Finite Group Databasebeta

← #15618100

Subgroups — #15618100

Order 2816.

2628 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623353C211yesmaximal, characteristic
2C2×#10623276C211yesmaximal, characteristic, complemented
3#13077531C218yesmaximal, complemented
4#13077523C218yesmaximal, complemented
5#13077517C218yesmaximal, complemented
6C2×#10622737C211yesmaximal, characteristic, complemented
7C2×#10622849C211yesmaximal, characteristic, complemented
8C2×#10622752C211yesmaximal, characteristic, complemented
9#13077034C211yesmaximal, characteristic, complemented
10C2×C11×#568C211yesmaximal, characteristic, complemented
11C22×C11×#41C2211yescharacteristic
12C22×#4339C2211yescharacteristic
13C11×#568—22no—
14C11×#568—22no—
15C11×#568C2214yescomplemented
16C11×#568C2214yescomplemented
17C2×C11×#131—22no—
18C2×C11×#131C2214yescomplemented
19C22×C11×M16—22no—
20C22×C11×M16C2211yescharacteristic
21C22×C11×M16C2211yescharacteristic
22C2×#67004C412yescomplemented
23#10623353C414yescomplemented
24#10623353C414yescomplemented
25#10623353C2214yes—
26#10623353C2214yes—
27C2×#67003C2214yes—
28C2×#67002C412yescomplemented
29C2×#66995C412yescomplemented
30C2×#66985C412yescomplemented
31C2×#66979C2211yescharacteristic
32C22×#4318C2211yescharacteristic
33C22×#4318C2211yescharacteristic
34#10623276—22no—
35#10623276—22no—
36#10623276C2214yescomplemented
37#10623276C2214yescomplemented
38C2×#66960—22no—
39C2×M16×D11—22no—
40C2×#66954C2214yescomplemented
41#10622849C2214yescomplemented
42#10622849C2214yescomplemented
43C2×#66901C2214yescomplemented
44#10622758C22132yescomplemented
45#10622757C22132yescomplemented
46#10622752C2214yescomplemented
47#10622752C2214yescomplemented
48C2×#66889C2214yescomplemented
49#10622737C2214yescomplemented
50#10622737C2214yescomplemented
51C2×#66886C2214yescomplemented
52#10622735C2214yescomplemented
53M16×Dic11C2214yescomplemented
54#10622714C2214yescomplemented
55C2×C11×#41—21no—
56C2×C11×#41—21no—
57C2×C11×#41—21no—
58C2×C11×#41—21no—
59C2×C11×#41—21no—
60C2×C11×#41—21no—
61C2×C11×#41C2×C412yes—
62C2×C11×#41C2×C412yes—
63C2×C11×#41C2×C412yes—
64C2×C11×#41C2312yes—
65C2×C11×#41C2312yes—
66C2×C11×#41C2312yes—
67C22×Q8×C11C2×C411yescharacteristic
68C22×D4×C11—21no—
69C22×D4×C11C2×C411yescharacteristic
70C23×C4×C11—21no—
71C23×C4×C11C2311yescharacteristic
72C22×C22⋊D11—21no—
73C2×#4339—21no—
74C2×#4339—21no—
75C2×#4339—21no—
76C2×#4339—21no—
77C2×#4339—21no—
78C2×#4339—21no—
79C2×#4339C2×C412yes—
80C2×#4339C2×C412yes—
81C2×#4339C2×C412yes—
82C2×#4339C2312yes—
83C2×#4339C2312yes—
84C2×#4339C2312yes—
85C22×D44C2×C411yescharacteristic
86C22×C4×D11—21no—
87C22×Dic22C2×C411yescharacteristic
88C11×#131—28no—
89C11×#131—28no—
90C11×#131—28no—
91C11×#131C23116yescomplemented
92C2×C11×M16—21no—
93C2×C11×M16—21no—
94C2×C11×M16—21no—
95C2×C11×M16—28no—
96C2×C11×M16—28no—
97C2×C11×M16—24no—
98C2×C11×M16D412yes—
99C2×C11×M16D412yes—
100C2×C11×M16D412yes—
101C2×C11×M16D412yes—
102C2×C11×M16C2312yes—
103C2×C11×M16C2312yes—
104C2×C11×M16C2312yes—
105C2×C11×M16C2312yes—
106C2×C11×M16C2312yes—
107C22×C8×C11—21no—
108C22×C8×C11—24no—
109C22×C8×C11C2312yes—
110C2×C22⋊Dic11—21no—
111#67004C2×C418yes—
112#67004C2×C418yescomplemented
113#67003C2×C4116yescomplemented
114#67003C23116yes—
115#67002C2×C418yes—
116#67002C2×C418yescomplemented
117C2×#4326C2×C414yescomplemented
118#66995C2×C418yes—
119#66995C2×C418yescomplemented
120C2×#4325C2×C414yescomplemented
121C2×#4324C2×C414yescomplemented
122#66985C2×C418yes—
123#66985C2×C418yescomplemented
124C2×#4323C2×C414yescomplemented
125#66979—21no—
126#66979—21no—
127#66979C2312yes—
128#66979C2312yes—
129C2×C4⋊Dic11—21no—
130C2×C4×Dic11C2312yes—
131C2×#4318—21no—
132C2×#4318—21no—
133C2×#4318—21no—
134C2×#4318C2×C412yes—
135C2×#4318C2×C412yes—
136C2×#4318C2×C412yes—
137C2×#4318C2×C412yes—
138C2×#4318C2312yes—
139C2×#4318C2312yes—
140C2×#4318C2312yes—
141C2×#4318C2312yes—
142C2×#4318C2312yes—
143C22×C11⋊C8—21no—
144C22×C11⋊C8C2312yes—
145#66960—28no—
146#66960—28no—
147M16×D11—28no—
148M16×D11—28no—
149#66954—28no—
150#66954C23116yescomplemented
151C2×#4313—24no—
152C2×C8×D11—24no—
153#66901C23116yescomplemented
154#66889C23116yescomplemented
155#66886C23116yescomplemented
156#66879C2318yescomplemented
157C8×Dic11C2318yescomplemented
158#60182—111nomaximal, Sylow
159C24×C11—21no—
160C24×C11#4111yescharacteristic
161C23×D11—21no—
162C11×#41—22no—
163C11×#41—22no—
164C11×#41—22no—
165C11×#41—22no—
166C11×#41—22no—
167C11×#41—22no—
168C11×#41—22no—
169C11×#41—22no—
170C11×#41—22no—
171C11×#41—22no—
172C11×#41—22no—
173C11×#41—22no—
174C11×#41C22×C414yes—
175C11×#41C22×C414yes—
176C11×#41C22×C414yes—
177C11×#41C2414yes—
178C2×Q8×C11—21no—
179C2×Q8×C11—21no—
180C2×Q8×C11—21no—
181C2×Q8×C11C22×C412yes—
182C2×Q8×C11C22×C412yes—
183C2×Q8×C11C22×C412yes—
184C2×D4×C11—22no—
185C2×D4×C11—22no—
186C2×D4×C11—22no—
187C2×D4×C11—22no—
188C2×D4×C11—22no—
189C2×D4×C11—22no—
190C2×D4×C11—21no—
191C2×D4×C11—21no—
192C2×D4×C11—21no—
193C2×D4×C11C22×C412yes—
194C2×D4×C11C22×C412yes—
195C2×D4×C11C22×C412yes—
196C22×C4×C11—21no—
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—22no—
202C22×C4×C11—22no—
203C22×C4×C11C22×C411yescharacteristic
204C22×C4×C11C22×C411yescharacteristic
205C22×C4×C11C22×C411yescharacteristic
206C22×C4×C11C22×C411yescharacteristic
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11#4111yescharacteristic
212C22×C4×C11#4111yescharacteristic
213C22×C4×C11#4111yescharacteristic
214C22×C4×C11C2411yescharacteristic
215C22×C4×C11C2411yescharacteristic
216C22×C4×C11C2411yescharacteristic
217C2×C22⋊D11—22no—
218C2×C22⋊D11—22no—
219C2×C22⋊D11—22no—
220C2×C22⋊D11—22no—
221C2×C22⋊D11—22no—
222C2×C22⋊D11—22no—
223C22×Dic11—21no—
224C22×Dic11—22no—
225#4339—22no—
226#4339—22no—
227#4339—22no—
228#4339—22no—
229#4339—22no—
230#4339—22no—
231#4339—22no—
232#4339—22no—
233#4339—22no—
234#4339—22no—
235#4339—22no—
236#4339—22no—
237#4339C22×C414yes—
238#4339C22×C414yes—
239#4339C22×C414yes—
240#4339C2414yes—
241C2×D44—21no—
242C2×D44—21no—
243C2×D44—21no—
244C2×D44C22×C412yes—
245C2×D44C22×C412yes—
246C2×D44C22×C412yes—
247C2×C4×D11—22no—
248C2×C4×D11—22no—
249C2×C4×D11—22no—
250C2×C4×D11—22no—
251C2×C4×D11—22no—
252C2×C4×D11—22no—
253C2×Dic22—21no—
254C2×Dic22—21no—
255C2×Dic22—21no—
256C2×Dic22C22×C412yes—
257C2×Dic22C22×C412yes—
258C2×Dic22C22×C412yes—
259C11×M16—216no—
260C11×M16—22no—
261C11×M16—22no—
262C11×M16—22no—
263C11×M16C2×D414yes—
264C11×M16C2×D414yes—
265C11×M16C2×D414yes—
266C11×M16C2×D414yes—
267C11×M16C2414yes—
268C2×C8×C11—216no—
269C2×C8×C11—22no—
270C2×C8×C11—22no—
271C2×C8×C11—22no—
272C2×C8×C11C2×D414yes—
273C2×C8×C11C2×D414yes—
274C2×C8×C11C2414yes—
275C22⋊Dic11—22no—
276C22⋊Dic11—22no—
277#4326C22×C4116yes—
278#4325C22×C4116yes—
279#4324C22×C4116yes—
280#4323C22×C4116yes—
281C4⋊Dic11—22no—
282C4⋊Dic11—22no—
283C4×Dic11—22no—
284C4×Dic11C2414yes—
285#4318—22no—
286#4318—22no—
287#4318—22no—
288#4318C22×C414yes—
289#4318C22×C414yes—
290#4318C22×C414yes—
291#4318C22×C414yes—
292#4318C2414yes—
293C2×C11⋊C8—22no—
294C2×C11⋊C8—22no—
295C2×C11⋊C8—22no—
296C2×C11⋊C8C22×C414yes—
297C2×C11⋊C8C22×C414yes—
298C2×C11⋊C8C2414yes—
299#4313—216no—
300C8×D11—216no—
301C2×#575—111no—
302C2×#568—111no—
303C2×#568D1111yescharacteristic, complemented
304#2957—118no—
305#2956—118no—
306#2955—118no—
307C2×#430—111no—
308C2×#421—111no—
309C2×#421—111no—
310#2873—111no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—81no—
315C23×C11—82no—
316C23×C11C4×D411yescharacteristic
317C23×C11C4×D411yescharacteristic
318C23×C11C4×D411yescharacteristic
319C23×C11C4×D411yescharacteristic
320C23×C11C2×#4111yescharacteristic
321C23×C11C2×#4111yescharacteristic
322C23×C11C2×#4111yescharacteristic
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—82no—
327Q8×C11—22no—
328Q8×C11—22no—
329Q8×C11—22no—
330Q8×C11C23×C414yes—
331D4×C11—24no—
332D4×C11—24no—
333D4×C11—24no—
334D4×C11—24no—
335D4×C11—22no—
336D4×C11—22no—
337D4×C11—22no—
338D4×C11C23×C414yes—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—24no—
343C2×C4×C11—24no—
344C2×C4×C11—24no—
345C2×C4×C11—24no—
346C2×C4×C11C4×D411yescharacteristic
347C2×C4×C11C4×D411yescharacteristic
348C2×C4×C11C4×D411yescharacteristic
349C2×C4×C11C4×D411yescharacteristic
350C2×C4×C11C4×D411yescharacteristic
351C2×C4×C11C4×D411yescharacteristic
352C2×C4×C11C4×D411yescharacteristic
353C2×C4×C11C4×D411yescharacteristic
354C2×C4×C11C4×D411yescharacteristic
355C2×C4×C11C4×D411yescharacteristic
356C2×C4×C11C4×D411yescharacteristic
357C2×C4×C11C4×D411yescharacteristic
358C2×C4×C11C23×C411yescharacteristic
359C2×C4×C11C23×C411yescharacteristic
360C2×C4×C11C23×C411yescharacteristic
361C2×C4×C11C23×C411yescharacteristic
362C2×C4×C11C23×C411yescharacteristic
363C2×C4×C11C23×C411yescharacteristic
364C2×C4×C11C22×D411yescharacteristic
365C2×C4×C11C22×D411yescharacteristic
366C2×C4×C11C22×D411yescharacteristic
367C2×C4×C11C22×D411yescharacteristic
368C2×C4×C11C22×D411yescharacteristic
369C2×C4×C11C22×D411yescharacteristic
370C2×C4×C11C2×#4111yescharacteristic
371C2×C4×C11C2×#4111yescharacteristic
372C2×C4×C11C2×#4111yescharacteristic
373C2×C4×C11C2511yescharacteristic
374C22⋊D11—24no—
375C22⋊D11—24no—
376C22⋊D11—24no—
377C22⋊D11—24no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—24no—
382C2×Dic11—82no—
383D44—22no—
384D44—22no—
385D44—22no—
386D44C23×C414yes—
387C4×D11—24no—
388C4×D11—24no—
389C4×D11—24no—
390C4×D11—24no—
391Dic22—22no—
392Dic22—22no—
393Dic22—22no—
394Dic22C23×C414yes—
395C8×C11—24no—
396C8×C11C22×D418yes—
397C11⋊C8—24no—
398C11⋊C8C23×C418yes—
399C22×#41—111no—
400C22×#41C2×D1111yescharacteristic
401#575—114no—
402#575—114no—
403#575—114no—
404#575—114no—
405C2×#137—112no—
406C2×#137—112no—
407C2×AGL(1,ℤ/8)—112no—
408C2×AGL(1,ℤ/8)—112no—
409C2×#135—114no—
410#568—22no—
411#568—22no—
412#568—114no—
413#568—114no—
414#568—222no—
415#568—222no—
416#568C2×D1114yescomplemented
417#568C2×D1114yescomplemented
418C2×#131—22no—
419C2×#131—114no—
420C2×#131—222no—
421C2×#131C2×D1114yescomplemented
422C22×M16—22no—
423C22×M16—111no—
424C22×M16—111no—
425C22×M16—222no—
426C22×M16C2×D1111yescharacteristic
427C22×M16C2×D1111yescharacteristic
428C2×#117—111no—
429#444—1132no—
430#443—1132no—
431#430—114no—
432#430—114no—
433C2×#108—114no—
434#421—114no—
435#421—114no—
436#421—114no—
437#421—114no—
438C2×#104—114no—
439C2×#104—114no—
440#405—114no—
441#405—114no—
442C4×M16—114no—
443C22×C11—24no—
444C22×C11—41no—
445C22×C11—41no—
446C22×C11—41no—
447C22×C11—41no—
448C22×C11—41no—
449C22×C11—41no—
450C22×C11—41no—
451C22×C11—44no—
452C22×C11—82no—
453C22×C11—82no—
454C22×C11C2×C4×D411yescharacteristic
455C22×C11C2×C4×D411yescharacteristic
456C22×C11C2×C4×D411yescharacteristic
457C22×C11C2×C4×D411yescharacteristic
458C22×C11C2×C4×D411yescharacteristic
459C22×C11C2×C4×D411yescharacteristic
460C22×C11C22×#4111yescharacteristic
461C2×D11—24no—
462C2×D11—44no—
463C2×D11—82no—
464C2×D11—82no—
465C4×C11—24no—
466C4×C11C2×C4×D411yescharacteristic
467C4×C11C2×C4×D411yescharacteristic
468C4×C11C2×C4×D411yescharacteristic
469C4×C11C2×C4×D411yescharacteristic
470C4×C11C2×C4×D411yescharacteristic
471C4×C11C2×C4×D411yescharacteristic
472C4×C11C24×C411yescharacteristic
473C4×C11C23×D411yescharacteristic
474Dic11—24no—
475Dic11—44no—
476C2×#41—21no—
477C2×#41—21no—
478C2×#41—21no—
479C2×#41—21no—
480C2×#41—21no—
481C2×#41—21no—
482C2×#41—112no—
483C2×#41—112no—
484C2×#41—112no—
485C2×#41—112no—
486C2×#41—112no—
487C2×#41—112no—
488C2×#41—221no—
489C2×#41—221no—
490C2×#41—221no—
491C2×#41—221no—
492C2×#41—221no—
493C2×#41—221no—
494C2×#41C4×D1112yes—
495C2×#41C4×D1112yes—
496C2×#41C4×D1112yes—
497C2×#41C22×D1112yes—
498C2×#41C22×D1112yes—
499C2×#41C22×D1112yes—
500C22×Q8—111no—
501C22×Q8C4×D1111yescharacteristic
502C22×D4—21no—
503C22×D4—111no—
504C22×D4—221no—
505C22×D4C4×D1111yescharacteristic
506C23×C4—21no—
507C23×C4—221no—
508C23×C4C22×D1111yescharacteristic
509#137—118no—
510#137—118no—
511#137—118no—
512#137—118no—
513AGL(1,ℤ/8)—118no—
514AGL(1,ℤ/8)—118no—
515AGL(1,ℤ/8)—118no—
516AGL(1,ℤ/8)—118no—
517#135—1116no—
518#135—1116no—
519C2×Q16—114no—
520C2×SD16—114no—
521C2×SD16—114no—
522C2×D8—114no—
523#131—28no—
524#131—28no—
525#131—28no—
526#131—1116no—
527#131—228no—
528#131—228no—
529#131—228no—
530#131C22×D11116yescomplemented
531C2×M16—21no—
532C2×M16—21no—
533C2×M16—21no—
534C2×M16—28no—
535C2×M16—28no—
536C2×M16—24no—
537C2×M16—112no—
538C2×M16—112no—
539C2×M16—112no—
540C2×M16—112no—
541C2×M16—112no—
542C2×M16—112no—
543C2×M16—112no—
544C2×M16—112no—
545C2×M16—112no—
546C2×M16—221no—
547C2×M16—221no—
548C2×M16—221no—
549C2×M16—228no—
550C2×M16—228no—
551C2×M16—224no—
552C2×M16C22⋊D1112yes—
553C2×M16C22⋊D1112yes—
554C2×M16C22⋊D1112yes—
555C2×M16C22⋊D1112yes—
556C2×M16C22×D1112yes—
557C2×M16C22×D1112yes—
558C2×M16C22×D1112yes—
559C2×M16C22×D1112yes—
560C2×M16C22×D1112yes—
561C22×C8—21no—
562C22×C8—24no—
563C22×C8—112no—
564C22×C8—221no—
565C22×C8—224no—
566C22×C8C22×D1112yes—
567#117—112no—
568#117—112no—
569#117—221no—
570#117—221no—
571C2×C4⋊C4—221no—
572C2×C22⋊C4—221no—
573C2×C42—112no—
574#108—1116no—
575#104—1116no—
576#104—1116no—
577#97—118no—
578C4×C8—118no—
579C2×C11—21no—
580C2×C11—21no—
581C2×C11—21no—
582C2×C11—21no—
583C2×C11—21no—
584C2×C11—21no—
585C2×C11—21no—
586C2×C11—44no—
587C2×C11C22×C4×D411yescharacteristic
588D11—44no—
589C24—21no—
590C24—221no—
591C24#433911yescharacteristic
592#41—22no—
593#41—22no—
594#41—22no—
595#41—22no—
596#41—22no—
597#41—22no—
598#41—22no—
599#41—22no—
600#41—22no—
601#41—22no—
602#41—22no—
603#41—22no—
604#41—114no—
605#41—114no—
606#41—114no—
607#41—114no—
608#41—222no—
609#41—222no—
610#41—222no—
611#41—222no—
612#41—222no—
613#41—222no—
614#41—222no—
615#41—222no—
616#41—222no—
617#41—222no—
618#41—222no—
619#41—222no—
620#41C2×C4×D1114yes—
621#41C2×C4×D1114yes—
622#41C2×C4×D1114yes—
623#41C23×D1114yes—
624C2×Q8—21no—
625C2×Q8—21no—
626C2×Q8—21no—
627C2×Q8—112no—
628C2×Q8—112no—
629C2×Q8—112no—
630C2×Q8—221no—
631C2×Q8—221no—
632C2×Q8—221no—
633C2×Q8C2×C4×D1112yes—
634C2×Q8C2×C4×D1112yes—
635C2×Q8C2×C4×D1112yes—
636C2×D4—22no—
637C2×D4—22no—
638C2×D4—22no—
639C2×D4—22no—
640C2×D4—22no—
641C2×D4—22no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—112no—
646C2×D4—112no—
647C2×D4—112no—
648C2×D4—222no—
649C2×D4—222no—
650C2×D4—222no—
651C2×D4—222no—
652C2×D4—222no—
653C2×D4—222no—
654C2×D4—221no—
655C2×D4—221no—
656C2×D4—221no—
657C2×D4C2×C4×D1112yes—
658C2×D4C2×C4×D1112yes—
659C2×D4C2×C4×D1112yes—
660C22×C4—21no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—221no—
668C22×C4—222no—
669C22×C4—222no—
670C22×C4—222no—
671C22×C4—222no—
672C22×C4—222no—
673C22×C4—222no—
674C22×C4—222no—
675C22×C4C2×C4×D1111yescharacteristic
676C22×C4C2×C4×D1111yescharacteristic
677C22×C4C2×C4×D1111yescharacteristic
678C22×C4C2×C4×D1111yescharacteristic
679C22×C4#433911yescharacteristic
680C22×C4#433911yescharacteristic
681C22×C4#433911yescharacteristic
682C22×C4C2×C22⋊D1111yescharacteristic
683C22×C4C2×C22⋊D1111yescharacteristic
684C22×C4C2×C22⋊D1111yescharacteristic
685C22×C4C2×C22⋊D1111yescharacteristic
686C22×C4C23×D1111yescharacteristic
687C22×C4C23×D1111yescharacteristic
688C22×C4C23×D1111yescharacteristic
689Q16—1116no—
690SD16—1116no—
691SD16—1116no—
692D8—1116no—
693M16—22no—
694M16—22no—
695M16—22no—
696M16—216no—
697M16—114no—
698M16—114no—
699M16—114no—
700M16—114no—
701M16—114no—
702M16—222no—
703M16—222no—
704M16—222no—
705M16—2216no—
706M16C2×C22⋊D1114yes—
707M16C2×C22⋊D1114yes—
708M16C2×C22⋊D1114yes—
709M16C2×C22⋊D1114yes—
710M16C23×D1114yes—
711C2×C8—22no—
712C2×C8—22no—
713C2×C8—22no—
714C2×C8—216no—
715C2×C8—114no—
716C2×C8—114no—
717C2×C8—114no—
718C2×C8—222no—
719C2×C8—222no—
720C2×C8—222no—
721C2×C8—2216no—
722C2×C8C2×C22⋊D1114yes—
723C2×C8C2×C22⋊D1114yes—
724C2×C8C23×D1114yes—
725C4⋊C4—222no—
726C4⋊C4—222no—
727C22⋊C4—222no—
728C22⋊C4—222no—
729C42—114no—
730C42—222no—
731C11#6018211yescharacteristic, complemented, Sylow
732C23—22no—
733C23—22no—
734C23—22no—
735C23—81no—
736C23—82no—
737C23—222no—
738C23—222no—
739C23—222no—
740C23—882no—
741C23C4×C22⋊D1111yescharacteristic
742C23C4×C22⋊D1111yescharacteristic
743C23C4×C22⋊D1111yescharacteristic
744C23C4×C22⋊D1111yescharacteristic
745C23C2×#433911yescharacteristic
746C23C2×#433911yescharacteristic
747C23C2×#433911yescharacteristic
748Q8—22no—
749Q8—22no—
750Q8—22no—
751Q8—114no—
752Q8—222no—
753Q8—222no—
754Q8—222no—
755Q8C22×C4×D1114yes—
756D4—24no—
757D4—24no—
758D4—24no—
759D4—24no—
760D4—22no—
761D4—22no—
762D4—22no—
763D4—114no—
764D4—224no—
765D4—224no—
766D4—224no—
767D4—224no—
768D4—222no—
769D4—222no—
770D4—222no—
771D4C22×C4×D1114yes—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—222no—
780C2×C4—222no—
781C2×C4—222no—
782C2×C4—224no—
783C2×C4—224no—
784C2×C4—224no—
785C2×C4—224no—
786C2×C4—224no—
787C2×C4—882no—
788C2×C4C4×C22⋊D1111yescharacteristic
789C2×C4C4×C22⋊D1111yescharacteristic
790C2×C4C4×C22⋊D1111yescharacteristic
791C2×C4C4×C22⋊D1111yescharacteristic
792C2×C4C4×C22⋊D1111yescharacteristic
793C2×C4C4×C22⋊D1111yescharacteristic
794C2×C4C4×C22⋊D1111yescharacteristic
795C2×C4C4×C22⋊D1111yescharacteristic
796C2×C4C4×C22⋊D1111yescharacteristic
797C2×C4C4×C22⋊D1111yescharacteristic
798C2×C4C4×C22⋊D1111yescharacteristic
799C2×C4C4×C22⋊D1111yescharacteristic
800C2×C4C22×C4×D1111yescharacteristic
801C2×C4C22×C4×D1111yescharacteristic
802C2×C4C22×C4×D1111yescharacteristic
803C2×C4C22×C4×D1111yescharacteristic
804C2×C4C22×C4×D1111yescharacteristic
805C2×C4C22×C4×D1111yescharacteristic
806C2×C4C2×#433911yescharacteristic
807C2×C4C2×#433911yescharacteristic
808C2×C4C2×#433911yescharacteristic
809C2×C4C22×C22⋊D1111yescharacteristic
810C2×C4C22×C22⋊D1111yescharacteristic
811C2×C4C22×C22⋊D1111yescharacteristic
812C2×C4C22×C22⋊D1111yescharacteristic
813C2×C4C22×C22⋊D1111yescharacteristic
814C2×C4C22×C22⋊D1111yescharacteristic
815C2×C4C24×D1111yescharacteristic
816C8—24no—
817C8—118no—
818C8—224no—
819C8C22×C22⋊D1118yes—
820C22—24no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—44no—
829C22—82no—
830C22—82no—
831C22—224no—
832C22—444no—
833C22—882no—
834C22—882no—
835C22C2×C4×C22⋊D1111yescharacteristic
836C22C2×C4×C22⋊D1111yescharacteristic
837C22C2×C4×C22⋊D1111yescharacteristic
838C22C2×C4×C22⋊D1111yescharacteristic
839C22C2×C4×C22⋊D1111yescharacteristic
840C22C2×C4×C22⋊D1111yescharacteristic
841C22C22×#433911yescharacteristic
842C4—24no—
843C4—224no—
844C4—444no—
845C4C2×C4×C22⋊D1111yescharacteristic
846C4C2×C4×C22⋊D1111yescharacteristic
847C4C2×C4×C22⋊D1111yescharacteristic
848C4C2×C4×C22⋊D1111yescharacteristic
849C4C2×C4×C22⋊D1111yescharacteristic
850C4C2×C4×C22⋊D1111yescharacteristic
851C4C23×C4×D1111yescharacteristic
852C4C23×C22⋊D1111yescharacteristic
853C2—21no—
854C2—21no—
855C2—21no—
856C2—21no—
857C2—21no—
858C2—21no—
859C2—21no—
860C2—44no—
861C2—444no—
862C2C22×C4×C22⋊D1111yescharacteristic
subgroupG/H
centerC4C23×C22⋊D11
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
FittingC2×C11×#568C2
socleC2×C11C22×C4×D4
prime radicalC2×#10623353C2
cosocleC2×C4×C11C25
hypercenterC2×#568D11
hypocenterC11#60182
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×M16 ◁ C2×#568

Complements

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

NH ≅ G/Ntype
2. C2×#10623276C2semidirect
3. #13077531C2semidirect
4. #13077523C2semidirect
5. #13077517C2semidirect
6. C2×#10622737C2semidirect
7. C2×#10622849C2semidirect
8. C2×#10622752C2semidirect
9. #13077034C2semidirect
10. C2×C11×#568C2semidirect
15. C11×#568C22semidirect
16. C11×#568C22semidirect
18. C2×C11×#131C22semidirect
22. C2×#67004C4semidirect
23. #10623353C4semidirect
24. #10623353C4semidirect
28. C2×#67002C4semidirect
29. C2×#66995C4semidirect
30. C2×#66985C4semidirect
36. #10623276C22semidirect
37. #10623276C22semidirect
40. C2×#66954C22semidirect
41. #10622849C22semidirect
42. #10622849C22semidirect
43. C2×#66901C22semidirect
44. #10622758C22semidirect
45. #10622757C22semidirect
46. #10622752C22semidirect
47. #10622752C22semidirect
48. C2×#66889C22semidirect
49. #10622737C22semidirect
50. #10622737C22semidirect
51. C2×#66886C22semidirect
52. #10622735C22semidirect
53. M16×Dic11C22semidirect
54. #10622714C22semidirect
91. C11×#131C23semidirect
112. #67004C2×C4semidirect
113. #67003C2×C4semidirect
116. #67002C2×C4semidirect
117. C2×#4326C2×C4semidirect
119. #66995C2×C4semidirect
120. C2×#4325C2×C4semidirect
121. C2×#4324C2×C4semidirect
123. #66985C2×C4semidirect
124. C2×#4323C2×C4semidirect
150. #66954C23semidirect
153. #66901C23semidirect
154. #66889C23semidirect
155. #66886C23semidirect
156. #66879C23semidirect
157. C8×Dic11C23semidirect
303. C2×#568D11semidirect
416. #568C2×D11semidirect
417. #568C2×D11semidirect
421. C2×#131C2×D11semidirect
530. #131C22×D11semidirect
731. C11#60182semidirect

Maximal subgroups

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

subgroupindex
C2×#106233532
C2×#106232762
#130775312
#130775232
#130775172
C2×#106227372
C2×#106228492
C2×#106227522
#130770342
C2×C11×#5682
#6018211