Finite Group Databasebeta

← #21456650

Subgroups — #21456650

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#16840275C211yesmaximal, characteristic
2C22⋊Q8×D61C211yesmaximal, characteristic, complemented
3#16840106C211yesmaximal, characteristic, complemented
4#16840102C211yesmaximal, characteristic, complemented
5#16840096C211yesmaximal, characteristic, complemented
6#16840082C211yesmaximal, characteristic, complemented
7#16840018C211yesmaximal, characteristic, complemented
8#16840010C211yesmaximal, characteristic, complemented
9#16840008C211yesmaximal, characteristic, complemented
10#16839927C211yesmaximal, characteristic, complemented
11#16839923C211yesmaximal, characteristic, complemented
12#16839916C211yesmaximal, characteristic, complemented
13#16839902C211yesmaximal, characteristic, complemented
14#16839725C211yesmaximal, characteristic, complemented
15C61×#470C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×Q8×D61C2211yescharacteristic
18C22×C4×D61C2211yescharacteristic
19C2×#11758202C2211yescharacteristic, complemented
20C2×#11758190C2211yescharacteristic, complemented
21C2×#11758201C2211yescharacteristic, complemented
22C2×#11758194C2211yescharacteristic
23#14519762—21no—
24#14519757C2211yescharacteristic
25#14519756C2211yescharacteristic
26#14519755—21no—
27#14519754—21no—
28#14519753C2211yescharacteristic
29#14519753C2211yescharacteristic
30#14519752C2211yescharacteristic
31#14519751C2211yescharacteristic
32#14519747—21no—
33#14519739—21no—
34#14519737—21no—
35#14519735C2211yescharacteristic
36C4⋊C4×D61—21no—
37C4⋊C4×D61C2211yescharacteristic
38C22⋊C4×D61—21no—
39#14519711C2211yescharacteristic, complemented
40#14519710C2211yescharacteristic, complemented
41#14519708C2211yescharacteristic, complemented
42#14519702C2211yescharacteristic, complemented
43#14519701C2211yescharacteristic, complemented
44#14519701C2211yescharacteristic, complemented
45#14519700C2211yescharacteristic, complemented
46#14519699C2211yescharacteristic, complemented
47#14519697C2211yescharacteristic, complemented
48#14519689C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519689C2211yescharacteristic
52C2×Q16×C61C2211yescharacteristic, complemented
53C2×M16×C61C2211yescharacteristic
54C22⋊Q8×C61C2211yescharacteristic
55C22⋊Q8×C61C2211yescharacteristic
56#106×C61C2211yescharacteristic, complemented
57#103×C61C2211yescharacteristic, complemented
58#103×C61C2211yescharacteristic, complemented
59C23×D61D411yescharacteristic
60C2×Q8×C61C2311yescharacteristic
61C2×Q8×C61C2311yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C2×C22⋊D61—21no—
64C22×Dic61D411yescharacteristic
65#11758226—41no—
66#11758226—41no—
67Q8×D61—41no—
68Q8×D61—41no—
69C2×D244—21no—
70C2×D244—21no—
71C2×D244C2311yescharacteristic
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61—41no—
76C2×C4×D61—41no—
77C2×C4×D61D411yescharacteristic
78C2×C4×D61D411yescharacteristic
79C2×C4×D61C2311yescharacteristic
80C2×C4×D61C2311yescharacteristic
81C2×Dic122—21no—
82C2×Dic122C2311yescharacteristic
83Q16×C61—41no—
84M16×C61—41no—
85C2×C8×C61C2311yescharacteristic
86C2×C8×C61C2311yescharacteristic
87C4⋊C4×C61—21no—
88C4⋊C4×C61—21no—
89C4⋊C4×C61C2311yescharacteristic
90C4⋊C4×C61C2311yescharacteristic
91C22⋊C4×C61—21no—
92C22⋊C4×C61—21no—
93C22⋊Dic61—21no—
94#11758202—41no—
95#11758201—41no—
96#11758198—21no—
97#11758198—21no—
98#11758198—21no—
99#11758198—21no—
100#11758198—21no—
101#11758198—21no—
102C4⋊Dic61—21no—
103C4⋊Dic61C2311yescharacteristic
104C4⋊Dic61C2311yescharacteristic
105#11758196—21no—
106#11758196—21no—
107#11758196—21no—
108#11758196—21no—
109C4×Dic61—21no—
110#11758194—41no—
111C2×#92418C2311yescharacteristic
112C2×#92418C2311yescharacteristic
113#11758190—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—
123Q8×C61—21no—
124Q8×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—21no—
131C2×C4×C61C2×D411yescharacteristic
132C2×C4×C61C2411yescharacteristic
133C22⋊D61—42no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—41no—
138C2×Dic61C2×D411yescharacteristic
139C2×Dic61C2×D411yescharacteristic
140D244—21no—
141D244—21no—
142D244—42no—
143D244—42no—
144C4×D61—21no—
145C4×D61—21no—
146C4×D61—21no—
147C4×D61—21no—
148C4×D61—41no—
149C4×D61—41no—
150C4×D61—42no—
151C4×D61—42no—
152C4×D61—42no—
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#485—611no—
198#484—611no—
199#481—611no—
200#470—611no—
201#470D6111yescharacteristic, complemented
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×Q16C2×D6111yescharacteristic, complemented
215C2×SD16—611no—
216C2×SD16—611no—
217C2×M16—611no—
218C2×M16C2×D6111yescharacteristic
219#123—1221no—
220C22⋊Q8—611no—
221C22⋊Q8—611no—
222C22⋊Q8—611no—
223C22⋊Q8—611no—
224C22⋊Q8—1221no—
225C22⋊Q8—1221no—
226C22⋊Q8C2×D6111yescharacteristic
227C22⋊Q8C2×D6111yescharacteristic
228#121—611no—
229#121—611no—
230#120—1221no—
231C4×D4—1221no—
232C4×D4—1221no—
233#117—611no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4—1221no—
236C2×C22⋊C4—1221no—
237#107—611no—
238#107—611no—
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⋊C8—611no—
253C24—611no—
254#41—2441no—
255#41—2441no—
256C2×Q8—611no—
257C2×Q8—1221no—
258C2×Q8—2441no—
259C2×Q8—2441no—
260C2×Q8C22×D6111yescharacteristic
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—41no—
278Q16—2441no—
279SD16—2441no—
280SD16—2441no—
281M16—41no—
282M16—2441no—
283C2×C8—611no—
284C2×C8—611no—
285C2×C8C22×D6111yescharacteristic
286C2×C8C22×D6111yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—611no—
290C4⋊C4—611no—
291C4⋊C4—1221no—
292C4⋊C4—1221no—
293C4⋊C4—1221no—
294C4⋊C4—1221no—
295C4⋊C4—1221no—
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—1221no—
308C23—611no—
309C23—611no—
310C23—1222no—
311C23—1221no—
312C23—2441no—
313C23—2441no—
314C23D4×D6111yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—21no—
318Q8—21no—
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#1451982211yescharacteristic
379C4#1451982311yescharacteristic
380C2—41no—
381C2—1222no—
382C2—4881no—
383C2—2441no—
384C2#1684032011yescharacteristic
385C2#137×D6111yescharacteristic
386C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#470C2
socleC22×C61C22×D4
hypercenter#470D61
hypocenterC61#3196
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
2. C22⋊Q8×D61C2semidirect
3. #16840106C2semidirect
4. #16840102C2semidirect
5. #16840096C2semidirect
6. #16840082C2semidirect
7. #16840018C2semidirect
8. #16840010C2semidirect
9. #16840008C2semidirect
10. #16839927C2semidirect
11. #16839923C2semidirect
12. #16839916C2semidirect
13. #16839902C2semidirect
14. #16839725C2semidirect
15. C61×#470C2semidirect
19. C2×#11758202C22semidirect
20. C2×#11758190C22semidirect
21. C2×#11758201C22semidirect
39. #14519711C22semidirect
40. #14519710C22semidirect
41. #14519708C22semidirect
42. #14519702C22semidirect
43. #14519701C22semidirect
44. #14519701C22semidirect
45. #14519700C22semidirect
46. #14519699C22semidirect
47. #14519697C22semidirect
52. C2×Q16×C61C22semidirect
56. #106×C61C22semidirect
57. #103×C61C22semidirect
58. #103×C61C22semidirect
201. #470D61semidirect
209. C61#3196semidirect
214. C2×Q16C2×D61semidirect
240. #106C2×D61semidirect
245. #103C2×D61semidirect
246. #103C2×D61semidirect