Finite Group Databasebeta

← #15622869

Subgroups — #15622869

Order 2816.

2130 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082527C211yesmaximal, characteristic, complemented
2#13078893C214yesmaximal, complemented
3#13078800C214yesmaximal, complemented
4#13078778C212yesmaximal, complemented
5#13078707C212yesmaximal, complemented
6#13078676C212yesmaximal, complemented
7#13078624C212yesmaximal, complemented
8#13078605C212yesmaximal, complemented
9#13078431C211yesmaximal, characteristic, complemented
10C2×#10622621C211yesmaximal, characteristic, complemented
11#13078080C211yesmaximal, characteristic, complemented
12#13078071C211yesmaximal, characteristic, complemented
13#13077920C212yesmaximal, complemented
14#13077497C212yesmaximal, complemented
15#13077448C212yesmaximal, complemented
16#13077282C211yesmaximal, characteristic, complemented
17C4×C11×H(5,𝔽2)C211yesmaximal, characteristic, complemented
18C2×C11×H(5,𝔽2)C2211yescharacteristic
19C11×#520—21no—
20C11×#520C2212yes—
21C11×#520C2211yescharacteristic
22C11×#520C2211yescharacteristic
23C11×#518—21no—
24C11×#518—22no—
25C11×#518C2212yes—
26C11×#518C2211yescharacteristic
27C4×C11×#41—21no—
28C4×C11×#41C2211yescharacteristic
29C4×C11×#41C2212yes—
30C4×C11×#41C2211yescharacteristic
31C2×C4×D4×C11—21no—
32C2×C4×D4×C11—22no—
33C2×C4×D4×C11C2211yescharacteristic
34C2×C4×D4×C11C2212yes—
35#10623364C2212yes—
36C2×#67003C2212yes—
37C2×#66985C2212yes—
38#10623115—21no—
39#10623110—21no—
40#10623096—22no—
41#10623094—21no—
42#10623083—22no—
43#10623082—21no—
44#10623065C2214yescomplemented
45#10623054C2212yescomplemented
46#10623008C2211yescharacteristic, complemented
47#10623008C2212yescomplemented
48#10623001C2212yescomplemented
49C2×#66922C2211yescharacteristic, complemented
50#10622852C2214yes—
51#10622851C2214yes—
52#10622847C2212yes—
53#10622845C2212yes—
54#10622831C2214yes—
55#10622830C2214yes—
56C2×#66896C2212yes—
57#10622644C2211yescharacteristic, complemented
58#10622643C2214yescomplemented
59#10622641C2212yescomplemented
60#10622640C2211yescharacteristic, complemented
61C4×#4325C2214yescomplemented
62#10622634C2212yescomplemented
63#10622633C2212yescomplemented
64#10622632C2211yescharacteristic, complemented
65#10622632C2212yescomplemented
66#10622631C2214yescomplemented
67C4×#4324C2214yescomplemented
68C4×#4324C2214yescomplemented
69#10622629C2212yescomplemented
70#10622629C2214yescomplemented
71#10622628C2211yescharacteristic, complemented
72#10622628C2212yescomplemented
73#10622627C2214yescomplemented
74#10622627C2214yescomplemented
75C4×#4323C2214yescomplemented
76#10622621C2214yescomplemented
77#10622621C2212yescomplemented
78#10622621C2212yescomplemented
79#10622621C2212yescomplemented
80#10622620C2212yescomplemented
81#10622616C2214yescomplemented
82#10622615C2212yescomplemented
83#10622613C2214yescomplemented
84#10622610C2212yescomplemented
85#10622609C2214yescomplemented
86#10622608C2212yescomplemented
87#10622584C2214yescomplemented
88#10622581C2214yescomplemented
89#10622579C2212yescomplemented
90C2×#66872C2212yescomplemented
91#10622539C2212yescomplemented
92#10622538C2212yescomplemented
93#10622537C2211yescharacteristic, complemented
94C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
95C11×H(5,𝔽2)—24no—
96C11×H(5,𝔽2)—24no—
97C2×C11×#41—21no—
98C2×C11×#41C2312yes—
99C2×C11×#41C2311yescharacteristic
100C2×C11×#41C2311yescharacteristic
101C22×D4×C11—21no—
102C22×D4×C11—22no—
103C22×D4×C11C2312yes—
104C22×D4×C11C2311yescharacteristic
105C23×C4×C11—21no—
106C23×C4×C11—22no—
107C2×#4339—22no—
108C2×#4339C2312yes—
109C22×Dic22—21no—
110C4×Q8×C11—21no—
111C4×Q8×C11D411yescharacteristic
112C4×Q8×C11D411yescharacteristic
113C4×Q8×C11C2311yescharacteristic
114C4×Q8×C11C2311yescharacteristic
115C4×Q8×C11C2312yes—
116C4×D4×C11—21no—
117C4×D4×C11—22no—
118C4×D4×C11—21no—
119C4×D4×C11—22no—
120C4×D4×C11—22no—
121C4×D4×C11—21no—
122C4×D4×C11—21no—
123C4×D4×C11—22no—
124C4×D4×C11—21no—
125C4×D4×C11—22no—
126C4×D4×C11—22no—
127C4×D4×C11—22no—
128C4×D4×C11—22no—
129C4×D4×C11—21no—
130C4×D4×C11—22no—
131C4×D4×C11—22no—
132C4×D4×C11—21no—
133C4×D4×C11D411yescharacteristic
134C4×D4×C11D412yes—
135C4×D4×C11D411yescharacteristic
136C4×D4×C11D412yes—
137C4×D4×C11C2312yes—
138C4×D4×C11C2311yescharacteristic
139C4×D4×C11C2312yes—
140C4×D4×C11C2312yes—
141C4×D4×C11C2312yes—
142C4×D4×C11C2311yescharacteristic
143C4×D4×C11C2312yes—
144C11×#117—21no—
145C11×#117—22no—
146C11×#117—22no—
147C11×#117—21no—
148C11×#117C2311yescharacteristic
149C11×#117C2312yes—
150C11×#117C2311yescharacteristic
151C11×#117C2312yes—
152C2×C11×C4⋊C4—21no—
153C2×C11×C4⋊C4—22no—
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2312yes—
156C2×C11×C22⋊C4—22no—
157C2×C11×C22⋊C4—21no—
158C2×C11×C22⋊C4—22no—
159C2×C11×C22⋊C4—22no—
160C2×C11×C22⋊C4—22no—
161C2×C42×C11—21no—
162C2×C42×C11—22no—
163C2×C42×C11C2311yescharacteristic
164C2×C42×C11C2312yes—
165#67003—28no—
166#66999—22no—
167C2×#4326C2312yes—
168C2×#4325C2312yes—
169#66992—24no—
170#66991—22no—
171C2×#4324C2314yes—
172C2×#4324C2312yes—
173#66985—28no—
174C2×#4323C2314yes—
175C2×#4323C2312yes—
176#66983—21no—
177#66983—22no—
178#66983—21no—
179#66983C2314yes—
180#66979—22no—
181C2×C4⋊Dic11—21no—
182C2×C4⋊Dic11C2312yes—
183#66977—22no—
184#66977C2314yes—
185C2×#4318C2312yes—
186C22×C11⋊C8C2312yes—
187#66951—24no—
188#66949—24no—
189#66945—22no—
190C4⋊C4×D11—22no—
191#66938—24no—
192#66936—24no—
193(C22⋊D11)⋊C4—24no—
194#66928—22no—
195#66928C2312yes—
196#66927C2311yescharacteristic
197C4×D44—21no—
198C4×D44—21no—
199C4×D44—22no—
200C4×D44C2314yes—
201#66923—22no—
202#66922—21no—
203#66922—21no—
204#66922C2311yescharacteristic
205#66922C2312yes—
206#66922C2312yes—
207C4×Dic22—22no—
208C4×Dic22C2314yes—
209#66899C2314yes—
210#66896C2314yes—
211#66896C2314yes—
212#66896C2314yes—
213C22⋊(C11⋊C8)C2314yes—
214C22⋊(C11⋊C8)C2314yes—
215#66874C2314yes—
216#66874C2312yes—
217#66874C2312yes—
218#66873C2314yes—
219#66873C2312yes—
220#66873C2312yes—
221#66872C2314yes—
222#66872C2314yes—
223#66872C2314yes—
224#66871C2314yes—
225C4⋊(C11⋊C8)C2311yescharacteristic
226C4⋊(C11⋊C8)C2311yescharacteristic
227C4⋊(C11⋊C8)C2312yes—
228C4⋊(C11⋊C8)C2312yes—
229C4⋊(C11⋊C8)C2312yes—
230#66867C2314yes—
231C4×C11⋊C8C2314yes—
232#60597—111nomaximal, Sylow
233C24×C11—22no—
234C24×C11—21no—
235C11×#41—28no—
236C11×#41—24no—
237C11×#41—24no—
238C11×#41—22no—
239C11×#41—22no—
240C11×#41—22no—
241C11×#41#4114yescomplemented
242C2×Q8×C11C2×D411yescharacteristic
243C2×Q8×C11C2411yescharacteristic
244C2×D4×C11—216no—
245C2×D4×C11—28no—
246C2×D4×C11—22no—
247C2×D4×C11—21no—
248C2×D4×C11—24no—
249C2×D4×C11—24no—
250C2×D4×C11—22no—
251C2×D4×C11—21no—
252C2×D4×C11—22no—
253C2×D4×C11C2×D411yescharacteristic
254C2×D4×C11C2×D412yes—
255C2×D4×C11#4114yescomplemented
256C2×D4×C11C2411yescharacteristic
257C2×D4×C11C2412yes—
258C22×C4×C11—22no—
259C22×C4×C11—21no—
260C22×C4×C11—22no—
261C22×C4×C11—21no—
262C22×C4×C11—21no—
263C22×C4×C11—22no—
264C22×C4×C11—22no—
265C22×C4×C11—21no—
266C22×C4×C11—22no—
267C22×C4×C11—22no—
268C22×C4×C11—22no—
269C22×C4×C11—82no—
270C22×C4×C11—84no—
271C22×C4×C11C2×D411yescharacteristic
272C22×C4×C11C2×D412yes—
273C22×C4×C11C2×D412yes—
274C22×C4×C11C2×D411yescharacteristic
275C22×C4×C11C2412yes—
276C22×C4×C11C2411yescharacteristic
277C2×C22⋊D11—22no—
278C2×C22⋊D11—24no—
279C22×Dic11—22no—
280#4339—24no—
281#4339—24no—
282#4339—84no—
283C2×D44—21no—
284C2×D44—21no—
285C2×D44C2412yes—
286C2×C4×D11—22no—
287C2×C4×D11—24no—
288C2×Dic22—22no—
289C2×Dic22—22no—
290C2×Dic22—82no—
291C2×Dic22C2412yes—
292C11×C4⋊C4—22no—
293C11×C4⋊C4—21no—
294C11×C4⋊C4—22no—
295C11×C4⋊C4—21no—
296C11×C4⋊C4—21no—
297C11×C4⋊C4C2×D411yescharacteristic
298C11×C4⋊C4C2×D411yescharacteristic
299C11×C4⋊C4C2×D412yes—
300C11×C4⋊C4C2×D412yes—
301C11×C4⋊C4C2411yescharacteristic
302C11×C4⋊C4C2412yes—
303C11×C4⋊C4C2411yescharacteristic
304C11×C22⋊C4—22no—
305C11×C22⋊C4—21no—
306C11×C22⋊C4—22no—
307C11×C22⋊C4—21no—
308C11×C22⋊C4—22no—
309C11×C22⋊C4—22no—
310C11×C22⋊C4—21no—
311C11×C22⋊C4—22no—
312C11×C22⋊C4—22no—
313C11×C22⋊C4C2×D412yes—
314C11×C22⋊C4C2×D412yes—
315C11×C22⋊C4C2×D412yes—
316C42×C11—21no—
317C42×C11—22no—
318C42×C11—21no—
319C42×C11—22no—
320C42×C11—21no—
321C42×C11C2×D412yes—
322C42×C11C2×D411yescharacteristic
323C42×C11C2×D411yescharacteristic
324C42×C11C2×D412yes—
325C42×C11C2412yes—
326C42×C11C2411yescharacteristic
327C42×C11C2411yescharacteristic
328C22⋊Dic11—24no—
329#4326—24no—
330#4325—24no—
331#4324—28no—
332#4324—24no—
333#4323—28no—
334#4323—24no—
335(C2×D11)⋊C4—24no—
336(C2×D11)⋊C4—22no—
337(C2×D11)⋊C4—22no—
338(C2×D11)⋊C4—24no—
339C4⋊Dic11—21no—
340C4⋊Dic11—22no—
341C4⋊Dic11—22no—
342C4⋊Dic11—22no—
343C4⋊Dic11—21no—
344C4⋊Dic11C2414yes—
345Dic11⋊C4—24no—
346Dic11⋊C4—24no—
347C4×Dic11—24no—
348#4318—24no—
349C2×C11⋊C8—24no—
350C2×C11⋊C8C2412yes—
351C2×C11⋊C8C2414yes—
352C2×C11⋊C8C2412yes—
353#3511—111no—
354C4×H(5,𝔽2)D1111yescharacteristic, complemented
355#3125—114no—
356#3118—114no—
357#3116—112no—
358#3109—112no—
359#3106—112no—
360#3101—112no—
361#3099—112no—
362#3079—111no—
363C2×#476—111no—
364#3036—111no—
365#3035—111no—
366#3012—112no—
367#2952—112no—
368#2946—112no—
369#2925—111no—
370C23×C11—28no—
371C23×C11—22no—
372C23×C11—21no—
373C23×C11—24no—
374C23×C11—81no—
375C23×C11—82no—
376C23×C11—81no—
377C23×C11—82no—
378C23×C11C22×D412yes—
379C23×C11C22×D411yescharacteristic
380C22×D11—22no—
381Q8×C11—22no—
382Q8×C11—21no—
383Q8×C11C2×#4112yes—
384D4×C11—28no—
385D4×C11—28no—
386D4×C11—24no—
387D4×C11—24no—
388D4×C11—22no—
389D4×C11—24no—
390D4×C11—22no—
391D4×C11—21no—
392D4×C11C2×#4112yes—
393D4×C11C2×#4114yes—
394C2×C4×C11—28no—
395C2×C4×C11—21no—
396C2×C4×C11—24no—
397C2×C4×C11—22no—
398C2×C4×C11—24no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—21no—
402C2×C4×C11—22no—
403C2×C4×C11—21no—
404C2×C4×C11—41no—
405C2×C4×C11—42no—
406C2×C4×C11—44no—
407C2×C4×C11—42no—
408C2×C4×C11—81no—
409C2×C4×C11—82no—
410C2×C4×C11—82no—
411C2×C4×C11—82no—
412C2×C4×C11—82no—
413C2×C4×C11—81no—
414C2×C4×C11—82no—
415C2×C4×C11C22×D412yes—
416C2×C4×C11C22×D412yes—
417C2×C4×C11C22×D412yes—
418C2×C4×C11C22×D411yescharacteristic
419C2×C4×C11C22×D411yescharacteristic
420C2×C4×C11C22×D411yescharacteristic
421C2×C4×C11C22×D411yescharacteristic
422C2×C4×C11C22×D411yescharacteristic
423C2×C4×C11C2×#4112yes—
424C2×C4×C11C2×#4112yes—
425C2×C4×C11C2511yescharacteristic
426C22⋊D11—44no—
427C22⋊D11—84no—
428C2×Dic11—22no—
429C2×Dic11—24no—
430C2×Dic11—82no—
431D44—22no—
432D44—22no—
433D44—42no—
434D44—42no—
435C4×D11—44no—
436C4×D11—84no—
437Dic22—22no—
438Dic22—22no—
439Dic22—44no—
440Dic22—82no—
441C11⋊C8—22no—
442C11⋊C8—22no—
443C11⋊C8—24no—
444C2×H(5,𝔽2)C2×D1111yescharacteristic
445C2×AGL(1,ℤ/8)—112no—
446C2×#135—112no—
447#556—221no—
448#555—221no—
449#554—221no—
450#553—222no—
451#548—222no—
452#547—221no—
453#542—114no—
454#537—112no—
455#533—112no—
456#532—112no—
457#532—111no—
458C2×C4⋊Q8—111no—
459#520—21no—
460#520—112no—
461#520C2×D1112yes—
462#520C2×D1111yescharacteristic
463#520C2×D1111yescharacteristic
464#518—21no—
465#518—22no—
466#518C2×D1112yes—
467#518C2×D1111yescharacteristic
468C4×#41—21no—
469C4×#41C2×D1111yescharacteristic
470C4×#41C2×D1112yes—
471C4×#41C2×D1111yescharacteristic
472C2×C4×D4—22no—
473C2×C4×D4—21no—
474C2×C4×D4C2×D1112yes—
475C2×C4×D4C2×D1111yescharacteristic
476#485—114no—
477#483—114no—
478#482—114no—
479#481—114no—
480#477—112no—
481#476—112no—
482#476—112no—
483#476—112no—
484#476—114no—
485#475—112no—
486#474—112no—
487#464—112no—
488#463—112no—
489#463—114no—
490#462—111no—
491#461—111no—
492#461—112no—
493#460—111no—
494#459—112no—
495#459—111no—
496#452—114no—
497#450—114no—
498#449—114no—
499#447—114no—
500#442—114no—
501#442—114no—
502#441—114no—
503#440—114no—
504C4×SD16—114no—
505C4×SD16—114no—
506C4×SD16—114no—
507C4×D8—114no—
508#433—114no—
509#432—112no—
510#431—112no—
511#428—112no—
512C2×#106—112no—
513#423—111no—
514C2×C4⋊C8—111no—
515#417—112no—
516#417—112no—
517#416—112no—
518C2×#102—112no—
519#408—112no—
520#405—112no—
521C22×C11—21no—
522C22×C11—21no—
523C22×C11—22no—
524C22×C11—22no—
525C22×C11—24no—
526C22×C11—22no—
527C22×C11—22no—
528C22×C11—42no—
529C22×C11—41no—
530C22×C11—42no—
531C22×C11—41no—
532C22×C11—84no—
533C22×C11—88no—
534C22×C11#52512yes—
535C22×C11C23×D411yescharacteristic
536C2×D11—42no—
537C2×D11—42no—
538C2×D11—42no—
539C4×C11—21no—
540C4×C11—21no—
541C4×C11—22no—
542C4×C11—22no—
543C4×C11—22no—
544C4×C11—22no—
545C4×C11—21no—
546C4×C11—41no—
547C4×C11—42no—
548C4×C11—41no—
549C4×C11#52512yes—
550C4×C11#57712yes—
551C4×C11C22×#4111yescharacteristic
552C4×C11C22×#4111yescharacteristic
553Dic11—44no—
554Dic11—42no—
555H(5,𝔽2)—24no—
556H(5,𝔽2)—24no—
557C2×#41—21no—
558C2×#41—112no—
559C2×#41—222no—
560C2×#41C22×D1112yes—
561C2×#41C22×D1111yescharacteristic
562C2×#41C22×D1111yescharacteristic
563C22×Q8—221no—
564C22×D4—22no—
565C22×D4—21no—
566C22×D4C22×D1112yes—
567C22×D4C22×D1111yescharacteristic
568C23×C4—21no—
569C23×C4—22no—
570AGL(1,ℤ/8)—228no—
571#135—228no—
572C2×Q16—112no—
573C2×SD16—112no—
574C2×SD16—112no—
575C2×SD16—114no—
576C2×D8—112no—
577C2×D8—114no—
578C2×M16—112no—
579C22×C8—112no—
580C4⋊Q8—112no—
581C4⋊Q8—112no—
582C4⋊Q8—111no—
583C4⋊Q8—221no—
584C4⋊Q8—221no—
585#127—111no—
586#126—224no—
587#125—222no—
588#124—112no—
589#124—224no—
590#124—222no—
591#123—224no—
592C22⋊Q8—114no—
593C22⋊Q8—222no—
594C22⋊Q8—222no—
595C22⋊Q8—224no—
596#121—114no—
597#121—222no—
598#121—224no—
599#121—221no—
600#121—221no—
601#121—222no—
602C4×Q8—21no—
603C4×Q8—114no—
604C4×Q8—222no—
605C4×Q8C22⋊D1111yescharacteristic
606C4×Q8C22⋊D1111yescharacteristic
607C4×Q8C22×D1111yescharacteristic
608C4×Q8C22×D1112yes—
609C4×Q8C22×D1111yescharacteristic
610C4×D4—22no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—22no—
614C4×D4—21no—
615C4×D4—22no—
616C4×D4—21no—
617C4×D4—22no—
618C4×D4—21no—
619C4×D4—22no—
620C4×D4—22no—
621C4×D4—22no—
622C4×D4—22no—
623C4×D4—22no—
624C4×D4—21no—
625C4×D4—21no—
626C4×D4—22no—
627C4×D4—114no—
628C4×D4—224no—
629C4×D4—221no—
630C4×D4—222no—
631C4×D4—221no—
632C4×D4C22⋊D1112yes—
633C4×D4C22⋊D1111yescharacteristic
634C4×D4C22⋊D1111yescharacteristic
635C4×D4C22⋊D1112yes—
636C4×D4C22×D1111yescharacteristic
637C4×D4C22×D1112yes—
638C4×D4C22×D1112yes—
639C4×D4C22×D1112yes—
640C4×D4C22×D1112yes—
641C4×D4C22×D1112yes—
642C4×D4C22×D1111yescharacteristic
643#117—21no—
644#117—22no—
645#117—21no—
646#117—22no—
647#117—222no—
648#117—222no—
649#117C22×D1111yescharacteristic
650#117C22×D1112yes—
651#117C22×D1111yescharacteristic
652#117C22×D1112yes—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—22no—
655C2×C4⋊C4—112no—
656C2×C4⋊C4—221no—
657C2×C4⋊C4—222no—
658C2×C4⋊C4C22×D1111yescharacteristic
659C2×C4⋊C4C22×D1112yes—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—22no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—22no—
664C2×C22⋊C4—22no—
665C2×C42—22no—
666C2×C42—21no—
667C2×C42C22×D1111yescharacteristic
668C2×C42C22×D1112yes—
669#107—114no—
670#106—114no—
671#106—114no—
672#106—114no—
673C4⋊C8—111no—
674C4⋊C8—111no—
675C4⋊C8—112no—
676C4⋊C8—112no—
677C4⋊C8—112no—
678#103—114no—
679#103—112no—
680#103—112no—
681#103—114no—
682#102—114no—
683#102—114no—
684#102—114no—
685#102—112no—
686#102—112no—
687#102—114no—
688C22⋊C8—114no—
689C22⋊C8—114no—
690#97—114no—
691C4×C8—114no—
692C2×C11—22no—
693C2×C11—42no—
694C2×C11—44no—
695C2×C11—42no—
696C2×C11C2×#52511yescharacteristic
697C2×C11C2×#57711yescharacteristic
698C2×C11#358511yescharacteristic
699D11—82no—
700C24—22no—
701C24—21no—
702#41—28no—
703#41—24no—
704#41—24no—
705#41—22no—
706#41—22no—
707#41—22no—
708#41—224no—
709#41—224no—
710#41—884no—
711#41#433914yescomplemented
712C2×Q8—112no—
713C2×Q8—222no—
714C2×Q8—222no—
715C2×Q8—882no—
716C2×Q8C2×C22⋊D1111yescharacteristic
717C2×Q8C23×D1111yescharacteristic
718C2×D4—216no—
719C2×D4—28no—
720C2×D4—22no—
721C2×D4—21no—
722C2×D4—24no—
723C2×D4—24no—
724C2×D4—22no—
725C2×D4—22no—
726C2×D4—21no—
727C2×D4—112no—
728C2×D4—222no—
729C2×D4—224no—
730C2×D4—221no—
731C2×D4—221no—
732C2×D4#433914yescomplemented
733C2×D4C2×C22⋊D1112yes—
734C2×D4C2×C22⋊D1111yescharacteristic
735C2×D4C23×D1111yescharacteristic
736C2×D4C23×D1112yes—
737C22×C4—22no—
738C22×C4—21no—
739C22×C4—22no—
740C22×C4—21no—
741C22×C4—22no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—82no—
749C22×C4—84no—
750C22×C4—222no—
751C22×C4—222no—
752C22×C4—224no—
753C22×C4C2×C22⋊D1111yescharacteristic
754C22×C4C2×C22⋊D1112yes—
755C22×C4C2×C22⋊D1111yescharacteristic
756C22×C4C2×C22⋊D1112yes—
757C22×C4C23×D1112yes—
758C22×C4C23×D1111yescharacteristic
759Q16—224no—
760SD16—224no—
761SD16—224no—
762SD16—228no—
763D8—224no—
764D8—228no—
765M16—224no—
766C2×C8—112no—
767C2×C8—114no—
768C2×C8—112no—
769C2×C8—224no—
770C4⋊C4—22no—
771C4⋊C4—21no—
772C4⋊C4—22no—
773C4⋊C4—21no—
774C4⋊C4—21no—
775C4⋊C4—114no—
776C4⋊C4—222no—
777C4⋊C4—222no—
778C4⋊C4—224no—
779C4⋊C4—222no—
780C4⋊C4—221no—
781C4⋊C4—221no—
782C4⋊C4—224no—
783C4⋊C4C2×C22⋊D1111yescharacteristic
784C4⋊C4C2×C22⋊D1112yes—
785C4⋊C4C2×C22⋊D1111yescharacteristic
786C4⋊C4C2×C22⋊D1112yes—
787C4⋊C4C23×D1111yescharacteristic
788C4⋊C4C23×D1112yes—
789C4⋊C4C23×D1111yescharacteristic
790C22⋊C4—22no—
791C22⋊C4—21no—
792C22⋊C4—22no—
793C22⋊C4—21no—
794C22⋊C4—22no—
795C22⋊C4—22no—
796C22⋊C4—22no—
797C22⋊C4—22no—
798C22⋊C4—21no—
799C22⋊C4—224no—
800C22⋊C4—224no—
801C22⋊C4—224no—
802C22⋊C4—222no—
803C22⋊C4—222no—
804C22⋊C4C2×C22⋊D1112yes—
805C22⋊C4C2×C22⋊D1112yes—
806C22⋊C4C2×C22⋊D1112yes—
807C42—21no—
808C42—21no—
809C42—22no—
810C42—22no—
811C42—21no—
812C42—224no—
813C42C2×C22⋊D1112yes—
814C42C2×C22⋊D1111yescharacteristic
815C42C2×C22⋊D1111yescharacteristic
816C42C2×C22⋊D1112yes—
817C42C23×D1112yes—
818C42C23×D1111yescharacteristic
819C42C23×D1111yescharacteristic
820C11#6059711yescharacteristic, complemented, Sylow
821C23—28no—
822C23—22no—
823C23—21no—
824C23—24no—
825C23—81no—
826C23—82no—
827C23—81no—
828C23—82no—
829C23—222no—
830C23C22×C22⋊D1112yes—
831C23C22×C22⋊D1111yescharacteristic
832Q8—22no—
833Q8—21no—
834Q8—222no—
835Q8—222no—
836Q8—444no—
837Q8—882no—
838Q8C2×#433912yes—
839D4—28no—
840D4—28no—
841D4—24no—
842D4—24no—
843D4—24no—
844D4—22no—
845D4—22no—
846D4—21no—
847D4—222no—
848D4—222no—
849D4—442no—
850D4—444no—
851D4—442no—
852D4—884no—
853D4C2×#433912yes—
854D4C2×#433914yes—
855C2×C4—28no—
856C2×C4—21no—
857C2×C4—24no—
858C2×C4—22no—
859C2×C4—24no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—22no—
865C2×C4—41no—
866C2×C4—42no—
867C2×C4—44no—
868C2×C4—42no—
869C2×C4—82no—
870C2×C4—81no—
871C2×C4—82no—
872C2×C4—82no—
873C2×C4—82no—
874C2×C4—81no—
875C2×C4—82no—
876C2×C4—222no—
877C2×C4—224no—
878C2×C4—444no—
879C2×C4—884no—
880C2×C4—882no—
881C2×C4C2×#433912yes—
882C2×C4C2×#433912yes—
883C2×C4C22×C22⋊D1112yes—
884C2×C4C22×C22⋊D1111yescharacteristic
885C2×C4C22×C22⋊D1112yes—
886C2×C4C22×C22⋊D1112yes—
887C2×C4C22×C22⋊D1111yescharacteristic
888C2×C4C22×C22⋊D1111yescharacteristic
889C2×C4C22×C22⋊D1111yescharacteristic
890C2×C4C22×C22⋊D1111yescharacteristic
891C2×C4C24×D1111yescharacteristic
892C8—222no—
893C8—222no—
894C8—224no—
895C22—21no—
896C22—21no—
897C22—22no—
898C22—24no—
899C22—22no—
900C22—22no—
901C22—22no—
902C22—42no—
903C22—41no—
904C22—42no—
905C22—41no—
906C22—84no—
907C22—88no—
908C22—442no—
909C22—442no—
910C22—442no—
911C22#1062332212yes—
912C22C23×C22⋊D1111yescharacteristic
913C4—22no—
914C4—22no—
915C4—21no—
916C4—22no—
917C4—21no—
918C4—22no—
919C4—21no—
920C4—41no—
921C4—42no—
922C4—41no—
923C4—442no—
924C4—444no—
925C4#1062332212yes—
926C4#1062336712yes—
927C4C22×#433911yescharacteristic
928C4C22×#433911yescharacteristic
929C2—22no—
930C2—42no—
931C2—44no—
932C2—42no—
933C2—882no—
934C2C2×#1062332211yescharacteristic
935C2C2×#1062336711yescharacteristic
936C2#1308339511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC4×C11×H(5,𝔽2)C2
socleC22×C11C23×D4
hypercenterC4×H(5,𝔽2)D11
hypocenterC11#60597
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ C4×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #13082527C2semidirect
2. #13078893C2semidirect
3. #13078800C2semidirect
4. #13078778C2semidirect
5. #13078707C2semidirect
6. #13078676C2semidirect
7. #13078624C2semidirect
8. #13078605C2semidirect
9. #13078431C2semidirect
10. C2×#10622621C2semidirect
11. #13078080C2semidirect
12. #13078071C2semidirect
13. #13077920C2semidirect
14. #13077497C2semidirect
15. #13077448C2semidirect
16. #13077282C2semidirect
17. C4×C11×H(5,𝔽2)C2semidirect
44. #10623065C22semidirect
45. #10623054C22semidirect
46. #10623008C22semidirect
47. #10623008C22semidirect
48. #10623001C22semidirect
49. C2×#66922C22semidirect
57. #10622644C22semidirect
58. #10622643C22semidirect
59. #10622641C22semidirect
60. #10622640C22semidirect
61. C4×#4325C22semidirect
62. #10622634C22semidirect
63. #10622633C22semidirect
64. #10622632C22semidirect
65. #10622632C22semidirect
66. #10622631C22semidirect
67. C4×#4324C22semidirect
68. C4×#4324C22semidirect
69. #10622629C22semidirect
70. #10622629C22semidirect
71. #10622628C22semidirect
72. #10622628C22semidirect
73. #10622627C22semidirect
74. #10622627C22semidirect
75. C4×#4323C22semidirect
76. #10622621C22semidirect
77. #10622621C22semidirect
78. #10622621C22semidirect
79. #10622621C22semidirect
80. #10622620C22semidirect
81. #10622616C22semidirect
82. #10622615C22semidirect
83. #10622613C22semidirect
84. #10622610C22semidirect
85. #10622609C22semidirect
86. #10622608C22semidirect
87. #10622584C22semidirect
88. #10622581C22semidirect
89. #10622579C22semidirect
90. C2×#66872C22semidirect
91. #10622539C22semidirect
92. #10622538C22semidirect
93. #10622537C22semidirect
94. C2×C4⋊(C11⋊C8)C22semidirect
241. C11×#41#41semidirect
255. C2×D4×C11#41semidirect
354. C4×H(5,𝔽2)D11semidirect
711. #41#4339semidirect
732. C2×D4#4339semidirect
820. C11#60597semidirect

Maximal subgroups

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

subgroupindex
#130825272
#130788932
#130788002
#130787782
#130787072
#130786762
#130786242
#130786052
#130784312
C2×#106226212
#130780802
#130780712
#130779202
#130774972
#130774482
#130772822
C4×C11×H(5,𝔽2)2
#6059711