Finite Group Databasebeta

← #21454650

Subgroups — #21454650

Order 7808.

506 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519804C211yesmaximal, characteristic
2#16840244C211yesmaximal, characteristic, complemented
3#16840234C211yesmaximal, characteristic, complemented
4#16839875C211yesmaximal, characteristic, complemented
5#16839871C211yesmaximal, characteristic, complemented
6#16839865C211yesmaximal, characteristic, complemented
7SD16×Dic61C211yesmaximal, characteristic, complemented
8C4×#11758201C211yesmaximal, characteristic, complemented
9#16839844C211yesmaximal, characteristic, complemented
10C4×#11758199C211yesmaximal, characteristic, complemented
11#16839803C211yesmaximal, characteristic, complemented
12#16839757C211yesmaximal, characteristic, complemented
13#102×D61C211yesmaximal, characteristic, complemented
14#16839719C211yesmaximal, characteristic, complemented
15C61×#440C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×D4×D61C2211yescharacteristic
18#14519804C418yescomplemented
19C2×#11758201C2211yescharacteristic
20C2×D488C2211yescharacteristic
21C2×#11758199C2211yescharacteristic
22C2×#11758189C2211yescharacteristic
23C2×C8×D61C2211yescharacteristic
24Q8×Dic61C2211yescharacteristic, complemented
25C4×D244—21no—
26C4×D244C2211yescharacteristic
27C4×D244C2211yescharacteristic, complemented
28D4×Dic61C2211yescharacteristic
29#14519739—21no—
30#14519739C2211yescharacteristic
31#14519739C2211yescharacteristic, complemented
32C4×C22⋊D61—21no—
33#14519737—21no—
34#14519735C2211yescharacteristic
35#14519734—21no—
36#14519734C2211yescharacteristic
37C4⋊C4×D61—21no—
38C4⋊C4×D61C2211yescharacteristic
39C2×#11758198—21no—
40C22⋊C4×D61—21no—
41#14519710C2211yescharacteristic, complemented
42#14519709C2211yescharacteristic, complemented
43#14519708C2211yescharacteristic, complemented
44#14519701C2211yescharacteristic, complemented
45#14519699C2211yescharacteristic
46#14519699C2211yescharacteristic, complemented
47#14519698C2211yescharacteristic
48#14519697C2211yescharacteristic
49#14519697C2211yescharacteristic, complemented
50#14519687C2211yescharacteristic, complemented
51C4×#92418C2211yescharacteristic, complemented
52C8×Dic61C2211yescharacteristic, complemented
53C2×SD16×C61C2211yescharacteristic
54C4×Q8×C61C2211yescharacteristic, complemented
55C4×D4×C61C2211yescharacteristic
56#107×C61C2211yescharacteristic, complemented
57#103×C61C2211yescharacteristic, complemented
58#102×C61C2211yescharacteristic
59#97×C61C2211yescharacteristic, complemented
60C23×D61—21no—
61C2×Q8×C61C2311yescharacteristic
62C2×D4×C61C2311yescharacteristic
63C22×C4×C61—21no—
64C2×C22⋊D61—21no—
65C22×Dic61—21no—
66#11758226—22no—
67#11758226C2×C414yescomplemented
68D4×D61—22no—
69D4×D61C2×C414yescomplemented
70C2×D244—21no—
71C2×D244C2311yescharacteristic
72C2×D244C2311yescharacteristic
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61C2311yescharacteristic
80SD16×C61C2×C414yescomplemented
81C2×C8×C61C2311yescharacteristic
82C2×C8×C61C2311yescharacteristic
83C4⋊C4×C61—21no—
84C4⋊C4×C61C2311yescharacteristic
85C4⋊C4×C61C2311yescharacteristic
86C22⋊C4×C61—21no—
87C42×C61—21no—
88C42×C61C2311yescharacteristic
89C22⋊Dic61—21no—
90#11758201C2×C414yescomplemented
91#11758199C2×C414yescomplemented
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97#11758198D411yescharacteristic
98#11758198D411yescharacteristic
99C4⋊Dic61—21no—
100C4⋊Dic61C2311yescharacteristic
101C4⋊Dic61C2311yescharacteristic
102#11758196—21no—
103#11758196D411yescharacteristic
104#11758196D411yescharacteristic
105C4×Dic61—21no—
106C4×Dic61—21no—
107C4×Dic61C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110D488C2×C414yescomplemented
111#11758189C2×C414yescomplemented
112C8×D61—22no—
113C23×C61—21no—
114C22×D61—21no—
115C22×D61—21no—
116C22×D61—24no—
117C22×D61—81no—
118C22×D61—81no—
119C22×D61C2×D411yescharacteristic
120Q8×C61—21no—
121Q8×C61C22×C412yes—
122D4×C61—21no—
123D4×C61C22×C412yes—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—81no—
128C2×C4×C61C2×D411yescharacteristic
129C2×C4×C61C2×D411yescharacteristic
130C2×C4×C61C2411yescharacteristic
131C22⋊D61—24no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—81no—
135C2×Dic61C2×D411yescharacteristic
136C2×Dic61C2×D411yescharacteristic
137C2×Dic61C2×D411yescharacteristic
138D244—24no—
139D244—21no—
140D244—21no—
141D244C22×C412yes—
142D244C22×C412yes—
143C4×D61—24no—
144C4×D61—81no—
145C4×D61—81no—
146C4×D61—81no—
147C4×D61—81no—
148C4×D61—81no—
149C4×D61C22×C412yes—
150C4×D61#4112yes—
151C8×C61—21no—
152C8×C61C22×C412yes—
153#92418—21no—
154#92418C22×C412yes—
155C22×C61—22no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61C22×D411yescharacteristic
159C2×D61—21no—
160C2×D61—21no—
161C2×D61—22no—
162C2×D61—22no—
163C2×D61—41no—
164C2×D61—41no—
165C2×D61—41no—
166C2×D61—41no—
167C2×D61—84no—
168C2×D61C4×D412yes—
169C4×C61—22no—
170C4×C61—21no—
171C4×C61—21no—
172C4×C61—41no—
173C4×C61—41no—
174C4×C61C23×C411yescharacteristic
175C4×C61C2×#4111yescharacteristic
176Dic61—21no—
177Dic61—21no—
178Dic61—41no—
179Dic61—41no—
180Dic61C4×D412yes—
181#2946—611nomaximal, Sylow
182C2×C61—42no—
183C2×C61C2×C4×D411yescharacteristic
184C2×C61#57611yescharacteristic
185C2×C61#57711yescharacteristic
186D61—22no—
187D61—42no—
188D61—42no—
189C2×AGL(1,ℤ/8)—611no—
190#520—611no—
191#518—611no—
192#442—611no—
193#442—611no—
194#440—611no—
195#440D6111yescharacteristic, complemented
196C4×SD16—611no—
197C4×SD16—611no—
198C4×D8—611no—
199C4×D8—611no—
200#428—611no—
201#416—611no—
202C2×#102—611no—
203#405—611no—
204C61#294611yescharacteristic, complemented, Sylow
205C2×#41—611no—
206C22×D4—611no—
207AGL(1,ℤ/8)—618no—
208C2×SD16—611no—
209C2×SD16C2×D6111yescharacteristic
210C2×D8—611no—
211C2×D8—611no—
212C2×M16—611no—
213C22×C8—611no—
214C4×Q8—611no—
215C4×Q8C2×D6111yescharacteristic, complemented
216C4×D4—611no—
217C4×D4—611no—
218C4×D4—611no—
219C4×D4—611no—
220C4×D4—611no—
221C4×D4—1221no—
222C4×D4—1221no—
223C4×D4—1221no—
224C4×D4—1221no—
225C4×D4C2×D6111yescharacteristic
226#117—611no—
227#117—611no—
228#117—1221no—
229C2×C4⋊C4—611no—
230C2×C4⋊C4—1221no—
231C2×C22⋊C4—1221no—
232C2×C22⋊C4—1221no—
233#107—611no—
234#107C2×D6111yescharacteristic, complemented
235#106—611no—
236#106—611no—
237#103—611no—
238#103C2×D6111yescharacteristic, complemented
239#102—611no—
240#102—611no—
241#102—611no—
242#102—611no—
243#102—611no—
244#102C2×D6111yescharacteristic
245#97—611no—
246#97C2×D6111yescharacteristic, complemented
247C4×C8—611no—
248C4×C8—611no—
249C24—1221no—
250#41—614no—
251#41—1222no—
252C2×Q8C22×D6111yescharacteristic
253C2×D4—614no—
254C2×D4—611no—
255C2×D4—611no—
256C2×D4—1221no—
257C2×D4—1222no—
258C2×D4—1221no—
259C2×D4C22×D6111yescharacteristic
260C22×C4—21no—
261C22×C4—611no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4—1221no—
265C22×C4—1221no—
266C22×C4—1221no—
267C22×C4—1221no—
268C22×C4—1221no—
269SD16—614no—
270SD16C4×D6114yescomplemented
271D8—614no—
272D8—614no—
273M16—614no—
274C2×C8—611no—
275C2×C8—611no—
276C2×C8—1222no—
277C2×C8C22×D6111yescharacteristic
278C2×C8C22×D6111yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—611no—
281C4⋊C4—611no—
282C4⋊C4—611no—
283C4⋊C4—611no—
284C4⋊C4—1221no—
285C4⋊C4—1221no—
286C4⋊C4C22×D6111yescharacteristic
287C4⋊C4C22×D6111yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—611no—
290C22⋊C4—611no—
291C22⋊C4—1221no—
292C22⋊C4—1221no—
293C22⋊C4—1221no—
294C22⋊C4—1221no—
295C22⋊C4—1221no—
296C22⋊C4—1221no—
297C42—21no—
298C42—611no—
299C42—1221no—
300C42—1221no—
301C42C22×D6111yescharacteristic
302C23—21no—
303C23—611no—
304C23—1224no—
305C23—1221no—
306C23—1221no—
307C23—4881no—
308C23—4881no—
309Q8—21no—
310Q8C2×C4×D6112yes—
311D4—21no—
312D4—612no—
313D4—612no—
314D4—1224no—
315D4—1224no—
316D4—1221no—
317D4—1221no—
318D4C2×C4×D6112yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—81no—
323C2×C4—611no—
324C2×C4—612no—
325C2×C4—612no—
326C2×C4—611no—
327C2×C4—611no—
328C2×C4—1224no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—4881no—
332C2×C4—4881no—
333C2×C4—4881no—
334C2×C4—4881no—
335C2×C4—4881no—
336C2×C4—4881no—
337C2×C4D4×D6111yescharacteristic
338C2×C4D4×D6111yescharacteristic
339C2×C4C23×D6111yescharacteristic
340C8—21no—
341C8—612no—
342C8—1221no—
343C8C2×C4×D6112yes—
344C22—22no—
345C22—41no—
346C22—41no—
347C22—612no—
348C22—1221no—
349C22—1221no—
350C22—1222no—
351C22—1222no—
352C22—4884no—
353C22—2441no—
354C22—2441no—
355C22—2441no—
356C22—2441no—
357C22C2×D4×D6111yescharacteristic
358C4—22no—
359C4—21no—
360C4—21no—
361C4—41no—
362C4—41no—
363C4—612no—
364C4—1221no—
365C4—1221no—
366C4—2441no—
367C4—2441no—
368C4C22×C4×D6111yescharacteristic
369C4#41×D6111yescharacteristic
370C2—42no—
371C2—1222no—
372C2—2442no—
373C2—2442no—
374C2C4×D4×D6111yescharacteristic
375C2#1684056611yescharacteristic
376C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC4×C61C23×C4
FrattiniC2×C4C23×D61
FittingC61×#440C2
socleC22×C61C22×D4
hypercenter#440D61
hypocenterC61#2946
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. #16840244C2semidirect
3. #16840234C2semidirect
4. #16839875C2semidirect
5. #16839871C2semidirect
6. #16839865C2semidirect
7. SD16×Dic61C2semidirect
8. C4×#11758201C2semidirect
9. #16839844C2semidirect
10. C4×#11758199C2semidirect
11. #16839803C2semidirect
12. #16839757C2semidirect
13. #102×D61C2semidirect
14. #16839719C2semidirect
15. C61×#440C2semidirect
18. #14519804C4semidirect
24. Q8×Dic61C22semidirect
27. C4×D244C22semidirect
31. #14519739C22semidirect
41. #14519710C22semidirect
42. #14519709C22semidirect
43. #14519708C22semidirect
44. #14519701C22semidirect
46. #14519699C22semidirect
49. #14519697C22semidirect
50. #14519687C22semidirect
51. C4×#92418C22semidirect
52. C8×Dic61C22semidirect
54. C4×Q8×C61C22semidirect
56. #107×C61C22semidirect
57. #103×C61C22semidirect
59. #97×C61C22semidirect
67. #11758226C2×C4semidirect
69. D4×D61C2×C4semidirect
80. SD16×C61C2×C4semidirect
90. #11758201C2×C4semidirect
91. #11758199C2×C4semidirect
110. D488C2×C4semidirect
111. #11758189C2×C4semidirect
195. #440D61semidirect
204. C61#2946semidirect
215. C4×Q8C2×D61semidirect
234. #107C2×D61semidirect
238. #103C2×D61semidirect
246. #97C2×D61semidirect
270. SD16C4×D61semidirect