Finite Group Databasebeta

← #15622193

Subgroups — #15622193

Order 2816.

2138 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081912C211yesmaximal, characteristic
2C22×C4×Dic22C211yesmaximal, characteristic, complemented
3#13078789C214yesmaximal, complemented
4#13078747C212yesmaximal, complemented
5#13078739C212yesmaximal, complemented
6#13078698C214yesmaximal, complemented
7#13078656C212yesmaximal, complemented
8#13078648C212yesmaximal, complemented
9#13078541C212yesmaximal, complemented
10#13078423C212yesmaximal, complemented
11#13078090C212yesmaximal, complemented
12#13077853C212yesmaximal, complemented
13C4×#66962C214yesmaximal, complemented
14C11×#2920C211yesmaximal, characteristic, complemented
15C23×Dic22C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17#10623322—21no—
18#10623322—21no—
19#10623322C2212yes—
20C22×C4⋊Dic11C2211yescharacteristic
21C22×Dic11⋊C4—21no—
22C22×C4×Dic11—21no—
23C2×#66962C2214yes—
24#10623010—21no—
25#10623010—21no—
26#10623010—21no—
27#10623010—21no—
28#10623010C2212yes—
29#10623010C2212yes—
30#10623008C2211yescharacteristic
31#10623008C2211yescharacteristic
32#10623008C2211yescharacteristic
33C4×#4339—21no—
34C4×#4339—21no—
35C4×#4339C2212yes—
36#10623001C2211yescharacteristic
37#10623001C2211yescharacteristic
38#10623001C2211yescharacteristic
39C2×C4×Dic22—21no—
40C2×C4×Dic22—21no—
41C2×C4×Dic22—21no—
42C2×C4×Dic22—21no—
43C2×C4×Dic22—21no—
44C2×C4×Dic22—21no—
45C2×C4×Dic22C2212yes—
46C2×C4×Dic22C2212yes—
47C2×C4×Dic22C2212yes—
48C2×C4×Dic22C2212yes—
49C2×C4×Dic22C2212yes—
50C2×C4×Dic22C2212yes—
51C11×#432C2212yes—
52C11×#432C2212yes—
53C11×#431C2212yes—
54C11×#431C2212yes—
55C11×#423C2212yes—
56C11×#407C2212yes—
57C4×C11×M16C2212yes—
58#10622746C2214yes—
59#10622734C2214yes—
60#10622733C2214yes—
61#10622464C2214yescomplemented
62#10622463C2214yescomplemented
63#10622462C2214yescomplemented
64#10622461C2214yescomplemented
65#10622458C2218yescomplemented
66#10622442C2218yescomplemented
67#10622352C2214yes—
68#10622352C2214yes—
69#10622351C2214yes—
70#10622351C2214yes—
71#10622349C2214yes—
72#10622348C2214yes—
73#10622335C2214yes—
74#10622334C2214yes—
75#10622329C2218yescomplemented
76#10622323C2218yescomplemented
77C4×Dic44C2218yescomplemented
78C4×#4314C2218yescomplemented
79C23×C4×C11D411yescharacteristic
80C23×C4×C11D411yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×Dic11—21no—
83C23×Dic11—21no—
84C2×#4339—21no—
85C2×#4339—21no—
86C2×#4339C2312yes—
87C22×Dic22—21no—
88C22×Dic22—21no—
89C22×Dic22—21no—
90C22×Dic22—28no—
91C22×Dic22C2312yes—
92C22×Dic22C2312yes—
93C22×Dic22C2312yes—
94C2×C11×M16C2314yes—
95C2×C42×C11D411yescharacteristic
96C2×C42×C11D411yescharacteristic
97C2×C42×C11D411yescharacteristic
98C2×C42×C11D411yescharacteristic
99C2×C42×C11D411yescharacteristic
100C2×C42×C11D411yescharacteristic
101C2×C42×C11C2311yescharacteristic
102C2×C42×C11C2311yescharacteristic
103C2×C42×C11C2311yescharacteristic
104C2×C42×C11C2311yescharacteristic
105C2×C42×C11C2311yescharacteristic
106C2×C42×C11C2311yescharacteristic
107#67006—22no—
108#66983—21no—
109#66983—21no—
110#66983—21no—
111#66983—21no—
112#66983C2312yes—
113#66983C2312yes—
114#66982—22no—
115#66982—22no—
116#66982—22no—
117C4×C22⋊D11—22no—
118C4×C22⋊D11—22no—
119C4×C22⋊D11—22no—
120C4×C22⋊D11—22no—
121C4×C22⋊D11—22no—
122C4×C22⋊D11—22no—
123#66979—21no—
124#66979—21no—
125#66979C2312yes—
126C2×C4⋊Dic11—21no—
127C2×C4⋊Dic11—21no—
128C2×C4⋊Dic11—21no—
129C2×C4⋊Dic11C2312yes—
130C2×C4⋊Dic11C2312yes—
131C2×C4⋊Dic11C2312yes—
132#66977—21no—
133#66977—21no—
134#66977—21no—
135#66977—21no—
136#66977C2312yes—
137#66977C2312yes—
138C2×Dic11⋊C4—22no—
139C2×Dic11⋊C4—22no—
140C2×Dic11⋊C4—22no—
141C2×Dic11⋊C4—22no—
142C2×Dic11⋊C4—22no—
143C2×Dic11⋊C4—22no—
144C2×C4×Dic11—22no—
145C2×C4×Dic11—22no—
146C2×C4×Dic11—22no—
147C2×C4×Dic11—22no—
148C2×C4×Dic11—22no—
149C2×C4×Dic11—22no—
150#66962—216no—
151C2×Dic44C2318yes—
152C2×#4314C2318yes—
153#66929—22no—
154#66929—22no—
155#66928—21no—
156#66928—21no—
157#66928C2312yes—
158#66927C2311yescharacteristic
159C4×D44—21no—
160C4×D44—21no—
161C4×D44—21no—
162C4×D44—21no—
163C4×D44C2312yes—
164C4×D44C2312yes—
165#66925—22no—
166#66925—22no—
167#66925—22no—
168C42×D11—22no—
169#66923—21no—
170#66923—21no—
171#66923C2312yes—
172#66922C2311yescharacteristic
173#66922C2311yescharacteristic
174#66922C2311yescharacteristic
175C4×Dic22—22no—
176C4×Dic22—22no—
177C4×Dic22—22no—
178C4×Dic22—22no—
179C4×Dic22—22no—
180C4×Dic22—22no—
181C4×Dic22—22no—
182C4×Dic22—22no—
183C4×Dic22—22no—
184C4×Dic22—22no—
185C4×Dic22—22no—
186C4×Dic22—22no—
187C4×Dic22—21no—
188C4×Dic22—21no—
189C4×Dic22—21no—
190C4×Dic22—21no—
191C4×Dic22C2314yes—
192C4×Dic22C2314yes—
193C4×Dic22C2314yes—
194C4×Dic22C2314yes—
195C4×Dic22C2312yes—
196C4×Dic22C2312yes—
197C11×C4⋊C8C2314yes—
198C11×C4⋊C8C2314yes—
199C11×C22⋊C8C2314yes—
200C11×C22⋊C8C2314yes—
201C11×#97C2314yes—
202C4×C8×C11C2314yes—
203#66885C2318yes—
204#66882C2318yes—
205#66881C2318yes—
206#66880C2318yes—
207#66880C2318yes—
208#66880C2318yes—
209#60560—111nomaximal, Sylow
210C24×C11C2×D411yescharacteristic
211C22×C4×C11—24no—
212C22×C4×C11—24no—
213C22×C4×C11—42no—
214C22×C4×C11C2×D411yescharacteristic
215C22×C4×C11C2×D411yescharacteristic
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2×D411yescharacteristic
220C22×C4×C11C2×D411yescharacteristic
221C22×C4×C11C2×D411yescharacteristic
222C22×C4×C11C2×D411yescharacteristic
223C22×C4×C11C2×D411yescharacteristic
224C22×C4×C11C2×D411yescharacteristic
225C22×C4×C11C2×D411yescharacteristic
226C22×C4×C11C2×D411yescharacteristic
227C22×C4×C11C2×D411yescharacteristic
228C22×C4×C11C2×D411yescharacteristic
229C22×C4×C11C2411yescharacteristic
230C22×C4×C11C2411yescharacteristic
231C22×C4×C11C2411yescharacteristic
232C2×C22⋊D11—22no—
233C2×C22⋊D11—22no—
234C2×C22⋊D11—22no—
235C22×Dic11—28no—
236C22×Dic11—22no—
237C22×Dic11—22no—
238C22×Dic11—22no—
239C22×Dic11—22no—
240C22×Dic11—22no—
241C22×Dic11—22no—
242C22×Dic11—44no—
243#4339—28no—
244#4339—44no—
245#4339—44no—
246C2×D44—21no—
247C2×D44—21no—
248C2×D44C2412yes—
249C2×C4×D11—22no—
250C2×C4×D11—22no—
251C2×C4×D11—22no—
252C2×Dic22—28no—
253C2×Dic22—28no—
254C2×Dic22—28no—
255C2×Dic22—28no—
256C2×Dic22—28no—
257C2×Dic22—22no—
258C2×Dic22—22no—
259C2×Dic22—22no—
260C2×Dic22—21no—
261C2×Dic22—21no—
262C2×Dic22—24no—
263C2×Dic22#4118yescomplemented
264C2×Dic22C2412yes—
265C2×Dic22C2414yes—
266C11×M16—28no—
267C2×C8×C11C2418yes—
268C42×C11C2×D411yescharacteristic
269C42×C11C2×D411yescharacteristic
270C42×C11C2×D411yescharacteristic
271C42×C11C2×D411yescharacteristic
272C42×C11C2×D411yescharacteristic
273C42×C11C2×D411yescharacteristic
274C42×C11C2×D411yescharacteristic
275C42×C11C2×D411yescharacteristic
276C42×C11C2×D411yescharacteristic
277C42×C11C2×D411yescharacteristic
278C42×C11C2×D411yescharacteristic
279C42×C11C2×D411yescharacteristic
280C42×C11C2411yescharacteristic
281C42×C11C2411yescharacteristic
282C42×C11C2411yescharacteristic
283C42×C11C2411yescharacteristic
284C22⋊Dic11—22no—
285C22⋊Dic11—22no—
286C22⋊Dic11—22no—
287(C2×D11)⋊C4—22no—
288(C2×D11)⋊C4—22no—
289(C2×D11)⋊C4—22no—
290(C2×D11)⋊C4—22no—
291(C2×D11)⋊C4—22no—
292(C2×D11)⋊C4—22no—
293C4⋊Dic11—22no—
294C4⋊Dic11—22no—
295C4⋊Dic11—22no—
296C4⋊Dic11—21no—
297C4⋊Dic11—21no—
298C4⋊Dic11—21no—
299C4⋊Dic11—21no—
300C4⋊Dic11C2412yes—
301C4⋊Dic11C2412yes—
302C4⋊Dic11C2414yes—
303Dic11⋊C4—24no—
304Dic11⋊C4—24no—
305Dic11⋊C4—24no—
306Dic11⋊C4—24no—
307Dic11⋊C4—22no—
308Dic11⋊C4—22no—
309Dic11⋊C4—22no—
310Dic11⋊C4—22no—
311Dic11⋊C4—22no—
312Dic11⋊C4—22no—
313C4×Dic11—24no—
314C4×Dic11—24no—
315C4×Dic11—24no—
316C4×Dic11—24no—
317C4×Dic11—22no—
318C4×Dic11—22no—
319C4×Dic11—22no—
320Dic44—216no—
321#4314—216no—
322#3444—111no—
323C22×C4×Q8—111no—
324#3117—114no—
325#3113—112no—
326#3112—112no—
327#3108—114no—
328#3104—112no—
329#3103—112no—
330#3092—112no—
331#3078—112no—
332#3037—112no—
333#3004—112no—
334C4×#137—114no—
335#2920D1111yescharacteristic, complemented
336C23×C11—22no—
337C23×C11—22no—
338C23×C11—22no—
339C23×C11C22×D411yescharacteristic
340C23×C11C22×D411yescharacteristic
341C23×C11C22×D411yescharacteristic
342C22×D11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
359C2×C4×C11#13714yescomplemented
360C2×C4×C11C22×D411yescharacteristic
361C2×C4×C11C22×D411yescharacteristic
362C2×C4×C11C22×D411yescharacteristic
363C2×C4×C11C22×D411yescharacteristic
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×C11C22×D411yescharacteristic
371C2×C4×C11C2×#4114yes—
372C2×C4×C11C2511yescharacteristic
373C22⋊D11—44no—
374C22⋊D11—44no—
375C22⋊D11—44no—
376C2×Dic11—28no—
377C2×Dic11—28no—
378C2×Dic11—28no—
379C2×Dic11—24no—
380C2×Dic11—24no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—44no—
385C2×Dic11—44no—
386C2×Dic11—44no—
387D44—24no—
388D44—42no—
389D44—42no—
390C4×D11—44no—
391C4×D11—44no—
392C4×D11—44no—
393Dic22—28no—
394Dic22—28no—
395Dic22—28no—
396Dic22—24no—
397Dic22—24no—
398Dic22—42no—
399Dic22—42no—
400Dic22C2×#4118yes—
401C8×C11—28no—
402C23×Q8—111no—
403C2×#137—114no—
404#533—111no—
405#533—111no—
406#533—111no—
407#532—111no—
408#532—111no—
409#532—111no—
410#529—112no—
411#529—112no—
412#529—221no—
413#529—221no—
414#529—221no—
415#529—221no—
416#525—112no—
417#525—221no—
418#525—221no—
419C4×#41—112no—
420C4×#41—221no—
421C4×#41—221no—
422C2×C4×Q8—112no—
423C2×C4×Q8—112no—
424C2×C4×Q8—112no—
425C2×C4×Q8—112no—
426C2×C4×Q8—112no—
427C2×C4×Q8—112no—
428C2×C4×Q8—221no—
429C2×C4×Q8—221no—
430C2×C4×Q8—221no—
431C2×C4×Q8—221no—
432C2×C4×Q8—221no—
433C2×C4×Q8—221no—
434C22×C4⋊C4—111no—
435C22×C4⋊C4—221no—
436C22×C42—221no—
437C22×C42C2×D1111yescharacteristic
438#484—114no—
439#483—114no—
440#481—114no—
441#480—114no—
442#479—118no—
443#477—114no—
444#475—114no—
445#464—118no—
446#462—114no—
447#460—114no—
448#451—114no—
449#451—114no—
450#448—114no—
451#448—114no—
452#441—118no—
453#440—118no—
454C4×Q16—118no—
455C4×SD16—118no—
456#432C2×D1112yes—
457#432C2×D1112yes—
458#431C2×D1112yes—
459#431C2×D1112yes—
460#428—114no—
461#423C2×D1112yes—
462#419—114no—
463#417—114no—
464#407C2×D1112yes—
465C4×M16C2×D1112yes—
466C22×C11—28no—
467C22×C11—21no—
468C22×C11—21no—
469C22×C11—21no—
470C22×C11—21no—
471C22×C11—21no—
472C22×C11—21no—
473C22×C11#52512yes—
474C22×C11C2×#13712yes—
475C22×C11#57512yes—
476C22×C11C23×D411yescharacteristic
477C2×D11—42no—
478C2×D11—42no—
479C2×D11—42no—
480C4×C11—21no—
481C4×C11—21no—
482C4×C11—21no—
483C4×C11—21no—
484C4×C11—21no—
485C4×C11—21no—
486C4×C11—21no—
487C4×C11—21no—
488C4×C11#52512yes—
489C4×C11C2×#13712yes—
490C4×C11C2×#13712yes—
491C4×C11C22×#4112yes—
492Dic11—28no—
493Dic11—42no—
494Dic11—42no—
495Dic11—42no—
496Dic11—44no—
497C2×#41—112no—
498C2×#41—221no—
499C2×#41—221no—
500C22×Q8—112no—
501C22×Q8—112no—
502C22×Q8—112no—
503C22×Q8—228no—
504C22×Q8—221no—
505C22×Q8—221no—
506C22×Q8—221no—
507C23×C4—221no—
508C23×C4—221no—
509C23×C4D4411yescharacteristic
510C23×C4D4411yescharacteristic
511C23×C4C22×D1111yescharacteristic
512#137—2216no—
513C2×Q16—118no—
514C2×SD16—118no—
515C2×M16C22×D1114yes—
516C4⋊Q8—111no—
517C4⋊Q8—111no—
518C4⋊Q8—111no—
519#127—111no—
520#126—222no—
521#126—222no—
522#125—112no—
523#125—221no—
524#125—221no—
525#124—112no—
526#124—221no—
527#124—221no—
528#123—222no—
529#123—222no—
530#123—222no—
531C22⋊Q8—112no—
532C22⋊Q8—112no—
533C22⋊Q8—221no—
534C22⋊Q8—221no—
535C22⋊Q8—221no—
536C22⋊Q8—221no—
537#121—112no—
538#121—112no—
539#121—221no—
540#121—221no—
541#121—221no—
542#121—221no—
543#120—222no—
544C4×Q8—114no—
545C4×Q8—114no—
546C4×Q8—114no—
547C4×Q8—114no—
548C4×Q8—112no—
549C4×Q8—112no—
550C4×Q8—222no—
551C4×Q8—222no—
552C4×Q8—222no—
553C4×Q8—222no—
554C4×Q8—222no—
555C4×Q8—222no—
556C4×Q8—222no—
557C4×Q8—222no—
558C4×Q8—222no—
559C4×Q8—222no—
560C4×Q8—222no—
561C4×Q8—222no—
562C4×Q8—221no—
563C4×Q8—221no—
564C4×Q8—221no—
565C4×Q8—221no—
566C4×D4—112no—
567C4×D4—112no—
568C4×D4—222no—
569C4×D4—222no—
570C4×D4—222no—
571C4×D4—222no—
572C4×D4—222no—
573C4×D4—222no—
574C4×D4—221no—
575C4×D4—221no—
576C4×D4—221no—
577C4×D4—221no—
578#117—112no—
579#117—221no—
580#117—221no—
581#117—222no—
582#117—222no—
583#117—222no—
584C2×C4⋊C4—112no—
585C2×C4⋊C4—112no—
586C2×C4⋊C4—112no—
587C2×C4⋊C4—221no—
588C2×C4⋊C4—221no—
589C2×C4⋊C4—221no—
590C2×C4⋊C4—222no—
591C2×C4⋊C4—222no—
592C2×C4⋊C4—222no—
593C2×C4⋊C4—222no—
594C2×C4⋊C4—222no—
595C2×C4⋊C4—222no—
596C2×C42—222no—
597C2×C42—222no—
598C2×C42—222no—
599C2×C42—222no—
600C2×C42—222no—
601C2×C42—222no—
602C2×C42—222no—
603C2×C42D4411yescharacteristic
604C2×C42D4411yescharacteristic
605C2×C42D4411yescharacteristic
606C2×C42D4411yescharacteristic
607C2×C42D4411yescharacteristic
608C2×C42D4411yescharacteristic
609C2×C42C22×D1111yescharacteristic
610C2×C42C22×D1111yescharacteristic
611C2×C42C22×D1111yescharacteristic
612C2×C42C22×D1111yescharacteristic
613C2×C42C22×D1111yescharacteristic
614C2×C42C22×D1111yescharacteristic
615#107—118no—
616#106—118no—
617C4⋊C8C22×D1114yes—
618C4⋊C8C22×D1114yes—
619#103—118no—
620#103—118no—
621#103—118no—
622#102—118no—
623C22⋊C8C22×D1114yes—
624C22⋊C8C22×D1114yes—
625#97C22×D1114yes—
626C4×C8C22×D1114yes—
627C2×C11—22no—
628C2×C11—22no—
629C2×C11—22no—
630C2×C11C2×#52511yescharacteristic
631C2×C11C22×#13711yescharacteristic
632C2×C11C2×#57511yescharacteristic
633D11—82no—
634C24C2×D4411yescharacteristic
635#41—228no—
636#41—444no—
637#41—444no—
638C2×Q8—118no—
639C2×Q8—114no—
640C2×Q8—112no—
641C2×Q8—228no—
642C2×Q8—228no—
643C2×Q8—228no—
644C2×Q8—228no—
645C2×Q8—228no—
646C2×Q8—222no—
647C2×Q8—222no—
648C2×Q8—222no—
649C2×Q8—221no—
650C2×Q8—221no—
651C2×Q8—224no—
652C2×D4—112no—
653C2×D4—222no—
654C2×D4—222no—
655C2×D4—222no—
656C2×D4—221no—
657C2×D4—221no—
658C22×C4—24no—
659C22×C4—24no—
660C22×C4—42no—
661C22×C4—228no—
662C22×C4—222no—
663C22×C4—222no—
664C22×C4—222no—
665C22×C4—222no—
666C22×C4—222no—
667C22×C4—222no—
668C22×C4—222no—
669C22×C4—222no—
670C22×C4—222no—
671C22×C4—444no—
672C22×C4C2×D4411yescharacteristic
673C22×C4C2×D4411yescharacteristic
674C22×C4C2×D4411yescharacteristic
675C22×C4C2×D4411yescharacteristic
676C22×C4C2×D4411yescharacteristic
677C22×C4C2×D4411yescharacteristic
678C22×C4C2×D4411yescharacteristic
679C22×C4C2×D4411yescharacteristic
680C22×C4C2×D4411yescharacteristic
681C22×C4C2×D4411yescharacteristic
682C22×C4C2×D4411yescharacteristic
683C22×C4C2×D4411yescharacteristic
684C22×C4C2×D4411yescharacteristic
685C22×C4C2×D4411yescharacteristic
686C22×C4C2×D4411yescharacteristic
687C22×C4C23×D1111yescharacteristic
688C22×C4C23×D1111yescharacteristic
689C22×C4C23×D1111yescharacteristic
690Q16—2216no—
691SD16—2216no—
692M16—28no—
693C2×C8C23×D1118yes—
694C4⋊C4—114no—
695C4⋊C4—112no—
696C4⋊C4—112no—
697C4⋊C4—222no—
698C4⋊C4—222no—
699C4⋊C4—222no—
700C4⋊C4—224no—
701C4⋊C4—224no—
702C4⋊C4—224no—
703C4⋊C4—224no—
704C4⋊C4—222no—
705C4⋊C4—222no—
706C4⋊C4—221no—
707C4⋊C4—221no—
708C4⋊C4—221no—
709C4⋊C4—221no—
710C4⋊C4—222no—
711C4⋊C4—222no—
712C4⋊C4—222no—
713C4⋊C4—222no—
714C22⋊C4—222no—
715C22⋊C4—222no—
716C22⋊C4—222no—
717C22⋊C4—222no—
718C22⋊C4—222no—
719C22⋊C4—222no—
720C22⋊C4—222no—
721C22⋊C4—222no—
722C22⋊C4—222no—
723C42—224no—
724C42—224no—
725C42—224no—
726C42—222no—
727C42—222no—
728C42—224no—
729C42—222no—
730C42C2×D4411yescharacteristic
731C42C2×D4411yescharacteristic
732C42C2×D4411yescharacteristic
733C42C2×D4411yescharacteristic
734C42C2×D4411yescharacteristic
735C42C2×D4411yescharacteristic
736C42C2×D4411yescharacteristic
737C42C2×D4411yescharacteristic
738C42C2×D4411yescharacteristic
739C42C2×D4411yescharacteristic
740C42C2×D4411yescharacteristic
741C42C2×D4411yescharacteristic
742C42C23×D1111yescharacteristic
743C42C23×D1111yescharacteristic
744C42C23×D1111yescharacteristic
745C42C23×D1111yescharacteristic
746C11#6056011yescharacteristic, complemented, Sylow
747C23—22no—
748C23—22no—
749C23—22no—
750C23—222no—
751C23C22×D4411yescharacteristic
752C23C22×D4411yescharacteristic
753C23C22×D4411yescharacteristic
754Q8—118no—
755Q8—228no—
756Q8—228no—
757Q8—228no—
758Q8—224no—
759Q8—224no—
760Q8—442no—
761Q8—442no—
762D4—224no—
763D4—442no—
764D4—444no—
765D4—444no—
766D4—444no—
767D4—442no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—228no—
785C2×C4—228no—
786C2×C4—228no—
787C2×C4—224no—
788C2×C4—224no—
789C2×C4—222no—
790C2×C4—222no—
791C2×C4—222no—
792C2×C4—444no—
793C2×C4—444no—
794C2×C4—444no—
795C2×C4—444no—
796C2×C4—444no—
797C2×C4—444no—
798C2×C4#6696214yescomplemented
799C2×C4C22×D4411yescharacteristic
800C2×C4C22×D4411yescharacteristic
801C2×C4C22×D4411yescharacteristic
802C2×C4C22×D4411yescharacteristic
803C2×C4C22×D4411yescharacteristic
804C2×C4C22×D4411yescharacteristic
805C2×C4C22×D4411yescharacteristic
806C2×C4C22×D4411yescharacteristic
807C2×C4C22×D4411yescharacteristic
808C2×C4C22×D4411yescharacteristic
809C2×C4C22×D4411yescharacteristic
810C2×C4#41×D1114yes—
811C2×C4C24×D1111yescharacteristic
812C8—28no—
813C22—28no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—442no—
821C22—442no—
822C22—442no—
823C22#1062305512yes—
824C22C2×#6696212yes—
825C22#1062327912yes—
826C22C23×D4411yescharacteristic
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—21no—
833C4—21no—
834C4—21no—
835C4—228no—
836C4—442no—
837C4—442no—
838C4—444no—
839C4—442no—
840C4#1062305512yes—
841C4C2×#6696212yes—
842C4C2×#6696212yes—
843C4C2×#41×D1112yes—
844C2—22no—
845C2—22no—
846C2—22no—
847C2—882no—
848C2C2×#1062305511yescharacteristic
849C2C22×#6696211yescharacteristic
850C2C2×#1062327911yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#2920C2
socleC22×C11C23×D4
prime radical#13081912C2
hypercenter#2920D11
hypocenterC11#60560
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ #2920

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic22C2semidirect
3. #13078789C2semidirect
4. #13078747C2semidirect
5. #13078739C2semidirect
6. #13078698C2semidirect
7. #13078656C2semidirect
8. #13078648C2semidirect
9. #13078541C2semidirect
10. #13078423C2semidirect
11. #13078090C2semidirect
12. #13077853C2semidirect
13. C4×#66962C2semidirect
14. C11×#2920C2semidirect
61. #10622464C22semidirect
62. #10622463C22semidirect
63. #10622462C22semidirect
64. #10622461C22semidirect
65. #10622458C22semidirect
66. #10622442C22semidirect
75. #10622329C22semidirect
76. #10622323C22semidirect
77. C4×Dic44C22semidirect
78. C4×#4314C22semidirect
263. C2×Dic22#41semidirect
335. #2920D11semidirect
359. C2×C4×C11#137semidirect
746. C11#60560semidirect
798. C2×C4#66962semidirect

Maximal subgroups

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

subgroupindex
#130819122
C22×C4×Dic222
#130787892
#130787472
#130787392
#130786982
#130786562
#130786482
#130785412
#130784232
#130780902
#130778532
C4×#669622
C11×#29202
#6056011