Finite Group Databasebeta

← #21456292

Subgroups — #21456292

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×#14519801C211yesmaximal, characteristic, complemented
3C2×#14519796C211yesmaximal, characteristic, complemented
4C2×SD16×D61C211yesmaximal, characteristic, complemented
5#16840332C211yesmaximal, characteristic, complemented
6#16840325C211yesmaximal, characteristic, complemented
7#16840156C211yesmaximal, characteristic, complemented
8#16840153C211yesmaximal, characteristic, complemented
9#16840150C211yesmaximal, characteristic, complemented
10#16840145C211yesmaximal, characteristic, complemented
11#16840144C211yesmaximal, characteristic, complemented
12#16840134C211yesmaximal, characteristic, complemented
13#16840133C211yesmaximal, characteristic, complemented
14#16839719C211yesmaximal, characteristic, complemented
15C61×#496C211yesmaximal, characteristic, complemented
16C2×#11758224C2211yescharacteristic
17C2×#11758224C2211yescharacteristic
18C2×Q8×D61C2211yescharacteristic
19C2×D4×D61C2211yescharacteristic
20#14519806—24no—
21#14519801—24no—
22#14519796—24no—
23C2×Dic244C2211yescharacteristic, complemented
24C2×Dic244C2211yescharacteristic, complemented
25C2×#11758202C2211yescharacteristic, complemented
26C2×#11758190C2211yescharacteristic
27C2×#11758190C2211yescharacteristic
28C2×#11758200C2211yescharacteristic
29C2×#11758200C2211yescharacteristic
30C2×#11758200C2211yescharacteristic, complemented
31C2×#11758200C2211yescharacteristic, complemented
32C2×#11758200C2211yescharacteristic, complemented
33C2×#11758201C2211yescharacteristic
34SD16×D61—24no—
35C2×#11758199C2211yescharacteristic
36C2×#11758189C2211yescharacteristic
37C2×C8×D61C2211yescharacteristic
38#14519777C2211yescharacteristic, complemented
39#14519775C2211yescharacteristic, complemented
40#14519773C2211yescharacteristic
41#14519765C2211yescharacteristic
42#14519764C2211yescharacteristic
43#14519764C2211yescharacteristic, complemented
44#14519759—22no—
45#14519754—22no—
46#14519749—22no—
47#14519745—22no—
48#14519734C2211yescharacteristic
49#14519687C2211yescharacteristic, complemented
50C4×#92418C2211yescharacteristic, complemented
51C8×Dic61C2211yescharacteristic, complemented
52C2×SD16×C61C2211yescharacteristic
53C2×SD16×C61C2211yescharacteristic, complemented
54C2×D8×C61C2211yescharacteristic
55C2×D8×C61C2211yescharacteristic, complemented
56#127×C61C2211yescharacteristic
57#124×C61C2211yescharacteristic, complemented
58#97×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C2×Q8×C61C2311yescharacteristic
61C2×D4×C61—22no—
62C2×D4×C61C2311yescharacteristic
63C2×D4×C61C2311yescharacteristic
64C2×D4×C61C2311yescharacteristic
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C2×C22⋊D61—22no—
69C22×Dic61—21no—
70C22×Dic61—21no—
71Q8×D61—22no—
72Q8×D61—22no—
73#11758224—22no—
74#11758224—22no—
75#11758224—22no—
76#11758224—22no—
77D4×D61—22no—
78D4×D61—22no—
79C2×D244C2311yescharacteristic
80C2×C4×D61—21no—
81C2×C4×D61C2311yescharacteristic
82C2×Dic122—21no—
83C2×Dic122C2311yescharacteristic
84C2×Dic122C2311yescharacteristic
85C2×Dic122C2311yescharacteristic
86SD16×C61—22no—
87SD16×C61—22no—
88D8×C61—22no—
89D8×C61—22no—
90C2×C8×C61C2311yescharacteristic
91C2×C8×C61C2311yescharacteristic
92C22⋊C4×C61—22no—
93C42×C61C2311yescharacteristic
94C22⋊Dic61—22no—
95C22⋊Dic61—22no—
96#11758202—22no—
97#11758201—22no—
98#11758200—22no—
99#11758200—22no—
100#11758200—22no—
101#11758200—22no—
102#11758200—22no—
103#11758199—22no—
104#11758198—22no—
105#11758198D412yes—
106C4⋊Dic61—22no—
107#11758196—22no—
108#11758196D412yes—
109C4×Dic61C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111C2×#92418C2311yescharacteristic
112Dic244—22no—
113Dic244—22no—
114#11758190—22no—
115#11758190—22no—
116#11758189D414yescomplemented
117C8×D61D414yescomplemented
118C23×C61—21no—
119C23×C61—21no—
120C23×C61—21no—
121C22×D61—21no—
122C22×D61—42no—
123C22×D61—82no—
124C22×D61C2×D411yescharacteristic
125Q8×C61—21no—
126Q8×C61—21no—
127D4×C61—21no—
128D4×C61—21no—
129D4×C61—21no—
130D4×C61—21no—
131D4×C61—21no—
132D4×C61—21no—
133D4×C61—82no—
134C2×C4×C61—21no—
135C2×C4×C61C2×D412yes—
136C2×C4×C61C2411yescharacteristic
137C22⋊D61—42no—
138C22⋊D61—42no—
139C22⋊D61—42no—
140C22⋊D61—82no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—42no—
145C2×Dic61—42no—
146C2×Dic61C2×D412yes—
147C2×Dic61C2×D411yescharacteristic
148D244—21no—
149D244—21no—
150C4×D61—42no—
151C4×D61C2×D412yes—
152C4×D61C2×D412yes—
153Dic122—21no—
154Dic122—21no—
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—41no—
167C22×C61—42no—
168C22×C61—42no—
169C22×C61—42no—
170C22×C61C22×D411yescharacteristic
171C2×D61—22no—
172C2×D61—41no—
173C2×D61—42no—
174C2×D61—84no—
175C2×D61#12712yes—
176C4×C61—22no—
177C4×C61—41no—
178C4×C61C22×D411yescharacteristic
179C4×C61C22×D411yescharacteristic
180Dic61—22no—
181Dic61—41no—
182Dic61—41no—
183Dic61—41no—
184Dic61#12712yes—
185#3154—611nomaximal, Sylow
186C2×C61—81no—
187C2×C61—81no—
188C2×C61—81no—
189C2×C61C2×#12711yescharacteristic
190C2×C61#57712yes—
191D61—22no—
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#496D6111yescharacteristic, complemented
203#495—611no—
204#495—611no—
205#492—611no—
206#492—611no—
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—611no—
226C2×SD16—611no—
227C2×SD16—1224no—
228C2×SD16C2×D6111yescharacteristic
229C2×SD16C2×D6111yescharacteristic, complemented
230C2×D8—611no—
231C2×D8C2×D6111yescharacteristic
232C2×D8C2×D6111yescharacteristic, complemented
233C2×M16—611no—
234C22×C8—611no—
235C4⋊Q8—611no—
236C4⋊Q8—611no—
237#127—611no—
238#127C2×D6111yescharacteristic
239#124—611no—
240#124—611no—
241#124—611no—
242#124C2×D6111yescharacteristic, complemented
243#123—1222no—
244C22⋊Q8—1222no—
245#121—1222no—
246#120—1222no—
247#117—611no—
248#97—611no—
249#97C2×D6111yescharacteristic, complemented
250C4×C8—611no—
251C4×C8—611no—
252C24—1221no—
253#41—1222no—
254#41—1222no—
255#41—1222no—
256#41—1222no—
257C2×Q8—611no—
258C2×Q8—611no—
259C2×Q8—611no—
260C2×Q8—1221no—
261C2×Q8—1222no—
262C2×Q8—1222no—
263C2×Q8C22×D6111yescharacteristic
264C2×D4—22no—
265C2×D4—611no—
266C2×D4—1222no—
267C2×D4—1222no—
268C2×D4—1222no—
269C2×D4—1221no—
270C2×D4—1221no—
271C2×D4—1221no—
272C2×D4C22×D6111yescharacteristic
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—1222no—
285SD16—1222no—
286SD16—1222no—
287SD16—1222no—
288SD16—1222no—
289SD16—1222no—
290SD16—1222no—
291SD16—1222no—
292D8—22no—
293D8—22no—
294D8—1222no—
295M16—614no—
296C2×C8—611no—
297C2×C8—611no—
298C2×C8—614no—
299C2×C8C22×D6111yescharacteristic
300C2×C8C22×D6111yescharacteristic
301C4⋊C4—612no—
302C4⋊C4—1222no—
303C4⋊C4—1222no—
304C22⋊C4—22no—
305C22⋊C4—612no—
306C22⋊C4—1222no—
307C22⋊C4—1222no—
308C22⋊C4—1222no—
309C42—611no—
310C42C22×D6111yescharacteristic
311C23—21no—
312C23—21no—
313C23—21no—
314C23—611no—
315C23—1221no—
316C23—4882no—
317C23—2442no—
318Q8—21no—
319Q8—21no—
320Q8—1221no—
321Q8—1221no—
322Q8—1221no—
323Q8—1221no—
324Q8—1221no—
325Q8—1221no—
326Q8—2442no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—82no—
334D4—1221no—
335D4—1221no—
336D4—4882no—
337D4—2442no—
338D4—2442no—
339D4—2442no—
340C2×C4—21no—
341C2×C4—611no—
342C2×C4—612no—
343C2×C4—612no—
344C2×C4—612no—
345C2×C4—1221no—
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—41no—
360C22—42no—
361C22—42no—
362C22—42no—
363C22—612no—
364C22—1222no—
365C22—4884no—
366C22—2441no—
367C22—2442no—
368C22C2×D4×D6111yescharacteristic
369C4—22no—
370C4—41no—
371C4—612no—
372C4—1222no—
373C4—2441no—
374C4—2441no—
375C4—2441no—
376C4C2×D4×D6111yescharacteristic
377C4C2×D4×D6111yescharacteristic
378C2—81no—
379C2—81no—
380C2—81no—
381C2—1222no—
382C2—4881no—
383C2#127×D6111yescharacteristic
384C2#1684057212yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#496C2
socleC22×C61C22×D4
hypercenter#496D61
hypocenterC61#3154
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. C2×#14519806C2semidirect
2. C2×#14519801C2semidirect
3. C2×#14519796C2semidirect
4. C2×SD16×D61C2semidirect
5. #16840332C2semidirect
6. #16840325C2semidirect
7. #16840156C2semidirect
8. #16840153C2semidirect
9. #16840150C2semidirect
10. #16840145C2semidirect
11. #16840144C2semidirect
12. #16840134C2semidirect
13. #16840133C2semidirect
14. #16839719C2semidirect
15. C61×#496C2semidirect
23. C2×Dic244C22semidirect
24. C2×Dic244C22semidirect
25. C2×#11758202C22semidirect
30. C2×#11758200C22semidirect
31. C2×#11758200C22semidirect
32. C2×#11758200C22semidirect
38. #14519777C22semidirect
39. #14519775C22semidirect
43. #14519764C22semidirect
49. #14519687C22semidirect
50. C4×#92418C22semidirect
51. C8×Dic61C22semidirect
53. C2×SD16×C61C22semidirect
55. C2×D8×C61C22semidirect
57. #124×C61C22semidirect
58. #97×C61C22semidirect
116. #11758189D4semidirect
117. C8×D61D4semidirect
202. #496D61semidirect
208. C61#3154semidirect
229. C2×SD16C2×D61semidirect
232. C2×D8C2×D61semidirect
242. #124C2×D61semidirect
249. #97C2×D61semidirect