Finite Group Databasebeta

← #21456713

Subgroups — #21456713

Order 7808.

378 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840338C211yesmaximal, characteristic
2#16840335C211yesmaximal, characteristic
3#16840106C211yesmaximal, characteristic, complemented
4#16840105C211yesmaximal, characteristic, complemented
5#16840103C211yesmaximal, characteristic, complemented
6#16840021C211yesmaximal, characteristic, complemented
7#16840019C211yesmaximal, characteristic, complemented
8#16840004C211yesmaximal, characteristic, complemented
9#16840002C211yesmaximal, characteristic, complemented
10#16839920C211yesmaximal, characteristic, complemented
11#16839919C211yesmaximal, characteristic, complemented
12#16839919C211yesmaximal, characteristic, complemented
13#16839917C211yesmaximal, characteristic, complemented
14#16839727C211yesmaximal, characteristic
15C61×#485C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C22×Dic122C2211yescharacteristic
18C2×Q8×D61C2211yescharacteristic
19C2×Dic244C2211yescharacteristic
20C2×Dic244C2211yescharacteristic
21C2×#11758202C2211yescharacteristic
22C2×#11758202C2211yescharacteristic
23C2×#11758189C2211yescharacteristic
24C2×C8×D61C2211yescharacteristic
25#14519777—21no—
26#14519776—21no—
27#14519765—21no—
28#14519763—21no—
29#14519762—21no—
30#14519761—21no—
31#14519761—21no—
32#14519759—21no—
33#14519757C2211yescharacteristic
34#14519757C2211yescharacteristic
35#14519757C2211yescharacteristic
36#14519757C2211yescharacteristic
37#14519757C2211yescharacteristic
38#14519756C2211yescharacteristic
39#14519753C2211yescharacteristic
40#14519735C2211yescharacteristic
41#14519710C2211yescharacteristic
42#14519708C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519702C2211yescharacteristic
45#14519700C2211yescharacteristic
46#14519700C2211yescharacteristic
47#14519700C2211yescharacteristic
48#14519700C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519689C2211yescharacteristic
52C22⋊Q8×C61C2211yescharacteristic
53#117×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic
55#106×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C22×C4×C61C2311yescharacteristic
61C2×C22⋊D61D411yescharacteristic
62C2×C22⋊D61D411yescharacteristic
63C22×Dic61—21no—
64Q8×D61—41no—
65Q8×D61—41no—
66#11758222—41no—
67#11758222—41no—
68C2×D244D411yescharacteristic
69C2×C4×D61—21no—
70C2×C4×D61C2311yescharacteristic
71C2×C4×D61C2311yescharacteristic
72C2×Dic122—21no—
73C2×Dic122—21no—
74C2×Dic122—41no—
75C2×Dic122—41no—
76C2×Dic122D411yescharacteristic
77C2×Dic122C2311yescharacteristic
78C2×Dic122C2311yescharacteristic
79C2×Dic122C2311yescharacteristic
80C2×C8×C61C2311yescharacteristic
81C2×C8×C61C2311yescharacteristic
82C4⋊C4×C61—21no—
83C4⋊C4×C61C2311yescharacteristic
84C4⋊C4×C61C2311yescharacteristic
85C4⋊C4×C61C2311yescharacteristic
86C22⋊C4×C61—21no—
87C22⋊C4×C61—21no—
88C42×C61—21no—
89C22⋊Dic61—21no—
90#11758202—41no—
91#11758202—41no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97#11758198—21no—
98#11758198—21no—
99C4⋊Dic61—21no—
100C4⋊Dic61—21no—
101C4⋊Dic61—21no—
102C4⋊Dic61—21no—
103C4⋊Dic61—21no—
104C4⋊Dic61C2311yescharacteristic
105#11758196—21no—
106#11758196—21no—
107C4×Dic61—21no—
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110Dic244—41no—
111Dic244—41no—
112#11758189—41no—
113C8×D61—41no—
114C23×C61C2×D411yescharacteristic
115C22×D61C2×D411yescharacteristic
116C22×D61C2×D411yescharacteristic
117Q8×C61—21no—
118Q8×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61C2×D411yescharacteristic
126C2×C4×C61C2411yescharacteristic
127C22⋊D61—41no—
128C22⋊D61—41no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—42no—
134C2×Dic61C2×D411yescharacteristic
135C2×Dic61C2×D411yescharacteristic
136D244—41no—
137C4×D61—21no—
138C4×D61—21no—
139C4×D61—21no—
140C4×D61—21no—
141C4×D61—42no—
142Dic122—21no—
143Dic122—21no—
144Dic122—21no—
145Dic122—21no—
146Dic122—21no—
147Dic122—21no—
148Dic122—41no—
149Dic122—42no—
150Dic122—42no—
151C8×C61—21no—
152C8×C61—21no—
153#92418—21no—
154#92418—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61C22×D411yescharacteristic
159C2×D61—21no—
160C2×D61—21no—
161C2×D61—21no—
162C2×D61—21no—
163C2×D61—21no—
164C2×D61—21no—
165C4×C61—21no—
166C4×C61—41no—
167C4×C61—41no—
168C4×C61—41no—
169C4×C61—41no—
170C4×C61H(5,𝔽2)11yescharacteristic
171C4×C61H(5,𝔽2)11yescharacteristic
172Dic61—21no—
173Dic61—21no—
174Dic61—41no—
175Dic61—41no—
176Dic61—41no—
177Dic61—41no—
178#3202—611nomaximal, Sylow
179C2×C61—41no—
180C2×C61#53411yescharacteristic
181C2×C61#57811yescharacteristic
182C2×C61#57811yescharacteristic
183D61—41no—
184D61—41no—
185#536—611no—
186#536—611no—
187#485—611no—
188#485—611no—
189#485—611no—
190#485D6111yescharacteristic, complemented
191#470—611no—
192#470—611no—
193#467—611no—
194#467—611no—
195#451—611no—
196#451—611no—
197#451—611no—
198#451—611no—
199#408—611no—
200C61#320211yescharacteristic, complemented, Sylow
201C2×#41—611no—
202C22×Q8—611no—
203C22×Q8—611no—
204C2×Q16—611no—
205C2×Q16—611no—
206C2×Q16—611no—
207C2×Q16—611no—
208C2×M16—611no—
209C22×C8—611no—
210C4⋊Q8—1221no—
211C4⋊Q8—1221no—
212#124—1221no—
213#124—1221no—
214#123—1221no—
215#123—1221no—
216#123—1221no—
217#123—1221no—
218C22⋊Q8—611no—
219C22⋊Q8—611no—
220C22⋊Q8—611no—
221C22⋊Q8—611no—
222C22⋊Q8—611no—
223C22⋊Q8—611no—
224C22⋊Q8—611no—
225C22⋊Q8C2×D6111yescharacteristic
226#117—611no—
227#117C2×D6111yescharacteristic
228#107—611no—
229#107C2×D6111yescharacteristic
230#106—611no—
231#106C2×D6111yescharacteristic
232#103—611no—
233#103—611no—
234#103—611no—
235#103—611no—
236#103—611no—
237#103—611no—
238#103C2×D6111yescharacteristic
239#103C2×D6111yescharacteristic
240C22⋊C8—611no—
241C22⋊C8—611no—
242C22⋊C8—611no—
243C22⋊C8C2×D6111yescharacteristic
244#41—2441no—
245#41—2441no—
246C2×Q8—611no—
247C2×Q8—611no—
248C2×Q8—611no—
249C2×Q8—611no—
250C2×Q8—1221no—
251C2×Q8—1221no—
252C2×Q8—2441no—
253C2×Q8—2441no—
254C2×Q8—2441no—
255C2×Q8—2441no—
256C2×Q8C22×D6111yescharacteristic
257C2×D4—611no—
258C2×D4—611no—
259C2×D4—611no—
260C22×C4—611no—
261C22×C4—611no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4C22×D6111yescharacteristic
265Q16—2441no—
266Q16—2441no—
267Q16—2441no—
268Q16—2441no—
269M16—2441no—
270C2×C8—611no—
271C2×C8—611no—
272C2×C8—2441no—
273C2×C8C22×D6111yescharacteristic
274C2×C8C22×D6111yescharacteristic
275C4⋊C4—21no—
276C4⋊C4—611no—
277C4⋊C4—1221no—
278C4⋊C4—1221no—
279C4⋊C4—1221no—
280C4⋊C4—1221no—
281C4⋊C4—1221no—
282C4⋊C4—1221no—
283C4⋊C4—1221no—
284C4⋊C4C22×D6111yescharacteristic
285C4⋊C4C22×D6111yescharacteristic
286C4⋊C4C22×D6111yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—1221no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C22⋊C4—1221no—
293C22⋊C4—1221no—
294C22⋊C4—1221no—
295C22⋊C4—1221no—
296C22⋊C4—1221no—
297C42—21no—
298C42—1221no—
299C23—611no—
300C23—611no—
301C23D4×D6111yescharacteristic
302Q8—21no—
303Q8—21no—
304Q8—1221no—
305Q8—1221no—
306Q8—1221no—
307Q8—1221no—
308Q8—1221no—
309Q8—1221no—
310Q8—2441no—
311Q8—2442no—
312Q8—2442no—
313D4—2441no—
314D4—2441no—
315D4—2441no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—611no—
323C2×C4—611no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—2442no—
333C2×C4—2442no—
334C2×C4D4×D6111yescharacteristic
335C2×C4C23×D6111yescharacteristic
336C8—21no—
337C8—21no—
338C8—1221no—
339C8—1221no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—1221no—
344C22—1221no—
345C22—1221no—
346C22—1221no—
347C22—1221no—
348C22—1221no—
349C22C2×D4×D6111yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—1221no—
356C4—1221no—
357C4—2441no—
358C4—2441no—
359C4—2441no—
360C4—2441no—
361C4#1451982311yescharacteristic
362C4#1451982311yescharacteristic
363C2—41no—
364C2—2441no—
365C2—2441no—
366C2#1684032311yescharacteristic
367C2#1684057611yescharacteristic
368C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#485C2
socleC22×C61C22×D4
hypercenter#485D61
hypocenterC61#3202
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
3. #16840106C2semidirect
4. #16840105C2semidirect
5. #16840103C2semidirect
6. #16840021C2semidirect
7. #16840019C2semidirect
8. #16840004C2semidirect
9. #16840002C2semidirect
10. #16839920C2semidirect
11. #16839919C2semidirect
12. #16839919C2semidirect
13. #16839917C2semidirect
15. C61×#485C2semidirect
190. #485D61semidirect
200. C61#3202semidirect