. #16839912C2semidirect
11. #16839907C2semidirect
12. #16839907C2semidirect
13. #16839895C2semidirect
14. #16839729C2semidirect
15. C61×#537C2semidirect
21. C2×#11758194C22semidirect
22. C22×#92418C22semidirect
32. #14519710C22semidirect
33. #14519710C22semidirect
34. #14519708C22semidirect
35. #14519708C22semidirect
36. #14519701C22semidirect
37. #14519701C22semidirect
38. #14519698C22semidirect
39. #14519698C22semidirect
46. C22⋊#92418C22semidirect
47. C22⋊#92418C22semidirect
49. C2×#41×C61C22semidirect
52. C22⋊Q8×C61C22semidirect
57. #121×C61C22semidirect
58. C2×C4⋊C4×C61C22semidirect
204. #537D61semidirect
219. C61#3198semidirect
221. C2×#41C2×D61semidirect
233. C22⋊Q8C2×D61semidirect
242. #121C2×D61semidirect
246. C2×C4⋊C4C2×D61semidirect