Finite Group Databasebeta

← #15646083

Subgroups — #15646083

Order 2816.

2178 conjugacy classes of subgroups.

The subgroup lattice has 1256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082388C211yesmaximal, characteristic, complemented
2#13082173C211yesmaximal, characteristic, complemented
3#13081640C211yesmaximal, characteristic, complemented
4#13081634C211yesmaximal, characteristic, complemented
5#13081328C211yesmaximal, characteristic, complemented
6#13081322C211yesmaximal, characteristic, complemented
7#13080852C211yesmaximal, characteristic, complemented
8#13080640C212yesmaximal, complemented
9#13080638C212yesmaximal, complemented
10#13080218C211yesmaximal, characteristic, complemented
11#13080212C211yesmaximal, characteristic, complemented
12#13080103C212yesmaximal, complemented
13#13080094C212yesmaximal, complemented
14#13079971C212yesmaximal, complemented
15#13079934C211yesmaximal, characteristic, complemented
16#13079632C212yesmaximal, complemented
17#13079558C211yesmaximal, characteristic, complemented
18#13078762C212yesmaximal, complemented
19#13078614C211yesmaximal, characteristic, complemented
20#13078095C212yesmaximal, complemented
21D11×#459C211yesmaximal, characteristic, complemented
22#13077731C211yesmaximal, characteristic, complemented
23C11×#3325C211yesmaximal, characteristic, complemented
24C2×#67037—21no—
25C11×#555C2211yescharacteristic, complemented
26D42×C11C2211yescharacteristic, complemented
27C2×#66993C2212yescomplemented
28D4×C22⋊D11—21no—
29D4×C22⋊D11C2212yes—
30C2×#66985C2212yescomplemented
31C2×D8×D11C2212yescomplemented
32C2×#66961C2212yescomplemented
33#10623261C2211yescharacteristic, complemented
34#10623259C2211yescharacteristic, complemented
35#10623249C2211yescharacteristic, complemented
36D11×#127C2211yescharacteristic
37#10623211—22no—
38#10623210—22no—
39#10623145—21no—
40#10623143C2212yescomplemented
41#10623140C2212yes—
42#10623138—21no—
43#10623137—21no—
44#10623131C2212yescomplemented
45#10623130—21no—
46#10623127C2212yescomplemented
47#10623123—22no—
48#10623121—22no—
49#10623084C2211yescharacteristic, complemented
50#10623082C2211yescharacteristic, complemented
51D4×D44C2211yescharacteristic, complemented
52#10623079C2211yescharacteristic
53C4×D4×D11C2211yescharacteristic, complemented
54#10623073C2211yescharacteristic, complemented
55C4×#4341C2211yescharacteristic
56#10623060—21no—
57#10623060C2212yescomplemented
58#10623053C2212yescomplemented
59D11×#117—21no—
60C11×#486C2211yescharacteristic, complemented
61C11×#482C2212yescomplemented
62C11×#476C2211yescharacteristic, complemented
63C11×#469C2212yescomplemented
64C11×#459C2211yescharacteristic, complemented
65C11×#447C2212yescomplemented
66C4×C11×D8C2211yescharacteristic, complemented
67C11×#436C2211yescharacteristic, complemented
68C11×#418C2212yescomplemented
69#10622831C2212yescomplemented
70#10622769C2211yescharacteristic, complemented
71#10622767C2212yescomplemented
72#10622767C2212yescomplemented
73#10622766C2212yescomplemented
74#10622763C2212yescomplemented
75#10622763C2211yescharacteristic, complemented
76#10622747C2212yescomplemented
77#10622740C2212yescomplemented
78#10622731C2212yescomplemented
79#10622701C2211yescharacteristic, complemented
80#10622697C2211yescharacteristic, complemented
81#10622689C2211yescharacteristic, complemented
82#10622685C2211yescharacteristic, complemented
83#10622655C2212yescomplemented
84#10622652C2212yescomplemented
85#10622650C2212yescomplemented
86#10622649C2212yescomplemented
87#10622632C2211yescharacteristic, complemented
88#10622628C2211yescharacteristic, complemented
89C4×#4323C2211yescharacteristic, complemented
90C4×#4323C2211yescharacteristic, complemented
91#10622625C2211yescharacteristic, complemented
92#10622616C2212yescomplemented
93#10622614C2212yescomplemented
94#10622503C2211yescharacteristic, complemented
95#10622502C2212yescomplemented
96#10622495C2211yescharacteristic, complemented
97#10622484C2212yescomplemented
98#10622482C2212yescomplemented
99#10622477C2212yescomplemented
100#10622467C2212yescomplemented
101#10622456C2211yescharacteristic, complemented
102#10622454C2211yescharacteristic, complemented
103D11×C4⋊C8C2211yescharacteristic, complemented
104#10622444C2211yescharacteristic, complemented
105#10622400C2212yescomplemented
106#10622399C2212yescomplemented
107#10622399C2212yescomplemented
108#10622399C2212yescomplemented
109#10622399C2211yescharacteristic, complemented
110#10622398C2212yescomplemented
111#10622391C2212yescomplemented
112#10622389C2212yescomplemented
113#10622389C2212yescomplemented
114#10622387C2211yescharacteristic, complemented
115#10622386C2211yescharacteristic, complemented
116D11×#102C2212yescomplemented
117#10622379C2212yescomplemented
118#10622377C2212yescomplemented
119#10622377C2212yescomplemented
120#10622375C2212yescomplemented
121#10622375C2212yescomplemented
122#10622375C2212yescomplemented
123#10622375C2212yescomplemented
124#10622375C2212yescomplemented
125#10622372C2211yescharacteristic, complemented
126#10622370C2212yescomplemented
127#10622347C2212yescomplemented
128#10622344C2212yescomplemented
129#10622341C2212yescomplemented
130#10622332C2212yescomplemented
131#10622306C2211yescharacteristic, complemented
132C4×D88C2211yescharacteristic, complemented
133#10622298C2211yescharacteristic, complemented
134#10622292C2211yescharacteristic, complemented
135C22×D4×C11—21no—
136C22×D4×C11C2312yes—
137C22×C22⋊D11—22no—
138C22×C22⋊D11—22no—
139C22×C22⋊D11—22no—
140#67037—48no—
141C2×#4341—22no—
142C2×#4341—21no—
143C2×#4341D411yescharacteristic
144C2×D4×D11—21no—
145C2×D4×D11—22no—
146C2×D4×D11—21no—
147C2×D4×D11—21no—
148C2×D4×D11C2311yescharacteristic
149C2×D4×D11C2312yes—
150C2×#4339—21no—
151C2×#4339—21no—
152C2×#4339C2312yes—
153C22×D44C2312yes—
154C22×C4×D11—21no—
155C2×C11×D8C2312yes—
156C2×C11×D8C2311yescharacteristic
157C2×C11×M16C2312yes—
158C11×C4⋊Q8C2311yescharacteristic
159C11×#127C2311yescharacteristic
160C11×#124—22no—
161C11×#121—21no—
162C11×#121—21no—
163C11×#121C2312yes—
164C11×#121C2312yes—
165C11×#120—22no—
166C4×D4×C11C2311yescharacteristic
167C4×D4×C11C2311yescharacteristic
168C4×D4×C11C2311yescharacteristic
169C11×#117—21no—
170C11×#117C2312yes—
171#67006—22no—
172#66999—21no—
173#66999—22no—
174Q8×Dic11—21no—
175#66993—21no—
176#66993—21no—
177#66993—22no—
178#66993—22no—
179#66993C2312yes—
180#66993C2312yes—
181#66993C2311yescharacteristic
182#66993C2312yes—
183#66992—22no—
184#66992—22no—
185#66992—22no—
186#66991—21no—
187#66991—22no—
188#66991—21no—
189#66991C2311yescharacteristic
190#66990—22no—
191#66990—22no—
192#66990—22no—
193#66989C2312yes—
194#66988—22no—
195D4×Dic11—22no—
196D4×Dic11D411yescharacteristic
197D4×Dic11C2312yes—
198D4×Dic11C2311yescharacteristic
199C2×#4324C2312yes—
200C2×#4324C2312yes—
201C2×#4324C2312yes—
202#66985—44no—
203C2×#4323C2311yescharacteristic
204C2×#4323C2312yes—
205C2×#4323C2311yescharacteristic
206C2×#4323C2312yes—
207#66983—21no—
208#66983C2312yes—
209C4×C22⋊D11—21no—
210C4×C22⋊D11—21no—
211C4×C22⋊D11C2312yes—
212#66979—21no—
213#66977—21no—
214#66977C2312yes—
215C2×C4×Dic11C2312yes—
216C2×#4318C2312yes—
217D8×D11—44no—
218#66961—44no—
219C2×D88C2312yes—
220C2×D88C2311yescharacteristic
221C2×#4314C2312yes—
222C2×#4314C2312yes—
223C2×#4314C2312yes—
224C2×C8×D11C2312yes—
225#66950—21no—
226#66950C2312yes—
227#66948—21no—
228#66948C2311yescharacteristic
229#66946C2312yes—
230#66946C2312yes—
231#66946C2311yescharacteristic
232#66945—21no—
233#66945D411yescharacteristic
234C4⋊C4×D11—21no—
235C4⋊C4×D11—21no—
236C4⋊C4×D11C2311yescharacteristic
237#66943—21no—
238#66943C2312yes—
239#66941C2311yescharacteristic
240#66940D411yescharacteristic
241#66940C2312yes—
242#66940C2312yes—
243#66938—21no—
244#66938—22no—
245#66937—21no—
246#66937—22no—
247#66937—22no—
248#66936—22no—
249#66936—22no—
250#66936—22no—
251#66935—22no—
252#66935—22no—
253(C22⋊D11)⋊C4—22no—
254(C22⋊D11)⋊C4—22no—
255(C22⋊D11)⋊C4—21no—
256(C22⋊D11)⋊C4—22no—
257(C22⋊D11)⋊C4D412yes—
258C22⋊C4×D11—21no—
259C22⋊C4×D11—22no—
260#66932—22no—
261#66932—22no—
262#66932—22no—
263#66930—22no—
264#66930D412yes—
265#66927C2311yescharacteristic
266C4×D44C2311yescharacteristic
267C4×D44C2311yescharacteristic
268#66925—22no—
269#66925—22no—
270C42×D11—22no—
271C42×D11C2311yescharacteristic
272#66923—22no—
273#66922C2311yescharacteristic
274C4×Dic22C2311yescharacteristic
275C11×#107C2311yescharacteristic
276C11×#106C2312yes—
277C11×C4⋊C8C2311yescharacteristic
278C11×#102C2312yes—
279C11×#102C2311yescharacteristic
280C11×#102C2311yescharacteristic
281C11×#102C2312yes—
282C11×#102C2312yes—
283C11×#102C2312yes—
284C11×C22⋊C8C2312yes—
285C4×C8×C11C2311yescharacteristic
286#66896C2311yescharacteristic
287#66896C2312yes—
288#66896C2311yescharacteristic
289C22⋊(C11⋊C8)C2312yes—
290#66885C2312yes—
291#66885C2311yescharacteristic
292#66885C2311yescharacteristic
293(C2×D11)⋊C8C2311yescharacteristic
294(C2×D11)⋊C8C2311yescharacteristic
295#66882C2311yescharacteristic
296#66880C2312yes—
297#66879C2312yes—
298#66879C2312yes—
299Dic11⋊C8C2312yes—
300Dic11⋊C8C2311yescharacteristic
301Dic11⋊C8C2312yes—
302Dic11⋊C8C2312yes—
303Dic11⋊C8C2311yescharacteristic
304#66874C2312yes—
305#66873C2312yes—
306#66873C2311yescharacteristic
307#66873C2312yes—
308#66873C2312yes—
309#66873C2311yescharacteristic
310#66873C2312yes—
311#66872C2312yes—
312#66871C2311yescharacteristic
313#66871C2311yescharacteristic
314C4⋊(C11⋊C8)C2311yescharacteristic
315C4×C11⋊C8C2311yescharacteristic
316#61959—111nomaximal, Sylow
317C24×C11—22no—
318C23×D11—22no—
319C23×D11—21no—
320C23×D11—22no—
321C2×Q8×C11—21no—
322C2×D4×C11—22no—
323C2×D4×C11—22no—
324C2×D4×C11—21no—
325C2×D4×C11—22no—
326C2×D4×C11—21no—
327C2×D4×C11—42no—
328C2×D4×C11—42no—
329C2×D4×C11—44no—
330C2×D4×C11C2×D411yescharacteristic
331C2×D4×C11C2412yes—
332C2×D4×C11C2411yescharacteristic
333C2×D4×C11C2411yescharacteristic
334C22×C4×C11—21no—
335C22×C4×C11—21no—
336C22×C4×C11C2412yes—
337C2×C22⋊D11—21no—
338C2×C22⋊D11—22no—
339C2×C22⋊D11—21no—
340C2×C22⋊D11—22no—
341C2×C22⋊D11—22no—
342C2×C22⋊D11—21no—
343C2×C22⋊D11—22no—
344C2×C22⋊D11—22no—
345C2×C22⋊D11—22no—
346C2×C22⋊D11—22no—
347C2×C22⋊D11—22no—
348C2×C22⋊D11—22no—
349C2×C22⋊D11—21no—
350C2×C22⋊D11—48no—
351C2×C22⋊D11—48no—
352C2×C22⋊D11—84no—
353C2×C22⋊D11C2×D412yes—
354C22×Dic11—21no—
355C22×Dic11—22no—
356C22×Dic11C2×D412yes—
357C22×Dic11C2×D412yes—
358#4341—24no—
359#4341—44no—
360#4341—48no—
361D4×D11—22no—
362D4×D11—41no—
363D4×D11—44no—
364D4×D11—42no—
365D4×D11—42no—
366D4×D11—48no—
367D4×D11—44no—
368D4×D11—82no—
369#4339—24no—
370#4339—42no—
371#4339—44no—
372#4339—44no—
373C2×D44—21no—
374C2×D44—21no—
375C2×D44—21no—
376C2×D44—22no—
377C2×D44—42no—
378C2×D44—42no—
379C2×D44C2411yescharacteristic
380C2×D44C2412yes—
381C2×D44C2411yescharacteristic
382C2×C4×D11—21no—
383C2×C4×D11—22no—
384C2×C4×D11—22no—
385C2×C4×D11—21no—
386C2×C4×D11—22no—
387C2×C4×D11—21no—
388C2×C4×D11—21no—
389C2×C4×D11—44no—
390C2×C4×D11C2×D411yescharacteristic
391C2×C4×D11C2×D411yescharacteristic
392C2×C4×D11C2411yescharacteristic
393C2×Dic22—21no—
394C2×Dic22C2×D411yescharacteristic
395C2×Dic22C2412yes—
396C11×D8—42no—
397C11×D8—41no—
398C11×M16—42no—
399C2×C8×C11C2411yescharacteristic
400C2×C8×C11C2412yes—
401C2×C8×C11C2411yescharacteristic
402C11×C4⋊C4—21no—
403C11×C4⋊C4C2×D411yescharacteristic
404C11×C4⋊C4C2411yescharacteristic
405C11×C4⋊C4C2411yescharacteristic
406C11×C4⋊C4C2412yes—
407C11×C22⋊C4—22no—
408C11×C22⋊C4—22no—
409C11×C22⋊C4—21no—
410C11×C22⋊C4—22no—
411C11×C22⋊C4—21no—
412C11×C22⋊C4C2×D412yes—
413C42×C11—22no—
414C42×C11C2411yescharacteristic
415C22⋊Dic11—22no—
416C22⋊Dic11—21no—
417C22⋊Dic11—22no—
418C22⋊Dic11—21no—
419C22⋊Dic11—22no—
420C22⋊Dic11—22no—
421C22⋊Dic11C2×D412yes—
422#4324—42no—
423#4324—42no—
424#4324—42no—
425#4323—24no—
426#4323—22no—
427#4323—42no—
428#4323—41no—
429(C2×D11)⋊C4—21no—
430(C2×D11)⋊C4—22no—
431(C2×D11)⋊C4—22no—
432(C2×D11)⋊C4—21no—
433(C2×D11)⋊C4—22no—
434(C2×D11)⋊C4—21no—
435(C2×D11)⋊C4—21no—
436(C2×D11)⋊C4—22no—
437(C2×D11)⋊C4C2×D412yes—
438C4⋊Dic11—22no—
439C4⋊Dic11—22no—
440C4⋊Dic11—21no—
441C4⋊Dic11—21no—
442C4⋊Dic11C2×D411yescharacteristic
443C4⋊Dic11C2411yescharacteristic
444C4⋊Dic11C2411yescharacteristic
445Dic11⋊C4—21no—
446Dic11⋊C4—22no—
447Dic11⋊C4—22no—
448Dic11⋊C4—22no—
449Dic11⋊C4—21no—
450Dic11⋊C4—22no—
451Dic11⋊C4C2×D412yes—
452Dic11⋊C4C2×D412yes—
453C4×Dic11—22no—
454C4×Dic11—22no—
455C4×Dic11C2×D412yes—
456C4×Dic11C2×D411yescharacteristic
457C4×Dic11C2×D411yescharacteristic
458C4×Dic11C2×D412yes—
459C4×Dic11C2411yescharacteristic
460C4×Dic11C2412yes—
461#4318—42no—
462C2×C11⋊C8C2411yescharacteristic
463C2×C11⋊C8C2411yescharacteristic
464C2×C11⋊C8C2412yes—
465D88—22no—
466D88—24no—
467#4314—42no—
468#4314—42no—
469#4314—42no—
470C8×D11—42no—
471#3498—111no—
472#3475—111no—
473#3397—111no—
474#3397—111no—
475#3366—111no—
476#3366—111no—
477#3325—111no—
478#3325D1111yescharacteristic, complemented
479#3310—112no—
480#3310—112no—
481#3272—111no—
482#3272—111no—
483#3264—112no—
484#3264—112no—
485#3251—112no—
486#3246—111no—
487#3217—112no—
488#3208—111no—
489#3115—112no—
490#3100—111no—
491#3038—112no—
492C2×#459—111no—
493#2989—111no—
494C23×C11—21no—
495C23×C11—22no—
496C23×C11—21no—
497C23×C11—44no—
498C23×C11—82no—
499C23×C11—82no—
500C23×C11C22×D412yes—
501C22×D11—21no—
502C22×D11—22no—
503C22×D11—21no—
504C22×D11—42no—
505C22×D11—44no—
506C22×D11—42no—
507C22×D11—44no—
508C22×D11—81no—
509C22×D11—82no—
510C22×D11—82no—
511C22×D11—82no—
512C22×D11—82no—
513C22×D11C22×D411yescharacteristic
514Q8×C11—81no—
515D4×C11—22no—
516D4×C11—21no—
517D4×C11—22no—
518D4×C11—21no—
519D4×C11—21no—
520D4×C11—22no—
521D4×C11—21no—
522D4×C11—44no—
523D4×C11—42no—
524D4×C11—81no—
525D4×C11—82no—
526D4×C11—82no—
527C2×C4×C11—22no—
528C2×C4×C11—22no—
529C2×C4×C11—21no—
530C2×C4×C11—22no—
531C2×C4×C11—21no—
532C2×C4×C11—42no—
533C2×C4×C11—42no—
534C2×C4×C11C22×D412yes—
535C2×C4×C11C22×D411yescharacteristic
536C2×C4×C11C22×D411yescharacteristic
537C2×C4×C11C2511yescharacteristic
538C22⋊D11—24no—
539C22⋊D11—42no—
540C22⋊D11—44no—
541C22⋊D11—44no—
542C22⋊D11—44no—
543C22⋊D11—42no—
544C22⋊D11—44no—
545C22⋊D11—44no—
546C22⋊D11—42no—
547C22⋊D11—42no—
548C22⋊D11—44no—
549C22⋊D11—82no—
550C22⋊D11—82no—
551C22⋊D11—82no—
552C2×Dic11—24no—
553C2×Dic11—22no—
554C2×Dic11—21no—
555C2×Dic11—21no—
556C2×Dic11—42no—
557C2×Dic11—44no—
558C2×Dic11—42no—
559C2×Dic11C22×D412yes—
560C2×Dic11C22×D411yescharacteristic
561C2×Dic11C22×D411yescharacteristic
562C2×Dic11C22×D412yes—
563C2×Dic11C22×D411yescharacteristic
564D44—21no—
565D44—22no—
566D44—21no—
567D44—22no—
568D44—21no—
569D44—42no—
570D44—42no—
571D44—82no—
572D44—81no—
573D44H(5,𝔽2)12yescomplemented
574C4×D11—21no—
575C4×D11—21no—
576C4×D11—41no—
577C4×D11—44no—
578C4×D11—44no—
579C4×D11—42no—
580C4×D11—42no—
581C4×D11—42no—
582C4×D11—42no—
583C4×D11—82no—
584C4×D11AGL(1,ℤ/8)14yescomplemented
585Dic22—22no—
586Dic22—22no—
587Dic22—22no—
588Dic22—42no—
589C8×C11—22no—
590C8×C11—21no—
591C8×C11—21no—
592C11⋊C8—22no—
593C11⋊C8—21no—
594C11⋊C8—21no—
595C2×H(5,𝔽2)—221no—
596C2×AGL(1,ℤ/8)—112no—
597C2×AGL(1,ℤ/8)—112no—
598C22×D8—112no—
599#556—111no—
600#555C2×D1111yescharacteristic, complemented
601#554—111no—
602#553—221no—
603#552—112no—
604#552—221no—
605#551—222no—
606#550—111no—
607#550—111no—
608#550—221no—
609#547—111no—
610#546—112no—
611D42—112no—
612D42—112no—
613D42—111no—
614D42—222no—
615D42—221no—
616D42C2×D1111yescharacteristic, complemented
617#535—222no—
618#535—221no—
619#533—111no—
620#532—112no—
621#532—111no—
622C2×#127—112no—
623C2×#127—111no—
624#529—112no—
625#529—222no—
626#525—221no—
627C4×#41—111no—
628C4×#41—112no—
629C2×C4×D4—111no—
630C2×#117—221no—
631#496—112no—
632#496—112no—
633#492—111no—
634#492—111no—
635#490—112no—
636#490—112no—
637#486—111no—
638#486C2×D1111yescharacteristic, complemented
639#482—112no—
640#482C2×D1112yescomplemented
641#480—111no—
642#480—111no—
643#478—112no—
644#478—112no—
645#476—111no—
646#476C2×D1111yescharacteristic, complemented
647#475—112no—
648#474—111no—
649#474—111no—
650#469—112no—
651#469C2×D1112yescomplemented
652#468—112no—
653#468—112no—
654#465—112no—
655#465—112no—
656#463—112no—
657#463—112no—
658#461—111no—
659#461—111no—
660#460—112no—
661#460—112no—
662#460—112no—
663#460—112no—
664#460—112no—
665#459—111no—
666#459—112no—
667#459—111no—
668#459—111no—
669#459—111no—
670#459—111no—
671#459—112no—
672#459—112no—
673#459—112no—
674#459C2×D1111yescharacteristic, complemented
675#450—112no—
676#450—112no—
677#450—112no—
678#450—112no—
679#449—112no—
680#449—112no—
681#447—111no—
682#447—112no—
683#447—111no—
684#447C2×D1112yescomplemented
685#446—111no—
686#446—111no—
687#442—112no—
688#442—112no—
689#440—112no—
690#440—112no—
691C4×D8—111no—
692C4×D8—111no—
693C4×D8—111no—
694C4×D8C2×D1111yescharacteristic, complemented
695#436—111no—
696#436C2×D1111yescharacteristic, complemented
697#435—112no—
698#435—112no—
699#432—112no—
700#431—111no—
701#423—112no—
702C2×C4⋊C8—111no—
703#418—112no—
704#418C2×D1112yescomplemented
705C2×#102—112no—
706C22×C11—22no—
707C22×C11—22no—
708C22×C11—22no—
709C22×C11—41no—
710C22×C11—42no—
711C22×C11—41no—
712C22×C11—41no—
713C22×C11—42no—
714C22×C11—41no—
715C22×C11—41no—
716C22×C11—41no—
717C22×C11—42no—
718C22×C11—164no—
719C22×C11C23×D411yescharacteristic
720C2×D11—21no—
721C2×D11—21no—
722C2×D11—22no—
723C2×D11—41no—
724C2×D11—41no—
725C2×D11—42no—
726C2×D11—41no—
727C2×D11—41no—
728C2×D11—42no—
729C2×D11—41no—
730C2×D11—42no—
731C2×D11—84no—
732C2×D11—164no—
733C2×D11—164no—
734C2×D11C2×AGL(1,ℤ/8)12yes—
735C4×C11—21no—
736C4×C11—22no—
737C4×C11—42no—
738C4×C11—41no—
739C4×C11—41no—
740C4×C11C2×AGL(1,ℤ/8)12yes—
741C4×C11C2×H(5,𝔽2)11yescharacteristic
742C4×C11#58511yescharacteristic
743Dic11—21no—
744Dic11—22no—
745Dic11—21no—
746Dic11—22no—
747Dic11—42no—
748Dic11—41no—
749Dic11—41no—
750Dic11C2×AGL(1,ℤ/8)12yes—
751H(5,𝔽2)—448no—
752C2×#41—111no—
753C2×#41—112no—
754C2×#41—221no—
755C2×#41—221no—
756C2×#41—222no—
757C2×#41—221no—
758C22×D4—21no—
759C22×D4—111no—
760C22×D4—112no—
761C22×D4—112no—
762C22×D4—221no—
763C22×D4—221no—
764C22×D4—222no—
765C22×D4—222no—
766C22×D4—222no—
767C22×D4—222no—
768C22×D4—221no—
769C22×D4C22×D1112yes—
770C23×C4—221no—
771AGL(1,ℤ/8)—444no—
772AGL(1,ℤ/8)—444no—
773C2×SD16—112no—
774C2×SD16—112no—
775C2×SD16—112no—
776C2×SD16—112no—
777C2×SD16—112no—
778C2×SD16—112no—
779C2×D8—112no—
780C2×D8—111no—
781C2×D8—112no—
782C2×D8—111no—
783C2×D8—112no—
784C2×D8—111no—
785C2×D8—444no—
786C2×D8C22×D1112yes—
787C2×D8C22×D1111yescharacteristic
788C2×M16—112no—
789C2×M16C22×D1112yes—
790C22×C8—112no—
791C4⋊Q8—111no—
792C4⋊Q8—111no—
793C4⋊Q8C22×D1111yescharacteristic
794#127—112no—
795#127—111no—
796#127—112no—
797#127—112no—
798#127—111no—
799#127—222no—
800#127—221no—
801#127—222no—
802#127—221no—
803#127C22×D1111yescharacteristic
804#126—222no—
805#126—222no—
806#126—222no—
807#125—112no—
808#125—222no—
809#125—221no—
810#124—22no—
811#124—112no—
812#124—222no—
813#124—221no—
814#123—222no—
815#123—222no—
816#123—222no—
817#123—222no—
818C22⋊Q8—112no—
819C22⋊Q8—112no—
820C22⋊Q8—221no—
821C22⋊Q8—222no—
822C22⋊Q8—221no—
823C22⋊Q8—221no—
824#121—21no—
825#121—21no—
826#121—111no—
827#121—112no—
828#121—111no—
829#121—222no—
830#121—222no—
831#121—221no—
832#121—222no—
833#121—221no—
834#121—222no—
835#121—221no—
836#121—222no—
837#121—222no—
838#121—221no—
839#121—221no—
840#121C22×D1112yes—
841#121C22×D1112yes—
842#120—22no—
843#120—222no—
844#120—222no—
845#120—222no—
846#120—222no—
847#120—222no—
848#120—222no—
849C4×Q8—111no—
850C4×Q8—111no—
851C4×Q8—112no—
852C4×Q8—112no—
853C4×Q8—221no—
854C4×D4—111no—
855C4×D4—112no—
856C4×D4—112no—
857C4×D4—111no—
858C4×D4—112no—
859C4×D4—111no—
860C4×D4—112no—
861C4×D4—112no—
862C4×D4—111no—
863C4×D4—111no—
864C4×D4—221no—
865C4×D4—222no—
866C4×D4—221no—
867C4×D4—221no—
868C4×D4—222no—
869C4×D4—222no—
870C4×D4—222no—
871C4×D4C22×D1111yescharacteristic
872C4×D4C22×D1111yescharacteristic
873C4×D4C22×D1111yescharacteristic
874#117—21no—
875#117—111no—
876#117—112no—
877#117—222no—
878#117—222no—
879#117—222no—
880#117—221no—
881#117—221no—
882#117C22×D1112yes—
883C2×C4⋊C4—111no—
884C2×C4⋊C4—221no—
885C2×C4⋊C4—221no—
886C2×C22⋊C4—222no—
887C2×C22⋊C4—221no—
888C2×C42—112no—
889C2×C42—111no—
890C2×C42—222no—
891#107—111no—
892#107—111no—
893#107—111no—
894#107C22×D1111yescharacteristic
895#106—112no—
896#106C22×D1112yes—
897C4⋊C8—112no—
898C4⋊C8—111no—
899C4⋊C8—112no—
900C4⋊C8—112no—
901C4⋊C8—111no—
902C4⋊C8—111no—
903C4⋊C8C22×D1111yescharacteristic
904#103—112no—
905#103—112no—
906#102—112no—
907#102—111no—
908#102—111no—
909#102—112no—
910#102—111no—
911#102—111no—
912#102—112no—
913#102—111no—
914#102—112no—
915#102—112no—
916#102—111no—
917#102—112no—
918#102C22×D1112yes—
919#102C22×D1111yescharacteristic
920#102C22×D1112yes—
921#102C22×D1112yes—
922#102C22×D1111yescharacteristic
923#102C22×D1112yes—
924C22⋊C8—112no—
925C22⋊C8—111no—
926C22⋊C8—111no—
927C22⋊C8C22×D1112yes—
928#97—112no—
929#97—112no—
930C4×C8—111no—
931C4×C8C22×D1111yescharacteristic
932C2×C11—42no—
933C2×C11—81no—
934C2×C11—82no—
935C2×C11—81no—
936C2×C11#348811yescharacteristic
937C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
938C2×C11#358511yescharacteristic
939D11—22no—
940D11—42no—
941D11—82no—
942D11—81no—
943C24—22no—
944C24—221no—
945C24—222no—
946C24—222no—
947#41—224no—
948#41—224no—
949#41—442no—
950#41—444no—
951#41—444no—
952#41—448no—
953#41—444no—
954C2×Q8—21no—
955C2×Q8—111no—
956C2×Q8—112no—
957C2×Q8—221no—
958C2×D4—22no—
959C2×D4—22no—
960C2×D4—21no—
961C2×D4—21no—
962C2×D4—22no—
963C2×D4—42no—
964C2×D4—42no—
965C2×D4—44no—
966C2×D4—112no—
967C2×D4—111no—
968C2×D4—111no—
969C2×D4—112no—
970C2×D4—221no—
971C2×D4—221no—
972C2×D4—221no—
973C2×D4—222no—
974C2×D4—222no—
975C2×D4—222no—
976C2×D4—221no—
977C2×D4—222no—
978C2×D4—222no—
979C2×D4—222no—
980C2×D4—222no—
981C2×D4—222no—
982C2×D4—221no—
983C2×D4—222no—
984C2×D4—222no—
985C2×D4—221no—
986C2×D4—221no—
987C2×D4—222no—
988C2×D4—442no—
989C2×D4—442no—
990C2×D4—444no—
991C2×D4—441no—
992C2×D4—442no—
993C2×D4—442no—
994C2×D4—448no—
995C2×D4—444no—
996C2×D4—448no—
997C2×D4—448no—
998C2×D4—882no—
999C2×D4—884no—
1000C2×D4D4×D1111yescharacteristic
1001C2×D4C23×D1112yes—
1002C2×D4C23×D1111yescharacteristic
1003C2×D4C23×D1111yescharacteristic
1004C22×C4—21no—
1005C22×C4—21no—
1006C22×C4—111no—
1007C22×C4—112no—
1008C22×C4—112no—
1009C22×C4—111no—
1010C22×C4—111no—
1011C22×C4—221no—
1012C22×C4—222no—
1013C22×C4—222no—
1014C22×C4—221no—
1015C22×C4—221no—
1016C22×C4—222no—
1017C22×C4—222no—
1018C22×C4—221no—
1019C22×C4—221no—
1020C22×C4—444no—
1021C22×C4C23×D1112yes—
1022SD16—442no—
1023SD16—442no—
1024SD16—442no—
1025SD16—442no—
1026SD16—442no—
1027SD16—442no—
1028D8—42no—
1029D8—41no—
1030D8—224no—
1031D8—222no—
1032D8—224no—
1033D8—222no—
1034D8—442no—
1035D8—441no—
1036M16—42no—
1037M16—442no—
1038C2×C8—111no—
1039C2×C8—111no—
1040C2×C8—112no—
1041C2×C8—442no—
1042C2×C8C23×D1111yescharacteristic
1043C2×C8C23×D1111yescharacteristic
1044C2×C8C23×D1112yes—
1045C4⋊C4—21no—
1046C4⋊C4—111no—
1047C4⋊C4—112no—
1048C4⋊C4—112no—
1049C4⋊C4—111no—
1050C4⋊C4—111no—
1051C4⋊C4—221no—
1052C4⋊C4—222no—
1053C4⋊C4—222no—
1054C4⋊C4—222no—
1055C4⋊C4—221no—
1056C4⋊C4—222no—
1057C4⋊C4—222no—
1058C4⋊C4—221no—
1059C4⋊C4—222no—
1060C4⋊C4—221no—
1061C4⋊C4D4×D1111yescharacteristic
1062C4⋊C4C23×D1112yes—
1063C4⋊C4C23×D1111yescharacteristic
1064C4⋊C4C23×D1111yescharacteristic
1065C22⋊C4—22no—
1066C22⋊C4—22no—
1067C22⋊C4—21no—
1068C22⋊C4—22no—
1069C22⋊C4—21no—
1070C22⋊C4—112no—
1071C22⋊C4—112no—
1072C22⋊C4—221no—
1073C22⋊C4—222no—
1074C22⋊C4—222no—
1075C22⋊C4—221no—
1076C22⋊C4—222no—
1077C22⋊C4—222no—
1078C22⋊C4—221no—
1079C22⋊C4—222no—
1080C22⋊C4—221no—
1081C22⋊C4—222no—
1082C22⋊C4—222no—
1083C22⋊C4—221no—
1084C22⋊C4—221no—
1085C22⋊C4—222no—
1086C22⋊C4D4×D1112yes—
1087C42—22no—
1088C42—112no—
1089C42—111no—
1090C42—112no—
1091C42—111no—
1092C42—112no—
1093C42—111no—
1094C42—222no—
1095C42—222no—
1096C42C23×D1111yescharacteristic
1097C11#6195911yescharacteristic, complemented, Sylow
1098C23—21no—
1099C23—21no—
1100C23—22no—
1101C23—44no—
1102C23—82no—
1103C23—82no—
1104C23—111no—
1105C23—221no—
1106C23—222no—
1107C23—221no—
1108C23—444no—
1109C23—442no—
1110C23—444no—
1111C23—442no—
1112C23—882no—
1113C23—882no—
1114C23—881no—
1115C23—882no—
1116C23—882no—
1117C23C2×D4×D1112yes—
1118Q8—81no—
1119Q8—222no—
1120Q8—222no—
1121Q8—222no—
1122Q8—442no—
1123D4—22no—
1124D4—21no—
1125D4—21no—
1126D4—22no—
1127D4—21no—
1128D4—22no—
1129D4—21no—
1130D4—44no—
1131D4—42no—
1132D4—82no—
1133D4—81no—
1134D4—82no—
1135D4—112no—
1136D4—224no—
1137D4—221no—
1138D4—221no—
1139D4—222no—
1140D4—222no—
1141D4—221no—
1142D4—442no—
1143D4—442no—
1144D4—444no—
1145D4—442no—
1146D4—444no—
1147D4—444no—
1148D4—444no—
1149D4—442no—
1150D4—444no—
1151D4—444no—
1152D4—442no—
1153D4—442no—
1154D4—882no—
1155D4—881no—
1156D4—882no—
1157D4—882no—
1158D4—882no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—21no—
1162C2×C4—22no—
1163C2×C4—21no—
1164C2×C4—42no—
1165C2×C4—42no—
1166C2×C4—111no—
1167C2×C4—114no—
1168C2×C4—111no—
1169C2×C4—112no—
1170C2×C4—111no—
1171C2×C4—112no—
1172C2×C4—224no—
1173C2×C4—221no—
1174C2×C4—221no—
1175C2×C4—222no—
1176C2×C4—221no—
1177C2×C4—221no—
1178C2×C4—441no—
1179C2×C4—444no—
1180C2×C4—442no—
1181C2×C4—444no—
1182C2×C4—442no—
1183C2×C4—442no—
1184C2×C4—442no—
1185C2×C4—444no—
1186C2×C4—442no—
1187C2×C4—442no—
1188C2×C4—882no—
1189C2×C4C2×D4×D1112yes—
1190C2×C4C2×D4×D1111yescharacteristic
1191C2×C4C2×D4×D1111yescharacteristic
1192C2×C4C24×D1111yescharacteristic
1193C8—21no—
1194C8—22no—
1195C8—21no—
1196C8—221no—
1197C8—222no—
1198C8—221no—
1199C22—22no—
1200C22—22no—
1201C22—22no—
1202C22—41no—
1203C22—42no—
1204C22—41no—
1205C22—41no—
1206C22—41no—
1207C22—42no—
1208C22—41no—
1209C22—42no—
1210C22—41no—
1211C22—112no—
1212C22—164no—
1213C22—221no—
1214C22—221no—
1215C22—222no—
1216C22—441no—
1217C22—441no—
1218C22—441no—
1219C22—442no—
1220C22—442no—
1221C22—441no—
1222C22—442no—
1223C22—441no—
1224C22—884no—
1225C22—1764no—
1226C22—1764no—
1227C22C22×D4×D1111yescharacteristic
1228C4—22no—
1229C4—21no—
1230C4—41no—
1231C4—41no—
1232C4—42no—
1233C4—112no—
1234C4—221no—
1235C4—222no—
1236C4—221no—
1237C4—222no—
1238C4—442no—
1239C4—441no—
1240C4—441no—
1241C4D11×AGL(1,ℤ/8)12yes—
1242C4#1062345311yescharacteristic
1243C4D11×H(5,𝔽2)11yescharacteristic
1244C2—42no—
1245C2—81no—
1246C2—82no—
1247C2—81no—
1248C2—222no—
1249C2—442no—
1250C2—881no—
1251C2—882no—
1252C2#1308227911yescharacteristic
1253C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
1254C2#1308339111yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3325C2
socleC22×C11C23×D4
hypercenter#3325D11
hypocenterC11#61959
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3325

Complements

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

NH ≅ G/Ntype
1. #13082388C2semidirect
2. #13082173C2semidirect
3. #13081640C2semidirect
4. #13081634C2semidirect
5. #13081328C2semidirect
6. #13081322C2semidirect
7. #13080852C2semidirect
8. #13080640C2semidirect
9. #13080638C2semidirect
10. #13080218C2semidirect
11. #13080212C2semidirect
12. #13080103C2semidirect
13. #13080094C2semidirect
14. #13079971C2semidirect
15. #13079934C2semidirect
16. #13079632C2semidirect
17. #13079558C2semidirect
18. #13078762C2semidirect
19. #13078614C2semidirect
20. #13078095C2semidirect
21. D11×#459C2semidirect
22. #13077731C2semidirect
23. C11×#3325C2semidirect
25. C11×#555C22semidirect
26. D42×C11C22semidirect
27. C2×#66993C22semidirect
30. C2×#66985C22semidirect
31. C2×D8×D11C22semidirect
32. C2×#66961C22semidirect
33. #10623261C22semidirect
34. #10623259C22semidirect
35. #10623249C22semidirect
40. #10623143C22semidirect
44. #10623131C22semidirect
46. #10623127C22semidirect
49. #10623084C22semidirect
50. #10623082C22semidirect
51. D4×D44C22semidirect
53. C4×D4×D11C22semidirect
54. #10623073C22semidirect
57. #10623060C22semidirect
58. #10623053C22semidirect
60. C11×#486C22semidirect
61. C11×#482C22semidirect
62. C11×#476C22semidirect
63. C11×#469C22semidirect
64. C11×#459C22semidirect
65. C11×#447C22semidirect
66. C4×C11×D8C22semidirect
67. C11×#436C22semidirect
68. C11×#418C22semidirect
69. #10622831C22semidirect
70. #10622769C22semidirect
71. #10622767C22semidirect
72. #10622767C22semidirect
73. #10622766C22semidirect
74. #10622763C22semidirect
75. #10622763C22semidirect
76. #10622747C22semidirect
77. #10622740C22semidirect
78. #10622731C22semidirect
79. #10622701C22semidirect
80. #10622697C22semidirect
81. #10622689C22semidirect
82. #10622685C22semidirect
83. #10622655C22semidirect
84. #10622652C22semidirect
85. #10622650C22semidirect
86. #10622649C22semidirect
87. #10622632C22semidirect
88. #10622628C22semidirect
89. C4×#4323C22semidirect
90. C4×#4323C22semidirect
91. #10622625C22semidirect
92. #10622616C22semidirect
93. #10622614C22semidirect
94. #10622503C22semidirect
95. #10622502C22semidirect
96. #10622495C22semidirect
97. #10622484C22semidirect
98. #10622482C22semidirect
99. #10622477C22semidirect
100. #10622467C22semidirect
101. #10622456C22semidirect
102. #10622454C22semidirect
103. D11×C4⋊C8C22semidirect
104. #10622444C22semidirect
105. #10622400C22semidirect
106. #10622399C22semidirect
107. #10622399C22semidirect
108. #10622399C22semidirect
109. #10622399C22semidirect
110. #10622398C22semidirect
111. #10622391C22semidirect
112. #10622389C22semidirect
113. #10622389C22semidirect
114. #10622387C22semidirect
115. #10622386C22semidirect
116. D11×#102C22semidirect
117. #10622379C22semidirect
118. #10622377C22semidirect
119. #10622377C22semidirect
120. #10622375C22semidirect
121. #10622375C22semidirect
122. #10622375C22semidirect
123. #10622375C22semidirect
124. #10622375C22semidirect
125. #10622372C22semidirect
126. #10622370C22semidirect
127. #10622347C22semidirect
128. #10622344C22semidirect
129. #10622341C22semidirect
130. #10622332C22semidirect
131. #10622306C22semidirect
132. C4×D88C22semidirect
133. #10622298C22semidirect
134. #10622292C22semidirect
478. #3325D11semidirect
573. D44H(5,𝔽2)semidirect
584. C4×D11AGL(1,ℤ/8)semidirect
600. #555C2×D11semidirect
616. D42C2×D11semidirect
638. #486C2×D11semidirect
640. #482C2×D11semidirect
646. #476C2×D11semidirect
651. #469C2×D11semidirect
674. #459C2×D11semidirect
684. #447C2×D11semidirect
694. C4×D8C2×D11semidirect
696. #436C2×D11semidirect
704. #418C2×D11semidirect
1097. C11#61959semidirect

Maximal subgroups

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

subgroupindex
#130823882
#130821732
#130816402
#130816342
#130813282
#130813222
#130808522
#130806402
#130806382
#130802182
#130802122
#130801032
#130800942
#130799712
#130799342
#130796322
#130795582
#130787622
#130786142
#130780952
D11×#4592
#130777312
C11×#33252
#6195911