Finite Group Databasebeta

← D11×#3333 #15630710

Subgroups — D11×#3333 #15630710

Order 2816.

2210 conjugacy classes of subgroups.

The subgroup lattice has 1222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#554C211yesmaximal, characteristic, complemented
2D11×#550C211yesmaximal, characteristic
3#13080957C211yesmaximal, characteristic, complemented
4#13080956C211yesmaximal, characteristic, complemented
5#13080955C211yesmaximal, characteristic, complemented
6#13080954C211yesmaximal, characteristic, complemented
7#13080953C211yesmaximal, characteristic, complemented
8#13080952C212yesmaximal, complemented
9#13080951C211yesmaximal, characteristic, complemented
10#13080950C212yesmaximal, complemented
11#13080949C212yesmaximal, complemented
12#13080948C211yesmaximal, characteristic, complemented
13#13080947C212yesmaximal, complemented
14D11×#486C211yesmaximal, characteristic, complemented
15D11×#480C212yesmaximal, complemented
16D11×#477C211yesmaximal, characteristic, complemented
17D11×#468C212yesmaximal, complemented
18D11×#460C211yesmaximal, characteristic, complemented
19D11×#452C212yesmaximal, complemented
20C4×Q16×D11C211yesmaximal, characteristic, complemented
21D11×#436C211yesmaximal, characteristic, complemented
22D11×#417C212yesmaximal, complemented
23C11×#3333C211yesmaximal, characteristic, complemented
24C2×#41×D11C2212yes—
25C11×#554C2211yescharacteristic, complemented
26C11×#550C2211yescharacteristic
27#10623365C2212yes—
28C2×Q16×D11C2211yescharacteristic
29C2×SD16×D11C2212yes—
30C2×M16×D11C2212yes—
31#10623261C2211yescharacteristic, complemented
32D11×C4⋊Q8C2211yescharacteristic
33#10623249—21no—
34#10623249C2211yescharacteristic
35D11×#127—21no—
36D11×#127C2211yescharacteristic
37#10623221—21no—
38D11×#125—21no—
39#10623167—22no—
40#10623166C2212yescomplemented
41D11×C22⋊Q8—22no—
42D11×C22⋊Q8C2212yes—
43D11×#121—22no—
44D11×#121C2212yes—
45#10623130—22no—
46#10623130C2212yes—
47#10623110C2211yescharacteristic, complemented
48#10623108C2211yescharacteristic
49C4×Q8×D11C2211yescharacteristic
50C4×Q8×D11C2211yescharacteristic
51#10623084—21no—
52#10623084C2211yescharacteristic
53C4×D4×D11—21no—
54C4×D4×D11—21no—
55C4×D4×D11C2211yescharacteristic
56#10623074C2211yescharacteristic, complemented
57#10623070—21no—
58#10623042C2212yescomplemented
59C2×C4⋊C4×D11C2212yes—
60C11×#486C2211yescharacteristic, complemented
61C11×#480C2212yescomplemented
62C11×#477C2211yescharacteristic, complemented
63C11×#468C2212yescomplemented
64C11×#460C2211yescharacteristic, complemented
65C11×#452C2212yescomplemented
66C4×C11×Q16C2211yescharacteristic, complemented
67C11×#436C2211yescharacteristic, complemented
68C11×#417C2212yescomplemented
69#10622852C2212yescomplemented
70#10622845C2212yescomplemented
71#10622800C2212yescomplemented
72Q16×Dic11C2211yescharacteristic, complemented
73#10622787C2212yescomplemented
74#10622786C2212yescomplemented
75#10622776C2212yescomplemented
76#10622747C2212yescomplemented
77#10622746C2212yescomplemented
78#10622741C2212yescomplemented
79#10622704C2211yescharacteristic, complemented
80#10622701C2211yescharacteristic, complemented
81#10622688C2211yescharacteristic, complemented
82#10622683C2211yescharacteristic, complemented
83#10622662C2212yescomplemented
84#10622660C2212yescomplemented
85#10622655C2212yescomplemented
86#10622646C2212yescomplemented
87C4×#4326C2211yescharacteristic, complemented
88C4×#4326C2211yescharacteristic, complemented
89#10622640C2211yescharacteristic, complemented
90#10622634C2211yescharacteristic, complemented
91#10622625C2211yescharacteristic, complemented
92#10622580C2212yescomplemented
93#10622579C2212yescomplemented
94#10622499C2212yescomplemented
95#10622495C2212yescomplemented
96#10622495C2212yescomplemented
97D11×#107C2212yes—
98D11×#107C2211yescharacteristic
99#10622488C2212yescomplemented
100#10622486C2211yescharacteristic, complemented
101#10622463C2211yescharacteristic, complemented
102#10622461C2211yescharacteristic, complemented
103#10622451C2211yescharacteristic, complemented
104D11×C4⋊C8C2211yescharacteristic
105#10622425C2212yescomplemented
106#10622423C2212yescomplemented
107#10622416C2212yescomplemented
108#10622416C2212yescomplemented
109D11×#103C2212yes—
110D11×#103C2211yescharacteristic
111D11×#103C2211yescharacteristic
112#10622407C2212yescomplemented
113#10622403C2211yescharacteristic, complemented
114#10622403C2211yescharacteristic, complemented
115#10622396C2212yescomplemented
116#10622393C2212yescomplemented
117#10622387C2212yescomplemented
118#10622387C2212yescomplemented
119#10622384C2212yescomplemented
120#10622384C2212yescomplemented
121D11×#102C2212yes—
122D11×#102C2212yes—
123D11×#102C2212yes—
124#10622375C2212yescomplemented
125#10622373C2212yescomplemented
126#10622373C2212yescomplemented
127#10622349C2212yescomplemented
128#10622346C2212yescomplemented
129#10622342C2212yescomplemented
130D11×C22⋊C8C2212yes—
131C4×Dic44C2211yescharacteristic, complemented
132#10622307C2211yescharacteristic, complemented
133#10622301C2211yescharacteristic, complemented
134C4×C8×D11C2211yescharacteristic
135C2×C11×#41C2312yes—
136#41×D11—28no—
137#41×D11—44no—
138C2×#4343C2312yes—
139C2×Q8×D11—21no—
140C2×Q8×D11C2311yescharacteristic
141C2×Q8×D11C2311yescharacteristic
142C2×#4341—22no—
143C2×#4341C2312yes—
144C2×D4×D11—22no—
145C2×D4×D11—22no—
146C2×D4×D11—21no—
147C2×D4×D11—21no—
148C2×D4×D11D411yescharacteristic
149C2×D4×D11C2312yes—
150C2×#4339—22no—
151C2×#4339C2312yes—
152C22×C4×D11—22no—
153C22×C4×D11—22no—
154C22×C4×D11C2312yes—
155C2×C11×Q16C2311yescharacteristic
156C2×C11×SD16C2312yes—
157C2×C11×M16C2312yes—
158C11×C4⋊Q8C2311yescharacteristic
159C11×#127—21no—
160C11×#127C2311yescharacteristic
161C11×#125—21no—
162C11×C22⋊Q8—22no—
163C11×C22⋊Q8C2312yes—
164C11×#121—22no—
165C11×#121C2312yes—
166C4×Q8×C11C2311yescharacteristic
167C4×Q8×C11C2311yescharacteristic
168C4×D4×C11—21no—
169C4×D4×C11—21no—
170C4×D4×C11C2311yescharacteristic
171C2×C11×C4⋊C4C2312yes—
172#66999—22no—
173#66999C2312yes—
174Q8×Dic11C2311yescharacteristic
175Q8×Dic11C2311yescharacteristic
176#66997—21no—
177C2×#4326C2311yescharacteristic
178C2×#4326C2311yescharacteristic
179C2×#4325C2312yes—
180#66993—21no—
181#66993—22no—
182#66993—22no—
183#66993—21no—
184#66993—21no—
185#66993—21no—
186#66993C2312yes—
187#66992—22no—
188#66992—22no—
189#66992—22no—
190#66991—22no—
191#66991C2312yes—
192D4×Dic11—21no—
193D4×Dic11—21no—
194D4×Dic11D411yescharacteristic
195C2×#4324C2312yes—
196#66983—22no—
197#66983C2312yes—
198C4×C22⋊D11—22no—
199C4×C22⋊D11—22no—
200C4×C22⋊D11C2312yes—
201C2×C4⋊Dic11C2312yes—
202#66977—22no—
203#66977C2312yes—
204C2×Dic11⋊C4—22no—
205C2×#4318C2312yes—
206Q16×D11—24no—
207SD16×D11—44no—
208M16×D11—44no—
209C2×Dic44C2311yescharacteristic
210C2×#4314C2312yes—
211C2×#4313C2312yes—
212C2×#4313C2312yes—
213C2×C8×D11C2312yes—
214C2×C8×D11C2311yescharacteristic
215C2×C8×D11C2311yescharacteristic
216#66950—22no—
217#66950C2312yes—
218#66949—22no—
219#66949—22no—
220#66949—22no—
221#66948—22no—
222#66948C2312yes—
223#66946—21no—
224#66946—21no—
225#66946D411yescharacteristic
226C4⋊C4×D11—21no—
227C4⋊C4×D11—22no—
228C4⋊C4×D11—22no—
229C4⋊C4×D11—21no—
230C4⋊C4×D11—21no—
231C4⋊C4×D11—22no—
232C4⋊C4×D11D411yescharacteristic
233C4⋊C4×D11C2312yes—
234C4⋊C4×D11C2311yescharacteristic
235C4⋊C4×D11C2311yescharacteristic
236C4⋊C4×D11C2312yes—
237C4⋊C4×D11C2312yes—
238#66943—21no—
239#66943—21no—
240#66942—22no—
241#66942—22no—
242#66941—21no—
243#66941C2312yes—
244#66940—21no—
245#66940—21no—
246#66940C2311yescharacteristic
247#66940C2311yescharacteristic
248#66937—22no—
249#66937—22no—
250#66937—22no—
251(C22⋊D11)⋊C4—22no—
252(C22⋊D11)⋊C4—22no—
253(C22⋊D11)⋊C4D412yes—
254C22⋊C4×D11—22no—
255C22⋊C4×D11—22no—
256C22⋊C4×D11D412yes—
257#66931—22no—
258#66931—22no—
259#66931—22no—
260#66927—21no—
261#66927C2311yescharacteristic
262C4×D44—21no—
263C4×D44—21no—
264C4×D44C2311yescharacteristic
265C42×D11—21no—
266C42×D11—21no—
267C42×D11C2311yescharacteristic
268#66923—21no—
269#66922C2311yescharacteristic
270C4×Dic22—21no—
271C4×Dic22—21no—
272C4×Dic22C2311yescharacteristic
273C4×Dic22C2311yescharacteristic
274C11×#107C2311yescharacteristic
275C11×#107C2312yes—
276C11×C4⋊C8C2311yescharacteristic
277C11×#103C2311yescharacteristic
278C11×#103C2312yes—
279C11×#103C2311yescharacteristic
280C11×#102C2312yes—
281C11×#102C2312yes—
282C11×#102C2312yes—
283C11×C22⋊C8C2312yes—
284C4×C8×C11C2311yescharacteristic
285#66899C2311yescharacteristic
286#66899C2311yescharacteristic
287#66899C2312yes—
288#66896C2312yes—
289#66896C2312yes—
290#66896C2312yes—
291C22⋊(C11⋊C8)C2312yes—
292#66885C2312yes—
293#66885C2312yes—
294#66885C2312yes—
295(C2×D11)⋊C8C2312yes—
296(C2×D11)⋊C8C2312yes—
297#66882C2312yes—
298#66882C2311yescharacteristic
299#66880C2312yes—
300#66880C2311yescharacteristic
301#66880C2311yescharacteristic
302Dic11⋊C8C2312yes—
303C8×Dic11C2311yescharacteristic
304C8×Dic11C2311yescharacteristic
305#66874C2311yescharacteristic
306#66874C2311yescharacteristic
307#66874C2312yes—
308#66873C2312yes—
309#66873C2312yes—
310#66873C2312yes—
311#66871C2312yes—
312#66871C2311yescharacteristic
313#66871C2311yescharacteristic
314#66871C2312yes—
315C4⋊(C11⋊C8)C2311yescharacteristic
316C4×C11⋊C8C2311yescharacteristic
317C2×#3333—111nomaximal, Sylow
318C23×D11—22no—
319C23×D11C2×D412yes—
320C11×#41—24no—
321C11×#41—42no—
322C2×Q8×C11—21no—
323C2×Q8×C11C2411yescharacteristic
324C2×Q8×C11C2411yescharacteristic
325C2×D4×C11—22no—
326C2×D4×C11—22no—
327C2×D4×C11—21no—
328C2×D4×C11—21no—
329C2×D4×C11C2×D411yescharacteristic
330C2×D4×C11C2412yes—
331C22×C4×C11—22no—
332C22×C4×C11—22no—
333C22×C4×C11C2412yes—
334C2×C22⋊D11—22no—
335C2×C22⋊D11—22no—
336C2×C22⋊D11—22no—
337C2×C22⋊D11—22no—
338C2×C22⋊D11—22no—
339C2×C22⋊D11—22no—
340C2×C22⋊D11—22no—
341C2×C22⋊D11C2×D412yes—
342C22×Dic11—22no—
343C22×Dic11—22no—
344C22×Dic11C2×D412yes—
345#4343—24no—
346#4343—42no—
347Q8×D11—22no—
348Q8×D11—22no—
349Q8×D11—22no—
350Q8×D11—82no—
351Q8×D11#4114yes—
352#4341—24no—
353#4341—42no—
354#4341—48no—
355D4×D11—24no—
356D4×D11—24no—
357D4×D11—24no—
358D4×D11—48no—
359D4×D11—44no—
360D4×D11—84no—
361D4×D11—82no—
362#4339—24no—
363#4339—42no—
364#4339—48no—
365C2×D44—22no—
366C2×D44—22no—
367C2×D44—21no—
368C2×D44—21no—
369C2×D44C2×D411yescharacteristic
370C2×D44C2412yes—
371C2×C4×D11—24no—
372C2×C4×D11—24no—
373C2×C4×D11—22no—
374C2×C4×D11—21no—
375C2×C4×D11—21no—
376C2×C4×D11—21no—
377C2×C4×D11—21no—
378C2×C4×D11—22no—
379C2×C4×D11—22no—
380C2×C4×D11—22no—
381C2×C4×D11—22no—
382C2×C4×D11—48no—
383C2×C4×D11—84no—
384C2×C4×D11C2×D411yescharacteristic
385C2×C4×D11C2×D412yes—
386C2×C4×D11C2×D412yes—
387C2×C4×D11C2×D411yescharacteristic
388C2×C4×D11C2412yes—
389C2×C4×D11C2411yescharacteristic
390C2×Dic22—21no—
391C2×Dic22—21no—
392C2×Dic22—22no—
393C2×Dic22—21no—
394C2×Dic22C2411yescharacteristic
395C2×Dic22C2411yescharacteristic
396C11×Q16—22no—
397C11×SD16—42no—
398C11×M16—42no—
399C2×C8×C11C2411yescharacteristic
400C2×C8×C11C2411yescharacteristic
401C2×C8×C11C2412yes—
402C11×C4⋊C4—21no—
403C11×C4⋊C4—21no—
404C11×C4⋊C4—21no—
405C11×C4⋊C4—22no—
406C11×C4⋊C4—22no—
407C11×C4⋊C4C2×D411yescharacteristic
408C11×C4⋊C4C2411yescharacteristic
409C11×C4⋊C4C2411yescharacteristic
410C11×C4⋊C4C2412yes—
411C11×C22⋊C4—22no—
412C11×C22⋊C4—22no—
413C11×C22⋊C4C2×D412yes—
414C42×C11—21no—
415C42×C11—21no—
416C42×C11C2411yescharacteristic
417C22⋊Dic11—22no—
418C22⋊Dic11—22no—
419C22⋊Dic11C2×D412yes—
420#4326—22no—
421#4326—22no—
422#4325—42no—
423#4324—42no—
424(C2×D11)⋊C4—22no—
425(C2×D11)⋊C4—22no—
426(C2×D11)⋊C4—22no—
427(C2×D11)⋊C4—22no—
428(C2×D11)⋊C4C2×D412yes—
429(C2×D11)⋊C4C2×D412yes—
430C4⋊Dic11—21no—
431C4⋊Dic11—21no—
432C4⋊Dic11—22no—
433C4⋊Dic11—21no—
434C4⋊Dic11—22no—
435C4⋊Dic11C2×D411yescharacteristic
436C4⋊Dic11C2411yescharacteristic
437C4⋊Dic11C2411yescharacteristic
438C4⋊Dic11C2412yes—
439Dic11⋊C4—21no—
440Dic11⋊C4—21no—
441Dic11⋊C4—21no—
442Dic11⋊C4—21no—
443Dic11⋊C4—22no—
444Dic11⋊C4—22no—
445Dic11⋊C4—22no—
446Dic11⋊C4—22no—
447Dic11⋊C4—22no—
448Dic11⋊C4—21no—
449Dic11⋊C4—21no—
450Dic11⋊C4—22no—
451Dic11⋊C4C2×D412yes—
452C4×Dic11—21no—
453C4×Dic11—21no—
454C4×Dic11—21no—
455C4×Dic11—21no—
456C4×Dic11—21no—
457C4×Dic11—21no—
458C4×Dic11C2×D411yescharacteristic
459C4×Dic11C2×D411yescharacteristic
460C4×Dic11C2411yescharacteristic
461#4318—42no—
462C2×C11⋊C8C2411yescharacteristic
463C2×C11⋊C8C2411yescharacteristic
464C2×C11⋊C8C2412yes—
465Dic44—22no—
466#4314—42no—
467#4313—42no—
468#4313—42no—
469C8×D11—22no—
470C8×D11—22no—
471C8×D11—24no—
472C2×#554—111no—
473C2×#550—111no—
474#3333—111no—
475#3333—112no—
476#3333—111no—
477#3333—112no—
478#3333—111no—
479#3333—112no—
480#3333—111no—
481#3333—111no—
482#3333—112no—
483#3333—111no—
484#3333—111no—
485#3333D1111yescharacteristic, direct product factor
486C2×#486—111no—
487C2×#480—112no—
488C2×#477—111no—
489C2×#468—112no—
490C2×#460—111no—
491C2×#452—112no—
492C2×C4×Q16—111no—
493C2×#436—111no—
494C2×#417—112no—
495C23×C11—22no—
496C23×C11C22×D412yes—
497C22×D11—24no—
498C22×D11—24no—
499C22×D11—24no—
500C22×D11—22no—
501C22×D11—44no—
502C22×D11—44no—
503C22×D11—44no—
504C22×D11C22×D412yes—
505C22×D11C22×D411yescharacteristic
506Q8×C11—21no—
507Q8×C11—21no—
508Q8×C11—21no—
509Q8×C11—81no—
510Q8×C11C2×#4112yes—
511D4×C11—22no—
512D4×C11—22no—
513D4×C11—22no—
514D4×C11—44no—
515D4×C11—42no—
516D4×C11—81no—
517D4×C11—82no—
518C2×C4×C11—21no—
519C2×C4×C11—22no—
520C2×C4×C11—22no—
521C2×C4×C11—21no—
522C2×C4×C11—21no—
523C2×C4×C11—21no—
524C2×C4×C11—22no—
525C2×C4×C11—44no—
526C2×C4×C11—82no—
527C2×C4×C11C22×D411yescharacteristic
528C2×C4×C11C22×D412yes—
529C2×C4×C11C22×D411yescharacteristic
530C2×C4×C11C2511yescharacteristic
531C22⋊D11—24no—
532C22⋊D11—44no—
533C22⋊D11—44no—
534C22⋊D11—44no—
535C22⋊D11—44no—
536C22⋊D11—82no—
537C22⋊D11—82no—
538C22⋊D11—82no—
539C2×Dic11—21no—
540C2×Dic11—24no—
541C2×Dic11—21no—
542C2×Dic11—21no—
543C2×Dic11—21no—
544C2×Dic11—22no—
545C2×Dic11—44no—
546C2×Dic11—82no—
547C2×Dic11C22×D411yescharacteristic
548C2×Dic11C22×D412yes—
549C2×Dic11C22×D411yescharacteristic
550C2×Dic11C22×D411yescharacteristic
551D44—22no—
552D44—22no—
553D44—22no—
554D44—44no—
555D44—42no—
556D44—81no—
557D44—82no—
558C4×D11—24no—
559C4×D11—24no—
560C4×D11—22no—
561C4×D11—22no—
562C4×D11—22no—
563C4×D11—24no—
564C4×D11—44no—
565C4×D11—44no—
566C4×D11—42no—
567C4×D11—42no—
568C4×D11—44no—
569C4×D11—42no—
570C4×D11—82no—
571C4×D11—82no—
572C4×D11#13714yes—
573C4×D11C2×#4112yes—
574C4×D11H(5,𝔽2)12yes—
575Dic22—21no—
576Dic22—24no—
577Dic22—21no—
578Dic22—21no—
579Dic22—42no—
580Dic22—82no—
581Dic22—81no—
582Dic22C2×#4112yes—
583C8×C11—21no—
584C8×C11—21no—
585C8×C11—22no—
586C11⋊C8—21no—
587C11⋊C8—21no—
588C11⋊C8—22no—
589C22×#41—112no—
590C22×Q16—111no—
591C22×SD16—112no—
592C22×M16—112no—
593#554—111no—
594#554—112no—
595#554—111no—
596#554—111no—
597#554—112no—
598#554—221no—
599#554—222no—
600#554—221no—
601#554C2×D1111yescharacteristic, complemented
602#550—112no—
603#550—111no—
604#550—112no—
605#550—111no—
606#550—111no—
607#550—221no—
608#550—222no—
609#550—221no—
610#550C2×D1111yescharacteristic
611C2×C4⋊Q8—111no—
612C2×#127—111no—
613C2×#127—221no—
614C2×#125—221no—
615C2×C22⋊Q8—112no—
616C2×C22⋊Q8—222no—
617C2×#121—112no—
618C2×#121—222no—
619C2×C4×Q8—111no—
620C2×C4×Q8—111no—
621C2×C4×D4—111no—
622C2×C4×D4—221no—
623C2×C4×D4—221no—
624C22×C4⋊C4—112no—
625#486—111no—
626#486—111no—
627#486—112no—
628#486—112no—
629#486—111no—
630#486C2×D1111yescharacteristic, complemented
631#480—112no—
632#480—112no—
633#480—112no—
634#480—112no—
635#480—112no—
636#480—112no—
637#480—112no—
638#480C2×D1112yescomplemented
639#477—111no—
640#477—111no—
641#477—112no—
642#477—111no—
643#477—112no—
644#477C2×D1111yescharacteristic, complemented
645#468—112no—
646#468—112no—
647#468—112no—
648#468—112no—
649#468—112no—
650#468—112no—
651#468—112no—
652#468C2×D1112yescomplemented
653#460—112no—
654#460—111no—
655#460—111no—
656#460—111no—
657#460—112no—
658#460C2×D1111yescharacteristic, complemented
659#452—112no—
660#452—112no—
661#452—112no—
662#452—112no—
663#452—112no—
664#452—112no—
665#452—112no—
666#452C2×D1112yescomplemented
667C4×Q16—111no—
668C4×Q16—111no—
669C4×Q16—111no—
670C4×Q16—111no—
671C4×Q16—111no—
672C4×Q16—111no—
673C4×Q16—111no—
674C4×Q16C2×D1111yescharacteristic, complemented
675#436—112no—
676#436—111no—
677#436—111no—
678#436—112no—
679#436—111no—
680#436C2×D1111yescharacteristic, complemented
681C2×#107—112no—
682C2×#107—111no—
683C2×C4⋊C8—111no—
684#417—112no—
685#417—112no—
686#417—112no—
687#417—112no—
688#417—112no—
689#417—112no—
690#417—112no—
691#417C2×D1112yescomplemented
692C2×#103—112no—
693C2×#103—111no—
694C2×#103—111no—
695C2×#102—112no—
696C2×#102—112no—
697C2×#102—112no—
698C2×C22⋊C8—112no—
699C2×C4×C8—111no—
700C22×C11—22no—
701C22×C11—22no—
702C22×C11—22no—
703C22×C11—42no—
704C22×C11—42no—
705C22×C11—42no—
706C22×C11C23×D411yescharacteristic
707C2×D11—22no—
708C2×D11—22no—
709C2×D11—22no—
710C2×D11—48no—
711C2×D11—42no—
712C2×D11—42no—
713C2×D11—42no—
714C2×D11—88no—
715C2×D11#54612yes—
716C2×D11C2×#13712yes—
717C2×D11#57612yes—
718C4×C11—22no—
719C4×C11—22no—
720C4×C11—21no—
721C4×C11—41no—
722C4×C11—41no—
723C4×C11—42no—
724C4×C11—41no—
725C4×C11C2×#13712yes—
726C4×C11C22×#4111yescharacteristic
727C4×C11C2×H(5,𝔽2)11yescharacteristic
728Dic11—22no—
729Dic11—22no—
730Dic11—21no—
731Dic11—41no—
732Dic11—42no—
733Dic11—41no—
734Dic11—41no—
735Dic11#54612yes—
736Dic11C2×#13712yes—
737C2×#41—112no—
738C2×#41—112no—
739C2×#41—112no—
740C2×#41—222no—
741C2×#41—222no—
742C2×#41—228no—
743C2×#41—444no—
744C2×#41C22×D1112yes—
745C22×Q8—111no—
746C22×Q8—111no—
747C22×Q8—221no—
748C22×D4—111no—
749C22×D4—112no—
750C22×D4—221no—
751C22×D4—221no—
752C22×D4—222no—
753C22×D4—222no—
754C23×C4—112no—
755C23×C4—222no—
756C23×C4—222no—
757C2×Q16—111no—
758C2×Q16—111no—
759C2×Q16—111no—
760C2×Q16—224no—
761C2×Q16C22×D1111yescharacteristic
762C2×SD16—112no—
763C2×SD16—112no—
764C2×SD16—112no—
765C2×SD16—444no—
766C2×SD16C22×D1112yes—
767C2×M16—112no—
768C2×M16—112no—
769C2×M16—112no—
770C2×M16—444no—
771C2×M16C22×D1112yes—
772C22×C8—111no—
773C22×C8—112no—
774C22×C8—111no—
775C4⋊Q8—112no—
776C4⋊Q8—111no—
777C4⋊Q8—221no—
778C4⋊Q8—221no—
779C4⋊Q8C22×D1111yescharacteristic
780#127—21no—
781#127—112no—
782#127—111no—
783#127—221no—
784#127—221no—
785#127—221no—
786#127—222no—
787#127—222no—
788#127—221no—
789#127—221no—
790#127C22×D1111yescharacteristic
791#125—21no—
792#125—221no—
793#125—222no—
794#125—222no—
795#125—221no—
796#125—221no—
797C22⋊Q8—22no—
798C22⋊Q8—112no—
799C22⋊Q8—112no—
800C22⋊Q8—112no—
801C22⋊Q8—222no—
802C22⋊Q8—222no—
803C22⋊Q8—222no—
804C22⋊Q8—222no—
805C22⋊Q8—222no—
806C22⋊Q8—222no—
807C22⋊Q8—222no—
808C22⋊Q8—222no—
809C22⋊Q8—222no—
810C22⋊Q8C22×D1112yes—
811#121—22no—
812#121—112no—
813#121—112no—
814#121—112no—
815#121—222no—
816#121—222no—
817#121—222no—
818#121—222no—
819#121—222no—
820#121—222no—
821#121—222no—
822#121—222no—
823#121—222no—
824#121C22×D1112yes—
825C4×Q8—111no—
826C4×Q8—111no—
827C4×Q8—111no—
828C4×Q8—111no—
829C4×Q8—111no—
830C4×Q8—111no—
831C4×Q8—221no—
832C4×Q8—221no—
833C4×Q8—221no—
834C4×Q8—221no—
835C4×Q8C22×D1111yescharacteristic
836C4×Q8C22×D1111yescharacteristic
837C4×D4—21no—
838C4×D4—21no—
839C4×D4—111no—
840C4×D4—112no—
841C4×D4—111no—
842C4×D4—112no—
843C4×D4—111no—
844C4×D4—221no—
845C4×D4—221no—
846C4×D4—222no—
847C4×D4—222no—
848C4×D4—221no—
849C4×D4—222no—
850C4×D4—221no—
851C4×D4—222no—
852C4×D4—221no—
853C4×D4—221no—
854C4×D4C22×D1111yescharacteristic
855C2×C4⋊C4—111no—
856C2×C4⋊C4—112no—
857C2×C4⋊C4—111no—
858C2×C4⋊C4—112no—
859C2×C4⋊C4—112no—
860C2×C4⋊C4—112no—
861C2×C4⋊C4—111no—
862C2×C4⋊C4—222no—
863C2×C4⋊C4—222no—
864C2×C4⋊C4—221no—
865C2×C4⋊C4—221no—
866C2×C4⋊C4—221no—
867C2×C4⋊C4—222no—
868C2×C4⋊C4—222no—
869C2×C4⋊C4C22×D1112yes—
870C2×C22⋊C4—112no—
871C2×C22⋊C4—222no—
872C2×C22⋊C4—222no—
873C2×C42—111no—
874C2×C42—221no—
875C2×C42—221no—
876#107—111no—
877#107—112no—
878#107—111no—
879#107—111no—
880#107—112no—
881#107—112no—
882#107C22×D1111yescharacteristic
883#107C22×D1112yes—
884C4⋊C8—112no—
885C4⋊C8—111no—
886C4⋊C8C22×D1111yescharacteristic
887#103—111no—
888#103—112no—
889#103—111no—
890#103—111no—
891#103—112no—
892#103—111no—
893#103—111no—
894#103—112no—
895#103—111no—
896#103C22×D1111yescharacteristic
897#103C22×D1112yes—
898#103C22×D1111yescharacteristic
899#102—112no—
900#102—112no—
901#102—112no—
902#102—112no—
903#102—112no—
904#102—112no—
905#102—112no—
906#102—112no—
907#102—112no—
908#102C22×D1112yes—
909#102C22×D1112yes—
910#102C22×D1112yes—
911C22⋊C8—112no—
912C22⋊C8—112no—
913C22⋊C8—112no—
914C22⋊C8C22×D1112yes—
915C4×C8—111no—
916C4×C8—111no—
917C4×C8—111no—
918C4×C8C22×D1111yescharacteristic
919C2×C11—42no—
920C2×C11—82no—
921C2×C11C2×#54611yescharacteristic
922C2×C11C22×#13711yescharacteristic
923C2×C11C2×#57611yescharacteristic
924D11—42no—
925D11—82no—
926D11#333314yesdirect product factor
927C24—112no—
928C24—222no—
929#41—24no—
930#41—42no—
931#41—224no—
932#41—224no—
933#41—224no—
934#41—442no—
935#41—448no—
936#41—442no—
937#41—448no—
938#41—442no—
939C2×Q8—21no—
940C2×Q8—114no—
941C2×Q8—111no—
942C2×Q8—111no—
943C2×Q8—221no—
944C2×Q8—221no—
945C2×Q8—222no—
946C2×Q8—222no—
947C2×Q8—222no—
948C2×Q8—222no—
949C2×Q8—221no—
950C2×Q8—882no—
951C2×Q8C23×D1111yescharacteristic
952C2×Q8C23×D1111yescharacteristic
953C2×D4—22no—
954C2×D4—22no—
955C2×D4—21no—
956C2×D4—21no—
957C2×D4—112no—
958C2×D4—111no—
959C2×D4—112no—
960C2×D4—222no—
961C2×D4—222no—
962C2×D4—224no—
963C2×D4—224no—
964C2×D4—224no—
965C2×D4—222no—
966C2×D4—222no—
967C2×D4—222no—
968C2×D4—222no—
969C2×D4—222no—
970C2×D4—222no—
971C2×D4—222no—
972C2×D4—221no—
973C2×D4—221no—
974C2×D4—444no—
975C2×D4—448no—
976C2×D4—882no—
977C2×D4—884no—
978C2×D4D4×D1111yescharacteristic
979C2×D4C23×D1112yes—
980C22×C4—22no—
981C22×C4—22no—
982C22×C4—111no—
983C22×C4—111no—
984C22×C4—112no—
985C22×C4—111no—
986C22×C4—112no—
987C22×C4—112no—
988C22×C4—112no—
989C22×C4—224no—
990C22×C4—224no—
991C22×C4—222no—
992C22×C4—221no—
993C22×C4—221no—
994C22×C4—221no—
995C22×C4—221no—
996C22×C4—222no—
997C22×C4—222no—
998C22×C4—222no—
999C22×C4—222no—
1000C22×C4—222no—
1001C22×C4—222no—
1002C22×C4—448no—
1003C22×C4—884no—
1004C22×C4C23×D1112yes—
1005Q16—22no—
1006Q16—222no—
1007Q16—222no—
1008Q16—222no—
1009SD16—42no—
1010SD16—442no—
1011SD16—442no—
1012SD16—442no—
1013M16—42no—
1014M16—442no—
1015M16—442no—
1016M16—442no—
1017C2×C8—111no—
1018C2×C8—111no—
1019C2×C8—112no—
1020C2×C8—222no—
1021C2×C8—224no—
1022C2×C8—222no—
1023C2×C8C23×D1111yescharacteristic
1024C2×C8C23×D1111yescharacteristic
1025C2×C8C23×D1112yes—
1026C4⋊C4—22no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—22no—
1031C4⋊C4—112no—
1032C4⋊C4—111no—
1033C4⋊C4—111no—
1034C4⋊C4—112no—
1035C4⋊C4—111no—
1036C4⋊C4—221no—
1037C4⋊C4—222no—
1038C4⋊C4—222no—
1039C4⋊C4—222no—
1040C4⋊C4—221no—
1041C4⋊C4—222no—
1042C4⋊C4—221no—
1043C4⋊C4—221no—
1044C4⋊C4—221no—
1045C4⋊C4—221no—
1046C4⋊C4—222no—
1047C4⋊C4—222no—
1048C4⋊C4—222no—
1049C4⋊C4—221no—
1050C4⋊C4—221no—
1051C4⋊C4—221no—
1052C4⋊C4—222no—
1053C4⋊C4D4×D1111yescharacteristic
1054C4⋊C4C23×D1111yescharacteristic
1055C4⋊C4C23×D1112yes—
1056C4⋊C4C23×D1111yescharacteristic
1057C22⋊C4—22no—
1058C22⋊C4—22no—
1059C22⋊C4—112no—
1060C22⋊C4—112no—
1061C22⋊C4—112no—
1062C22⋊C4—222no—
1063C22⋊C4—222no—
1064C22⋊C4—222no—
1065C22⋊C4—222no—
1066C22⋊C4—222no—
1067C22⋊C4—222no—
1068C22⋊C4D4×D1112yes—
1069C42—21no—
1070C42—21no—
1071C42—111no—
1072C42—111no—
1073C42—111no—
1074C42—221no—
1075C42—221no—
1076C42—221no—
1077C42—221no—
1078C42—221no—
1079C42—221no—
1080C42C23×D1111yescharacteristic
1081C11C2×#333311yescharacteristic, complemented, Sylow
1082C23—22no—
1083C23—111no—
1084C23—112no—
1085C23—224no—
1086C23—224no—
1087C23—224no—
1088C23—222no—
1089C23—444no—
1090C23—444no—
1091C23—444no—
1092C23C2×D4×D1112yes—
1093Q8—21no—
1094Q8—21no—
1095Q8—21no—
1096Q8—81no—
1097Q8—112no—
1098Q8—224no—
1099Q8—221no—
1100Q8—221no—
1101Q8—221no—
1102Q8—442no—
1103Q8—881no—
1104Q8—882no—
1105Q8#41×D1112yes—
1106D4—22no—
1107D4—22no—
1108D4—22no—
1109D4—44no—
1110D4—42no—
1111D4—81no—
1112D4—82no—
1113D4—224no—
1114D4—222no—
1115D4—222no—
1116D4—222no—
1117D4—444no—
1118D4—444no—
1119D4—444no—
1120D4—444no—
1121D4—444no—
1122D4—442no—
1123D4—881no—
1124D4—882no—
1125D4—882no—
1126D4—882no—
1127D4—882no—
1128C2×C4—21no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—22no—
1135C2×C4—44no—
1136C2×C4—82no—
1137C2×C4—111no—
1138C2×C4—111no—
1139C2×C4—114no—
1140C2×C4—112no—
1141C2×C4—112no—
1142C2×C4—111no—
1143C2×C4—112no—
1144C2×C4—224no—
1145C2×C4—224no—
1146C2×C4—222no—
1147C2×C4—224no—
1148C2×C4—224no—
1149C2×C4—221no—
1150C2×C4—222no—
1151C2×C4—222no—
1152C2×C4—221no—
1153C2×C4—221no—
1154C2×C4—221no—
1155C2×C4—222no—
1156C2×C4—444no—
1157C2×C4—444no—
1158C2×C4—442no—
1159C2×C4—444no—
1160C2×C4—442no—
1161C2×C4—442no—
1162C2×C4—444no—
1163C2×C4—882no—
1164C2×C4—882no—
1165C2×C4—882no—
1166C2×C4C2×D4×D1111yescharacteristic
1167C2×C4C2×D4×D1112yes—
1168C2×C4C2×D4×D1111yescharacteristic
1169C2×C4C24×D1111yescharacteristic
1170C8—21no—
1171C8—21no—
1172C8—22no—
1173C8—221no—
1174C8—221no—
1175C8—222no—
1176C22—22no—
1177C22—22no—
1178C22—22no—
1179C22—42no—
1180C22—42no—
1181C22—42no—
1182C22—112no—
1183C22—112no—
1184C22—112no—
1185C22—222no—
1186C22—222no—
1187C22—222no—
1188C22—448no—
1189C22—442no—
1190C22—442no—
1191C22—442no—
1192C22—888no—
1193C22C22×D4×D1111yescharacteristic
1194C4—22no—
1195C4—22no—
1196C4—21no—
1197C4—41no—
1198C4—41no—
1199C4—42no—
1200C4—41no—
1201C4—112no—
1202C4—112no—
1203C4—222no—
1204C4—222no—
1205C4—221no—
1206C4—441no—
1207C4—441no—
1208C4—442no—
1209C4—441no—
1210C4D11×#13712yes—
1211C4C2×#41×D1111yescharacteristic
1212C4D11×H(5,𝔽2)11yescharacteristic
1213C2—42no—
1214C2—82no—
1215C2—114no—
1216C2—442no—
1217C2—882no—
1218C2D11×#54611yescharacteristic
1219C2C2×D11×#13711yescharacteristic
1220C2D11×#57611yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3333C2
socleC22×C11C23×D4
prime radicalD11×#550C2
hypercenter#3333D11
hypocenterC11C2×#3333
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3333

Complements

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

NH ≅ G/Ntype
1. D11×#554C2semidirect
3. #13080957C2semidirect
4. #13080956C2semidirect
5. #13080955C2semidirect
6. #13080954C2semidirect
7. #13080953C2semidirect
8. #13080952C2semidirect
9. #13080951C2semidirect
10. #13080950C2semidirect
11. #13080949C2semidirect
12. #13080948C2semidirect
13. #13080947C2semidirect
14. D11×#486C2semidirect
15. D11×#480C2semidirect
16. D11×#477C2semidirect
17. D11×#468C2semidirect
18. D11×#460C2semidirect
19. D11×#452C2semidirect
20. C4×Q16×D11C2semidirect
21. D11×#436C2semidirect
22. D11×#417C2semidirect
23. C11×#3333C2semidirect
25. C11×#554C22semidirect
31. #10623261C22semidirect
40. #10623166C22semidirect
47. #10623110C22semidirect
56. #10623074C22semidirect
58. #10623042C22semidirect
60. C11×#486C22semidirect
61. C11×#480C22semidirect
62. C11×#477C22semidirect
63. C11×#468C22semidirect
64. C11×#460C22semidirect
65. C11×#452C22semidirect
66. C4×C11×Q16C22semidirect
67. C11×#436C22semidirect
68. C11×#417C22semidirect
69. #10622852C22semidirect
70. #10622845C22semidirect
71. #10622800C22semidirect
72. Q16×Dic11C22semidirect
73. #10622787C22semidirect
74. #10622786C22semidirect
75. #10622776C22semidirect
76. #10622747C22semidirect
77. #10622746C22semidirect
78. #10622741C22semidirect
79. #10622704C22semidirect
80. #10622701C22semidirect
81. #10622688C22semidirect
82. #10622683C22semidirect
83. #10622662C22semidirect
84. #10622660C22semidirect
85. #10622655C22semidirect
86. #10622646C22semidirect
87. C4×#4326C22semidirect
88. C4×#4326C22semidirect
89. #10622640C22semidirect
90. #10622634C22semidirect
91. #10622625C22semidirect
92. #10622580C22semidirect
93. #10622579C22semidirect
94. #10622499C22semidirect
95. #10622495C22semidirect
96. #10622495C22semidirect
99. #10622488C22semidirect
100. #10622486C22semidirect
101. #10622463C22semidirect
102. #10622461C22semidirect
103. #10622451C22semidirect
105. #10622425C22semidirect
106. #10622423C22semidirect
107. #10622416C22semidirect
108. #10622416C22semidirect
112. #10622407C22semidirect
113. #10622403C22semidirect
114. #10622403C22semidirect
115. #10622396C22semidirect
116. #10622393C22semidirect
117. #10622387C22semidirect
118. #10622387C22semidirect
119. #10622384C22semidirect
120. #10622384C22semidirect
124. #10622375C22semidirect
125. #10622373C22semidirect
126. #10622373C22semidirect
127. #10622349C22semidirect
128. #10622346C22semidirect
129. #10622342C22semidirect
131. C4×Dic44C22semidirect
132. #10622307C22semidirect
133. #10622301C22semidirect
485. #3333D11direct (N × H)
601. #554C2×D11semidirect
630. #486C2×D11semidirect
638. #480C2×D11semidirect
644. #477C2×D11semidirect
652. #468C2×D11semidirect
658. #460C2×D11semidirect
666. #452C2×D11semidirect
674. C4×Q16C2×D11semidirect
680. #436C2×D11semidirect
691. #417C2×D11semidirect
926. D11#3333direct (N × H)
1081. C11C2×#3333semidirect

Maximal subgroups

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

subgroupindex
D11×#5542
D11×#5502
#130809572
#130809562
#130809552
#130809542
#130809532
#130809522
#130809512
#130809502
#130809492
#130809482
#130809472
D11×#4862
D11×#4802
D11×#4772
D11×#4682
D11×#4602
D11×#4522
C4×Q16×D112
D11×#4362
D11×#4172
C11×#33332
C2×#333311