Finite Group Databasebeta

← #21458836

Subgroups — #21458836

Order 7808.

406 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840481C211yesmaximal, characteristic, complemented
2#16840432C211yesmaximal, characteristic, complemented
3#16840150C211yesmaximal, characteristic, complemented
4#16840133C211yesmaximal, characteristic, complemented
5#16839975C211yesmaximal, characteristic, complemented
6#16839974C211yesmaximal, characteristic, complemented
7#16839965C211yesmaximal, characteristic, complemented
8#16839960C211yesmaximal, characteristic, complemented
9#16839959C211yesmaximal, characteristic, complemented
10#16839955C211yesmaximal, characteristic, complemented
11#16839890C211yesmaximal, characteristic, complemented
12#16839864C211yesmaximal, characteristic, complemented
13#16839863C211yesmaximal, characteristic, complemented
14D8×Dic61C211yesmaximal, characteristic, complemented
15C61×#496C211yesmaximal, characteristic, complemented
16C2×#11758224—21no—
17C2×#11758190C2211yescharacteristic
18C2×#11758200C2211yescharacteristic
19C2×#11758200C2211yescharacteristic
20C2×#11758201C2211yescharacteristic
21C2×#11758199C2211yescharacteristic
22#14519775C2211yescharacteristic
23#14519773C2211yescharacteristic
24#14519773C2211yescharacteristic
25#14519770—21no—
26#14519770—21no—
27#14519764C2211yescharacteristic
28#14519754—21no—
29#14519749—21no—
30#14519749—21no—
31#14519748—21no—
32Q8×Dic61C2211yescharacteristic
33C4×Dic122C2211yescharacteristic
34C4×Dic122C2211yescharacteristic
35C4×D244C2211yescharacteristic
36D4×Dic61C2211yescharacteristic
37D4×Dic61C2211yescharacteristic
38D4×Dic61C2211yescharacteristic
39#14519733—21no—
40#14519711C2211yescharacteristic
41C4⋊#92418C2211yescharacteristic
42#14519706C2211yescharacteristic
43#14519706C2211yescharacteristic
44#14519702C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519698C2211yescharacteristic
49#14519698C2211yescharacteristic
50#14519687C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C2×SD16×C61C2211yescharacteristic
53C2×SD16×C61C2211yescharacteristic
54C2×D8×C61C2211yescharacteristic
55C2×D8×C61C2211yescharacteristic
56#127×C61C2211yescharacteristic
57#124×C61C2211yescharacteristic
58#97×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×D4×C61—21no—
61C2×D4×C61—21no—
62C2×D4×C61C2311yescharacteristic
63C2×D4×C61C2311yescharacteristic
64C2×D4×C61C2311yescharacteristic
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—21no—
72#11758224—44no—
73C2×D244C2311yescharacteristic
74C2×C4×D61—21no—
75C2×Dic122D411yescharacteristic
76C2×Dic122C2311yescharacteristic
77SD16×C61—22no—
78SD16×C61—41no—
79D8×C61—22no—
80D8×C61—41no—
81C2×C8×C61C2311yescharacteristic
82C2×C8×C61C2311yescharacteristic
83C22⋊C4×C61—21no—
84C22⋊C4×C61—21no—
85C42×C61C2311yescharacteristic
86C22⋊Dic61—21no—
87C22⋊Dic61—21no—
88C22⋊Dic61—21no—
89C22⋊Dic61—21no—
90C22⋊Dic61—21no—
91#11758201—41no—
92#11758200—41no—
93#11758200—41no—
94#11758199—41no—
95#11758198—21no—
96C4⋊Dic61—21no—
97C4⋊Dic61D411yescharacteristic
98C4⋊Dic61C2311yescharacteristic
99C4⋊Dic61C2311yescharacteristic
100#11758196—21no—
101#11758196—21no—
102#11758196—21no—
103#11758196D411yescharacteristic
104#11758196D411yescharacteristic
105C4×Dic61—21no—
106C4×Dic61—21no—
107C4×Dic61C2311yescharacteristic
108C4×Dic61C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111#11758190—22no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—21no—
115C22×D61—21no—
116Q8×C61—21no—
117Q8×C61—21no—
118D4×C61—21no—
119D4×C61—21no—
120D4×C61—21no—
121D4×C61—21no—
122D4×C61—21no—
123D4×C61—21no—
124D4×C61—42no—
125D4×C61—81no—
126C2×C4×C61—21no—
127C2×C4×C61C2×D411yescharacteristic
128C2×C4×C61C2×D411yescharacteristic
129C2×C4×C61C2411yescharacteristic
130C22⋊D61—42no—
131C22⋊D61—42no—
132C22⋊D61—81no—
133C22⋊D61—81no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—42no—
138C2×Dic61—42no—
139C2×Dic61—42no—
140C2×Dic61C2×D411yescharacteristic
141C2×Dic61C2×D411yescharacteristic
142C2×Dic61C2×D411yescharacteristic
143C2×Dic61C2×D411yescharacteristic
144D244—21no—
145D244—21no—
146C4×D61—42no—
147Dic122—22no—
148Dic122—21no—
149Dic122—21no—
150C8×C61—21no—
151C8×C61#4112yescomplemented
152#92418—21no—
153#92418—21no—
154C22×C61—41no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61C22×D411yescharacteristic
164C2×D61—41no—
165C2×D61—41no—
166C2×D61—41no—
167C4×C61—21no—
168C4×C61—21no—
169C4×C61—41no—
170C4×C61C2×#4111yescharacteristic
171C4×C61H(5,𝔽2)11yescharacteristic
172Dic61—21no—
173Dic61—21no—
174Dic61—21no—
175Dic61—41no—
176Dic61—41no—
177Dic61—41no—
178Dic61AGL(1,ℤ/8)12yes—
179#3397—611nomaximal, Sylow
180C2×C61—81no—
181C2×C61—81no—
182C2×C61—81no—
183C2×C61#55011yescharacteristic
184C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
185C2×C61#57711yescharacteristic
186D61—81no—
187#556—611no—
188#550—611no—
189#496—611no—
190#496D6111yescharacteristic, complemented
191#492—611no—
192#463—611no—
193#463—611no—
194#461—611no—
195#460—611no—
196#460—611no—
197#459—611no—
198#446—611no—
199#440—611no—
200#440—611no—
201C4×D8—611no—
202C61#339711yescharacteristic, complemented, Sylow
203C2×#41—1221no—
204C2×SD16—611no—
205C2×SD16—611no—
206C2×SD16—611no—
207C2×SD16—611no—
208C2×SD16C2×D6111yescharacteristic
209C2×SD16C2×D6111yescharacteristic
210C2×D8—611no—
211C2×D8C2×D6111yescharacteristic
212C2×D8C2×D6111yescharacteristic
213C4⋊Q8—611no—
214#127—611no—
215#127—611no—
216#127C2×D6111yescharacteristic
217#126—1221no—
218#126—1221no—
219#124—611no—
220#124C2×D6111yescharacteristic
221C22⋊Q8—1221no—
222#121—1221no—
223#121—1221no—
224#121—1221no—
225C4×Q8—611no—
226C4×Q8—611no—
227C4×Q8—611no—
228C4×D4—611no—
229C4×D4—611no—
230C4×D4—611no—
231C4×D4—611no—
232#117—1221no—
233#107—611no—
234C4⋊C8—611no—
235C4⋊C8—611no—
236C4⋊C8—611no—
237#103—611no—
238#103—611no—
239#102—611no—
240#102—611no—
241#102—611no—
242#102—611no—
243#97—611no—
244#97C2×D6111yescharacteristic
245C4×C8—611no—
246#41—2444no—
247C2×Q8—611no—
248C2×Q8—611no—
249C2×Q8C22×D6111yescharacteristic
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—611no—
253C2×D4—1221no—
254C2×D4—1221no—
255C2×D4—1221no—
256C2×D4—1221no—
257C2×D4C22×D6111yescharacteristic
258C2×D4C22×D6111yescharacteristic
259C2×D4C22×D6111yescharacteristic
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—1221no—
264SD16—22no—
265SD16—41no—
266SD16—1222no—
267SD16—2441no—
268SD16—2441no—
269SD16—2441no—
270D8—22no—
271D8—41no—
272D8—2441no—
273C2×C8—611no—
274C2×C8—611no—
275C2×C8C22×D6111yescharacteristic
276C2×C8C22×D6111yescharacteristic
277C4⋊C4—611no—
278C4⋊C4—611no—
279C4⋊C4—611no—
280C4⋊C4—611no—
281C4⋊C4—611no—
282C4⋊C4—1221no—
283C4⋊C4—1221no—
284C4⋊C4—1221no—
285C4⋊C4—1221no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—1221no—
289C22⋊C4—1221no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C22⋊C4—1221no—
293C22⋊C4—1221no—
294C42—611no—
295C42—611no—
296C42—1221no—
297C42—1221no—
298C42C22×D6111yescharacteristic
299C23—21no—
300C23—21no—
301C23—21no—
302C23—1221no—
303Q8—21no—
304Q8—21no—
305Q8—1222no—
306Q8—1221no—
307Q8—1221no—
308D4—21no—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—21no—
313D4—21no—
314D4—42no—
315D4—81no—
316D4—1221no—
317D4—1221no—
318D4—4881no—
319D4—4881no—
320D4—2442no—
321D4—2442no—
322C2×C4—21no—
323C2×C4—611no—
324C2×C4—611no—
325C2×C4—611no—
326C2×C4—611no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—2442no—
331C2×C4—2442no—
332C2×C4—2442no—
333C2×C4—2442no—
334C2×C4D4×D6111yescharacteristic
335C2×C4D4×D6111yescharacteristic
336C2×C4C23×D6111yescharacteristic
337C8—21no—
338C8—1221no—
339C8—1221no—
340C8#1175822412yescomplemented
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—2441no—
351C22—2441no—
352C22—2441no—
353C22C2×D4×D6111yescharacteristic
354C4—21no—
355C4—21no—
356C4—41no—
357C4—612no—
358C4—1221no—
359C4—1221no—
360C4—1221no—
361C4—2441no—
362C4—2441no—
363C4—2441no—
364C4C2×#1175822411yescharacteristic
365C4#1451982211yescharacteristic
366C2—81no—
367C2—81no—
368C2—81no—
369C2—4881no—
370C2#1684043211yescharacteristic
371C2AGL(1,ℤ/8)×D6111yescharacteristic
372C2#1684057211yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#496C2
socleC22×C61C22×D4
hypercenter#496D61
hypocenterC61#3397
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #16840481C2semidirect
2. #16840432C2semidirect
3. #16840150C2semidirect
4. #16840133C2semidirect
5. #16839975C2semidirect
6. #16839974C2semidirect
7. #16839965C2semidirect
8. #16839960C2semidirect
9. #16839959C2semidirect
10. #16839955C2semidirect
11. #16839890C2semidirect
12. #16839864C2semidirect
13. #16839863C2semidirect
14. D8×Dic61C2semidirect
15. C61×#496C2semidirect
151. C8×C61#41semidirect
190. #496D61semidirect
202. C61#3397semidirect
340. C8#11758224semidirect