Finite Group Databasebeta

← C2×#13079394 #15624322

Subgroups — C2×#13079394 #15624322

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×#10623137C211yesmaximal, characteristic
2C22×#66999C211yesmaximal, characteristic, complemented
3#13079394C2116yesmaximal, direct product factor
4C2×#10622428C212yesmaximal, complemented
5C2×#10622334C211yesmaximal, characteristic, complemented
6C2×#10622646C211yesmaximal, characteristic, complemented
7C2×#10622426C212yesmaximal, complemented
8C2×#10622784C212yesmaximal, complemented
9C2×#10622786C212yesmaximal, complemented
10C2×#10622841C211yesmaximal, characteristic, complemented
11C2×D11×C22⋊C8C211yesmaximal, characteristic, complemented
12C2×C11×#448C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2211yescharacteristic
14C22×#4341C2211yescharacteristic
15C23×C4×D11C2211yescharacteristic
16C22×C11×SD16C2212yescomplemented
17C2×C11×#121C2211yescharacteristic
18C2×#66999—21no—
19C2×#66999—21no—
20C2×#66999—24no—
21C2×#66999C2212yes—
22C2×#66999C2212yes—
23C2×#66999C2218yescomplemented
24C22×#4326C2212yescomplemented
25C2×#66991C2211yescharacteristic
26C2×#66990—21no—
27C2×D4×Dic11—21no—
28C22×(C2×D11)⋊C4—21no—
29C22×C4⋊Dic11C2211yescharacteristic
30C2×#66977C2211yescharacteristic
31C22×Dic11⋊C4—21no—
32C22×C8×D11C2212yes—
33#10623137—24no—
34#10623137C2218yes—
35C2×#66950C2211yescharacteristic
36C2×#66945C2211yescharacteristic
37C2×#66936—21no—
38C2×(C22⋊D11)⋊C4—21no—
39C11×#448C2218yescomplemented
40C2×C11×#103C2212yescomplemented
41C2×C11×C22⋊C8C2211yescharacteristic
42#10622841C2218yescomplemented
43C2×#66899C2212yescomplemented
44C2×#66896C2212yescomplemented
45C2×C22⋊(C11⋊C8)C2211yescharacteristic
46#10622786C22116yescomplemented
47#10622784C22116yescomplemented
48C2×(C2×D11)⋊C8C2212yes—
49C2×#66881C2212yescomplemented
50C2×#66880C2212yescomplemented
51#10622646C2218yescomplemented
52C2×#66871C2212yescomplemented
53#10622428C22116yescomplemented
54#10622426C22116yescomplemented
55D11×C22⋊C8C2218yescomplemented
56#10622334C2218yescomplemented
57C24×D11D411yescharacteristic
58C22×Q8×C11—21no—
59C22×Q8×C11—22no—
60C22×Q8×C11—44no—
61C22×Q8×C11C2312yes—
62C22×Q8×C11C2314yes—
63C22×D4×C11—21no—
64C22×D4×C11C2311yescharacteristic
65C23×C4×C11—21no—
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11—21no—
68C22×C22⋊D11—21no—
69C23×Dic11—21no—
70C23×Dic11—21no—
71C23×Dic11D411yescharacteristic
72C2×#4341—22no—
73C2×#4341—44no—
74C2×#4341C2314yes—
75C22×C4×D11—44no—
76C22×C4×D11D411yescharacteristic
77C22×C4×D11D411yescharacteristic
78C22×C4×D11D414yes—
79C22×C4×D11C2311yescharacteristic
80C22×C4×D11C2311yescharacteristic
81C22×C4×D11C2314yes—
82C22×Dic22C2311yescharacteristic
83C2×C11×SD16—44no—
84C2×C11×SD16C2318yescomplemented
85C22×C8×C11C2312yes—
86C11×#121—22no—
87C11×#121C2314yes—
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C22⋊C4—21no—
90C2×C22⋊Dic11—21no—
91C2×C22⋊Dic11—21no—
92#66999—24no—
93#66999—24no—
94#66999—28no—
95#66999—28no—
96#66999C2318yes—
97#66999C2318yes—
98C2×#4326—44no—
99C2×#4326C2318yescomplemented
100#66991—22no—
101#66991C2314yes—
102#66990—28no—
103D4×Dic11—28no—
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—22no—
107C2×(C2×D11)⋊C4—22no—
108C2×(C2×D11)⋊C4—28no—
109C2×C4⋊Dic11—21no—
110C2×C4⋊Dic11—22no—
111C2×C4⋊Dic11—21no—
112C2×C4⋊Dic11C2311yescharacteristic
113C2×C4⋊Dic11C2312yes—
114C2×C4⋊Dic11C2314yes—
115#66977—22no—
116#66977C2314yes—
117C2×Dic11⋊C4—21no—
118C2×Dic11⋊C4—22no—
119C2×Dic11⋊C4—22no—
120C2×Dic11⋊C4—28no—
121C2×C4×Dic11—21no—
122C22×C11⋊C8C2312yes—
123C2×C8×D11—44no—
124C2×C8×D11C2318yes—
125#66950—22no—
126#66950C2314yes—
127#66945—22no—
128#66945C2314yes—
129#66936—28no—
130(C22⋊D11)⋊C4—28no—
131C11×#103C2318yescomplemented
132C11×C22⋊C8C2314yes—
133#66899C2318yescomplemented
134#66896C2318yescomplemented
135C22⋊(C11⋊C8)C2314yes—
136(C2×D11)⋊C8C2318yes—
137#66881C2318yescomplemented
138#66880C2318yescomplemented
139#66871C2318yescomplemented
140C2×#3190—111nomaximal, Sylow
141C24×C11—21no—
142C24×C11C2×D411yescharacteristic
143C23×D11—24no—
144C23×D11—24no—
145C23×D11—42no—
146C23×D11C2×D411yescharacteristic
147C23×D11C2×D414yes—
148C23×D11C2×D411yescharacteristic
149C2×Q8×C11—24no—
150C2×Q8×C11—22no—
151C2×Q8×C11—24no—
152C2×Q8×C11—24no—
153C2×Q8×C11—48no—
154C2×Q8×C11—44no—
155C2×Q8×C11—48no—
156C2×Q8×C11C2414yes—
157C2×D4×C11—24no—
158C2×D4×C11—21no—
159C2×D4×C11—24no—
160C2×D4×C11—44no—
161C2×D4×C11C2412yes—
162C22×C4×C11—24no—
163C22×C4×C11—21no—
164C22×C4×C11—24no—
165C22×C4×C11—22no—
166C22×C4×C11—44no—
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D412yes—
169C22×C4×C11C2412yes—
170C22×C4×C11C2411yescharacteristic
171C2×C22⋊D11—24no—
172C2×C22⋊D11—24no—
173C2×C22⋊D11—44no—
174C2×C22⋊D11—44no—
175C22×Dic11—24no—
176C22×Dic11—21no—
177C22×Dic11—24no—
178C22×Dic11—22no—
179C22×Dic11—21no—
180C22×Dic11—42no—
181C22×Dic11—44no—
182C22×Dic11—44no—
183C22×Dic11C2×D411yescharacteristic
184C22×Dic11C2×D411yescharacteristic
185C22×Dic11C2×D414yes—
186#4341—48no—
187#4341—48no—
188C2×C4×D11—24no—
189C2×C4×D11—24no—
190C2×C4×D11—42no—
191C2×C4×D11—42no—
192C2×C4×D11—48no—
193C2×C4×D11—48no—
194C2×C4×D11C2×D412yes—
195C2×C4×D11C2×D412yes—
196C2×C4×D11C2×D414yes—
197C2×C4×D11C2×D414yes—
198C2×C4×D11C2412yes—
199C2×C4×D11C2412yes—
200C2×Dic22—21no—
201C2×Dic22—24no—
202C2×Dic22C2412yes—
203C11×SD16—48no—
204C2×C8×C11—24no—
205C2×C8×C11C2414yes—
206C11×C4⋊C4—21no—
207C11×C4⋊C4C2412yes—
208C11×C22⋊C4—24no—
209C22⋊Dic11—24no—
210C22⋊Dic11—24no—
211#4326—48no—
212(C2×D11)⋊C4—24no—
213(C2×D11)⋊C4—24no—
214(C2×D11)⋊C4—28no—
215(C2×D11)⋊C4—28no—
216C4⋊Dic11—24no—
217C4⋊Dic11—21no—
218C4⋊Dic11—24no—
219C4⋊Dic11—22no—
220C4⋊Dic11C2414yes—
221C4⋊Dic11C2412yes—
222Dic11⋊C4—28no—
223Dic11⋊C4—28no—
224Dic11⋊C4—24no—
225C4×Dic11—24no—
226C2×C11⋊C8—24no—
227C2×C11⋊C8C2414yes—
228C8×D11—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×#448D1111yescharacteristic, complemented
240C22×C22⋊C8—111no—
241C23×C11—22no—
242C23×C11—22no—
243C23×C11—22no—
244C23×C11—42no—
245C23×C11—42no—
246C23×C11—42no—
247C23×C11#13514yes—
248C23×C11C22×D412yes—
249C23×C11C22×D411yescharacteristic
250C22×D11—22no—
251C22×D11—22no—
252C22×D11—22no—
253C22×D11—28no—
254C22×D11—22no—
255C22×D11—22no—
256C22×D11—28no—
257C22×D11—44no—
258C22×D11—416no—
259C22×D11#13714yes—
260C22×D11C22×D412yes—
261C22×D11C22×D412yes—
262Q8×C11—24no—
263Q8×C11—24no—
264Q8×C11—48no—
265Q8×C11—44no—
266D4×C11—24no—
267D4×C11—48no—
268D4×C11—42no—
269C2×C4×C11—22no—
270C2×C4×C11—24no—
271C2×C4×C11—24no—
272C2×C4×C11—22no—
273C2×C4×C11—24no—
274C2×C4×C11—48no—
275C2×C4×C11—44no—
276C2×C4×C11—42no—
277C2×C4×C11C22×D412yes—
278C2×C4×C11C22×D411yescharacteristic
279C2×C4×C11H(5,𝔽2)14yes—
280C2×C4×C11C2511yescharacteristic
281C22⋊D11—48no—
282C22⋊D11—48no—
283C2×Dic11—22no—
284C2×Dic11—22no—
285C2×Dic11—22no—
286C2×Dic11—24no—
287C2×Dic11—22no—
288C2×Dic11—44no—
289C2×Dic11—48no—
290C2×Dic11—42no—
291C2×Dic11—48no—
292C2×Dic11—44no—
293C2×Dic11—42no—
294C2×Dic11C22×D412yes—
295C2×Dic11C22×D412yes—
296C4×D11—24no—
297C4×D11—24no—
298C4×D11—24no—
299C4×D11—24no—
300C4×D11—44no—
301C4×D11—44no—
302Dic22—24no—
303Dic22—42no—
304C8×C11—24no—
305C11⋊C8—24no—
306C22×#41—111no—
307C23×Q8C2×D1111yescharacteristic
308C24×C4—111no—
309C22×Q16—112no—
310C22×SD16C2×D1112yescomplemented
311C23×C8—112no—
312#525—118no—
313#525—224no—
314C2×#123—221no—
315C2×C22⋊Q8—112no—
316C2×C22⋊Q8—112no—
317C2×C22⋊Q8—118no—
318C2×C22⋊Q8—111no—
319C2×C22⋊Q8—111no—
320C2×C22⋊Q8—221no—
321C2×C22⋊Q8—221no—
322C2×C22⋊Q8—224no—
323C2×#121—111no—
324C2×#121C2×D1111yescharacteristic
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#448C2×D1118yescomplemented
340C2×#107—112no—
341C2×#106—112no—
342C2×#103—112no—
343C2×#103—112no—
344C2×#103C2×D1112yescomplemented
345C2×#102—112no—
346C2×C22⋊C8—111no—
347C2×C22⋊C8—112no—
348C2×C22⋊C8—118no—
349C2×C22⋊C8C2×D1111yescharacteristic
350C22×C11—22no—
351C22×C11—28no—
352C22×C11—22no—
353C22×C11—42no—
354C22×C11—42no—
355C22×C11—42no—
356C22×C11—84no—
357C22×C11#53412yes—
358C22×C11C2×#13514yes—
359C22×C11C2×#13512yes—
360C22×C11C2×#13712yes—
361C22×C11C23×D411yescharacteristic
362C2×D11—22no—
363C2×D11—28no—
364C2×D11—22no—
365C2×D11—22no—
366C2×D11—22no—
367C2×D11—22no—
368C2×D11—416no—
369C2×D11—44no—
370C2×D11C2×#13714yes—
371C4×C11—22no—
372C4×C11—44no—
373C4×C11—42no—
374C4×C11#53412yes—
375C4×C11C2×H(5,𝔽2)12yes—
376Dic11—22no—
377Dic11—22no—
378Dic11—42no—
379Dic11—44no—
380Dic11—42no—
381C25—111no—
382C2×#41—114no—
383C2×#41—222no—
384C2×#41—444no—
385C22×Q8—22no—
386C22×Q8—21no—
387C22×Q8—44no—
388C22×Q8—111no—
389C22×Q8C22×D1112yes—
390C22×Q8C22×D1114yes—
391C22×D4—21no—
392C22×D4—221no—
393C22×D4—221no—
394C22×D4C22×D1111yescharacteristic
395C23×C4—21no—
396C23×C4—111no—
397C23×C4—111no—
398C23×C4—111no—
399C23×C4—111no—
400C23×C4—111no—
401C23×C4—114no—
402C23×C4—114no—
403C23×C4—221no—
404C23×C4—221no—
405C23×C4—444no—
406C23×C4C22×D1111yescharacteristic
407C2×Q16—118no—
408C2×Q16—444no—
409C2×SD16—44no—
410C2×SD16C22×D1118yescomplemented
411C22×C8—112no—
412C22×C8—118no—
413C22×C8—444no—
414C22×C8C22×D1112yes—
415#123—228no—
416C22⋊Q8—118no—
417C22⋊Q8—118no—
418C22⋊Q8—114no—
419C22⋊Q8—114no—
420C22⋊Q8—222no—
421C22⋊Q8—224no—
422C22⋊Q8—224no—
423C22⋊Q8—228no—
424C22⋊Q8—228no—
425C22⋊Q8—222no—
426#121—22no—
427#121—114no—
428#121—222no—
429#121C22×D1114yes—
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—228no—
439C2×C4⋊C4—222no—
440C2×C4⋊C4—222no—
441C2×C4⋊C4—221no—
442C2×C4⋊C4—222no—
443C2×C4⋊C4—221no—
444C2×C4⋊C4—221no—
445C2×C4⋊C4C22×D1111yescharacteristic
446C2×C22⋊C4—21no—
447C2×C22⋊C4—228no—
448C2×C22⋊C4—222no—
449C2×C22⋊C4—222no—
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#103C22×D1118yescomplemented
460#102—118no—
461C22⋊C8—114no—
462C22⋊C8—118no—
463C22⋊C8C22×D1114yes—
464C2×C11—24no—
465C2×C11—82no—
466C2×C11#319014yescomplemented
467C2×C11C2×#53411yescharacteristic
468C2×C11C22×#13511yescharacteristic
469C2×C11C22×#13711yescharacteristic
470D11—24no—
471D11—42no—
472C24—21no—
473C24—111no—
474C24—111no—
475C24—114no—
476C24—224no—
477C24—224no—
478C24—442no—
479C24D4×D1111yescharacteristic
480#41—448no—
481#41—448no—
482C2×Q8—24no—
483C2×Q8—22no—
484C2×Q8—24no—
485C2×Q8—24no—
486C2×Q8—48no—
487C2×Q8—44no—
488C2×Q8—48no—
489C2×Q8—112no—
490C2×Q8—221no—
491C2×Q8—224no—
492C2×Q8C23×D1114yes—
493C2×D4—24no—
494C2×D4—21no—
495C2×D4—24no—
496C2×D4—44no—
497C2×D4—224no—
498C2×D4—224no—
499C2×D4—444no—
500C2×D4—444no—
501C2×D4C23×D1112yes—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—44no—
507C22×C4—111no—
508C22×C4—111no—
509C22×C4—114no—
510C22×C4—112no—
511C22×C4—112no—
512C22×C4—112no—
513C22×C4—112no—
514C22×C4—114no—
515C22×C4—114no—
516C22×C4—224no—
517C22×C4—224no—
518C22×C4—224no—
519C22×C4—224no—
520C22×C4—221no—
521C22×C4—222no—
522C22×C4—221no—
523C22×C4—448no—
524C22×C4—448no—
525C22×C4—442no—
526C22×C4—442no—
527C22×C4—442no—
528C22×C4—444no—
529C22×C4—444no—
530C22×C4D4×D1112yes—
531C22×C4D4×D1111yescharacteristic
532C22×C4C23×D1112yes—
533C22×C4C23×D1111yescharacteristic
534Q16—448no—
535SD16—48no—
536C2×C8—24no—
537C2×C8—114no—
538C2×C8—224no—
539C2×C8—448no—
540C2×C8C23×D1114yes—
541C4⋊C4—21no—
542C4⋊C4—114no—
543C4⋊C4—112no—
544C4⋊C4—228no—
545C4⋊C4—228no—
546C4⋊C4—224no—
547C4⋊C4—224no—
548C4⋊C4—222no—
549C4⋊C4—221no—
550C4⋊C4—224no—
551C4⋊C4C23×D1112yes—
552C22⋊C4—24no—
553C22⋊C4—228no—
554C22⋊C4—228no—
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—42no—
565C23—42no—
566C23—42no—
567C23—114no—
568C23—112no—
569C23—112no—
570C23—228no—
571C23—222no—
572C23—222no—
573C23—228no—
574C23—222no—
575C23—222no—
576C23—222no—
577C23—444no—
578C23—4416no—
579C23#6696914yes—
580C23C2×D4×D1112yes—
581C23C2×D4×D1111yescharacteristic
582Q8—24no—
583Q8—24no—
584Q8—48no—
585Q8—44no—
586Q8—224no—
587Q8—442no—
588D4—24no—
589D4—48no—
590D4—42no—
591D4—448no—
592D4—448no—
593C2×C4—22no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—22no—
597C2×C4—24no—
598C2×C4—48no—
599C2×C4—42no—
600C2×C4—44no—
601C2×C4—112no—
602C2×C4—112no—
603C2×C4—222no—
604C2×C4—222no—
605C2×C4—224no—
606C2×C4—224no—
607C2×C4—224no—
608C2×C4—224no—
609C2×C4—222no—
610C2×C4—224no—
611C2×C4—222no—
612C2×C4—444no—
613C2×C4—444no—
614C2×C4—444no—
615C2×C4—448no—
616C2×C4—448no—
617C2×C4—444no—
618C2×C4—442no—
619C2×C4—442no—
620C2×C4C2×D4×D1112yes—
621C2×C4C2×D4×D1111yescharacteristic
622C2×C4#6703714yes—
623C2×C4C24×D1111yescharacteristic
624C8—24no—
625C8—224no—
626C22—22no—
627C22—28no—
628C22—22no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—84no—
633C22—114no—
634C22—222no—
635C22—228no—
636C22—222no—
637C22—222no—
638C22—222no—
639C22—222no—
640C22—4416no—
641C22—444no—
642C22#1062312012yes—
643C22C2×#6696914yes—
644C22C2×#6696912yes—
645C22D11×#13712yes—
646C22C22×D4×D1111yescharacteristic
647C4—22no—
648C4—44no—
649C4—42no—
650C4—222no—
651C4—222no—
652C4—442no—
653C4—444no—
654C4—442no—
655C4#1062312012yes—
656C4C2×#6703712yes—
657C2—24no—
658C2—82no—
659C2—224no—
660C2—442no—
661C2#1307939414yesdirect product factor
662C2C2×#1062312011yescharacteristic
663C2C22×#6696911yescharacteristic
664C2C2×D11×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#448C2
socleC23×C11C22×D4
prime radicalC2×#10623137C2
hypercenterC2×#448D11
hypocenterC11C2×#3190
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
2. C22×#66999C2semidirect
3. #13079394C2direct (N × H)
4. C2×#10622428C2semidirect
5. C2×#10622334C2semidirect
6. C2×#10622646C2semidirect
7. C2×#10622426C2semidirect
8. C2×#10622784C2semidirect
9. C2×#10622786C2semidirect
10. C2×#10622841C2semidirect
11. C2×D11×C22⋊C8C2semidirect
12. C2×C11×#448C2semidirect
16. C22×C11×SD16C22semidirect
23. C2×#66999C22semidirect
24. C22×#4326C22semidirect
39. C11×#448C22semidirect
40. C2×C11×#103C22semidirect
42. #10622841C22semidirect
43. C2×#66899C22semidirect
44. C2×#66896C22semidirect
46. #10622786C22semidirect
47. #10622784C22semidirect
49. C2×#66881C22semidirect
50. C2×#66880C22semidirect
51. #10622646C22semidirect
52. C2×#66871C22semidirect
53. #10622428C22semidirect
54. #10622426C22semidirect
55. D11×C22⋊C8C22semidirect
56. #10622334C22semidirect
84. C2×C11×SD16C23semidirect
99. C2×#4326C23semidirect
131. C11×#103C23semidirect
133. #66899C23semidirect
134. #66896C23semidirect
137. #66881C23semidirect
138. #66880C23semidirect
139. #66871C23semidirect
239. C2×#448D11semidirect
310. C22×SD16C2×D11semidirect
339. #448C2×D11semidirect
344. C2×#103C2×D11semidirect
410. C2×SD16C22×D11semidirect
459. #103C22×D11semidirect
466. C2×C11#3190semidirect
560. C11C2×#3190semidirect
661. C2#13079394direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231372
C22×#669992
#130793942
C2×#106224282
C2×#106223342
C2×#106226462
C2×#106224262
C2×#106227842
C2×#106227862
C2×#106228412
C2×D11×C22⋊C82
C2×C11×#4482
C2×#319011