Finite Group Databasebeta

← C2×#31827212 #49135387

Subgroups — C2×#31827212 #49135387

Order 36224.

1152 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827212C2116yesmaximal, direct product factor
2C2×#22583601C211yesmaximal, characteristic, complemented
3C2×#22583596C211yesmaximal, characteristic, complemented
4C2×#22583596C211yesmaximal, characteristic, complemented
5C2×#22583595C211yesmaximal, characteristic, complemented
6C2×#22583594C211yesmaximal, characteristic, complemented
7C2×#22583592C211yesmaximal, characteristic, complemented
8C2×#22583590C211yesmaximal, characteristic, complemented
9C2×#22583589C211yesmaximal, characteristic, complemented
10C2×#22583588C211yesmaximal, characteristic, complemented
11C2×#22583587C211yesmaximal, characteristic, complemented
12C2×#22583584C211yesmaximal, characteristic, complemented
13C2×#22583583C211yesmaximal, characteristic, complemented
14C2×#22583582C211yesmaximal, characteristic, complemented
15C2×#22583581C211yesmaximal, characteristic, complemented
16C2×#123×C283C211yesmaximal, characteristic, complemented
17C22×Dic566C2211yescharacteristic
18C22×Dic566C2211yescharacteristic
19C22×D1132C2211yescharacteristic
20C22×C22⋊D283C2211yescharacteristic
21C22×C22⋊D283C2211yescharacteristic
22C22×C22⋊D283C2211yescharacteristic
23C22×C22⋊D283C2211yescharacteristic
24C23×Dic283C2211yescharacteristic
25C22×C4×D283C2211yescharacteristic
26C22×C4×D283C2211yescharacteristic
27#22583601C2218yescomplemented
28#22583596C2218yescomplemented
29#22583596C2218yescomplemented
30#22583595C2218yescomplemented
31#22583594C2218yescomplemented
32#22583592C2218yescomplemented
33#22583590C2218yescomplemented
34#22583589C2218yescomplemented
35#22583588C2218yescomplemented
36#22583587C2218yescomplemented
37#22583584C2218yescomplemented
38#22583583C2218yescomplemented
39#22583582C2218yescomplemented
40#22583581C2218yescomplemented
41C2×C4⋊Dic283C2211yescharacteristic
42C2×C4⋊Dic283C2211yescharacteristic
43C2×C4⋊Dic283C2211yescharacteristic
44C2×C4⋊Dic283C2211yescharacteristic
45C2×Dic283⋊C4C2211yescharacteristic
46C2×Dic283⋊C4C2211yescharacteristic
47C2×Dic283⋊C4C2211yescharacteristic
48C2×Dic283⋊C4C2211yescharacteristic
49C2×C22⋊Dic283C2211yescharacteristic
50C2×C22⋊Dic283C2211yescharacteristic
51C2×C22⋊Dic283C2211yescharacteristic
52C2×(C2×D283)⋊C4C2211yescharacteristic
53C2×(C2×D283)⋊C4C2211yescharacteristic
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
61#123×C283C2218yescomplemented
62C2×C4⋊C4×C283C2211yescharacteristic
63C2×C4⋊C4×C283C2211yescharacteristic
64C2×C22⋊C4×C283C2211yescharacteristic
65C2×C22⋊C4×C283C2211yescharacteristic
66C2×C22⋊C4×C283C2211yescharacteristic
67C23×D283C2311yescharacteristic
68C23×D283C2311yescharacteristic
69C2×Dic566—42no—
70C2×Dic566—42no—
71C2×Dic566C2314yes—
72C2×Dic566C2314yes—
73C2×D1132—42no—
74C2×D1132C2314yes—
75C2×C22⋊D283—42no—
76C2×C22⋊D283—42no—
77C2×C22⋊D283—42no—
78C2×C22⋊D283—42no—
79C2×C22⋊D283C2314yes—
80C2×C22⋊D283C2314yes—
81C2×C22⋊D283C2314yes—
82C2×C22⋊D283C2314yes—
83C22×Dic283—42no—
84C22×Dic283C2311yescharacteristic
85C22×Dic283C2311yescharacteristic
86C22×Dic283C2311yescharacteristic
87C22×Dic283C2311yescharacteristic
88C22×Dic283C2311yescharacteristic
89C22×Dic283C2311yescharacteristic
90C22×Dic283C2314yes—
91C2×C4×D283—42no—
92C2×C4×D283—42no—
93C2×C4×D283C2314yes—
94C2×C4×D283C2314yes—
95C4⋊Dic283C2314yes—
96C4⋊Dic283C2314yes—
97C4⋊Dic283C2314yes—
98C4⋊Dic283C2314yes—
99Dic283⋊C4C2314yes—
100Dic283⋊C4C2314yes—
101Dic283⋊C4C2314yes—
102Dic283⋊C4C2314yes—
103C22⋊Dic283C2314yes—
104C22⋊Dic283C2314yes—
105C22⋊Dic283C2314yes—
106(C2×D283)⋊C4C2314yes—
107(C2×D283)⋊C4C2314yes—
108(C2×D283)⋊C4C2314yes—
109(C2×D283)⋊C4C2314yes—
110(C2×D283)⋊C4C2314yes—
111(C2×D283)⋊C4C2314yes—
112C4×Dic283C2314yes—
113C24×C283C2311yescharacteristic
114C24×C283C2311yescharacteristic
115C2×D4×C283—42no—
116C2×D4×C283C2314yes—
117C22×C4×C283—42no—
118C22×C4×C283C2311yescharacteristic
119C22×C4×C283C2311yescharacteristic
120C22×C4×C283C2311yescharacteristic
121C22×C4×C283C2311yescharacteristic
122C22×C4×C283C2311yescharacteristic
123C22×C4×C283C2314yes—
124C4⋊C4×C283C2314yes—
125C4⋊C4×C283C2314yes—
126C22⋊C4×C283C2314yes—
127C22⋊C4×C283C2314yes—
128C22⋊C4×C283C2314yes—
129C22×D283—22no—
130C22×D283—22no—
131C22×D283—22no—
132C22×D283—22no—
133C22×D283—22no—
134C22×D283—22no—
135C22×D283C2412yes—
136C22×D283C2412yes—
137Dic566—44no—
138Dic566—44no—
139D1132—44no—
140C22⋊D283—44no—
141C22⋊D283—44no—
142C22⋊D283—44no—
143C22⋊D283—44no—
144C2×Dic283—22no—
145C2×Dic283—22no—
146C2×Dic283—22no—
147C2×Dic283—22no—
148C2×Dic283—22no—
149C2×Dic283—22no—
150C2×Dic283—44no—
151C2×Dic283C2412yes—
152C2×Dic283C2412yes—
153C2×Dic283C2412yes—
154C2×Dic283C2412yes—
155C2×Dic283C2412yes—
156C2×Dic283C2412yes—
157C4×D283—44no—
158C4×D283—44no—
159C23×C283—22no—
160C23×C283—22no—
161C23×C283—22no—
162C23×C283—22no—
163C23×C283—22no—
164C23×C283—22no—
165C23×C283C2412yes—
166C23×C283C2412yes—
167C23×C283C2411yescharacteristic
168D4×C283—44no—
169C2×C4×C283—22no—
170C2×C4×C283—22no—
171C2×C4×C283—22no—
172C2×C4×C283—22no—
173C2×C4×C283—22no—
174C2×C4×C283—44no—
175C2×C4×C283C2412yes—
176C2×C4×C283C2412yes—
177C2×C4×C283C2412yes—
178C2×C4×C283C2412yes—
179C2×C4×C283C2412yes—
180C22×C283—22no—
181C22×C283—22no—
182C22×C283—22no—
183C22×C283—22no—
184C22×C283—22no—
185C22×C283—22no—
186C22×C283—44no—
187C22×C283—44no—
188C22×C283H(5,𝔽2)12yes—
189C22×C283H(5,𝔽2)12yes—
190C22×C2832−1+412yes—
191C22×C283C2511yescharacteristic
192C2×D283—22no—
193C2×D283—22no—
194C2×D283—22no—
195C2×D283—22no—
196C2×D283—22no—
197C2×D283—22no—
198C2×D283—44no—
199C2×D283—44no—
200C4×C283—22no—
201C4×C283—22no—
202C4×C283—22no—
203C4×C283—22no—
204C4×C283—22no—
205Dic283—22no—
206Dic283—22no—
207Dic283—22no—
208Dic283—22no—
209Dic283—22no—
210Dic283—22no—
211C2×C283—42no—
212C2×C283—42no—
213C2×C283#56214yescomplemented
214C2×C283C2×H(5,𝔽2)11yescharacteristic
215C2×C283C2×H(5,𝔽2)11yescharacteristic
216C2×C283C2×2−1+411yescharacteristic
217D283—42no—
218D283—42no—
219C283C2×#56211yescharacteristic, complemented, Sylow
220C2×#562—2831nomaximal, Sylow
221#562—28316no—
222C2×#125—2831no—
223C2×#124—2831no—
224C2×#124—2831no—
225C2×#123—2831no—
226C2×#123—2831no—
227C2×#123—2831no—
228C2×#123D28311yescharacteristic, complemented
229C2×C22⋊Q8—2831no—
230C2×C22⋊Q8—2831no—
231C2×C22⋊Q8—2831no—
232C2×C22⋊Q8—2831no—
233C2×#121—2831no—
234C2×#121—2831no—
235C2×#121—2831no—
236C2×#121—2831no—
237C22×Q8—2831no—
238C22×Q8—2831no—
239C22×D4—2831no—
240C22×D4—2831no—
241C22×D4—2831no—
242C22×D4—2831no—
243C22×D4—2831no—
244C22×D4C2×D28311yescharacteristic
245C23×C4—2831no—
246C23×C4—2831no—
247C23×C4—2831no—
248C23×C4C2×D28311yescharacteristic
249#125—2838no—
250#124—2838no—
251#124—2838no—
252#123—2838no—
253#123—2838no—
254#123—2838no—
255#123C2×D28318yescomplemented
256C22⋊Q8—2838no—
257C22⋊Q8—2838no—
258C22⋊Q8—2838no—
259C22⋊Q8—2838no—
260#121—2838no—
261#121—2838no—
262#121—2838no—
263#121—2838no—
264C2×C4⋊C4—2831no—
265C2×C4⋊C4—2831no—
266C2×C4⋊C4—2831no—
267C2×C4⋊C4—2831no—
268C2×C4⋊C4—2831no—
269C2×C4⋊C4—2831no—
270C2×C4⋊C4—2831no—
271C2×C4⋊C4—2831no—
272C2×C4⋊C4C2×D28311yescharacteristic
273C2×C4⋊C4C2×D28311yescharacteristic
274C2×C22⋊C4—2831no—
275C2×C22⋊C4—2831no—
276C2×C22⋊C4—2831no—
277C2×C22⋊C4—2831no—
278C2×C22⋊C4—2831no—
279C2×C22⋊C4—2831no—
280C2×C22⋊C4—2831no—
281C2×C22⋊C4—2831no—
282C2×C22⋊C4—2831no—
283C2×C22⋊C4C2×D28311yescharacteristic
284C2×C22⋊C4C2×D28311yescharacteristic
285C2×C22⋊C4C2×D28311yescharacteristic
286C2×C42—2831no—
287C24—2831no—
288C24—2831no—
289C24C22×D28311yescharacteristic
290C24C22×D28311yescharacteristic
291C2×Q8—2834no—
292C2×Q8—2834no—
293C2×Q8—11322no—
294C2×Q8—11322no—
295C2×D4—42no—
296C2×D4—2834no—
297C2×D4—2834no—
298C2×D4—2834no—
299C2×D4—2834no—
300C2×D4—2834no—
301C2×D4—11322no—
302C2×D4—11322no—
303C2×D4—11322no—
304C2×D4—11322no—
305C2×D4—11322no—
306C2×D4C22×D28314yes—
307C22×C4—42no—
308C22×C4—2831no—
309C22×C4—2831no—
310C22×C4—2831no—
311C22×C4—2831no—
312C22×C4—2831no—
313C22×C4—2831no—
314C22×C4—2834no—
315C22×C4—2834no—
316C22×C4—2834no—
317C22×C4—11322no—
318C22×C4—11322no—
319C22×C4—11322no—
320C22×C4C22×D28311yescharacteristic
321C22×C4C22×D28311yescharacteristic
322C22×C4C22×D28311yescharacteristic
323C22×C4C22×D28311yescharacteristic
324C22×C4C22×D28311yescharacteristic
325C22×C4C22×D28314yes—
326C4⋊C4—2834no—
327C4⋊C4—2834no—
328C4⋊C4—2834no—
329C4⋊C4—2834no—
330C4⋊C4—2834no—
331C4⋊C4—2834no—
332C4⋊C4—2834no—
333C4⋊C4—2834no—
334C4⋊C4C22×D28314yes—
335C4⋊C4C22×D28314yes—
336C22⋊C4—2834no—
337C22⋊C4—2834no—
338C22⋊C4—2834no—
339C22⋊C4—2834no—
340C22⋊C4—2834no—
341C22⋊C4—2834no—
342C22⋊C4—2834no—
343C22⋊C4—2834no—
344C22⋊C4—2834no—
345C22⋊C4C22×D28314yes—
346C22⋊C4C22×D28314yes—
347C22⋊C4C22×D28314yes—
348C42—2834no—
349C23—22no—
350C23—22no—
351C23—22no—
352C23—22no—
353C23—22no—
354C23—22no—
355C23—2832no—
356C23—2832no—
357C23—5662no—
358C23—5662no—
359C23—5662no—
360C23—5662no—
361C23—5662no—
362C23—5662no—
363C23C23×D28312yes—
364C23C23×D28312yes—
365C23C23×D28311yescharacteristic
366Q8—11324no—
367Q8—11324no—
368D4—44no—
369D4—11324no—
370D4—11324no—
371D4—11324no—
372D4—11324no—
373D4—11324no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—44no—
380C2×C4—2832no—
381C2×C4—2832no—
382C2×C4—2832no—
383C2×C4—2832no—
384C2×C4—2832no—
385C2×C4—2832no—
386C2×C4—5662no—
387C2×C4—5662no—
388C2×C4—5662no—
389C2×C4—5662no—
390C2×C4—5662no—
391C2×C4—5662no—
392C2×C4—11324no—
393C2×C4—11324no—
394C2×C4—11324no—
395C2×C4C23×D28312yes—
396C2×C4C23×D28312yes—
397C2×C4C23×D28312yes—
398C2×C4C23×D28312yes—
399C2×C4C23×D28312yes—
400C22—22no—
401C22—22no—
402C22—22no—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—44no—
407C22—44no—
408C22—5662no—
409C22—5662no—
410C22—5662no—
411C22—5662no—
412C22—5662no—
413C22—5662no—
414C22—11324no—
415C22—11324no—
416C22#2258365512yes—
417C22#2258365612yes—
418C22#2258365712yes—
419C22C24×D28311yescharacteristic
420C4—22no—
421C4—22no—
422C4—22no—
423C4—22no—
424C4—22no—
425C4—5662no—
426C4—5662no—
427C4—5662no—
428C4—5662no—
429C4—5662no—
430C4—5662no—
431C2—42no—
432C2—42no—
433C2—11322no—
434C2—11322no—
435C2#3182721214yesdirect product factor
436C2C2×#2258365511yescharacteristic
437C2C2×#2258365611yescharacteristic
438C2C2×#2258365711yescharacteristic
subgroupG/H
centerC23C23×D283
commutator, cosocleC22×C283C25
FrattiniC22C24×D283
FittingC2×#123×C283C2
socleC23×C283C24
hypercenterC2×#123D283
hypocenterC283C2×#562
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. #31827212C2direct (N × H)
2. C2×#22583601C2semidirect
3. C2×#22583596C2semidirect
4. C2×#22583596C2semidirect
5. C2×#22583595C2semidirect
6. C2×#22583594C2semidirect
7. C2×#22583592C2semidirect
8. C2×#22583590C2semidirect
9. C2×#22583589C2semidirect
10. C2×#22583588C2semidirect
11. C2×#22583587C2semidirect
12. C2×#22583584C2semidirect
13. C2×#22583583C2semidirect
14. C2×#22583582C2semidirect
15. C2×#22583581C2semidirect
16. C2×#123×C283C2semidirect
27. #22583601C22semidirect
28. #22583596C22semidirect
29. #22583596C22semidirect
30. #22583595C22semidirect
31. #22583594C22semidirect
32. #22583592C22semidirect
33. #22583590C22semidirect
34. #22583589C22semidirect
35. #22583588C22semidirect
36. #22583587C22semidirect
37. #22583584C22semidirect
38. #22583583C22semidirect
39. #22583582C22semidirect
40. #22583581C22semidirect
61. #123×C283C22semidirect
213. C2×C283#562semidirect
219. C283C2×#562semidirect
228. C2×#123D283semidirect
255. #123C2×D283semidirect
435. C2#31827212direct (N × H)

Maximal subgroups

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

subgroupindex
#318272122
C2×#225836012
C2×#225835962
C2×#225835952
C2×#225835942
C2×#225835922
C2×#225835902
C2×#225835892
C2×#225835882
C2×#225835872
C2×#225835842
C2×#225835832
C2×#225835822
C2×#225835812
C2×#123×C2832
C2×#562283