Finite Group Databasebeta

← C2×#31827061 #49134611

Subgroups — C2×#31827061 #49134611

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#31827061C2116yesmaximal, direct product factor
2C2×#22583605C211yesmaximal, characteristic, complemented
3C2×#22583603C211yesmaximal, characteristic, complemented
4C2×#22583600C211yesmaximal, characteristic, complemented
5C2×#22583600C211yesmaximal, characteristic, complemented
6C2×#22583595C211yesmaximal, characteristic, complemented
7C2×#22583593C211yesmaximal, characteristic, complemented
8C2×#22583592C211yesmaximal, characteristic, complemented
9C2×#22583592C211yesmaximal, characteristic, complemented
10C2×#22583586C211yesmaximal, characteristic, complemented
11C2×#22583586C211yesmaximal, characteristic, complemented
12C2×#22583583C211yesmaximal, characteristic
13C2×#22583572C211yesmaximal, characteristic, complemented
14C2×C4×C22⋊D283C211yesmaximal, characteristic, complemented
15C2×C4⋊C4×D283C211yesmaximal, characteristic, complemented
16C2×C22⋊Q8×C283C211yesmaximal, characteristic, complemented
17C22×D1132C2211yescharacteristic
18C22×C22⋊D283C2211yescharacteristic
19C22×C22⋊D283C2211yescharacteristic
20C22×C4×D283C2211yescharacteristic
21C22×C4×D283C2211yescharacteristic
22C22×C4×D283C2211yescharacteristic
23C22×C4×D283C2211yescharacteristic
24#22583605C2218yescomplemented
25#22583603C2218yescomplemented
26#22583600C2218yescomplemented
27#22583600C2218yescomplemented
28#22583595C2218yescomplemented
29#22583593C2218yescomplemented
30#22583592C2218yescomplemented
31#22583592C2218yescomplemented
32#22583586C2218yescomplemented
33#22583586C2218yescomplemented
34#22583583C2218yes—
35#22583572C2218yescomplemented
36C4×C22⋊D283C2218yescomplemented
37C2×C4⋊Dic283C2211yescharacteristic
38C2×C4⋊Dic283C2211yescharacteristic
39C2×C4⋊Dic283C2211yescharacteristic
40C2×Dic283⋊C4C2211yescharacteristic
41C2×Dic283⋊C4C2211yescharacteristic
42C2×Dic283⋊C4C2211yescharacteristic
43C2×Dic283⋊C4C2211yescharacteristic
44C2×Dic283⋊C4C2211yescharacteristic
45C2×Dic283⋊C4C2211yescharacteristic
46C2×Dic283⋊C4C2211yescharacteristic
47C2×Dic283⋊C4C2211yescharacteristic
48C4⋊C4×D283C2218yescomplemented
49C2×C22⋊Dic283C2211yescharacteristic
50C2×C22⋊Dic283C2211yescharacteristic
51C2×(C2×D283)⋊C4C2211yescharacteristic
52C2×(C2×D283)⋊C4C2211yescharacteristic
53C2×(C2×D283)⋊C4C2211yescharacteristic
54C2×(C2×D283)⋊C4C2211yescharacteristic
55C2×(C2×D283)⋊C4C2211yescharacteristic
56C2×(C2×D283)⋊C4C2211yescharacteristic
57C2×C4×Dic283C2211yescharacteristic
58C2×C4×Dic283C2211yescharacteristic
59C22×Q8×C283C2211yescharacteristic
60C23×C4×C283C2211yescharacteristic
61C22⋊Q8×C283C2218yescomplemented
62C2×C4⋊C4×C283C2211yescharacteristic
63C2×C4⋊C4×C283C2211yescharacteristic
64C2×C4⋊C4×C283C2211yescharacteristic
65C2×C22⋊C4×C283C2211yescharacteristic
66C2×C22⋊C4×C283C2211yescharacteristic
67C23×D283C2311yescharacteristic
68C23×D283C2311yescharacteristic
69C2×D1132—24no—
70C2×D1132C2314yes—
71C2×C22⋊D283—24no—
72C2×C22⋊D283—42no—
73C2×C22⋊D283C2314yes—
74C2×C22⋊D283C2314yes—
75C22×Dic283C2311yescharacteristic
76C22×Dic283C2311yescharacteristic
77C22×Dic283C2311yescharacteristic
78C22×Dic283C2311yescharacteristic
79C22×Dic283C2311yescharacteristic
80C22×Dic283C2311yescharacteristic
81C2×C4×D283—24no—
82C2×C4×D283—42no—
83C2×C4×D283—42no—
84C2×C4×D283—42no—
85C2×C4×D283C2314yes—
86C2×C4×D283C2314yes—
87C2×C4×D283C2314yes—
88C2×C4×D283C2314yes—
89C4⋊Dic283C2314yes—
90C4⋊Dic283C2314yes—
91C4⋊Dic283C2314yes—
92Dic283⋊C4C2314yes—
93Dic283⋊C4C2314yes—
94Dic283⋊C4C2314yes—
95Dic283⋊C4C2314yes—
96Dic283⋊C4C2314yes—
97Dic283⋊C4C2314yes—
98Dic283⋊C4C2314yes—
99Dic283⋊C4C2314yes—
100C22⋊Dic283C2314yes—
101C22⋊Dic283C2314yes—
102(C2×D283)⋊C4C2314yes—
103(C2×D283)⋊C4C2314yes—
104(C2×D283)⋊C4C2314yes—
105(C2×D283)⋊C4C2314yes—
106(C2×D283)⋊C4C2314yes—
107(C2×D283)⋊C4C2314yes—
108C4×Dic283C2314yes—
109C4×Dic283C2314yes—
110C24×C283C2311yescharacteristic
111C2×Q8×C283—42no—
112C2×Q8×C283C2314yes—
113C22×C4×C283—42no—
114C22×C4×C283C2311yescharacteristic
115C22×C4×C283C2311yescharacteristic
116C22×C4×C283C2311yescharacteristic
117C22×C4×C283C2311yescharacteristic
118C22×C4×C283C2311yescharacteristic
119C22×C4×C283C2311yescharacteristic
120C22×C4×C283C2314yes—
121C4⋊C4×C283C2314yes—
122C4⋊C4×C283C2314yes—
123C4⋊C4×C283C2314yes—
124C22⋊C4×C283C2314yes—
125C22⋊C4×C283C2314yes—
126C22×D283—22no—
127C22×D283—22no—
128C22×D283—22no—
129C22×D283—22no—
130C22×D283—22no—
131C22×D283#4114yes—
132C22×D283C2412yes—
133C22×D283C2412yes—
134D1132—28no—
135C22⋊D283—28no—
136C22⋊D283—44no—
137C2×Dic283—22no—
138C2×Dic283—22no—
139C2×Dic283—22no—
140C2×Dic283—22no—
141C2×Dic283—22no—
142C2×Dic283—22no—
143C2×Dic283C2412yes—
144C2×Dic283C2412yes—
145C2×Dic283C2412yes—
146C2×Dic283C2412yes—
147C2×Dic283C2412yes—
148C2×Dic283C2412yes—
149C4×D283—28no—
150C4×D283—44no—
151C4×D283—44no—
152C4×D283—44no—
153C23×C283—22no—
154C23×C283—22no—
155C23×C283—22no—
156C23×C283C2412yes—
157C23×C283C2411yescharacteristic
158Q8×C283—44no—
159C2×C4×C283—22no—
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×C283C2412yes—
167C2×C4×C283C2412yes—
168C2×C4×C283C2412yes—
169C2×C4×C283C2412yes—
170C2×C4×C283C2412yes—
171C2×C4×C283C2412yes—
172C22×C283—22no—
173C22×C283—22no—
174C22×C283—22no—
175C22×C283—44no—
176C22×C283C2×#4112yes—
177C22×C283H(5,𝔽2)12yes—
178C22×C2832−1+412yes—
179C22×C283C2511yescharacteristic
180C2×D283—28no—
181C2×D283—22no—
182C2×D283—22no—
183C2×D283—22no—
184C2×D283—22no—
185C2×D283—22no—
186C2×D283—44no—
187C2×D283C2×#4114yes—
188C4×C283—22no—
189C4×C283—22no—
190C4×C283—22no—
191C4×C283—22no—
192C4×C283—22no—
193C4×C283—22no—
194Dic283—22no—
195Dic283—22no—
196Dic283—22no—
197Dic283—22no—
198Dic283—22no—
199Dic283—22no—
200C2×C283—42no—
201C2×C283#53914yescomplemented
202C2×C283C22×#4111yescharacteristic
203C2×C283C2×H(5,𝔽2)11yescharacteristic
204C2×C283C2×2−1+411yescharacteristic
205D283—24no—
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⋊Q8D28311yescharacteristic, complemented
221C2×#121—2831no—
222C2×C4×D4—2831no—
223C2×C4×D4—2831no—
224C22×C4⋊C4—2831no—
225C22×Q8C2×D28311yescharacteristic
226C22×D4—2831no—
227C22×D4—2831no—
228C22×D4—2831no—
229C23×C4—2831no—
230C23×C4—2831no—
231C23×C4—2831no—
232C23×C4—2831no—
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⋊Q8C2×D28318yescomplemented
245#121—2838no—
246C4×D4—2838no—
247C4×D4—2838no—
248C2×C4⋊C4—2831no—
249C2×C4⋊C4—2831no—
250C2×C4⋊C4—2831no—
251C2×C4⋊C4—2831no—
252C2×C4⋊C4—2831no—
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—2838no—
260C2×C4⋊C4C2×D28311yescharacteristic
261C2×C4⋊C4C2×D28311yescharacteristic
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×C42—2831no—
275C24—2831no—
276C24—2831no—
277C24C22×D28311yescharacteristic
278C2×Q8—42no—
279C2×Q8C22×D28314yes—
280C2×D4—2834no—
281C2×D4—2834no—
282C2×D4—2834no—
283C2×D4—5664no—
284C2×D4—5664no—
285C2×D4—11322no—
286C22×C4—42no—
287C22×C4—2831no—
288C22×C4—2831no—
289C22×C4—2831no—
290C22×C4—2831no—
291C22×C4—2831no—
292C22×C4—2831no—
293C22×C4—2834no—
294C22×C4—2834no—
295C22×C4—2834no—
296C22×C4—2834no—
297C22×C4—5664no—
298C22×C4—11322no—
299C22×C4—11322no—
300C22×C4—11322no—
301C22×C4C22×D28311yescharacteristic
302C22×C4C22×D28311yescharacteristic
303C22×C4C22×D28311yescharacteristic
304C22×C4C22×D28311yescharacteristic
305C22×C4C22×D28311yescharacteristic
306C22×C4C22×D28311yescharacteristic
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⋊C4C22×D28314yes—
320C4⋊C4C22×D28314yes—
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—
333C42—2834no—
334C23—22no—
335C23—22no—
336C23—22no—
337C23—2834no—
338C23—2832no—
339C23—2832no—
340C23—5662no—
341C23—5662no—
342C23—5662no—
343C23—5662no—
344C23—5662no—
345C23C23×D28312yes—
346C23C23×D28311yescharacteristic
347Q8—44no—
348D4—5668no—
349D4—5668no—
350D4—11324no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—44no—
358C2×C4—2832no—
359C2×C4—2832no—
360C2×C4—2832no—
361C2×C4—2832no—
362C2×C4—2832no—
363C2×C4—2832no—
364C2×C4—5668no—
365C2×C4—5662no—
366C2×C4—5662no—
367C2×C4—5662no—
368C2×C4—5662no—
369C2×C4—5662no—
370C2×C4—5662no—
371C2×C4—11324no—
372C2×C4—11324no—
373C2×C4—11324no—
374C2×C4C23×D28312yes—
375C2×C4C23×D28312yes—
376C2×C4C23×D28312yes—
377C2×C4C23×D28312yes—
378C2×C4C23×D28312yes—
379C2×C4C23×D28312yes—
380C22—22no—
381C22—22no—
382C22—22no—
383C22—44no—
384C22—2834no—
385C22—5662no—
386C22—5662no—
387C22—5668no—
388C22—5662no—
389C22—5662no—
390C22—5662no—
391C22—11324no—
392C22#41×D28312yes—
393C22#2258365512yes—
394C22#2258365812yes—
395C22C24×D28311yescharacteristic
396C4—22no—
397C4—22no—
398C4—22no—
399C4—22no—
400C4—22no—
401C4—22no—
402C4—5662no—
403C4—5662no—
404C4—5662no—
405C4—5662no—
406C4—5662no—
407C4—5662no—
408C2—42no—
409C2—5664no—
410C2—11322no—
411C2#3182706114yesdirect product factor
412C2C2×#41×D28311yescharacteristic
413C2C2×#2258365511yescharacteristic
414C2C2×#2258365811yescharacteristic
subgroupG/H
centerC23C23×D283
commutator, cosocleC22×C283C25
FrattiniC22C24×D283
FittingC2×C22⋊Q8×C283C2
socleC23×C283C24
prime radicalC2×#22583583C2
hypercenterC2×C22⋊Q8D283
hypocenterC283C2×#539
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #31827061C2direct (N × H)
2. C2×#22583605C2semidirect
3. C2×#22583603C2semidirect
4. C2×#22583600C2semidirect
5. C2×#22583600C2semidirect
6. C2×#22583595C2semidirect
7. C2×#22583593C2semidirect
8. C2×#22583592C2semidirect
9. C2×#22583592C2semidirect
10. C2×#22583586C2semidirect
11. C2×#22583586C2semidirect
13. C2×#22583572C2semidirect
14. C2×C4×C22⋊D283C2semidirect
15. C2×C4⋊C4×D283C2semidirect
16. C2×C22⋊Q8×C283C2semidirect
24. #22583605C22semidirect
25. #22583603C22semidirect
26. #22583600C22semidirect
27. #22583600C22semidirect
28. #22583595C22semidirect
29. #22583593C22semidirect
30. #22583592C22semidirect
31. #22583592C22semidirect
32. #22583586C22semidirect
33. #22583586C22semidirect
35. #22583572C22semidirect
36. C4×C22⋊D283C22semidirect
48. C4⋊C4×D283C22semidirect
61. C22⋊Q8×C283C22semidirect
201. C2×C283#539semidirect
207. C283C2×#539semidirect
220. C2×C22⋊Q8D283semidirect
244. C22⋊Q8C2×D283semidirect
411. C2#31827061direct (N × H)

Maximal subgroups

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

subgroupindex
#318270612
C2×#225836052
C2×#225836032
C2×#225836002
C2×#225835952
C2×#225835932
C2×#225835922
C2×#225835862
C2×#225835832
C2×#225835722
C2×C4×C22⋊D2832
C2×C4⋊C4×D2832
C2×C22⋊Q8×C2832
C2×#539283