Finite Group Databasebeta

← C2×#13079596 #15624997

Subgroups — C2×#13079596 #15624997

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×#10623247C211yesmaximal, characteristic, complemented
2C2×#10623111C211yesmaximal, characteristic, complemented
3#13079596C2116yesmaximal, direct product factor
4C2×#10622781C212yesmaximal, complemented
5C2×#10622381C212yesmaximal, complemented
6C2×#10622644C211yesmaximal, characteristic, complemented
7C2×#10622454C211yesmaximal, characteristic, complemented
8C2×#10622685C211yesmaximal, characteristic, complemented
9C2×#10622786C212yesmaximal, complemented
10C2×#10622394C212yesmaximal, complemented
11C2×#10622446C211yesmaximal, characteristic, complemented
12C2×C11×#460C211yesmaximal, characteristic, complemented
13C22×#4341C2212yes—
14C22×C11×SD16C2212yes—
15C2×C11×#127C2211yescharacteristic
16C2×C4×Q8×C11C2211yescharacteristic
17C2×#67000C2211yescharacteristic
18C2×#66999C2211yescharacteristic
19C22×#4326C2212yes—
20C2×#66991—21no—
21C2×#66991—21no—
22C2×#66989C2212yes—
23C2×D4×Dic11—21no—
24C2×D4×Dic11—21no—
25C22×#4323C2212yes—
26C22×#4314C2212yes—
27#10623247—24no—
28#10623247C2218yescomplemented
29#10623111—24no—
30#10623111C2218yescomplemented
31C2×#66951—21no—
32C2×#66948C2211yescharacteristic
33C2×#66947—21no—
34C2×#66943C2211yescharacteristic
35C2×C4×D44—21no—
36C2×C4×D44C2211yescharacteristic
37C2×#66925—21no—
38C2×C42×D11C2211yescharacteristic
39C2×#66922C2211yescharacteristic
40C11×#460C2218yescomplemented
41C2×C11×C4⋊C8C2211yescharacteristic
42C2×C11×#102C2212yes—
43C2×#66896C2212yes—
44#10622786C22116yescomplemented
45#10622781C22116yescomplemented
46C2×(C2×D11)⋊C8C2212yes—
47C2×#66880C2212yes—
48C2×C8×Dic11C2212yes—
49#10622685C2218yescomplemented
50#10622644C2218yescomplemented
51C2×#66874C2212yes—
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53#10622454C2218yescomplemented
54#10622446C2218yescomplemented
55#10622394C22116yescomplemented
56#10622381C22116yescomplemented
57C22×Q8×C11C2311yescharacteristic
58C22×D4×C11—21no—
59C22×D4×C11—21no—
60C22×D4×C11C2312yes—
61C22×C22⋊D11—22no—
62C23×Dic11—22no—
63C2×#4341—24no—
64C2×#4341—44no—
65C2×#4341—44no—
66C2×#4341C2318yes—
67C22×D44—21no—
68C22×D44C2311yescharacteristic
69C22×C4×D11—21no—
70C22×C4×D11D411yescharacteristic
71C22×C4×D11D411yescharacteristic
72C22×C4×D11C2311yescharacteristic
73C22×Dic22C2312yes—
74C2×C11×SD16—44no—
75C2×C11×SD16C2318yes—
76C22×C8×C11C2312yes—
77C11×#127—22no—
78C11×#127C2314yes—
79C4×Q8×C11—22no—
80C4×Q8×C11C2314yes—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C42×C11—21no—
84C2×C42×C11C2311yescharacteristic
85C2×C22⋊Dic11—22no—
86C2×C22⋊Dic11—22no—
87#67000—22no—
88#67000C2314yes—
89#66999—22no—
90#66999C2314yes—
91C2×#4326—44no—
92C2×#4326C2318yes—
93#66991—28no—
94#66991—28no—
95#66989—24no—
96#66989C2318yes—
97D4×Dic11—28no—
98D4×Dic11—28no—
99C2×#4323—44no—
100C2×#4323C2318yes—
101C2×(C2×D11)⋊C4—21no—
102C2×(C2×D11)⋊C4—21no—
103C2×(C2×D11)⋊C4—21no—
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4—21no—
106C2×C4⋊Dic11—21no—
107C2×C4⋊Dic11—21no—
108C2×C4⋊Dic11—21no—
109C2×C4⋊Dic11C2311yescharacteristic
110C2×Dic11⋊C4—21no—
111C2×Dic11⋊C4—21no—
112C2×C4×Dic11D411yescharacteristic
113C2×C4×Dic11D411yescharacteristic
114C2×C4×Dic11C2311yescharacteristic
115C22×C11⋊C8C2312yes—
116C2×#4314—44no—
117C2×#4314C2318yes—
118#66951—28no—
119#66948—22no—
120#66948C2314yes—
121#66947—28no—
122#66943—22no—
123#66943C2314yes—
124C4×D44—28no—
125C4×D44—22no—
126C4×D44C2314yes—
127#66925—28no—
128C42×D11D414yes—
129C42×D11C2314yes—
130#66922—22no—
131#66922C2314yes—
132C11×C4⋊C8C2314yes—
133C11×#102C2318yes—
134#66896C2318yes—
135(C2×D11)⋊C8C2318yes—
136#66880C2318yes—
137C8×Dic11C2318yes—
138#66874C2318yes—
139C4⋊(C11⋊C8)C2314yes—
140C2×#3212—111nomaximal, Sylow
141C24×C11—22no—
142C23×D11—21no—
143C23×D11C2×D411yescharacteristic
144C2×Q8×C11—21no—
145C2×Q8×C11—22no—
146C2×Q8×C11—22no—
147C2×Q8×C11C2412yes—
148C2×D4×C11—24no—
149C2×D4×C11—24no—
150C2×D4×C11—22no—
151C2×D4×C11—24no—
152C2×D4×C11—24no—
153C2×D4×C11—44no—
154C2×D4×C11—44no—
155C2×D4×C11C2414yes—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2411yescharacteristic
161C2×C22⋊D11—28no—
162C2×C22⋊D11—48no—
163C22×Dic11—28no—
164C22×Dic11—21no—
165C22×Dic11—22no—
166C22×Dic11—48no—
167C22×Dic11C2×D411yescharacteristic
168C22×Dic11C2×D411yescharacteristic
169C22×Dic11C2×D411yescharacteristic
170#4341—48no—
171#4341—48no—
172#4341—416no—
173C2×D44—24no—
174C2×D44—21no—
175C2×D44—22no—
176C2×D44—22no—
177C2×D44—44no—
178C2×D44C2412yes—
179C2×C4×D11—24no—
180C2×C4×D11—24no—
181C2×C4×D11—22no—
182C2×C4×D11—22no—
183C2×C4×D11—42no—
184C2×C4×D11—44no—
185C2×C4×D11C2×D412yes—
186C2×C4×D11C2×D414yes—
187C2×C4×D11C2×D414yes—
188C2×C4×D11C2412yes—
189C2×Dic22—22no—
190C2×Dic22—24no—
191C2×Dic22—24no—
192C2×Dic22C2414yes—
193C11×SD16—48no—
194C2×C8×C11—24no—
195C2×C8×C11C2414yes—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—24no—
198C11×C4⋊C4C2412yes—
199C42×C11—24no—
200C42×C11C2×D412yes—
201C42×C11C2412yes—
202C22⋊Dic11—28no—
203C22⋊Dic11—28no—
204#4326—48no—
205#4323—48no—
206(C2×D11)⋊C4—24no—
207(C2×D11)⋊C4—24no—
208(C2×D11)⋊C4—24no—
209(C2×D11)⋊C4—24no—
210(C2×D11)⋊C4—24no—
211C4⋊Dic11—24no—
212C4⋊Dic11—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—
224#4314—48no—
225C2×#532—111no—
226C2×#529—111no—
227#3212—1116no—
228C2×#495—112no—
229C2×#488—112no—
230C2×#462—111no—
231C2×#460D1111yescharacteristic, complemented
232C2×#461—111no—
233C2×#459—111no—
234C2×#452—112no—
235C2×#449—112no—
236C2×#431—111no—
237C23×C11—24no—
238C23×C11—44no—
239C23×C11—44no—
240C23×C11—44no—
241C23×C11C22×D411yescharacteristic
242C22×D11—22no—
243C22×D11—22no—
244C22×D11—22no—
245C22×D11—22no—
246C22×D11—42no—
247C22×D11—42no—
248C22×D11—42no—
249C22×D11C22×D412yes—
250Q8×C11—22no—
251Q8×C11—22no—
252Q8×C11—42no—
253D4×C11—24no—
254D4×C11—24no—
255D4×C11—48no—
256D4×C11—44no—
257D4×C11—48no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
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
270C22⋊D11—416no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—24no—
276C2×Dic11—416no—
277C2×Dic11—44no—
278C2×Dic11—42no—
279C2×Dic11C22×D412yes—
280C2×Dic11C22×D412yes—
281C2×Dic11C22×D412yes—
282D44—22no—
283D44—22no—
284D44—48no—
285D44—42no—
286C4×D11—24no—
287C4×D11—28no—
288C4×D11—22no—
289C4×D11—22no—
290C4×D11—44no—
291C4×D11—48no—
292Dic22—24no—
293Dic22—24no—
294Dic22—44no—
295C8×C11—24no—
296C11⋊C8—24no—
297C22×#41—112no—
298C22×Q16—112no—
299C22×SD16—112no—
300C22×SD16C2×D1112yes—
301C22×D8—112no—
302#532—118no—
303#532—224no—
304C2×C4⋊Q8—111no—
305C2×#127C2×D1111yescharacteristic
306#529—118no—
307#529—224no—
308C2×#126—221no—
309C2×#125—111no—
310C2×#124—111no—
311C2×#124—112no—
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#462—118no—
327#461—118no—
328#460C2×D1118yescomplemented
329#459—118no—
330#452—1116no—
331#449—1116no—
332#431—118no—
333C2×C4⋊C8—111no—
334C2×C4⋊C8C2×D1111yescharacteristic
335C2×#103—112no—
336C2×#103—112no—
337C2×#102—112no—
338C2×#102C2×D1112yes—
339C2×C22⋊C8—112no—
340C2×C4×C8—112no—
341C22×C11—44no—
342C22×C11—44no—
343C22×C11—44no—
344C22×C11—88no—
345C22×C11#53512yes—
346C22×C11C2×#13512yes—
347C22×C11#57512yes—
348C22×C11C23×D411yescharacteristic
349C2×D11—22no—
350C2×D11—22no—
351C2×D11—22no—
352C2×D11—44no—
353C2×D11—42no—
354C2×D11—42no—
355C2×D11—42no—
356C2×D11—84no—
357C4×C11—22no—
358C4×C11—42no—
359C4×C11—42no—
360C4×C11#53512yes—
361C4×C11C2×#13514yes—
362C4×C11C2×H(5,𝔽2)11yescharacteristic
363C4×C11C2×H(5,𝔽2)11yescharacteristic
364Dic11—22no—
365Dic11—22no—
366Dic11—22no—
367Dic11—44no—
368Dic11—42no—
369C2×#41—118no—
370C2×#41—224no—
371C2×#41—444no—
372C2×#41—444no—
373C22×Q8—112no—
374C22×Q8C22×D1111yescharacteristic
375C22×D4—21no—
376C22×D4—21no—
377C22×D4—111no—
378C22×D4—221no—
379C22×D4—222no—
380C22×D4C22×D1112yes—
381C23×C4—111no—
382C23×C4—111no—
383C23×C4—111no—
384C23×C4—222no—
385C23×C4—221no—
386C2×Q16—118no—
387C2×Q16—444no—
388C2×SD16—44no—
389C2×SD16—118no—
390C2×SD16—444no—
391C2×SD16C22×D1118yes—
392C2×D8—118no—
393C2×D8—444no—
394C22×C8—112no—
395C22×C8C22×D1112yes—
396C4⋊Q8—114no—
397C4⋊Q8—222no—
398#127—22no—
399#127C22×D1114yes—
400#126—228no—
401#125—114no—
402#125—222no—
403#124—114no—
404#124—118no—
405#124—224no—
406#124—222no—
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—111no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4—221no—
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—221no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—222no—
435C2×C22⋊C4—222no—
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#103—118no—
448#102—118no—
449#102C22×D1118yes—
450C22⋊C8—118no—
451C4×C8—118no—
452C2×C11—84no—
453C2×C11#321214yescomplemented
454C2×C11C2×#53511yescharacteristic
455C2×C11C22×#13511yescharacteristic
456C2×C11C2×#57511yescharacteristic
457D11—42no—
458D11—82no—
459C24—22no—
460C24—111no—
461C24—221no—
462#41—448no—
463#41—448no—
464#41—4416no—
465C2×Q8—21no—
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—114no—
469C2×Q8—222no—
470C2×Q8—224no—
471C2×Q8—224no—
472C2×Q8C23×D1112yes—
473C2×D4—24no—
474C2×D4—24no—
475C2×D4—22no—
476C2×D4—24no—
477C2×D4—24no—
478C2×D4—44no—
479C2×D4—44no—
480C2×D4—112no—
481C2×D4—224no—
482C2×D4—228no—
483C2×D4—221no—
484C2×D4—222no—
485C2×D4—222no—
486C2×D4—444no—
487C2×D4—448no—
488C2×D4C23×D1114yes—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—111no—
492C22×C4—111no—
493C22×C4—111no—
494C22×C4—114no—
495C22×C4—112no—
496C22×C4—112no—
497C22×C4—114no—
498C22×C4—228no—
499C22×C4—224no—
500C22×C4—222no—
501C22×C4—222no—
502C22×C4—221no—
503C22×C4—222no—
504C22×C4—224no—
505C22×C4—442no—
506C22×C4—448no—
507C22×C4—444no—
508C22×C4D4×D1111yescharacteristic
509C22×C4D4×D1111yescharacteristic
510C22×C4C23×D1111yescharacteristic
511Q16—448no—
512SD16—48no—
513SD16—448no—
514D8—448no—
515C2×C8—24no—
516C2×C8—114no—
517C2×C8—224no—
518C2×C8C23×D1114yes—
519C4⋊C4—24no—
520C4⋊C4—21no—
521C4⋊C4—112no—
522C4⋊C4—224no—
523C4⋊C4—224no—
524C4⋊C4—224no—
525C4⋊C4—221no—
526C4⋊C4—224no—
527C4⋊C4—224no—
528C4⋊C4C23×D1112yes—
529C22⋊C4—224no—
530C22⋊C4—224no—
531C22⋊C4—224no—
532C22⋊C4—224no—
533C22⋊C4—228no—
534C22⋊C4—228no—
535C22⋊C4—224no—
536C42—24no—
537C42—114no—
538C42—114no—
539C42—112no—
540C42—112no—
541C42D4×D1112yes—
542C42C23×D1112yes—
543C11C2×#321211yescharacteristic, complemented, Sylow
544C23—24no—
545C23—44no—
546C23—44no—
547C23—44no—
548C23—112no—
549C23—222no—
550C23—222no—
551C23—222no—
552C23—222no—
553C23—442no—
554C23—442no—
555C23—442no—
556C23C2×D4×D1111yescharacteristic
557Q8—22no—
558Q8—22no—
559Q8—42no—
560Q8—224no—
561Q8—224no—
562Q8—444no—
563D4—24no—
564D4—24no—
565D4—48no—
566D4—48no—
567D4—44no—
568D4—222no—
569D4—222no—
570D4—448no—
571D4—4416no—
572D4—442no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—112no—
579C2×C4—112no—
580C2×C4—112no—
581C2×C4—222no—
582C2×C4—222no—
583C2×C4—222no—
584C2×C4—228no—
585C2×C4—224no—
586C2×C4—222no—
587C2×C4—222no—
588C2×C4—222no—
589C2×C4—224no—
590C2×C4—444no—
591C2×C4—4416no—
592C2×C4—442no—
593C2×C4—444no—
594C2×C4—448no—
595C2×C4#6696914yes—
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—44no—
605C22—44no—
606C22—44no—
607C22—88no—
608C22—222no—
609C22—222no—
610C22—222no—
611C22—444no—
612C22—442no—
613C22—442no—
614C22—442no—
615C22—884no—
616C22#1062313812yes—
617C22C2×#6696912yes—
618C22#1062330412yes—
619C22C22×D4×D1111yescharacteristic
620C4—22no—
621C4—42no—
622C4—42no—
623C4—222no—
624C4—222no—
625C4—222no—
626C4—444no—
627C4—442no—
628C4#1062313812yes—
629C4C2×#6696914yes—
630C4C2×#6703711yescharacteristic
631C4C2×#6704211yescharacteristic
632C2—84no—
633C2—442no—
634C2—882no—
635C2#1307959614yesdirect product factor
636C2C2×#1062313811yescharacteristic
637C2C22×#6696911yescharacteristic
638C2C2×#1062330411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#460C2
socleC23×C11C22×D4
hypercenterC2×#460D11
hypocenterC11C2×#3212
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
1. C2×#10623247C2semidirect
2. C2×#10623111C2semidirect
3. #13079596C2direct (N × H)
4. C2×#10622781C2semidirect
5. C2×#10622381C2semidirect
6. C2×#10622644C2semidirect
7. C2×#10622454C2semidirect
8. C2×#10622685C2semidirect
9. C2×#10622786C2semidirect
10. C2×#10622394C2semidirect
11. C2×#10622446C2semidirect
12. C2×C11×#460C2semidirect
28. #10623247C22semidirect
30. #10623111C22semidirect
40. C11×#460C22semidirect
44. #10622786C22semidirect
45. #10622781C22semidirect
49. #10622685C22semidirect
50. #10622644C22semidirect
53. #10622454C22semidirect
54. #10622446C22semidirect
55. #10622394C22semidirect
56. #10622381C22semidirect
231. C2×#460D11semidirect
328. #460C2×D11semidirect
453. C2×C11#3212semidirect
543. C11C2×#3212semidirect
635. C2#13079596direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232472
C2×#106231112
#130795962
C2×#106227812
C2×#106223812
C2×#106226442
C2×#106224542
C2×#106226852
C2×#106227862
C2×#106223942
C2×#106224462
C2×C11×#4602
C2×#321211