Finite Group Databasebeta

← #14755686

Subgroups — #14755686

Order 2816.

1704 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623353C211yesmaximal, characteristic
2#13081819C211yesmaximal, characteristic, complemented
3C2×#10622752C211yesmaximal, characteristic, complemented
4C2×#10622619C211yesmaximal, characteristic, complemented
5#13069115C218yesmaximal, complemented
6C2×#10622194C211yesmaximal, characteristic, complemented
7#13068325C211yesmaximal, characteristic, complemented
8C2×C11×#421C211yesmaximal, characteristic, complemented
9C22×C11×#41C2211yescharacteristic
10C22×#4339C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13#10623358—22no—
14#10623358—22no—
15#41×Dic11—22no—
16#41×Dic11C2214yescomplemented
17C2×#67004C412yescomplemented
18#10623353—22no—
19#10623353—22no—
20#10623353C414yescomplemented
21#10623353C2214yes—
22C2×#67003—22no—
23C2×#67002C412yescomplemented
24#10623343—21no—
25C2×#66995—21no—
26#10623329—21no—
27#10623329—22no—
28C2×#66985—21no—
29C2×#66979—22no—
30C2×#66979C2211yescharacteristic
31C2×#66979C2211yescharacteristic
32C22×#4318C2211yescharacteristic
33C11×#421—22no—
34C11×#421C2214yescomplemented
35C2×C11×#104—22no—
36#10622752—22no—
37#10622752—22no—
38C2×#66889C2214yescomplemented
39#10622619—22no—
40#10622619C2214yescomplemented
41C2×#66870—22no—
42#10622194C2214yescomplemented
43#10622170C2214yescomplemented
44C2×C11×#41—21no—
45C2×C11×#41—21no—
46C2×C11×#41—21no—
47C2×C11×#41—21no—
48C2×C11×#41—21no—
49C2×C11×#41—21no—
50C2×C11×#41C2×C412yes—
51C2×C11×#41C2×C412yes—
52C2×C11×#41D412yes—
53C2×C11×#41D412yes—
54C2×C11×#41D412yes—
55C2×C11×#41C2312yes—
56C22×Q8×C11D411yescharacteristic
57C22×D4×C11—21no—
58C22×D4×C11D411yescharacteristic
59C23×C4×C11—21no—
60C23×C4×C11C2311yescharacteristic
61C22×C22⋊D11—21no—
62C2×#4339—21no—
63C2×#4339—21no—
64C2×#4339—21no—
65C2×#4339—21no—
66C2×#4339—21no—
67C2×#4339—21no—
68C2×#4339—21no—
69C2×#4339—21no—
70C2×#4339—21no—
71C2×#4339—21no—
72C2×#4339C2×C412yescomplemented
73C2×#4339C2312yes—
74C22×D44C2×C411yescharacteristic, complemented
75C22×C4×D11—21no—
76C22×Dic22C2×C411yescharacteristic, complemented
77C2×C11×M16—21no—
78C2×C11×M16—21no—
79C2×C11×M16—21no—
80C2×C11×M16—21no—
81C2×C11×M16—21no—
82C2×C11×M16C2312yes—
83C22×C8×C11—21no—
84C11×#117—21no—
85C11×#117—21no—
86C11×#117—21no—
87C11×#117C2312yes—
88C2×C11×C4⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C42×C11—21no—
91C2×C22⋊Dic11—24no—
92C2×C22⋊Dic11—21no—
93C2×C22⋊Dic11D412yes—
94#67004—24no—
95#67004C2×C418yescomplemented
96#67003—28no—
97#67003—28no—
98#67002—24no—
99#67002C2×C418yescomplemented
100Q8×Dic11—24no—
101Q8×Dic11—24no—
102C2×#4326—22no—
103#66995—24no—
104#66995—24no—
105C2×#4325—22no—
106D4×Dic11—28no—
107D4×Dic11—24no—
108D4×Dic11—24no—
109D4×Dic11—28no—
110C2×#4324—22no—
111#66985—24no—
112#66985—24no—
113C2×#4323—22no—
114#66979—24no—
115#66979—24no—
116#66979—21no—
117#66979—21no—
118#66979—21no—
119#66979—21no—
120#66979—24no—
121#66979D412yes—
122#66979D412yes—
123#66979D412yes—
124#66979C2312yes—
125C2×C4⋊Dic11—24no—
126C2×C4⋊Dic11—21no—
127C2×C4⋊Dic11—21no—
128C2×C4×Dic11—21no—
129C2×C4×Dic11—24no—
130C2×C4×Dic11C2312yes—
131C2×#4318—21no—
132C2×#4318—21no—
133C2×#4318—21no—
134C2×#4318C2×C412yescomplemented
135C2×#4318C2×C412yescomplemented
136C2×#4318C2312yes—
137C22×C11⋊C8—21no—
138C11×#104—28no—
139#66889—28no—
140#66870—28no—
141#21000—111nomaximal, Sylow
142C24×C11—21no—
143C24×C11C2×D411yescharacteristic
144C23×D11—21no—
145C11×#41—22no—
146C11×#41—22no—
147C11×#41—22no—
148C11×#41—22no—
149C11×#41—22no—
150C11×#41—22no—
151C11×#41—22no—
152C11×#41—22no—
153C11×#41—22no—
154C11×#41—22no—
155C11×#41—22no—
156C11×#41—22no—
157C11×#41C22⋊C414yes—
158C11×#41C22⋊C414yes—
159C11×#41C22×C414yes—
160C11×#41C2×D414yes—
161C2×Q8×C11—21no—
162C2×Q8×C11—21no—
163C2×Q8×C11—21no—
164C2×Q8×C11C22⋊C412yes—
165C2×Q8×C11C22⋊C412yes—
166C2×Q8×C11C2×D412yes—
167C2×D4×C11—22no—
168C2×D4×C11—22no—
169C2×D4×C11—22no—
170C2×D4×C11—22no—
171C2×D4×C11—22no—
172C2×D4×C11—22no—
173C2×D4×C11—21no—
174C2×D4×C11—21no—
175C2×D4×C11—21no—
176C2×D4×C11C22⋊C412yes—
177C2×D4×C11C22⋊C412yes—
178C2×D4×C11C2×D412yes—
179C22×C4×C11—21no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—22no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11—41no—
187C22×C4×C11C22×C411yescharacteristic
188C22×C4×C11C22×C411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11#4111yescharacteristic
197C22×C4×C11#4111yescharacteristic
198C22×C4×C11#4111yescharacteristic
199C22×C4×C11#4111yescharacteristic
200C22×C4×C11C2411yescharacteristic
201C2×C22⋊D11—22no—
202C2×C22⋊D11—22no—
203C2×C22⋊D11—41no—
204C2×C22⋊D11—41no—
205C2×C22⋊D11—41no—
206C2×C22⋊D11—41no—
207C22×Dic11—28no—
208C22×Dic11—21no—
209C22×Dic11—22no—
210C22×Dic11—22no—
211#4339—22no—
212#4339—22no—
213#4339—22no—
214#4339—22no—
215#4339—22no—
216#4339—22no—
217#4339—22no—
218#4339—22no—
219#4339—41no—
220#4339—41no—
221#4339—41no—
222#4339—41no—
223#4339—41no—
224#4339—41no—
225#4339—41no—
226#4339—41no—
227C2×D44—21no—
228C2×D44—21no—
229C2×D44—21no—
230C2×D44—21no—
231C2×D44—21no—
232C2×D44C22×C412yes—
233C2×C4×D11—22no—
234C2×C4×D11—22no—
235C2×C4×D11—41no—
236C2×C4×D11—41no—
237C2×C4×D11—41no—
238C2×C4×D11—41no—
239C2×Dic22—21no—
240C2×Dic22—21no—
241C2×Dic22—21no—
242C2×Dic22—21no—
243C2×Dic22—21no—
244C2×Dic22C22×C412yes—
245C11×M16—22no—
246C11×M16—22no—
247C11×M16—41no—
248C11×M16—41no—
249C2×C8×C11—22no—
250C2×C8×C11—41no—
251C2×C8×C11—41no—
252C11×C4⋊C4—22no—
253C11×C4⋊C4—41no—
254C11×C22⋊C4—22no—
255C11×C22⋊C4—41no—
256C42×C11—22no—
257C42×C11—41no—
258C22⋊Dic11—28no—
259C22⋊Dic11—22no—
260C22⋊Dic11—22no—
261C22⋊Dic11—22no—
262C22⋊Dic11C2×D414yes—
263#4326—28no—
264#4325—28no—
265#4324—28no—
266#4323—28no—
267C4⋊Dic11—28no—
268C4⋊Dic11—22no—
269C4⋊Dic11—22no—
270C4⋊Dic11—22no—
271C4⋊Dic11—22no—
272C4×Dic11—28no—
273C4×Dic11—22no—
274C4×Dic11—22no—
275C4×Dic11—22no—
276C4×Dic11C2×D414yes—
277#4318—22no—
278#4318—22no—
279#4318—22no—
280#4318C22×C414yes—
281C2×C11⋊C8—22no—
282C2×C11⋊C8—22no—
283C2×C11⋊C8—22no—
284C2×#575—111no—
285#3428—111no—
286C2×#421—111no—
287C2×#421D1111yescharacteristic, complemented
288C2×#410—111no—
289#1906—118no—
290C2×#344—111no—
291#1733—111no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—81no—
296C23×C11—82no—
297C23×C11C4×D411yescharacteristic
298C23×C11C4×D411yescharacteristic
299C23×C11#12011yescharacteristic
300C23×C11#12011yescharacteristic
301C23×C11#12111yescharacteristic
302C23×C11#12111yescharacteristic
303C23×C11C22×D411yescharacteristic
304C22×D11—22no—
305C22×D11—41no—
306C22×D11—41no—
307C22×D11—82no—
308Q8×C11—22no—
309Q8×C11—22no—
310Q8×C11—22no—
311Q8×C11C2×C22⋊C414yes—
312D4×C11—24no—
313D4×C11—24no—
314D4×C11—24no—
315D4×C11—24no—
316D4×C11—22no—
317D4×C11—22no—
318D4×C11—22no—
319D4×C11C2×C22⋊C414yes—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—24no—
324C2×C4×C11—24no—
325C2×C4×C11—24no—
326C2×C4×C11—24no—
327C2×C4×C11—42no—
328C2×C4×C11—82no—
329C2×C4×C11C2×C22⋊C411yescharacteristic
330C2×C4×C11C2×C22⋊C411yescharacteristic
331C2×C4×C11C2×C22⋊C411yescharacteristic
332C2×C4×C11C2×C22⋊C411yescharacteristic
333C2×C4×C11C4×D411yescharacteristic
334C2×C4×C11C4×D411yescharacteristic
335C2×C4×C11C4×D411yescharacteristic
336C2×C4×C11C4×D411yescharacteristic
337C2×C4×C11C4×D411yescharacteristic
338C2×C4×C11C4×D411yescharacteristic
339C2×C4×C11#12011yescharacteristic
340C2×C4×C11#12011yescharacteristic
341C2×C4×C11#12111yescharacteristic
342C2×C4×C11#12111yescharacteristic
343C2×C4×C11#12111yescharacteristic
344C2×C4×C11#12111yescharacteristic
345C2×C4×C11#12111yescharacteristic
346C2×C4×C11#12111yescharacteristic
347C2×C4×C11#12311yescharacteristic
348C2×C4×C11#12311yescharacteristic
349C2×C4×C11#12311yescharacteristic
350C2×C4×C11#12311yescharacteristic
351C2×C4×C11C23×C411yescharacteristic
352C2×C4×C11C22×D411yescharacteristic
353C2×C4×C11C22×D411yescharacteristic
354C2×C4×C11C22×D411yescharacteristic
355C2×C4×C11C2×#4111yescharacteristic
356C2×C4×C11C2×#4111yescharacteristic
357C22⋊D11—42no—
358C22⋊D11—42no—
359C22⋊D11—42no—
360C22⋊D11—42no—
361C2×Dic11—22no—
362C2×Dic11—24no—
363C2×Dic11—24no—
364C2×Dic11—41no—
365C2×Dic11—41no—
366C2×Dic11—82no—
367C2×Dic11—82no—
368C2×Dic11—88no—
369D44—22no—
370D44—22no—
371D44—41no—
372D44—41no—
373C4×D11—42no—
374C4×D11—42no—
375C4×D11—42no—
376C4×D11—42no—
377Dic22—22no—
378Dic22—22no—
379Dic22—41no—
380Dic22—41no—
381C8×C11—42no—
382C11⋊C8—24no—
383C22×#41—111no—
384C22×#41C2×D1111yescharacteristic
385#575—114no—
386#575—114no—
387#575—222no—
388#575—222no—
389C2×#137—112no—
390C2×#137—221no—
391C2×AGL(1,ℤ/8)—112no—
392C2×AGL(1,ℤ/8)—221no—
393C2×#135—222no—
394C22×M16—111no—
395C22×M16C2×D1111yescharacteristic
396#520—222no—
397#520—222no—
398#519—221no—
399#518—222no—
400#518—221no—
401C4×#41—114no—
402C4×#41—222no—
403C2×#117—111no—
404C2×#117—111no—
405C2×#117—222no—
406C2×#117C2×D1111yescharacteristic
407#421—22no—
408#421—222no—
409#421—222no—
410#421C2×D1114yescomplemented
411C2×#104—22no—
412C2×#104—114no—
413#410—114no—
414#410—222no—
415C2×#99—222no—
416#344—114no—
417#339—114no—
418C22×C11—24no—
419C22×C11—41no—
420C22×C11—41no—
421C22×C11—41no—
422C22×C11—41no—
423C22×C11—41no—
424C22×C11—41no—
425C22×C11—41no—
426C22×C11—44no—
427C22×C11—82no—
428C22×C11—82no—
429C22×C11#38611yescharacteristic
430C22×C11#38611yescharacteristic
431C22×C11#38611yescharacteristic
432C22×C11#38611yescharacteristic
433C22×C11C2×C4×D411yescharacteristic
434C22×C11C2×#12011yescharacteristic
435C22×C11C2×#12111yescharacteristic
436C2×D11—42no—
437C2×D11—82no—
438C2×D11—82no—
439C2×D11—82no—
440C4×C11—24no—
441C4×C11—82no—
442C4×C11#38611yescharacteristic
443C4×C11#38611yescharacteristic
444C4×C11#38611yescharacteristic
445C4×C11#38611yescharacteristic
446C4×C11C22×C22⋊C411yescharacteristic
447C4×C11C2×C4×D411yescharacteristic
448C4×C11C2×#12111yescharacteristic
449C4×C11C2×#12311yescharacteristic
450Dic11—44no—
451Dic11—44no—
452Dic11—42no—
453C2×#41—21no—
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—112no—
460C2×#41—112no—
461C2×#41—221no—
462C2×#41—221no—
463C2×#41—221no—
464C2×#41—221no—
465C2×#41—221no—
466C2×#41—221no—
467C2×#41—221no—
468C2×#41—221no—
469C2×#41—221no—
470C2×#41—221no—
471C2×#41C4×D1112yes—
472C2×#41C4×D1112yes—
473C2×#41D4412yes—
474C2×#41C22⋊D1112yes—
475C2×#41C22⋊D1112yes—
476C2×#41C22×D1112yes—
477C22×Q8—111no—
478C22×Q8D4411yescharacteristic
479C22×D4—21no—
480C22×D4—111no—
481C22×D4—221no—
482C22×D4D4411yescharacteristic
483C23×C4—21no—
484C23×C4—221no—
485C23×C4C22×D1111yescharacteristic
486#137—118no—
487#137—224no—
488#137—224no—
489#137—224no—
490AGL(1,ℤ/8)—118no—
491AGL(1,ℤ/8)—224no—
492AGL(1,ℤ/8)—224no—
493AGL(1,ℤ/8)—224no—
494#135—228no—
495#135—228no—
496C2×Q16—222no—
497C2×SD16—222no—
498C2×SD16—222no—
499C2×D8—222no—
500C2×M16—21no—
501C2×M16—21no—
502C2×M16—21no—
503C2×M16—21no—
504C2×M16—21no—
505C2×M16—112no—
506C2×M16—112no—
507C2×M16—112no—
508C2×M16—221no—
509C2×M16—221no—
510C2×M16—221no—
511C2×M16C22×D1112yes—
512C22×C8—21no—
513C22×C8—221no—
514C4×Q8—224no—
515C4×Q8—224no—
516C4×D4—228no—
517C4×D4—228no—
518C4×D4—224no—
519C4×D4—224no—
520#117—21no—
521#117—21no—
522#117—21no—
523#117—112no—
524#117—112no—
525#117—112no—
526#117—112no—
527#117—224no—
528#117—224no—
529#117—224no—
530#117—221no—
531#117—221no—
532#117—221no—
533#117—221no—
534#117C22×D1112yes—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—224no—
537C2×C4⋊C4—221no—
538C2×C4⋊C4—221no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—112no—
541C2×C22⋊C4—224no—
542C2×C22⋊C4—221no—
543C2×C42—21no—
544C2×C42—112no—
545C2×C42—224no—
546C2×C42—221no—
547#104—28no—
548#104—228no—
549#99—228no—
550C2×C11—21no—
551C2×C11—21no—
552C2×C11—21no—
553C2×C11—21no—
554C2×C11—21no—
555C2×C11—21no—
556C2×C11—21no—
557C2×C11—44no—
558C2×C11C2×#38611yescharacteristic
559D11—82no—
560C24—21no—
561C24—221no—
562C24D4×D1111yescharacteristic
563#41—22no—
564#41—22no—
565#41—22no—
566#41—22no—
567#41—22no—
568#41—22no—
569#41—22no—
570#41—22no—
571#41—22no—
572#41—22no—
573#41—22no—
574#41—22no—
575#41—222no—
576#41—222no—
577#41—222no—
578#41—222no—
579#41—222no—
580#41—222no—
581#41—222no—
582#41—222no—
583#41—441no—
584#41—441no—
585#41—441no—
586#41—441no—
587#41—441no—
588#41—441no—
589#41—441no—
590#41—441no—
591#41(C2×D11)⋊C414yes—
592#41(C2×D11)⋊C414yes—
593#41C2×C4×D1114yes—
594#41C2×C22⋊D1114yes—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—112no—
599C2×Q8—221no—
600C2×Q8—221no—
601C2×Q8—221no—
602C2×Q8—221no—
603C2×Q8—221no—
604C2×Q8(C2×D11)⋊C412yes—
605C2×Q8(C2×D11)⋊C412yes—
606C2×Q8C2×D4412yes—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—112no—
617C2×D4—222no—
618C2×D4—222no—
619C2×D4—221no—
620C2×D4—221no—
621C2×D4—221no—
622C2×D4—221no—
623C2×D4—221no—
624C2×D4—441no—
625C2×D4—441no—
626C2×D4—441no—
627C2×D4—441no—
628C2×D4(C2×D11)⋊C412yes—
629C2×D4(C2×D11)⋊C412yes—
630C2×D4C2×D4412yes—
631C22×C4—21no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—41no—
639C22×C4—221no—
640C22×C4—228no—
641C22×C4—222no—
642C22×C4—222no—
643C22×C4—222no—
644C22×C4—222no—
645C22×C4—441no—
646C22×C4—441no—
647C22×C4—441no—
648C22×C4—441no—
649C22×C4C2×C4×D1111yescharacteristic
650C22×C4C2×C4×D1111yescharacteristic
651C22×C4C2×D4411yescharacteristic
652C22×C4C2×D4411yescharacteristic
653C22×C4D4×D1111yescharacteristic
654C22×C4D4×D1111yescharacteristic
655C22×C4D4×D1111yescharacteristic
656C22×C4#434111yescharacteristic
657C22×C4#434111yescharacteristic
658C22×C4#434111yescharacteristic
659C22×C4#434111yescharacteristic
660C22×C4C2×C22⋊D1111yescharacteristic
661C22×C4C2×C22⋊D1111yescharacteristic
662C22×C4C23×D1111yescharacteristic
663Q16—228no—
664SD16—228no—
665SD16—228no—
666D8—228no—
667M16—22no—
668M16—22no—
669M16—41no—
670M16—41no—
671M16—114no—
672M16—222no—
673M16—222no—
674M16—222no—
675C2×C8—22no—
676C2×C8—41no—
677C2×C8—41no—
678C2×C8—222no—
679C2×C8—222no—
680C2×C8—222no—
681C4⋊C4—22no—
682C4⋊C4—41no—
683C4⋊C4—228no—
684C4⋊C4—222no—
685C4⋊C4—222no—
686C4⋊C4—222no—
687C4⋊C4—222no—
688C22⋊C4—22no—
689C22⋊C4—41no—
690C22⋊C4—114no—
691C22⋊C4—228no—
692C22⋊C4—222no—
693C22⋊C4—222no—
694C22⋊C4—222no—
695C42—22no—
696C42—41no—
697C42—114no—
698C42—228no—
699C42—222no—
700C42—222no—
701C42—222no—
702C11#2100011yescharacteristic, complemented, Sylow
703C23—22no—
704C23—22no—
705C23—22no—
706C23—81no—
707C23—82no—
708C23—222no—
709C23—441no—
710C23—441no—
711C23—882no—
712C23(C22⋊D11)⋊C411yescharacteristic
713C23(C22⋊D11)⋊C411yescharacteristic
714C23#6693511yescharacteristic
715C23#6693511yescharacteristic
716C23#6699211yescharacteristic
717C23#6699211yescharacteristic
718C23C2×D4×D1111yescharacteristic
719Q8—22no—
720Q8—22no—
721Q8—22no—
722Q8—222no—
723Q8—222no—
724Q8—441no—
725Q8—441no—
726Q8C2×(C2×D11)⋊C414yes—
727D4—24no—
728D4—24no—
729D4—24no—
730D4—24no—
731D4—22no—
732D4—22no—
733D4—22no—
734D4—222no—
735D4—222no—
736D4—442no—
737D4—442no—
738D4—442no—
739D4—442no—
740D4—441no—
741D4—441no—
742D4C2×(C2×D11)⋊C414yes—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—42no—
751C2×C4—82no—
752C2×C4—222no—
753C2×C4—224no—
754C2×C4—224no—
755C2×C4—441no—
756C2×C4—441no—
757C2×C4—442no—
758C2×C4—442no—
759C2×C4—442no—
760C2×C4—442no—
761C2×C4—882no—
762C2×C4—882no—
763C2×C4—888no—
764C2×C4(C22⋊D11)⋊C411yescharacteristic
765C2×C4(C22⋊D11)⋊C411yescharacteristic
766C2×C4(C22⋊D11)⋊C411yescharacteristic
767C2×C4(C22⋊D11)⋊C411yescharacteristic
768C2×C4(C22⋊D11)⋊C411yescharacteristic
769C2×C4(C22⋊D11)⋊C411yescharacteristic
770C2×C4#6693511yescharacteristic
771C2×C4#6693511yescharacteristic
772C2×C4#6693911yescharacteristic
773C2×C4#6693911yescharacteristic
774C2×C4#6693911yescharacteristic
775C2×C4#6693911yescharacteristic
776C2×C4C2×(C2×D11)⋊C411yescharacteristic
777C2×C4C2×(C2×D11)⋊C411yescharacteristic
778C2×C4C2×(C2×D11)⋊C411yescharacteristic
779C2×C4C2×(C2×D11)⋊C411yescharacteristic
780C2×C4#6699211yescharacteristic
781C2×C4#6699211yescharacteristic
782C2×C4#6699211yescharacteristic
783C2×C4#6699211yescharacteristic
784C2×C4#6699211yescharacteristic
785C2×C4#6699211yescharacteristic
786C2×C4C22×C4×D1111yescharacteristic
787C2×C4C22×D4411yescharacteristic
788C2×C4C2×D4×D1111yescharacteristic
789C2×C4C2×#434111yescharacteristic
790C2×C4C2×#434111yescharacteristic
791C2×C4C22×C22⋊D1111yescharacteristic
792C8—42no—
793C8—224no—
794C22—24no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—44no—
803C22—82no—
804C22—82no—
805C22—442no—
806C22—882no—
807C22—882no—
808C22—882no—
809C22#1062257111yescharacteristic
810C22#1062257111yescharacteristic
811C22#1062257111yescharacteristic
812C22#1062257111yescharacteristic
813C22C2×(C22⋊D11)⋊C411yescharacteristic
814C22C2×#6693511yescharacteristic
815C22C2×#6699211yescharacteristic
816C4—24no—
817C4—82no—
818C4—444no—
819C4—444no—
820C4—442no—
821C4#1062257111yescharacteristic
822C4#1062257111yescharacteristic
823C4#1062257111yescharacteristic
824C4#1062257111yescharacteristic
825C4C2×(C22⋊D11)⋊C411yescharacteristic
826C4C2×#6693911yescharacteristic
827C4C22×(C2×D11)⋊C411yescharacteristic
828C4C2×#6699211yescharacteristic
829C2—21no—
830C2—21no—
831C2—21no—
832C2—21no—
833C2—21no—
834C2—21no—
835C2—21no—
836C2—44no—
837C2—882no—
838C2C2×#1062257111yescharacteristic
subgroupG/H
centerC4C2×#66992
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#421C2
socleC2×C11C2×#386
prime radicalC2×#10623353C2
cosocleC22×C4×C11C24
hypercenterC2×#421D11
hypocenterC11#21000
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. #13081819C2semidirect
3. C2×#10622752C2semidirect
4. C2×#10622619C2semidirect
5. #13069115C2semidirect
6. C2×#10622194C2semidirect
7. #13068325C2semidirect
8. C2×C11×#421C2semidirect
16. #41×Dic11C22semidirect
17. C2×#67004C4semidirect
20. #10623353C4semidirect
23. C2×#67002C4semidirect
34. C11×#421C22semidirect
38. C2×#66889C22semidirect
40. #10622619C22semidirect
42. #10622194C22semidirect
43. #10622170C22semidirect
72. C2×#4339C2×C4semidirect
74. C22×D44C2×C4semidirect
76. C22×Dic22C2×C4semidirect
95. #67004C2×C4semidirect
99. #67002C2×C4semidirect
134. C2×#4318C2×C4semidirect
135. C2×#4318C2×C4semidirect
287. C2×#421D11semidirect
410. #421C2×D11semidirect
702. C11#21000semidirect

Maximal subgroups

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

subgroupindex
C2×#106233532
#130818192
C2×#106227522
C2×#106226192
#130691152
C2×#106221942
#130683252
C2×C11×#4212
#2100011