Finite Group Databasebeta

← #21457669

Subgroups — #21457669

Order 7808.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840458C211yesmaximal, characteristic, complemented
2#16840116C211yesmaximal, characteristic, complemented
3#16840095C211yesmaximal, characteristic, complemented
4#16840083C211yesmaximal, characteristic, complemented
5#16840062C211yesmaximal, characteristic, complemented
6#16839996C211yesmaximal, characteristic, complemented
7#16839993C211yesmaximal, characteristic, complemented
8#16839974C211yesmaximal, characteristic, complemented
9#16839907C211yesmaximal, characteristic, complemented
10#16839896C211yesmaximal, characteristic, complemented
11C4×#11758199C211yesmaximal, characteristic, complemented
12D4×#92418C211yesmaximal, characteristic, complemented
13#16839758C211yesmaximal, characteristic, complemented
14C2×#14519698C211yesmaximal, characteristic, complemented
15C61×#546C211yesmaximal, characteristic, complemented
16C2×#11758201C2211yescharacteristic, complemented
17C2×#11758199C2211yescharacteristic
18C2×#11758199C2211yescharacteristic
19C22×#92418C2211yescharacteristic
20C22×#92418C2211yescharacteristic, complemented
21#14519772—21no—
22#14519769C2211yescharacteristic, complemented
23#14519759—21no—
24#14519751C2211yescharacteristic
25#14519751C2211yescharacteristic, complemented
26#14519749—21no—
27C4×D244C2211yescharacteristic, complemented
28#14519737—21no—
29#14519736C2211yescharacteristic, complemented
30C2×C4⋊Dic61C2211yescharacteristic
31#14519710C2211yescharacteristic, complemented
32#14519710C2211yescharacteristic, complemented
33#14519708C2211yescharacteristic, complemented
34C4⋊#92418C2211yescharacteristic, complemented
35#14519701C2211yescharacteristic, complemented
36#14519701C2211yescharacteristic, complemented
37#14519701C2211yescharacteristic, complemented
38#14519698C2211yescharacteristic
39#14519698C2211yescharacteristic
40#14519698C2211yescharacteristic
41#14519698C2211yescharacteristic
42#14519698C2211yescharacteristic
43#14519698C2211yescharacteristic
44#14519697C2211yescharacteristic, complemented
45C22⋊#92418C2211yescharacteristic
46C22⋊#92418C2211yescharacteristic, complemented
47C4×#92418C2211yescharacteristic, complemented
48C2×#41×C61C2211yescharacteristic
49C22×D4×C61C2211yescharacteristic
50#124×C61C2211yescharacteristic
51#123×C61—21no—
52C22⋊Q8×C61C2211yescharacteristic
53#121×C61—21no—
54#121×C61C2211yescharacteristic
55#120×C61—21no—
56C4×D4×C61C2211yescharacteristic
57C4×D4×C61C2211yescharacteristic
58C2×C22⋊C4×C61—21no—
59C24×C61—21no—
60#41×C61—22no—
61#41×C61—41no—
62C2×Q8×C61C2311yescharacteristic
63C2×D4×C61—22no—
64C2×D4×C61—21no—
65C2×D4×C61—21no—
66C2×D4×C61—21no—
67C2×D4×C61—41no—
68C2×D4×C61D411yescharacteristic
69C2×D4×C61C2311yescharacteristic
70C2×D4×C61C2311yescharacteristic
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61C2311yescharacteristic
74C22×C4×C61C2311yescharacteristic
75C2×C22⋊D61—21no—
76C2×C22⋊D61—21no—
77C22×Dic61—21no—
78C2×D244C2311yescharacteristic
79C2×C4×D61—21no—
80C4⋊C4×C61—21no—
81C4⋊C4×C61D411yescharacteristic
82C4⋊C4×C61C2311yescharacteristic
83C22⋊C4×C61—21no—
84C22⋊C4×C61—21no—
85C22⋊C4×C61—21no—
86C22⋊C4×C61—21no—
87C22⋊C4×C61—21no—
88C22⋊C4×C61D411yescharacteristic
89C22⋊C4×C61D411yescharacteristic
90C42×C61C2311yescharacteristic
91C22⋊Dic61—21no—
92#11758201—41no—
93#11758199—22no—
94#11758199—41no—
95#11758198—21no—
96#11758198—21no—
97#11758198—21no—
98C4⋊Dic61—21no—
99C4⋊Dic61C2311yescharacteristic
100C4⋊Dic61C2311yescharacteristic
101C4⋊Dic61C2311yescharacteristic
102#11758196—21no—
103#11758196—21no—
104C4×Dic61—21no—
105C2×#92418—41no—
106C2×#92418—41no—
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—42no—
114C23×C61—42no—
115C23×C61—81no—
116C23×C61C2×D411yescharacteristic
117C23×C61C2×D411yescharacteristic
118C22×D61—21no—
119Q8×C61—21no—
120Q8×C61—21no—
121D4×C61—22no—
122D4×C61—21no—
123D4×C61—21no—
124D4×C61—21no—
125D4×C61—42no—
126D4×C61—42no—
127D4×C61—81no—
128D4×C61#4112yes—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—42no—
136C2×C4×C61—81no—
137C2×C4×C61C2×D411yescharacteristic
138C2×C4×C61C2×D411yescharacteristic
139C2×C4×C61C2×D411yescharacteristic
140C2×C4×C61C2×D411yescharacteristic
141C2×C4×C61C2411yescharacteristic
142C22⋊D61—42no—
143C22⋊D61—81no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—81no—
148D244—21no—
149D244—21no—
150C4×D61—81no—
151#92418—21no—
152#92418—21no—
153#92418—21no—
154#92418—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—22no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—84no—
167C22×C61#13512yes—
168C22×C61C22×D411yescharacteristic
169C2×D61—41no—
170C2×D61—41no—
171C2×D61—41no—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—21no—
176C4×C61—41no—
177C4×C61—41no—
178C4×C61C2×#4111yescharacteristic
179C4×C61H(5,𝔽2)11yescharacteristic
180Dic61—41no—
181Dic61—41no—
182Dic61—41no—
183#3297—611nomaximal, Sylow
184C2×C61—22no—
185C2×C61—41no—
186C2×C61—42no—
187C2×C61—81no—
188C2×C61#54611yescharacteristic
189C2×C61C2×#13511yescharacteristic
190C2×C61#57611yescharacteristic
191D61—81no—
192#553—611no—
193#546D6111yescharacteristic, complemented
194#488—611no—
195#484—611no—
196#482—611no—
197#478—611no—
198#466—611no—
199#465—611no—
200#463—611no—
201#449—611no—
202#447—611no—
203C4×D8—611no—
204C8×D4—611no—
205#416—611no—
206C2×#102—611no—
207C61#329711yescharacteristic, complemented, Sylow
208C2×#41C2×D6111yescharacteristic
209C22×D4C2×D6111yescharacteristic
210C2×SD16—611no—
211C2×D8—611no—
212C2×D8—611no—
213C22×C8—611no—
214C22×C8—611no—
215#126—1221no—
216#125—611no—
217#124C2×D6111yescharacteristic
218#123—21no—
219#123—1221no—
220C22⋊Q8C2×D6111yescharacteristic
221#121—21no—
222#121—611no—
223#121—611no—
224#121—1221no—
225#121C2×D6111yescharacteristic
226#120—21no—
227C4×D4—611no—
228C4×D4—1221no—
229C4×D4C2×D6111yescharacteristic
230C4×D4C2×D6111yescharacteristic
231#117—611no—
232C2×C4⋊C4—611no—
233C2×C22⋊C4—21no—
234#107—611no—
235#107—611no—
236#106—611no—
237C4⋊C8—611no—
238#103—611no—
239#103—611no—
240#103—611no—
241#102—611no—
242#102—611no—
243#102—611no—
244#102—611no—
245#102—611no—
246#102—611no—
247#102—611no—
248C22⋊C8—611no—
249C22⋊C8—611no—
250C4×C8—611no—
251C24—21no—
252#41—22no—
253#41—41no—
254C2×Q8C22×D6111yescharacteristic
255C2×D4—22no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—41no—
260C2×D4—611no—
261C2×D4—1221no—
262C2×D4—1221no—
263C2×D4C22⋊D6111yescharacteristic
264C2×D4C22×D6111yescharacteristic
265C2×D4C22×D6111yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—1221no—
269C22×C4—1221no—
270C22×C4C22×D6111yescharacteristic
271C22×C4C22×D6111yescharacteristic
272SD16—2441no—
273D8—1222no—
274D8—2441no—
275C2×C8—611no—
276C2×C8—611no—
277C2×C8—611no—
278C2×C8—611no—
279C2×C8—2441no—
280C2×C8—2441no—
281C4⋊C4—21no—
282C4⋊C4—611no—
283C4⋊C4—611no—
284C4⋊C4—611no—
285C4⋊C4—1221no—
286C4⋊C4—1221no—
287C4⋊C4—1221no—
288C4⋊C4C22⋊D6111yescharacteristic
289C4⋊C4C22×D6111yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—1221no—
296C22⋊C4—1221no—
297C22⋊C4—1221no—
298C22⋊C4—1221no—
299C22⋊C4C22⋊D6111yescharacteristic
300C22⋊C4C22⋊D6111yescharacteristic
301C42—1221no—
302C42C22×D6111yescharacteristic
303C23—21no—
304C23—21no—
305C23—42no—
306C23—42no—
307C23—81no—
308C23—1221no—
309C23C2×C22⋊D6111yescharacteristic
310C23C2×C22⋊D6111yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—22no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—42no—
318D4—42no—
319D4—81no—
320D4—1221no—
321D4—1221no—
322D4—4881no—
323D4—2442no—
324D4#1175822412yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—42no—
332C2×C4—81no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—4881no—
337C2×C4—4881no—
338C2×C4C2×C22⋊D6111yescharacteristic
339C2×C4C2×C22⋊D6111yescharacteristic
340C2×C4C2×C22⋊D6111yescharacteristic
341C2×C4C2×C22⋊D6111yescharacteristic
342C2×C4C23×D6111yescharacteristic
343C8—1221no—
344C8—1221no—
345C8—1221no—
346C8—1221no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—22no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—84no—
359C22—2441no—
360C22—2441no—
361C22—2441no—
362C22#1451979712yes—
363C22C22×C22⋊D6111yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—41no—
369C4—41no—
370C4—2441no—
371C4—2441no—
372C4—2441no—
373C4C2×#1175822411yescharacteristic
374C4#1451982211yescharacteristic
375C2—22no—
376C2—41no—
377C2—42no—
378C2—81no—
379C2—4881no—
380C2#1684040611yescharacteristic
381C2C2×#1451979711yescharacteristic
382C2#1684056511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#546C2
socleC22×C61C22×D4
hypercenter#546D61
hypocenterC61#3297
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #16840458C2semidirect
2. #16840116C2semidirect
3. #16840095C2semidirect
4. #16840083C2semidirect
5. #16840062C2semidirect
6. #16839996C2semidirect
7. #16839993C2semidirect
8. #16839974C2semidirect
9. #16839907C2semidirect
10. #16839896C2semidirect
11. C4×#11758199C2semidirect
12. D4×#92418C2semidirect
13. #16839758C2semidirect
14. C2×#14519698C2semidirect
15. C61×#546C2semidirect
16. C2×#11758201C22semidirect
20. C22×#92418C22semidirect
22. #14519769C22semidirect
25. #14519751C22semidirect
27. C4×D244C22semidirect
29. #14519736C22semidirect
31. #14519710C22semidirect
32. #14519710C22semidirect
33. #14519708C22semidirect
34. C4⋊#92418C22semidirect
35. #14519701C22semidirect
36. #14519701C22semidirect
37. #14519701C22semidirect
44. #14519697C22semidirect
46. C22⋊#92418C22semidirect
47. C4×#92418C22semidirect
193. #546D61semidirect
207. C61#3297semidirect