Finite Group Databasebeta

← #21459610

Subgroups — #21459610

Order 7808.

1540 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519825C211yesmaximal, characteristic, complemented
2C2×#14519823C211yesmaximal, characteristic, complemented
3#16840424C211yesmaximal, characteristic, complemented
4#16840423C211yesmaximal, characteristic, complemented
5#16840419C211yesmaximal, characteristic, complemented
6#16840409C213yesmaximal, complemented
7#16840408C213yesmaximal, complemented
8#16840405C213yesmaximal, complemented
9#16840403C213yesmaximal, complemented
10#16840335C213yesmaximal, complemented
11#16840328C213yesmaximal, complemented
12#16840309C213yesmaximal, complemented
13#124×D61C213yesmaximal, complemented
14C4×#11758226C211yesmaximal, characteristic, complemented
15C61×#548C211yesmaximal, characteristic, complemented
16#14519825—28no—
17#14519823—28no—
18C2×#11758226C2211yescharacteristic
19C2×#11758226C2211yescharacteristic
20C2×#11758226C2213yescomplemented
21C2×#11758222C2213yes—
22C2×#11758222C2213yescomplemented
23C2×#11758222C2213yescomplemented
24C2×Q8×D61C2213yescomplemented
25C2×Q8×D61C2211yescharacteristic, complemented
26C22×D244C2213yes—
27C2×D4×D61C2213yes—
28C2×D4×D61C2213yes—
29#14519776C2213yescomplemented
30#14519773C2213yescomplemented
31#14519766C2213yescomplemented
32#14519765C2213yescomplemented
33#14519764C2213yescomplemented
34#14519763C2213yescomplemented
35#14519763C2216yescomplemented
36#14519763C2211yescharacteristic, complemented
37#14519762C2216yescomplemented
38#14519759C2216yescomplemented
39#14519757C2213yescomplemented
40#14519756C2213yescomplemented
41#14519753C2213yescomplemented
42#14519752C2213yescomplemented
43#14519752C2213yescomplemented
44#14519751C2213yescomplemented
45#14519750C2213yescomplemented
46#14519750C2213yescomplemented
47#14519748C2213yescomplemented
48#14519748C2213yescomplemented
49#14519747C2216yescomplemented
50#14519745C2216yescomplemented
51Q8×Dic61C2211yescharacteristic, complemented
52C4×D244C2213yescomplemented
53C4×D244C2213yescomplemented
54#14519739C2213yescomplemented
55C4×C22⋊D61C2213yescomplemented
56C4×C22⋊D61C2213yescomplemented
57#14519735C2213yescomplemented
58C22⋊C4×D61C2216yescomplemented
59C22⋊C4×D61C2216yescomplemented
60C42×D61C2213yescomplemented
61C2×#41×C61C2211yescharacteristic
62C22×Q8×C61C2211yescharacteristic, complemented
63#124×C61C2213yescomplemented
64C22⋊Q8×C61C2213yescomplemented
65#121×C61C2213yescomplemented
66C4×Q8×C61C2211yescharacteristic, complemented
67C4×D4×C61C2213yescomplemented
68C23×D61C2316yes—
69#41×C61—24no—
70C2×Q8×C61—24no—
71C2×Q8×C61C2313yes—
72C2×Q8×C61C2311yescharacteristic
73C2×D4×C61C2313yes—
74C2×D4×C61C2313yes—
75C22×C4×C61C2313yes—
76C22×C4×C61C2313yes—
77C2×C22⋊D61C2313yes—
78C2×C22⋊D61C2313yes—
79C2×C22⋊D61C2313yes—
80C2×C22⋊D61C2311yescharacteristic
81C2×C22⋊D61C2313yes—
82C2×C22⋊D61C2313yes—
83#11758226—24no—
84#11758226—212no—
85#11758226D418yescomplemented
86Q8×D61—24no—
87Q8×D61—212no—
88D4×D61—212no—
89D4×D61—212no—
90#11758222—212no—
91#11758222—212no—
92#11758222—212no—
93C2×D244—212no—
94C2×D244C2313yes—
95C2×D244C2313yes—
96C2×D244C2313yes—
97C2×D244C2313yes—
98C2×D244C2313yes—
99C2×C4×D61C2313yes—
100C2×C4×D61C2316yes—
101C2×C4×D61C2313yes—
102C2×C4×D61C2313yes—
103C2×C4×D61C2313yes—
104C2×C4×D61C2313yes—
105C2×Dic122C2313yes—
106C2×Dic122C2313yes—
107C2×Dic122C2311yescharacteristic
108C4⋊C4×C61C2313yes—
109C4⋊C4×C61C2313yes—
110C22⋊C4×C61C2311yescharacteristic
111C22⋊C4×C61C2313yes—
112C22⋊C4×C61C2316yes—
113C42×C61C2313yes—
114C22⋊Dic61C2313yes—
115C22⋊Dic61C2316yes—
116C22⋊Dic61C2311yescharacteristic
117#11758198C2313yes—
118#11758198C2313yes—
119#11758198C2316yes—
120#11758198C2316yes—
121#11758198C2316yes—
122#11758198C2311yescharacteristic
123#11758198C2311yescharacteristic
124C4⋊Dic61C2313yes—
125C4⋊Dic61C2313yes—
126#11758196C2313yes—
127#11758196C2313yes—
128C4×Dic61C2311yescharacteristic
129C4×Dic61C2313yes—
130C4×Dic61C2313yes—
131C23×C61C2413yes—
132C23×C61C2411yescharacteristic
133C22×D61—212no—
134C22×D61—46no—
135C22×D61—46no—
136C22×D61C2413yes—
137C22×D61C2411yescharacteristic
138C22×D61C2413yes—
139Q8×C61—26no—
140Q8×C61C2×D414yes—
141D4×C61—26no—
142D4×C61—43no—
143C2×C4×C61—26no—
144C2×C4×C61—26no—
145C2×C4×C61C2413yes—
146C2×C4×C61C2411yescharacteristic
147C2×C4×C61C2411yescharacteristic
148C2×C4×C61C2413yes—
149C2×C4×C61C2413yes—
150C22⋊D61—26no—
151C22⋊D61—26no—
152C22⋊D61—22no—
153C22⋊D61—26no—
154C22⋊D61—43no—
155C22⋊D61—43no—
156C2×Dic61C2411yescharacteristic
157C2×Dic61C2413yes—
158C2×Dic61C2411yescharacteristic
159C2×Dic61C2413yes—
160C2×Dic61C2411yescharacteristic
161D244—26no—
162D244—26no—
163D244—26no—
164D244—43no—
165D244C2×D4112yes—
166C4×D61—212no—
167C4×D61—26no—
168C4×D61—26no—
169C4×D61—43no—
170C4×D61—43no—
171C4×D61C2×D4112yes—
172Dic122—26no—
173Dic122—22no—
174Dic122—26no—
175C22×C61—21no—
176C22×C61—23no—
177C22×C61—21no—
178C22×C61—23no—
179C22×C61—21no—
180C22×C61—23no—
181C22×C61C2511yescharacteristic
182C2×D61—23no—
183C2×D61—23no—
184C2×D61—21no—
185C2×D61—23no—
186C2×D61—21no—
187C2×D61—23no—
188C2×D61—21no—
189C2×D61—23no—
190C2×D61—812no—
191C2×D61C22×D416yes—
192C4×C61—23no—
193C4×C61—21no—
194C4×C61—21no—
195C4×C61—23no—
196C4×C61C22×D416yes—
197Dic61—23no—
198Dic61—21no—
199Dic61—21no—
200Dic61—23no—
201Dic61C22×D412yes—
202#3500—611nomaximal, Sylow
203C2×C61—43no—
204C2×C61—41no—
205C2×C61C23×D411yescharacteristic
206C2×C61#58511yescharacteristic
207C2×C61#58511yescharacteristic
208D61—26no—
209D61—41no—
210D61—43no—
211C2×2−1+4—611no—
212C2×H(5,𝔽2)—611no—
213#548—611no—
214#548—611no—
215#548—611no—
216#548D6111yescharacteristic, complemented
217#546—613no—
218#546—613no—
219#546—613no—
220#546—613no—
221#536—613no—
222#535—613no—
223#532—613no—
224C2×#124—613no—
225C4×#41—611no—
226C61#350011yescharacteristic, complemented, Sylow
2272−1+4—1228no—
228H(5,𝔽2)—1228no—
229C2×#41—611no—
230C2×#41—611no—
231C2×#41—613no—
232C2×#41—613no—
233C2×#41—613no—
234C2×#41—613no—
235C2×#41C2×D6111yescharacteristic
236C22×Q8—613no—
237C22×Q8—611no—
238C22×Q8C2×D6111yescharacteristic, complemented
239C22×D4—613no—
240C22×D4—613no—
241C22×D4—613no—
242C4⋊Q8—613no—
243#127—613no—
244#124—613no—
245#124—613no—
246#124—613no—
247#124—616no—
248#124—611no—
249#124—613no—
250#124C2×D6113yescomplemented
251#123—616no—
252#123—616no—
253C22⋊Q8—613no—
254C22⋊Q8—613no—
255C22⋊Q8—613no—
256C22⋊Q8C2×D6113yescomplemented
257#121—613no—
258#121—613no—
259#121—613no—
260#121—613no—
261#121—613no—
262#121—613no—
263#121—613no—
264#121C2×D6113yescomplemented
265#120—616no—
266#120—616no—
267C4×Q8—611no—
268C4×Q8C2×D6111yescharacteristic, complemented
269C4×D4—613no—
270C4×D4—613no—
271C4×D4—613no—
272C4×D4—613no—
273C4×D4—613no—
274C4×D4C2×D6113yescomplemented
275#117—613no—
276C2×C22⋊C4—616no—
277C2×C22⋊C4—616no—
278C2×C42—613no—
279C24—616no—
280#41—24no—
281#41—618no—
282#41—12212no—
283#41—12212no—
284#41—12212no—
285#41—12212no—
286#41—1224no—
287C2×Q8—24no—
288C2×Q8—613no—
289C2×Q8—613no—
290C2×Q8—611no—
291C2×Q8—12212no—
292C2×Q8—1224no—
293C2×Q8C22×D6113yes—
294C2×Q8C22×D6111yescharacteristic
295C2×D4—613no—
296C2×D4—613no—
297C2×D4—613no—
298C2×D4—611no—
299C2×D4—613no—
300C2×D4—613no—
301C2×D4—613no—
302C2×D4—613no—
303C2×D4—613no—
304C2×D4—613no—
305C2×D4—613no—
306C2×D4—12212no—
307C2×D4—12212no—
308C2×D4—12212no—
309C2×D4C22×D6113yes—
310C2×D4C22×D6113yes—
311C22×C4—613no—
312C22×C4—616no—
313C22×C4—613no—
314C22×C4—613no—
315C22×C4—613no—
316C22×C4—613no—
317C22×C4C22×D6113yes—
318C22×C4C22×D6113yes—
319C4⋊C4—613no—
320C4⋊C4—613no—
321C4⋊C4—613no—
322C4⋊C4—613no—
323C4⋊C4C22×D6113yes—
324C4⋊C4C22×D6113yes—
325C22⋊C4—613no—
326C22⋊C4—616no—
327C22⋊C4—611no—
328C22⋊C4—613no—
329C22⋊C4—613no—
330C22⋊C4—616no—
331C22⋊C4—616no—
332C22⋊C4—616no—
333C22⋊C4—611no—
334C22⋊C4—611no—
335C22⋊C4C22×D6113yes—
336C22⋊C4C22×D6116yes—
337C22⋊C4C22×D6111yescharacteristic
338C42—611no—
339C42—613no—
340C42—613no—
341C42C22×D6113yes—
342C23—613no—
343C23—613no—
344C23—611no—
345C23—12212no—
346C23—2446no—
347C23—2446no—
348C23C23×D6113yes—
349C23C23×D6111yescharacteristic
350Q8—26no—
351Q8—1226no—
352Q8—1222no—
353Q8—1226no—
354Q8D4×D6114yes—
355D4—26no—
356D4—43no—
357D4—6112no—
358D4—1226no—
359D4—1226no—
360D4—1226no—
361D4—1222no—
362D4—1226no—
363D4—1226no—
364D4—1226no—
365D4—2443no—
366D4—2443no—
367D4—2443no—
368C2×C4—26no—
369C2×C4—26no—
370C2×C4—611no—
371C2×C4—6112no—
372C2×C4—611no—
373C2×C4—613no—
374C2×C4—613no—
375C2×C4—611no—
376C2×C4—12212no—
377C2×C4—1226no—
378C2×C4—1226no—
379C2×C4—2443no—
380C2×C4—2443no—
381C2×C4C23×D6111yescharacteristic
382C2×C4C23×D6113yes—
383C2×C4C23×D6113yes—
384C2×C4C23×D6111yescharacteristic
385C2×C4C23×D6113yes—
386C22—21no—
387C22—23no—
388C22—21no—
389C22—23no—
390C22—21no—
391C22—23no—
392C22—616no—
393C22—1223no—
394C22—1223no—
395C22—1221no—
396C22—1223no—
397C22—1221no—
398C22—1223no—
399C22—1221no—
400C22—1223no—
401C22—48812no—
402C22C24×D6111yescharacteristic
403C4—21no—
404C4—23no—
405C4—23no—
406C4—21no—
407C4—612no—
408C4—1221no—
409C4—1223no—
410C4—1221no—
411C4—1223no—
412C4C2×D4×D6116yes—
413C2—43no—
414C2—41no—
415C2—1226no—
416C2—2443no—
417C2—2441no—
418C2C22×D4×D6111yescharacteristic
419C2#1684059811yescharacteristic
420C2#1684059911yescharacteristic
subgroupG/H
center, FrattiniC22C24×D61
commutator, socleC22×C61C25
FittingC61×#548C2
hypercenter#548D61
hypocenterC61#3500
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#14519825C2semidirect
2. C2×#14519823C2semidirect
3. #16840424C2semidirect
4. #16840423C2semidirect
5. #16840419C2semidirect
6. #16840409C2semidirect
7. #16840408C2semidirect
8. #16840405C2semidirect
9. #16840403C2semidirect
10. #16840335C2semidirect
11. #16840328C2semidirect
12. #16840309C2semidirect
13. #124×D61C2semidirect
14. C4×#11758226C2semidirect
15. C61×#548C2semidirect
20. C2×#11758226C22semidirect
22. C2×#11758222C22semidirect
23. C2×#11758222C22semidirect
24. C2×Q8×D61C22semidirect
25. C2×Q8×D61C22semidirect
29. #14519776C22semidirect
30. #14519773C22semidirect
31. #14519766C22semidirect
32. #14519765C22semidirect
33. #14519764C22semidirect
34. #14519763C22semidirect
35. #14519763C22semidirect
36. #14519763C22semidirect
37. #14519762C22semidirect
38. #14519759C22semidirect
39. #14519757C22semidirect
40. #14519756C22semidirect
41. #14519753C22semidirect
42. #14519752C22semidirect
43. #14519752C22semidirect
44. #14519751C22semidirect
45. #14519750C22semidirect
46. #14519750C22semidirect
47. #14519748C22semidirect
48. #14519748C22semidirect
49. #14519747C22semidirect
50. #14519745C22semidirect
51. Q8×Dic61C22semidirect
52. C4×D244C22semidirect
53. C4×D244C22semidirect
54. #14519739C22semidirect
55. C4×C22⋊D61C22semidirect
56. C4×C22⋊D61C22semidirect
57. #14519735C22semidirect
58. C22⋊C4×D61C22semidirect
59. C22⋊C4×D61C22semidirect
60. C42×D61C22semidirect
62. C22×Q8×C61C22semidirect
63. #124×C61C22semidirect
64. C22⋊Q8×C61C22semidirect
65. #121×C61C22semidirect
66. C4×Q8×C61C22semidirect
67. C4×D4×C61C22semidirect
85. #11758226D4semidirect
216. #548D61semidirect
226. C61#3500semidirect
238. C22×Q8C2×D61semidirect
250. #124C2×D61semidirect
256. C22⋊Q8C2×D61semidirect
264. #121C2×D61semidirect
268. C4×Q8C2×D61semidirect
274. C4×D4C2×D61semidirect