Finite Group Databasebeta

← #21459487

Subgroups — #21459487

Order 7808.

1658 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519823C211yesmaximal, characteristic, complemented
2C2×#41×D61C211yesmaximal, characteristic, complemented
3#16840431C211yesmaximal, characteristic, complemented
4#16840424C211yesmaximal, characteristic, complemented
5#16840419C211yesmaximal, characteristic, complemented
6#16840409C213yesmaximal, complemented
7#16840408C213yesmaximal, complemented
8#16840397C213yesmaximal, complemented
9#16840396C213yesmaximal, complemented
10#16840341C213yesmaximal, complemented
11#16840325C213yesmaximal, complemented
12#16840271C213yesmaximal, complemented
13#121×D61C213yesmaximal, complemented
14#16840244C211yesmaximal, characteristic, complemented
15C61×#550C211yesmaximal, characteristic, complemented
16#14519823—28no—
17C2×#11758226C2211yescharacteristic
18C2×#11758226C2211yescharacteristic, complemented
19C2×#11758222C2213yescomplemented
20C2×#11758222C2213yescomplemented
21C2×#11758224C2213yescomplemented
22#41×D61—28no—
23C2×Q8×D61C2211yescharacteristic, complemented
24C22×D244C2213yescomplemented
25C2×D4×D61C2213yescomplemented
26C2×D4×D61C2213yescomplemented
27C2×D4×D61C2213yescomplemented
28C2×D4×D61C2216yescomplemented
29C22×C4×D61C2213yescomplemented
30#14519773C2213yescomplemented
31#14519765C2213yescomplemented
32#14519764C2213yescomplemented
33#14519762C2213yescomplemented
34#14519759C2213yescomplemented
35#14519757C2213yescomplemented
36#14519756C2213yescomplemented
37#14519755C2211yescharacteristic, complemented
38#14519754C2213yescomplemented
39#14519752C2213yescomplemented
40#14519751C2213yescomplemented
41#14519750C2213yescomplemented
42#14519750C2216yescomplemented
43#14519749C2216yescomplemented
44#14519749C2213yescomplemented
45#14519748C2213yescomplemented
46#14519748C2216yescomplemented
47#14519748C2213yescomplemented
48#14519747C2213yescomplemented
49#14519745C2213yescomplemented
50#14519745C2216yescomplemented
51#14519745C2216yescomplemented
52Q8×Dic61C2211yescharacteristic, complemented
53C4×D244C2213yescomplemented
54C4×D244C2213yescomplemented
55#14519739C2213yescomplemented
56C4×C22⋊D61C2213yescomplemented
57C4×C22⋊D61C2213yescomplemented
58#14519734C2213yescomplemented
59C4⋊C4×D61C2213yescomplemented
60C22⋊C4×D61C2216yescomplemented
61C2×#41×C61C2211yescharacteristic, complemented
62C2×#41×C61C2211yescharacteristic, complemented
63#127×C61C2213yescomplemented
64#121×C61C2213yescomplemented
65#121×C61C2213yescomplemented
66C4×Q8×C61C2211yescharacteristic, complemented
67C4×D4×C61C2213yescomplemented
68C23×D61C2313yes—
69C23×D61C2316yes—
70#41×C61—24no—
71#41×C61—24no—
72C2×Q8×C61C2311yescharacteristic
73C2×D4×C61C2313yes—
74C2×D4×C61C2313yes—
75C2×D4×C61C2316yes—
76C2×D4×C61C2313yes—
77C22×C4×C61C2313yes—
78C22×C4×C61C2313yes—
79C2×C22⋊D61C2313yes—
80C2×C22⋊D61C2313yes—
81C2×C22⋊D61C2313yes—
82C2×C22⋊D61C2316yes—
83C2×C22⋊D61C2316yes—
84C2×C22⋊D61C2313yes—
85C22×Dic61C2313yes—
86#11758226—24no—
87#11758226D418yescomplemented
88Q8×D61—24no—
89#11758224—212no—
90D4×D61—212no—
91D4×D61—212no—
92D4×D61—212no—
93D4×D61—412no—
94#11758222—212no—
95#11758222—212no—
96C2×D244—212no—
97C2×D244C2313yes—
98C2×D244C2313yes—
99C2×D244C2313yes—
100C2×D244C2313yes—
101C2×C4×D61—212no—
102C2×C4×D61C2311yescharacteristic
103C2×C4×D61C2313yes—
104C2×C4×D61C2313yes—
105C2×C4×D61C2313yes—
106C2×C4×D61C2316yes—
107C2×C4×D61C2313yes—
108C2×Dic122C2313yes—
109C2×Dic122C2311yescharacteristic
110C4⋊C4×C61C2311yescharacteristic
111C4⋊C4×C61C2313yes—
112C22⋊C4×C61C2313yes—
113C22⋊C4×C61C2313yes—
114C42×C61C2313yes—
115C22⋊Dic61C2316yes—
116C22⋊Dic61C2313yes—
117C22⋊Dic61C2313yes—
118#11758198C2313yes—
119#11758198C2316yes—
120#11758198C2313yes—
121#11758198C2313yes—
122#11758198C2311yescharacteristic
123#11758198C2311yescharacteristic
124#11758198C2313yes—
125C4⋊Dic61C2313yes—
126C4⋊Dic61C2313yes—
127#11758196C2313yes—
128#11758196C2311yescharacteristic
129#11758196C2311yescharacteristic
130#11758196C2313yes—
131C4×Dic61C2313yes—
132C23×C61C2413yes—
133C23×C61C2413yes—
134C22×D61—26no—
135C22×D61—26no—
136C22×D61—212no—
137C22×D61—43no—
138C22×D61—46no—
139C22×D61—46no—
140C22×D61C2413yes—
141C22×D61C2413yes—
142C22×D61C2411yescharacteristic
143Q8×C61C2×D414yescomplemented
144D4×C61—26no—
145D4×C61—26no—
146D4×C61—46no—
147D4×C61—43no—
148C2×C4×C61—26no—
149C2×C4×C61—26no—
150C2×C4×C61C2411yescharacteristic
151C2×C4×C61C2413yes—
152C2×C4×C61C2411yescharacteristic
153C2×C4×C61C2411yescharacteristic
154C2×C4×C61C2413yes—
155C22⋊D61—26no—
156C22⋊D61—212no—
157C22⋊D61—26no—
158C22⋊D61—26no—
159C22⋊D61—46no—
160C22⋊D61—43no—
161C2×Dic61—26no—
162C2×Dic61C2411yescharacteristic
163C2×Dic61C2413yes—
164C2×Dic61C2411yescharacteristic
165C2×Dic61C2413yes—
166C2×Dic61C2411yescharacteristic
167D244—26no—
168D244—26no—
169D244—26no—
170D244C2×D4112yescomplemented
171C4×D61—26no—
172C4×D61—26no—
173C4×D61—26no—
174C4×D61—22no—
175C4×D61—46no—
176C4×D61C2×D4112yescomplemented
177Dic122—26no—
178Dic122—22no—
179C22×C61—23no—
180C22×C61—23no—
181C22×C61—23no—
182C22×C61—23no—
183C22×C61—23no—
184C22×C61—23no—
185C22×C61C2511yescharacteristic
186C2×D61—21no—
187C2×D61—23no—
188C2×D61—21no—
189C2×D61—23no—
190C2×D61—23no—
191C2×D61—23no—
192C2×D61—23no—
193C2×D61—412no—
194C2×D61—812no—
195C2×D61C22×D416yes—
196C2×D61H(5,𝔽2)12yescomplemented
197C4×C61—21no—
198C4×C61—21no—
199C4×C61—23no—
200C4×C61—21no—
201C4×C61C22×D416yes—
202Dic61—23no—
203Dic61—21no—
204Dic61—23no—
205Dic61—21no—
206Dic61C22×D412yes—
207#3488—611nomaximal, Sylow
208C2×C61—43no—
209C2×C61—43no—
210C2×C61C23×D411yescharacteristic
211C2×C61C2×H(5,𝔽2)11yescharacteristic
212C2×C61#58511yescharacteristic
213D61—22no—
214D61—26no—
215D61—43no—
216C2×H(5,𝔽2)—611no—
217C22×#41—611no—
218#550—611no—
219#550D6111yescharacteristic, complemented
220#548—611no—
221#548—611no—
222#546—613no—
223#546—613no—
224D42—613no—
225D42—613no—
226#537—613no—
227#535—613no—
228#525—613no—
229C2×#121—613no—
230#520—611no—
231C61#348811yescharacteristic, complemented, Sylow
232H(5,𝔽2)—1228no—
233C2×#41—611no—
234C2×#41—611no—
235C2×#41—613no—
236C2×#41—613no—
237C2×#41—613no—
238C2×#41—1228no—
239C2×#41C2×D6111yescharacteristic, complemented
240C2×#41C2×D6111yescharacteristic, complemented
241C22×Q8—611no—
242C22×D4—613no—
243C22×D4—613no—
244C22×D4—613no—
245C22×D4—616no—
246C22×D4—613no—
247C23×C4—613no—
248#127—613no—
249#127C2×D6113yescomplemented
250#124—613no—
251#124—613no—
252#123—613no—
253#123—613no—
254C22⋊Q8—613no—
255C22⋊Q8—611no—
256C22⋊Q8—613no—
257C22⋊Q8—613no—
258#121—616no—
259#121—613no—
260#121—613no—
261#121—616no—
262#121—613no—
263#121—613no—
264#121—613no—
265#121—613no—
266#121—616no—
267#121C2×D6113yescomplemented
268#121C2×D6113yescomplemented
269#120—613no—
270#120—616no—
271#120—616no—
272#120—613no—
273C4×Q8—611no—
274C4×Q8C2×D6111yescharacteristic, complemented
275C4×D4—613no—
276C4×D4—613no—
277C4×D4—613no—
278C4×D4—613no—
279C4×D4—613no—
280C4×D4C2×D6113yescomplemented
281#117—613no—
282C2×C4⋊C4—613no—
283C2×C22⋊C4—616no—
284C24—613no—
285C24—616no—
286#41—24no—
287#41—24no—
288#41—618no—
289#41—12212no—
290#41—12212no—
291#41—12212no—
292#41—1224no—
293C2×Q8—611no—
294C2×Q8—613no—
295C2×Q8—1224no—
296C2×Q8C22×D6111yescharacteristic
297C2×D4—613no—
298C2×D4—616no—
299C2×D4—613no—
300C2×D4—613no—
301C2×D4—613no—
302C2×D4—616no—
303C2×D4—613no—
304C2×D4—613no—
305C2×D4—613no—
306C2×D4—613no—
307C2×D4—12212no—
308C2×D4—12212no—
309C2×D4—12212no—
310C2×D4—12212no—
311C2×D4—24412no—
312C2×D4C22×D6113yes—
313C2×D4C22×D6113yes—
314C2×D4C22×D6113yes—
315C2×D4C22×D6116yes—
316C22×C4—613no—
317C22×C4—613no—
318C22×C4—613no—
319C22×C4—613no—
320C22×C4—613no—
321C22×C4—611no—
322C22×C4—616no—
323C22×C4—12212no—
324C22×C4C22×D6113yes—
325C22×C4C22×D6113yes—
326C4⋊C4—613no—
327C4⋊C4—613no—
328C4⋊C4—611no—
329C4⋊C4—611no—
330C4⋊C4—613no—
331C4⋊C4—613no—
332C4⋊C4C22×D6113yes—
333C4⋊C4C22×D6111yescharacteristic
334C22⋊C4—616no—
335C22⋊C4—613no—
336C22⋊C4—613no—
337C22⋊C4—613no—
338C22⋊C4—616no—
339C22⋊C4—613no—
340C22⋊C4—613no—
341C22⋊C4—611no—
342C22⋊C4—611no—
343C22⋊C4—613no—
344C22⋊C4C22×D6113yes—
345C22⋊C4C22×D6113yes—
346C42—613no—
347C42C22×D6113yes—
348C23—613no—
349C23—611no—
350C23—613no—
351C23—12212no—
352C23—1226no—
353C23—1226no—
354C23—2446no—
355C23—2446no—
356C23—2443no—
357C23C23×D6113yes—
358C23C23×D6113yes—
359Q8—1222no—
360Q8—1226no—
361Q8D4×D6114yescomplemented
362D4—26no—
363D4—26no—
364D4—46no—
365D4—43no—
366D4—6112no—
367D4—1226no—
368D4—1226no—
369D4—1226no—
370D4—1226no—
371D4—12212no—
372D4—1226no—
373D4—1226no—
374D4—2443no—
375D4—2446no—
376C2×C4—26no—
377C2×C4—26no—
378C2×C4—611no—
379C2×C4—6112no—
380C2×C4—611no—
381C2×C4—613no—
382C2×C4—613no—
383C2×C4—611no—
384C2×C4—1222no—
385C2×C4—1226no—
386C2×C4—1226no—
387C2×C4—1226no—
388C2×C4—1226no—
389C2×C4—2446no—
390C2×C4C23×D6111yescharacteristic
391C2×C4C23×D6113yes—
392C2×C4C23×D6111yescharacteristic
393C2×C4C23×D6111yescharacteristic
394C2×C4C23×D6113yes—
395C22—23no—
396C22—23no—
397C22—23no—
398C22—23no—
399C22—23no—
400C22—23no—
401C22—616no—
402C22—612no—
403C22—1221no—
404C22—1223no—
405C22—1223no—
406C22—1221no—
407C22—1223no—
408C22—1223no—
409C22—1223no—
410C22—48812no—
411C22—24412no—
412C22C24×D6111yescharacteristic
413C4—21no—
414C4—21no—
415C4—23no—
416C4—21no—
417C4—612no—
418C4—1221no—
419C4—1223no—
420C4—1223no—
421C4—1221no—
422C4C2×D4×D6116yes—
423C2—43no—
424C2—43no—
425C2—1226no—
426C2—1222no—
427C2—2443no—
428C2C22×D4×D6111yescharacteristic
429C2H(5,𝔽2)×D6111yescharacteristic
430C2#1684059811yescharacteristic
subgroupG/H
center, FrattiniC22C24×D61
commutator, socleC22×C61C25
FittingC61×#550C2
hypercenter#550D61
hypocenterC61#3488
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C2×#14519823C2semidirect
2. C2×#41×D61C2semidirect
3. #16840431C2semidirect
4. #16840424C2semidirect
5. #16840419C2semidirect
6. #16840409C2semidirect
7. #16840408C2semidirect
8. #16840397C2semidirect
9. #16840396C2semidirect
10. #16840341C2semidirect
11. #16840325C2semidirect
12. #16840271C2semidirect
13. #121×D61C2semidirect
14. #16840244C2semidirect
15. C61×#550C2semidirect
18. C2×#11758226C22semidirect
19. C2×#11758222C22semidirect
20. C2×#11758222C22semidirect
21. C2×#11758224C22semidirect
23. C2×Q8×D61C22semidirect
24. C22×D244C22semidirect
25. C2×D4×D61C22semidirect
26. C2×D4×D61C22semidirect
27. C2×D4×D61C22semidirect
28. C2×D4×D61C22semidirect
29. C22×C4×D61C22semidirect
30. #14519773C22semidirect
31. #14519765C22semidirect
32. #14519764C22semidirect
33. #14519762C22semidirect
34. #14519759C22semidirect
35. #14519757C22semidirect
36. #14519756C22semidirect
37. #14519755C22semidirect
38. #14519754C22semidirect
39. #14519752C22semidirect
40. #14519751C22semidirect
41. #14519750C22semidirect
42. #14519750C22semidirect
43. #14519749C22semidirect
44. #14519749C22semidirect
45. #14519748C22semidirect
46. #14519748C22semidirect
47. #14519748C22semidirect
48. #14519747C22semidirect
49. #14519745C22semidirect
50. #14519745C22semidirect
51. #14519745C22semidirect
52. Q8×Dic61C22semidirect
53. C4×D244C22semidirect
54. C4×D244C22semidirect
55. #14519739C22semidirect
56. C4×C22⋊D61C22semidirect
57. C4×C22⋊D61C22semidirect
58. #14519734C22semidirect
59. C4⋊C4×D61C22semidirect
60. C22⋊C4×D61C22semidirect
61. C2×#41×C61C22semidirect
62. C2×#41×C61C22semidirect
63. #127×C61C22semidirect
64. #121×C61C22semidirect
65. #121×C61C22semidirect
66. C4×Q8×C61C22semidirect
67. C4×D4×C61C22semidirect
87. #11758226D4semidirect
143. Q8×C61C2×D4semidirect
170. D244C2×D4semidirect
176. C4×D61C2×D4semidirect
196. C2×D61H(5,𝔽2)semidirect
219. #550D61semidirect
231. C61#3488semidirect
239. C2×#41C2×D61semidirect
240. C2×#41C2×D61semidirect
249. #127C2×D61semidirect
267. #121C2×D61semidirect
268. #121C2×D61semidirect
274. C4×Q8C2×D61semidirect
280. C4×D4C2×D61semidirect
361. Q8D4×D61semidirect