Finite Group Databasebeta

← #14769766

Subgroups — #14769766

Order 2816.

1346 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622810C211yesmaximal, characteristic, complemented
2#13077492C211yesmaximal, characteristic, complemented
3#13077149C211yesmaximal, characteristic, complemented
4#13077142C211yesmaximal, characteristic, complemented
5#13069521C211yesmaximal, characteristic, complemented
6#13069499C211yesmaximal, characteristic, complemented
7#13069133C211yesmaximal, characteristic, complemented
8#13069126C211yesmaximal, characteristic, complemented
9#13068994C211yesmaximal, characteristic, complemented
10#13068987C211yesmaximal, characteristic, complemented
11#13068680C211yesmaximal, characteristic, complemented
12#13068575C211yesmaximal, characteristic, complemented
13#13068570C211yesmaximal, characteristic, complemented
14#13068458C211yesmaximal, characteristic, complemented
15C2×C11×#577C211yesmaximal, characteristic
16C2×C11×2−1+4C2211yescharacteristic
17C2×C11×H(5,𝔽2)C2211yescharacteristic
18C11×#577—24no—
19C11×#577C418yescomplemented
20C2×C11×#137—21no—
21C2×C11×#137C2211yescharacteristic
22C2×C11×AGL(1,ℤ/8)—21no—
23C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
24C2×C11×#135—21no—
25C2×C11×#135C2211yescharacteristic
26C22×C11×SD16—21no—
27C22×C11×SD16C2211yescharacteristic
28C2×C11×#131C2211yescharacteristic
29#10623358C2211yescharacteristic
30#10623358C2211yescharacteristic, complemented
31C2×#67001C2211yescharacteristic
32C2×#67001C2211yescharacteristic, complemented
33C2×#66901C2211yescharacteristic
34C2×#66901C2211yescharacteristic
35C2×#66901C2211yescharacteristic, complemented
36#10622846—21no—
37#10622846—21no—
38#10622846C2211yescharacteristic
39#10622845—21no—
40#10622845—21no—
41#10622845C2211yescharacteristic
42#10622845C2211yescharacteristic
43#10622845C2211yescharacteristic
44#10622845C2211yescharacteristic, complemented
45#10622843C2211yescharacteristic, complemented
46C2×#66900C2211yescharacteristic, complemented
47#10622838—21no—
48#10622838C2211yescharacteristic, complemented
49C2×#66899—21no—
50C2×#66899C2211yescharacteristic, complemented
51#10622834C2211yescharacteristic
52C2×#66897C2211yescharacteristic
53#10622828—21no—
54#10622828C2211yescharacteristic
55C2×#66896—21no—
56C2×#66896C2211yescharacteristic
57#10622810—24no—
58Q16×Dic11—21no—
59#10622777—21no—
60#10622777—21no—
61D8×Dic11—21no—
62C2×#66883C2211yescharacteristic, complemented
63C2×#66882C2211yescharacteristic, complemented
64#10622714C2211yescharacteristic, complemented
65C2×#66879C2211yescharacteristic, complemented
66#10622196C2211yescharacteristic, complemented
67#10622193C2211yescharacteristic, complemented
68#10622192C2211yescharacteristic, complemented
69#10622192C2211yescharacteristic, complemented
70C11×2−1+4—22no—
71C11×2−1+4—22no—
72C11×2−1+4—41no—
73C11×2−1+4C2×C414yescomplemented
74C11×H(5,𝔽2)—22no—
75C11×H(5,𝔽2)—22no—
76C11×H(5,𝔽2)—41no—
77C11×H(5,𝔽2)C2×C414yescomplemented
78C2×C11×#41—21no—
79C2×C11×#41—21no—
80C2×C11×#41—21no—
81C2×C11×#41—21no—
82C2×C11×#41—41no—
83C2×C11×#41C2311yescharacteristic
84C2×C11×#41C2311yescharacteristic
85C2×C11×#41C2311yescharacteristic
86C22×Q8×C11—21no—
87C22×Q8×C11—21no—
88C22×Q8×C11C2311yescharacteristic
89C22×D4×C11—21no—
90C22×D4×C11—21no—
91C22×D4×C11—41no—
92C22×D4×C11C2311yescharacteristic
93C11×#137—22no—
94C11×#137—28no—
95C11×#137C2×C414yescomplemented
96C11×AGL(1,ℤ/8)—22no—
97C11×AGL(1,ℤ/8)—28no—
98C11×AGL(1,ℤ/8)C2×C414yescomplemented
99C11×#135—28no—
100C11×#135C2×C414yes—
101C11×#135D414yes—
102C2×C11×Q16—21no—
103C2×C11×Q16D411yescharacteristic
104C2×C11×SD16—21no—
105C2×C11×SD16—21no—
106C2×C11×SD16—28no—
107C2×C11×SD16—21no—
108C2×C11×SD16—21no—
109C2×C11×SD16—22no—
110C2×C11×SD16C2×C414yescomplemented
111C2×C11×SD16D411yescharacteristic
112C2×C11×SD16D411yescharacteristic
113C2×C11×D8—21no—
114C2×C11×D8D411yescharacteristic
115C11×#131—22no—
116C11×#131C2×C414yescomplemented
117C2×C11×M16—21no—
118C2×C11×M16C2311yescharacteristic
119C22×C8×C11—21no—
120C22×C8×C11C2311yescharacteristic
121C2×C22⋊Dic11—41no—
122#67001—22no—
123#67001—22no—
124#67001—41no—
125#67001—41no—
126Q8×Dic11—21no—
127Q8×Dic11—21no—
128D4×Dic11—21no—
129D4×Dic11—21no—
130D4×Dic11—41no—
131D4×Dic11—41no—
132#66979—21no—
133#66979—21no—
134#66979C2311yescharacteristic
135C2×C4⋊Dic11—21no—
136C2×C4⋊Dic11—21no—
137C2×C4⋊Dic11C2311yescharacteristic
138C2×C4⋊Dic11C2311yescharacteristic
139C2×C4×Dic11C2311yescharacteristic
140C2×#4318—21no—
141C2×#4318—21no—
142C2×#4318C2311yescharacteristic
143C2×#4318C2311yescharacteristic
144C2×#4318C2311yescharacteristic
145C22×C11⋊C8—21no—
146C22×C11⋊C8—21no—
147C22×C11⋊C8C2311yescharacteristic
148#66901—22no—
149#66901—22no—
150#66901—22no—
151#66900—41no—
152#66899—21no—
153#66899—21no—
154#66899—21no—
155#66899—21no—
156#66899—21no—
157#66899—21no—
158#66899—21no—
159#66899—21no—
160#66899D411yescharacteristic
161#66899D411yescharacteristic
162#66897—41no—
163#66896—21no—
164#66896—21no—
165#66896—21no—
166#66896—21no—
167#66896—21no—
168#66896—21no—
169#66896—21no—
170#66896—21no—
171#66896D411yescharacteristic
172#66896D411yescharacteristic
173C11⋊#95—41no—
174#66883—22no—
175#66882—21no—
176#66882—21no—
177#66879—21no—
178#66879—22no—
179C8×Dic11—21no—
180#22464—111nomaximal, Sylow
181C24×C11—21no—
182C24×C11—41no—
183C11×#41—21no—
184C11×#41—21no—
185C11×#41—21no—
186C11×#41—21no—
187C11×#41—21no—
188C11×#41—21no—
189C11×#41—24no—
190C11×#41—24no—
191C11×#41—24no—
192C11×#41—24no—
193C11×#41—44no—
194C11×#41—42no—
195C11×#41—42no—
196C11×#41—42no—
197C11×#41—42no—
198C11×#41—44no—
199C11×#41C22×C412yes—
200C11×#41C22×C412yes—
201C11×#41C22×C412yes—
202C11×#41C2×D412yes—
203C11×#41C2×D412yes—
204C11×#41#4112yes—
205C2×Q8×C11—21no—
206C2×Q8×C11—24no—
207C2×Q8×C11—24no—
208C2×Q8×C11—21no—
209C2×Q8×C11—21no—
210C2×Q8×C11—21no—
211C2×Q8×C11—21no—
212C2×Q8×C11—41no—
213C2×Q8×C11—42no—
214C2×Q8×C11—42no—
215C2×Q8×C11C22×C412yes—
216C2×Q8×C11C2×D411yescharacteristic
217C2×Q8×C11C2×D411yescharacteristic
218C2×Q8×C11C2×D411yescharacteristic
219C2×D4×C11—21no—
220C2×D4×C11—21no—
221C2×D4×C11—21no—
222C2×D4×C11—24no—
223C2×D4×C11—24no—
224C2×D4×C11—21no—
225C2×D4×C11—21no—
226C2×D4×C11—21no—
227C2×D4×C11—21no—
228C2×D4×C11—21no—
229C2×D4×C11—42no—
230C2×D4×C11—42no—
231C2×D4×C11—41no—
232C2×D4×C11—41no—
233C2×D4×C11—44no—
234C2×D4×C11—44no—
235C2×D4×C11—41no—
236C2×D4×C11C22×C412yes—
237C2×D4×C11C2×D411yescharacteristic
238C2×D4×C11C2×D411yescharacteristic
239C2×D4×C11C2×D411yescharacteristic
240C22×C4×C11—21no—
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11—41no—
245C22×C4×C11—41no—
246C22×C4×C11—41no—
247C22×C4×C11C2411yescharacteristic
248C22×Dic11—21no—
249C22×Dic11—21no—
250C22×Dic11—21no—
251C22×Dic11—41no—
252C22×Dic11—41no—
253C11×Q16—24no—
254C11×Q16C22⋊C414yescomplemented
255C11×SD16—24no—
256C11×SD16—24no—
257C11×SD16—24no—
258C11×SD16—24no—
259C11×SD16C22⋊C414yescomplemented
260C11×SD16C22⋊C414yescomplemented
261C11×D8—24no—
262C11×D8C22⋊C414yescomplemented
263C11×M16—24no—
264C11×M16—21no—
265C11×M16C22×C412yes—
266C2×C8×C11—24no—
267C2×C8×C11—21no—
268C2×C8×C11C22×C412yes—
269C2×C8×C11C2×D411yescharacteristic
270C2×C8×C11C2×D411yescharacteristic
271C2×C8×C11C2×D412yes—
272C22⋊Dic11—21no—
273C22⋊Dic11—41no—
274C22⋊Dic11—41no—
275C22⋊Dic11—82no—
276C4⋊Dic11—21no—
277C4⋊Dic11—21no—
278C4⋊Dic11—21no—
279C4⋊Dic11—21no—
280C4⋊Dic11—41no—
281C4⋊Dic11—41no—
282C4⋊Dic11C2×D411yescharacteristic
283C4⋊Dic11C2×D411yescharacteristic
284C4×Dic11—21no—
285C4×Dic11—21no—
286C4×Dic11—21no—
287C4×Dic11—41no—
288C4×Dic11—41no—
289#4318—21no—
290#4318—21no—
291#4318—21no—
292#4318—21no—
293#4318—21no—
294#4318—21no—
295#4318—42no—
296#4318—42no—
297C2×C11⋊C8—21no—
298C2×C11⋊C8—21no—
299C2×C11⋊C8—21no—
300C2×C11⋊C8—21no—
301C2×C11⋊C8—21no—
302C2×C11⋊C8—42no—
303C2×C11⋊C8—42no—
304C2×C11⋊C8C2×D411yescharacteristic
305C2×C11⋊C8C2×D411yescharacteristic
306C2×#577D1111yescharacteristic
307C2×#444—111no—
308#2951—111no—
309#2898—111no—
310#2897—111no—
311#1977—111no—
312#1973—111no—
313#1908—111no—
314#1907—111no—
315#1883—111no—
316#1882—111no—
317#1816—111no—
318#1793—111no—
319#1792—111no—
320#1765—111no—
321C23×C11—21no—
322C23×C11—21no—
323C23×C11—21no—
324C23×C11—22no—
325C23×C11—44no—
326C23×C11—41no—
327C23×C11—41no—
328C23×C11—81no—
329C23×C11—81no—
330C23×C11—161no—
331C23×C11—161no—
332C23×C11H(5,𝔽2)11yescharacteristic
333Q8×C11—21no—
334Q8×C11—21no—
335Q8×C11—21no—
336Q8×C11—22no—
337Q8×C11—22no—
338Q8×C11—44no—
339Q8×C11—41no—
340Q8×C11—41no—
341Q8×C11C2×C22⋊C412yes—
342Q8×C11C2×C22⋊C412yes—
343Q8×C11C4×D412yes—
344D4×C11—22no—
345D4×C11—22no—
346D4×C11—22no—
347D4×C11—22no—
348D4×C11—22no—
349D4×C11—22no—
350D4×C11—22no—
351D4×C11—22no—
352D4×C11—21no—
353D4×C11—21no—
354D4×C11—21no—
355D4×C11—44no—
356D4×C11—44no—
357D4×C11—44no—
358D4×C11—41no—
359D4×C11—41no—
360D4×C11C2×C22⋊C412yes—
361D4×C11C2×C22⋊C412yes—
362D4×C11C4×D412yes—
363C2×C4×C11—21no—
364C2×C4×C11—21no—
365C2×C4×C11—21no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—44no—
374C2×C4×C11—44no—
375C2×C4×C11—44no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11C23×C411yescharacteristic
379C2×C4×C11C22×D411yescharacteristic
380C2×C4×C11C22×D411yescharacteristic
381C2×C4×C11C22×D411yescharacteristic
382C2×C4×C11C2×#4111yescharacteristic
383C2×C4×C11H(5,𝔽2)11yescharacteristic
384C2×Dic11—21no—
385C2×Dic11—21no—
386C2×Dic11—41no—
387C2×Dic11—41no—
388C2×Dic11—41no—
389C2×Dic11—41no—
390C2×Dic11—41no—
391C2×Dic11—81no—
392C2×Dic11—81no—
393C2×Dic11—161no—
394C2×Dic11—161no—
395C8×C11—22no—
396C8×C11C2×C22⋊C412yes—
397C8×C11C2×C22⋊C412yes—
398C11⋊C8—21no—
399C11⋊C8—21no—
400C11⋊C8—41no—
401C11⋊C8—41no—
402C11⋊C8—41no—
403C2×2−1+4C2×D1111yescharacteristic
404C2×H(5,𝔽2)C2×D1111yescharacteristic
405#577—24no—
406#577Dic1118yescomplemented
407C2×#137—21no—
408C2×#137C2×D1111yescharacteristic
409C2×AGL(1,ℤ/8)—21no—
410C2×AGL(1,ℤ/8)C2×D1111yescharacteristic
411C2×#135—21no—
412C2×#135C2×D1111yescharacteristic
413C22×SD16—21no—
414C22×SD16C2×D1111yescharacteristic
415C2×#131—111no—
416C2×#131—111no—
417C2×#131C2×D1111yescharacteristic
418#520—111no—
419#520—111no—
420#444—224no—
421#440—221no—
422#440—221no—
423C4×Q16—221no—
424C4×D8—221no—
425C2×#108—111no—
426C2×#107—111no—
427C2×#104—111no—
428C2×#104—111no—
429C2×#104—111no—
430#419—111no—
431#419—221no—
432#418—111no—
433#418—221no—
434#417—111no—
435#417—111no—
436#417—111no—
437#417—111no—
438#417—221no—
439#417—221no—
440#416—111no—
441#416—221no—
442#416—221no—
443C2×#103—111no—
444C2×#103—221no—
445C2×#102—111no—
446C2×#102—221no—
447C2×#101—111no—
448C2×#100—111no—
449#405—111no—
450C2×#97—111no—
451#391—111no—
452#390—111no—
453#343—111no—
454#343—111no—
455#341—111no—
456#339—111no—
457C22×C11—21no—
458C22×C11—21no—
459C22×C11—22no—
460C22×C11—22no—
461C22×C11—22no—
462C22×C11—41no—
463C22×C11—41no—
464C22×C11—41no—
465C22×C11—41no—
466C22×C11—41no—
467C22×C11—41no—
468C22×C11—42no—
469C22×C11—82no—
470C22×C11—81no—
471C22×C11—81no—
472C22×C11—161no—
473C22×C11—164no—
474C22×C11#51811yescharacteristic
475C22×C11D4211yescharacteristic
476C22×C11#54611yescharacteristic
477C4×C11—22no—
478C4×C11—22no—
479C4×C11—22no—
480C4×C11—42no—
481C4×C11C22×C22⋊C411yescharacteristic
482C4×C11C2×C4×D411yescharacteristic
483C4×C11D4211yescharacteristic
484C4×C11#54611yescharacteristic
485Dic11—41no—
486Dic11—41no—
487Dic11—81no—
488Dic11—81no—
489Dic11—81no—
4902−1+4—22no—
4912−1+4—22no—
4922−1+4—41no—
4932−1+4C2×Dic1114yescomplemented
494H(5,𝔽2)—22no—
495H(5,𝔽2)—22no—
496H(5,𝔽2)—41no—
497H(5,𝔽2)C2×Dic1114yescomplemented
498C2×#41—21no—
499C2×#41—21no—
500C2×#41—21no—
501C2×#41—21no—
502C2×#41—41no—
503C2×#41C22×D1111yescharacteristic
504C2×#41C22×D1111yescharacteristic
505C2×#41C22×D1111yescharacteristic
506C22×Q8—21no—
507C22×Q8—21no—
508C22×Q8C22×D1111yescharacteristic
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—41no—
512C22×D4C22×D1111yescharacteristic
513#137—22no—
514#137—28no—
515#137C2×Dic1114yescomplemented
516AGL(1,ℤ/8)—22no—
517AGL(1,ℤ/8)—28no—
518AGL(1,ℤ/8)C2×Dic1114yescomplemented
519#135—28no—
520#135C2×Dic1114yes—
521#135C22⋊D1114yes—
522C2×Q16—21no—
523C2×Q16C22⋊D1111yescharacteristic
524C2×SD16—21no—
525C2×SD16—21no—
526C2×SD16—28no—
527C2×SD16—21no—
528C2×SD16—21no—
529C2×SD16—22no—
530C2×SD16C2×Dic1114yescomplemented
531C2×SD16C22⋊D1111yescharacteristic
532C2×SD16C22⋊D1111yescharacteristic
533C2×D8—21no—
534C2×D8C22⋊D1111yescharacteristic
535#131—22no—
536#131—222no—
537#131—222no—
538#131—441no—
539#131—441no—
540#131C2×Dic1114yescomplemented
541C2×M16—21no—
542C2×M16—111no—
543C2×M16—111no—
544C2×M16—111no—
545C2×M16—221no—
546C2×M16—221no—
547C2×M16C22×D1111yescharacteristic
548C22×C8—21no—
549C22×C8—111no—
550C22×C8—221no—
551C22×C8—221no—
552C22×C8C22×D1111yescharacteristic
553C4×Q8—221no—
554C4×Q8—221no—
555C4×D4—221no—
556C4×D4—221no—
557C4×D4—441no—
558C4×D4—441no—
559#117—111no—
560#117—221no—
561#117—221no—
562C2×C4⋊C4—111no—
563C2×C4⋊C4—111no—
564C2×C4⋊C4—221no—
565C2×C4⋊C4—221no—
566C2×C22⋊C4—441no—
567C2×C42—111no—
568#108—222no—
569#107—221no—
570#107—221no—
571#104—222no—
572#104—222no—
573#104—222no—
574#103—111no—
575#103—111no—
576#103—221no—
577#103—221no—
578#103—221no—
579#103—221no—
580#103—221no—
581#103—221no—
582#103—221no—
583#103—221no—
584#102—111no—
585#102—111no—
586#102—221no—
587#102—221no—
588#102—221no—
589#102—221no—
590#102—221no—
591#102—221no—
592#102—221no—
593#102—221no—
594#101—441no—
595#100—441no—
596#97—222no—
597#97—221no—
598C4×C8—221no—
599#95—441no—
600C2×C11—21no—
601C2×C11—21no—
602C2×C11—42no—
603C2×C11—42no—
604C2×C11—42no—
605C2×C11—82no—
606C2×C11D4×C22⋊C411yescharacteristic
607C2×C11#328811yescharacteristic
608C2×C11#328911yescharacteristic
609C24—21no—
610C24—41no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—24no—
618#41—24no—
619#41—24no—
620#41—24no—
621#41—44no—
622#41—42no—
623#41—42no—
624#41—42no—
625#41—42no—
626#41—44no—
627#41#434112yes—
628#41C22×Dic1112yes—
629#41C22×Dic1112yes—
630#41C22×Dic1112yes—
631#41C2×C22⋊D1112yes—
632#41C2×C22⋊D1112yes—
633C2×Q8—21no—
634C2×Q8—24no—
635C2×Q8—24no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—41no—
641C2×Q8—42no—
642C2×Q8—42no—
643C2×Q8D4×D1111yescharacteristic
644C2×Q8C22×Dic1112yes—
645C2×Q8C2×C22⋊D1111yescharacteristic
646C2×Q8C2×C22⋊D1111yescharacteristic
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—24no—
651C2×D4—24no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—42no—
658C2×D4—42no—
659C2×D4—41no—
660C2×D4—41no—
661C2×D4—44no—
662C2×D4—44no—
663C2×D4—41no—
664C2×D4D4×D1111yescharacteristic
665C2×D4C22×Dic1112yes—
666C2×D4C2×C22⋊D1111yescharacteristic
667C2×D4C2×C22⋊D1111yescharacteristic
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—41no—
673C22×C4—41no—
674C22×C4—41no—
675C22×C4—221no—
676C22×C4—221no—
677C22×C4—221no—
678C22×C4—441no—
679C22×C4—441no—
680C22×C4C23×D1111yescharacteristic
681Q16—24no—
682Q16C22⋊Dic1114yescomplemented
683SD16—24no—
684SD16—24no—
685SD16—24no—
686SD16—24no—
687SD16C22⋊Dic1114yescomplemented
688SD16C22⋊Dic1114yescomplemented
689D8—24no—
690D8C22⋊Dic1114yescomplemented
691M16—21no—
692M16—24no—
693M16—221no—
694M16—221no—
695M16—221no—
696M16—221no—
697M16—221no—
698M16—221no—
699M16—442no—
700M16—442no—
701M16C22×Dic1112yes—
702C2×C8—21no—
703C2×C8—24no—
704C2×C8—111no—
705C2×C8—111no—
706C2×C8—221no—
707C2×C8—221no—
708C2×C8—221no—
709C2×C8—221no—
710C2×C8—221no—
711C2×C8—442no—
712C2×C8—442no—
713C2×C8C22×Dic1112yes—
714C2×C8C2×C22⋊D1111yescharacteristic
715C2×C8C2×C22⋊D1111yescharacteristic
716C2×C8C2×C22⋊D1112yes—
717C4⋊C4—111no—
718C4⋊C4—111no—
719C4⋊C4—221no—
720C4⋊C4—221no—
721C4⋊C4—221no—
722C4⋊C4—221no—
723C4⋊C4—441no—
724C4⋊C4—441no—
725C22⋊C4—221no—
726C22⋊C4—441no—
727C22⋊C4—441no—
728C22⋊C4—882no—
729C42—221no—
730C42—221no—
731C42—221no—
732C42—441no—
733C42—441no—
734C11#2246411yescharacteristic, complemented, Sylow
735C23—21no—
736C23—21no—
737C23—21no—
738C23—22no—
739C23—44no—
740C23—41no—
741C23—41no—
742C23—81no—
743C23—81no—
744C23—161no—
745C23—161no—
746C23#6703711yescharacteristic
747Q8—21no—
748Q8—21no—
749Q8—21no—
750Q8—22no—
751Q8—22no—
752Q8—44no—
753Q8—41no—
754Q8—41no—
755Q8D4×Dic1112yes—
756Q8C2×C22⋊Dic1112yes—
757Q8C2×C22⋊Dic1112yes—
758D4—22no—
759D4—22no—
760D4—22no—
761D4—22no—
762D4—22no—
763D4—22no—
764D4—22no—
765D4—21no—
766D4—21no—
767D4—21no—
768D4—22no—
769D4—44no—
770D4—44no—
771D4—44no—
772D4—41no—
773D4—41no—
774D4D4×Dic1112yes—
775D4C2×C22⋊Dic1112yes—
776D4C2×C22⋊Dic1112yes—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—221no—
793C2×C4—221no—
794C2×C4—441no—
795C2×C4—441no—
796C2×C4—441no—
797C2×C4—441no—
798C2×C4—441no—
799C2×C4—881no—
800C2×C4—881no—
801C2×C4—1761no—
802C2×C4—1761no—
803C2×C4C2×D4×D1111yescharacteristic
804C2×C4C2×#434111yescharacteristic
805C2×C4#6703711yescharacteristic
806C2×C4C23×Dic1111yescharacteristic
807C2×C4C22×C22⋊D1111yescharacteristic
808C2×C4C22×C22⋊D1111yescharacteristic
809C8—22no—
810C8—221no—
811C8—221no—
812C8—441no—
813C8—441no—
814C8—441no—
815C8C2×C22⋊Dic1112yes—
816C8C2×C22⋊Dic1112yes—
817C22—21no—
818C22—21no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—42no—
829C22—82no—
830C22—81no—
831C22—81no—
832C22—161no—
833C22—164no—
834C22#1062332911yescharacteristic
835C22D4×C22⋊D1111yescharacteristic
836C22#1062333711yescharacteristic
837C4—22no—
838C4—22no—
839C4—22no—
840C4—42no—
841C4—441no—
842C4—441no—
843C4—881no—
844C4—881no—
845C4—881no—
846C4C2×D4×Dic1111yescharacteristic
847C4D4×C22⋊D1111yescharacteristic
848C4#1062333711yescharacteristic
849C4C22×C22⋊Dic1111yescharacteristic
850C2—21no—
851C2—21no—
852C2—42no—
853C2—42no—
854C2—42no—
855C2—82no—
856C2D4×C22⋊Dic1111yescharacteristic
857C2#1308037811yescharacteristic
858C2#1308038911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#577C2
socleC22×C11D42
cosocleC22×C4×C11C24
hypercenterC2×#577D11
hypocenterC11#22464
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#577

Complements

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

NH ≅ G/Ntype
1. C2×#10622810C2semidirect
2. #13077492C2semidirect
3. #13077149C2semidirect
4. #13077142C2semidirect
5. #13069521C2semidirect
6. #13069499C2semidirect
7. #13069133C2semidirect
8. #13069126C2semidirect
9. #13068994C2semidirect
10. #13068987C2semidirect
11. #13068680C2semidirect
12. #13068575C2semidirect
13. #13068570C2semidirect
14. #13068458C2semidirect
19. C11×#577C4semidirect
30. #10623358C22semidirect
32. C2×#67001C22semidirect
35. C2×#66901C22semidirect
44. #10622845C22semidirect
45. #10622843C22semidirect
46. C2×#66900C22semidirect
48. #10622838C22semidirect
50. C2×#66899C22semidirect
62. C2×#66883C22semidirect
63. C2×#66882C22semidirect
64. #10622714C22semidirect
65. C2×#66879C22semidirect
66. #10622196C22semidirect
67. #10622193C22semidirect
68. #10622192C22semidirect
69. #10622192C22semidirect
73. C11×2−1+4C2×C4semidirect
77. C11×H(5,𝔽2)C2×C4semidirect
95. C11×#137C2×C4semidirect
98. C11×AGL(1,ℤ/8)C2×C4semidirect
110. C2×C11×SD16C2×C4semidirect
116. C11×#131C2×C4semidirect
254. C11×Q16C22⋊C4semidirect
259. C11×SD16C22⋊C4semidirect
260. C11×SD16C22⋊C4semidirect
262. C11×D8C22⋊C4semidirect
406. #577Dic11semidirect
493. 2−1+4C2×Dic11semidirect
497. H(5,𝔽2)C2×Dic11semidirect
515. #137C2×Dic11semidirect
518. AGL(1,ℤ/8)C2×Dic11semidirect
530. C2×SD16C2×Dic11semidirect
540. #131C2×Dic11semidirect
682. Q16C22⋊Dic11semidirect
687. SD16C22⋊Dic11semidirect
688. SD16C22⋊Dic11semidirect
690. D8C22⋊Dic11semidirect
734. C11#22464semidirect

Maximal subgroups

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

subgroupindex
C2×#106228102
#130774922
#130771492
#130771422
#130695212
#130694992
#130691332
#130691262
#130689942
#130689872
#130686802
#130685752
#130685702
#130684582
C2×C11×#5772
#2246411