Finite Group Databasebeta

← C2×#31827057 #49134607

Subgroups — C2×#31827057 #49134607

Order 36224.

1144 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827057C2116yesmaximal, direct product factor
2C2×#22583604C211yesmaximal, characteristic, complemented
3C2×#22583603C211yesmaximal, characteristic, complemented
4C2×#22583602C211yesmaximal, characteristic, complemented
5C2×#22583600C211yesmaximal, characteristic, complemented
6C2×#22583594C211yesmaximal, characteristic, complemented
7C2×#22583593C211yesmaximal, characteristic, complemented
8C2×#22583592C211yesmaximal, characteristic, complemented
9C2×#22583591C211yesmaximal, characteristic, complemented
10C2×#22583589C211yesmaximal, characteristic, complemented
11C2×#22583588C211yesmaximal, characteristic, complemented
12C2×#22583587C211yesmaximal, characteristic, complemented
13C2×#22583582C211yesmaximal, characteristic
14C2×C4×C22⋊D283C211yesmaximal, characteristic, complemented
15C22×Dic283⋊C4C211yesmaximal, characteristic, complemented
16C2×C4×D4×C283C211yesmaximal, characteristic, complemented
17C22×Dic566C2211yescharacteristic
18C22×C22⋊D283C2211yescharacteristic
19C22×C22⋊D283C2211yescharacteristic
20C23×Dic283C2211yescharacteristic
21C23×Dic283C2211yescharacteristic
22C22×C4×D283C2211yescharacteristic
23#22583604C2218yescomplemented
24#22583603C2218yescomplemented
25#22583602C2218yescomplemented
26#22583600C2218yescomplemented
27#22583594C2218yescomplemented
28#22583593C2218yescomplemented
29#22583592C2218yescomplemented
30#22583591C2218yescomplemented
31#22583589C2218yescomplemented
32#22583588C2218yescomplemented
33#22583587C2218yescomplemented
34#22583582C2218yes—
35C4×C22⋊D283C2218yescomplemented
36C2×C4⋊Dic283C2211yescharacteristic
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×Dic283⋊C4C2211yescharacteristic
47C2×Dic283⋊C4C2211yescharacteristic
48C2×Dic283⋊C4C2211yescharacteristic
49C2×Dic283⋊C4C2218yescomplemented
50C2×C22⋊Dic283C2211yescharacteristic
51C2×C22⋊Dic283C2211yescharacteristic
52C2×C22⋊Dic283C2211yescharacteristic
53C2×C22⋊Dic283C2211yescharacteristic
54C2×(C2×D283)⋊C4C2211yescharacteristic
55C2×(C2×D283)⋊C4C2211yescharacteristic
56C2×(C2×D283)⋊C4C2211yescharacteristic
57C2×(C2×D283)⋊C4C2211yescharacteristic
58C2×C4×Dic283C2211yescharacteristic
59C22×D4×C283C2211yescharacteristic
60C23×C4×C283C2211yescharacteristic
61C23×C4×C283C2211yescharacteristic
62C4×D4×C283C2218yescomplemented
63C2×C4⋊C4×C283C2211yescharacteristic
64C2×C22⋊C4×C283C2211yescharacteristic
65C2×C22⋊C4×C283C2211yescharacteristic
66C2×C42×C283C2211yescharacteristic
67C23×D283C2311yescharacteristic
68C2×Dic566—42no—
69C2×Dic566C2314yes—
70C2×C22⋊D283—24no—
71C2×C22⋊D283—42no—
72C2×C22⋊D283C2314yes—
73C2×C22⋊D283C2314yes—
74C22×Dic283—24no—
75C22×Dic283—42no—
76C22×Dic283C2311yescharacteristic
77C22×Dic283C2311yescharacteristic
78C22×Dic283C2311yescharacteristic
79C22×Dic283C2311yescharacteristic
80C22×Dic283C2311yescharacteristic
81C22×Dic283C2311yescharacteristic
82C22×Dic283C2311yescharacteristic
83C22×Dic283C2314yes—
84C22×Dic283C2314yes—
85C2×C4×D283—42no—
86C2×C4×D283C2314yes—
87C4⋊Dic283C2314yes—
88C4⋊Dic283C2314yes—
89C4⋊Dic283C2314yes—
90Dic283⋊C4C2314yes—
91Dic283⋊C4C2314yes—
92Dic283⋊C4C2314yes—
93Dic283⋊C4C2314yes—
94Dic283⋊C4C2314yes—
95Dic283⋊C4C2314yes—
96Dic283⋊C4C2314yes—
97Dic283⋊C4C2314yes—
98Dic283⋊C4C2314yes—
99Dic283⋊C4C2314yes—
100C22⋊Dic283C2314yes—
101C22⋊Dic283C2314yes—
102C22⋊Dic283C2314yes—
103C22⋊Dic283C2314yes—
104(C2×D283)⋊C4C2314yes—
105(C2×D283)⋊C4C2314yes—
106(C2×D283)⋊C4C2314yes—
107(C2×D283)⋊C4C2314yes—
108C4×Dic283C2314yes—
109C24×C283C2311yescharacteristic
110C24×C283C2311yescharacteristic
111C2×D4×C283—24no—
112C2×D4×C283C2314yes—
113C22×C4×C283—42no—
114C22×C4×C283—42no—
115C22×C4×C283C2311yescharacteristic
116C22×C4×C283C2311yescharacteristic
117C22×C4×C283C2311yescharacteristic
118C22×C4×C283C2311yescharacteristic
119C22×C4×C283C2311yescharacteristic
120C22×C4×C283C2314yes—
121C22×C4×C283C2314yes—
122C4⋊C4×C283C2314yes—
123C22⋊C4×C283C2314yes—
124C22⋊C4×C283C2314yes—
125C42×C283C2314yes—
126C22×D283—22no—
127C22×D283—22no—
128C22×D283—22no—
129C22×D283C2412yes—
130Dic566—44no—
131C22⋊D283—28no—
132C22⋊D283—44no—
133C2×Dic283—28no—
134C2×Dic283—22no—
135C2×Dic283—22no—
136C2×Dic283—22no—
137C2×Dic283—22no—
138C2×Dic283—22no—
139C2×Dic283—22no—
140C2×Dic283—22no—
141C2×Dic283—44no—
142C2×Dic283C2412yes—
143C2×Dic283C2412yes—
144C2×Dic283C2412yes—
145C2×Dic283C2412yes—
146C2×Dic283C2412yes—
147C2×Dic283C2412yes—
148C2×Dic283C2412yes—
149C4×D283—44no—
150C23×C283—22no—
151C23×C283—22no—
152C23×C283—22no—
153C23×C283—22no—
154C23×C283—22no—
155C23×C283#4114yes—
156C23×C283C2412yes—
157C23×C283C2412yes—
158C23×C283C2411yescharacteristic
159D4×C283—28no—
160C2×C4×C283—22no—
161C2×C4×C283—22no—
162C2×C4×C283—22no—
163C2×C4×C283—22no—
164C2×C4×C283—22no—
165C2×C4×C283—44no—
166C2×C4×C283—44no—
167C2×C4×C283C2412yes—
168C2×C4×C283C2412yes—
169C2×C4×C283C2412yes—
170C2×C4×C283C2412yes—
171C2×C4×C283C2412yes—
172C22×C283—28no—
173C22×C283—22no—
174C22×C283—22no—
175C22×C283—22no—
176C22×C283—22no—
177C22×C283—22no—
178C22×C283—44no—
179C22×C283C2×#4114yes—
180C22×C283C2×#4112yes—
181C22×C283H(5,𝔽2)12yes—
182C22×C2832−1+412yes—
183C22×C283C2511yescharacteristic
184C2×D283—22no—
185C2×D283—22no—
186C2×D283—22no—
187C2×D283—44no—
188C4×C283—22no—
189C4×C283—22no—
190C4×C283—22no—
191C4×C283—22no—
192C4×C283—22no—
193Dic283—22no—
194Dic283—22no—
195Dic283—22no—
196Dic283—22no—
197Dic283—22no—
198Dic283—22no—
199Dic283—22no—
200C2×C283—24no—
201C2×C283—42no—
202C2×C283#53914yescomplemented
203C2×C283C22×#4111yescharacteristic
204C2×C283C2×H(5,𝔽2)11yescharacteristic
205C2×C283C2×2−1+411yescharacteristic
206D283—42no—
207C283C2×#53911yescharacteristic, complemented, Sylow
208C2×#539—2831nomaximal, Sylow
209#539—28316no—
210C2×#126—2831no—
211C2×#126—2831no—
212C2×#125—2831no—
213C2×#125—2831no—
214C2×#123—2831no—
215C2×#123—2831no—
216C2×#123—2831no—
217C2×#123—2831no—
218C2×C22⋊Q8—2831no—
219C2×C22⋊Q8—2831no—
220C2×C22⋊Q8—2831no—
221C2×#121—2831no—
222C2×C4×D4—2831no—
223C2×C4×D4D28311yescharacteristic, complemented
224C22×C4⋊C4—2831no—
225C22×Q8—2831no—
226C22×D4—2831no—
227C22×D4—2831no—
228C22×D4C2×D28311yescharacteristic
229C23×C4—2831no—
230C23×C4—2831no—
231C23×C4—2831no—
232C23×C4C2×D28311yescharacteristic
233C23×C4C2×D28311yescharacteristic
234#126—2838no—
235#126—2838no—
236#125—2838no—
237#125—2838no—
238#123—2838no—
239#123—2838no—
240#123—2838no—
241#123—2838no—
242C22⋊Q8—2838no—
243C22⋊Q8—2838no—
244C22⋊Q8—2838no—
245#121—2838no—
246C4×D4—2838no—
247C4×D4C2×D28318yescomplemented
248C2×C4⋊C4—2831no—
249C2×C4⋊C4—2831no—
250C2×C4⋊C4—2831no—
251C2×C4⋊C4—2831no—
252C2×C4⋊C4—2838no—
253C2×C4⋊C4—2831no—
254C2×C4⋊C4—2831no—
255C2×C4⋊C4—2831no—
256C2×C4⋊C4—2831no—
257C2×C4⋊C4—2831no—
258C2×C4⋊C4—2831no—
259C2×C4⋊C4—2831no—
260C2×C4⋊C4—2831no—
261C2×C4⋊C4—2831no—
262C2×C4⋊C4C2×D28311yescharacteristic
263C2×C22⋊C4—2831no—
264C2×C22⋊C4—2831no—
265C2×C22⋊C4—2831no—
266C2×C22⋊C4—2831no—
267C2×C22⋊C4—2831no—
268C2×C22⋊C4—2831no—
269C2×C22⋊C4—2831no—
270C2×C22⋊C4—2831no—
271C2×C22⋊C4C2×D28311yescharacteristic
272C2×C22⋊C4C2×D28311yescharacteristic
273C2×C42—2831no—
274C2×C42C2×D28311yescharacteristic
275C24—2831no—
276C24C22×D28311yescharacteristic
277C24C22×D28311yescharacteristic
278C2×Q8—2834no—
279C2×Q8—11322no—
280C2×D4—24no—
281C2×D4—2834no—
282C2×D4—2834no—
283C2×D4—5664no—
284C2×D4—11322no—
285C2×D4C22×D28314yes—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—2834no—
289C22×C4—2831no—
290C22×C4—2831no—
291C22×C4—2831no—
292C22×C4—2831no—
293C22×C4—2831no—
294C22×C4—2831no—
295C22×C4—2831no—
296C22×C4—2834no—
297C22×C4—2834no—
298C22×C4—5664no—
299C22×C4—11322no—
300C22×C4—11322no—
301C22×C4C22×D28311yescharacteristic
302C22×C4C22×D28311yescharacteristic
303C22×C4C22×D28311yescharacteristic
304C22×C4C22×D28311yescharacteristic
305C22×C4C22×D28311yescharacteristic
306C22×C4C22×D28314yes—
307C22×C4C22×D28314yes—
308C4⋊C4—2834no—
309C4⋊C4—2834no—
310C4⋊C4—2834no—
311C4⋊C4—2834no—
312C4⋊C4—2834no—
313C4⋊C4—2834no—
314C4⋊C4—2834no—
315C4⋊C4—2834no—
316C4⋊C4—2834no—
317C4⋊C4—2834no—
318C4⋊C4—2834no—
319C4⋊C4—2834no—
320C4⋊C4—2834no—
321C4⋊C4C22×D28314yes—
322C22⋊C4—2834no—
323C22⋊C4—2834no—
324C22⋊C4—2834no—
325C22⋊C4—2834no—
326C22⋊C4—2834no—
327C22⋊C4—2834no—
328C22⋊C4—2834no—
329C22⋊C4—2834no—
330C22⋊C4C22×D28314yes—
331C22⋊C4C22×D28314yes—
332C42—2834no—
333C42C22×D28314yes—
334C23—22no—
335C23—22no—
336C23—22no—
337C23—22no—
338C23—22no—
339C23—2832no—
340C23—5662no—
341C23—5662no—
342C23—5662no—
343C23#1798539214yes—
344C23C23×D28312yes—
345C23C23×D28312yes—
346C23C23×D28311yescharacteristic
347Q8—11324no—
348D4—28no—
349D4—5668no—
350D4—11324no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—44no—
357C2×C4—44no—
358C2×C4—2832no—
359C2×C4—2832no—
360C2×C4—2832no—
361C2×C4—2832no—
362C2×C4—2832no—
363C2×C4—2832no—
364C2×C4—2832no—
365C2×C4—5668no—
366C2×C4—5662no—
367C2×C4—5662no—
368C2×C4—5662no—
369C2×C4—5662no—
370C2×C4—5662no—
371C2×C4—5662no—
372C2×C4—5662no—
373C2×C4—11324no—
374C2×C4—11324no—
375C2×C4C23×D28312yes—
376C2×C4C23×D28312yes—
377C2×C4C23×D28312yes—
378C2×C4C23×D28312yes—
379C2×C4C23×D28312yes—
380C22—22no—
381C22—22no—
382C22—28no—
383C22—22no—
384C22—22no—
385C22—22no—
386C22—44no—
387C22—5662no—
388C22—5662no—
389C22—5662no—
390C22—11324no—
391C22C2×#1798539214yes—
392C22C2×#1798539212yes—
393C22#2258365512yes—
394C22#2258365712yes—
395C22C24×D28311yescharacteristic
396C4—22no—
397C4—22no—
398C4—22no—
399C4—22no—
400C4—22no—
401C4—5662no—
402C4—5662no—
403C4—5662no—
404C4—5662no—
405C4—5662no—
406C4—5662no—
407C4—5662no—
408C2—24no—
409C2—42no—
410C2—11322no—
411C2#3182705714yesdirect product factor
412C2C22×#1798539211yescharacteristic
413C2C2×#2258365511yescharacteristic
414C2C2×#2258365711yescharacteristic
subgroupG/H
centerC23C23×D283
commutator, cosocleC22×C283C25
FrattiniC22C24×D283
FittingC2×C4×D4×C283C2
socleC23×C283C24
prime radicalC2×#22583582C2
hypercenterC2×C4×D4D283
hypocenterC283C2×#539
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #31827057C2direct (N × H)
2. C2×#22583604C2semidirect
3. C2×#22583603C2semidirect
4. C2×#22583602C2semidirect
5. C2×#22583600C2semidirect
6. C2×#22583594C2semidirect
7. C2×#22583593C2semidirect
8. C2×#22583592C2semidirect
9. C2×#22583591C2semidirect
10. C2×#22583589C2semidirect
11. C2×#22583588C2semidirect
12. C2×#22583587C2semidirect
14. C2×C4×C22⋊D283C2semidirect
15. C22×Dic283⋊C4C2semidirect
16. C2×C4×D4×C283C2semidirect
23. #22583604C22semidirect
24. #22583603C22semidirect
25. #22583602C22semidirect
26. #22583600C22semidirect
27. #22583594C22semidirect
28. #22583593C22semidirect
29. #22583592C22semidirect
30. #22583591C22semidirect
31. #22583589C22semidirect
32. #22583588C22semidirect
33. #22583587C22semidirect
35. C4×C22⋊D283C22semidirect
49. C2×Dic283⋊C4C22semidirect
62. C4×D4×C283C22semidirect
202. C2×C283#539semidirect
207. C283C2×#539semidirect
223. C2×C4×D4D283semidirect
247. C4×D4C2×D283semidirect
411. C2#31827057direct (N × H)

Maximal subgroups

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

subgroupindex
#318270572
C2×#225836042
C2×#225836032
C2×#225836022
C2×#225836002
C2×#225835942
C2×#225835932
C2×#225835922
C2×#225835912
C2×#225835892
C2×#225835882
C2×#225835872
C2×#225835822
C2×C4×C22⋊D2832
C22×Dic283⋊C42
C2×C4×D4×C2832
C2×#539283