Finite Group Databasebeta

← D11×#3397 #15634723

Subgroups — D11×#3397 #15634723

Order 2816.

2250 conjugacy classes of subgroups.

The subgroup lattice has 1250 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#556C211yesmaximal, characteristic, complemented
2D11×#550C211yesmaximal, characteristic, complemented
3#13081641C211yesmaximal, characteristic, complemented
4#13081640C211yesmaximal, characteristic, complemented
5#13081639C212yesmaximal, complemented
6#13081638C211yesmaximal, characteristic, complemented
7#13081637C212yesmaximal, complemented
8#13081636C211yesmaximal, characteristic, complemented
9#13081635C211yesmaximal, characteristic, complemented
10#13081634C211yesmaximal, characteristic, complemented
11#13081633C212yesmaximal, complemented
12#13081632C211yesmaximal, characteristic, complemented
13#13081631C212yesmaximal, complemented
14D11×#496C212yesmaximal, complemented
15D11×#492C211yesmaximal, characteristic, complemented
16D11×#460C212yesmaximal, complemented
17D11×#463C212yesmaximal, complemented
18D11×#461C211yesmaximal, characteristic, complemented
19D11×#459C211yesmaximal, characteristic, complemented
20D11×#446C211yesmaximal, characteristic, complemented
21D11×#440C212yesmaximal, complemented
22C4×D8×D11C211yesmaximal, characteristic, complemented
23C11×#3397C211yesmaximal, characteristic, complemented
24C2×#41×D11—21no—
25C11×#556C2211yescharacteristic, complemented
26C11×#550C2211yescharacteristic, complemented
27#10623365—21no—
28C2×SD16×D11C2212yes—
29C2×SD16×D11C2212yes—
30C2×SD16×D11C2212yes—
31C2×D8×D11C2211yescharacteristic
32C2×D8×D11C2212yes—
33#10623263C2211yescharacteristic, complemented
34D11×C4⋊Q8C2211yescharacteristic
35#10623249C2212yescomplemented
36#10623249C2211yescharacteristic, complemented
37D11×#127C2212yes—
38D11×#127C2211yescharacteristic
39D11×#126—22no—
40#10623233—22no—
41D11×#124C2212yes—
42#10623202C2212yescomplemented
43#10623172—21no—
44D11×C22⋊Q8—21no—
45D11×#121—22no—
46D11×#121—21no—
47#10623130—22no—
48#10623130—21no—
49#10623115C2211yescharacteristic, complemented
50#10623108C2211yescharacteristic, complemented
51C4×Q8×D11C2212yes—
52C4×Q8×D11C2211yescharacteristic
53#10623099C2212yescomplemented
54#10623084C2211yescharacteristic, complemented
55#10623084C2212yescomplemented
56C4×D4×D11C2211yescharacteristic
57C4×D4×D11C2211yescharacteristic
58C4×D4×D11C2212yes—
59#10623073C2211yescharacteristic, complemented
60#10623064—21no—
61D11×#117—21no—
62C11×#496C2212yescomplemented
63C11×#492C2211yescharacteristic, complemented
64C11×#463C2212yescomplemented
65C11×#461C2211yescharacteristic, complemented
66C11×#460C2212yescomplemented
67C11×#459C2211yescharacteristic, complemented
68C11×#446C2211yescharacteristic, complemented
69C11×#440C2212yescomplemented
70C4×C11×D8C2211yescharacteristic, complemented
71#10622789C2212yescomplemented
72#10622789C2212yescomplemented
73#10622788C2212yescomplemented
74#10622788C2212yescomplemented
75#10622778C2212yescomplemented
76#10622777C2212yescomplemented
77#10622776C2212yescomplemented
78#10622776C2212yescomplemented
79#10622775C2212yescomplemented
80#10622767C2212yescomplemented
81#10622767C2212yescomplemented
82#10622766C2212yescomplemented
83#10622763C2212yescomplemented
84D8×Dic11C2211yescharacteristic, complemented
85#10622698C2211yescharacteristic, complemented
86#10622696C2211yescharacteristic, complemented
87#10622689C2211yescharacteristic, complemented
88#10622688C2212yescomplemented
89#10622687C2212yescomplemented
90#10622685C2211yescharacteristic, complemented
91#10622671C2212yescomplemented
92#10622670C2212yescomplemented
93#10622640C2212yescomplemented
94#10622639C2212yescomplemented
95#10622637C2211yescharacteristic, complemented
96#10622632C2211yescharacteristic, complemented
97#10622631C2212yescomplemented
98#10622629C2212yescomplemented
99#10622628C2211yescharacteristic, complemented
100C4×#4323C2211yescharacteristic, complemented
101C4×#4323C2211yescharacteristic, complemented
102#10622502C2212yescomplemented
103D11×#107C2211yescharacteristic
104#10622485C2211yescharacteristic, complemented
105#10622461C2212yescomplemented
106#10622457C2212yescomplemented
107#10622456C2211yescharacteristic, complemented
108#10622454C2211yescharacteristic, complemented
109D11×C4⋊C8C2211yescharacteristic
110D11×C4⋊C8C2212yes—
111#10622444C2211yescharacteristic, complemented
112#10622441C2212yescomplemented
113#10622432C2212yescomplemented
114#10622431C2212yescomplemented
115#10622430C2212yescomplemented
116D11×#103C2212yes—
117#10622400C2212yescomplemented
118#10622399C2212yescomplemented
119D11×#102C2212yes—
120D11×#102C2211yescharacteristic
121D11×#102C2211yescharacteristic
122#10622375C2212yescomplemented
123#10622375C2212yescomplemented
124#10622370C2212yescomplemented
125#10622369C2211yescharacteristic, complemented
126#10622369C2211yescharacteristic, complemented
127#10622325C2212yescomplemented
128#10622323C2212yescomplemented
129D11×#97C2212yes—
130#10622314C2212yescomplemented
131#10622306C2211yescharacteristic, complemented
132C4×D88C2211yescharacteristic, complemented
133C4×C8×D11C2211yescharacteristic
134#10622292C2211yescharacteristic, complemented
135C2×C11×#41—21no—
136#41×D11—48no—
137C2×#4343—21no—
138C2×Q8×D11D411yescharacteristic
139C2×Q8×D11C2312yes—
140C2×#4341—22no—
141C2×#4341—21no—
142C2×D4×D11—22no—
143C2×D4×D11—21no—
144C2×D4×D11—22no—
145C2×D4×D11—21no—
146C2×D4×D11C2311yescharacteristic
147C2×D4×D11C2312yes—
148C2×D4×D11C2311yescharacteristic
149C2×#4339—22no—
150C2×#4339—21no—
151C22×C4×D11—21no—
152C22×C4×D11—22no—
153C22×C4×D11—21no—
154C2×C11×SD16C2312yes—
155C2×C11×SD16C2312yes—
156C2×C11×SD16C2312yes—
157C2×C11×D8C2311yescharacteristic
158C2×C11×D8C2312yes—
159C11×C4⋊Q8C2311yescharacteristic
160C11×#127C2311yescharacteristic
161C11×#127C2312yes—
162C11×#126—22no—
163C11×#124C2312yes—
164C11×C22⋊Q8—21no—
165C11×#121—21no—
166C11×#121—22no—
167C4×Q8×C11C2312yes—
168C4×Q8×C11C2311yescharacteristic
169C4×D4×C11C2311yescharacteristic
170C4×D4×C11C2311yescharacteristic
171C4×D4×C11C2312yes—
172C11×#117—21no—
173#67000C2312yes—
174#66999—21no—
175Q8×Dic11D411yescharacteristic
176Q8×Dic11C2312yes—
177#66997C2312yes—
178C2×#4325C2312yes—
179C2×#4325C2312yes—
180C2×#4325C2312yes—
181#66993—22no—
182#66993—21no—
183#66993—22no—
184#66993—21no—
185#66993C2312yes—
186#66993C2312yes—
187#66993C2312yes—
188#66992—22no—
189#66992—22no—
190#66992—22no—
191#66991—22no—
192#66991—21no—
193#66989C2312yes—
194D4×Dic11C2311yescharacteristic
195D4×Dic11C2312yes—
196D4×Dic11C2311yescharacteristic
197C2×#4324C2312yes—
198C2×#4324C2312yes—
199C2×#4324C2312yes—
200C2×#4323C2311yescharacteristic
201C2×#4323C2311yescharacteristic
202C2×#4323C2312yes—
203C2×#4323C2312yes—
204#66983—22no—
205#66983—21no—
206C4×C22⋊D11—21no—
207C4×C22⋊D11—22no—
208C4×C22⋊D11—21no—
209#66979—21no—
210#66977—21no—
211SD16×D11—28no—
212SD16×D11—44no—
213SD16×D11—44no—
214D8×D11—24no—
215D8×D11—44no—
216C2×D88C2311yescharacteristic
217C2×D88C2312yes—
218C2×#4314C2312yes—
219C2×#4314C2312yes—
220C2×#4314C2312yes—
221C2×C8×D11C2312yes—
222C2×C8×D11C2311yescharacteristic
223C2×C8×D11C2311yescharacteristic
224#66951—22no—
225#66951—22no—
226#66951—22no—
227#66950—21no—
228#66949—22no—
229#66948—21no—
230#66948—22no—
231#66946C2311yescharacteristic
232#66946C2311yescharacteristic
233#66946C2312yes—
234#66945—21no—
235#66945—21no—
236C4⋊C4×D11—21no—
237C4⋊C4×D11—22no—
238C4⋊C4×D11—21no—
239C4⋊C4×D11D412yes—
240C4⋊C4×D11D411yescharacteristic
241C4⋊C4×D11C2311yescharacteristic
242C4⋊C4×D11C2311yescharacteristic
243#66941—21no—
244#66941—21no—
245#66940—22no—
246#66940D412yes—
247#66940D411yescharacteristic
248#66940C2312yes—
249#66938—22no—
250#66938—22no—
251#66937—22no—
252#66937—22no—
253#66937—22no—
254(C22⋊D11)⋊C4—21no—
255(C22⋊D11)⋊C4—22no—
256(C22⋊D11)⋊C4—21no—
257C22⋊C4×D11—21no—
258C22⋊C4×D11—22no—
259C22⋊C4×D11—22no—
260C22⋊C4×D11—22no—
261C22⋊C4×D11—21no—
262#66932—22no—
263#66932—22no—
264#66932—22no—
265#66931—22no—
266#66930—22no—
267#66929—22no—
268#66928C2312yes—
269#66927C2311yescharacteristic
270#66927C2312yes—
271C4×D44C2311yescharacteristic
272C4×D44C2312yes—
273C4×D44C2311yescharacteristic
274#66925—22no—
275C42×D11—22no—
276C42×D11C2311yescharacteristic
277C42×D11C2312yes—
278#66922C2311yescharacteristic
279C4×Dic22—22no—
280C4×Dic22C2312yes—
281C4×Dic22C2311yescharacteristic
282C4×Dic22C2312yes—
283C11×#107C2311yescharacteristic
284C11×C4⋊C8C2311yescharacteristic
285C11×C4⋊C8C2312yes—
286C11×#103C2312yes—
287C11×#102C2311yescharacteristic
288C11×#102C2311yescharacteristic
289C11×#102C2312yes—
290C11×#97C2312yes—
291C4×C8×C11C2311yescharacteristic
292#66899C2312yes—
293#66896C2311yescharacteristic
294#66896C2311yescharacteristic
295#66896C2312yes—
296#66885C2312yes—
297#66885C2311yescharacteristic
298#66885C2311yescharacteristic
299#66882C2311yescharacteristic
300#66880C2312yes—
301#66879C2312yes—
302#66879C2312yes—
303Dic11⋊C8C2312yes—
304Dic11⋊C8C2312yes—
305Dic11⋊C8C2312yes—
306C8×Dic11C2311yescharacteristic
307C8×Dic11C2311yescharacteristic
308#66874C2312yes—
309#66873C2311yescharacteristic
310#66873C2311yescharacteristic
311#66873C2312yes—
312#66871C2311yescharacteristic
313#66871C2311yescharacteristic
314C4⋊(C11⋊C8)C2311yescharacteristic
315C4⋊(C11⋊C8)C2312yes—
316#66867C2312yes—
317C4×C11⋊C8C2311yescharacteristic
318C2×#3397—111nomaximal, Sylow
319C23×D11—21no—
320C23×D11—21no—
321C23×D11—22no—
322C11×#41—44no—
323C2×Q8×C11C2×D411yescharacteristic
324C2×Q8×C11C2412yes—
325C2×D4×C11—22no—
326C2×D4×C11—21no—
327C2×D4×C11—22no—
328C2×D4×C11—21no—
329C2×D4×C11C2411yescharacteristic
330C2×D4×C11C2411yescharacteristic
331C2×D4×C11C2412yes—
332C22×C4×C11—21no—
333C22×C4×C11—22no—
334C22×C4×C11—21no—
335C2×C22⋊D11—21no—
336C2×C22⋊D11—21no—
337C2×C22⋊D11—22no—
338C2×C22⋊D11—22no—
339C2×C22⋊D11—22no—
340C2×C22⋊D11—22no—
341C2×C22⋊D11—22no—
342C2×C22⋊D11—22no—
343C2×C22⋊D11—22no—
344C22×Dic11—21no—
345C22×Dic11—22no—
346C22×Dic11—21no—
347#4343—44no—
348Q8×D11—24no—
349Q8×D11—24no—
350Q8×D11—24no—
351#4341—48no—
352#4341—44no—
353D4×D11—22no—
354D4×D11—22no—
355D4×D11—24no—
356D4×D11—22no—
357D4×D11—24no—
358D4×D11—22no—
359D4×D11—48no—
360D4×D11—44no—
361D4×D11—84no—
362D4×D11—82no—
363#4339—48no—
364#4339—44no—
365C2×D44—22no—
366C2×D44—21no—
367C2×D44—22no—
368C2×D44—21no—
369C2×D44C2412yes—
370C2×D44C2411yescharacteristic
371C2×D44C2411yescharacteristic
372C2×C4×D11—21no—
373C2×C4×D11—22no—
374C2×C4×D11—21no—
375C2×C4×D11—21no—
376C2×C4×D11—22no—
377C2×C4×D11—21no—
378C2×C4×D11—21no—
379C2×C4×D11—22no—
380C2×C4×D11—21no—
381C2×C4×D11—48no—
382C2×C4×D11—44no—
383C2×C4×D11—44no—
384C2×C4×D11C2×D412yes—
385C2×C4×D11C2×D411yescharacteristic
386C2×C4×D11C2×D412yes—
387C2×C4×D11C2×D411yescharacteristic
388C2×C4×D11C2411yescharacteristic
389C2×Dic22—22no—
390C2×Dic22C2×D412yes—
391C2×Dic22C2×D411yescharacteristic
392C2×Dic22C2412yes—
393C11×SD16—24no—
394C11×SD16—42no—
395C11×SD16—42no—
396C11×D8—22no—
397C11×D8—42no—
398C2×C8×C11C2411yescharacteristic
399C2×C8×C11C2412yes—
400C2×C8×C11C2411yescharacteristic
401C11×C4⋊C4—22no—
402C11×C4⋊C4—21no—
403C11×C4⋊C4—21no—
404C11×C4⋊C4C2×D411yescharacteristic
405C11×C4⋊C4C2×D412yes—
406C11×C4⋊C4C2411yescharacteristic
407C11×C4⋊C4C2411yescharacteristic
408C11×C22⋊C4—22no—
409C11×C22⋊C4—22no—
410C11×C22⋊C4—21no—
411C11×C22⋊C4—22no—
412C11×C22⋊C4—21no—
413C42×C11—22no—
414C42×C11C2411yescharacteristic
415C42×C11C2412yes—
416C22⋊Dic11—22no—
417C22⋊Dic11—22no—
418C22⋊Dic11—21no—
419C22⋊Dic11—22no—
420C22⋊Dic11—21no—
421#4325—24no—
422#4325—42no—
423#4325—42no—
424#4324—24no—
425#4324—42no—
426#4324—42no—
427#4323—22no—
428#4323—22no—
429#4323—42no—
430#4323—42no—
431(C2×D11)⋊C4—22no—
432(C2×D11)⋊C4—21no—
433(C2×D11)⋊C4—22no—
434(C2×D11)⋊C4—22no—
435(C2×D11)⋊C4—21no—
436(C2×D11)⋊C4—22no—
437(C2×D11)⋊C4—22no—
438(C2×D11)⋊C4—21no—
439(C2×D11)⋊C4—21no—
440(C2×D11)⋊C4—22no—
441C4⋊Dic11—22no—
442C4⋊Dic11—21no—
443C4⋊Dic11—21no—
444C4⋊Dic11C2×D412yes—
445C4⋊Dic11C2×D411yescharacteristic
446C4⋊Dic11C2411yescharacteristic
447C4⋊Dic11C2411yescharacteristic
448Dic11⋊C4—21no—
449Dic11⋊C4—22no—
450Dic11⋊C4—22no—
451Dic11⋊C4—22no—
452Dic11⋊C4—21no—
453Dic11⋊C4—22no—
454Dic11⋊C4C2×D412yes—
455Dic11⋊C4C2×D412yes—
456Dic11⋊C4C2×D412yes—
457C4×Dic11—22no—
458C4×Dic11—22no—
459C4×Dic11—22no—
460C4×Dic11C2×D412yes—
461C4×Dic11C2×D411yescharacteristic
462C4×Dic11C2×D412yes—
463C4×Dic11C2×D411yescharacteristic
464C4×Dic11C2411yescharacteristic
465C4×Dic11C2412yes—
466C2×C11⋊C8C2411yescharacteristic
467C2×C11⋊C8C2412yes—
468C2×C11⋊C8C2411yescharacteristic
469D88—22no—
470D88—42no—
471#4314—24no—
472#4314—42no—
473#4314—42no—
474C8×D11—24no—
475C8×D11—22no—
476C8×D11#4114yescomplemented
477C2×#556—111no—
478C2×#550—111no—
479#3397—112no—
480#3397—111no—
481#3397—112no—
482#3397—111no—
483#3397—112no—
484#3397—111no—
485#3397—111no—
486#3397—112no—
487#3397—111no—
488#3397—111no—
489#3397—111no—
490#3397D1111yescharacteristic, direct product factor
491C2×#496—112no—
492C2×#492—111no—
493C2×#460—112no—
494C2×#463—112no—
495C2×#461—111no—
496C2×#459—111no—
497C2×#446—111no—
498C2×#440—112no—
499C2×C4×D8—111no—
500C23×C11—21no—
501C23×C11—21no—
502C23×C11—22no—
503C22×D11—21no—
504C22×D11—22no—
505C22×D11—21no—
506C22×D11—42no—
507C22×D11—42no—
508C22×D11—44no—
509C22×D11—44no—
510C22×D11—42no—
511C22×D11—42no—
512C22×D11—42no—
513C22×D11—44no—
514C22×D11—42no—
515C22×D11C22×D411yescharacteristic
516Q8×C11—22no—
517Q8×C11—22no—
518Q8×C11—22no—
519D4×C11—21no—
520D4×C11—21no—
521D4×C11—22no—
522D4×C11—21no—
523D4×C11—22no—
524D4×C11—21no—
525D4×C11—44no—
526D4×C11—42no—
527D4×C11—82no—
528D4×C11—81no—
529C2×C4×C11—21no—
530C2×C4×C11—22no—
531C2×C4×C11—21no—
532C2×C4×C11—44no—
533C2×C4×C11—42no—
534C2×C4×C11—42no—
535C2×C4×C11C22×D412yes—
536C2×C4×C11C22×D412yes—
537C2×C4×C11C22×D411yescharacteristic
538C2×C4×C11C22×D411yescharacteristic
539C2×C4×C11C2511yescharacteristic
540C22⋊D11—44no—
541C22⋊D11—44no—
542C22⋊D11—42no—
543C22⋊D11—42no—
544C22⋊D11—44no—
545C22⋊D11—44no—
546C22⋊D11—82no—
547C22⋊D11—82no—
548C22⋊D11—82no—
549C2×Dic11—21no—
550C2×Dic11—22no—
551C2×Dic11—21no—
552C2×Dic11—44no—
553C2×Dic11—42no—
554C2×Dic11—42no—
555C2×Dic11C22×D412yes—
556C2×Dic11C22×D411yescharacteristic
557C2×Dic11C22×D412yes—
558C2×Dic11C22×D411yescharacteristic
559C2×Dic11C22×D411yescharacteristic
560D44—22no—
561D44—21no—
562D44—21no—
563D44—21no—
564D44—22no—
565D44—21no—
566D44—44no—
567D44—42no—
568D44—82no—
569D44—81no—
570C4×D11—24no—
571C4×D11—24no—
572C4×D11—22no—
573C4×D11—44no—
574C4×D11—44no—
575C4×D11—44no—
576C4×D11—42no—
577C4×D11—42no—
578C4×D11—42no—
579C4×D11—42no—
580C4×D11—42no—
581C4×D11—42no—
582C4×D11AGL(1,ℤ/8)14yes—
583C4×D11C2×#4112yes—
584C4×D11H(5,𝔽2)12yes—
585Dic22—22no—
586Dic22—24no—
587Dic22—22no—
588Dic22—22no—
589Dic22—44no—
590C8×C11—21no—
591C8×C11—22no—
592C8×C11C2×#4112yescomplemented
593C11⋊C8—22no—
594C11⋊C8—21no—
595C11⋊C8C2×#4112yescomplemented
596C22×#41—221no—
597C22×SD16—112no—
598C22×SD16—112no—
599C22×SD16—112no—
600C22×D8—111no—
601C22×D8—112no—
602#556—111no—
603#556—112no—
604#556—112no—
605#556—111no—
606#556—111no—
607#556—221no—
608#556—221no—
609#556—222no—
610#556C2×D1111yescharacteristic, complemented
611#550—112no—
612#550—111no—
613#550—111no—
614#550—112no—
615#550—111no—
616#550—222no—
617#550—221no—
618#550—221no—
619#550C2×D1111yescharacteristic, complemented
620C2×C4⋊Q8—111no—
621C2×#127—111no—
622C2×#127—112no—
623C2×#126—222no—
624C2×#124—112no—
625C2×C22⋊Q8—221no—
626C2×#121—221no—
627C2×#121—222no—
628C2×C4×Q8—111no—
629C2×C4×Q8—112no—
630C2×C4×D4—111no—
631C2×C4×D4—111no—
632C2×C4×D4—112no—
633C2×#117—221no—
634#496—112no—
635#496—112no—
636#496—112no—
637#496—112no—
638#496—112no—
639#496—112no—
640#496—112no—
641#496C2×D1112yescomplemented
642#492—112no—
643#492—112no—
644#492—111no—
645#492—111no—
646#492—111no—
647#492C2×D1111yescharacteristic, complemented
648#463—112no—
649#463—112no—
650#463—112no—
651#463—112no—
652#463—112no—
653#463—112no—
654#463—112no—
655#463C2×D1112yescomplemented
656#461—112no—
657#461—111no—
658#461—111no—
659#461—111no—
660#461—112no—
661#461C2×D1111yescharacteristic, complemented
662#460—112no—
663#460—112no—
664#460—112no—
665#460—112no—
666#460—112no—
667#460—112no—
668#460—112no—
669#460C2×D1112yescomplemented
670#459—112no—
671#459—111no—
672#459—111no—
673#459—111no—
674#459—112no—
675#459C2×D1111yescharacteristic, complemented
676#446—111no—
677#446—112no—
678#446—111no—
679#446—112no—
680#446—111no—
681#446C2×D1111yescharacteristic, complemented
682#440—112no—
683#440—112no—
684#440—112no—
685#440—112no—
686#440—112no—
687#440—112no—
688#440—112no—
689#440C2×D1112yescomplemented
690C4×D8—111no—
691C4×D8—111no—
692C4×D8—111no—
693C4×D8—111no—
694C4×D8—111no—
695C4×D8—111no—
696C4×D8—111no—
697C4×D8C2×D1111yescharacteristic, complemented
698C2×#107—111no—
699C2×C4⋊C8—111no—
700C2×C4⋊C8—112no—
701C2×#103—112no—
702C2×#102—111no—
703C2×#102—111no—
704C2×#102—112no—
705C2×#97—112no—
706C2×C4×C8—111no—
707C22×C11—41no—
708C22×C11—41no—
709C22×C11—42no—
710C22×C11—42no—
711C22×C11—41no—
712C22×C11—41no—
713C22×C11—41no—
714C22×C11—42no—
715C22×C11—41no—
716C22×C11C23×D411yescharacteristic
717C2×D11—41no—
718C2×D11—42no—
719C2×D11—41no—
720C2×D11—41no—
721C2×D11—42no—
722C2×D11—41no—
723C2×D11—41no—
724C2×D11—42no—
725C2×D11—41no—
726C2×D11—84no—
727C2×D11—88no—
728C2×D11—84no—
729C2×D11#55012yes—
730C2×D11C2×AGL(1,ℤ/8)12yes—
731C2×D11#57712yes—
732C4×C11—22no—
733C4×C11—22no—
734C4×C11—21no—
735C4×C11—42no—
736C4×C11—41no—
737C4×C11—41no—
738C4×C11C2×AGL(1,ℤ/8)12yes—
739C4×C11C22×#4111yescharacteristic
740C4×C11C2×H(5,𝔽2)11yescharacteristic
741Dic11—22no—
742Dic11—22no—
743Dic11—21no—
744Dic11—42no—
745Dic11—41no—
746Dic11—41no—
747Dic11#55012yes—
748Dic11C2×AGL(1,ℤ/8)12yes—
749C2×#41—21no—
750C2×#41—222no—
751C2×#41—221no—
752C2×#41—222no—
753C2×#41—221no—
754C2×#41—221no—
755C2×#41—448no—
756C22×Q8—111no—
757C22×Q8—112no—
758C22×D4—111no—
759C22×D4—111no—
760C22×D4—112no—
761C22×D4—221no—
762C22×D4—222no—
763C22×D4—222no—
764C22×D4—221no—
765C23×C4—221no—
766C23×C4—221no—
767C23×C4—222no—
768C2×SD16—112no—
769C2×SD16—112no—
770C2×SD16—112no—
771C2×SD16—112no—
772C2×SD16—112no—
773C2×SD16—112no—
774C2×SD16—112no—
775C2×SD16—112no—
776C2×SD16—112no—
777C2×SD16—228no—
778C2×SD16—444no—
779C2×SD16—444no—
780C2×SD16C22×D1112yes—
781C2×SD16C22×D1112yes—
782C2×SD16C22×D1112yes—
783C2×D8—111no—
784C2×D8—111no—
785C2×D8—112no—
786C2×D8—112no—
787C2×D8—111no—
788C2×D8—112no—
789C2×D8—224no—
790C2×D8—444no—
791C2×D8C22×D1111yescharacteristic
792C2×D8C22×D1112yes—
793C22×C8—111no—
794C22×C8—112no—
795C22×C8—111no—
796C4⋊Q8—112no—
797C4⋊Q8—111no—
798C4⋊Q8—221no—
799C4⋊Q8—221no—
800C4⋊Q8C22×D1111yescharacteristic
801#127—112no—
802#127—112no—
803#127—112no—
804#127—111no—
805#127—112no—
806#127—221no—
807#127—221no—
808#127—222no—
809#127—222no—
810#127C22×D1111yescharacteristic
811#127C22×D1112yes—
812#126—22no—
813#126—222no—
814#126—222no—
815#126—222no—
816#126—222no—
817#126—222no—
818#126—222no—
819#126—222no—
820#124—112no—
821#124—112no—
822#124—112no—
823#124—222no—
824#124—222no—
825#124C22×D1112yes—
826C22⋊Q8—21no—
827C22⋊Q8—222no—
828C22⋊Q8—222no—
829C22⋊Q8—221no—
830C22⋊Q8—221no—
831C22⋊Q8—221no—
832#121—21no—
833#121—22no—
834#121—222no—
835#121—222no—
836#121—222no—
837#121—221no—
838#121—222no—
839#121—221no—
840#121—222no—
841#121—222no—
842#121—222no—
843#121—222no—
844#121—221no—
845#121—222no—
846C4×Q8—111no—
847C4×Q8—112no—
848C4×Q8—111no—
849C4×Q8—112no—
850C4×Q8—111no—
851C4×Q8—112no—
852C4×Q8—112no—
853C4×Q8—112no—
854C4×Q8—222no—
855C4×Q8—222no—
856C4×Q8C22×D1112yes—
857C4×Q8C22×D1111yescharacteristic
858C4×D4—111no—
859C4×D4—112no—
860C4×D4—111no—
861C4×D4—111no—
862C4×D4—112no—
863C4×D4—111no—
864C4×D4—111no—
865C4×D4—112no—
866C4×D4—111no—
867C4×D4—221no—
868C4×D4—222no—
869C4×D4—221no—
870C4×D4—221no—
871C4×D4—222no—
872C4×D4—221no—
873C4×D4C22×D1111yescharacteristic
874C4×D4C22×D1112yes—
875C4×D4C22×D1111yescharacteristic
876#117—21no—
877#117—222no—
878#117—222no—
879#117—221no—
880#117—221no—
881#117—221no—
882C2×C4⋊C4—111no—
883C2×C4⋊C4—112no—
884C2×C4⋊C4—111no—
885C2×C4⋊C4—111no—
886C2×C4⋊C4—221no—
887C2×C4⋊C4—222no—
888C2×C4⋊C4—221no—
889C2×C22⋊C4—222no—
890C2×C22⋊C4—222no—
891C2×C22⋊C4—221no—
892C2×C22⋊C4—221no—
893C2×C22⋊C4—222no—
894C2×C42—111no—
895C2×C42—112no—
896C2×C42—222no—
897#107—111no—
898#107—111no—
899#107—111no—
900#107C22×D1111yescharacteristic
901C4⋊C8—112no—
902C4⋊C8—112no—
903C4⋊C8—112no—
904C4⋊C8—111no—
905C4⋊C8—112no—
906C4⋊C8C22×D1111yescharacteristic
907C4⋊C8C22×D1112yes—
908#103—112no—
909#103—112no—
910#103—112no—
911#103C22×D1112yes—
912#102—111no—
913#102—111no—
914#102—112no—
915#102—111no—
916#102—111no—
917#102—112no—
918#102—111no—
919#102—111no—
920#102—112no—
921#102C22×D1111yescharacteristic
922#102C22×D1111yescharacteristic
923#102C22×D1112yes—
924#97—112no—
925#97—112no—
926#97—112no—
927#97C22×D1112yes—
928C4×C8—111no—
929C4×C8—111no—
930C4×C8—111no—
931C4×C8C22×D1111yescharacteristic
932C2×C11—81no—
933C2×C11—82no—
934C2×C11—81no—
935C2×C11C2×#55011yescharacteristic
936C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
937C2×C11C2×#57711yescharacteristic
938D11—81no—
939D11—82no—
940D11—81no—
941D11#339714yesdirect product factor
942C24—221no—
943C24—221no—
944C24—222no—
945#41—44no—
946#41—448no—
947#41—444no—
948#41—448no—
949#41—444no—
950#41—444no—
951C2×Q8—112no—
952C2×Q8—111no—
953C2×Q8—112no—
954C2×Q8—222no—
955C2×Q8—224no—
956C2×Q8—224no—
957C2×Q8—224no—
958C2×Q8D4×D1111yescharacteristic
959C2×Q8C23×D1112yes—
960C2×D4—22no—
961C2×D4—21no—
962C2×D4—22no—
963C2×D4—21no—
964C2×D4—111no—
965C2×D4—111no—
966C2×D4—112no—
967C2×D4—222no—
968C2×D4—222no—
969C2×D4—222no—
970C2×D4—224no—
971C2×D4—224no—
972C2×D4—222no—
973C2×D4—221no—
974C2×D4—221no—
975C2×D4—222no—
976C2×D4—222no—
977C2×D4—222no—
978C2×D4—222no—
979C2×D4—222no—
980C2×D4—222no—
981C2×D4—222no—
982C2×D4—222no—
983C2×D4—221no—
984C2×D4—222no—
985C2×D4—221no—
986C2×D4—444no—
987C2×D4—448no—
988C2×D4—884no—
989C2×D4—882no—
990C2×D4C23×D1111yescharacteristic
991C2×D4C23×D1111yescharacteristic
992C2×D4C23×D1112yes—
993C22×C4—21no—
994C22×C4—22no—
995C22×C4—21no—
996C22×C4—111no—
997C22×C4—111no—
998C22×C4—112no—
999C22×C4—111no—
1000C22×C4—112no—
1001C22×C4—221no—
1002C22×C4—221no—
1003C22×C4—222no—
1004C22×C4—221no—
1005C22×C4—222no—
1006C22×C4—221no—
1007C22×C4—221no—
1008C22×C4—221no—
1009C22×C4—222no—
1010C22×C4—221no—
1011C22×C4—222no—
1012C22×C4—221no—
1013C22×C4—444no—
1014C22×C4—444no—
1015C22×C4—448no—
1016SD16—24no—
1017SD16—42no—
1018SD16—42no—
1019SD16—224no—
1020SD16—224no—
1021SD16—224no—
1022SD16—442no—
1023SD16—442no—
1024SD16—442no—
1025SD16—442no—
1026SD16—442no—
1027SD16—442no—
1028D8—22no—
1029D8—42no—
1030D8—222no—
1031D8—222no—
1032D8—222no—
1033D8—442no—
1034D8—442no—
1035D8—442no—
1036C2×C8—111no—
1037C2×C8—114no—
1038C2×C8—111no—
1039C2×C8—112no—
1040C2×C8—224no—
1041C2×C8—222no—
1042C2×C8C23×D1111yescharacteristic
1043C2×C8C23×D1112yes—
1044C2×C8C23×D1111yescharacteristic
1045C4⋊C4—21no—
1046C4⋊C4—22no—
1047C4⋊C4—21no—
1048C4⋊C4—112no—
1049C4⋊C4—111no—
1050C4⋊C4—112no—
1051C4⋊C4—112no—
1052C4⋊C4—112no—
1053C4⋊C4—111no—
1054C4⋊C4—111no—
1055C4⋊C4—221no—
1056C4⋊C4—221no—
1057C4⋊C4—222no—
1058C4⋊C4—222no—
1059C4⋊C4—222no—
1060C4⋊C4—222no—
1061C4⋊C4—221no—
1062C4⋊C4—222no—
1063C4⋊C4—221no—
1064C4⋊C4D4×D1111yescharacteristic
1065C4⋊C4D4×D1112yes—
1066C4⋊C4C23×D1111yescharacteristic
1067C4⋊C4C23×D1111yescharacteristic
1068C22⋊C4—22no—
1069C22⋊C4—22no—
1070C22⋊C4—21no—
1071C22⋊C4—21no—
1072C22⋊C4—22no—
1073C22⋊C4—222no—
1074C22⋊C4—222no—
1075C22⋊C4—221no—
1076C22⋊C4—221no—
1077C22⋊C4—222no—
1078C22⋊C4—222no—
1079C22⋊C4—222no—
1080C22⋊C4—221no—
1081C22⋊C4—221no—
1082C22⋊C4—222no—
1083C22⋊C4—222no—
1084C22⋊C4—222no—
1085C22⋊C4—221no—
1086C22⋊C4—221no—
1087C22⋊C4—222no—
1088C42—22no—
1089C42—111no—
1090C42—111no—
1091C42—112no—
1092C42—112no—
1093C42—111no—
1094C42—112no—
1095C42—222no—
1096C42—222no—
1097C42—222no—
1098C42C23×D1111yescharacteristic
1099C42C23×D1112yes—
1100C11C2×#339711yescharacteristic, complemented, Sylow
1101C23—21no—
1102C23—22no—
1103C23—21no—
1104C23—111no—
1105C23—221no—
1106C23—222no—
1107C23—221no—
1108C23—442no—
1109C23—444no—
1110C23—442no—
1111C23—442no—
1112C23—442no—
1113C23—444no—
1114C23—442no—
1115C23—444no—
1116C23—442no—
1117Q8—22no—
1118Q8—22no—
1119Q8—22no—
1120Q8—224no—
1121Q8—222no—
1122Q8—222no—
1123Q8—222no—
1124Q8—444no—
1125D4—21no—
1126D4—21no—
1127D4—22no—
1128D4—21no—
1129D4—22no—
1130D4—21no—
1131D4—44no—
1132D4—42no—
1133D4—82no—
1134D4—81no—
1135D4—221no—
1136D4—221no—
1137D4—222no—
1138D4—221no—
1139D4—222no—
1140D4—221no—
1141D4—444no—
1142D4—442no—
1143D4—442no—
1144D4—444no—
1145D4—444no—
1146D4—444no—
1147D4—444no—
1148D4—442no—
1149D4—882no—
1150D4—881no—
1151D4—882no—
1152D4—882no—
1153D4—882no—
1154C2×C4—21no—
1155C2×C4—22no—
1156C2×C4—21no—
1157C2×C4—44no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—111no—
1161C2×C4—111no—
1162C2×C4—114no—
1163C2×C4—112no—
1164C2×C4—112no—
1165C2×C4—112no—
1166C2×C4—111no—
1167C2×C4—112no—
1168C2×C4—224no—
1169C2×C4—224no—
1170C2×C4—222no—
1171C2×C4—221no—
1172C2×C4—222no—
1173C2×C4—221no—
1174C2×C4—444no—
1175C2×C4—442no—
1176C2×C4—442no—
1177C2×C4—444no—
1178C2×C4—442no—
1179C2×C4—442no—
1180C2×C4—444no—
1181C2×C4—442no—
1182C2×C4—442no—
1183C2×C4—444no—
1184C2×C4—442no—
1185C2×C4—442no—
1186C2×C4C2×D4×D1112yes—
1187C2×C4C2×D4×D1111yescharacteristic
1188C2×C4C2×D4×D1112yes—
1189C2×C4C2×D4×D1111yescharacteristic
1190C2×C4C24×D1111yescharacteristic
1191C8—22no—
1192C8—21no—
1193C8—112no—
1194C8—222no—
1195C8—221no—
1196C8#41×D1112yescomplemented
1197C22—42no—
1198C22—41no—
1199C22—41no—
1200C22—42no—
1201C22—41no—
1202C22—41no—
1203C22—41no—
1204C22—41no—
1205C22—42no—
1206C22—112no—
1207C22—112no—
1208C22—112no—
1209C22—442no—
1210C22—441no—
1211C22—441no—
1212C22—442no—
1213C22—441no—
1214C22—441no—
1215C22—441no—
1216C22—441no—
1217C22—442no—
1218C22—884no—
1219C22—888no—
1220C22—884no—
1221C22C22×D4×D1111yescharacteristic
1222C4—22no—
1223C4—22no—
1224C4—21no—
1225C4—41no—
1226C4—41no—
1227C4—42no—
1228C4—112no—
1229C4—112no—
1230C4—222no—
1231C4—222no—
1232C4—221no—
1233C4—441no—
1234C4—441no—
1235C4—442no—
1236C4D11×AGL(1,ℤ/8)12yes—
1237C4C2×#41×D1111yescharacteristic
1238C4D11×H(5,𝔽2)11yescharacteristic
1239C2—82no—
1240C2—81no—
1241C2—81no—
1242C2—114no—
1243C2—882no—
1244C2—881no—
1245C2—881no—
1246C2D11×#55011yescharacteristic
1247C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
1248C2D11×#57711yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3397C2
socleC22×C11C23×D4
hypercenter#3397D11
hypocenterC11C2×#3397
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #3397

Complements

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

NH ≅ G/Ntype
1. D11×#556C2semidirect
2. D11×#550C2semidirect
3. #13081641C2semidirect
4. #13081640C2semidirect
5. #13081639C2semidirect
6. #13081638C2semidirect
7. #13081637C2semidirect
8. #13081636C2semidirect
9. #13081635C2semidirect
10. #13081634C2semidirect
11. #13081633C2semidirect
12. #13081632C2semidirect
13. #13081631C2semidirect
14. D11×#496C2semidirect
15. D11×#492C2semidirect
16. D11×#460C2semidirect
17. D11×#463C2semidirect
18. D11×#461C2semidirect
19. D11×#459C2semidirect
20. D11×#446C2semidirect
21. D11×#440C2semidirect
22. C4×D8×D11C2semidirect
23. C11×#3397C2semidirect
25. C11×#556C22semidirect
26. C11×#550C22semidirect
33. #10623263C22semidirect
35. #10623249C22semidirect
36. #10623249C22semidirect
42. #10623202C22semidirect
49. #10623115C22semidirect
50. #10623108C22semidirect
53. #10623099C22semidirect
54. #10623084C22semidirect
55. #10623084C22semidirect
59. #10623073C22semidirect
62. C11×#496C22semidirect
63. C11×#492C22semidirect
64. C11×#463C22semidirect
65. C11×#461C22semidirect
66. C11×#460C22semidirect
67. C11×#459C22semidirect
68. C11×#446C22semidirect
69. C11×#440C22semidirect
70. C4×C11×D8C22semidirect
71. #10622789C22semidirect
72. #10622789C22semidirect
73. #10622788C22semidirect
74. #10622788C22semidirect
75. #10622778C22semidirect
76. #10622777C22semidirect
77. #10622776C22semidirect
78. #10622776C22semidirect
79. #10622775C22semidirect
80. #10622767C22semidirect
81. #10622767C22semidirect
82. #10622766C22semidirect
83. #10622763C22semidirect
84. D8×Dic11C22semidirect
85. #10622698C22semidirect
86. #10622696C22semidirect
87. #10622689C22semidirect
88. #10622688C22semidirect
89. #10622687C22semidirect
90. #10622685C22semidirect
91. #10622671C22semidirect
92. #10622670C22semidirect
93. #10622640C22semidirect
94. #10622639C22semidirect
95. #10622637C22semidirect
96. #10622632C22semidirect
97. #10622631C22semidirect
98. #10622629C22semidirect
99. #10622628C22semidirect
100. C4×#4323C22semidirect
101. C4×#4323C22semidirect
102. #10622502C22semidirect
104. #10622485C22semidirect
105. #10622461C22semidirect
106. #10622457C22semidirect
107. #10622456C22semidirect
108. #10622454C22semidirect
111. #10622444C22semidirect
112. #10622441C22semidirect
113. #10622432C22semidirect
114. #10622431C22semidirect
115. #10622430C22semidirect
117. #10622400C22semidirect
118. #10622399C22semidirect
122. #10622375C22semidirect
123. #10622375C22semidirect
124. #10622370C22semidirect
125. #10622369C22semidirect
126. #10622369C22semidirect
127. #10622325C22semidirect
128. #10622323C22semidirect
130. #10622314C22semidirect
131. #10622306C22semidirect
132. C4×D88C22semidirect
134. #10622292C22semidirect
476. C8×D11#41semidirect
490. #3397D11direct (N × H)
592. C8×C11C2×#41semidirect
595. C11⋊C8C2×#41semidirect
610. #556C2×D11semidirect
619. #550C2×D11semidirect
641. #496C2×D11semidirect
647. #492C2×D11semidirect
655. #463C2×D11semidirect
661. #461C2×D11semidirect
669. #460C2×D11semidirect
675. #459C2×D11semidirect
681. #446C2×D11semidirect
689. #440C2×D11semidirect
697. C4×D8C2×D11semidirect
941. D11#3397direct (N × H)
1100. C11C2×#3397semidirect
1196. C8#41×D11semidirect

Maximal subgroups

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

subgroupindex
D11×#5562
D11×#5502
#130816412
#130816402
#130816392
#130816382
#130816372
#130816362
#130816352
#130816342
#130816332
#130816322
#130816312
D11×#4962
D11×#4922
D11×#4602
D11×#4632
D11×#4612
D11×#4592
D11×#4462
D11×#4402
C4×D8×D112
C11×#33972
C2×#339711