Finite Group Databasebeta

← #21456653

Subgroups — #21456653

Order 7808.

414 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840274C211yesmaximal, characteristic
2C22⋊Q8×D61C211yesmaximal, characteristic, complemented
3#16840103C211yesmaximal, characteristic, complemented
4#16840099C211yesmaximal, characteristic, complemented
5#16840082C211yesmaximal, characteristic, complemented
6#16840021C211yesmaximal, characteristic, complemented
7#16840019C211yesmaximal, characteristic, complemented
8#16840011C211yesmaximal, characteristic, complemented
9#16840009C211yesmaximal, characteristic, complemented
10#16839926C211yesmaximal, characteristic, complemented
11#16839922C211yesmaximal, characteristic, complemented
12#16839919C211yesmaximal, characteristic, complemented
13#16839902C211yesmaximal, characteristic, complemented
14#16839724C211yesmaximal, characteristic, complemented
15C61×#485C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×Q8×D61C2211yescharacteristic
18C22×C4×D61C2211yescharacteristic
19C2×Dic244C2211yescharacteristic, complemented
20C2×#11758202C2211yescharacteristic, complemented
21C2×#11758190C2211yescharacteristic, complemented
22C2×#11758201C2211yescharacteristic, complemented
23C2×#11758189C2211yescharacteristic
24C2×#11758189C2211yescharacteristic
25#14519761—21no—
26#14519757C2211yescharacteristic
27#14519757C2211yescharacteristic
28#14519757C2211yescharacteristic
29#14519756C2211yescharacteristic
30#14519755—21no—
31#14519754—21no—
32#14519753C2211yescharacteristic
33#14519752C2211yescharacteristic
34#14519752C2211yescharacteristic
35#14519747—21no—
36C4×D244—21no—
37C4×D244—21no—
38C4⋊C4×D61—21no—
39C4⋊C4×D61C2211yescharacteristic
40C22⋊C4×D61—21no—
41#14519710C2211yescharacteristic, complemented
42#14519708C2211yescharacteristic, complemented
43#14519702C2211yescharacteristic, complemented
44#14519700C2211yescharacteristic, complemented
45#14519700C2211yescharacteristic, complemented
46#14519700C2211yescharacteristic, complemented
47#14519699C2211yescharacteristic, complemented
48#14519697C2211yescharacteristic, complemented
49C22⋊#92418C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519689C2211yescharacteristic
52C22⋊Q8×C61C2211yescharacteristic
53#117×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic, complemented
55#106×C61C2211yescharacteristic, complemented
56#103×C61C2211yescharacteristic, complemented
57#103×C61C2211yescharacteristic, complemented
58C22⋊C8×C61C2211yescharacteristic
59C23×D61D411yescharacteristic
60C2×Q8×C61C2311yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C2×C22⋊D61—21no—
63C22×Dic61D411yescharacteristic
64Q8×D61—41no—
65Q8×D61—41no—
66#11758222—41no—
67#11758222—41no—
68C2×D244—21no—
69C2×D244—21no—
70C2×D244C2311yescharacteristic
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61—41no—
75C2×C4×D61—41no—
76C2×C4×D61D411yescharacteristic
77C2×C4×D61D411yescharacteristic
78C2×C4×D61C2311yescharacteristic
79C2×C4×D61C2311yescharacteristic
80C2×Dic122—21no—
81C2×Dic122C2311yescharacteristic
82C2×Dic122C2311yescharacteristic
83C2×C8×C61C2311yescharacteristic
84C2×C8×C61C2311yescharacteristic
85C4⋊C4×C61—21no—
86C4⋊C4×C61C2311yescharacteristic
87C4⋊C4×C61C2311yescharacteristic
88C4⋊C4×C61C2311yescharacteristic
89C22⋊C4×C61—21no—
90C22⋊C4×C61—21no—
91C42×C61—21no—
92C22⋊Dic61—21no—
93#11758202—41no—
94#11758201—41no—
95#11758198—21no—
96#11758198—21no—
97#11758198—21no—
98#11758198—21no—
99#11758198—21no—
100#11758198—21no—
101C4⋊Dic61—21no—
102C4⋊Dic61—21no—
103C4⋊Dic61—21no—
104C4⋊Dic61C2311yescharacteristic
105#11758196—21no—
106#11758196—21no—
107#11758196—21no—
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110Dic244—41no—
111#11758190—41no—
112#11758189—41no—
113#11758189—41no—
114C23×C61C2×D411yescharacteristic
115C22×D61—22no—
116C22×D61—21no—
117C22×D61—41no—
118C22×D61—41no—
119C22×D61C2×D411yescharacteristic
120C22×D61C2×D411yescharacteristic
121Q8×C61—21no—
122Q8×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×C61C2×D411yescharacteristic
130C2×C4×C61C2411yescharacteristic
131C22⋊D61—42no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—41no—
136C2×Dic61C2×D411yescharacteristic
137C2×Dic61C2×D411yescharacteristic
138D244—21no—
139D244—21no—
140D244—42no—
141D244—42no—
142C4×D61—21no—
143C4×D61—21no—
144C4×D61—21no—
145C4×D61—21no—
146C4×D61—41no—
147C4×D61—41no—
148C4×D61—42no—
149C4×D61—42no—
150C4×D61—42no—
151Dic122—21no—
152Dic122—21no—
153Dic122—21no—
154Dic122—21no—
155Dic122—42no—
156C8×C61—21no—
157C8×C61—21no—
158#92418—21no—
159#92418—21no—
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—21no—
163C22×C61C22×D411yescharacteristic
164C2×D61—21no—
165C2×D61—21no—
166C2×D61—21no—
167C2×D61—21no—
168C2×D61—21no—
169C2×D61—44no—
170C2×D61—41no—
171C2×D61—41no—
172C2×D61—41no—
173C2×D61#13712yes—
174C4×C61—21no—
175C4×C61—41no—
176C4×C61—41no—
177C4×C61—41no—
178C4×C61—41no—
179C4×C61H(5,𝔽2)11yescharacteristic
180C4×C61H(5,𝔽2)11yescharacteristic
181Dic61—21no—
182Dic61—21no—
183Dic61—41no—
184Dic61—41no—
185Dic61—41no—
186#3196—611nomaximal, Sylow
187C2×C61—41no—
188C2×C61#53411yescharacteristic
189C2×C61C2×#13711yescharacteristic
190C2×C61#57511yescharacteristic
191D61—22no—
192D61—41no—
193D61—81no—
194#525—611no—
195C2×C22⋊Q8—611no—
196#485—611no—
197#485D6111yescharacteristic, complemented
198#484—611no—
199#481—611no—
200#470—611no—
201#470—611no—
202#468—611no—
203#468—611no—
204#452—611no—
205#452—611no—
206#451—611no—
207#448—611no—
208#407—611no—
209C61#319611yescharacteristic, complemented, Sylow
210C2×#41—611no—
211C22×Q8—611no—
212C23×C4—611no—
213C2×Q16—611no—
214C2×Q16—611no—
215C2×SD16—611no—
216C2×SD16—611no—
217C2×M16—611no—
218C2×M16—611no—
219#123—1221no—
220C22⋊Q8—611no—
221C22⋊Q8—611no—
222C22⋊Q8—611no—
223C22⋊Q8—611no—
224C22⋊Q8—611no—
225C22⋊Q8—1221no—
226C22⋊Q8—1221no—
227C22⋊Q8C2×D6111yescharacteristic
228#121—611no—
229#121—611no—
230#120—1221no—
231C4×D4—1221no—
232C4×D4—1221no—
233#117C2×D6111yescharacteristic
234C2×C4⋊C4—611no—
235C2×C4⋊C4—1221no—
236C2×C22⋊C4—1221no—
237#107—611no—
238#107C2×D6111yescharacteristic, complemented
239#106—611no—
240#106C2×D6111yescharacteristic, complemented
241#103—611no—
242#103—611no—
243#103—611no—
244#103—611no—
245#103C2×D6111yescharacteristic, complemented
246#103C2×D6111yescharacteristic, complemented
247#102—611no—
248#102—611no—
249C22⋊C8—611no—
250C22⋊C8—611no—
251C22⋊C8—611no—
252C22⋊C8C2×D6111yescharacteristic
253C24—611no—
254#41—2441no—
255#41—2441no—
256C2×Q8—611no—
257C2×Q8—611no—
258C2×Q8—1221no—
259C2×Q8—2441no—
260C2×Q8—2441no—
261C2×Q8C22×D6111yescharacteristic
262C2×D4—611no—
263C2×D4—1221no—
264C2×D4—1221no—
265C2×D4—1221no—
266C22×C4—611no—
267C22×C4—611no—
268C22×C4—611no—
269C22×C4—611no—
270C22×C4—611no—
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4—2441no—
275C22×C4—2441no—
276C22×C4C22×D6111yescharacteristic
277Q16—2441no—
278Q16—2441no—
279SD16—2441no—
280SD16—2441no—
281M16—2441no—
282M16—2441no—
283C2×C8—611no—
284C2×C8—611no—
285C2×C8C22×D6111yescharacteristic
286C2×C8C22×D6111yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—611no—
289C4⋊C4—1221no—
290C4⋊C4—1221no—
291C4⋊C4—1221no—
292C4⋊C4—1221no—
293C4⋊C4—1221no—
294C4⋊C4—1221no—
295C4⋊C4C22×D6111yescharacteristic
296C4⋊C4C22×D6111yescharacteristic
297C4⋊C4C22×D6111yescharacteristic
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—1221no—
301C22⋊C4—1221no—
302C22⋊C4—1221no—
303C22⋊C4—1221no—
304C22⋊C4—1221no—
305C22⋊C4—1221no—
306C22⋊C4—1221no—
307C42—21no—
308C23—611no—
309C23—611no—
310C23—1222no—
311C23—1221no—
312C23—2441no—
313C23—2441no—
314C23D4×D6111yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—1221no—
318Q8—1221no—
319Q8—1221no—
320Q8—1221no—
321Q8—2442no—
322D4—1221no—
323D4—1221no—
324D4—2442no—
325D4—2442no—
326D4—2442no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—611no—
334C2×C4—611no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—2441no—
343C2×C4—2441no—
344C2×C4—2442no—
345C2×C4—2442no—
346C2×C4—2442no—
347C2×C4—2441no—
348C2×C4D4×D6111yescharacteristic
349C2×C4C23×D6111yescharacteristic
350C8—21no—
351C8—21no—
352C8—1221no—
353C8—1221no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—612no—
358C22—1221no—
359C22—1221no—
360C22—1221no—
361C22—1221no—
362C22—1221no—
363C22—2444no—
364C22—2441no—
365C22—2441no—
366C22—2441no—
367C22C2×D4×D6111yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—1221no—
374C4—1221no—
375C4—2441no—
376C4—2441no—
377C4—2441no—
378C4#1451982311yescharacteristic
379C4#1451982311yescharacteristic
380C2—41no—
381C2—1222no—
382C2—4881no—
383C2—2441no—
384C2#1684032311yescharacteristic
385C2#137×D6111yescharacteristic
386C2#1684055911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#485C2
socleC22×C61C22×D4
hypercenter#485D61
hypocenterC61#3196
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
2. C22⋊Q8×D61C2semidirect
3. #16840103C2semidirect
4. #16840099C2semidirect
5. #16840082C2semidirect
6. #16840021C2semidirect
7. #16840019C2semidirect
8. #16840011C2semidirect
9. #16840009C2semidirect
10. #16839926C2semidirect
11. #16839922C2semidirect
12. #16839919C2semidirect
13. #16839902C2semidirect
14. #16839724C2semidirect
15. C61×#485C2semidirect
19. C2×Dic244C22semidirect
20. C2×#11758202C22semidirect
21. C2×#11758190C22semidirect
22. C2×#11758201C22semidirect
41. #14519710C22semidirect
42. #14519708C22semidirect
43. #14519702C22semidirect
44. #14519700C22semidirect
45. #14519700C22semidirect
46. #14519700C22semidirect
47. #14519699C22semidirect
48. #14519697C22semidirect
54. #107×C61C22semidirect
55. #106×C61C22semidirect
56. #103×C61C22semidirect
57. #103×C61C22semidirect
197. #485D61semidirect
209. C61#3196semidirect
238. #107C2×D61semidirect
240. #106C2×D61semidirect
245. #103C2×D61semidirect
246. #103C2×D61semidirect