Finite Group Databasebeta

← #21456290

Subgroups — #21456290

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×#14519809C211yesmaximal, characteristic, complemented
2C2×#14519801C211yesmaximal, characteristic, complemented
3C2×#14519798C211yesmaximal, characteristic, complemented
4C2×SD16×D61C211yesmaximal, characteristic, complemented
5#16840332C211yesmaximal, characteristic, complemented
6#16840330C211yesmaximal, characteristic, complemented
7#16840157C211yesmaximal, characteristic, complemented
8#16840155C211yesmaximal, characteristic, complemented
9#16840152C211yesmaximal, characteristic, complemented
10#16840150C211yesmaximal, characteristic, complemented
11#16840143C211yesmaximal, characteristic, complemented
12#16840135C211yesmaximal, characteristic, complemented
13#16840133C211yesmaximal, characteristic, complemented
14#16839716C211yesmaximal, characteristic, complemented
15C61×#495C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758224C2211yescharacteristic
18C2×Q8×D61C2211yescharacteristic
19C2×D4×D61C2211yescharacteristic
20#14519809—24no—
21#14519801—24no—
22#14519798—24no—
23C2×#11758202C2211yescharacteristic, complemented
24C2×#11758202C2211yescharacteristic, complemented
25C2×#11758190C2211yescharacteristic
26C2×#11758190C2211yescharacteristic
27C2×#11758190C2211yescharacteristic, complemented
28C2×#11758190C2211yescharacteristic, complemented
29C2×#11758200C2211yescharacteristic
30C2×#11758200C2211yescharacteristic
31C2×#11758201C2211yescharacteristic
32C2×#11758201C2211yescharacteristic, complemented
33SD16×D61—24no—
34C2×#11758199C2211yescharacteristic
35C2×#11758199C2211yescharacteristic, complemented
36C2×#11758189C2211yescharacteristic
37C2×C8×D61C2211yescharacteristic
38#14519777C2211yescharacteristic, complemented
39#14519775C2211yescharacteristic, complemented
40#14519774C2211yescharacteristic
41#14519773C2211yescharacteristic
42#14519766C2211yescharacteristic
43#14519764C2211yescharacteristic, complemented
44#14519759—22no—
45#14519754—22no—
46#14519750—22no—
47#14519747—22no—
48#14519734C2211yescharacteristic
49#14519688C2211yescharacteristic, complemented
50#14519687C2211yescharacteristic, complemented
51C8×Dic61C2211yescharacteristic, complemented
52C2×Q16×C61C2211yescharacteristic, complemented
53C2×SD16×C61C2211yescharacteristic
54C2×SD16×C61C2211yescharacteristic, complemented
55C2×D8×C61C2211yescharacteristic
56#124×C61C2211yescharacteristic
57#124×C61C2211yescharacteristic, complemented
58C4×C8×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C2×Q8×C61C2311yescharacteristic
61C2×Q8×C61C2311yescharacteristic
62C2×D4×C61C2311yescharacteristic
63C2×D4×C61C2311yescharacteristic
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C2×C22⋊D61—22no—
67C22×Dic61—21no—
68#11758226—22no—
69#11758226—22no—
70Q8×D61—22no—
71Q8×D61—22no—
72#11758224—22no—
73#11758224—22no—
74D4×D61—22no—
75D4×D61—22no—
76C2×D244—21no—
77C2×D244—22no—
78C2×D244C2311yescharacteristic
79C2×D244C2311yescharacteristic
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61C2311yescharacteristic
83C2×Dic122—21no—
84C2×Dic122C2311yescharacteristic
85C2×Dic122C2311yescharacteristic
86Q16×C61—22no—
87SD16×C61—22no—
88SD16×C61—22no—
89D8×C61—22no—
90C2×C8×C61C2311yescharacteristic
91C2×C8×C61C2311yescharacteristic
92C22⋊C4×C61—22no—
93C22⋊C4×C61—22no—
94C42×C61C2311yescharacteristic
95C22⋊Dic61—22no—
96#11758202—22no—
97#11758202—22no—
98#11758201—22no—
99#11758201—22no—
100#11758200—22no—
101#11758200—22no—
102#11758199—22no—
103#11758199—22no—
104#11758198—22no—
105#11758198D412yes—
106C4⋊Dic61—22no—
107#11758196—22no—
108#11758196D412yes—
109C4×Dic61C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111C2×#92418C2311yescharacteristic
112#11758190—22no—
113#11758190—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—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61C2×D412yes—
136C2×C4×C61C2411yescharacteristic
137C22⋊D61—42no—
138C22⋊D61—42no—
139C22⋊D61—82no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—42no—
143C2×Dic61C2×D412yes—
144C2×Dic61C2×D411yescharacteristic
145D244—21no—
146D244—21no—
147D244—21no—
148D244—21no—
149D244—42no—
150D244—82no—
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#495D6111yescharacteristic, complemented
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×Q16C2×D6111yescharacteristic, complemented
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×D8—611no—
232C2×D8C2×D6111yescharacteristic
233C2×M16—611no—
234C22×C8—611no—
235C4⋊Q8—611no—
236C4⋊Q8—611no—
237#127—611no—
238#127—611no—
239#124—611no—
240#124—611no—
241#124C2×D6111yescharacteristic
242#124C2×D6111yescharacteristic, complemented
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—611no—
265C2×D4—611no—
266C2×D4—1221no—
267C2×D4—1222no—
268C2×D4—1222no—
269C2×D4—1222no—
270C2×D4—1221no—
271C2×D4—1221no—
272C2×D4—1222no—
273C2×D4C22×D6111yescharacteristic
274C2×D4C22×D6111yescharacteristic
275C22×C4—611no—
276C22×C4—1221no—
277C22×C4—1221no—
278C22×C4—1221no—
279Q16—22no—
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—1222no—
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—22no—
306C22⋊C4—612no—
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—1221no—
332D4—1221no—
333D4—1221no—
334D4—1221no—
335D4—4882no—
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#1684056912yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#495C2
socleC22×C61C22×D4
hypercenter#495D61
hypocenterC61#3154
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C2×#14519809C2semidirect
2. C2×#14519801C2semidirect
3. C2×#14519798C2semidirect
4. C2×SD16×D61C2semidirect
5. #16840332C2semidirect
6. #16840330C2semidirect
7. #16840157C2semidirect
8. #16840155C2semidirect
9. #16840152C2semidirect
10. #16840150C2semidirect
11. #16840143C2semidirect
12. #16840135C2semidirect
13. #16840133C2semidirect
14. #16839716C2semidirect
15. C61×#495C2semidirect
23. C2×#11758202C22semidirect
24. C2×#11758202C22semidirect
27. C2×#11758190C22semidirect
28. C2×#11758190C22semidirect
32. C2×#11758201C22semidirect
35. C2×#11758199C22semidirect
38. #14519777C22semidirect
39. #14519775C22semidirect
43. #14519764C22semidirect
49. #14519688C22semidirect
50. #14519687C22semidirect
51. C8×Dic61C22semidirect
52. C2×Q16×C61C22semidirect
54. C2×SD16×C61C22semidirect
57. #124×C61C22semidirect
58. C4×C8×C61C22semidirect
116. #11758189D4semidirect
117. C8×D61D4semidirect
204. #495D61semidirect
208. C61#3154semidirect
218. C2×Q16C2×D61semidirect
229. C2×SD16C2×D61semidirect
242. #124C2×D61semidirect
251. C4×C8C2×D61semidirect