Finite Group Databasebeta

← #15630959

Subgroups — #15630959

Order 2816.

2182 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#4339C211yesmaximal, characteristic, complemented
2#13080904C212yesmaximal, complemented
3#13080852C212yesmaximal, complemented
4#13080796C214yesmaximal, complemented
5#13080766C214yesmaximal, complemented
6#13080560C212yesmaximal, complemented
7#13080538C212yesmaximal, complemented
8#13079012C211yesmaximal, characteristic, complemented
9#13078547C212yesmaximal, complemented
10#13078425C211yesmaximal, characteristic, complemented
11#13078231C212yesmaximal, complemented
12#13078080C211yesmaximal, characteristic, complemented
13#13077866C212yesmaximal, complemented
14C4×#66985C211yesmaximal, characteristic, complemented
15D4×#4318C211yesmaximal, characteristic, complemented
16#13077133C212yesmaximal, complemented
17C2×C11×#555C211yesmaximal, characteristic, complemented
18C22×#4339C2212yes—
19C11×#555—21no—
20C11×#555—21no—
21C11×#555—22no—
22C11×#555C2212yes—
23C11×#555C2214yescomplemented
24C11×#555C2212yescomplemented
25C2×C11×C4⋊Q8C2211yescharacteristic, complemented
26C2×C11×#124—22no—
27C2×C11×#121—21no—
28C2×C11×#121C2212yescomplemented
29C2×C4×D4×C11C2211yescharacteristic
30C2×C4×D4×C11C2211yescharacteristic, complemented
31C2×C11×#117—21no—
32C2×C11×#117C2212yescomplemented
33D4×C22⋊D11—21no—
34C2×#66985C2211yescharacteristic
35C2×#66985C2212yescomplemented
36#10623322C2212yes—
37C22×#4318C2212yescomplemented
38#10623084C2211yescharacteristic, complemented
39#10623083C2212yescomplemented
40#10623082C2211yescharacteristic, complemented
41#10623081C2212yescomplemented
42D4×D44C2211yescharacteristic, complemented
43#10623079—21no—
44#10623078—22no—
45C4×D4×D11—21no—
46D4×Dic22C2211yescharacteristic, complemented
47#10623038—21no—
48#10623021—22no—
49#10623008C2211yescharacteristic
50C4×#4339C2211yescharacteristic
51#10622828C2211yescharacteristic, complemented
52#10622820C2212yescomplemented
53#10622707C2212yescomplemented
54#10622706C2212yescomplemented
55#10622704C2212yescomplemented
56#10622702C2214yescomplemented
57#10622701C2212yescomplemented
58#10622700C2212yescomplemented
59#10622697C2212yescomplemented
60#10622655C2214yescomplemented
61#10622654C2214yescomplemented
62#10622653C2214yescomplemented
63#10622652C2214yescomplemented
64#10622651C2214yescomplemented
65#10622650C2214yescomplemented
66#10622650C2214yescomplemented
67#10622649C2214yescomplemented
68#10622632C2212yescomplemented
69#10622631C2212yescomplemented
70C4×#4324C2212yescomplemented
71#10622629C2214yescomplemented
72#10622628C2212yescomplemented
73#10622627C2212yescomplemented
74C4×#4323C2212yescomplemented
75#10622625C2212yescomplemented
76#10622624C2214yescomplemented
77D4×C11⋊C8C2212yescomplemented
78#10622617C2214yescomplemented
79#10622616C2214yescomplemented
80#10622616C2214yescomplemented
81#10622615C2214yescomplemented
82#10622615C2214yescomplemented
83#10622614C2214yescomplemented
84#10622609C2214yescomplemented
85#10622609C2214yescomplemented
86#10622579C2212yes—
87#10622579C2211yescharacteristic
88#10622579C2212yescomplemented
89#10622579C2212yescomplemented
90#10622579C2212yescomplemented
91#10622577C2211yescharacteristic, complemented
92#10622577C2212yescomplemented
93#10622537C2211yescharacteristic, complemented
94C4×#4318C2211yescharacteristic, complemented
95C22×Q8×C11—21no—
96C22×D4×C11—22no—
97C22×D4×C11D411yescharacteristic
98C22×D4×C11C2311yescharacteristic
99C23×C4×C11—21no—
100C23×C4×C11C2312yes—
101C22×C22⋊D11—22no—
102C2×D4×D11—21no—
103C2×#4339—22no—
104C2×#4339—22no—
105C2×#4339—28no—
106C2×#4339—44no—
107C2×#4339C2312yes—
108C2×#4339C2312yes—
109C2×#4339C2312yes—
110C2×#4339C2311yescharacteristic
111C22×D44C2312yes—
112C22×C4×D11—22no—
113C22×Dic22C2312yes—
114C11×C4⋊Q8—21no—
115C11×C4⋊Q8—21no—
116C11×C4⋊Q8C2312yes—
117C11×C4⋊Q8C2312yes—
118C11×#124—24no—
119C11×#124—24no—
120C11×#124—24no—
121C11×#124—24no—
122C11×#121—22no—
123C11×#121—22no—
124C11×#121—24no—
125C11×#121—22no—
126C11×#121—22no—
127C11×#121C2314yes—
128C11×#121C2314yes—
129C4×D4×C11—21no—
130C4×D4×C11—21no—
131C4×D4×C11D411yescharacteristic
132C4×D4×C11D412yes—
133C4×D4×C11D411yescharacteristic
134C4×D4×C11C2312yes—
135C4×D4×C11C2312yes—
136C4×D4×C11C2311yescharacteristic
137C4×D4×C11C2312yes—
138C4×D4×C11C2311yescharacteristic
139C11×#117—22no—
140C11×#117—22no—
141C11×#117—22no—
142C11×#117—22no—
143C11×#117—24no—
144C11×#117C2314yes—
145C11×#117C2314yes—
146C2×C11×C4⋊C4—21no—
147C2×C11×C4⋊C4D411yescharacteristic
148C2×C11×C4⋊C4C2311yescharacteristic
149C2×C11×C4⋊C4C2312yes—
150C2×C11×C22⋊C4—22no—
151C2×C11×C22⋊C4—22no—
152C2×C11×C22⋊C4—21no—
153C2×C11×C22⋊C4D412yes—
154C2×C42×C11—22no—
155C2×C42×C11C2311yescharacteristic
156#67006—22no—
157#66993—21no—
158#66992—22no—
159#66991—21no—
160#66990—22no—
161D4×Dic11—21no—
162C2×#4324C2312yes—
163C2×#4324C2314yes—
164#66985—24no—
165#66985—44no—
166C2×#4323C2312yes—
167C2×#4323C2314yes—
168#66983—21no—
169#66983—21no—
170#66983C2312yes—
171#66983C2312yes—
172#66982—22no—
173C4×C22⋊D11—21no—
174C4×C22⋊D11—21no—
175C4×C22⋊D11—22no—
176C4×C22⋊D11—22no—
177#66979C2311yescharacteristic
178#66977C2312yes—
179#66977C2312yes—
180C2×#4318—44no—
181C2×#4318C2311yescharacteristic
182C2×#4318C2311yescharacteristic
183C2×#4318C2312yes—
184C2×#4318C2314yes—
185C22×C11⋊C8C2314yes—
186#66949—22no—
187#66948—21no—
188#66947—22no—
189#66946—21no—
190C4⋊C4×D11—21no—
191#66941—21no—
192#66938—22no—
193#66937—22no—
194#66937—22no—
195#66936—22no—
196#66935—22no—
197(C22⋊D11)⋊C4—22no—
198C22⋊C4×D11—22no—
199#66931—22no—
200#66928C2312yes—
201#66927C2311yescharacteristic
202C4×D44—21no—
203C4×D44—21no—
204C4×D44C2311yescharacteristic
205C4×D44C2311yescharacteristic
206#66925—21no—
207C42×D11—21no—
208#66922C2311yescharacteristic
209C4×Dic22C2311yescharacteristic
210C4×Dic22C2311yescharacteristic
211#66896C2312yes—
212#66896C2312yes—
213C22⋊(C11⋊C8)C2314yes—
214C22⋊(C11⋊C8)C2314yes—
215#66874C2312yes—
216#66874C2314yes—
217#66874C2314yes—
218#66874C2314yes—
219#66874C2314yes—
220#66873C2312yes—
221#66873C2314yes—
222#66873C2314yes—
223#66873C2314yes—
224#66873C2314yes—
225#66872C2312yes—
226#66872C2314yes—
227#66871C2312yes—
228#66871C2314yes—
229C4⋊(C11⋊C8)C2312yes—
230C4⋊(C11⋊C8)C2312yes—
231#66867C2312yes—
232C4×C11⋊C8C2312yes—
233#61166—111nomaximal, Sylow
234C24×C11—21no—
235C24×C11C2×D412yes—
236C23×D11—22no—
237C2×Q8×C11—22no—
238C2×Q8×C11—22no—
239C2×Q8×C11—82no—
240C2×D4×C11—24no—
241C2×D4×C11—24no—
242C2×D4×C11—21no—
243C2×D4×C11—22no—
244C2×D4×C11—22no—
245C2×D4×C11—42no—
246C2×D4×C11—84no—
247C2×D4×C11C2×D411yescharacteristic
248C2×D4×C11C2×D411yescharacteristic
249C2×D4×C11C2×D412yes—
250C2×D4×C11C2412yes—
251C22×C4×C11—24no—
252C22×C4×C11—24no—
253C22×C4×C11—21no—
254C22×C4×C11—22no—
255C22×C4×C11—22no—
256C22×C4×C11—22no—
257C22×C4×C11—44no—
258C22×C4×C11C2×D411yescharacteristic
259C22×C4×C11C2×D412yes—
260C22×C4×C11C2×D412yes—
261C22×C4×C11C2×D412yes—
262C22×C4×C11C2×D411yescharacteristic
263C22×C4×C11C2412yes—
264C22×C4×C11C2412yes—
265C22×C4×C11C2411yescharacteristic
266C2×C22⋊D11—21no—
267C2×C22⋊D11—22no—
268C2×C22⋊D11—22no—
269C2×C22⋊D11—22no—
270C2×C22⋊D11—22no—
271C2×C22⋊D11—22no—
272C2×C22⋊D11—48no—
273C22×Dic11—22no—
274D4×D11—44no—
275#4339—24no—
276#4339—24no—
277#4339—24no—
278#4339—22no—
279#4339—24no—
280#4339—42no—
281#4339—42no—
282#4339—48no—
283#4339—48no—
284#4339#4114yes—
285C2×D44—24no—
286C2×D44—21no—
287C2×D44—22no—
288C2×D44—21no—
289C2×D44—42no—
290C2×D44C2412yes—
291C2×D44C2411yescharacteristic
292C2×C4×D11—21no—
293C2×C4×D11—21no—
294C2×C4×D11—22no—
295C2×C4×D11—22no—
296C2×C4×D11—22no—
297C2×C4×D11—21no—
298C2×C4×D11—48no—
299C2×Dic22—24no—
300C2×Dic22—22no—
301C2×Dic22—42no—
302C2×Dic22C2412yes—
303C2×Dic22C2411yescharacteristic
304C11×C4⋊C4—22no—
305C11×C4⋊C4—22no—
306C11×C4⋊C4—21no—
307C11×C4⋊C4—22no—
308C11×C4⋊C4C2×D411yescharacteristic
309C11×C4⋊C4C2×D411yescharacteristic
310C11×C4⋊C4C2×D412yes—
311C11×C4⋊C4C2412yes—
312C11×C4⋊C4C2414yes—
313C11×C22⋊C4—24no—
314C11×C22⋊C4—24no—
315C11×C22⋊C4—24no—
316C11×C22⋊C4—24no—
317C11×C22⋊C4—22no—
318C11×C22⋊C4—22no—
319C11×C22⋊C4C2×D412yes—
320C11×C22⋊C4C2×D412yes—
321C11×C22⋊C4C2×D412yes—
322C11×C22⋊C4C2×D412yes—
323C42×C11—24no—
324C42×C11—24no—
325C42×C11C2×D411yescharacteristic
326C42×C11C2×D411yescharacteristic
327C42×C11C2411yescharacteristic
328C42×C11C2411yescharacteristic
329C22⋊Dic11—22no—
330C22⋊Dic11—22no—
331C22⋊Dic11—21no—
332#4324—24no—
333#4324—44no—
334#4323—24no—
335#4323—44no—
336(C2×D11)⋊C4—21no—
337(C2×D11)⋊C4—21no—
338(C2×D11)⋊C4—22no—
339(C2×D11)⋊C4—22no—
340(C2×D11)⋊C4—22no—
341(C2×D11)⋊C4—22no—
342C4⋊Dic11—21no—
343C4⋊Dic11—21no—
344C4⋊Dic11C2411yescharacteristic
345C4⋊Dic11C2411yescharacteristic
346Dic11⋊C4—21no—
347Dic11⋊C4—21no—
348Dic11⋊C4—22no—
349Dic11⋊C4—22no—
350C4×Dic11—21no—
351C4×Dic11—21no—
352C4×Dic11—21no—
353#4318—22no—
354#4318—22no—
355#4318—24no—
356#4318—44no—
357C2×C11⋊C8—44no—
358C2×C11⋊C8C2412yes—
359C2×C11⋊C8C2412yes—
360C2×C11⋊C8C2414yes—
361C2×#555D1111yescharacteristic, complemented
362D4×#41—111no—
363#3329—112no—
364#3325—112no—
365#3321—114no—
366#3319—114no—
367#3305—112no—
368#3303—112no—
369#3141—111no—
370#3093—112no—
371#3079—111no—
372#3055—112no—
373#3036—111no—
374#3006—112no—
375C4×AGL(1,ℤ/8)—111no—
376D4×M16—111no—
377#2896—112no—
378C23×C11—24no—
379C23×C11—22no—
380C23×C11—42no—
381C23×C11—42no—
382C23×C11—42no—
383C23×C11—42no—
384C23×C11—42no—
385C23×C11C22×D412yes—
386C23×C11C22×D412yes—
387C23×C11C22×D411yescharacteristic
388C22×D11—21no—
389C22×D11—22no—
390C22×D11—44no—
391C22×D11—44no—
392C22×D11—82no—
393Q8×C11—82no—
394Q8×C11—82no—
395D4×C11—22no—
396D4×C11—22no—
397D4×C11—22no—
398D4×C11—22no—
399D4×C11—42no—
400D4×C11—42no—
401D4×C11—84no—
402D4×C11—84no—
403C2×C4×C11—24no—
404C2×C4×C11—24no—
405C2×C4×C11—24no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—24no—
413C2×C4×C11—41no—
414C2×C4×C11—44no—
415C2×C4×C11—42no—
416C2×C4×C11—44no—
417C2×C4×C11—44no—
418C2×C4×C11C22×D411yescharacteristic
419C2×C4×C11C22×D411yescharacteristic
420C2×C4×C11C22×D411yescharacteristic
421C2×C4×C11C22×D412yes—
422C2×C4×C11C22×D412yes—
423C2×C4×C11C22×D411yescharacteristic
424C2×C4×C11C22×D411yescharacteristic
425C2×C4×C11C2×#4112yes—
426C2×C4×C11H(5,𝔽2)12yes—
427C2×C4×C11C2511yescharacteristic
428C22⋊D11—24no—
429C22⋊D11—44no—
430C22⋊D11—44no—
431C22⋊D11—44no—
432C22⋊D11—44no—
433C22⋊D11—82no—
434C2×Dic11—21no—
435C2×Dic11—21no—
436C2×Dic11—21no—
437C2×Dic11—22no—
438C2×Dic11—44no—
439D44—22no—
440D44—21no—
441D44—22no—
442D44—44no—
443D44—42no—
444D44—81no—
445D44C2×#4112yes—
446C4×D11—24no—
447C4×D11—44no—
448C4×D11—44no—
449C4×D11—44no—
450C4×D11—42no—
451C4×D11—81no—
452Dic22—21no—
453Dic22—22no—
454Dic22—22no—
455Dic22—44no—
456Dic22C2×#4112yes—
457C11⋊C8—22no—
458C11⋊C8—22no—
459C11⋊C8—24no—
460C22×#41—112no—
461C2×AGL(1,ℤ/8)—111no—
462C2×AGL(1,ℤ/8)—112no—
463C22×M16—112no—
464#555—21no—
465#555—21no—
466#555—22no—
467#555C2×D1112yes—
468#555C2×D1112yescomplemented
469#555C2×D1114yescomplemented
470#550—111no—
471D4×Q8—111no—
472#548—112no—
473#547—111no—
474#547—221no—
475#546—112no—
476#546—222no—
477D42—111no—
478D42—221no—
479#532—111no—
480#532—221no—
481C2×C4⋊Q8C2×D1111yescharacteristic, complemented
482C2×#124—22no—
483#525—112no—
484#525—222no—
485C2×#121—21no—
486C2×#121C2×D1112yescomplemented
487C4×#41—111no—
488C2×C4×D4—221no—
489C2×C4×D4C2×D1111yescharacteristic
490C2×C4×D4C2×D1111yescharacteristic, complemented
491C2×#117—21no—
492C2×#117C2×D1112yescomplemented
493#489—114no—
494#487—112no—
495#486—112no—
496#485—114no—
497#485—114no—
498#482—114no—
499#482—114no—
500#477—112no—
501#476—112no—
502#475—112no—
503#474—112no—
504#469—114no—
505#468—114no—
506#466—114no—
507#465—114no—
508#463—114no—
509#461—112no—
510#459—112no—
511#449—114no—
512#449—114no—
513#448—114no—
514#447—114no—
515#442—112no—
516#440—112no—
517C4×SD16—112no—
518C4×D8—112no—
519#436—112no—
520#435—114no—
521C8×D4—112no—
522#428—112no—
523#428—111no—
524#423—111no—
525#419—114no—
526#418—111no—
527#418—114no—
528#417—112no—
529#417—112no—
530#417—112no—
531#417—112no—
532#417—111no—
533#416—114no—
534#416—114no—
535#407—112no—
536C4×M16—111no—
537C22×C11—21no—
538C22×C11—21no—
539C22×C11—22no—
540C22×C11—22no—
541C22×C11—22no—
542C22×C11—22no—
543C22×C11—22no—
544C22×C11—22no—
545C22×C11—42no—
546C22×C11—42no—
547C22×C11—42no—
548C22×C11—84no—
549C22×C11—84no—
550C22×C11#54612yes—
551C22×C11C23×D411yescharacteristic
552C2×D11—22no—
553C2×D11—41no—
554C2×D11—41no—
555C2×D11—42no—
556C2×D11—42no—
557C2×D11—42no—
558C2×D11—88no—
559C4×C11—21no—
560C4×C11—21no—
561C4×C11—22no—
562C4×C11—22no—
563C4×C11—21no—
564C4×C11—44no—
565C4×C11—42no—
566C4×C11#54612yes—
567C4×C11#57512yes—
568C4×C11C22×#4111yescharacteristic
569C4×C11C2×H(5,𝔽2)11yescharacteristic
570Dic11—22no—
571Dic11—41no—
572Dic11—42no—
573Dic11—41no—
574C2×#41—111no—
575C2×#41—112no—
576C2×#41—112no—
577C2×#41—112no—
578C2×#41—228no—
579C2×#41—222no—
580C2×#41—222no—
581C2×#41—444no—
582C22×Q8—21no—
583C22×Q8—112no—
584C22×D4—22no—
585C22×D4—112no—
586C22×D4—222no—
587C22×D4—221no—
588C22×D4C22⋊D1111yescharacteristic
589C22×D4C22×D1111yescharacteristic
590C23×C4—21no—
591C23×C4—222no—
592C23×C4C22×D1112yes—
593AGL(1,ℤ/8)—224no—
594AGL(1,ℤ/8)—444no—
595C2×SD16—112no—
596C2×SD16—114no—
597C2×D8—112no—
598C2×D8—114no—
599C2×M16—111no—
600C2×M16—112no—
601C2×M16—111no—
602C2×M16—114no—
603C2×M16—444no—
604C22×C8—114no—
605C4⋊Q8—21no—
606C4⋊Q8—21no—
607C4⋊Q8—111no—
608C4⋊Q8—221no—
609C4⋊Q8C22×D1112yes—
610C4⋊Q8C22×D1112yes—
611#127—111no—
612#127—221no—
613#124—24no—
614#124—24no—
615#124—24no—
616#124—24no—
617#124—112no—
618#124—222no—
619#123—222no—
620#123—222no—
621#123—222no—
622C22⋊Q8—112no—
623C22⋊Q8—112no—
624C22⋊Q8—222no—
625C22⋊Q8—222no—
626#121—22no—
627#121—22no—
628#121—24no—
629#121—22no—
630#121—22no—
631#121—112no—
632#121—112no—
633#121—222no—
634#121—221no—
635#121—221no—
636#121—221no—
637#121—221no—
638#121—222no—
639#121—222no—
640#121C22×D1114yes—
641#121C22×D1114yes—
642#120—222no—
643#120—222no—
644#120—222no—
645C4×Q8—111no—
646C4×Q8—111no—
647C4×D4—21no—
648C4×D4—21no—
649C4×D4—111no—
650C4×D4—111no—
651C4×D4—221no—
652C4×D4—222no—
653C4×D4—221no—
654C4×D4—221no—
655C4×D4—222no—
656C4×D4—221no—
657C4×D4—222no—
658C4×D4—221no—
659C4×D4—221no—
660C4×D4C22⋊D1111yescharacteristic
661C4×D4C22⋊D1112yes—
662C4×D4C22⋊D1111yescharacteristic
663C4×D4C22×D1112yes—
664C4×D4C22×D1112yes—
665C4×D4C22×D1111yescharacteristic
666C4×D4C22×D1112yes—
667C4×D4C22×D1111yescharacteristic
668#117—22no—
669#117—22no—
670#117—22no—
671#117—22no—
672#117—24no—
673#117—111no—
674#117—221no—
675#117C22×D1114yes—
676#117C22×D1114yes—
677C2×C4⋊C4—21no—
678C2×C4⋊C4—221no—
679C2×C4⋊C4C22⋊D1111yescharacteristic
680C2×C4⋊C4C22×D1111yescharacteristic
681C2×C4⋊C4C22×D1112yes—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—222no—
686C2×C22⋊C4C22⋊D1112yes—
687C2×C42—22no—
688C2×C42—221no—
689C2×C42C22×D1111yescharacteristic
690#107—112no—
691#107—114no—
692#106—112no—
693#106—114no—
694C4⋊C8—112no—
695C4⋊C8—112no—
696#103—112no—
697#103—114no—
698#103—114no—
699#103—114no—
700#103—114no—
701#102—112no—
702#102—112no—
703#102—112no—
704#102—114no—
705#102—114no—
706#102—114no—
707#102—114no—
708C22⋊C8—114no—
709C22⋊C8—114no—
710#97—112no—
711C4×C8—112no—
712C2×C11—22no—
713C2×C11—42no—
714C2×C11—42no—
715C2×C11—82no—
716C2×C11C2×#54611yescharacteristic
717C2×C11C2×#57511yescharacteristic
718C2×C11#358511yescharacteristic
719D11—42no—
720D11—82no—
721C24—21no—
722C24—222no—
723C24C2×C22⋊D1112yes—
724#41—114no—
725#41—224no—
726#41—224no—
727#41—222no—
728#41—224no—
729#41—224no—
730#41—448no—
731#41—442no—
732#41—442no—
733#41—448no—
734C2×Q8—22no—
735C2×Q8—22no—
736C2×Q8—82no—
737C2×Q8—111no—
738C2×Q8—112no—
739C2×Q8—224no—
740C2×Q8—222no—
741C2×Q8—442no—
742C2×D4—24no—
743C2×D4—24no—
744C2×D4—22no—
745C2×D4—22no—
746C2×D4—21no—
747C2×D4—42no—
748C2×D4—84no—
749C2×D4—111no—
750C2×D4—112no—
751C2×D4—224no—
752C2×D4—221no—
753C2×D4—222no—
754C2×D4—222no—
755C2×D4—222no—
756C2×D4—222no—
757C2×D4—222no—
758C2×D4—221no—
759C2×D4—222no—
760C2×D4—221no—
761C2×D4—442no—
762C2×D4—444no—
763C2×D4—448no—
764C2×D4C2×C22⋊D1111yescharacteristic
765C2×D4C2×C22⋊D1111yescharacteristic
766C2×D4C2×C22⋊D1112yes—
767C2×D4C23×D1112yes—
768C22×C4—24no—
769C22×C4—24no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—44no—
775C22×C4—221no—
776C22×C4—222no—
777C22×C4—221no—
778C22×C4—222no—
779C22×C4—222no—
780C22×C4—222no—
781C22×C4—221no—
782C22×C4—448no—
783C22×C4C2×C22⋊D1112yes—
784C22×C4C2×C22⋊D1111yescharacteristic
785C22×C4C2×C22⋊D1112yes—
786C22×C4C2×C22⋊D1112yes—
787C22×C4C2×C22⋊D1111yescharacteristic
788C22×C4C23×D1112yes—
789C22×C4C23×D1112yes—
790C22×C4C23×D1111yescharacteristic
791SD16—224no—
792SD16—444no—
793D8—224no—
794D8—444no—
795M16—222no—
796M16—222no—
797M16—224no—
798M16—444no—
799C2×C8—112no—
800C2×C8—112no—
801C2×C8—114no—
802C2×C8—444no—
803C4⋊C4—22no—
804C4⋊C4—22no—
805C4⋊C4—21no—
806C4⋊C4—22no—
807C4⋊C4—111no—
808C4⋊C4—111no—
809C4⋊C4—221no—
810C4⋊C4—222no—
811C4⋊C4—221no—
812C4⋊C4—221no—
813C4⋊C4—222no—
814C4⋊C4—221no—
815C4⋊C4C2×C22⋊D1111yescharacteristic
816C4⋊C4C2×C22⋊D1111yescharacteristic
817C4⋊C4C2×C22⋊D1112yes—
818C4⋊C4C23×D1112yes—
819C4⋊C4C23×D1114yes—
820C22⋊C4—24no—
821C22⋊C4—24no—
822C22⋊C4—24no—
823C22⋊C4—24no—
824C22⋊C4—22no—
825C22⋊C4—22no—
826C22⋊C4—222no—
827C22⋊C4—221no—
828C22⋊C4—222no—
829C22⋊C4—222no—
830C22⋊C4—222no—
831C22⋊C4—221no—
832C22⋊C4—221no—
833C22⋊C4—222no—
834C22⋊C4—222no—
835C22⋊C4C2×C22⋊D1112yes—
836C22⋊C4C2×C22⋊D1112yes—
837C22⋊C4C2×C22⋊D1112yes—
838C22⋊C4C2×C22⋊D1112yes—
839C42—24no—
840C42—24no—
841C42—221no—
842C42—221no—
843C42—221no—
844C42C2×C22⋊D1111yescharacteristic
845C42C2×C22⋊D1111yescharacteristic
846C42C23×D1111yescharacteristic
847C42C23×D1111yescharacteristic
848C11#6116611yescharacteristic, complemented, Sylow
849C23—24no—
850C23—22no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—221no—
857C23—222no—
858C23—444no—
859C23—444no—
860C23—882no—
861C23C22×C22⋊D1112yes—
862C23C22×C22⋊D1112yes—
863C23C22×C22⋊D1111yescharacteristic
864Q8—82no—
865Q8—82no—
866Q8—112no—
867Q8—221no—
868Q8—222no—
869Q8—222no—
870Q8—444no—
871D4—22no—
872D4—22no—
873D4—22no—
874D4—22no—
875D4—42no—
876D4—42no—
877D4—84no—
878D4—84no—
879D4—112no—
880D4—224no—
881D4—222no—
882D4—221no—
883D4—222no—
884D4—444no—
885D4—444no—
886D4—444no—
887D4—444no—
888D4—444no—
889D4—442no—
890D4—881no—
891D4—882no—
892C2×C4—24no—
893C2×C4—22no—
894C2×C4—24no—
895C2×C4—24no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—24no—
902C2×C4—41no—
903C2×C4—44no—
904C2×C4—42no—
905C2×C4—44no—
906C2×C4—44no—
907C2×C4—221no—
908C2×C4—224no—
909C2×C4—221no—
910C2×C4—221no—
911C2×C4—222no—
912C2×C4—444no—
913C2×C4—444no—
914C2×C4—444no—
915C2×C4—442no—
916C2×C4—444no—
917C2×C4—881no—
918C2×C4#41×D1112yes—
919C2×C4#6704212yes—
920C2×C4C22×C22⋊D1112yes—
921C2×C4C22×C22⋊D1112yes—
922C2×C4C22×C22⋊D1111yescharacteristic
923C2×C4C22×C22⋊D1111yescharacteristic
924C2×C4C22×C22⋊D1111yescharacteristic
925C2×C4C22×C22⋊D1111yescharacteristic
926C2×C4C22×C22⋊D1111yescharacteristic
927C2×C4C24×D1111yescharacteristic
928C8—222no—
929C8—222no—
930C8—224no—
931C22—21no—
932C22—21no—
933C22—22no—
934C22—22no—
935C22—22no—
936C22—22no—
937C22—22no—
938C22—22no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—84no—
943C22—84no—
944C22—222no—
945C22—441no—
946C22—441no—
947C22—442no—
948C22—442no—
949C22—442no—
950C22—888no—
951C22#1062336012yes—
952C22C23×C22⋊D1111yescharacteristic
953C4—21no—
954C4—21no—
955C4—22no—
956C4—22no—
957C4—21no—
958C4—44no—
959C4—42no—
960C4—222no—
961C4—441no—
962C4—442no—
963C4—441no—
964C4#1062335312yes—
965C4#1062336012yes—
966C4C2×#41×D1111yescharacteristic
967C4C2×#6704211yescharacteristic
968C2—22no—
969C2—42no—
970C2—42no—
971C2—82no—
972C2—442no—
973C2—882no—
974C2C2×#1062336011yescharacteristic
975C2C2×#1062335311yescharacteristic
976C2#1308339611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#555C2
socleC22×C11C23×D4
hypercenterC2×#555D11
hypocenterC11#61166
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
1. D4×#4339C2semidirect
2. #13080904C2semidirect
3. #13080852C2semidirect
4. #13080796C2semidirect
5. #13080766C2semidirect
6. #13080560C2semidirect
7. #13080538C2semidirect
8. #13079012C2semidirect
9. #13078547C2semidirect
10. #13078425C2semidirect
11. #13078231C2semidirect
12. #13078080C2semidirect
13. #13077866C2semidirect
14. C4×#66985C2semidirect
15. D4×#4318C2semidirect
16. #13077133C2semidirect
17. C2×C11×#555C2semidirect
23. C11×#555C22semidirect
24. C11×#555C22semidirect
25. C2×C11×C4⋊Q8C22semidirect
28. C2×C11×#121C22semidirect
30. C2×C4×D4×C11C22semidirect
32. C2×C11×#117C22semidirect
35. C2×#66985C22semidirect
37. C22×#4318C22semidirect
38. #10623084C22semidirect
39. #10623083C22semidirect
40. #10623082C22semidirect
41. #10623081C22semidirect
42. D4×D44C22semidirect
46. D4×Dic22C22semidirect
51. #10622828C22semidirect
52. #10622820C22semidirect
53. #10622707C22semidirect
54. #10622706C22semidirect
55. #10622704C22semidirect
56. #10622702C22semidirect
57. #10622701C22semidirect
58. #10622700C22semidirect
59. #10622697C22semidirect
60. #10622655C22semidirect
61. #10622654C22semidirect
62. #10622653C22semidirect
63. #10622652C22semidirect
64. #10622651C22semidirect
65. #10622650C22semidirect
66. #10622650C22semidirect
67. #10622649C22semidirect
68. #10622632C22semidirect
69. #10622631C22semidirect
70. C4×#4324C22semidirect
71. #10622629C22semidirect
72. #10622628C22semidirect
73. #10622627C22semidirect
74. C4×#4323C22semidirect
75. #10622625C22semidirect
76. #10622624C22semidirect
77. D4×C11⋊C8C22semidirect
78. #10622617C22semidirect
79. #10622616C22semidirect
80. #10622616C22semidirect
81. #10622615C22semidirect
82. #10622615C22semidirect
83. #10622614C22semidirect
84. #10622609C22semidirect
85. #10622609C22semidirect
88. #10622579C22semidirect
89. #10622579C22semidirect
90. #10622579C22semidirect
91. #10622577C22semidirect
92. #10622577C22semidirect
93. #10622537C22semidirect
94. C4×#4318C22semidirect
361. C2×#555D11semidirect
468. #555C2×D11semidirect
469. #555C2×D11semidirect
481. C2×C4⋊Q8C2×D11semidirect
486. C2×#121C2×D11semidirect
490. C2×C4×D4C2×D11semidirect
492. C2×#117C2×D11semidirect
848. C11#61166semidirect

Maximal subgroups

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

subgroupindex
D4×#43392
#130809042
#130808522
#130807962
#130807662
#130805602
#130805382
#130790122
#130785472
#130784252
#130782312
#130780802
#130778662
C4×#669852
D4×#43182
#130771332
C2×C11×#5552
#6116611