Finite Group Databasebeta

← C2×#13079597 #15624998

Subgroups — C2×#13079597 #15624998

Order 2816.

2218 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623256C211yesmaximal, characteristic, complemented
2C2×#10623111C211yesmaximal, characteristic, complemented
3#13079597C2116yesmaximal, direct product factor
4C2×#10622804C212yesmaximal, complemented
5C2×#10622413C212yesmaximal, complemented
6C2×#10622640C211yesmaximal, characteristic, complemented
7C2×#10622696C211yesmaximal, characteristic, complemented
8C2×#10622456C211yesmaximal, characteristic, complemented
9C2×#10622800C212yesmaximal, complemented
10C2×#10622424C212yesmaximal, complemented
11C2×#10622446C211yesmaximal, characteristic, complemented
12C2×C11×#462C211yesmaximal, characteristic, complemented
13C22×#4343C2212yes—
14C22×C11×Q16C2212yes—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C4×Q8×C11C2211yescharacteristic
17C2×#67000C2211yescharacteristic
18C2×#67000C2212yes—
19C2×#66999C2211yescharacteristic
20C22×#4325C2212yes—
21C22×#4325C2212yes—
22C22×D88C2212yes—
23#10623256—24no—
24#10623256C2218yescomplemented
25#10623111—24no—
26#10623111C2218yescomplemented
27C2×#66951—21no—
28C2×#66948—21no—
29C2×#66948—21no—
30C2×#66948C2211yescharacteristic
31C2×#66947—21no—
32C2×#66946—21no—
33C2×#66946—21no—
34C2×#66943C2211yescharacteristic
35C2×#66927C2211yescharacteristic
36C2×C4×D44—21no—
37C2×C4×D44C2211yescharacteristic
38C2×#66925—21no—
39C2×C42×D11C2211yescharacteristic
40C11×#462C2218yescomplemented
41C2×C11×C4⋊C8C2211yescharacteristic
42C2×C11×#103C2212yes—
43C2×#66899C2212yes—
44#10622804C22116yescomplemented
45#10622800C22116yescomplemented
46C2×#66885C2212yes—
47C2×(C2×D11)⋊C8C2212yes—
48C2×C8×Dic11C2212yes—
49#10622696C2218yescomplemented
50#10622640C2218yescomplemented
51C2×#66873C2212yes—
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53#10622456C2218yescomplemented
54#10622446C2218yescomplemented
55#10622424C22116yescomplemented
56#10622413C22116yescomplemented
57C22×Q8×C11C2311yescharacteristic
58C22×Q8×C11C2312yes—
59C2×#4343—24no—
60C2×#4343—44no—
61C2×#4343—44no—
62C2×#4343C2318yes—
63C22×D44—21no—
64C22×D44—22no—
65C22×D44—21no—
66C22×D44—21no—
67C22×D44C2312yes—
68C22×D44C2311yescharacteristic
69C22×C4×D11—21no—
70C22×C4×D11—22no—
71C22×C4×D11D411yescharacteristic
72C22×C4×D11D411yescharacteristic
73C22×C4×D11C2311yescharacteristic
74C2×C11×Q16—44no—
75C2×C11×Q16C2318yes—
76C22×C8×C11C2312yes—
77C11×C4⋊Q8—22no—
78C11×C4⋊Q8C2314yes—
79C4×Q8×C11—22no—
80C4×Q8×C11C2314yes—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C42×C11—21no—
86C2×C42×C11C2311yescharacteristic
87#67000—24no—
88#67000—22no—
89#67000C2318yes—
90#67000C2314yes—
91#66999—22no—
92#66999C2314yes—
93C2×#4325—44no—
94C2×#4325—44no—
95C2×#4325C2318yes—
96C2×#4325C2318yes—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4—21no—
101C2×(C2×D11)⋊C4—21no—
102C2×(C2×D11)⋊C4—22no—
103C2×(C2×D11)⋊C4—22no—
104C2×C4⋊Dic11—21no—
105C2×C4⋊Dic11C2311yescharacteristic
106C2×Dic11⋊C4—21no—
107C2×Dic11⋊C4—21no—
108C2×C4×Dic11D411yescharacteristic
109C2×C4×Dic11D411yescharacteristic
110C2×C4×Dic11C2311yescharacteristic
111C22×C11⋊C8C2312yes—
112C2×D88—44no—
113C2×D88C2318yes—
114#66951—28no—
115#66948—28no—
116#66948—28no—
117#66948—22no—
118#66948C2314yes—
119#66947—28no—
120#66946—28no—
121#66946—28no—
122#66943—22no—
123#66943C2314yes—
124#66927—22no—
125#66927C2314yes—
126C4×D44—28no—
127C4×D44—22no—
128C4×D44C2314yes—
129#66925—28no—
130C42×D11D414yes—
131C42×D11C2314yes—
132C11×C4⋊C8C2314yes—
133C11×#103C2318yes—
134#66899C2318yes—
135#66885C2318yes—
136(C2×D11)⋊C8C2318yes—
137C8×Dic11C2318yes—
138#66873C2318yes—
139C4⋊(C11⋊C8)C2314yes—
140C2×#3212—111nomaximal, Sylow
141C23×D11—21no—
142C23×D11—22no—
143C23×D11C2×D411yescharacteristic
144C2×Q8×C11—21no—
145C2×Q8×C11—22no—
146C2×Q8×C11—22no—
147C2×Q8×C11—24no—
148C2×Q8×C11—22no—
149C2×Q8×C11—24no—
150C2×Q8×C11C2414yes—
151C2×Q8×C11C2412yes—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—22no—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2411yescharacteristic
158C22×Dic11—21no—
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161C22×Dic11C2×D411yescharacteristic
162#4343—48no—
163#4343—48no—
164#4343—416no—
165C2×D44—24no—
166C2×D44—28no—
167C2×D44—21no—
168C2×D44—22no—
169C2×D44—24no—
170C2×D44—24no—
171C2×D44—22no—
172C2×D44—24no—
173C2×D44—22no—
174C2×D44—24no—
175C2×D44—44no—
176C2×D44—44no—
177C2×D44—48no—
178C2×D44—44no—
179C2×D44C2414yes—
180C2×D44C2412yes—
181C2×C4×D11—28no—
182C2×C4×D11—24no—
183C2×C4×D11—24no—
184C2×C4×D11—22no—
185C2×C4×D11—22no—
186C2×C4×D11—42no—
187C2×C4×D11—48no—
188C2×C4×D11—44no—
189C2×C4×D11C2×D412yes—
190C2×C4×D11C2×D414yes—
191C2×C4×D11C2×D414yes—
192C2×C4×D11C2412yes—
193C11×Q16—48no—
194C2×C8×C11—24no—
195C2×C8×C11C2414yes—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—24no—
198C11×C4⋊C4—24no—
199C11×C4⋊C4—24no—
200C11×C4⋊C4C2412yes—
201C42×C11—24no—
202C42×C11C2×D412yes—
203C42×C11C2412yes—
204#4325—48no—
205#4325—48no—
206(C2×D11)⋊C4—24no—
207(C2×D11)⋊C4—24no—
208(C2×D11)⋊C4—24no—
209(C2×D11)⋊C4—28no—
210(C2×D11)⋊C4—28no—
211(C2×D11)⋊C4—24no—
212(C2×D11)⋊C4—24no—
213C4⋊Dic11—24no—
214C4⋊Dic11—21no—
215C4⋊Dic11C2412yes—
216Dic11⋊C4—24no—
217Dic11⋊C4—24no—
218C4×Dic11C2×D412yes—
219C4×Dic11C2×D414yes—
220C4×Dic11C2×D414yes—
221C4×Dic11C2412yes—
222C2×C11⋊C8—24no—
223C2×C11⋊C8C2414yes—
224D88—48no—
225C2×#532—111no—
226C2×#529—111no—
227#3212—1116no—
228C2×#495—112no—
229C2×#488—112no—
230C2×#462D1111yescharacteristic, complemented
231C2×#460—111no—
232C2×#461—111no—
233C2×#459—111no—
234C2×#452—112no—
235C2×#449—112no—
236C2×#431—111no—
237C23×C11C22×D411yescharacteristic
238C22×D11—22no—
239C22×D11—22no—
240C22×D11—22no—
241C22×D11—22no—
242C22×D11—24no—
243C22×D11—44no—
244C22×D11—42no—
245C22×D11—42no—
246C22×D11—44no—
247C22×D11—44no—
248C22×D11—42no—
249C22×D11C22×D412yes—
250Q8×C11—22no—
251Q8×C11—24no—
252Q8×C11—22no—
253Q8×C11—24no—
254Q8×C11—44no—
255Q8×C11—42no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—24no—
260C2×C4×C11—44no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11#13514yes—
264C2×C4×C11C22×D412yes—
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C22×D412yes—
267C2×C4×C11H(5,𝔽2)12yes—
268C2×C4×C11H(5,𝔽2)12yes—
269C2×C4×C11C2511yescharacteristic
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—42no—
275C2×Dic11C22×D412yes—
276C2×Dic11C22×D412yes—
277C2×Dic11C22×D412yes—
278D44—22no—
279D44—24no—
280D44—22no—
281D44—24no—
282D44—48no—
283D44—48no—
284D44—416no—
285D44—42no—
286D44—44no—
287D44—48no—
288C4×D11—24no—
289C4×D11—28no—
290C4×D11—22no—
291C4×D11—22no—
292C4×D11—44no—
293C4×D11—416no—
294C4×D11—48no—
295C8×C11—24no—
296C11⋊C8—24no—
297C22×#41—112no—
298C22×Q16C2×D1112yes—
299C22×SD16—112no—
300C22×SD16—112no—
301C22×D8—112no—
302#532—118no—
303#532—224no—
304C2×C4⋊Q8C2×D1111yescharacteristic
305C2×#127—111no—
306#529—118no—
307#529—224no—
308C2×#126—221no—
309C2×#125—111no—
310C2×#124—112no—
311C2×#124—111no—
312C2×#123—221no—
313C2×C22⋊Q8—111no—
314C2×#121—111no—
315C2×#121—221no—
316C2×#121—221no—
317C2×C4×Q8C2×D1111yescharacteristic
318C2×C4×D4—111no—
319C2×C4×D4—221no—
320C2×C4×D4—221no—
321C2×C4×D4—221no—
322C2×#117—221no—
323C22×C42—111no—
324#495—1116no—
325#488—1116no—
326#462C2×D1118yescomplemented
327#461—118no—
328#460—118no—
329#459—118no—
330#452—1116no—
331#449—1116no—
332#431—118no—
333C2×C4⋊C8—111no—
334C2×C4⋊C8C2×D1111yescharacteristic
335C2×#103—112no—
336C2×#103C2×D1112yes—
337C2×#102—112no—
338C2×#102—112no—
339C2×C22⋊C8—112no—
340C2×C4×C8—112no—
341C22×C11#53512yes—
342C22×C11C2×#13512yes—
343C22×C11#57512yes—
344C22×C11C23×D411yescharacteristic
345C2×D11—22no—
346C2×D11—22no—
347C2×D11—22no—
348C2×D11—44no—
349C2×D11—44no—
350C2×D11—42no—
351C2×D11—42no—
352C2×D11—44no—
353C2×D11—42no—
354C2×D11—44no—
355C2×D11—88no—
356C2×D11—84no—
357C4×C11—22no—
358C4×C11—42no—
359C4×C11—44no—
360C4×C11—42no—
361C4×C11#53512yes—
362C4×C11C2×#13514yes—
363C4×C11C2×H(5,𝔽2)11yescharacteristic
364C4×C11C2×H(5,𝔽2)11yescharacteristic
365Dic11—22no—
366Dic11—22no—
367Dic11—22no—
368Dic11—42no—
369C2×#41—118no—
370C2×#41—224no—
371C2×#41—444no—
372C2×#41—444no—
373C22×Q8C22×D1111yescharacteristic
374C22×Q8C22×D1112yes—
375C22×D4—111no—
376C22×D4—112no—
377C22×D4—221no—
378C22×D4—222no—
379C22×D4—221no—
380C22×D4—221no—
381C23×C4—111no—
382C23×C4—111no—
383C23×C4—111no—
384C23×C4—222no—
385C23×C4—221no—
386C2×Q16—44no—
387C2×Q16C22×D1118yes—
388C2×SD16—118no—
389C2×SD16—118no—
390C2×SD16—444no—
391C2×SD16—444no—
392C2×D8—118no—
393C2×D8—444no—
394C22×C8—112no—
395C22×C8C22×D1112yes—
396C4⋊Q8—22no—
397C4⋊Q8C22×D1114yes—
398#127—114no—
399#127—222no—
400#126—228no—
401#125—114no—
402#125—222no—
403#124—114no—
404#124—118no—
405#124—222no—
406#124—224no—
407#123—228no—
408C22⋊Q8—114no—
409C22⋊Q8—222no—
410#121—114no—
411#121—222no—
412#121—228no—
413#121—228no—
414C4×Q8—22no—
415C4×Q8C22×D1114yes—
416C4×D4—114no—
417C4×D4—228no—
418C4×D4—228no—
419C4×D4—228no—
420C4×D4—222no—
421#117—228no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4C22×D1111yescharacteristic
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—222no—
433C2×C22⋊C4—222no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C22⋊C4—221no—
437C2×C42—21no—
438C2×C42—111no—
439C2×C42—111no—
440C2×C42—111no—
441C2×C42—114no—
442C2×C42—114no—
443C2×C42C22×D1111yescharacteristic
444C4⋊C8—114no—
445C4⋊C8C22×D1114yes—
446#103—118no—
447#103C22×D1118yes—
448#102—118no—
449#102—118no—
450C22⋊C8—118no—
451C4×C8—118no—
452C2×C11#321214yescomplemented
453C2×C11C2×#53511yescharacteristic
454C2×C11C22×#13511yescharacteristic
455C2×C11C2×#57511yescharacteristic
456D11—42no—
457D11—84no—
458D11—82no—
459C24—111no—
460C24—221no—
461C24—222no—
462#41—448no—
463#41—448no—
464#41—4416no—
465C2×Q8—21no—
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—24no—
469C2×Q8—22no—
470C2×Q8—24no—
471C2×Q8C23×D1114yes—
472C2×Q8C23×D1112yes—
473C2×D4—114no—
474C2×D4—112no—
475C2×D4—224no—
476C2×D4—228no—
477C2×D4—221no—
478C2×D4—224no—
479C2×D4—224no—
480C2×D4—222no—
481C2×D4—222no—
482C2×D4—224no—
483C2×D4—222no—
484C2×D4—224no—
485C2×D4—444no—
486C2×D4—448no—
487C2×D4—444no—
488C2×D4—444no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—111no—
493C22×C4—111no—
494C22×C4—111no—
495C22×C4—114no—
496C22×C4—112no—
497C22×C4—112no—
498C22×C4—114no—
499C22×C4—228no—
500C22×C4—224no—
501C22×C4—222no—
502C22×C4—222no—
503C22×C4—221no—
504C22×C4—224no—
505C22×C4—442no—
506C22×C4—448no—
507C22×C4—444no—
508C22×C4D4×D1111yescharacteristic
509C22×C4D4×D1111yescharacteristic
510C22×C4C23×D1111yescharacteristic
511Q16—48no—
512SD16—448no—
513SD16—448no—
514D8—448no—
515C2×C8—24no—
516C2×C8—114no—
517C2×C8—224no—
518C2×C8C23×D1114yes—
519C4⋊C4—24no—
520C4⋊C4—24no—
521C4⋊C4—24no—
522C4⋊C4—21no—
523C4⋊C4—112no—
524C4⋊C4—224no—
525C4⋊C4—224no—
526C4⋊C4—224no—
527C4⋊C4—221no—
528C4⋊C4C23×D1112yes—
529C22⋊C4—224no—
530C22⋊C4—224no—
531C22⋊C4—228no—
532C22⋊C4—228no—
533C22⋊C4—224no—
534C22⋊C4—224no—
535C22⋊C4—224no—
536C42—24no—
537C42—114no—
538C42—114no—
539C42—112no—
540C42—112no—
541C42D4×D1112yes—
542C42C23×D1112yes—
543C11C2×#321211yescharacteristic, complemented, Sylow
544C23—112no—
545C23—222no—
546C23—222no—
547C23—222no—
548C23—222no—
549C23—224no—
550C23—442no—
551C23—444no—
552C23—444no—
553C23—442no—
554C23—444no—
555C23—442no—
556C23C2×D4×D1111yescharacteristic
557Q8—22no—
558Q8—24no—
559Q8—22no—
560Q8—24no—
561Q8—42no—
562Q8—44no—
563D4—222no—
564D4—224no—
565D4—222no—
566D4—224no—
567D4—448no—
568D4—4416no—
569D4—448no—
570D4—448no—
571D4—444no—
572D4—442no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—42no—
578C2×C4—44no—
579C2×C4—42no—
580C2×C4—112no—
581C2×C4—112no—
582C2×C4—112no—
583C2×C4—222no—
584C2×C4—222no—
585C2×C4—222no—
586C2×C4—228no—
587C2×C4—224no—
588C2×C4—222no—
589C2×C4—222no—
590C2×C4—222no—
591C2×C4—444no—
592C2×C4—4416no—
593C2×C4—442no—
594C2×C4—448no—
595C2×C4#6697214yes—
596C2×C4C2×D4×D1112yes—
597C2×C4C2×D4×D1112yes—
598C2×C4C2×D4×D1111yescharacteristic
599C2×C4#6703712yes—
600C2×C4#6704212yes—
601C2×C4C24×D1111yescharacteristic
602C8—24no—
603C8—224no—
604C22—222no—
605C22—222no—
606C22—222no—
607C22—444no—
608C22—444no—
609C22—442no—
610C22—442no—
611C22—444no—
612C22—444no—
613C22—442no—
614C22—884no—
615C22—888no—
616C22#1062313812yes—
617C22C2×#6697212yes—
618C22#1062330812yes—
619C22C22×D4×D1111yescharacteristic
620C4—22no—
621C4—44no—
622C4—42no—
623C4—42no—
624C4—222no—
625C4—222no—
626C4—222no—
627C4—442no—
628C4#1062313812yes—
629C4C2×#6697214yes—
630C4C2×#6703711yescharacteristic
631C4C2×#6704211yescharacteristic
632C2—442no—
633C2—884no—
634C2—882no—
635C2#1307959714yesdirect product factor
636C2C2×#1062313811yescharacteristic
637C2C22×#6697211yescharacteristic
638C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#462C2
socleC23×C11C22×D4
hypercenterC2×#462D11
hypocenterC11C2×#3212
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
1. C2×#10623256C2semidirect
2. C2×#10623111C2semidirect
3. #13079597C2direct (N × H)
4. C2×#10622804C2semidirect
5. C2×#10622413C2semidirect
6. C2×#10622640C2semidirect
7. C2×#10622696C2semidirect
8. C2×#10622456C2semidirect
9. C2×#10622800C2semidirect
10. C2×#10622424C2semidirect
11. C2×#10622446C2semidirect
12. C2×C11×#462C2semidirect
24. #10623256C22semidirect
26. #10623111C22semidirect
40. C11×#462C22semidirect
44. #10622804C22semidirect
45. #10622800C22semidirect
49. #10622696C22semidirect
50. #10622640C22semidirect
53. #10622456C22semidirect
54. #10622446C22semidirect
55. #10622424C22semidirect
56. #10622413C22semidirect
230. C2×#462D11semidirect
326. #462C2×D11semidirect
452. C2×C11#3212semidirect
543. C11C2×#3212semidirect
635. C2#13079597direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232562
C2×#106231112
#130795972
C2×#106228042
C2×#106224132
C2×#106226402
C2×#106226962
C2×#106224562
C2×#106228002
C2×#106224242
C2×#106224462
C2×C11×#4622
C2×#321211