Finite Group Databasebeta

← C2×#13074256 #14924541

Subgroups — C2×#13074256 #14924541

Order 2816.

2594 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic22C211yesmaximal, characteristic, complemented
2#13074256C2116yesmaximal, direct product factor
3C2×#10622599C211yesmaximal, characteristic, complemented
4C2×#10622562C211yesmaximal, characteristic
5C2×#10622592C211yesmaximal, characteristic, complemented
6C2×#10622560C211yesmaximal, characteristic
7C2×#10622585C212yesmaximal, complemented
8C2×#10622558C212yesmaximal
9C2×#10622557C212yesmaximal
10C2×#10622591C212yesmaximal, complemented
11C2×#10622545C211yesmaximal, characteristic, complemented
12C22×C11×#126C211yesmaximal, characteristic
13C23×Dic22C2211yescharacteristic
14C2×C11×#126—28no—
15C2×C11×#126C2218yes—
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C42×C11C2211yescharacteristic
23C22×C22⋊Dic11C2212yes—
24C22×C22⋊Dic11C2212yes—
25C22×C4⋊Dic11C2211yescharacteristic
26C22×Dic11⋊C4C2212yes—
27C22×Dic11⋊C4C2212yes—
28C22×Dic11⋊C4C2212yes—
29C22×C4×Dic11C2212yes—
30C22×C4×Dic11C2212yes—
31C2×C4×Dic22—28no—
32C2×C4×Dic22C2218yescomplemented
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2211yescharacteristic
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40#10622599C2218yescomplemented
41#10622592C2218yescomplemented
42#10622591C22116yescomplemented
43#10622585C22116yescomplemented
44#10622562C2218yes—
45#10622560C2218yes—
46#10622558C22116yes—
47#10622557C22116yes—
48#10622545C2218yescomplemented
49C25×C11C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×Dic11C2312yes—
57C23×Dic11C2312yes—
58C23×Dic11C2312yes—
59C23×Dic11C2312yes—
60C22×Dic22—24no—
61C22×Dic22—28no—
62C22×Dic22C2314yes—
63C11×#126—232no—
64C2×C11×C4⋊C4—24no—
65C2×C11×C4⋊C4—24no—
66C2×C11×C4⋊C4—24no—
67C2×C11×C4⋊C4C2314yes—
68C2×C11×C4⋊C4C2314yes—
69C2×C11×C4⋊C4C2314yes—
70C2×C11×C22⋊C4—24no—
71C2×C11×C22⋊C4—24no—
72C2×C11×C22⋊C4—24no—
73C2×C11×C22⋊C4C2314yes—
74C2×C11×C22⋊C4C2314yes—
75C2×C11×C22⋊C4C2314yes—
76C2×C42×C11D418yes—
77C2×C42×C11C2314yes—
78C2×C22⋊Dic11—28no—
79C2×C22⋊Dic11—28no—
80C2×C22⋊Dic11C2318yes—
81C2×C22⋊Dic11C2318yes—
82C2×C4⋊Dic11—24no—
83C2×C4⋊Dic11C2314yes—
84C2×Dic11⋊C4—28no—
85C2×Dic11⋊C4—28no—
86C2×Dic11⋊C4—28no—
87C2×Dic11⋊C4C2318yes—
88C2×Dic11⋊C4C2318yes—
89C2×Dic11⋊C4C2318yes—
90C2×C4×Dic11—28no—
91C2×C4×Dic11—28no—
92C2×C4×Dic11C2318yes—
93C2×C4×Dic11C2318yes—
94C4×Dic22—232no—
95C11⋊#95C2318yes—
96C11⋊#95C2314yes—
97C11⋊#95C2314yes—
98C11⋊#95C2318yes—
99C11⋊#95C2318yes—
100C11⋊#95C2318yes—
101C11⋊#95C2318yes—
102C2×#2604—111nomaximal, Sylow
103C24×C11—22no—
104C24×C11—24no—
105C24×C11—24no—
106C24×C11—22no—
107C24×C11—22no—
108C24×C11C2412yes—
109C24×C11C2411yescharacteristic
110C22×C4×C11—24no—
111C22×C4×C11—24no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—24no—
118C22×C4×C11—24no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11C2×D414yes—
122C22×C4×C11C2×D414yes—
123C22×C4×C11C2×D414yes—
124C22×C4×C11C2412yes—
125C22×C4×C11C2412yes—
126C22×C4×C11C2412yes—
127C22×C4×C11C2412yes—
128C22×C4×C11C2412yes—
129C22×C4×C11C2412yes—
130C22×Dic11—24no—
131C22×Dic11—24no—
132C22×Dic11—24no—
133C22×Dic11—24no—
134C22×Dic11—24no—
135C22×Dic11—24no—
136C22×Dic11—24no—
137C22×Dic11—24no—
138C22×Dic11—24no—
139C22×Dic11—24no—
140C22×Dic11#4118yes—
141C22×Dic11#4118yes—
142C22×Dic11C2414yes—
143C22×Dic11C2414yes—
144C22×Dic11C2414yes—
145C22×Dic11C2414yes—
146C2×Dic22—232no—
147C2×Dic22—216no—
148C2×Dic22—28no—
149C11×C4⋊C4—28no—
150C11×C4⋊C4—28no—
151C11×C4⋊C4—28no—
152C11×C22⋊C4—28no—
153C11×C22⋊C4—28no—
154C11×C22⋊C4—28no—
155C42×C11C2×D4116yes—
156C22⋊Dic11—216no—
157C22⋊Dic11—216no—
158C4⋊Dic11—28no—
159Dic11⋊C4—216no—
160Dic11⋊C4—216no—
161Dic11⋊C4—216no—
162C4×Dic11—216no—
163C4×Dic11—216no—
164C22×#126D1111yescharacteristic
165C22×C4×Q8—111no—
166#2604—1116no—
167C2×#400—111no—
168C2×#399—111no—
169C2×#395—111no—
170C2×#393—111no—
171C2×#389—112no—
172C2×#388—112no—
173C2×#388—112no—
174C2×#387—112no—
175C2×#376—111no—
176C23×C11—22no—
177C23×C11—24no—
178C23×C11—24no—
179C23×C11—22no—
180C23×C11—22no—
181C23×C11—44no—
182C23×C11—44no—
183C23×C11—44no—
184C23×C11—48no—
185C23×C11—48no—
186C23×C11C22×D412yes—
187C23×C11C2×#4114yes—
188C23×C11C2×#4114yes—
189C23×C112−1+412yes—
190C23×C112−1+412yes—
191C23×C11C2511yescharacteristic
192C2×C4×C11—28no—
193C2×C4×C11—28no—
194C2×C4×C11—28no—
195C2×C4×C11—24no—
196C2×C4×C11—24no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—24no—
203C2×C4×C11—24no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—44no—
207C2×C4×C11—44no—
208C2×C4×C11—44no—
209C2×C4×C11C22×D414yes—
210C2×C4×C11C22×D414yes—
211C2×C4×C11C22×D414yes—
212C2×Dic11—216no—
213C2×Dic11—216no—
214C2×Dic11—24no—
215C2×Dic11—24no—
216C2×Dic11—24no—
217C2×Dic11—24no—
218C2×Dic11—24no—
219C2×Dic11—24no—
220C2×Dic11—24no—
221C2×Dic11—24no—
222C2×Dic11—24no—
223C2×Dic11—24no—
224C2×Dic11—48no—
225C2×Dic11—48no—
226C2×Dic11C2×#4118yes—
227C2×Dic11C2×#4118yes—
228Dic22—232no—
229C23×Q8—111no—
230C2×#126—28no—
231C2×#126C2×D1118yes—
232C2×C4×Q8—118no—
233C2×C4×Q8—228no—
234C22×C4⋊C4—112no—
235C22×C4⋊C4—112no—
236C22×C4⋊C4—112no—
237C22×C4⋊C4—111no—
238C22×C4⋊C4C2×D1111yescharacteristic
239C22×C4⋊C4C2×D1111yescharacteristic
240C22×C4⋊C4C2×D1111yescharacteristic
241C22×C22⋊C4—112no—
242C22×C22⋊C4—112no—
243C22×C22⋊C4C2×D1111yescharacteristic
244C22×C22⋊C4C2×D1111yescharacteristic
245C22×C22⋊C4C2×D1111yescharacteristic
246C22×C42—112no—
247C22×C42—112no—
248C22×C42C2×D1111yescharacteristic
249#400—118no—
250#399—118no—
251#395—118no—
252#393—118no—
253#389—1116no—
254#388—1116no—
255#388—1116no—
256#387—1116no—
257#376—118no—
258C2×#95—111no—
259C2×#95—112no—
260C2×#95—111no—
261C2×#95—112no—
262C2×#95—112no—
263C2×#95—112no—
264C2×#95—112no—
265C22×C11—42no—
266C22×C11—42no—
267C22×C11—42no—
268C22×C11—44no—
269C22×C11—44no—
270C22×C11—88no—
271C22×C11#52514yes—
272C22×C11#53214yes—
273C22×C11#53614yes—
274C22×C11#55218yes—
275C22×C11#55618yes—
276C22×C11C23×D411yescharacteristic
277C22×C11C22×#4112yes—
278C22×C11C22×#4112yes—
279C22×C11C2×2−1+411yescharacteristic
280C22×C11C2×2−1+411yescharacteristic
281C4×C11—24no—
282C4×C11—24no—
283C4×C11—24no—
284C4×C11—42no—
285C4×C11—42no—
286C4×C11—42no—
287Dic11—28no—
288Dic11—28no—
289Dic11—44no—
290Dic11—44no—
291C25C22×D1111yescharacteristic
292C22×Q8—114no—
293C22×Q8—228no—
294C22×Q8—224no—
295C23×C4—112no—
296C23×C4—112no—
297C23×C4—112no—
298C23×C4—112no—
299C23×C4C22×D1111yescharacteristic
300C23×C4C22×D1111yescharacteristic
301C23×C4C22×D1111yescharacteristic
302C23×C4C22×D1111yescharacteristic
303C23×C4C22×D1111yescharacteristic
304C23×C4C22×D1111yescharacteristic
305#126—232no—
306C4×Q8—2232no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—118no—
311C2×C4⋊C4—114no—
312C2×C4⋊C4—118no—
313C2×C4⋊C4—118no—
314C2×C4⋊C4—228no—
315C2×C4⋊C4—228no—
316C2×C4⋊C4—228no—
317C2×C4⋊C4—224no—
318C2×C4⋊C4C22×D1114yes—
319C2×C4⋊C4C22×D1114yes—
320C2×C4⋊C4C22×D1114yes—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—118no—
325C2×C22⋊C4—118no—
326C2×C22⋊C4—228no—
327C2×C22⋊C4—228no—
328C2×C22⋊C4C22×D1114yes—
329C2×C22⋊C4C22×D1114yes—
330C2×C22⋊C4C22×D1114yes—
331C2×C42—118no—
332C2×C42—118no—
333C2×C42—228no—
334C2×C42—228no—
335C2×C42C22⋊D1118yes—
336C2×C42C22×D1114yes—
337#95—118no—
338#95—114no—
339#95—114no—
340#95—118no—
341#95—118no—
342#95—118no—
343#95—118no—
344C2×C11—82no—
345C2×C11#260418yescomplemented
346C2×C11C2×#52511yescharacteristic
347C2×C11C2×#53211yescharacteristic
348C2×C11C2×#53611yescharacteristic
349C2×C11C2×#55212yes—
350C2×C11C2×#55612yes—
351C24—24no—
352C24—24no—
353C24—22no—
354C24—22no—
355C24—22no—
356C24C23×D1112yes—
357C24C23×D1111yescharacteristic
358C2×Q8—2216no—
359C2×Q8—2232no—
360C2×Q8—228no—
361C22×C4—24no—
362C22×C4—24no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—24no—
366C22×C4—24no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—118no—
373C22×C4—118no—
374C22×C4—114no—
375C22×C4—114no—
376C22×C4—114no—
377C22×C4—114no—
378C22×C4—224no—
379C22×C4—224no—
380C22×C4—224no—
381C22×C4—224no—
382C22×C4—224no—
383C22×C4—224no—
384C22×C4—224no—
385C22×C4—224no—
386C22×C4—224no—
387C22×C4—224no—
388C22×C4C2×C22⋊D1114yes—
389C22×C4C2×C22⋊D1114yes—
390C22×C4C2×C22⋊D1114yes—
391C22×C4C23×D1112yes—
392C22×C4C23×D1112yes—
393C22×C4C23×D1112yes—
394C22×C4C23×D1112yes—
395C22×C4C23×D1112yes—
396C22×C4C23×D1112yes—
397C4⋊C4—28no—
398C4⋊C4—28no—
399C4⋊C4—28no—
400C4⋊C4—2216no—
401C4⋊C4—2216no—
402C4⋊C4—2216no—
403C4⋊C4—228no—
404C22⋊C4—28no—
405C22⋊C4—28no—
406C22⋊C4—28no—
407C22⋊C4—2216no—
408C22⋊C4—2216no—
409C42—2216no—
410C42—2216no—
411C42C2×C22⋊D11116yes—
412C11C2×#260411yescharacteristic, complemented, Sylow
413C23—24no—
414C23—24no—
415C23—22no—
416C23—22no—
417C23—22no—
418C23—48no—
419C23—48no—
420C23—44no—
421C23—44no—
422C23—44no—
423C23#41×D1114yes—
424C23#41×D1114yes—
425C23#6704312yes—
426C23#6704312yes—
427C23C22×C22⋊D1112yes—
428C23C24×D1111yescharacteristic
429Q8—2232no—
430C2×C4—28no—
431C2×C4—28no—
432C2×C4—28no—
433C2×C4—24no—
434C2×C4—24no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—44no—
445C2×C4—44no—
446C2×C4—44no—
447C2×C4—118no—
448C2×C4—118no—
449C2×C4—2216no—
450C2×C4—2216no—
451C2×C4—224no—
452C2×C4—224no—
453C2×C4—224no—
454C2×C4—224no—
455C2×C4—224no—
456C2×C4—224no—
457C2×C4—224no—
458C2×C4—224no—
459C2×C4—224no—
460C2×C4—224no—
461C2×C4—448no—
462C2×C4—448no—
463C2×C4C22×C22⋊D1114yes—
464C2×C4C22×C22⋊D1114yes—
465C2×C4C22×C22⋊D1114yes—
466C22—44no—
467C22—42no—
468C22—44no—
469C22—42no—
470C22—42no—
471C22—88no—
472C22#1062323318yes—
473C22#1062323918yes—
474C22#1062335614yes—
475C22#1062335914yes—
476C22#1062336314yes—
477C22C2×#41×D1112yes—
478C22C2×#41×D1112yes—
479C22C2×#6704311yescharacteristic
480C22C2×#6704311yescharacteristic
481C22C23×C22⋊D1111yescharacteristic
482C4—24no—
483C4—24no—
484C4—24no—
485C4—42no—
486C4—42no—
487C4—42no—
488C4—228no—
489C4—228no—
490C4—444no—
491C4—444no—
492C2—82no—
493C2#1307425618yesdirect product factor
494C2C2×#1062335911yescharacteristic
495C2C2×#1062336311yescharacteristic
496C2C2×#1062335611yescharacteristic
497C2C2×#1062323912yes—
498C2C2×#1062323312yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#126C2
socleC24×C11C24
prime radicalC25×C11C23
hypercenterC22×#126D11
hypocenterC11C2×#2604
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#126

Complements

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

NH ≅ G/Ntype
1. C22×C4×Dic22C2semidirect
2. #13074256C2direct (N × H)
3. C2×#10622599C2semidirect
5. C2×#10622592C2semidirect
7. C2×#10622585C2semidirect
10. C2×#10622591C2semidirect
11. C2×#10622545C2semidirect
32. C2×C4×Dic22C22semidirect
40. #10622599C22semidirect
41. #10622592C22semidirect
42. #10622591C22semidirect
43. #10622585C22semidirect
48. #10622545C22semidirect
345. C2×C11#2604semidirect
412. C11C2×#2604semidirect
493. C2#13074256direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×Dic222
#130742562
C2×#106225992
C2×#106225622
C2×#106225922
C2×#106225602
C2×#106225852
C2×#106225582
C2×#106225572
C2×#106225912
C2×#106225452
C22×C11×#1262
C2×#260411