Finite Group Databasebeta

← C2×#13082238 #15660871

Subgroups — C2×#13082238 #15660871

Order 2816.

7706 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082238C2132yesmaximal, direct product factor
2C2×#10623101C211yesmaximal, characteristic, complemented
3C2×#10623073C213yesmaximal, complemented
4C2×#10623060C216yesmaximal, complemented
5C2×Q8×D44C211yesmaximal, characteristic, complemented
6C2×#10623362C212yesmaximal, complemented
7C2×#10623082C213yesmaximal, complemented
8C2×#10623001C213yesmaximal, complemented
9C2×#10623088C216yesmaximal, complemented
10C2×C4×#4339C213yesmaximal, complemented
11C2×C4×Q8×D11C212yesmaximal, complemented
12C2×C4×C11×#41C211yesmaximal, characteristic, complemented
13C22×C11×#41C2211yescharacteristic
14C22×Q8×D11C2212yes—
15C22×#4339C2213yes—
16C4×C11×#41C22116yescomplemented
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×D4×C11C2213yes—
20C2×C4×D4×C11C2213yes—
21C2×C11×#117C2213yes—
22C22×C42×C11C2213yes—
23#10623362C22132yescomplemented
24C2×Q8×Dic11C2212yes—
25C2×#66991C2216yes—
26C2×#66989C2216yes—
27C2×C4×C22⋊D11C2216yes—
28C2×C4×C22⋊D11C2216yes—
29C2×#66979C2216yes—
30C2×#66979C2213yes—
31C2×#66977C2216yes—
32C2×#66977C2216yes—
33Q8×D44C22116yescomplemented
34C4×Q8×D11C22132yescomplemented
35#10623101C22116yescomplemented
36#10623088C22196yescomplemented
37#10623082C22148yescomplemented
38#10623073C22148yescomplemented
39#10623060C22196yescomplemented
40C2×#66950C2216yes—
41C2×C4⋊C4×D11C2216yes—
42C2×#66943C2216yes—
43C2×#66940C2216yes—
44C2×#66936C22112yes—
45C2×#66932C22112yes—
46C4×#4339C22148yescomplemented
47C2×C4×D44C2211yescharacteristic
48C2×C4×D44C2213yes—
49C2×#66925C2216yes—
50C2×C42×D11C2216yes—
51#10623001C22148yescomplemented
52C2×#66923C2216yes—
53C2×#66922C2213yes—
54C2×#66922C2213yes—
55C2×C4×Dic22C2216yes—
56C2×C4×Dic22C2213yes—
57C2×C4×Dic22C2213yes—
58C2×C11×#41—28no—
59C2×C11×#41C2318yes—
60C22×Q8×C11C2311yescharacteristic
61C22×D4×C11C2313yes—
62C23×C4×C11C2313yes—
63C23×C4×C11C2313yes—
64C23×C4×C11C2313yes—
65C22×C22⋊D11C2316yes—
66C2×Q8×D11—216no—
67C2×Q8×D11C23116yes—
68C2×#4339—224no—
69C2×#4339C23124yes—
70C22×D44C2311yescharacteristic
71C22×C4×D11C2312yes—
72C22×C4×D11C2316yes—
73C22×C4×D11C2316yes—
74C22×Dic22C2313yes—
75C22×Dic22C2316yes—
76C4×Q8×C11C2318yes—
77C4×Q8×C11C2318yes—
78C4×D4×C11C23124yes—
79C4×D4×C11C23124yes—
80C11×#117C23124yes—
81C2×C11×C4⋊C4C2313yes—
82C2×C11×C4⋊C4C2313yes—
83C2×C11×C22⋊C4C2316yes—
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2313yes—
86C2×C42×C11C2313yes—
87C2×C42×C11C2313yes—
88C2×C42×C11C23124yes—
89C2×C22⋊Dic11C2316yes—
90C2×C22⋊Dic11C23112yes—
91Q8×Dic11C23116yes—
92#66991C23148yes—
93#66989C23148yes—
94C4×C22⋊D11C23148yes—
95C4×C22⋊D11C23148yes—
96C2×(C2×D11)⋊C4C2312yes—
97C2×(C2×D11)⋊C4C2316yes—
98#66979C23148yes—
99#66979C23124yes—
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2313yes—
102C2×C4⋊Dic11C2316yes—
103C2×C4⋊Dic11C2316yes—
104C2×C4⋊Dic11C2316yes—
105#66977C23148yes—
106#66977C23148yes—
107C2×Dic11⋊C4C2316yes—
108C2×Dic11⋊C4C23112yes—
109C2×Dic11⋊C4C2316yes—
110C2×C4×Dic11C2316yes—
111C2×C4×Dic11C2316yes—
112C2×C4×Dic11C2316yes—
113#66950C23148yes—
114C4⋊C4×D11C23148yes—
115#66943C23148yes—
116#66940C23148yes—
117#66936C23196yes—
118#66932C23196yes—
119C4×D44C2318yes—
120C4×D44C23124yes—
121#66925C23148yes—
122C42×D11C23148yes—
123#66923C23148yes—
124#66922C23124yes—
125#66922C23124yes—
126C4×Dic22C23124yes—
127C4×Dic22C23148yes—
128C4×Dic22C23124yes—
129C2×#3482—111nomaximal, Sylow
130C24×C11C2413yes—
131C23×D11C2412yes—
132C11×#41—232no—
133C2×Q8×C11#4118yescomplemented
134C2×Q8×C11C2414yes—
135C2×D4×C11—212no—
136C2×D4×C11C24112yes—
137C22×C4×C11—212no—
138C22×C4×C11—212no—
139C22×C4×C11—212no—
140C22×C4×C11C2413yes—
141C22×C4×C11C2411yescharacteristic
142C22×C4×C11C2413yes—
143C22×C4×C11C24112yes—
144C22×C4×C11C24112yes—
145C22×C4×C11C24112yes—
146C22×C4×C11C2413yes—
147C22×C4×C11C2411yescharacteristic
148C22×C4×C11C2411yescharacteristic
149C2×C22⋊D11—224no—
150C2×C22⋊D11C24124yes—
151C22×Dic11C2412yes—
152C22×Dic11C2416yes—
153C22×Dic11C2416yes—
154Q8×D11—264no—
155#4339—296no—
156C2×D44#4118yescomplemented
157C2×D44C2414yes—
158C2×C4×D11—224no—
159C2×C4×D11—224no—
160C2×C4×D11—28no—
161C2×C4×D11C2418yes—
162C2×C4×D11C24124yes—
163C2×C4×D11C24124yes—
164C2×Dic22—212no—
165C2×Dic22—224no—
166C2×Dic22C24112yes—
167C2×Dic22C24124yes—
168C11×C4⋊C4C24112yes—
169C11×C4⋊C4C24112yes—
170C11×C22⋊C4C24124yes—
171C42×C11C2414yes—
172C42×C11C24112yes—
173C42×C11C24112yes—
174C42×C11C24112yes—
175C22⋊Dic11C24124yes—
176C22⋊Dic11C24148yes—
177(C2×D11)⋊C4C2418yes—
178(C2×D11)⋊C4C24124yes—
179C4⋊Dic11C2414yes—
180C4⋊Dic11C24112yes—
181C4⋊Dic11C24124yes—
182C4⋊Dic11C24124yes—
183C4⋊Dic11C24124yes—
184Dic11⋊C4C24124yes—
185Dic11⋊C4C24148yes—
186Dic11⋊C4C24124yes—
187C4×Dic11C24124yes—
188C4×Dic11C24124yes—
189C4×Dic11C24124yes—
190#3482—1132no—
191C2×#557—111no—
192C2×#556—113no—
193C2×#552—116no—
194C2×D4×Q8—111no—
195C2×#548—112no—
196C2×#547—113no—
197C2×#533—113no—
198C2×#529—116no—
199C2×C4×#41—113no—
200C2×C4×#41D1111yescharacteristic, complemented
201C22×C4×Q8—112no—
202C23×C11—26no—
203C23×C11—26no—
204C23×C11—26no—
205C23×C11C2516yes—
206C23×C11C2511yescharacteristic
207C22×D11—24no—
208C22×D11—24no—
209C22×D11C2×#4118yes—
210C22×D11C2514yes—
211Q8×C11C2×#41116yescomplemented
212D4×C11—224no—
213C2×C4×C11—26no—
214C2×C4×C11—22no—
215C2×C4×C11—26no—
216C2×C4×C11—224no—
217C2×C4×C11—224no—
218C2×C4×C11—224no—
219C2×C4×C11C2×#41112yes—
220C2×C4×C11C2×#4114yes—
221C2×C4×C112−1+414yes—
222C2×C4×C11C2516yes—
223C2×C4×C11C2512yes—
224C2×C4×C11C2516yes—
225C2×C4×C11C2516yes—
226C2×C4×C11C2512yes—
227C2×C4×C11C2512yes—
228C22⋊D11—248no—
229C2×Dic11—212no—
230C2×Dic11—212no—
231C2×Dic11—24no—
232C2×Dic11C2514yes—
233C2×Dic11C25112yes—
234C2×Dic11C25112yes—
235D44C2×#41116yescomplemented
236C4×D11—248no—
237C4×D11—248no—
238C4×D11—216no—
239Dic22—224no—
240Dic22—248no—
241C22×#41—113no—
242C22×#41C2×D1111yescharacteristic
243C23×Q8—112no—
244#557—1116no—
245#556—1148no—
246#552—1196no—
247D4×Q8—1116no—
248#548—1132no—
249#547—1148no—
250#533—1148no—
251C2×C4⋊Q8—113no—
252C2×C4⋊Q8—113no—
253#529—1196no—
254C2×#126—1112no—
255C2×#125—116no—
256C2×#125—116no—
257C2×#124—116no—
258C2×#123—1112no—
259C2×C22⋊Q8—116no—
260C2×C22⋊Q8—116no—
261C2×C22⋊Q8—116no—
262C2×#121—116no—
263C4×#41—1148no—
264C4×#41C2×D11116yescomplemented
265C2×C4×Q8—112no—
266C2×C4×Q8—1132no—
267C2×C4×Q8—116no—
268C2×C4×Q8—116no—
269C2×C4×Q8—113no—
270C2×C4×Q8—113no—
271C2×C4×Q8C2×D1111yescharacteristic
272C2×C4×Q8C2×D1111yescharacteristic
273C2×C4×D4—116no—
274C2×C4×D4—116no—
275C2×C4×D4—111no—
276C2×C4×D4—113no—
277C2×C4×D4C2×D1113yes—
278C2×C4×D4C2×D1113yes—
279C2×#117—113no—
280C2×#117—116no—
281C2×#117—116no—
282C2×#117C2×D1113yes—
283C22×C4⋊C4—116no—
284C22×C42—116no—
285C22×C42C2×D1113yes—
286C22×C11—26no—
287C22×C11—26no—
288C22×C11—26no—
289C22×C11—412no—
290C22×C11C22×#4112yes—
291C22×C11C22×#4112yes—
292C22×C11C2×2−1+412yes—
293C22×C11C2611yescharacteristic
294C2×D11—24no—
295C2×D11—24no—
296C2×D11—216no—
297C2×D11C22×#4118yes—
298C4×C11—22no—
299C4×C11—26no—
300C4×C11—26no—
301C4×C11C22×#41112yes—
302C4×C11C22×#4114yes—
303C4×C11C2×2−1+414yes—
304Dic11—212no—
305Dic11—212no—
306Dic11—24no—
307C2×#41—28no—
308C2×#41—1124no—
309C2×#41—2224no—
310C2×#41C22×D1118yes—
311C22×Q8—1116no—
312C22×Q8—116no—
313C22×Q8—113no—
314C22×Q8—2216no—
315C22×Q8C22×D1111yescharacteristic
316C22×D4—116no—
317C22×D4—111no—
318C22×D4C22×D1113yes—
319C23×C4—116no—
320C23×C4—116no—
321C23×C4—112no—
322C23×C4C22×D1113yes—
323C23×C4C22×D1113yes—
324C23×C4C22×D1113yes—
325C4⋊Q8—1124no—
326C4⋊Q8—1124no—
327#126—1196no—
328#125—1148no—
329#125—1148no—
330#124—1148no—
331#123—1196no—
332C22⋊Q8—1148no—
333C22⋊Q8—1148no—
334C22⋊Q8—1148no—
335#121—1148no—
336C4×Q8—1116no—
337C4×Q8—1148no—
338C4×Q8—1148no—
339C4×Q8—1124no—
340C4×Q8—1124no—
341C4×Q8C22×D1118yes—
342C4×Q8C22×D1118yes—
343C4×D4—1148no—
344C4×D4—1148no—
345C4×D4—118no—
346C4×D4—1124no—
347C4×D4C22×D11124yes—
348C4×D4C22×D11124yes—
349#117—1124no—
350#117—1148no—
351#117—1148no—
352#117C22×D11124yes—
353C2×C4⋊C4—116no—
354C2×C4⋊C4—1112no—
355C2×C4⋊C4—111no—
356C2×C4⋊C4—116no—
357C2×C4⋊C4—113no—
358C2×C4⋊C4—116no—
359C2×C4⋊C4—116no—
360C2×C4⋊C4—116no—
361C2×C4⋊C4—1148no—
362C2×C4⋊C4C22×D1113yes—
363C2×C4⋊C4C22×D1113yes—
364C2×C22⋊C4—116no—
365C2×C22⋊C4—1112no—
366C2×C22⋊C4—112no—
367C2×C22⋊C4—116no—
368C2×C22⋊C4C22×D1116yes—
369C2×C42—116no—
370C2×C42—116no—
371C2×C42—116no—
372C2×C42—1148no—
373C2×C42C22×D1113yes—
374C2×C42C22×D1113yes—
375C2×C42C22×D11124yes—
376C2×C42C22×D1111yescharacteristic
377C2×C42C22×D1113yes—
378C2×C11—46no—
379C2×C11#348214yescomplemented
380C2×C11C23×#4111yescharacteristic
381C2×C11C23×#4111yescharacteristic
382C2×C11C22×2−1+411yescharacteristic
383D11—28no—
384C24—112no—
385C24C23×D1113yes—
386#41—232no—
387#41—2296no—
388C2×Q8—1124no—
389C2×Q8—1112no—
390C2×Q8—2264no—
391C2×Q8—2224no—
392C2×Q8—2212no—
393C2×Q8#433918yescomplemented
394C2×Q8C23×D1114yes—
395C2×D4—212no—
396C2×D4—1124no—
397C2×D4—118no—
398C2×D4—114no—
399C2×D4—2224no—
400C2×D4C23×D11112yes—
401C22×C4—212no—
402C22×C4—212no—
403C22×C4—212no—
404C22×C4—112no—
405C22×C4—116no—
406C22×C4—116no—
407C22×C4—118no—
408C22×C4—1124no—
409C22×C4—1124no—
410C22×C4—2224no—
411C22×C4—2224no—
412C22×C4—228no—
413C22×C4C23×D1113yes—
414C22×C4C23×D1111yescharacteristic
415C22×C4C23×D1113yes—
416C22×C4C23×D11112yes—
417C22×C4C23×D11112yes—
418C22×C4C23×D11112yes—
419C22×C4C23×D1113yes—
420C22×C4C23×D1111yescharacteristic
421C22×C4C23×D1111yescharacteristic
422C4⋊C4—1124no—
423C4⋊C4—1148no—
424C4⋊C4—114no—
425C4⋊C4—1124no—
426C4⋊C4—1112no—
427C4⋊C4—1124no—
428C4⋊C4—1124no—
429C4⋊C4—1124no—
430C4⋊C4C23×D11112yes—
431C4⋊C4C23×D11112yes—
432C22⋊C4—1124no—
433C22⋊C4—1148no—
434C22⋊C4—118no—
435C22⋊C4—1124no—
436C22⋊C4C23×D11124yes—
437C42—1124no—
438C42—1124no—
439C42—1124no—
440C42C23×D11112yes—
441C42C23×D1114yes—
442C42C23×D11112yes—
443C42C23×D11112yes—
444C11C2×#348211yescharacteristic, complemented, Sylow
445C23—26no—
446C23—26no—
447C23—26no—
448C23—118no—
449C23—114no—
450C23—224no—
451C23—224no—
452C23C24×D1116yes—
453C23C24×D1111yescharacteristic
454Q8—2248no—
455Q8—2224no—
456Q8C2×#4339116yescomplemented
457D4—224no—
458D4—1116no—
459D4—2248no—
460C2×C4—22no—
461C2×C4—26no—
462C2×C4—26no—
463C2×C4—224no—
464C2×C4—224no—
465C2×C4—224no—
466C2×C4—114no—
467C2×C4—1112no—
468C2×C4—1112no—
469C2×C4—2248no—
470C2×C4—2212no—
471C2×C4—2212no—
472C2×C4—224no—
473C2×C4—2248no—
474C2×C4—2216no—
475C2×C4C2×#4339112yes—
476C2×C4#41×D1114yes—
477C2×C4#6704314yes—
478C2×C4C24×D1116yes—
479C2×C4C24×D1112yes—
480C2×C4C24×D1116yes—
481C2×C4C24×D1116yes—
482C2×C4C24×D1112yes—
483C2×C4C24×D1112yes—
484C22—26no—
485C22—26no—
486C22—26no—
487C22—412no—
488C22—118no—
489C22—224no—
490C22—224no—
491C22—2216no—
492C22C22×#433912yes—
493C22C2×#41×D1112yes—
494C22C2×#6704312yes—
495C22C25×D1111yescharacteristic
496C4—26no—
497C4—22no—
498C4—26no—
499C4—2212no—
500C4—2212no—
501C4—224no—
502C4C22×#4339112yes—
503C4C2×#41×D1114yes—
504C4C2×#6704314yes—
505C2—46no—
506C2—228no—
507C2#1308223814yesdirect product factor
508C2C22×#41×D1111yescharacteristic
509C2C23×#433911yescharacteristic
510C2C22×#6704311yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C4×C11×#41C2
socleC23×C11C25
hypercenterC2×C4×#41D11
hypocenterC11C2×#3482
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #13082238C2direct (N × H)
2. C2×#10623101C2semidirect
3. C2×#10623073C2semidirect
4. C2×#10623060C2semidirect
5. C2×Q8×D44C2semidirect
6. C2×#10623362C2semidirect
7. C2×#10623082C2semidirect
8. C2×#10623001C2semidirect
9. C2×#10623088C2semidirect
10. C2×C4×#4339C2semidirect
11. C2×C4×Q8×D11C2semidirect
12. C2×C4×C11×#41C2semidirect
16. C4×C11×#41C22semidirect
23. #10623362C22semidirect
33. Q8×D44C22semidirect
34. C4×Q8×D11C22semidirect
35. #10623101C22semidirect
36. #10623088C22semidirect
37. #10623082C22semidirect
38. #10623073C22semidirect
39. #10623060C22semidirect
46. C4×#4339C22semidirect
51. #10623001C22semidirect
133. C2×Q8×C11#41semidirect
156. C2×D44#41semidirect
200. C2×C4×#41D11semidirect
211. Q8×C11C2×#41semidirect
235. D44C2×#41semidirect
264. C4×#41C2×D11semidirect
379. C2×C11#3482semidirect
393. C2×Q8#4339semidirect
444. C11C2×#3482semidirect
456. Q8C2×#4339semidirect
507. C2#13082238direct (N × H)

Maximal subgroups

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

subgroupindex
#130822382
C2×#106231012
C2×#106230732
C2×#106230602
C2×Q8×D442
C2×#106233622
C2×#106230822
C2×#106230012
C2×#106230882
C2×C4×#43392
C2×C4×Q8×D112
C2×C4×C11×#412
C2×#348211