Finite Group Databasebeta

← #21456820

Subgroups — #21456820

Order 7808.

400 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#16840316C211yesmaximal, characteristic, complemented
2#124×D61C211yesmaximal, characteristic
3#16840155C211yesmaximal, characteristic, complemented
4#16840153C211yesmaximal, characteristic, complemented
5#16840123C211yesmaximal, characteristic, complemented
6#16840120C211yesmaximal, characteristic, complemented
7#16839985C211yesmaximal, characteristic, complemented
8#16839984C211yesmaximal, characteristic, complemented
9#16839981C211yesmaximal, characteristic, complemented
10#16839919C211yesmaximal, characteristic, complemented
11#16839916C211yesmaximal, characteristic, complemented
12#16839914C211yesmaximal, characteristic
13#16839911C211yesmaximal, characteristic
14#16839818C211yesmaximal, characteristic, complemented
15C61×#464C211yesmaximal, characteristic, complemented
16C2×Q8×D61C2211yescharacteristic
17C2×D4×D61C2211yescharacteristic
18C2×Dic244C2211yescharacteristic, complemented
19C2×#11758202C2211yescharacteristic, complemented
20C2×#11758202C2211yescharacteristic, complemented
21C2×#11758190C2211yescharacteristic
22C2×#11758200C2211yescharacteristic
23C2×#11758201C2211yescharacteristic
24#14519776C2211yescharacteristic, complemented
25#14519775C2211yescharacteristic, complemented
26#14519767—21no—
27#14519766C2211yescharacteristic
28#14519765C2211yescharacteristic
29#14519764C2211yescharacteristic
30#14519763—21no—
31#14519763—21no—
32#14519757C2211yescharacteristic
33#14519755—21no—
34#14519753C2211yescharacteristic
35C4×Dic122—21no—
36C4×Dic122C2211yescharacteristic, complemented
37#14519734—21no—
38C22⋊C4×D61—21no—
39C22⋊C4×D61—21no—
40C42×D61C2211yescharacteristic
41C4⋊#92418C2211yescharacteristic, complemented
42#14519702C2211yescharacteristic, complemented
43#14519701C2211yescharacteristic, complemented
44#14519700C2211yescharacteristic, complemented
45#14519699C2211yescharacteristic
46#14519698C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519689C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519687C2211yescharacteristic, complemented
51#14519687C2211yescharacteristic, complemented
52C2×Q16×C61C2211yescharacteristic, complemented
53C2×SD16×C61C2211yescharacteristic
54#124×C61C2211yescharacteristic
55C4×Q8×C61C2211yescharacteristic, complemented
56C4⋊C8×C61C2211yescharacteristic, complemented
57#103×C61C2211yescharacteristic, complemented
58#102×C61C2211yescharacteristic
59C23×D61—21no—
60C2×Q8×C61C2311yescharacteristic
61C2×Q8×C61C2311yescharacteristic
62C2×D4×C61C2311yescharacteristic
63C2×C22⋊D61—21no—
64Q8×D61—41no—
65Q8×D61—41no—
66D4×D61—41no—
67D4×D61—41no—
68C2×D244C2311yescharacteristic
69C2×C4×D61—21no—
70C2×C4×D61D411yescharacteristic
71C2×C4×D61D411yescharacteristic
72C2×C4×D61C2311yescharacteristic
73C2×Dic122—21no—
74C2×Dic122—21no—
75C2×Dic122C2311yescharacteristic
76C2×Dic122C2311yescharacteristic
77Q16×C61—41no—
78SD16×C61—41no—
79C2×C8×C61C2311yescharacteristic
80C2×C8×C61C2311yescharacteristic
81C4⋊C4×C61—21no—
82C4⋊C4×C61C2311yescharacteristic
83C22⋊C4×C61—21no—
84C22⋊C4×C61—21no—
85C42×C61—21no—
86C42×C61C2311yescharacteristic
87C22⋊Dic61—21no—
88C22⋊Dic61—21no—
89#11758202—41no—
90#11758202—41no—
91#11758201—41no—
92#11758200—41no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97#11758198—21no—
98#11758198—21no—
99C4⋊Dic61—21no—
100C4⋊Dic61C2311yescharacteristic
101#11758196—21no—
102#11758196—21no—
103#11758196—21no—
104#11758196—21no—
105#11758196—21no—
106C4×Dic61—21no—
107C4×Dic61D411yescharacteristic
108C4×Dic61D411yescharacteristic
109C4×Dic61C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111C2×#92418C2311yescharacteristic
112Dic244—41no—
113#11758190—41no—
114C23×C61—21no—
115C22×D61—21no—
116C22×D61—42no—
117C22×D61—42no—
118C22×D61—42no—
119C22×D61C2×D411yescharacteristic
120Q8×C61—21no—
121Q8×C61—21no—
122Q8×C61—21no—
123Q8×C61—21no—
124D4×C61—21no—
125D4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61C2×D411yescharacteristic
130C2×C4×C61C2×D411yescharacteristic
131C2×C4×C61C2411yescharacteristic
132C22⋊D61—42no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61C2×D411yescharacteristic
137C2×Dic61C2×D411yescharacteristic
138C2×Dic61C2×D411yescharacteristic
139D244—21no—
140D244—21no—
141C4×D61—22no—
142C4×D61—21no—
143C4×D61—21no—
144C4×D61—41no—
145C4×D61—42no—
146Dic122—21no—
147Dic122—21no—
148Dic122—21no—
149Dic122—21no—
150Dic122—42no—
151Dic122—42no—
152C8×C61—21no—
153C8×C61—21no—
154#92418—21no—
155#92418—21no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61—41no—
159C22×C61C22×D411yescharacteristic
160C2×D61—21no—
161C2×D61—21no—
162C2×D61—41no—
163C2×D61—41no—
164C2×D61—41no—
165C2×D61—84no—
166C2×D61#13712yes—
167C4×C61—21no—
168C4×C61—21no—
169C4×C61—41no—
170C4×C61—41no—
171C4×C61—41no—
172C4×C61H(5,𝔽2)11yescharacteristic
173C4×C61H(5,𝔽2)11yescharacteristic
174Dic61—21no—
175Dic61—21no—
176Dic61—21no—
177Dic61—41no—
178Dic61—41no—
179Dic61—41no—
180#3215—611nomaximal, Sylow
181C2×C61—81no—
182C2×C61#53511yescharacteristic
183C2×C61C2×#13711yescharacteristic
184C2×C61#57511yescharacteristic
185D61—22no—
186D61—81no—
187#533—611no—
188C2×#124—611no—
189#497—611no—
190#497—611no—
191#489—611no—
192#489—611no—
193#464—611no—
194#464—611no—
195#464—611no—
196#464D6111yescharacteristic, complemented
197#451—611no—
198#451—611no—
199#450—611no—
200#450—611no—
201#432—611no—
202C61#321511yescharacteristic, complemented, Sylow
203C22×Q8—611no—
204C22×D4—611no—
205C2×Q16—611no—
206C2×Q16—611no—
207C2×Q16—611no—
208C2×Q16C2×D6111yescharacteristic, complemented
209C2×SD16—611no—
210C2×SD16—611no—
211C2×SD16—611no—
212C2×SD16C2×D6111yescharacteristic
213C4⋊Q8—611no—
214C4⋊Q8—611no—
215#125—1221no—
216#124—611no—
217#124—611no—
218#124—611no—
219#124—1221no—
220#124—1221no—
221#124C2×D6111yescharacteristic
222C22⋊Q8—611no—
223C22⋊Q8—611no—
224C22⋊Q8—1221no—
225C4×Q8—611no—
226C4×Q8—1221no—
227C4×Q8C2×D6111yescharacteristic, complemented
228#117—1221no—
229C2×C22⋊C4—1221no—
230C2×C22⋊C4—1221no—
231C2×C42—611no—
232C4⋊C8—611no—
233C4⋊C8C2×D6111yescharacteristic, complemented
234#103—611no—
235#103—611no—
236#103—611no—
237#103C2×D6111yescharacteristic, complemented
238#102—611no—
239#102—611no—
240#102—611no—
241#102C2×D6111yescharacteristic
242C22⋊C8—611no—
243C22⋊C8—611no—
244#97—611no—
245#97—611no—
246C24—1221no—
247C2×Q8—611no—
248C2×Q8—611no—
249C2×Q8—1221no—
250C2×Q8—1221no—
251C2×Q8—2441no—
252C2×Q8—2441no—
253C2×Q8C22×D6111yescharacteristic
254C2×Q8C22×D6111yescharacteristic
255C2×D4—611no—
256C2×D4—1221no—
257C2×D4—2441no—
258C2×D4—2441no—
259C2×D4C22×D6111yescharacteristic
260C22×C4—611no—
261C22×C4—611no—
262C22×C4—611no—
263C22×C4—1221no—
264Q16—41no—
265Q16—2441no—
266Q16—2441no—
267Q16—2441no—
268SD16—41no—
269SD16—2441no—
270SD16—2441no—
271SD16—2441no—
272C2×C8—611no—
273C2×C8—611no—
274C2×C8C22×D6111yescharacteristic
275C2×C8C22×D6111yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—611no—
278C4⋊C4—1221no—
279C4⋊C4—1221no—
280C4⋊C4—1221no—
281C4⋊C4—1221no—
282C4⋊C4—1221no—
283C4⋊C4—1221no—
284C4⋊C4C22×D6111yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—1221no—
288C22⋊C4—1221no—
289C22⋊C4—1221no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C22⋊C4—1221no—
293C22⋊C4—1221no—
294C22⋊C4—1221no—
295C42—21no—
296C42—611no—
297C42—611no—
298C42—611no—
299C42—1221no—
300C42C22×D6111yescharacteristic
301C23—21no—
302C23—611no—
303C23—1221no—
304C23—2442no—
305C23—2442no—
306C23—2442no—
307Q8—21no—
308Q8—21no—
309Q8—21no—
310Q8—21no—
311Q8—1221no—
312Q8—1221no—
313Q8—1221no—
314Q8—1221no—
315Q8—2442no—
316Q8—2442no—
317D4—21no—
318D4—21no—
319D4—1221no—
320D4—1221no—
321D4—2442no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—611no—
326C2×C4—611no—
327C2×C4—611no—
328C2×C4—1222no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—2441no—
335C2×C4—2442no—
336C2×C4D4×D6111yescharacteristic
337C2×C4D4×D6111yescharacteristic
338C2×C4C23×D6111yescharacteristic
339C8—21no—
340C8—21no—
341C8—1221no—
342C8—1221no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—612no—
347C22—1221no—
348C22—1221no—
349C22—4884no—
350C22—2441no—
351C22—2441no—
352C22—2441no—
353C22C2×D4×D6111yescharacteristic
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—1221no—
360C4—1221no—
361C4—1221no—
362C4—2441no—
363C4—2441no—
364C4—2441no—
365C4#1451982211yescharacteristic
366C4#1451982311yescharacteristic
367C2—81no—
368C2—1222no—
369C2—4881no—
370C2#1684032811yescharacteristic
371C2#137×D6111yescharacteristic
372C2#1684055911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#464C2
socleC22×C61C22×D4
hypercenter#464D61
hypocenterC61#3215
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #16840316C2semidirect
3. #16840155C2semidirect
4. #16840153C2semidirect
5. #16840123C2semidirect
6. #16840120C2semidirect
7. #16839985C2semidirect
8. #16839984C2semidirect
9. #16839981C2semidirect
10. #16839919C2semidirect
11. #16839916C2semidirect
14. #16839818C2semidirect
15. C61×#464C2semidirect
18. C2×Dic244C22semidirect
19. C2×#11758202C22semidirect
20. C2×#11758202C22semidirect
24. #14519776C22semidirect
25. #14519775C22semidirect
36. C4×Dic122C22semidirect
41. C4⋊#92418C22semidirect
42. #14519702C22semidirect
43. #14519701C22semidirect
44. #14519700C22semidirect
50. #14519687C22semidirect
51. #14519687C22semidirect
52. C2×Q16×C61C22semidirect
55. C4×Q8×C61C22semidirect
56. C4⋊C8×C61C22semidirect
57. #103×C61C22semidirect
196. #464D61semidirect
202. C61#3215semidirect
208. C2×Q16C2×D61semidirect
227. C4×Q8C2×D61semidirect
233. C4⋊C8C2×D61semidirect
237. #103C2×D61semidirect