Finite Group Databasebeta

← C2×#13079399 #15624327

Subgroups — C2×#13079399 #15624327

Order 2816.

2374 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623322C211yesmaximal, characteristic
2C22×#66977C211yesmaximal, characteristic, complemented
3#13079399C2116yesmaximal, direct product factor
4C2×#10622336C212yesmaximal, complemented
5C2×#10622334C211yesmaximal, characteristic, complemented
6C2×#10622349C211yesmaximal, characteristic, complemented
7C2×#10622729C212yesmaximal, complemented
8C2×#10622727C212yesmaximal, complemented
9C2×#10622346C212yesmaximal, complemented
10C2×#10622352C211yesmaximal, characteristic, complemented
11C2×#10622351C211yesmaximal, characteristic, complemented
12C22×C11×C22⋊C8C211yesmaximal, characteristic, complemented
13C24×C4×C11C2211yescharacteristic
14C22×#4339C2211yescharacteristic
15C23×Dic22C2211yescharacteristic
16C23×C8×C11C2212yes—
17C2×#67006—21no—
18C22×C22⋊Dic11—21no—
19#10623322—24no—
20#10623322C2218yes—
21C2×#66983C2211yescharacteristic
22C2×#66983C2211yescharacteristic
23C2×#66982—21no—
24C2×C4×C22⋊D11—21no—
25C2×C4×C22⋊D11—21no—
26C2×#66979C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C2×#66977—21no—
29C2×#66977—21no—
30C2×#66977—24no—
31C2×#66977C2211yescharacteristic
32C2×#66977C2211yescharacteristic
33C2×#66977C2212yes—
34C2×#66977C2212yes—
35C2×#66977C2218yescomplemented
36C22×Dic11⋊C4—21no—
37C22×Dic44C2212yescomplemented
38C22×#4314C2212yescomplemented
39C2×C11×C22⋊C8C2211yescharacteristic
40C2×C11×C22⋊C8C2211yescharacteristic
41C2×C11×C22⋊C8C2212yes—
42C2×C11×C22⋊C8C2218yescomplemented
43#10622729C22116yescomplemented
44#10622727C22116yescomplemented
45C2×#66885C2212yescomplemented
46C2×#66882C2212yescomplemented
47C2×#66881C2212yescomplemented
48C2×#66880C2212yescomplemented
49C2×#66880C2212yescomplemented
50C2×#66880C2212yescomplemented
51#10622352C2218yescomplemented
52#10622351C2218yescomplemented
53#10622349C2218yescomplemented
54#10622346C22116yescomplemented
55#10622336C22116yescomplemented
56#10622334C2218yescomplemented
57C25×C11D411yescharacteristic
58C23×C4×C11—44no—
59C23×C4×C11D411yescharacteristic
60C23×C4×C11D411yescharacteristic
61C23×C4×C11D411yescharacteristic
62C23×C4×C11D414yes—
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2314yes—
67C22×C22⋊D11—21no—
68C22×C22⋊D11—21no—
69C22×C22⋊D11—21no—
70C23×Dic11—21no—
71C23×Dic11—21no—
72C2×#4339—22no—
73C2×#4339—44no—
74C2×#4339C2314yes—
75C22×D44C2311yescharacteristic
76C22×C4×D11—21no—
77C22×Dic22—21no—
78C22×Dic22—22no—
79C22×Dic22—44no—
80C22×Dic22C2312yes—
81C22×Dic22C2311yescharacteristic
82C22×Dic22C2314yes—
83C22×C8×C11—44no—
84C22×C8×C11C2312yes—
85C22×C8×C11C2312yes—
86C22×C8×C11C2318yes—
87#67006—28no—
88C2×C22⋊Dic11—22no—
89C2×C22⋊Dic11—22no—
90C2×C22⋊Dic11—28no—
91C2×C22⋊Dic11—21no—
92C2×C22⋊Dic11—21no—
93C2×C22⋊Dic11—21no—
94#66983—22no—
95#66983—22no—
96#66983C2314yes—
97#66983C2314yes—
98#66982—28no—
99C4×C22⋊D11—28no—
100C4×C22⋊D11—28no—
101C2×(C2×D11)⋊C4—21no—
102C2×(C2×D11)⋊C4—21no—
103#66979—22no—
104#66979C2314yes—
105C2×C4⋊Dic11—21no—
106C2×C4⋊Dic11—22no—
107C2×C4⋊Dic11C2312yes—
108C2×C4⋊Dic11C2311yescharacteristic
109C2×C4⋊Dic11C2311yescharacteristic
110C2×C4⋊Dic11C2314yes—
111#66977—24no—
112#66977—24no—
113#66977—28no—
114#66977—28no—
115#66977—22no—
116#66977—22no—
117#66977C2318yes—
118#66977C2314yes—
119#66977C2318yes—
120#66977C2314yes—
121C2×Dic11⋊C4—22no—
122C2×Dic11⋊C4—22no—
123C2×Dic11⋊C4—28no—
124C2×Dic11⋊C4—21no—
125C2×Dic11⋊C4—21no—
126C2×C4×Dic11—21no—
127C2×Dic44—44no—
128C2×Dic44C2318yescomplemented
129C2×#4314—44no—
130C2×#4314C2318yescomplemented
131C11×C22⋊C8C2314yes—
132C11×C22⋊C8C2318yes—
133C11×C22⋊C8C2314yes—
134#66885C2318yescomplemented
135#66882C2318yescomplemented
136#66881C2318yescomplemented
137#66880C2318yescomplemented
138#66880C2318yescomplemented
139#66880C2318yescomplemented
140C2×#3190—111nomaximal, Sylow
141C24×C11—24no—
142C24×C11—24no—
143C24×C11—42no—
144C24×C11C2×D411yescharacteristic
145C24×C11C2×D414yes—
146C24×C11C2×D411yescharacteristic
147C24×C11C2×D411yescharacteristic
148C23×D11—21no—
149C22×C4×C11—24no—
150C22×C4×C11—24no—
151C22×C4×C11—24no—
152C22×C4×C11—48no—
153C22×C4×C11—48no—
154C22×C4×C11—42no—
155C22×C4×C11—42no—
156C22×C4×C11—42no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D414yes—
164C22×C4×C11C2×D414yes—
165C22×C4×C11C2×D414yes—
166C22×C4×C11C2412yes—
167C22×C4×C11C2412yes—
168C22×C4×C11C2412yes—
169C22×C4×C11C2411yescharacteristic
170C2×C22⋊D11—24no—
171C2×C22⋊D11—24no—
172C2×C22⋊D11—24no—
173C2×C22⋊D11—44no—
174C2×C22⋊D11—44no—
175C2×C22⋊D11—44no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—24no—
179C22×Dic11—22no—
180C22×Dic11—24no—
181C22×Dic11—22no—
182C22×Dic11—21no—
183C22×Dic11—44no—
184C22×Dic11—44no—
185#4339—48no—
186#4339—48no—
187C2×D44—21no—
188C2×D44—24no—
189C2×D44C2412yes—
190C2×C4×D11—24no—
191C2×C4×D11—44no—
192C2×Dic22—24no—
193C2×Dic22—22no—
194C2×Dic22—21no—
195C2×Dic22—24no—
196C2×Dic22—24no—
197C2×Dic22—24no—
198C2×Dic22—48no—
199C2×Dic22—44no—
200C2×Dic22—48no—
201C2×Dic22C2414yes—
202C2×Dic22C2412yes—
203C2×C8×C11—24no—
204C2×C8×C11—24no—
205C2×C8×C11—48no—
206C2×C8×C11C2414yes—
207C2×C8×C11C2414yes—
208C22⋊Dic11—28no—
209C22⋊Dic11—28no—
210C22⋊Dic11—24no—
211C22⋊Dic11—24no—
212C22⋊Dic11—24no—
213(C2×D11)⋊C4—24no—
214(C2×D11)⋊C4—24no—
215C4⋊Dic11—24no—
216C4⋊Dic11—22no—
217C4⋊Dic11—21no—
218C4⋊Dic11—21no—
219C4⋊Dic11C2412yes—
220C4⋊Dic11C2412yes—
221C4⋊Dic11C2414yes—
222Dic11⋊C4—28no—
223Dic11⋊C4—28no—
224Dic11⋊C4—24no—
225Dic11⋊C4—24no—
226C4×Dic11—24no—
227Dic44—48no—
228#4314—48no—
229C2×#525—111no—
230C22×C22⋊Q8—111no—
231#3190—1116no—
232C2×#485—112no—
233C2×#483—111no—
234C2×#480—111no—
235C2×#467—112no—
236C2×#465—112no—
237C2×#452—112no—
238C2×#451—111no—
239C2×#448—111no—
240C22×C22⋊C8D1111yescharacteristic, complemented
241C23×C11—22no—
242C23×C11—22no—
243C23×C11—22no—
244C23×C11—22no—
245C23×C11—22no—
246C23×C11—28no—
247C23×C11—22no—
248C23×C11—28no—
249C23×C11—22no—
250C23×C11—44no—
251C23×C11—416no—
252C23×C11#13514yes—
253C23×C11#13714yes—
254C23×C11C22×D412yes—
255C23×C11C22×D412yes—
256C23×C11C22×D412yes—
257C23×C11C22×D411yescharacteristic
258C22×D11—22no—
259C22×D11—42no—
260C22×D11—42no—
261C22×D11—42no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—24no—
266C2×C4×C11—24no—
267C2×C4×C11—24no—
268C2×C4×C11—24no—
269C2×C4×C11—24no—
270C2×C4×C11—24no—
271C2×C4×C11—44no—
272C2×C4×C11—44no—
273C2×C4×C11—44no—
274C2×C4×C11C22×D412yes—
275C2×C4×C11C22×D412yes—
276C2×C4×C11C22×D412yes—
277C2×C4×C11C22×D411yescharacteristic
278C2×C4×C11H(5,𝔽2)14yes—
279C2×C4×C11C2511yescharacteristic
280C22⋊D11—48no—
281C22⋊D11—48no—
282C22⋊D11—48no—
283C2×Dic11—22no—
284C2×Dic11—22no—
285C2×Dic11—24no—
286C2×Dic11—24no—
287C2×Dic11—22no—
288C2×Dic11—48no—
289C2×Dic11—44no—
290C2×Dic11—42no—
291C2×Dic11—48no—
292C2×Dic11—44no—
293C2×Dic11—42no—
294C2×Dic11—42no—
295D44—24no—
296D44—42no—
297C4×D11—48no—
298Dic22—24no—
299Dic22—24no—
300Dic22—24no—
301Dic22—48no—
302Dic22—44no—
303Dic22—42no—
304C8×C11—24no—
305C8×C11—24no—
306C22×#41—111no—
307C23×Q8—111no—
308C24×C4C2×D1111yescharacteristic
309C22×Q16—112no—
310C22×SD16—112no—
311C23×C8C2×D1112yes—
312#525—118no—
313#525—224no—
314C2×#123—221no—
315C2×C22⋊Q8—111no—
316C2×C22⋊Q8—112no—
317C2×C22⋊Q8—112no—
318C2×C22⋊Q8—111no—
319C2×C22⋊Q8—118no—
320C2×C22⋊Q8—221no—
321C2×C22⋊Q8—221no—
322C2×C22⋊Q8—224no—
323C2×#121—111no—
324C2×#121—111no—
325C2×#120—221no—
326C2×C4×D4—221no—
327C2×C4×D4—221no—
328C2×#117—111no—
329C22×C4⋊C4—111no—
330C22×C4⋊C4—221no—
331C22×C22⋊C4—221no—
332#485—1116no—
333#483—118no—
334#480—118no—
335#467—1116no—
336#465—1116no—
337#452—1116no—
338#451—118no—
339#448—118no—
340C2×#107—112no—
341C2×#106—112no—
342C2×#103—112no—
343C2×#103—112no—
344C2×#103—112no—
345C2×#102—112no—
346C2×C22⋊C8C2×D1111yescharacteristic
347C2×C22⋊C8C2×D1111yescharacteristic
348C2×C22⋊C8C2×D1112yes—
349C2×C22⋊C8C2×D1118yescomplemented
350C22×C11—22no—
351C22×C11—22no—
352C22×C11—28no—
353C22×C11—28no—
354C22×C11—22no—
355C22×C11—22no—
356C22×C11—22no—
357C22×C11—22no—
358C22×C11—22no—
359C22×C11—416no—
360C22×C11—44no—
361C22×C11#53412yes—
362C22×C11C2×#13514yes—
363C22×C11C2×#13512yes—
364C22×C11C2×#13714yes—
365C22×C11C2×#13712yes—
366C22×C11C23×D411yescharacteristic
367C2×D11—42no—
368C2×D11—42no—
369C2×D11—42no—
370C2×D11—84no—
371C4×C11—22no—
372C4×C11—22no—
373C4×C11—22no—
374C4×C11#53412yes—
375C4×C11C2×H(5,𝔽2)12yes—
376Dic11—44no—
377Dic11—42no—
378Dic11—44no—
379Dic11—42no—
380Dic11—42no—
381C25D4411yescharacteristic
382C2×#41—114no—
383C2×#41—222no—
384C2×#41—444no—
385C22×Q8—112no—
386C22×Q8—111no—
387C22×Q8—114no—
388C22×Q8—222no—
389C22×Q8—221no—
390C22×Q8—444no—
391C22×D4—111no—
392C22×D4—221no—
393C22×D4—221no—
394C22×D4—221no—
395C23×C4—44no—
396C23×C4—221no—
397C23×C4—221no—
398C23×C4—221no—
399C23×C4D4411yescharacteristic
400C23×C4D4411yescharacteristic
401C23×C4D4411yescharacteristic
402C23×C4D4414yes—
403C23×C4C22×D1111yescharacteristic
404C23×C4C22×D1111yescharacteristic
405C23×C4C22×D1111yescharacteristic
406C23×C4C22×D1114yes—
407C2×Q16—118no—
408C2×Q16—444no—
409C2×SD16—118no—
410C2×SD16—444no—
411C22×C8—44no—
412C22×C8C22×D1112yes—
413C22×C8C22×D1112yes—
414C22×C8C22×D1118yes—
415#123—228no—
416C22⋊Q8—118no—
417C22⋊Q8—118no—
418C22⋊Q8—114no—
419C22⋊Q8—114no—
420C22⋊Q8—224no—
421C22⋊Q8—224no—
422C22⋊Q8—228no—
423C22⋊Q8—228no—
424C22⋊Q8—222no—
425C22⋊Q8—222no—
426#121—114no—
427#121—114no—
428#121—222no—
429#121—222no—
430#120—228no—
431C4×D4—228no—
432C4×D4—228no—
433#117—114no—
434#117—222no—
435C2×C4⋊C4—112no—
436C2×C4⋊C4—114no—
437C2×C4⋊C4—111no—
438C2×C4⋊C4—111no—
439C2×C4⋊C4—222no—
440C2×C4⋊C4—221no—
441C2×C4⋊C4—228no—
442C2×C4⋊C4—222no—
443C2×C4⋊C4—222no—
444C2×C4⋊C4—221no—
445C2×C4⋊C4—221no—
446C2×C22⋊C4—228no—
447C2×C22⋊C4—222no—
448C2×C22⋊C4—222no—
449C2×C22⋊C4—221no—
450C2×C22⋊C4—221no—
451C2×C22⋊C4—221no—
452C2×C22⋊C4—221no—
453C2×C22⋊C4—221no—
454C2×C42—221no—
455#107—118no—
456#106—118no—
457#103—118no—
458#103—118no—
459#103—118no—
460#102—118no—
461C22⋊C8C22×D1114yes—
462C22⋊C8C22×D1114yes—
463C22⋊C8C22×D1118yes—
464C2×C11—24no—
465C2×C11—24no—
466C2×C11—42no—
467C2×C11#319014yescomplemented
468C2×C11C2×#53411yescharacteristic
469C2×C11C22×#13511yescharacteristic
470C2×C11C22×#13711yescharacteristic
471D11—82no—
472C24—24no—
473C24—24no—
474C24—42no—
475C24—221no—
476C24C2×D4411yescharacteristic
477C24C2×D4414yes—
478C24C2×D4411yescharacteristic
479C24C2×D4411yescharacteristic
480#41—448no—
481#41—448no—
482C2×Q8—114no—
483C2×Q8—112no—
484C2×Q8—224no—
485C2×Q8—222no—
486C2×Q8—221no—
487C2×Q8—224no—
488C2×Q8—224no—
489C2×Q8—224no—
490C2×Q8—448no—
491C2×Q8—444no—
492C2×Q8—448no—
493C2×D4—112no—
494C2×D4—224no—
495C2×D4—224no—
496C2×D4—224no—
497C2×D4—221no—
498C2×D4—224no—
499C2×D4—444no—
500C2×D4—444no—
501C2×D4—444no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—48no—
506C22×C4—48no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—224no—
511C22×C4—224no—
512C22×C4—221no—
513C22×C4—221no—
514C22×C4—222no—
515C22×C4—221no—
516C22×C4—222no—
517C22×C4—224no—
518C22×C4—444no—
519C22×C4—444no—
520C22×C4—444no—
521C22×C4C2×D4412yes—
522C22×C4C2×D4412yes—
523C22×C4C2×D4412yes—
524C22×C4C2×D4411yescharacteristic
525C22×C4C2×D4411yescharacteristic
526C22×C4C2×D4411yescharacteristic
527C22×C4C2×D4414yes—
528C22×C4C2×D4414yes—
529C22×C4C2×D4414yes—
530C22×C4C23×D1112yes—
531C22×C4C23×D1112yes—
532C22×C4C23×D1112yes—
533C22×C4C23×D1111yescharacteristic
534Q16—448no—
535SD16—448no—
536C2×C8—24no—
537C2×C8—24no—
538C2×C8—48no—
539C2×C8C23×D1114yes—
540C2×C8C23×D1114yes—
541C4⋊C4—114no—
542C4⋊C4—112no—
543C4⋊C4—112no—
544C4⋊C4—224no—
545C4⋊C4—222no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C4⋊C4—228no—
549C4⋊C4—228no—
550C4⋊C4—224no—
551C4⋊C4—224no—
552C22⋊C4—228no—
553C22⋊C4—228no—
554C22⋊C4—224no—
555C22⋊C4—224no—
556C22⋊C4—224no—
557C22⋊C4—224no—
558C22⋊C4—224no—
559C42—224no—
560C11C2×#319011yescharacteristic, complemented, Sylow
561C23—22no—
562C23—22no—
563C23—22no—
564C23—22no—
565C23—28no—
566C23—22no—
567C23—28no—
568C23—22no—
569C23—22no—
570C23—44no—
571C23—416no—
572C23—222no—
573C23—442no—
574C23—442no—
575C23—442no—
576C23#6695714yes—
577C23#6696214yes—
578C23C22×D4412yes—
579C23C22×D4412yes—
580C23C22×D4412yes—
581C23C22×D4411yescharacteristic
582Q8—224no—
583Q8—224no—
584Q8—224no—
585Q8—448no—
586Q8—444no—
587Q8—442no—
588D4—224no—
589D4—448no—
590D4—448no—
591D4—448no—
592D4—442no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—24no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—44no—
603C2×C4—44no—
604C2×C4—44no—
605C2×C4—222no—
606C2×C4—222no—
607C2×C4—224no—
608C2×C4—222no—
609C2×C4—224no—
610C2×C4—448no—
611C2×C4—448no—
612C2×C4—448no—
613C2×C4—444no—
614C2×C4—442no—
615C2×C4—442no—
616C2×C4—442no—
617C2×C4—444no—
618C2×C4C22×D4412yes—
619C2×C4C22×D4412yes—
620C2×C4C22×D4412yes—
621C2×C4C22×D4411yescharacteristic
622C2×C4#6703714yes—
623C2×C4C24×D1111yescharacteristic
624C8—24no—
625C8—24no—
626C22—22no—
627C22—22no—
628C22—28no—
629C22—28no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—416no—
636C22—44no—
637C22—442no—
638C22—442no—
639C22—442no—
640C22—884no—
641C22#1062302412yes—
642C22C2×#6695714yes—
643C22C2×#6695712yes—
644C22C2×#6696214yes—
645C22C2×#6696212yes—
646C22C23×D4411yescharacteristic
647C4—22no—
648C4—22no—
649C4—22no—
650C4—442no—
651C4—444no—
652C4—444no—
653C4—442no—
654C4—442no—
655C4#1062302412yes—
656C4C2×#6703712yes—
657C2—24no—
658C2—24no—
659C2—42no—
660C2—882no—
661C2#1307939914yesdirect product factor
662C2C2×#1062302411yescharacteristic
663C2C22×#6695711yescharacteristic
664C2C22×#6696211yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×C22⋊C8C2
socleC23×C11C22×D4
prime radicalC2×#10623322C2
hypercenterC22×C22⋊C8D11
hypocenterC11C2×#3190
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C22×#66977C2semidirect
3. #13079399C2direct (N × H)
4. C2×#10622336C2semidirect
5. C2×#10622334C2semidirect
6. C2×#10622349C2semidirect
7. C2×#10622729C2semidirect
8. C2×#10622727C2semidirect
9. C2×#10622346C2semidirect
10. C2×#10622352C2semidirect
11. C2×#10622351C2semidirect
12. C22×C11×C22⋊C8C2semidirect
35. C2×#66977C22semidirect
37. C22×Dic44C22semidirect
38. C22×#4314C22semidirect
42. C2×C11×C22⋊C8C22semidirect
43. #10622729C22semidirect
44. #10622727C22semidirect
45. C2×#66885C22semidirect
46. C2×#66882C22semidirect
47. C2×#66881C22semidirect
48. C2×#66880C22semidirect
49. C2×#66880C22semidirect
50. C2×#66880C22semidirect
51. #10622352C22semidirect
52. #10622351C22semidirect
53. #10622349C22semidirect
54. #10622346C22semidirect
55. #10622336C22semidirect
56. #10622334C22semidirect
128. C2×Dic44C23semidirect
130. C2×#4314C23semidirect
134. #66885C23semidirect
135. #66882C23semidirect
136. #66881C23semidirect
137. #66880C23semidirect
138. #66880C23semidirect
139. #66880C23semidirect
240. C22×C22⋊C8D11semidirect
349. C2×C22⋊C8C2×D11semidirect
467. C2×C11#3190semidirect
560. C11C2×#3190semidirect
661. C2#13079399direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233222
C22×#669772
#130793992
C2×#106223362
C2×#106223342
C2×#106223492
C2×#106227292
C2×#106227272
C2×#106223462
C2×#106223522
C2×#106223512
C22×C11×C22⋊C82
C2×#319011