Finite Group Databasebeta

← #21457825

Subgroups — #21457825

Order 7808.

404 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840458C211yesmaximal, characteristic, complemented
2#16840126C211yesmaximal, characteristic, complemented
3#16840083C211yesmaximal, characteristic, complemented
4#16840073C211yesmaximal, characteristic, complemented
5#16840069C211yesmaximal, characteristic, complemented
6#16840013C211yesmaximal, characteristic, complemented
7#16839996C211yesmaximal, characteristic, complemented
8#16839954C211yesmaximal, characteristic, complemented
9#16839907C211yesmaximal, characteristic, complemented
10#16839907C211yesmaximal, characteristic, complemented
11#16839860C211yesmaximal, characteristic, complemented
12#16839834C211yesmaximal, characteristic, complemented
13#16839763C211yesmaximal, characteristic, complemented
14#16839758C211yesmaximal, characteristic, complemented
15C61×#550C211yesmaximal, characteristic, complemented
16C2×#11758201C2211yescharacteristic
17C2×#11758199C2211yescharacteristic
18C2×#11758199C2211yescharacteristic
19C2×#11758194C2211yescharacteristic
20C22×#92418C2211yescharacteristic
21#14519772—21no—
22#14519769C2211yescharacteristic
23#14519759—21no—
24#14519751C2211yescharacteristic
25#14519751C2211yescharacteristic
26#14519749—21no—
27C4×D244C2211yescharacteristic
28#14519737—21no—
29#14519736C2211yescharacteristic
30C2×C4⋊Dic61C2211yescharacteristic
31#14519710C2211yescharacteristic
32#14519710C2211yescharacteristic
33#14519708C2211yescharacteristic
34C4⋊#92418C2211yescharacteristic
35#14519701C2211yescharacteristic
36#14519701C2211yescharacteristic
37#14519701C2211yescharacteristic
38#14519698C2211yescharacteristic
39#14519698C2211yescharacteristic
40#14519698C2211yescharacteristic
41#14519698C2211yescharacteristic
42#14519698C2211yescharacteristic
43#14519698C2211yescharacteristic
44#14519697C2211yescharacteristic
45C22⋊#92418C2211yescharacteristic
46C22⋊#92418C2211yescharacteristic
47#14519688C2211yescharacteristic
48C2×#41×C61C2211yescharacteristic
49C2×#41×C61C2211yescharacteristic
50#127×C61—21no—
51#127×C61C2211yescharacteristic
52#121×C61—21no—
53#121×C61—21no—
54#121×C61C2211yescharacteristic
55#121×C61C2211yescharacteristic
56C4×Q8×C61C2211yescharacteristic
57C4×D4×C61—21no—
58C4×D4×C61C2211yescharacteristic
59#41×C61—22no—
60#41×C61—22no—
61#41×C61—41no—
62#41×C61—41no—
63C2×Q8×C61C2311yescharacteristic
64C2×D4×C61—21no—
65C2×D4×C61—21no—
66C2×D4×C61—21no—
67C2×D4×C61—21no—
68C2×D4×C61—21no—
69C2×D4×C61—21no—
70C2×D4×C61D411yescharacteristic
71C2×D4×C61C2311yescharacteristic
72C2×D4×C61C2311yescharacteristic
73C22×C4×C61—21no—
74C22×C4×C61—21no—
75C22×C4×C61C2311yescharacteristic
76C22×C4×C61C2311yescharacteristic
77C2×C22⋊D61—21no—
78C2×C22⋊D61—21no—
79C22×Dic61—21no—
80C2×D244C2311yescharacteristic
81C2×C4×D61—21no—
82C4⋊C4×C61—21no—
83C4⋊C4×C61D411yescharacteristic
84C4⋊C4×C61C2311yescharacteristic
85C22⋊C4×C61—21no—
86C22⋊C4×C61—21no—
87C22⋊C4×C61D411yescharacteristic
88C22⋊C4×C61D411yescharacteristic
89C42×C61—21no—
90C42×C61C2311yescharacteristic
91C22⋊Dic61—21no—
92#11758201—22no—
93#11758199—41no—
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—
105#11758194—41no—
106C2×#92418—41no—
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111C23×C61—21no—
112C23×C61—21no—
113C23×C61C2×D411yescharacteristic
114C23×C61C2×D411yescharacteristic
115C22×D61—21no—
116Q8×C61—21no—
117Q8×C61#4112yes—
118D4×C61—21no—
119D4×C61—21no—
120D4×C61—21no—
121D4×C61—21no—
122D4×C61—41no—
123D4×C61—42no—
124D4×C61—42no—
125D4×C61—42no—
126D4×C61—81no—
127D4×C61—81no—
128D4×C61—81no—
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—42no—
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—21no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61C22×D411yescharacteristic
168C2×D61—41no—
169C2×D61—41no—
170C2×D61—41no—
171C4×C61—21no—
172C4×C61—21no—
173C4×C61—22no—
174C4×C61—21no—
175C4×C61—21no—
176C4×C61—41no—
177C4×C61C2×#4111yescharacteristic
178C4×C61H(5,𝔽2)11yescharacteristic
179Dic61—41no—
180Dic61—41no—
181Dic61—41no—
182#3309—611nomaximal, Sylow
183C2×C61—41no—
184C2×C61—41no—
185C2×C61—81no—
186C2×C61—81no—
187C2×C61#54611yescharacteristic
188C2×C61#57511yescharacteristic
189C2×C61#57611yescharacteristic
190D61—81no—
191#553—611no—
192#550D6111yescharacteristic, complemented
193#490—611no—
194#482—611no—
195#480—611no—
196#479—611no—
197#469—611no—
198#466—611no—
199#459—611no—
200#449—611no—
201#449—611no—
202#440—611no—
203#435—611no—
204#417—611no—
205#416—611no—
206C61#330911yescharacteristic, complemented, Sylow
207C2×#41C2×D6111yescharacteristic
208C2×#41C2×D6111yescharacteristic
209C2×SD16—611no—
210C2×D8—611no—
211C2×D8—611no—
212C2×M16—611no—
213C22×C8—611no—
214#127—21no—
215#127C2×D6111yescharacteristic
216#126—1221no—
217#125—611no—
218#123—1221no—
219#121—21no—
220#121—21no—
221#121—611no—
222#121—611no—
223#121—1221no—
224#121C2×D6111yescharacteristic
225#121C2×D6111yescharacteristic
226C4×Q8C2×D6111yescharacteristic
227C4×D4—21no—
228C4×D4—611no—
229C4×D4—1221no—
230C4×D4C2×D6111yescharacteristic
231#117—611no—
232C2×C4⋊C4—611no—
233#107—611no—
234#107—611no—
235#106—611no—
236C4⋊C8—611no—
237#103—611no—
238#103—611no—
239#103—611no—
240#102—611no—
241#102—611no—
242#102—611no—
243#102—611no—
244#102—611no—
245#102—611no—
246#102—611no—
247C22⋊C8—611no—
248C22⋊C8—611no—
249#97—611no—
250#41—22no—
251#41—22no—
252#41—41no—
253#41—41no—
254C2×Q8C22×D6111yescharacteristic
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—611no—
262C2×D4—1221no—
263C2×D4—1221no—
264C2×D4C22⋊D6111yescharacteristic
265C2×D4C22×D6111yescharacteristic
266C2×D4C22×D6111yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—1221no—
270C22×C4—1221no—
271C22×C4C22×D6111yescharacteristic
272C22×C4C22×D6111yescharacteristic
273SD16—1222no—
274D8—2441no—
275D8—2441no—
276M16—2441no—
277C2×C8—611no—
278C2×C8—611no—
279C2×C8—611no—
280C2×C8—611no—
281C2×C8—2441no—
282C4⋊C4—21no—
283C4⋊C4—611no—
284C4⋊C4—611no—
285C4⋊C4—611no—
286C4⋊C4—1221no—
287C4⋊C4—1221no—
288C4⋊C4—1221no—
289C4⋊C4C22⋊D6111yescharacteristic
290C4⋊C4C22×D6111yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—1221no—
294C22⋊C4—1221no—
295C22⋊C4—1221no—
296C22⋊C4—1221no—
297C22⋊C4C22⋊D6111yescharacteristic
298C22⋊C4C22⋊D6111yescharacteristic
299C42—21no—
300C42—1221no—
301C42C22×D6111yescharacteristic
302C23—21no—
303C23—21no—
304C23—1221no—
305C23C2×C22⋊D6111yescharacteristic
306C23C2×C22⋊D6111yescharacteristic
307Q8—21no—
308Q8#1175822412yes—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—21no—
313D4—41no—
314D4—42no—
315D4—42no—
316D4—42no—
317D4—81no—
318D4—81no—
319D4—81no—
320D4—1221no—
321D4—1221no—
322D4—4881no—
323D4—2442no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—4881no—
336C2×C4—4881no—
337C2×C4C2×C22⋊D6111yescharacteristic
338C2×C4C2×C22⋊D6111yescharacteristic
339C2×C4C2×C22⋊D6111yescharacteristic
340C2×C4C2×C22⋊D6111yescharacteristic
341C2×C4C23×D6111yescharacteristic
342C8—1221no—
343C8—1221no—
344C8—1221no—
345C8—1221no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—2441no—
359C22—2441no—
360C22—2441no—
361C22C22×C22⋊D6111yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—22no—
367C4—41no—
368C4—2441no—
369C4—2441no—
370C4—2441no—
371C4C2×#1175822411yescharacteristic
372C4#1451982211yescharacteristic
373C2—41no—
374C2—41no—
375C2—81no—
376C2—81no—
377C2—4881no—
378C2#1684040611yescharacteristic
379C2#1684056011yescharacteristic
380C2#1684056511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#550C2
socleC22×C61C22×D4
hypercenter#550D61
hypocenterC61#3309
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #550

Complements

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

NH ≅ G/Ntype
1. #16840458C2semidirect
2. #16840126C2semidirect
3. #16840083C2semidirect
4. #16840073C2semidirect
5. #16840069C2semidirect
6. #16840013C2semidirect
7. #16839996C2semidirect
8. #16839954C2semidirect
9. #16839907C2semidirect
10. #16839907C2semidirect
11. #16839860C2semidirect
12. #16839834C2semidirect
13. #16839763C2semidirect
14. #16839758C2semidirect
15. C61×#550C2semidirect
192. #550D61semidirect
206. C61#3309semidirect