Finite Group Databasebeta

← C2×#13079618 #15625028

Subgroups — C2×#13079618 #15625028

Order 2816.

2242 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623153C211yesmaximal, characteristic, complemented
2C22×#67000C211yesmaximal, characteristic
3#13079618C2116yesmaximal, direct product factor
4C2×#10622803C212yesmaximal, complemented
5C2×#10622408C212yesmaximal, complemented
6C2×#10622411C212yesmaximal, complemented
7C2×#10622798C212yesmaximal, complemented
8C2×#10622841C211yesmaximal, characteristic, complemented
9C2×#10622344C211yesmaximal, characteristic
10C2×#10622659C211yesmaximal, characteristic
11C2×#10622332C211yesmaximal, characteristic, complemented
12C2×C11×#451C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2211yescharacteristic
14C23×D44C2211yescharacteristic
15C22×C11×Q16C2212yescomplemented
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×#67000—21no—
18C2×#67000—21no—
19C2×#67000—24no—
20C2×#67000C2212yes—
21C2×#67000C2212yes—
22C2×#67000C2218yes—
23C2×Q8×Dic11C2211yescharacteristic, complemented
24C2×#66997C2211yescharacteristic, complemented
25C22×#4326C2212yescomplemented
26C22×#4325C2212yes—
27C22×(C2×D11)⋊C4—21no—
28C22×(C2×D11)⋊C4—21no—
29C2×#66977C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C22×#4314C2212yes—
32#10623153—24no—
33#10623153C2218yescomplemented
34C2×#66942—21no—
35C2×#66941C2211yescharacteristic, complemented
36C2×#66940—21no—
37C2×#66940C2211yescharacteristic, complemented
38C2×#66931—21no—
39C2×#66930—21no—
40C11×#451C2218yescomplemented
41C2×C11×#103C2212yescomplemented
42C2×C11×C22⋊C8C2211yescharacteristic
43#10622841C2218yescomplemented
44C2×#66899C2212yescomplemented
45C2×C22⋊(C11⋊C8)C2211yescharacteristic
46#10622803C22116yescomplemented
47#10622798C22116yescomplemented
48C2×#66885C2212yes—
49C2×#66879C2212yescomplemented
50C2×Dic11⋊C8C2212yescomplemented
51#10622659C2218yes—
52C2×#66873C2212yes—
53#10622411C22116yescomplemented
54#10622408C22116yescomplemented
55#10622344C2218yes—
56#10622332C2218yescomplemented
57C24×D11—21no—
58C22×Q8×C11—21no—
59C22×Q8×C11—22no—
60C22×Q8×C11—44no—
61C22×Q8×C11C2311yescharacteristic
62C22×Q8×C11C2312yes—
63C22×Q8×C11C2314yes—
64C23×C4×C11—21no—
65C23×C4×C11C2311yescharacteristic
66C23×Dic11D411yescharacteristic
67C23×Dic11D411yescharacteristic
68C22×D44—21no—
69C22×D44—22no—
70C22×D44—44no—
71C22×D44C2312yes—
72C22×D44C2314yes—
73C22×Dic22—21no—
74C22×Dic22C2311yescharacteristic
75C2×C11×Q16—44no—
76C2×C11×Q16C2318yescomplemented
77C22×C8×C11C2312yes—
78C11×C22⋊Q8—22no—
79C11×C22⋊Q8C2314yes—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C22⋊C4—21no—
83C2×C22⋊Dic11—21no—
84#67000—28no—
85#67000—24no—
86#67000—24no—
87#67000—28no—
88#67000C2318yes—
89#67000C2318yes—
90Q8×Dic11—22no—
91Q8×Dic11C2314yescomplemented
92#66997—22no—
93#66997C2314yescomplemented
94C2×#4326—44no—
95C2×#4326C2318yescomplemented
96C2×#4325—44no—
97C2×#4325C2318yes—
98C2×(C2×D11)⋊C4—28no—
99C2×(C2×D11)⋊C4—22no—
100C2×(C2×D11)⋊C4—22no—
101C2×(C2×D11)⋊C4—22no—
102C2×(C2×D11)⋊C4—22no—
103C2×(C2×D11)⋊C4—28no—
104C2×C4⋊Dic11—21no—
105C2×C4⋊Dic11C2311yescharacteristic
106#66977—22no—
107#66977C2314yes—
108C2×Dic11⋊C4—21no—
109C2×Dic11⋊C4—21no—
110C2×Dic11⋊C4—21no—
111C2×Dic11⋊C4—21no—
112C2×Dic11⋊C4—21no—
113C2×C4×Dic11—21no—
114C2×C4×Dic11—21no—
115C2×C4×Dic11D411yescharacteristic
116C2×C4×Dic11D411yescharacteristic
117C2×C4×Dic11D414yes—
118C2×C4×Dic11C2311yescharacteristic
119C2×C4×Dic11C2311yescharacteristic
120C2×C4×Dic11C2314yes—
121C22×C11⋊C8C2312yes—
122C2×#4314—44no—
123C2×#4314C2318yes—
124#66942—28no—
125#66941—22no—
126#66941C2314yescomplemented
127#66940—28no—
128#66940—22no—
129#66940C2314yescomplemented
130#66931—28no—
131#66930—28no—
132C11×#103C2318yescomplemented
133C11×C22⋊C8C2314yes—
134#66899C2318yescomplemented
135C22⋊(C11⋊C8)C2314yes—
136#66885C2318yes—
137#66879C2318yescomplemented
138Dic11⋊C8C2318yescomplemented
139#66873C2318yes—
140C2×#3215—111nomaximal, Sylow
141C24×C11C2×D411yescharacteristic
142C23×D11—24no—
143C23×D11—22no—
144C23×D11—44no—
145C23×D11—44no—
146C23×D11—44no—
147C2×Q8×C11—21no—
148C2×Q8×C11—24no—
149C2×Q8×C11—22no—
150C2×Q8×C11—24no—
151C2×Q8×C11—24no—
152C2×Q8×C11—24no—
153C2×Q8×C11—48no—
154C2×Q8×C11—44no—
155C2×Q8×C11—48no—
156C2×Q8×C11C2414yes—
157C2×Q8×C11C2412yes—
158C22×C4×C11—24no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—24no—
162C22×C4×C11—22no—
163C22×C4×C11—44no—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2412yes—
167C22×C4×C11C2411yescharacteristic
168C22×Dic11—24no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—42no—
172C22×Dic11C2×D414yes—
173C22×Dic11C2×D411yescharacteristic
174C22×Dic11C2×D411yescharacteristic
175C22×Dic11C2×D411yescharacteristic
176C22×Dic11C2×D411yescharacteristic
177C22×Dic11C2×D414yes—
178C2×D44—24no—
179C2×D44—22no—
180C2×D44—24no—
181C2×D44—24no—
182C2×D44—48no—
183C2×D44—44no—
184C2×D44—48no—
185C2×D44C2414yes—
186C2×Dic22—24no—
187C2×Dic22—21no—
188C2×Dic22—24no—
189C2×Dic22—44no—
190C2×Dic22C2412yes—
191C11×Q16—48no—
192C2×C8×C11—24no—
193C2×C8×C11C2414yes—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—24no—
196C11×C4⋊C4C2412yes—
197C11×C22⋊C4—24no—
198C22⋊Dic11—24no—
199#4326—48no—
200#4325—48no—
201(C2×D11)⋊C4—28no—
202(C2×D11)⋊C4—28no—
203(C2×D11)⋊C4—28no—
204(C2×D11)⋊C4—28no—
205C4⋊Dic11—24no—
206C4⋊Dic11—21no—
207C4⋊Dic11C2412yes—
208Dic11⋊C4—24no—
209Dic11⋊C4—24no—
210Dic11⋊C4—24no—
211Dic11⋊C4—24no—
212Dic11⋊C4—24no—
213C4×Dic11—24no—
214C4×Dic11—24no—
215C4×Dic11C2×D414yes—
216C4×Dic11C2×D412yes—
217C4×Dic11C2×D412yes—
218C4×Dic11C2×D414yes—
219C4×Dic11C2412yes—
220C4×Dic11C2412yes—
221C2×C11⋊C8—24no—
222C2×C11⋊C8C2414yes—
223#4314—48no—
224C2×#533—111no—
225C22×#124—111no—
226#3215—1116no—
227C2×#497—112no—
228C2×#489—112no—
229C2×#464—112no—
230C2×#464—112no—
231C2×#451—111no—
232C2×#451D1111yescharacteristic, complemented
233C2×#450—111no—
234C2×#450—111no—
235C2×#432—111no—
236C23×C11—22no—
237C23×C11—22no—
238C23×C11#13714yes—
239C23×C11C22×D412yes—
240C23×C11C22×D411yescharacteristic
241C22×D11—24no—
242C22×D11—48no—
243C22×D11—48no—
244C22×D11—44no—
245C22×D11—48no—
246C22×D11—44no—
247C22×D11—44no—
248C22×D11—816no—
249Q8×C11—24no—
250Q8×C11—24no—
251Q8×C11—24no—
252Q8×C11—48no—
253Q8×C11—42no—
254Q8×C11—44no—
255C2×C4×C11—22no—
256C2×C4×C11—24no—
257C2×C4×C11—24no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—24no—
261C2×C4×C11—48no—
262C2×C4×C11—44no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11C22×D412yes—
266C2×C4×C11C22×D411yescharacteristic
267C2×C4×C11H(5,𝔽2)14yes—
268C2×C4×C11C2511yescharacteristic
269C2×Dic11—28no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—44no—
277C2×Dic11—42no—
278C2×Dic11—42no—
279C2×Dic11C22×D412yes—
280C2×Dic11C22×D412yes—
281C2×Dic11C22×D412yes—
282C2×Dic11C22×D412yes—
283D44—24no—
284D44—24no—
285D44—48no—
286D44—44no—
287Dic22—24no—
288Dic22—48no—
289Dic22—42no—
290C8×C11—24no—
291C11⋊C8—24no—
292C23×Q8C2×D1111yescharacteristic
293C23×D4—111no—
294C22×Q16—112no—
295C22×Q16C2×D1112yescomplemented
296C22×SD16—112no—
297C22×SD16—112no—
298#533—118no—
299#533—224no—
300C2×C4⋊Q8—111no—
301C2×C4⋊Q8—111no—
302C2×#125—221no—
303C2×#124—112no—
304C2×#124—118no—
305C2×#124—112no—
306C2×#124—221no—
307C2×#124—221no—
308C2×#124—224no—
309C2×C22⋊Q8—111no—
310C2×C22⋊Q8—221no—
311C2×C22⋊Q8C2×D1111yescharacteristic
312C2×C4×Q8—111no—
313C2×C4×Q8—111no—
314C2×C4×Q8—221no—
315C2×#117—221no—
316C22×C22⋊C4—221no—
317C22×C22⋊C4—221no—
318C22×C42—111no—
319#497—1116no—
320#489—1116no—
321#464—1116no—
322#464—1116no—
323#451—118no—
324#451C2×D1118yescomplemented
325#450—118no—
326#450—118no—
327#432—118no—
328C2×C4⋊C8—112no—
329C2×#103—112no—
330C2×#103C2×D1112yescomplemented
331C2×#102—112no—
332C2×#102—112no—
333C2×C22⋊C8—111no—
334C2×C22⋊C8C2×D1111yescharacteristic
335C2×#97—112no—
336C22×C11—22no—
337C22×C11—28no—
338C22×C11—22no—
339C22×C11#53512yes—
340C22×C11C2×#13714yes—
341C22×C11C2×#13712yes—
342C22×C11#57512yes—
343C22×C11C23×D411yescharacteristic
344C2×D11—44no—
345C2×D11—44no—
346C2×D11—44no—
347C2×D11—816no—
348C2×D11—88no—
349C4×C11—22no—
350C4×C11—44no—
351C4×C11—42no—
352C4×C11—42no—
353C4×C11#53512yes—
354C4×C11C2×H(5,𝔽2)12yes—
355Dic11—22no—
356Dic11—22no—
357Dic11—22no—
358Dic11—22no—
359Dic11—42no—
360Dic11—42no—
361C25—221no—
362C22×Q8—22no—
363C22×Q8—21no—
364C22×Q8—44no—
365C22×Q8—111no—
366C22×Q8—221no—
367C22×Q8C22×D1111yescharacteristic
368C22×Q8C22×D1112yes—
369C22×Q8C22×D1114yes—
370C22×D4—112no—
371C22×D4—114no—
372C22×D4—222no—
373C22×D4—221no—
374C22×D4—444no—
375C23×C4—21no—
376C23×C4—111no—
377C23×C4—111no—
378C23×C4C22×D1111yescharacteristic
379C2×Q16—44no—
380C2×Q16—118no—
381C2×Q16—444no—
382C2×Q16C22×D1118yescomplemented
383C2×SD16—118no—
384C2×SD16—118no—
385C2×SD16—444no—
386C2×SD16—444no—
387C22×C8—112no—
388C22×C8C22×D1112yes—
389C4⋊Q8—114no—
390C4⋊Q8—114no—
391C4⋊Q8—222no—
392C4⋊Q8—222no—
393#125—228no—
394#124—118no—
395#124—118no—
396#124—228no—
397#124—224no—
398#124—228no—
399#124—224no—
400C22⋊Q8—22no—
401C22⋊Q8—114no—
402C22⋊Q8—228no—
403C22⋊Q8—222no—
404C22⋊Q8C22×D1114yes—
405C4×Q8—114no—
406C4×Q8—114no—
407C4×Q8—222no—
408C4×Q8—228no—
409C4×Q8—222no—
410#117—228no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4C22×D1111yescharacteristic
420C2×C22⋊C4—21no—
421C2×C22⋊C4—228no—
422C2×C22⋊C4—228no—
423C2×C22⋊C4—222no—
424C2×C22⋊C4—222no—
425C2×C22⋊C4—222no—
426C2×C22⋊C4—222no—
427C2×C22⋊C4—221no—
428C2×C42—111no—
429C2×C42—111no—
430C2×C42—114no—
431C2×C42—111no—
432C2×C42—111no—
433C2×C42—114no—
434C2×C42—221no—
435C2×C42—221no—
436C4⋊C8—118no—
437#103—118no—
438#103C22×D1118yescomplemented
439#102—118no—
440#102—118no—
441C22⋊C8—114no—
442C22⋊C8C22×D1114yes—
443#97—118no—
444C2×C11—24no—
445C2×C11#321514yescomplemented
446C2×C11C2×#53511yescharacteristic
447C2×C11C22×#13711yescharacteristic
448C2×C11C2×#57511yescharacteristic
449D11—84no—
450C24—224no—
451C24—222no—
452C24—444no—
453C24—444no—
454C24—444no—
455C24D4×D1111yescharacteristic
456C2×Q8—21no—
457C2×Q8—24no—
458C2×Q8—22no—
459C2×Q8—24no—
460C2×Q8—24no—
461C2×Q8—24no—
462C2×Q8—48no—
463C2×Q8—44no—
464C2×Q8—48no—
465C2×Q8—112no—
466C2×Q8—224no—
467C2×Q8—221no—
468C2×Q8—224no—
469C2×Q8—444no—
470C2×Q8C23×D1114yes—
471C2×Q8C23×D1112yes—
472C2×D4—114no—
473C2×D4—224no—
474C2×D4—222no—
475C2×D4—224no—
476C2×D4—224no—
477C2×D4—448no—
478C2×D4—444no—
479C2×D4—448no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—44no—
486C22×C4—114no—
487C22×C4—111no—
488C22×C4—111no—
489C22×C4—111no—
490C22×C4—111no—
491C22×C4—114no—
492C22×C4—224no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—442no—
496C22×C4D4×D1112yes—
497C22×C4D4×D1111yescharacteristic
498C22×C4C23×D1112yes—
499C22×C4C23×D1111yescharacteristic
500Q16—48no—
501Q16—448no—
502SD16—448no—
503SD16—448no—
504C2×C8—24no—
505C2×C8—114no—
506C2×C8—224no—
507C2×C8C23×D1114yes—
508C4⋊C4—24no—
509C4⋊C4—21no—
510C4⋊C4—112no—
511C4⋊C4—224no—
512C4⋊C4—224no—
513C4⋊C4—224no—
514C4⋊C4—224no—
515C4⋊C4—224no—
516C4⋊C4—221no—
517C4⋊C4—224no—
518C4⋊C4C23×D1112yes—
519C22⋊C4—24no—
520C22⋊C4—228no—
521C22⋊C4—228no—
522C22⋊C4—228no—
523C22⋊C4—228no—
524C22⋊C4—224no—
525C42—112no—
526C42—114no—
527C42—114no—
528C42—112no—
529C42—112no—
530C42—112no—
531C42—224no—
532C42—224no—
533C11C2×#321511yescharacteristic, complemented, Sylow
534C23—22no—
535C23—22no—
536C23—224no—
537C23—448no—
538C23—448no—
539C23—448no—
540C23—444no—
541C23—444no—
542C23—444no—
543C23—8816no—
544C23#6697114yes—
545C23C2×D4×D1112yes—
546C23C2×D4×D1111yescharacteristic
547Q8—24no—
548Q8—24no—
549Q8—24no—
550Q8—48no—
551Q8—42no—
552Q8—44no—
553Q8—224no—
554Q8—448no—
555Q8—442no—
556D4—224no—
557D4—224no—
558D4—448no—
559D4—444no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—24no—
566C2×C4—48no—
567C2×C4—42no—
568C2×C4—44no—
569C2×C4—42no—
570C2×C4—112no—
571C2×C4—112no—
572C2×C4—112no—
573C2×C4—112no—
574C2×C4—228no—
575C2×C4—222no—
576C2×C4—222no—
577C2×C4—222no—
578C2×C4—222no—
579C2×C4—222no—
580C2×C4—222no—
581C2×C4—444no—
582C2×C4—442no—
583C2×C4—442no—
584C2×C4C2×D4×D1112yes—
585C2×C4C2×D4×D1111yescharacteristic
586C2×C4#6703714yes—
587C2×C4C24×D1111yescharacteristic
588C8—24no—
589C8—224no—
590C22—28no—
591C22—22no—
592C22—22no—
593C22—444no—
594C22—444no—
595C22—444no—
596C22—8816no—
597C22—888no—
598C22#1062312312yes—
599C22C2×#6697114yes—
600C22C2×#6697112yes—
601C22#1062330812yes—
602C22C22×D4×D1111yescharacteristic
603C4—22no—
604C4—44no—
605C4—42no—
606C4—42no—
607C4—222no—
608C4—222no—
609C4—222no—
610C4—222no—
611C4—442no—
612C4—442no—
613C4#1062312312yes—
614C4C2×#6703712yes—
615C2—24no—
616C2—884no—
617C2#1307961814yesdirect product factor
618C2C2×#1062312311yescharacteristic
619C2C22×#6697111yescharacteristic
620C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#451C2
socleC23×C11C22×D4
prime radicalC23×D44C22
hypercenterC2×#451D11
hypocenterC11C2×#3215
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
1. C2×#10623153C2semidirect
3. #13079618C2direct (N × H)
4. C2×#10622803C2semidirect
5. C2×#10622408C2semidirect
6. C2×#10622411C2semidirect
7. C2×#10622798C2semidirect
8. C2×#10622841C2semidirect
11. C2×#10622332C2semidirect
12. C2×C11×#451C2semidirect
15. C22×C11×Q16C22semidirect
23. C2×Q8×Dic11C22semidirect
24. C2×#66997C22semidirect
25. C22×#4326C22semidirect
33. #10623153C22semidirect
35. C2×#66941C22semidirect
37. C2×#66940C22semidirect
40. C11×#451C22semidirect
41. C2×C11×#103C22semidirect
43. #10622841C22semidirect
44. C2×#66899C22semidirect
46. #10622803C22semidirect
47. #10622798C22semidirect
49. C2×#66879C22semidirect
50. C2×Dic11⋊C8C22semidirect
53. #10622411C22semidirect
54. #10622408C22semidirect
56. #10622332C22semidirect
76. C2×C11×Q16C23semidirect
91. Q8×Dic11C23semidirect
93. #66997C23semidirect
95. C2×#4326C23semidirect
126. #66941C23semidirect
129. #66940C23semidirect
132. C11×#103C23semidirect
134. #66899C23semidirect
137. #66879C23semidirect
138. Dic11⋊C8C23semidirect
232. C2×#451D11semidirect
295. C22×Q16C2×D11semidirect
324. #451C2×D11semidirect
330. C2×#103C2×D11semidirect
382. C2×Q16C22×D11semidirect
438. #103C22×D11semidirect
445. C2×C11#3215semidirect
533. C11C2×#3215semidirect
617. C2#13079618direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231532
C22×#670002
#130796182
C2×#106228032
C2×#106224082
C2×#106224112
C2×#106227982
C2×#106228412
C2×#106223442
C2×#106226592
C2×#106223322
C2×C11×#4512
C2×#321511