Finite Group Databasebeta

← C2×#104×D283 #49129796

Subgroups — C2×#104×D283 #49129796

Order 36224.

856 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D283C211yesmaximal, characteristic
2C2×M16×D283C211yesmaximal, characteristic, complemented
3C2×C42×D283C211yesmaximal, characteristic, complemented
4C2×#22583538C211yesmaximal, characteristic, complemented
5C2×#22583537C211yesmaximal, characteristic, complemented
6C2×#22583536C211yesmaximal, characteristic, complemented
7#104×D283C218yesmaximal, direct product factor
8C2×#104×C283C211yesmaximal, characteristic, complemented
9C2×#17985393C411yescharacteristic, complemented
10C2×#17985392—21no—
11C2×#17985392C2211yescharacteristic
12C2×#17985391—21no—
13C2×#17985391C411yescharacteristic, complemented
14#41×D283—22no—
15#41×D283—22no—
16#41×D283C414yescomplemented
17#41×D283C2214yes—
18C2×Q8×D283C411yescharacteristic, complemented
19C2×D4×D283—21no—
20C2×D4×D283C411yescharacteristic, complemented
21C22×C4×D283—21no—
22C22×C4×D283—21no—
23C22×C4×D283C2211yescharacteristic
24C2×#17985376C2211yescharacteristic, complemented
25C2×#17985375—21no—
26M16×D283—22no—
27M16×D283C2214yescomplemented
28C2×C8×D283—21no—
29C2×C4×Dic283—21no—
30C2×C4×Dic283C2211yescharacteristic, complemented
31C42×D283—22no—
32C42×D283C2214yescomplemented
33#22583538C2214yescomplemented
34#22583537C2214yescomplemented
35#22583536C2214yescomplemented
36C2×#41×C283C2211yescharacteristic
37C2×M16×C283C2211yescharacteristic, complemented
38C2×C42×C283C2211yescharacteristic, complemented
39#104×C283C2214yescomplemented
40C23×D283—21no—
41C23×D283D411yescharacteristic
42#17985393—22no—
43#17985393C2×C414yescomplemented
44#17985392—24no—
45#17985392—24no—
46#17985392—21no—
47#17985392—21no—
48#17985392C2×C412yescomplemented
49#17985392C2312yes—
50#17985391—24no—
51#17985391—24no—
52#17985391—22no—
53#17985391C2×C414yescomplemented
54C2×Dic566—21no—
55C2×Dic566C2×C411yescharacteristic, complemented
56Q8×D283—22no—
57Q8×D283C2×C414yescomplemented
58C2×D1132—21no—
59C2×D1132C2×C411yescharacteristic, complemented
60C2×C22⋊D283—21no—
61C2×C22⋊D283—21no—
62C2×C22⋊D283—21no—
63D4×D283—24no—
64D4×D283—24no—
65D4×D283—22no—
66D4×D283C2×C414yescomplemented
67C22×Dic283—21no—
68C22×Dic283—21no—
69C22×Dic283D411yescharacteristic
70C2×C4×D283—28no—
71C2×C4×D283—21no—
72C2×C4×D283—24no—
73C2×C4×D283—21no—
74C2×C4×D283—24no—
75C2×C4×D283—24no—
76C2×C4×D283—21no—
77C2×C4×D283C2×C411yescharacteristic
78C2×C4×D283C2×C412yes—
79C2×C4×D283C2×C411yescharacteristic
80C2×C4×D283D412yes—
81C2×C4×D283D411yescharacteristic
82C2×C4×D283D412yes—
83C2×C4×D283D411yescharacteristic
84C2×C4×D283C2312yes—
85#17985376—21no—
86#17985376C2312yescomplemented
87#17985375—24no—
88C2×C283⋊C8—21no—
89C8×D283—24no—
90C4×Dic283—24no—
91C4×Dic283—21no—
92C4×Dic283C2312yescomplemented
93#41×C283—21no—
94#41×C283—21no—
95#41×C283C2×C412yescomplemented
96#41×C283C2312yes—
97C2×Q8×C283C2×C411yescharacteristic, complemented
98C2×D4×C283—21no—
99C2×D4×C283C2×C411yescharacteristic, complemented
100C22×C4×C283—21no—
101C22×C4×C283—21no—
102C22×C4×C283C2311yescharacteristic
103M16×C283—21no—
104M16×C283C2312yescomplemented
105C2×C8×C283—21no—
106C42×C283—21no—
107C42×C283C2312yescomplemented
108C22×D283—24no—
109C22×D283—21no—
110C22×D283—24no—
111C22×D283—44no—
112C22×D283C22⋊C412yes—
113C22×D283C22⋊C411yescharacteristic
114C22×D283C22⋊C411yescharacteristic
115C22×D283C2×D412yes—
116Dic566—21no—
117Dic566—24no—
118Dic566C22×C412yescomplemented
119D1132—24no—
120D1132—21no—
121D1132C22×C412yescomplemented
122C22⋊D283—22no—
123C22⋊D283—22no—
124C22⋊D283—24no—
125C22⋊D283—24no—
126C2×Dic283—24no—
127C2×Dic283—21no—
128C2×Dic283—22no—
129C2×Dic283—24no—
130C2×Dic283C22⋊C411yescharacteristic
131C2×Dic283C22⋊C411yescharacteristic
132C2×Dic283C22⋊C412yes—
133C2×Dic283C2×D412yes—
134C4×D283—216no—
135C4×D283—24no—
136C4×D283—22no—
137C4×D283—22no—
138C4×D283—24no—
139C4×D283C22⋊C412yes—
140C4×D283C22⋊C412yes—
141C4×D283C22⋊C412yes—
142C4×D283C22⋊C412yes—
143C4×D283C22×C412yes—
144C4×D283C22×C412yes—
145C4×D283C2×D412yes—
146C4×D283C2×D412yes—
147C283⋊C8—22no—
148C23×C283—21no—
149C23×C283C2×D411yescharacteristic
150Q8×C283—21no—
151Q8×C283C22×C412yescomplemented
152D4×C283—22no—
153D4×C283—22no—
154D4×C283—21no—
155D4×C283C22×C412yescomplemented
156C2×C4×C283—24no—
157C2×C4×C283—21no—
158C2×C4×C283—22no—
159C2×C4×C283—22no—
160C2×C4×C283—22no—
161C2×C4×C283C22×C411yescharacteristic
162C2×C4×C283C22×C411yescharacteristic
163C2×C4×C283C2×D411yescharacteristic
164C2×C4×C283C2×D411yescharacteristic
165C2×C4×C283C2×D411yescharacteristic
166C2×C4×C283C2411yescharacteristic
167C8×C283—22no—
168C22×C283—22no—
169C22×C283—22no—
170C22×C283—42no—
171C22×C283C2×C22⋊C411yescharacteristic
172C22×C283C2×C22⋊C411yescharacteristic
173C22×C283C22×D411yescharacteristic
174C2×D283—22no—
175C2×D283—24no—
176C2×D283—24no—
177C2×D283—22no—
178C2×D283—42no—
179C2×D283—48no—
180C2×D283#10414yesdirect product factor
181C2×D283C2×C22⋊C412yes—
182C2×D283C2×C22⋊C412yes—
183C4×C283—24no—
184C4×C283—22no—
185C4×C283C2×C22⋊C411yescharacteristic
186C4×C283C2×C22⋊C411yescharacteristic
187C4×C283C23×C411yescharacteristic
188C4×C283C22×D411yescharacteristic
189Dic283—24no—
190Dic283—22no—
191Dic283C2×C22⋊C412yes—
192Dic283C2×C22⋊C412yes—
193C2×C283—21no—
194C2×C283—21no—
195C2×C283—42no—
196C2×C283C2×#10412yescomplemented
197C2×C283C22×C22⋊C411yescharacteristic
198D283—22no—
199D283—42no—
200D283C2×#10414yesdirect product factor
201C283C22×#10411yescharacteristic, complemented, Sylow
202C22×#104—2831nomaximal, Sylow
203C22×#41—2831no—
204C22×M16—2831no—
205C22×C42—2831no—
206C2×#104—2831no—
207C2×#104—2831no—
208C2×#104—2831no—
209C2×#104—2838no—
210C2×#104D28311yescharacteristic, direct product factor
211C2×#41—2834no—
212C2×#41—2834no—
213C2×#41—2831no—
214C2×#41—2831no—
215C2×#41—2831no—
216C2×#41—5661no—
217C2×#41—5661no—
218C2×#41—5662no—
219C2×#41—5662no—
220C2×#41C2×D28311yescharacteristic
221C22×Q8—2831no—
222C22×D4—2831no—
223C22×D4—5661no—
224C23×C4—2831no—
225C23×C4—5661no—
226C23×C4—5661no—
227C2×M16—2831no—
228C2×M16—2834no—
229C2×M16—5661no—
230C2×M16—5662no—
231C2×M16C2×D28311yescharacteristic, complemented
232C22×C8—5661no—
233C2×C42—2831no—
234C2×C42—2834no—
235C2×C42—5662no—
236C2×C42—5661no—
237C2×C42C2×D28311yescharacteristic, complemented
238#104—2834no—
239#104—2834no—
240#104—2834no—
241#104C2×D28314yesdirect product factor
242C24—2831no—
243C24—5661no—
244#41—21no—
245#41—21no—
246#41—2834no—
247#41—2834no—
248#41—2832no—
249#41—2832no—
250#41—5664no—
251#41—5664no—
252#41—5664no—
253#41—5664no—
254#41—5662no—
255#41—5662no—
256#41—5661no—
257#41—5661no—
258#41C4×D28312yescomplemented
259#41C22×D28312yes—
260C2×Q8—2834no—
261C2×Q8—2831no—
262C2×Q8—5661no—
263C2×Q8—5662no—
264C2×Q8C4×D28311yescharacteristic, complemented
265C2×D4—21no—
266C2×D4—2834no—
267C2×D4—2831no—
268C2×D4—5661no—
269C2×D4—5662no—
270C2×D4—5661no—
271C2×D4—5664no—
272C2×D4—5664no—
273C2×D4—5661no—
274C2×D4—5661no—
275C2×D4C4×D28311yescharacteristic, complemented
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—2831no—
279C22×C4—2831no—
280C22×C4—2831no—
281C22×C4—2832no—
282C22×C4—2832no—
283C22×C4—2832no—
284C22×C4—2831no—
285C22×C4—2831no—
286C22×C4—2832no—
287C22×C4—5661no—
288C22×C4—5664no—
289C22×C4—5664no—
290C22×C4—5664no—
291C22×C4—5661no—
292C22×C4—5668no—
293C22×C4—5661no—
294C22×C4—5661no—
295C22×C4—5661no—
296C22×C4C22×D28311yescharacteristic
297M16—21no—
298M16—2832no—
299M16—5664no—
300M16—5661no—
301M16C22×D28312yescomplemented
302C2×C8—21no—
303C2×C8—5664no—
304C2×C8—5661no—
305C42—21no—
306C42—2832no—
307C42—5664no—
308C42—5661no—
309C42C22×D28312yescomplemented
310C23—21no—
311C23—2831no—
312C23—2832no—
313C23—2831no—
314C23—2832no—
315C23—5664no—
316C23—5664no—
317C23—5661no—
318C23—11324no—
319C23D4×D28311yescharacteristic
320Q8—21no—
321Q8—2832no—
322Q8—5664no—
323Q8—5661no—
324Q8C2×C4×D28312yescomplemented
325D4—22no—
326D4—22no—
327D4—21no—
328D4—2832no—
329D4—5664no—
330D4—5664no—
331D4—5664no—
332D4—5662no—
333D4—5662no—
334D4—5661no—
335D4C2×C4×D28312yescomplemented
336C2×C4—24no—
337C2×C4—21no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—2831no—
342C2×C4—2831no—
343C2×C4—2832no—
344C2×C4—2832no—
345C2×C4—2832no—
346C2×C4—2832no—
347C2×C4—2832no—
348C2×C4—2832no—
349C2×C4—2832no—
350C2×C4—2832no—
351C2×C4—2832no—
352C2×C4—2832no—
353C2×C4—5664no—
354C2×C4—5664no—
355C2×C4—56616no—
356C2×C4—5664no—
357C2×C4—5664no—
358C2×C4—5661no—
359C2×C4—5662no—
360C2×C4—5662no—
361C2×C4—5662no—
362C2×C4C2×C4×D28311yescharacteristic
363C2×C4C2×C4×D28311yescharacteristic
364C2×C4D4×D28311yescharacteristic
365C2×C4D4×D28311yescharacteristic
366C2×C4D4×D28311yescharacteristic
367C2×C4C23×D28311yescharacteristic
368C8—22no—
369C8—5662no—
370C22—22no—
371C22—22no—
372C22—42no—
373C22—2834no—
374C22—2832no—
375C22—2832no—
376C22—5664no—
377C22—5664no—
378C22—5662no—
379C22—5662no—
380C22—11328no—
381C22—11322no—
382C22C22⋊C4×D28311yescharacteristic
383C22C22⋊C4×D28311yescharacteristic
384C22C2×D4×D28311yescharacteristic
385C4—24no—
386C4—22no—
387C4—2832no—
388C4—2832no—
389C4—5664no—
390C4—5662no—
391C4C22⋊C4×D28311yescharacteristic
392C4C22⋊C4×D28311yescharacteristic
393C4C22×C4×D28311yescharacteristic
394C4C2×D4×D28311yescharacteristic
395C2—21no—
396C2—21no—
397C2—42no—
398C2—2834no—
399C2—5662no—
400C2—11322no—
401C2#104×D28312yesdirect product factor
402C2C2×C22⋊C4×D28311yescharacteristic
subgroupG/H
centerC2×C4D4×D283
commutatorC4×C283C23×C4
FrattiniC2×C4C23×D283
FittingC2×#104×C283C2
socleC22×C283C2×C22⋊C4
prime radicalC2×#41×D283C2
cosocleC2×C4×C283C24
hypercenterC2×#104D283
hypocenterC283C22×#104
LCSG ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×M16×D283C2semidirect
3. C2×C42×D283C2semidirect
4. C2×#22583538C2semidirect
5. C2×#22583537C2semidirect
6. C2×#22583536C2semidirect
7. #104×D283C2direct (N × H)
8. C2×#104×C283C2semidirect
9. C2×#17985393C4semidirect
13. C2×#17985391C4semidirect
16. #41×D283C4semidirect
18. C2×Q8×D283C4semidirect
20. C2×D4×D283C4semidirect
24. C2×#17985376C22semidirect
27. M16×D283C22semidirect
30. C2×C4×Dic283C22semidirect
32. C42×D283C22semidirect
33. #22583538C22semidirect
34. #22583537C22semidirect
35. #22583536C22semidirect
37. C2×M16×C283C22semidirect
38. C2×C42×C283C22semidirect
39. #104×C283C22semidirect
43. #17985393C2×C4semidirect
48. #17985392C2×C4semidirect
53. #17985391C2×C4semidirect
55. C2×Dic566C2×C4semidirect
57. Q8×D283C2×C4semidirect
59. C2×D1132C2×C4semidirect
66. D4×D283C2×C4semidirect
86. #17985376C23semidirect
92. C4×Dic283C23semidirect
95. #41×C283C2×C4semidirect
97. C2×Q8×C283C2×C4semidirect
99. C2×D4×C283C2×C4semidirect
104. M16×C283C23semidirect
107. C42×C283C23semidirect
118. Dic566C22×C4semidirect
121. D1132C22×C4semidirect
151. Q8×C283C22×C4semidirect
155. D4×C283C22×C4semidirect
180. C2×D283#104direct (N × H)
196. C2×C283C2×#104semidirect
200. D283C2×#104direct (N × H)
201. C283C22×#104semidirect
210. C2×#104D283direct (N × H)
231. C2×M16C2×D283semidirect
237. C2×C42C2×D283semidirect
241. #104C2×D283direct (N × H)
258. #41C4×D283semidirect
264. C2×Q8C4×D283semidirect
275. C2×D4C4×D283semidirect
301. M16C22×D283semidirect
309. C42C22×D283semidirect
324. Q8C2×C4×D283semidirect
335. D4C2×C4×D283semidirect
401. C2#104×D283direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#41×D2832
C2×M16×D2832
C2×C42×D2832
C2×#225835382
C2×#225835372
C2×#225835362
#104×D2832
C2×#104×C2832
C22×#104283