Finite Group Databasebeta

← C2×#13073770 #14924148

Subgroups — C2×#13073770 #14924148

Order 2816.

4166 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66999C211yesmaximal, characteristic, complemented
2C22×C22⋊C4×D11C211yesmaximal, characteristic
3#13073770C2116yesmaximal, direct product factor
4C2×#10622287C211yesmaximal, characteristic, complemented
5C2×#10622566C211yesmaximal, characteristic, complemented
6C2×#10622844C211yesmaximal, characteristic, complemented
7C2×#10622282C212yesmaximal, complemented
8C2×#10622557C212yesmaximal, complemented
9C2×#10622277C212yesmaximal, complemented
10C2×#10622568C212yesmaximal
11C2×#10622279C211yesmaximal, characteristic, complemented
12C2×C11×#393C211yesmaximal, characteristic, complemented
13C25×D11C2211yescharacteristic
14C23×Q8×C11C2211yescharacteristic, complemented
15C23×C4×D11C2211yescharacteristic
16C23×C4×D11C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2212yes—
19C22×C22⋊Dic11C2212yes—
20C22×C22⋊Dic11C2211yescharacteristic
21C2×#66999—28no—
22C2×#66999C2218yescomplemented
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2212yes—
29C22×C4⋊Dic11C2211yescharacteristic, complemented
30C22×Dic11⋊C4C2212yescomplemented
31C22×C4×Dic11C2212yescomplemented
32C2×C22⋊C4×D11—28no—
33C2×C22⋊C4×D11C2218yes—
34C11×#393C2218yescomplemented
35C2×C11×#95C2211yescharacteristic, complemented
36C2×C11×#95C2212yescomplemented
37#10622844C2218yescomplemented
38C2×C11⋊#95C2211yescharacteristic, complemented
39C2×C11⋊#95C2212yescomplemented
40C2×C11⋊#95C2212yescomplemented
41C2×C11⋊#95C2212yescomplemented
42#10622568C22116yes—
43#10622566C2218yescomplemented
44#10622557C22116yescomplemented
45#10622287C2218yescomplemented
46#10622282C22116yescomplemented
47#10622279C2218yescomplemented
48#10622277C22116yescomplemented
49C25×C11C2311yescharacteristic
50C24×D11—24no—
51C24×D11—24no—
52C24×D11—24no—
53C24×D11—28no—
54C24×D11—44no—
55C24×D11C2311yescharacteristic
56C24×D11C2314yes—
57C24×D11C2311yescharacteristic
58C22×Q8×C11—24no—
59C22×Q8×C11—44no—
60C22×Q8×C11C2314yescomplemented
61C23×C4×C11C2312yes—
62C23×C4×C11C2312yes—
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×Dic11C2312yes—
66C23×Dic11C2312yes—
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C22×C4×D11—24no—
70C22×C4×D11—28no—
71C22×C4×D11—44no—
72C22×C4×D11D418yes—
73C22×C4×D11C2314yes—
74C22×C4×D11C2314yes—
75C2×C11×C22⋊C4—24no—
76C2×C11×C22⋊C4—44no—
77C2×C11×C22⋊C4C2314yes—
78C2×C11×C22⋊C4C2318yes—
79C2×C22⋊Dic11—28no—
80C2×C22⋊Dic11—24no—
81C2×C22⋊Dic11C2314yes—
82C2×C22⋊Dic11C2318yes—
83#66999—232no—
84C2×(C2×D11)⋊C4—28no—
85C2×(C2×D11)⋊C4—28no—
86C2×(C2×D11)⋊C4—28no—
87C2×(C2×D11)⋊C4—24no—
88C2×(C2×D11)⋊C4—24no—
89C2×(C2×D11)⋊C4—44no—
90C2×(C2×D11)⋊C4C2314yes—
91C2×(C2×D11)⋊C4C2314yes—
92C2×(C2×D11)⋊C4C2318yes—
93C2×(C2×D11)⋊C4C2318yes—
94C2×(C2×D11)⋊C4C2318yes—
95C2×(C2×D11)⋊C4C2318yes—
96C2×C4⋊Dic11—24no—
97C2×C4⋊Dic11C2314yescomplemented
98C2×Dic11⋊C4—28no—
99C2×Dic11⋊C4C2318yescomplemented
100C2×C4×Dic11—44no—
101C2×C4×Dic11C2318yescomplemented
102C22⋊C4×D11—232no—
103C11×#95C2318yescomplemented
104C11×#95C2314yescomplemented
105C11⋊#95C2318yescomplemented
106C11⋊#95C2318yescomplemented
107C11⋊#95C2318yescomplemented
108C11⋊#95C2314yescomplemented
109C2×#2561—111nomaximal, Sylow
110C24×C11—22no—
111C24×C11—22no—
112C24×C11—24no—
113C24×C11—24no—
114C24×C11#4114yes—
115C24×C11C2412yes—
116C24×C11C2411yescharacteristic
117C23×D11—22no—
118C23×D11—22no—
119C23×D11—24no—
120C23×D11—232no—
121C23×D11—22no—
122C23×D11—28no—
123C23×D11—22no—
124C23×D11—24no—
125C23×D11—24no—
126C23×D11—28no—
127C23×D11—28no—
128C23×D11—216no—
129C23×D11—48no—
130C23×D11—432no—
131C23×D11—432no—
132C23×D11—416no—
133C23×D11—416no—
134C23×D11C2×D414yes—
135C23×D11#4114yes—
136C23×D11#4118yes—
137C23×D11C2412yes—
138C23×D11C2412yes—
139C2×Q8×C11—28no—
140C2×Q8×C11—48no—
141C2×Q8×C11—416no—
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11—22no—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—24no—
148C22×C4×C11—24no—
149C22×C4×C11—24no—
150C22×C4×C11—24no—
151C22×C4×C11C2×D414yes—
152C22×C4×C11C2412yes—
153C22×C4×C11C2414yes—
154C22×C4×C11C2414yes—
155C22×C4×C11C2412yes—
156C22×Dic11—24no—
157C22×Dic11—22no—
158C22×Dic11—24no—
159C22×Dic11—24no—
160C22×Dic11—24no—
161C22×Dic11—24no—
162C22×Dic11—24no—
163C22×Dic11—24no—
164C22×Dic11—24no—
165C22×Dic11C2×D414yes—
166C22×Dic11C2412yes—
167C22×Dic11C2414yes—
168C22×Dic11C2414yes—
169C22×Dic11C2412yes—
170C2×C4×D11—28no—
171C2×C4×D11—216no—
172C2×C4×D11—416no—
173C2×C4×D11—48no—
174C2×C4×D11—416no—
175C2×C4×D11C2×D4116yes—
176C11×C22⋊C4—28no—
177C11×C22⋊C4—48no—
178C22⋊Dic11—28no—
179C22⋊Dic11—216no—
180(C2×D11)⋊C4—28no—
181(C2×D11)⋊C4—216no—
182(C2×D11)⋊C4—216no—
183(C2×D11)⋊C4—216no—
184(C2×D11)⋊C4—28no—
185(C2×D11)⋊C4—48no—
186C4⋊Dic11—28no—
187Dic11⋊C4—216no—
188C4×Dic11—48no—
189C22×C22⋊Q8—111no—
190C23×C22⋊C4—111no—
191#2561—1116no—
192C2×#397—111no—
193C2×#397—111no—
194C2×#393—111no—
195C2×#393D1111yescharacteristic, complemented
196C2×#388—112no—
197C2×#388—112no—
198C2×#381—112no—
199C2×#379—112no—
200C2×C4×C22⋊C4—111no—
201C23×C11—28no—
202C23×C11—216no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—24no—
206C23×C11—24no—
207C23×C11—44no—
208C23×C11—44no—
209C23×C11—48no—
210C23×C11C22×D412yes—
211C23×C11C2×#4114yes—
212C23×C11C2×#4112yes—
213C23×C11C2×#4112yes—
214C23×C11C2×#4114yes—
215C23×C11H(5,𝔽2)14yes—
216C23×C11C2511yescharacteristic
217C22×D11—28no—
218C22×D11—28no—
219C22×D11—216no—
220C22×D11—216no—
221C22×D11—22no—
222C22×D11—22no—
223C22×D11—24no—
224C22×D11—232no—
225C22×D11—28no—
226C22×D11—216no—
227C22×D11—22no—
228C22×D11—22no—
229C22×D11—24no—
230C22×D11—24no—
231C22×D11—432no—
232C22×D11—432no—
233C22×D11—4128no—
234C22×D11—416no—
235C22×D11—44no—
236C22×D11—44no—
237C22×D11—48no—
238C22×D11—416no—
239C22×D11#124116yes—
240C22×D11C22×D414yes—
241C22×D11C2×#4114yes—
242C22×D11C2×#4118yes—
243Q8×C11—416no—
244C2×C4×C11—28no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—22no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—44no—
255C2×C4×C11—48no—
256C2×C4×C11—48no—
257C2×C4×C11C22×D414yes—
258C2×Dic11—28no—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—22no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—48no—
269C2×Dic11—44no—
270C2×Dic11—48no—
271C2×Dic11C22×D414yes—
272C4×D11—416no—
273C4×D11—416no—
274C26—111no—
275C23×Q8C2×D1111yescharacteristic, complemented
276C24×C4—111no—
277C24×C4—111no—
278C2×C22⋊Q8—118no—
279C2×C22⋊Q8—228no—
280C22×C4⋊C4—112no—
281C22×C4⋊C4—111no—
282C22×C22⋊C4—112no—
283C22×C22⋊C4—111no—
284C22×C22⋊C4—111no—
285C22×C22⋊C4—112no—
286C22×C22⋊C4—111no—
287C22×C22⋊C4—112no—
288C22×C22⋊C4—112no—
289C22×C22⋊C4—112no—
290C22×C22⋊C4—118no—
291C22×C22⋊C4—228no—
292C22×C22⋊C4C2×D1111yescharacteristic
293C22×C22⋊C4C2×D1112yes—
294C22×C42—112no—
295#397—118no—
296#397—118no—
297#393—118no—
298#393C2×D1118yescomplemented
299#388—1116no—
300#388—1116no—
301#381—1116no—
302#379—1116no—
303C4×C22⋊C4—118no—
304C2×#95—111no—
305C2×#95—112no—
306C2×#95—112no—
307C2×#95—112no—
308C2×#95C2×D1111yescharacteristic, complemented
309C2×#95C2×D1112yescomplemented
310C22×C11—24no—
311C22×C11—28no—
312C22×C11—416no—
313C22×C11—42no—
314C22×C11—42no—
315C22×C11—44no—
316C22×C11#52514yes—
317C22×C11C2×#12414yes—
318C22×C11#53414yes—
319C22×C11#55118yes—
320C22×C11#55118yes—
321C22×C11C23×D411yescharacteristic
322C22×C11C22×#4111yescharacteristic
323C22×C11C22×#4111yescharacteristic
324C22×C11C22×#4112yes—
325C22×C11C2×H(5,𝔽2)12yes—
326C2×D11—232no—
327C2×D11—24no—
328C2×D11—24no—
329C2×D11—28no—
330C2×D11—28no—
331C2×D11—24no—
332C2×D11—28no—
333C2×D11—464no—
334C2×D11—416no—
335C2×D11—42no—
336C2×D11—42no—
337C2×D11—44no—
338C2×D11C2×#12418yes—
339C4×C11—24no—
340C4×C11—42no—
341C4×C11—44no—
342C4×C11—44no—
343Dic11—24no—
344Dic11—44no—
345Dic11—42no—
346Dic11—44no—
347C25—111no—
348C25—111no—
349C25—114no—
350C25—224no—
351C25—224no—
352C25—228no—
353C25—224no—
354C25—444no—
355C25C22×D1111yescharacteristic
356C22×Q8—24no—
357C22×Q8—44no—
358C22×Q8C22×D1114yescomplemented
359C23×C4—111no—
360C23×C4—118no—
361C23×C4—114no—
362C23×C4—112no—
363C23×C4—112no—
364C23×C4—111no—
365C23×C4—114no—
366C23×C4—224no—
367C23×C4—228no—
368C23×C4—444no—
369C23×C4C22×D1112yes—
370C23×C4C22×D1112yes—
371C23×C4C22×D1111yescharacteristic
372C23×C4C22×D1111yescharacteristic
373C22⋊Q8—2232no—
374C2×C4⋊C4—118no—
375C2×C4⋊C4—114no—
376C2×C4⋊C4—228no—
377C2×C4⋊C4—224no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—114no—
381C2×C22⋊C4—118no—
382C2×C22⋊C4—114no—
383C2×C22⋊C4—114no—
384C2×C22⋊C4—118no—
385C2×C22⋊C4—118no—
386C2×C22⋊C4—118no—
387C2×C22⋊C4—118no—
388C2×C22⋊C4—2232no—
389C2×C22⋊C4—224no—
390C2×C22⋊C4—228no—
391C2×C22⋊C4—228no—
392C2×C22⋊C4—228no—
393C2×C22⋊C4—224no—
394C2×C22⋊C4—228no—
395C2×C22⋊C4—224no—
396C2×C22⋊C4—444no—
397C2×C22⋊C4C22×D1114yes—
398C2×C22⋊C4C22×D1118yes—
399C2×C42—118no—
400C2×C42—444no—
401#95—114no—
402#95—118no—
403#95—118no—
404#95—118no—
405#95C22×D1114yescomplemented
406#95C22×D1118yescomplemented
407C2×C11—44no—
408C2×C11#256118yescomplemented
409C2×C11C2×#52511yescharacteristic
410C2×C11C22×#12411yescharacteristic
411C2×C11C2×#53411yescharacteristic
412C2×C11C2×#55112yes—
413C2×C11C2×#55112yes—
414D11—28no—
415D11—44no—
416C24—22no—
417C24—24no—
418C24—22no—
419C24—24no—
420C24—114no—
421C24—118no—
422C24—112no—
423C24—114no—
424C24—112no—
425C24—228no—
426C24—228no—
427C24—2216no—
428C24—2232no—
429C24—224no—
430C24—222no—
431C24—222no—
432C24—222no—
433C24—224no—
434C24—228no—
435C24—222no—
436C24—224no—
437C24—448no—
438C24—4432no—
439C24—4416no—
440C24—4432no—
441C24—4416no—
442C24#434314yes—
443C24C23×D1112yes—
444C24C23×D1111yescharacteristic
445C2×Q8—28no—
446C2×Q8—48no—
447C2×Q8—416no—
448C22×C4—24no—
449C22×C4—22no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—114no—
458C22×C4—112no—
459C22×C4—1116no—
460C22×C4—112no—
461C22×C4—114no—
462C22×C4—114no—
463C22×C4—228no—
464C22×C4—2216no—
465C22×C4—224no—
466C22×C4—222no—
467C22×C4—224no—
468C22×C4—224no—
469C22×C4—224no—
470C22×C4—224no—
471C22×C4—224no—
472C22×C4—224no—
473C22×C4—224no—
474C22×C4—4416no—
475C22×C4—448no—
476C22×C4—4416no—
477C22×C4D4×D1114yes—
478C22×C4C23×D1112yes—
479C22×C4C23×D1114yes—
480C22×C4C23×D1114yes—
481C22×C4C23×D1112yes—
482C4⋊C4—2216no—
483C4⋊C4—228no—
484C22⋊C4—28no—
485C22⋊C4—48no—
486C22⋊C4—228no—
487C22⋊C4—2216no—
488C22⋊C4—2216no—
489C22⋊C4—2216no—
490C22⋊C4—228no—
491C22⋊C4—2216no—
492C22⋊C4—228no—
493C22⋊C4—448no—
494C42—448no—
495C11C2×#256111yescharacteristic, complemented, Sylow
496C23—28no—
497C23—216no—
498C23—22no—
499C23—24no—
500C23—24no—
501C23—22no—
502C23—44no—
503C23—44no—
504C23—48no—
505C23—114no—
506C23—118no—
507C23—1116no—
508C23—114no—
509C23—2232no—
510C23—228no—
511C23—228no—
512C23—2216no—
513C23—224no—
514C23—222no—
515C23—222no—
516C23—2216no—
517C23—228no—
518C23—222no—
519C23—224no—
520C23—222no—
521C23—224no—
522C23—2216no—
523C23—4432no—
524C23—4416no—
525C23—4432no—
526C23—4416no—
527C23—44128no—
528C23—444no—
529C23—448no—
530C23—444no—
531C23C2×D4×D1112yes—
532C23#6703714yes—
533C23C2×#434314yes—
534C23C2×#434312yes—
535C23#41×D1112yes—
536C23#41×D1114yes—
537C23C24×D1111yescharacteristic
538Q8—416no—
539C2×C4—28no—
540C2×C4—24no—
541C2×C4—22no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—48no—
550C2×C4—44no—
551C2×C4—48no—
552C2×C4—114no—
553C2×C4—228no—
554C2×C4—224no—
555C2×C4—222no—
556C2×C4—224no—
557C2×C4—224no—
558C2×C4—224no—
559C2×C4—224no—
560C2×C4—224no—
561C2×C4—224no—
562C2×C4—224no—
563C2×C4—4416no—
564C2×C4—4416no—
565C2×C4—448no—
566C2×C4—448no—
567C2×C4—444no—
568C2×C4C2×D4×D1114yes—
569C22—28no—
570C22—24no—
571C22—42no—
572C22—44no—
573C22—42no—
574C22—416no—
575C22—118no—
576C22—228no—
577C22—224no—
578C22—228no—
579C22—224no—
580C22—2232no—
581C22—224no—
582C22—228no—
583C22—4464no—
584C22—444no—
585C22—442no—
586C22—442no—
587C22—4416no—
588C22#1062312014yes—
589C22#1062315814yes—
590C22#1062316818yes—
591C22D11×#12414yes—
592C22#1062321018yes—
593C22C22×D4×D1111yescharacteristic
594C22C2×#6703712yes—
595C22C22×#434311yescharacteristic
596C22C2×#41×D1112yes—
597C22C2×#41×D1111yescharacteristic
598C4—24no—
599C4—42no—
600C4—44no—
601C4—44no—
602C4—224no—
603C4—444no—
604C4—444no—
605C4—442no—
606C2—44no—
607C2—228no—
608C2—444no—
609C2#1307377018yesdirect product factor
610C2C2×#1062315811yescharacteristic
611C2C2×D11×#12411yescharacteristic
612C2C2×#1062312011yescharacteristic
613C2C2×#1062316812yes—
614C2C2×#1062321012yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#393C2
socleC24×C11C24
prime radicalC25×D11C22
hypercenterC2×#393D11
hypocenterC11C2×#2561
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. C22×#66999C2semidirect
3. #13073770C2direct (N × H)
4. C2×#10622287C2semidirect
5. C2×#10622566C2semidirect
6. C2×#10622844C2semidirect
7. C2×#10622282C2semidirect
8. C2×#10622557C2semidirect
9. C2×#10622277C2semidirect
11. C2×#10622279C2semidirect
12. C2×C11×#393C2semidirect
14. C23×Q8×C11C22semidirect
22. C2×#66999C22semidirect
29. C22×C4⋊Dic11C22semidirect
30. C22×Dic11⋊C4C22semidirect
31. C22×C4×Dic11C22semidirect
34. C11×#393C22semidirect
35. C2×C11×#95C22semidirect
36. C2×C11×#95C22semidirect
37. #10622844C22semidirect
38. C2×C11⋊#95C22semidirect
39. C2×C11⋊#95C22semidirect
40. C2×C11⋊#95C22semidirect
41. C2×C11⋊#95C22semidirect
43. #10622566C22semidirect
44. #10622557C22semidirect
45. #10622287C22semidirect
46. #10622282C22semidirect
47. #10622279C22semidirect
48. #10622277C22semidirect
60. C22×Q8×C11C23semidirect
97. C2×C4⋊Dic11C23semidirect
99. C2×Dic11⋊C4C23semidirect
101. C2×C4×Dic11C23semidirect
103. C11×#95C23semidirect
104. C11×#95C23semidirect
105. C11⋊#95C23semidirect
106. C11⋊#95C23semidirect
107. C11⋊#95C23semidirect
108. C11⋊#95C23semidirect
195. C2×#393D11semidirect
275. C23×Q8C2×D11semidirect
298. #393C2×D11semidirect
308. C2×#95C2×D11semidirect
309. C2×#95C2×D11semidirect
358. C22×Q8C22×D11semidirect
405. #95C22×D11semidirect
406. #95C22×D11semidirect
408. C2×C11#2561semidirect
495. C11C2×#2561semidirect
609. C2#13073770direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669992
C22×C22⋊C4×D112
#130737702
C2×#106222872
C2×#106225662
C2×#106228442
C2×#106222822
C2×#106225572
C2×#106222772
C2×#106225682
C2×#106222792
C2×C11×#3932
C2×#256111