Finite Group Databasebeta

← C2×#31827182 #49134804

Subgroups — C2×#31827182 #49134804

Order 36224.

1112 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827182C2116yesmaximal, direct product factor
2C2×#22583609C211yesmaximal, characteristic, complemented
3C2×#22583605C211yesmaximal, characteristic, complemented
4C2×#22583605C211yesmaximal, characteristic, complemented
5C2×#22583603C211yesmaximal, characteristic, complemented
6C2×#22583596C211yesmaximal, characteristic
7C2×#22583596C211yesmaximal, characteristic
8C2×#22583588C211yesmaximal, characteristic, complemented
9C2×#22583587C211yesmaximal, characteristic, complemented
10C2×C4×Dic566C211yesmaximal, characteristic, complemented
11C2×#22583575C211yesmaximal, characteristic, complemented
12C2×#22583575C211yesmaximal, characteristic, complemented
13C2×(C22⋊D283)⋊C4C211yesmaximal, characteristic
14C2×#22583567C211yesmaximal, characteristic, complemented
15C2×#22583566C211yesmaximal, characteristic, complemented
16C2×#126×C283C211yesmaximal, characteristic, complemented
17C22×Dic566C2211yescharacteristic
18C22×Dic566C2211yescharacteristic
19C22×Dic566C2211yescharacteristic
20C22×C22⋊D283C2211yescharacteristic
21C23×Dic283C2211yescharacteristic
22C22×C4×D283C2211yescharacteristic
23#22583609C2218yescomplemented
24#22583605C2218yescomplemented
25#22583605C2218yescomplemented
26#22583603C2218yescomplemented
27#22583596C2218yes—
28#22583596C2218yes—
29#22583588C2218yescomplemented
30#22583587C2218yescomplemented
31C4×Dic566C2218yescomplemented
32#22583575C2218yescomplemented
33#22583575C2218yescomplemented
34(C22⋊D283)⋊C4C2218yes—
35#22583567C2218yescomplemented
36#22583566C2218yescomplemented
37C2×C4⋊Dic283C2211yescharacteristic
38C2×C4⋊Dic283C2211yescharacteristic
39C2×Dic283⋊C4C2211yescharacteristic
40C2×Dic283⋊C4C2211yescharacteristic
41C2×Dic283⋊C4C2211yescharacteristic
42C2×Dic283⋊C4C2211yescharacteristic
43C2×Dic283⋊C4C2211yescharacteristic
44C2×Dic283⋊C4C2211yescharacteristic
45C2×Dic283⋊C4C2211yescharacteristic
46C2×C22⋊Dic283C2211yescharacteristic
47C2×C22⋊Dic283C2211yescharacteristic
48C2×(C2×D283)⋊C4C2211yescharacteristic
49C2×(C2×D283)⋊C4C2211yescharacteristic
50C2×(C2×D283)⋊C4C2211yescharacteristic
51C2×(C2×D283)⋊C4C2211yescharacteristic
52C2×(C2×D283)⋊C4C2211yescharacteristic
53C2×C4×Dic283C2211yescharacteristic
54C2×C4×Dic283C2211yescharacteristic
55C2×C4×Dic283C2211yescharacteristic
56C2×C4×Dic283C2211yescharacteristic
57C2×C4×Dic283C2211yescharacteristic
58C2×C4×Dic283C2211yescharacteristic
59#126×C283C2218yescomplemented
60C2×C4⋊C4×C283C2211yescharacteristic
61C2×C4⋊C4×C283C2211yescharacteristic
62C2×C4⋊C4×C283C2211yescharacteristic
63C2×C22⋊C4×C283C2211yescharacteristic
64C2×C22⋊C4×C283C2211yescharacteristic
65C2×C22⋊C4×C283C2211yescharacteristic
66C2×C42×C283C2211yescharacteristic
67C23×D283C2311yescharacteristic
68C2×Dic566—24no—
69C2×Dic566—24no—
70C2×Dic566—24no—
71C2×Dic566C2314yes—
72C2×Dic566C2314yes—
73C2×Dic566C2314yes—
74C2×C22⋊D283—24no—
75C2×C22⋊D283C2314yes—
76C22×Dic283—24no—
77C22×Dic283C2311yescharacteristic
78C22×Dic283C2311yescharacteristic
79C22×Dic283C2311yescharacteristic
80C22×Dic283C2311yescharacteristic
81C22×Dic283C2311yescharacteristic
82C22×Dic283C2314yes—
83C22×Dic283C2311yescharacteristic
84C22×Dic283C2311yescharacteristic
85C2×C4×D283—24no—
86C2×C4×D283C2314yes—
87C4⋊Dic283C2314yes—
88C4⋊Dic283C2314yes—
89Dic283⋊C4C2314yes—
90Dic283⋊C4C2314yes—
91Dic283⋊C4C2314yes—
92Dic283⋊C4C2314yes—
93Dic283⋊C4C2314yes—
94Dic283⋊C4C2314yes—
95Dic283⋊C4C2314yes—
96C22⋊Dic283C2314yes—
97C22⋊Dic283C2314yes—
98(C2×D283)⋊C4C2314yes—
99(C2×D283)⋊C4C2314yes—
100(C2×D283)⋊C4C2314yes—
101(C2×D283)⋊C4C2314yes—
102(C2×D283)⋊C4C2314yes—
103C4×Dic283C2314yes—
104C4×Dic283C2314yes—
105C4×Dic283C2314yes—
106C4×Dic283C2314yes—
107C4×Dic283C2314yes—
108C4×Dic283C2314yes—
109C24×C283C2311yescharacteristic
110C22×C4×C283C2311yescharacteristic
111C22×C4×C283C2311yescharacteristic
112C22×C4×C283C2311yescharacteristic
113C22×C4×C283C2311yescharacteristic
114C22×C4×C283C2311yescharacteristic
115C22×C4×C283C2311yescharacteristic
116C4⋊C4×C283C2314yes—
117C4⋊C4×C283C2314yes—
118C4⋊C4×C283C2314yes—
119C22⋊C4×C283C2314yes—
120C22⋊C4×C283C2314yes—
121C22⋊C4×C283C2314yes—
122C42×C283C2314yes—
123C22×D283—22no—
124C22×D283—22no—
125C22×D283—22no—
126C22×D283C2412yes—
127Dic566—28no—
128Dic566—28no—
129Dic566—28no—
130C22⋊D283—28no—
131C2×Dic283—22no—
132C2×Dic283—22no—
133C2×Dic283—22no—
134C2×Dic283—22no—
135C2×Dic283—22no—
136C2×Dic283—28no—
137C2×Dic283#4114yes—
138C2×Dic283#4114yes—
139C2×Dic283C2412yes—
140C2×Dic283C2412yes—
141C2×Dic283C2412yes—
142C2×Dic283C2412yes—
143C2×Dic283C2412yes—
144C2×Dic283C2412yes—
145C2×Dic283C2412yes—
146C4×D283—28no—
147C23×C283—22no—
148C23×C283—22no—
149C23×C283—22no—
150C23×C283C2412yes—
151C23×C283C2411yescharacteristic
152C2×C4×C283—22no—
153C2×C4×C283—22no—
154C2×C4×C283—22no—
155C2×C4×C283—22no—
156C2×C4×C283—22no—
157C2×C4×C283—22no—
158C2×C4×C283C2412yes—
159C2×C4×C283C2412yes—
160C2×C4×C283C2412yes—
161C2×C4×C283C2412yes—
162C2×C4×C283C2412yes—
163C2×C4×C283C2412yes—
164C22×C283—22no—
165C22×C283—22no—
166C22×C283—22no—
167C22×C283—44no—
168C22×C283C2×#4112yes—
169C22×C283C2×#4112yes—
170C22×C2832−1+412yes—
171C22×C283C2511yescharacteristic
172C2×D283—22no—
173C2×D283—22no—
174C2×D283—22no—
175C2×D283—44no—
176C4×C283—22no—
177C4×C283—22no—
178C4×C283—22no—
179C4×C283—22no—
180C4×C283—22no—
181C4×C283—22no—
182Dic283—22no—
183Dic283—22no—
184Dic283—22no—
185Dic283—22no—
186Dic283—22no—
187Dic283C2×#4114yes—
188Dic283C2×#4114yes—
189C2×C283—42no—
190C2×C283#55614yescomplemented
191C2×C283C22×#4111yescharacteristic
192C2×C283C22×#4111yescharacteristic
193C2×C283C2×2−1+411yescharacteristic
194D283—42no—
195C283C2×#55611yescharacteristic, complemented, Sylow
196C2×#556—2831nomaximal, Sylow
197#556—28316no—
198C2×C4⋊Q8—2831no—
199C2×#126—2831no—
200C2×#126—2831no—
201C2×#126—2831no—
202C2×#126D28311yescharacteristic, complemented
203C2×#124—2831no—
204C2×#124—2831no—
205C2×C22⋊Q8—2831no—
206C2×C22⋊Q8—2831no—
207C2×C4×Q8—2831no—
208C2×C4×Q8—2831no—
209C2×C4×Q8—2831no—
210C2×C4×D4—2831no—
211C2×#117—2831no—
212C2×#117—2831no—
213C22×Q8—2831no—
214C22×Q8—2831no—
215C22×Q8—2831no—
216C22×D4—2831no—
217C23×C4—2831no—
218C23×C4—2831no—
219C4⋊Q8—2838no—
220#126—2838no—
221#126—2838no—
222#126—2838no—
223#126C2×D28318yescomplemented
224#124—2838no—
225#124—2838no—
226C22⋊Q8—2838no—
227C22⋊Q8—2838no—
228C4×Q8—2838no—
229C4×Q8—2838no—
230C4×Q8—2838no—
231C4×D4—2838no—
232#117—2838no—
233#117—2838no—
234C2×C4⋊C4—2831no—
235C2×C4⋊C4—2831no—
236C2×C4⋊C4—2831no—
237C2×C4⋊C4—2831no—
238C2×C4⋊C4—2831no—
239C2×C4⋊C4—2831no—
240C2×C4⋊C4—2831no—
241C2×C4⋊C4—2831no—
242C2×C4⋊C4—2831no—
243C2×C4⋊C4C2×D28311yescharacteristic
244C2×C4⋊C4C2×D28311yescharacteristic
245C2×C4⋊C4C2×D28311yescharacteristic
246C2×C22⋊C4—2831no—
247C2×C22⋊C4—2831no—
248C2×C22⋊C4—2831no—
249C2×C22⋊C4—2831no—
250C2×C22⋊C4—2831no—
251C2×C22⋊C4—2831no—
252C2×C22⋊C4—2831no—
253C2×C22⋊C4C2×D28311yescharacteristic
254C2×C22⋊C4C2×D28311yescharacteristic
255C2×C22⋊C4C2×D28311yescharacteristic
256C2×C42—2831no—
257C2×C42—2831no—
258C2×C42—2831no—
259C2×C42—2831no—
260C2×C42—2831no—
261C2×C42—2831no—
262C2×C42C2×D28311yescharacteristic
263C24—2831no—
264C24C22×D28311yescharacteristic
265C2×Q8—2834no—
266C2×Q8—2834no—
267C2×Q8—2834no—
268C2×Q8—5664no—
269C2×Q8—5664no—
270C2×Q8—5664no—
271C2×D4—2834no—
272C2×D4—5664no—
273C22×C4—2831no—
274C22×C4—2831no—
275C22×C4—2834no—
276C22×C4—2831no—
277C22×C4—2831no—
278C22×C4—2831no—
279C22×C4—2831no—
280C22×C4—2831no—
281C22×C4—2834no—
282C22×C4—5664no—
283C22×C4—5664no—
284C22×C4C22×D28311yescharacteristic
285C22×C4C22×D28311yescharacteristic
286C22×C4C22×D28311yescharacteristic
287C22×C4C22×D28311yescharacteristic
288C22×C4C22×D28311yescharacteristic
289C22×C4C22×D28311yescharacteristic
290C4⋊C4—2834no—
291C4⋊C4—2834no—
292C4⋊C4—2834no—
293C4⋊C4—2834no—
294C4⋊C4—2834no—
295C4⋊C4—2834no—
296C4⋊C4—2834no—
297C4⋊C4—2834no—
298C4⋊C4—2834no—
299C4⋊C4C22×D28314yes—
300C4⋊C4C22×D28314yes—
301C4⋊C4C22×D28314yes—
302C22⋊C4—2834no—
303C22⋊C4—2834no—
304C22⋊C4—2834no—
305C22⋊C4—2834no—
306C22⋊C4—2834no—
307C22⋊C4—2834no—
308C22⋊C4—2834no—
309C22⋊C4C22×D28314yes—
310C22⋊C4C22×D28314yes—
311C22⋊C4C22×D28314yes—
312C42—2834no—
313C42—2834no—
314C42—2834no—
315C42—2834no—
316C42—2834no—
317C42—2834no—
318C42C22×D28314yes—
319C23—22no—
320C23—22no—
321C23—22no—
322C23—2832no—
323C23—5662no—
324C23—5662no—
325C23—5662no—
326C23C23×D28312yes—
327C23C23×D28311yescharacteristic
328Q8—5668no—
329Q8—5668no—
330Q8—5668no—
331D4—5668no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—2834no—
339C2×C4—2834no—
340C2×C4—2832no—
341C2×C4—2832no—
342C2×C4—2832no—
343C2×C4—2832no—
344C2×C4—2832no—
345C2×C4—2832no—
346C2×C4—2832no—
347C2×C4—5668no—
348C2×C4—5668no—
349C2×C4—5662no—
350C2×C4—5662no—
351C2×C4—5662no—
352C2×C4—5662no—
353C2×C4—5662no—
354C2×C4C23×D28312yes—
355C2×C4C23×D28312yes—
356C2×C4C23×D28312yes—
357C2×C4C23×D28312yes—
358C2×C4C23×D28312yes—
359C2×C4C23×D28312yes—
360C22—22no—
361C22—22no—
362C22—22no—
363C22—44no—
364C22—5662no—
365C22—5662no—
366C22—5662no—
367C22—11324no—
368C22#41×D28312yes—
369C22#41×D28312yes—
370C22#2258365712yes—
371C22C24×D28311yescharacteristic
372C4—22no—
373C4—22no—
374C4—22no—
375C4—22no—
376C4—22no—
377C4—22no—
378C4—2834no—
379C4—2834no—
380C4—5662no—
381C4—5662no—
382C4—5662no—
383C4—5662no—
384C4—5662no—
385C2—42no—
386C2—11322no—
387C2#3182718214yesdirect product factor
388C2C2×#41×D28311yescharacteristic
389C2C2×#41×D28311yescharacteristic
390C2C2×#2258365711yescharacteristic
subgroupG/H
centerC23C23×D283
commutator, cosocleC22×C283C25
FrattiniC22C24×D283
FittingC2×#126×C283C2
socleC23×C283C24
prime radicalC22×C22⋊D283C22
hypercenterC2×#126D283
hypocenterC283C2×#556
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #31827182C2direct (N × H)
2. C2×#22583609C2semidirect
3. C2×#22583605C2semidirect
4. C2×#22583605C2semidirect
5. C2×#22583603C2semidirect
8. C2×#22583588C2semidirect
9. C2×#22583587C2semidirect
10. C2×C4×Dic566C2semidirect
11. C2×#22583575C2semidirect
12. C2×#22583575C2semidirect
14. C2×#22583567C2semidirect
15. C2×#22583566C2semidirect
16. C2×#126×C283C2semidirect
23. #22583609C22semidirect
24. #22583605C22semidirect
25. #22583605C22semidirect
26. #22583603C22semidirect
29. #22583588C22semidirect
30. #22583587C22semidirect
31. C4×Dic566C22semidirect
32. #22583575C22semidirect
33. #22583575C22semidirect
35. #22583567C22semidirect
36. #22583566C22semidirect
59. #126×C283C22semidirect
190. C2×C283#556semidirect
195. C283C2×#556semidirect
202. C2×#126D283semidirect
223. #126C2×D283semidirect
387. C2#31827182direct (N × H)

Maximal subgroups

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

subgroupindex
#318271822
C2×#225836092
C2×#225836052
C2×#225836032
C2×#225835962
C2×#225835882
C2×#225835872
C2×C4×Dic5662
C2×#225835752
C2×(C22⋊D283)⋊C42
C2×#225835672
C2×#225835662
C2×#126×C2832
C2×#556283