Finite Group Databasebeta

← #21457894

Subgroups — #21457894

Order 7808.

410 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840408C211yesmaximal, characteristic
2#16840124C211yesmaximal, characteristic, complemented
3#16840097C211yesmaximal, characteristic, complemented
4#16840075C211yesmaximal, characteristic, complemented
5#16840039C211yesmaximal, characteristic, complemented
6#16840010C211yesmaximal, characteristic, complemented
7#16840001C211yesmaximal, characteristic, complemented
8#16839984C211yesmaximal, characteristic, complemented
9#16839922C211yesmaximal, characteristic, complemented
10#16839912C211yesmaximal, characteristic, complemented
11#16839860C211yesmaximal, characteristic, complemented
12#16839834C211yesmaximal, characteristic, complemented
13#16839761C211yesmaximal, characteristic, complemented
14C2×#14519697C211yesmaximal, characteristic, complemented
15C61×#554C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C22×D244C2211yescharacteristic
18C2×#11758202C2211yescharacteristic, complemented
19C2×#11758201C2211yescharacteristic
20C2×#11758201C2211yescharacteristic
21C2×#11758194C2211yescharacteristic, complemented
22C22×#92418C2211yescharacteristic
23#14519765C2211yescharacteristic
24#14519762—21no—
25#14519756C2211yescharacteristic
26#14519751C2211yescharacteristic
27#14519750—21no—
28#14519745—21no—
29C4×D244C2211yescharacteristic
30C22⋊C4×D61—21no—
31#14519710C2211yescharacteristic, complemented
32#14519710C2211yescharacteristic, complemented
33#14519710C2211yescharacteristic, complemented
34C4⋊#92418C2211yescharacteristic, complemented
35#14519701C2211yescharacteristic, complemented
36#14519700C2211yescharacteristic, complemented
37#14519700C2211yescharacteristic, complemented
38#14519700C2211yescharacteristic, complemented
39#14519697C2211yescharacteristic
40#14519697C2211yescharacteristic
41#14519697C2211yescharacteristic
42#14519697C2211yescharacteristic
43#14519697C2211yescharacteristic
44#14519697C2211yescharacteristic
45C22⋊#92418C2211yescharacteristic
46C22⋊#92418C2211yescharacteristic, complemented
47#14519688C2211yescharacteristic, complemented
48C4⋊Q8×C61C2211yescharacteristic, complemented
49#125×C61—21no—
50C22⋊Q8×C61—21no—
51C22⋊Q8×C61—21no—
52C22⋊Q8×C61C2211yescharacteristic
53C22⋊Q8×C61C2211yescharacteristic, complemented
54C4×Q8×C61C2211yescharacteristic, complemented
55C4×D4×C61—21no—
56C4×D4×C61C2211yescharacteristic
57C2×C4⋊C4×C61C2211yescharacteristic
58C2×C4⋊C4×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C2×Q8×C61—21no—
61C2×Q8×C61C2311yescharacteristic
62C2×D4×C61D411yescharacteristic
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61C2311yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69#11758222—22no—
70#11758222—41no—
71C2×D244—22no—
72C2×D244—21no—
73C2×D244—41no—
74C2×D244C2311yescharacteristic
75C2×D244C2311yescharacteristic
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×Dic122C2311yescharacteristic
79C4⋊C4×C61—21no—
80C4⋊C4×C61—21no—
81C4⋊C4×C61—21no—
82C4⋊C4×C61—21no—
83C4⋊C4×C61—21no—
84C4⋊C4×C61—21no—
85C4⋊C4×C61D411yescharacteristic
86C4⋊C4×C61C2311yescharacteristic
87C4⋊C4×C61C2311yescharacteristic
88C4⋊C4×C61C2311yescharacteristic
89C22⋊C4×C61—21no—
90C22⋊C4×C61—21no—
91C22⋊C4×C61D411yescharacteristic
92C22⋊C4×C61D411yescharacteristic
93C42×C61—21no—
94C42×C61C2311yescharacteristic
95C22⋊Dic61—21no—
96#11758202—41no—
97#11758201—22no—
98#11758201—41no—
99#11758198—21no—
100#11758198—21no—
101#11758198—21no—
102#11758198—21no—
103C4⋊Dic61C2311yescharacteristic
104#11758196—21no—
105#11758194—41no—
106C2×#92418—41no—
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111C23×C61C2×D411yescharacteristic
112C23×C61C2×D411yescharacteristic
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—42no—
116C22×D61—42no—
117C22×D61—81no—
118Q8×C61—21no—
119Q8×C61—21no—
120Q8×C61—81no—
121D4×C61—22no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—81no—
131C2×C4×C61—81no—
132C2×C4×C61C2×D411yescharacteristic
133C2×C4×C61C2×D411yescharacteristic
134C2×C4×C61C2×D411yescharacteristic
135C2×C4×C61C2×D411yescharacteristic
136C2×C4×C61C2411yescharacteristic
137C22⋊D61—42no—
138C22⋊D61—81no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141D244—21no—
142D244—21no—
143D244—21no—
144D244—42no—
145D244#4112yes—
146C4×D61—42no—
147C4×D61—81no—
148Dic122—21no—
149Dic122—21no—
150#92418—21no—
151#92418—21no—
152#92418—21no—
153#92418—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—21no—
159C22×C61#13712yes—
160C22×C61C22×D411yescharacteristic
161C2×D61—22no—
162C2×D61—41no—
163C2×D61—41no—
164C2×D61—41no—
165C2×D61—41no—
166C2×D61—41no—
167C2×D61—84no—
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—21no—
172C4×C61—41no—
173C4×C61—41no—
174C4×C61—41no—
175C4×C61—41no—
176C4×C61C2×#4111yescharacteristic
177C4×C61H(5,𝔽2)11yescharacteristic
178Dic61—41no—
179Dic61—41no—
180#3314—611nomaximal, Sylow
181C2×C61—22no—
182C2×C61—41no—
183C2×C61#54611yescharacteristic
184C2×C61C2×#13711yescharacteristic
185C2×C61#57611yescharacteristic
186D61—42no—
187D61—81no—
188#554D6111yescharacteristic, complemented
189#546—611no—
190#489—611no—
191#484—611no—
192#480—611no—
193#474—611no—
194#468—611no—
195#467—611no—
196#464—611no—
197#452—611no—
198#450—611no—
199#440—611no—
200#435—611no—
201#417—611no—
202C2×#102—611no—
203C61#331411yescharacteristic, complemented, Sylow
204C2×#41—611no—
205C22×D4—611no—
206C2×Q16—611no—
207C2×SD16—611no—
208C2×SD16—611no—
209C2×M16—611no—
210C22×C8—611no—
211C4⋊Q8C2×D6111yescharacteristic, complemented
212#125—21no—
213#124—611no—
214#123—1221no—
215C22⋊Q8—21no—
216C22⋊Q8—21no—
217C22⋊Q8—611no—
218C22⋊Q8C2×D6111yescharacteristic
219C22⋊Q8C2×D6111yescharacteristic, complemented
220#121—611no—
221#121—1221no—
222#120—1221no—
223C4×Q8C2×D6111yescharacteristic, complemented
224C4×D4—21no—
225C4×D4—611no—
226C4×D4C2×D6111yescharacteristic
227C2×C4⋊C4C2×D6111yescharacteristic
228C2×C4⋊C4C2×D6111yescharacteristic, complemented
229C2×C22⋊C4—1221no—
230#107—611no—
231#107—611no—
232#107—611no—
233C4⋊C8—611no—
234#103—611no—
235#103—611no—
236#103—611no—
237#103—611no—
238#102—611no—
239#102—611no—
240#102—611no—
241#102—611no—
242#102—611no—
243#102—611no—
244C22⋊C8—611no—
245C22⋊C8—611no—
246#97—611no—
247C24—1221no—
248#41—1222no—
249#41—2441no—
250C2×Q8—21no—
251C2×Q8—611no—
252C2×Q8C22×D6111yescharacteristic
253C2×D4—611no—
254C2×D4—611no—
255C2×D4—1222no—
256C2×D4—1221no—
257C2×D4—1221no—
258C2×D4—1221no—
259C2×D4—2441no—
260C2×D4C22⋊D6111yescharacteristic
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—1221no—
264C22×C4—1221no—
265C22×C4C22×D6111yescharacteristic
266C22×C4C22×D6111yescharacteristic
267Q16—2441no—
268SD16—1222no—
269SD16—2441no—
270M16—2441no—
271C2×C8—611no—
272C2×C8—611no—
273C2×C8—611no—
274C2×C8—611no—
275C2×C8—2441no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—611no—
283C4⋊C4—1221no—
284C4⋊C4C22⋊D6111yescharacteristic
285C4⋊C4C22×D6111yescharacteristic
286C4⋊C4C22×D6111yescharacteristic
287C4⋊C4C22×D6111yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C22⋊C4—1221no—
293C22⋊C4—1221no—
294C22⋊C4—1221no—
295C22⋊C4C22⋊D6111yescharacteristic
296C22⋊C4C22⋊D6111yescharacteristic
297C42—21no—
298C42C22×D6111yescharacteristic
299C23—1221no—
300C23—1221no—
301C23—4881no—
302C23—2442no—
303C23—2442no—
304C23C2×C22⋊D6111yescharacteristic
305C23C2×C22⋊D6111yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—81no—
309Q8—1221no—
310Q8—1221no—
311D4—22no—
312D4—612no—
313D4—1221no—
314D4—1221no—
315D4—1221no—
316D4—4881no—
317D4—2442no—
318D4—2442no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—4881no—
332C2×C4—2442no—
333C2×C4C2×C22⋊D6111yescharacteristic
334C2×C4C2×C22⋊D6111yescharacteristic
335C2×C4C2×C22⋊D6111yescharacteristic
336C2×C4C2×C22⋊D6111yescharacteristic
337C2×C4C23×D6111yescharacteristic
338C8—1221no—
339C8—1221no—
340C8—1221no—
341C8—1221no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—1222no—
348C22—4884no—
349C22—2441no—
350C22—2441no—
351C22—2441no—
352C22—2441no—
353C22—2441no—
354C22#1451980812yes—
355C22C22×C22⋊D6111yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—41no—
363C4—41no—
364C4—2441no—
365C4—2441no—
366C4#41×D6111yescharacteristic
367C4#1451982311yescharacteristic
368C2—22no—
369C2—41no—
370C2—4881no—
371C2—2442no—
372C2#1684040011yescharacteristic
373C2C2×#1451980811yescharacteristic
374C2#1684056511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#554C2
socleC22×C61C22×D4
hypercenter#554D61
hypocenterC61#3314
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #554

Complements

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

NH ≅ G/Ntype
2. #16840124C2semidirect
3. #16840097C2semidirect
4. #16840075C2semidirect
5. #16840039C2semidirect
6. #16840010C2semidirect
7. #16840001C2semidirect
8. #16839984C2semidirect
9. #16839922C2semidirect
10. #16839912C2semidirect
11. #16839860C2semidirect
12. #16839834C2semidirect
13. #16839761C2semidirect
14. C2×#14519697C2semidirect
15. C61×#554C2semidirect
18. C2×#11758202C22semidirect
21. C2×#11758194C22semidirect
31. #14519710C22semidirect
32. #14519710C22semidirect
33. #14519710C22semidirect
34. C4⋊#92418C22semidirect
35. #14519701C22semidirect
36. #14519700C22semidirect
37. #14519700C22semidirect
38. #14519700C22semidirect
46. C22⋊#92418C22semidirect
47. #14519688C22semidirect
48. C4⋊Q8×C61C22semidirect
53. C22⋊Q8×C61C22semidirect
54. C4×Q8×C61C22semidirect
58. C2×C4⋊C4×C61C22semidirect
188. #554D61semidirect
203. C61#3314semidirect
211. C4⋊Q8C2×D61semidirect
219. C22⋊Q8C2×D61semidirect
223. C4×Q8C2×D61semidirect
228. C2×C4⋊C4C2×D61semidirect