Finite Group Databasebeta

← #21456288

Subgroups — #21456288

Order 7808.

564 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519806C211yesmaximal, characteristic, complemented
2C2×#14519804C211yesmaximal, characteristic, complemented
3C2×#14519798C211yesmaximal, characteristic, complemented
4C2×SD16×D61C211yesmaximal, characteristic, complemented
5#16840337C211yesmaximal, characteristic, complemented
6#16840325C211yesmaximal, characteristic, complemented
7#16840154C211yesmaximal, characteristic, complemented
8#16840153C211yesmaximal, characteristic, complemented
9#16840149C211yesmaximal, characteristic, complemented
10#16840148C211yesmaximal, characteristic, complemented
11#16840146C211yesmaximal, characteristic, complemented
12#16840143C211yesmaximal, characteristic, complemented
13#16840133C211yesmaximal, characteristic, complemented
14#16839716C211yesmaximal, characteristic, complemented
15C61×#492C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758224C2211yescharacteristic
18C2×Q8×D61C2211yescharacteristic
19C2×D4×D61C2211yescharacteristic
20#14519806—24no—
21#14519804—24no—
22#14519798—24no—
23C2×Dic244C2211yescharacteristic, complemented
24C2×#11758202C2211yescharacteristic, complemented
25C2×#11758202C2211yescharacteristic, complemented
26C2×#11758190C2211yescharacteristic
27C2×#11758190C2211yescharacteristic, complemented
28C2×#11758200C2211yescharacteristic
29C2×#11758200C2211yescharacteristic, complemented
30C2×#11758201C2211yescharacteristic
31C2×#11758201C2211yescharacteristic
32SD16×D61—24no—
33C2×D488C2211yescharacteristic
34C2×#11758199C2211yescharacteristic
35C2×#11758199C2211yescharacteristic, complemented
36C2×#11758189C2211yescharacteristic
37C2×C8×D61C2211yescharacteristic
38#14519775C2211yescharacteristic, complemented
39#14519773C2211yescharacteristic
40#14519766C2211yescharacteristic, complemented
41#14519765C2211yescharacteristic
42#14519765C2211yescharacteristic, complemented
43#14519764C2211yescharacteristic
44#14519762—22no—
45#14519755—22no—
46#14519749—22no—
47#14519745—22no—
48#14519734C2211yescharacteristic
49#14519688C2211yescharacteristic, complemented
50#14519687C2211yescharacteristic, complemented
51C8×Dic61C2211yescharacteristic, complemented
52C2×SD16×C61C2211yescharacteristic
53C2×SD16×C61C2211yescharacteristic
54C2×SD16×C61C2211yescharacteristic, complemented
55C2×SD16×C61C2211yescharacteristic, complemented
56C4⋊Q8×C61C2211yescharacteristic, complemented
57#127×C61C2211yescharacteristic
58C4×C8×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C2×Q8×C61C2311yescharacteristic
61C2×Q8×C61C2311yescharacteristic
62C2×D4×C61—22no—
63C2×D4×C61C2311yescharacteristic
64C2×D4×C61C2311yescharacteristic
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61—22no—
68C22×Dic61—21no—
69#11758226—22no—
70#11758226—22no—
71Q8×D61—22no—
72Q8×D61—22no—
73#11758224—22no—
74#11758224—22no—
75D4×D61—22no—
76D4×D61—22no—
77C2×D244—21no—
78C2×D244C2311yescharacteristic
79C2×D244C2311yescharacteristic
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61C2311yescharacteristic
83C2×Dic122—21no—
84C2×Dic122C2311yescharacteristic
85C2×Dic122C2311yescharacteristic
86SD16×C61—22no—
87SD16×C61—22no—
88SD16×C61—22no—
89SD16×C61—22no—
90C2×C8×C61C2311yescharacteristic
91C2×C8×C61C2311yescharacteristic
92C4⋊C4×C61—22no—
93C42×C61C2311yescharacteristic
94C22⋊Dic61—22no—
95#11758202—22no—
96#11758202—22no—
97#11758201—22no—
98#11758201—22no—
99#11758200—22no—
100#11758200—22no—
101#11758199—22no—
102#11758199—22no—
103#11758198—22no—
104#11758198—22no—
105#11758198—22no—
106#11758198D412yes—
107#11758196—22no—
108#11758196D412yes—
109C4×Dic61C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111C2×#92418C2311yescharacteristic
112Dic244—22no—
113D488—22no—
114#11758190—22no—
115#11758190—22no—
116#11758189D414yescomplemented
117C8×D61D414yescomplemented
118C23×C61—21no—
119C23×C61—21no—
120C22×D61—21no—
121C22×D61—21no—
122C22×D61—42no—
123C22×D61—82no—
124C22×D61C2×D411yescharacteristic
125Q8×C61—21no—
126Q8×C61—21no—
127Q8×C61—21no—
128Q8×C61—21no—
129D4×C61—21no—
130D4×C61—21no—
131D4×C61—21no—
132D4×C61—21no—
133D4×C61—82no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61C2×D412yes—
137C2×C4×C61C2411yescharacteristic
138C22⋊D61—42no—
139C22⋊D61—42no—
140C22⋊D61—82no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—42no—
144C2×Dic61C2×D412yes—
145C2×Dic61C2×D411yescharacteristic
146D244—21no—
147D244—21no—
148D244—21no—
149D244—21no—
150D244—42no—
151C4×D61—42no—
152C4×D61—42no—
153C4×D61C2×D412yes—
154C4×D61C2×D412yes—
155Dic122—21no—
156Dic122—21no—
157Dic122—21no—
158Dic122—21no—
159Dic122—42no—
160C8×C61C2×D412yes—
161C8×C61C2×D412yes—
162#92418C2×D412yes—
163#92418C2×D412yes—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—42no—
167C22×C61—42no—
168C22×C61C22×D411yescharacteristic
169C2×D61—22no—
170C2×D61—41no—
171C2×D61—41no—
172C2×D61—42no—
173C2×D61—42no—
174C2×D61—84no—
175C2×D61#12712yes—
176C4×C61—22no—
177C4×C61—41no—
178C4×C61—41no—
179C4×C61C22×D411yescharacteristic
180C4×C61C22×D411yescharacteristic
181Dic61—22no—
182Dic61—41no—
183Dic61—41no—
184Dic61#12712yes—
185#3154—611nomaximal, Sylow
186C2×C61—81no—
187C2×C61—81no—
188C2×C61C2×#12711yescharacteristic
189C2×C61#57712yes—
190D61—22no—
191D61—81no—
192D61—81no—
193C2×#137—611no—
194C2×AGL(1,ℤ/8)—611no—
195C2×#135—611no—
196C22×SD16—611no—
197#536—611no—
198#535—611no—
199#497—611no—
200#497—611no—
201#496—611no—
202#496—611no—
203#495—611no—
204#495—611no—
205#492—611no—
206#492D6111yescharacteristic, complemented
207#405—611no—
208C61#315411yescharacteristic, complemented, Sylow
209C2×#41—611no—
210C2×#41—611no—
211C22×Q8—611no—
212C22×D4—611no—
213#137—1224no—
214AGL(1,ℤ/8)—1224no—
215#135—1224no—
216C2×Q16—611no—
217C2×Q16—611no—
218C2×Q16—611no—
219C2×SD16—611no—
220C2×SD16—611no—
221C2×SD16—611no—
222C2×SD16—611no—
223C2×SD16—611no—
224C2×SD16—611no—
225C2×SD16—1224no—
226C2×SD16C2×D6111yescharacteristic
227C2×SD16C2×D6111yescharacteristic
228C2×SD16C2×D6111yescharacteristic, complemented
229C2×SD16C2×D6111yescharacteristic, complemented
230C2×D8—611no—
231C2×D8—611no—
232C2×D8—611no—
233C2×M16—611no—
234C22×C8—611no—
235C4⋊Q8—611no—
236C4⋊Q8C2×D6111yescharacteristic, complemented
237#127—611no—
238#127C2×D6111yescharacteristic
239#124—611no—
240#124—611no—
241#124—611no—
242#124—611no—
243#123—1222no—
244C22⋊Q8—1222no—
245#121—1222no—
246#120—1222no—
247#117—611no—
248#97—611no—
249#97—611no—
250C4×C8—611no—
251C4×C8C2×D6111yescharacteristic, complemented
252C24—1221no—
253#41—1222no—
254#41—1222no—
255#41—1222no—
256#41—1222no—
257C2×Q8—611no—
258C2×Q8—611no—
259C2×Q8—1221no—
260C2×Q8—1222no—
261C2×Q8—1222no—
262C2×Q8C22×D6111yescharacteristic
263C2×Q8C22×D6111yescharacteristic
264C2×D4—22no—
265C2×D4—611no—
266C2×D4—611no—
267C2×D4—1221no—
268C2×D4—1222no—
269C2×D4—1222no—
270C2×D4—1222no—
271C2×D4—1221no—
272C2×D4—1221no—
273C2×D4C22×D6111yescharacteristic
274C2×D4C22×D6111yescharacteristic
275C22×C4—611no—
276C22×C4—1221no—
277C22×C4—1221no—
278C22×C4—1221no—
279Q16—1222no—
280Q16—1222no—
281Q16—1222no—
282SD16—22no—
283SD16—22no—
284SD16—22no—
285SD16—22no—
286SD16—1222no—
287SD16—1222no—
288SD16—1222no—
289SD16—1222no—
290SD16—1222no—
291SD16—1222no—
292D8—1222no—
293D8—1222no—
294D8—1222no—
295M16—614no—
296C2×C8—611no—
297C2×C8—611no—
298C2×C8—614no—
299C2×C8C22×D6111yescharacteristic
300C2×C8C22×D6111yescharacteristic
301C4⋊C4—22no—
302C4⋊C4—612no—
303C4⋊C4—1222no—
304C22⋊C4—612no—
305C22⋊C4—1222no—
306C22⋊C4—1222no—
307C22⋊C4—1222no—
308C22⋊C4—1222no—
309C42—611no—
310C42C22×D6111yescharacteristic
311C23—21no—
312C23—21no—
313C23—611no—
314C23—1221no—
315C23—1221no—
316C23—4882no—
317C23—2442no—
318Q8—21no—
319Q8—21no—
320Q8—21no—
321Q8—21no—
322Q8—1221no—
323Q8—1221no—
324Q8—1221no—
325Q8—1221no—
326Q8—2442no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—82no—
332D4—1221no—
333D4—1221no—
334D4—1221no—
335D4—1221no—
336D4—4882no—
337D4—2442no—
338D4—2442no—
339D4—2442no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—611no—
343C2×C4—612no—
344C2×C4—612no—
345C2×C4—612no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—2442no—
349C2×C4—2442no—
350C2×C4—2442no—
351C2×C4D4×D6112yes—
352C2×C4C23×D6111yescharacteristic
353C8—612no—
354C8—612no—
355C8D4×D6112yes—
356C8D4×D6112yes—
357C22—41no—
358C22—41no—
359C22—42no—
360C22—42no—
361C22—612no—
362C22—1222no—
363C22—4884no—
364C22—2441no—
365C22—2441no—
366C22—2442no—
367C22—2442no—
368C22C2×D4×D6111yescharacteristic
369C4—22no—
370C4—41no—
371C4—41no—
372C4—612no—
373C4—1222no—
374C4—2441no—
375C4—2441no—
376C4C2×D4×D6111yescharacteristic
377C4C2×D4×D6111yescharacteristic
378C2—81no—
379C2—81no—
380C2—1222no—
381C2—4881no—
382C2—4881no—
383C2#127×D6111yescharacteristic
384C2#1684056812yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#492C2
socleC22×C61C22×D4
hypercenter#492D61
hypocenterC61#3154
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. C2×#14519806C2semidirect
2. C2×#14519804C2semidirect
3. C2×#14519798C2semidirect
4. C2×SD16×D61C2semidirect
5. #16840337C2semidirect
6. #16840325C2semidirect
7. #16840154C2semidirect
8. #16840153C2semidirect
9. #16840149C2semidirect
10. #16840148C2semidirect
11. #16840146C2semidirect
12. #16840143C2semidirect
13. #16840133C2semidirect
14. #16839716C2semidirect
15. C61×#492C2semidirect
23. C2×Dic244C22semidirect
24. C2×#11758202C22semidirect
25. C2×#11758202C22semidirect
27. C2×#11758190C22semidirect
29. C2×#11758200C22semidirect
35. C2×#11758199C22semidirect
38. #14519775C22semidirect
40. #14519766C22semidirect
42. #14519765C22semidirect
49. #14519688C22semidirect
50. #14519687C22semidirect
51. C8×Dic61C22semidirect
54. C2×SD16×C61C22semidirect
55. C2×SD16×C61C22semidirect
56. C4⋊Q8×C61C22semidirect
58. C4×C8×C61C22semidirect
116. #11758189D4semidirect
117. C8×D61D4semidirect
206. #492D61semidirect
208. C61#3154semidirect
228. C2×SD16C2×D61semidirect
229. C2×SD16C2×D61semidirect
236. C4⋊Q8C2×D61semidirect
251. C4×C8C2×D61semidirect