Finite Group Databasebeta

← D11×#3332 #15630698

Subgroups — D11×#3332 #15630698

Order 2816.

2426 conjugacy classes of subgroups.

The subgroup lattice has 1274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#550C211yesmaximal, characteristic, complemented
2D11×#547C211yesmaximal, characteristic, complemented
3#13080946C211yesmaximal, characteristic, complemented
4#13080945C211yesmaximal, characteristic, complemented
5#13080944C211yesmaximal, characteristic, complemented
6#13080943C211yesmaximal, characteristic, complemented
7#13080942C211yesmaximal, characteristic, complemented
8#13080941C212yesmaximal, complemented
9#13080940C211yesmaximal, characteristic, complemented
10#13080939C212yesmaximal, complemented
11#13080938C212yesmaximal, complemented
12#13080937C211yesmaximal, characteristic, complemented
13#13080936C212yesmaximal, complemented
14D11×#486C211yesmaximal, characteristic, complemented
15D11×#481C212yesmaximal, complemented
16D11×#475C211yesmaximal, characteristic, complemented
17D11×#469C212yesmaximal, complemented
18D11×#459C211yesmaximal, characteristic, complemented
19D11×#449C212yesmaximal, complemented
20C4×SD16×D11C211yesmaximal, characteristic, complemented
21D11×#436C211yesmaximal, characteristic, complemented
22D11×#417C212yesmaximal, complemented
23C11×#3332C211yesmaximal, characteristic, complemented
24C2×#41×D11—21no—
25C2×#41×D11C2212yes—
26C11×#550C2211yescharacteristic, complemented
27C11×#547C2211yescharacteristic, complemented
28#10623365C2212yescomplemented
29#10623355—21no—
30C2×SD16×D11C2211yescharacteristic
31C2×D8×D11C2212yes—
32C2×M16×D11C2212yes—
33#10623257C2211yescharacteristic, complemented
34D11×C4⋊Q8C2211yescharacteristic
35#10623249—21no—
36#10623249C2211yescharacteristic, complemented
37D11×#127—21no—
38D11×#127C2211yescharacteristic
39#10623186—22no—
40D11×#123—22no—
41#10623162—21no—
42D11×C22⋊Q8—21no—
43#10623142C2212yescomplemented
44D11×#121—22no—
45D11×#121C2212yes—
46D11×#121C2212yes—
47#10623130—22no—
48#10623130C2212yescomplemented
49#10623108C2211yescharacteristic, complemented
50C4×Q8×D11C2211yescharacteristic
51#10623086C2211yescharacteristic, complemented
52#10623084—21no—
53#10623084C2211yescharacteristic, complemented
54#10623082C2211yescharacteristic, complemented
55C4×D4×D11—21no—
56C4×D4×D11C2211yescharacteristic
57C4×D4×D11C2211yescharacteristic
58#10623038C2212yescomplemented
59C2×C4⋊C4×D11C2212yes—
60C11×#486C2211yescharacteristic, complemented
61C11×#481C2212yescomplemented
62C11×#475C2211yescharacteristic, complemented
63C11×#469C2212yescomplemented
64C11×#459C2211yescharacteristic, complemented
65C11×#449C2212yescomplemented
66C4×C11×SD16C2211yescharacteristic, complemented
67C11×#436C2211yescharacteristic, complemented
68C11×#417C2212yescomplemented
69#10622851C2212yescomplemented
70#10622845C2212yescomplemented
71#10622785C2212yescomplemented
72SD16×Dic11C2211yescharacteristic, complemented
73#10622772C2212yescomplemented
74#10622771C2212yescomplemented
75#10622763C2212yescomplemented
76#10622748C2212yescomplemented
77#10622746C2212yescomplemented
78#10622741C2212yescomplemented
79#10622707C2211yescharacteristic, complemented
80#10622701C2211yescharacteristic, complemented
81#10622685C2211yescharacteristic, complemented
82#10622683C2211yescharacteristic, complemented
83#10622652C2212yescomplemented
84#10622652C2212yescomplemented
85#10622650C2212yescomplemented
86#10622647C2212yescomplemented
87C4×#4325C2211yescharacteristic, complemented
88#10622633C2211yescharacteristic, complemented
89C4×#4324C2211yescharacteristic, complemented
90#10622628C2211yescharacteristic, complemented
91#10622625C2211yescharacteristic, complemented
92#10622581C2212yescomplemented
93#10622579C2212yescomplemented
94#10622478C2212yescomplemented
95#10622476C2212yescomplemented
96#10622476C2212yescomplemented
97D11×#106C2212yes—
98D11×#106C2211yescharacteristic
99#10622467C2212yescomplemented
100#10622465C2211yescharacteristic, complemented
101#10622464C2211yescharacteristic, complemented
102#10622456C2211yescharacteristic, complemented
103#10622451C2211yescharacteristic, complemented
104D11×C4⋊C8C2211yescharacteristic
105#10622424C2212yescomplemented
106#10622416C2212yescomplemented
107#10622416C2212yescomplemented
108D11×#103C2212yes—
109D11×#103C2211yescharacteristic
110#10622404C2212yescomplemented
111#10622401C2211yescharacteristic, complemented
112#10622399C2212yescomplemented
113#10622395C2212yescomplemented
114#10622395C2212yescomplemented
115#10622394C2212yescomplemented
116#10622390C2212yescomplemented
117#10622390C2212yescomplemented
118#10622384C2212yescomplemented
119#10622384C2212yescomplemented
120D11×#102C2212yes—
121D11×#102C2212yes—
122D11×#102C2211yescharacteristic
123D11×#102C2212yes—
124#10622373C2212yescomplemented
125#10622373C2212yescomplemented
126#10622371C2211yescharacteristic, complemented
127#10622348C2212yescomplemented
128#10622347C2212yescomplemented
129#10622342C2212yescomplemented
130D11×C22⋊C8C2212yes—
131#10622307C2211yescharacteristic, complemented
132C4×#4314C2211yescharacteristic, complemented
133#10622301C2211yescharacteristic, complemented
134C4×C8×D11C2211yescharacteristic
135C2×C11×#41—21no—
136C2×C11×#41C2312yes—
137#41×D11—28no—
138#41×D11—44no—
139#41×D11—48no—
140C2×#4343—21no—
141C2×#4343C2312yes—
142C2×Q8×D11—21no—
143C2×Q8×D11C2311yescharacteristic
144C2×#4341—21no—
145C2×#4341—22no—
146C2×#4341—22no—
147C2×#4341C2312yes—
148C2×D4×D11—22no—
149C2×D4×D11—22no—
150C2×D4×D11—22no—
151C2×D4×D11—21no—
152C2×D4×D11—21no—
153C2×D4×D11D411yescharacteristic
154C2×D4×D11C2312yes—
155C2×D4×D11C2311yescharacteristic
156C2×#4339—22no—
157C2×#4339—21no—
158C2×#4339—22no—
159C2×#4339C2312yes—
160C22×C4×D11—22no—
161C22×C4×D11—22no—
162C22×C4×D11—21no—
163C22×C4×D11C2312yes—
164C2×C11×SD16C2311yescharacteristic
165C2×C11×D8C2312yes—
166C2×C11×M16C2312yes—
167C11×C4⋊Q8C2311yescharacteristic
168C11×#127—21no—
169C11×#127C2311yescharacteristic
170C11×#123—22no—
171C11×C22⋊Q8—21no—
172C11×#121—22no—
173C11×#121C2312yes—
174C11×#121C2312yes—
175C4×Q8×C11C2311yescharacteristic
176C4×D4×C11—21no—
177C4×D4×C11C2311yescharacteristic
178C4×D4×C11C2311yescharacteristic
179C2×C11×C4⋊C4C2312yes—
180#66999—21no—
181Q8×Dic11C2311yescharacteristic
182#66997—21no—
183C2×#4325C2311yescharacteristic
184#66993—21no—
185#66993—22no—
186#66993—22no—
187#66993—21no—
188#66993—21no—
189#66993—21no—
190#66993C2312yes—
191#66992—22no—
192#66992—22no—
193#66992—22no—
194#66992—22no—
195#66991—22no—
196#66991C2312yes—
197#66991C2312yes—
198#66988—22no—
199D4×Dic11—21no—
200D4×Dic11D411yescharacteristic
201D4×Dic11C2311yescharacteristic
202C2×#4324C2311yescharacteristic
203C2×#4323C2312yes—
204C2×#4323C2312yes—
205#66983—22no—
206#66983C2312yes—
207#66983C2312yes—
208#66982—22no—
209C4×C22⋊D11—22no—
210C4×C22⋊D11—21no—
211C4×C22⋊D11C2312yes—
212C2×C4⋊Dic11C2312yes—
213#66977—21no—
214C2×Dic11⋊C4—22no—
215C2×#4318C2312yes—
216SD16×D11—24no—
217D8×D11—44no—
218M16×D11—44no—
219C2×D88C2312yes—
220C2×#4314C2311yescharacteristic
221C2×#4313C2312yes—
222C2×#4313C2312yes—
223C2×C8×D11C2312yes—
224C2×C8×D11C2311yescharacteristic
225C2×C8×D11C2311yescharacteristic
226#66950—21no—
227#66949—22no—
228#66948—22no—
229#66948C2312yes—
230#66948C2312yes—
231#66947—22no—
232#66947—22no—
233#66946—21no—
234#66946D411yescharacteristic
235#66946C2311yescharacteristic
236C4⋊C4×D11—21no—
237C4⋊C4×D11—22no—
238C4⋊C4×D11—22no—
239C4⋊C4×D11—21no—
240C4⋊C4×D11D411yescharacteristic
241C4⋊C4×D11C2311yescharacteristic
242C4⋊C4×D11C2312yes—
243C4⋊C4×D11C2311yescharacteristic
244C4⋊C4×D11C2312yes—
245C4⋊C4×D11C2312yes—
246#66941—21no—
247#66941C2312yes—
248#66940—21no—
249#66940C2311yescharacteristic
250#66939—22no—
251#66937—22no—
252#66937—22no—
253#66937—22no—
254#66937—22no—
255#66936—22no—
256#66936—22no—
257(C22⋊D11)⋊C4—22no—
258(C22⋊D11)⋊C4—21no—
259(C22⋊D11)⋊C4D412yes—
260C22⋊C4×D11—22no—
261C22⋊C4×D11—21no—
262C22⋊C4×D11—22no—
263C22⋊C4×D11D412yes—
264#66931—22no—
265#66927—21no—
266#66927C2311yescharacteristic
267C4×D44—21no—
268C4×D44C2311yescharacteristic
269C4×D44C2311yescharacteristic
270C42×D11—21no—
271C42×D11C2311yescharacteristic
272#66922C2311yescharacteristic
273C4×Dic22—21no—
274C4×Dic22C2311yescharacteristic
275C11×#106C2311yescharacteristic
276C11×#106C2312yes—
277C11×C4⋊C8C2311yescharacteristic
278C11×#103C2311yescharacteristic
279C11×#103C2312yes—
280C11×#102C2311yescharacteristic
281C11×#102C2312yes—
282C11×#102C2312yes—
283C11×#102C2312yes—
284C11×C22⋊C8C2312yes—
285C4×C8×C11C2311yescharacteristic
286#66899C2311yescharacteristic
287#66899C2312yes—
288#66896C2312yes—
289#66896C2312yes—
290#66896C2311yescharacteristic
291#66896C2312yes—
292C22⋊(C11⋊C8)C2312yes—
293#66885C2312yes—
294#66885C2312yes—
295#66885C2312yes—
296#66885C2311yescharacteristic
297(C2×D11)⋊C8C2312yes—
298(C2×D11)⋊C8C2312yes—
299#66881C2312yes—
300#66881C2311yescharacteristic
301#66880C2312yes—
302#66880C2311yescharacteristic
303Dic11⋊C8C2312yes—
304C8×Dic11C2311yescharacteristic
305C8×Dic11C2311yescharacteristic
306#66874C2311yescharacteristic
307#66874C2312yes—
308#66873C2311yescharacteristic
309#66873C2312yes—
310#66873C2312yes—
311#66873C2312yes—
312#66872C2312yes—
313#66872C2311yescharacteristic
314#66872C2311yescharacteristic
315#66872C2312yes—
316C4⋊(C11⋊C8)C2311yescharacteristic
317C4×C11⋊C8C2311yescharacteristic
318C2×#3332—111nomaximal, Sylow
319C23×D11—21no—
320C23×D11—22no—
321C23×D11C2×D412yes—
322C11×#41—24no—
323C11×#41—42no—
324C11×#41—44no—
325C2×Q8×C11—21no—
326C2×Q8×C11C2411yescharacteristic
327C2×D4×C11—22no—
328C2×D4×C11—22no—
329C2×D4×C11—22no—
330C2×D4×C11—21no—
331C2×D4×C11—21no—
332C2×D4×C11C2×D411yescharacteristic
333C2×D4×C11C2412yes—
334C2×D4×C11C2411yescharacteristic
335C22×C4×C11—22no—
336C22×C4×C11—21no—
337C22×C4×C11—22no—
338C22×C4×C11C2412yes—
339C2×C22⋊D11—21no—
340C2×C22⋊D11—22no—
341C2×C22⋊D11—22no—
342C2×C22⋊D11—22no—
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⋊D11C2×D412yes—
350C22×Dic11—21no—
351C22×Dic11—22no—
352C22×Dic11—22no—
353C22×Dic11C2×D412yes—
354#4343—24no—
355#4343—42no—
356#4343—44no—
357Q8×D11—22no—
358Q8×D11—44no—
359Q8×D11#4114yescomplemented
360#4341—24no—
361#4341—42no—
362#4341—44no—
363#4341—48no—
364#4341—48no—
365D4×D11—24no—
366D4×D11—22no—
367D4×D11—24no—
368D4×D11—22no—
369D4×D11—24no—
370D4×D11—48no—
371D4×D11—48no—
372D4×D11—44no—
373D4×D11—84no—
374D4×D11—82no—
375#4339—24no—
376#4339—42no—
377#4339—48no—
378#4339—44no—
379#4339—48no—
380C2×D44—22no—
381C2×D44—22no—
382C2×D44—22no—
383C2×D44—21no—
384C2×D44—21no—
385C2×D44C2×D411yescharacteristic
386C2×D44C2412yes—
387C2×D44C2411yescharacteristic
388C2×C4×D11—24no—
389C2×C4×D11—24no—
390C2×C4×D11—22no—
391C2×C4×D11—21no—
392C2×C4×D11—21no—
393C2×C4×D11—21no—
394C2×C4×D11—21no—
395C2×C4×D11—22no—
396C2×C4×D11—22no—
397C2×C4×D11—22no—
398C2×C4×D11—21no—
399C2×C4×D11—22no—
400C2×C4×D11—48no—
401C2×C4×D11—48no—
402C2×C4×D11—44no—
403C2×C4×D11C2×D411yescharacteristic
404C2×C4×D11C2×D412yes—
405C2×C4×D11C2×D412yes—
406C2×C4×D11C2×D411yescharacteristic
407C2×C4×D11C2412yes—
408C2×C4×D11C2411yescharacteristic
409C2×Dic22—21no—
410C2×Dic22—22no—
411C2×Dic22—21no—
412C2×Dic22C2411yescharacteristic
413C11×SD16—22no—
414C11×D8—42no—
415C11×M16—42no—
416C2×C8×C11C2411yescharacteristic
417C2×C8×C11C2411yescharacteristic
418C2×C8×C11C2412yes—
419C11×C4⋊C4—21no—
420C11×C4⋊C4—21no—
421C11×C4⋊C4—22no—
422C11×C4⋊C4C2×D411yescharacteristic
423C11×C4⋊C4C2411yescharacteristic
424C11×C4⋊C4C2412yes—
425C11×C4⋊C4C2411yescharacteristic
426C11×C22⋊C4—22no—
427C11×C22⋊C4—21no—
428C11×C22⋊C4—22no—
429C11×C22⋊C4C2×D412yes—
430C42×C11—21no—
431C42×C11C2411yescharacteristic
432C22⋊Dic11—22no—
433C22⋊Dic11—21no—
434C22⋊Dic11—22no—
435C22⋊Dic11C2×D412yes—
436#4325—22no—
437#4324—22no—
438#4323—42no—
439#4323—42no—
440(C2×D11)⋊C4—22no—
441(C2×D11)⋊C4—21no—
442(C2×D11)⋊C4—22no—
443(C2×D11)⋊C4—21no—
444(C2×D11)⋊C4—22no—
445(C2×D11)⋊C4—22no—
446(C2×D11)⋊C4C2×D412yes—
447(C2×D11)⋊C4C2×D412yes—
448C4⋊Dic11—21no—
449C4⋊Dic11—21no—
450C4⋊Dic11—22no—
451C4⋊Dic11C2×D411yescharacteristic
452C4⋊Dic11C2411yescharacteristic
453C4⋊Dic11C2412yes—
454C4⋊Dic11C2411yescharacteristic
455Dic11⋊C4—21no—
456Dic11⋊C4—21no—
457Dic11⋊C4—22no—
458Dic11⋊C4—21no—
459Dic11⋊C4—22no—
460Dic11⋊C4—22no—
461Dic11⋊C4—22no—
462Dic11⋊C4—21no—
463Dic11⋊C4C2×D412yes—
464C4×Dic11—21no—
465C4×Dic11—21no—
466C4×Dic11—21no—
467C4×Dic11C2×D411yescharacteristic
468C4×Dic11C2×D411yescharacteristic
469C4×Dic11C2411yescharacteristic
470#4318—42no—
471C2×C11⋊C8C2411yescharacteristic
472C2×C11⋊C8C2411yescharacteristic
473C2×C11⋊C8C2412yes—
474D88—42no—
475#4314—22no—
476#4313—42no—
477#4313—42no—
478C8×D11—22no—
479C8×D11—22no—
480C8×D11—24no—
481C2×#550—111no—
482C2×#547—111no—
483#3332—111no—
484#3332—112no—
485#3332—111no—
486#3332—112no—
487#3332—111no—
488#3332—112no—
489#3332—111no—
490#3332—111no—
491#3332—112no—
492#3332—111no—
493#3332—111no—
494#3332D1111yescharacteristic, direct product factor
495C2×#486—111no—
496C2×#481—112no—
497C2×#475—111no—
498C2×#469—112no—
499C2×#459—111no—
500C2×#449—112no—
501C2×C4×SD16—111no—
502C2×#436—111no—
503C2×#417—112no—
504C23×C11—21no—
505C23×C11—22no—
506C23×C11C22×D412yes—
507C22×D11—24no—
508C22×D11—24no—
509C22×D11—24no—
510C22×D11—21no—
511C22×D11—22no—
512C22×D11—44no—
513C22×D11—42no—
514C22×D11—42no—
515C22×D11—44no—
516C22×D11—44no—
517C22×D11—42no—
518C22×D11C22×D412yes—
519C22×D11C22×D411yescharacteristic
520Q8×C11—21no—
521Q8×C11—42no—
522Q8×C11C2×#4112yescomplemented
523D4×C11—22no—
524D4×C11—21no—
525D4×C11—22no—
526D4×C11—21no—
527D4×C11—22no—
528D4×C11—44no—
529D4×C11—44no—
530D4×C11—42no—
531D4×C11—81no—
532D4×C11—82no—
533C2×C4×C11—21no—
534C2×C4×C11—22no—
535C2×C4×C11—22no—
536C2×C4×C11—21no—
537C2×C4×C11—22no—
538C2×C4×C11—21no—
539C2×C4×C11—44no—
540C2×C4×C11—44no—
541C2×C4×C11—42no—
542C2×C4×C11C22×D411yescharacteristic
543C2×C4×C11C22×D412yes—
544C2×C4×C11C22×D411yescharacteristic
545C2×C4×C11C2511yescharacteristic
546C22⋊D11—24no—
547C22⋊D11—44no—
548C22⋊D11—44no—
549C22⋊D11—44no—
550C22⋊D11—44no—
551C22⋊D11—44no—
552C22⋊D11—42no—
553C22⋊D11—44no—
554C22⋊D11—82no—
555C22⋊D11—82no—
556C22⋊D11—82no—
557C2×Dic11—21no—
558C2×Dic11—24no—
559C2×Dic11—21no—
560C2×Dic11—22no—
561C2×Dic11—21no—
562C2×Dic11—44no—
563C2×Dic11—44no—
564C2×Dic11—42no—
565C2×Dic11C22×D411yescharacteristic
566C2×Dic11C22×D412yes—
567C2×Dic11C22×D411yescharacteristic
568C2×Dic11C22×D411yescharacteristic
569D44—22no—
570D44—21no—
571D44—22no—
572D44—21no—
573D44—22no—
574D44—44no—
575D44—44no—
576D44—42no—
577D44—81no—
578D44—82no—
579C4×D11—24no—
580C4×D11—24no—
581C4×D11—22no—
582C4×D11—22no—
583C4×D11—22no—
584C4×D11—24no—
585C4×D11—44no—
586C4×D11—44no—
587C4×D11—44no—
588C4×D11—44no—
589C4×D11—42no—
590C4×D11—44no—
591C4×D11—42no—
592C4×D11—42no—
593C4×D11—42no—
594C4×D11AGL(1,ℤ/8)14yes—
595C4×D11C2×#4112yes—
596C4×D11H(5,𝔽2)12yes—
597Dic22—21no—
598Dic22—24no—
599Dic22—42no—
600Dic22—44no—
601Dic22C2×#4112yescomplemented
602C8×C11—21no—
603C8×C11—21no—
604C8×C11—22no—
605C11⋊C8—21no—
606C11⋊C8—21no—
607C11⋊C8—22no—
608C22×#41—112no—
609C22×#41—221no—
610C22×SD16—111no—
611C22×D8—112no—
612C22×M16—112no—
613#550—112no—
614#550—111no—
615#550—112no—
616#550—111no—
617#550—111no—
618#550—221no—
619#550—222no—
620#550—221no—
621#550C2×D1111yescharacteristic, complemented
622#547—111no—
623#547—112no—
624#547—111no—
625#547—111no—
626#547—112no—
627#547—221no—
628#547—222no—
629#547—221no—
630#547C2×D1111yescharacteristic, complemented
631C2×C4⋊Q8—111no—
632C2×#127—111no—
633C2×#127—221no—
634C2×#123—222no—
635C2×C22⋊Q8—221no—
636C2×#121—112no—
637C2×#121—112no—
638C2×#121—222no—
639C2×C4×Q8—111no—
640C2×C4×D4—111no—
641C2×C4×D4—111no—
642C2×C4×D4—221no—
643C22×C4⋊C4—112no—
644#486—111no—
645#486—111no—
646#486—112no—
647#486—112no—
648#486—111no—
649#486C2×D1111yescharacteristic, complemented
650#481—112no—
651#481—112no—
652#481—112no—
653#481—112no—
654#481—112no—
655#481—112no—
656#481—112no—
657#481C2×D1112yescomplemented
658#475—111no—
659#475—111no—
660#475—112no—
661#475—111no—
662#475—112no—
663#475C2×D1111yescharacteristic, complemented
664#469—112no—
665#469—112no—
666#469—112no—
667#469—112no—
668#469—112no—
669#469—112no—
670#469—112no—
671#469C2×D1112yescomplemented
672#459—112no—
673#459—111no—
674#459—111no—
675#459—111no—
676#459—112no—
677#459C2×D1111yescharacteristic, complemented
678#449—112no—
679#449—112no—
680#449—112no—
681#449—112no—
682#449—112no—
683#449—112no—
684#449—112no—
685#449C2×D1112yescomplemented
686C4×SD16—111no—
687C4×SD16—111no—
688C4×SD16—111no—
689C4×SD16—111no—
690C4×SD16—111no—
691C4×SD16—111no—
692C4×SD16—111no—
693C4×SD16C2×D1111yescharacteristic, complemented
694#436—112no—
695#436—111no—
696#436—111no—
697#436—112no—
698#436—111no—
699#436C2×D1111yescharacteristic, complemented
700C2×#106—112no—
701C2×#106—111no—
702C2×C4⋊C8—111no—
703#417—112no—
704#417—112no—
705#417—112no—
706#417—112no—
707#417—112no—
708#417—112no—
709#417—112no—
710#417C2×D1112yescomplemented
711C2×#103—112no—
712C2×#103—111no—
713C2×#102—112no—
714C2×#102—112no—
715C2×#102—112no—
716C2×#102—111no—
717C2×C22⋊C8—112no—
718C2×C4×C8—111no—
719C22×C11—22no—
720C22×C11—22no—
721C22×C11—22no—
722C22×C11—42no—
723C22×C11—41no—
724C22×C11—41no—
725C22×C11—42no—
726C22×C11—42no—
727C22×C11—41no—
728C22×C11C23×D411yescharacteristic
729C2×D11—22no—
730C2×D11—22no—
731C2×D11—22no—
732C2×D11—48no—
733C2×D11—42no—
734C2×D11—41no—
735C2×D11—41no—
736C2×D11—42no—
737C2×D11—41no—
738C2×D11—42no—
739C2×D11—88no—
740C2×D11—84no—
741C2×D11#54612yes—
742C2×D11C2×AGL(1,ℤ/8)12yes—
743C2×D11#57712yes—
744C4×C11—22no—
745C4×C11—22no—
746C4×C11—21no—
747C4×C11—41no—
748C4×C11—42no—
749C4×C11—41no—
750C4×C11C2×AGL(1,ℤ/8)12yes—
751C4×C11C22×#4111yescharacteristic
752C4×C11C2×H(5,𝔽2)11yescharacteristic
753Dic11—22no—
754Dic11—22no—
755Dic11—21no—
756Dic11—42no—
757Dic11—41no—
758Dic11—41no—
759Dic11#54612yes—
760Dic11C2×AGL(1,ℤ/8)12yes—
761C2×#41—21no—
762C2×#41—112no—
763C2×#41—112no—
764C2×#41—112no—
765C2×#41—222no—
766C2×#41—222no—
767C2×#41—221no—
768C2×#41—222no—
769C2×#41—222no—
770C2×#41—221no—
771C2×#41—221no—
772C2×#41—228no—
773C2×#41—444no—
774C2×#41—448no—
775C2×#41C22×D1112yes—
776C22×Q8—111no—
777C22×Q8—221no—
778C22×D4—111no—
779C22×D4—111no—
780C22×D4—112no—
781C22×D4—221no—
782C22×D4—221no—
783C22×D4—222no—
784C22×D4—222no—
785C22×D4—222no—
786C23×C4—112no—
787C23×C4—221no—
788C23×C4—222no—
789C23×C4—222no—
790C2×SD16—111no—
791C2×SD16—111no—
792C2×SD16—111no—
793C2×SD16—224no—
794C2×SD16C22×D1111yescharacteristic
795C2×D8—112no—
796C2×D8—112no—
797C2×D8—112no—
798C2×D8—444no—
799C2×D8C22×D1112yes—
800C2×M16—112no—
801C2×M16—112no—
802C2×M16—112no—
803C2×M16—444no—
804C2×M16C22×D1112yes—
805C22×C8—111no—
806C22×C8—112no—
807C22×C8—111no—
808C4⋊Q8—112no—
809C4⋊Q8—111no—
810C4⋊Q8—221no—
811C4⋊Q8—221no—
812C4⋊Q8C22×D1111yescharacteristic
813#127—21no—
814#127—112no—
815#127—111no—
816#127—221no—
817#127—221no—
818#127—221no—
819#127—222no—
820#127—222no—
821#127—221no—
822#127—221no—
823#127C22×D1111yescharacteristic
824#123—22no—
825#123—222no—
826#123—222no—
827#123—222no—
828#123—222no—
829#123—222no—
830#123—222no—
831#123—222no—
832C22⋊Q8—21no—
833C22⋊Q8—222no—
834C22⋊Q8—222no—
835C22⋊Q8—221no—
836C22⋊Q8—221no—
837C22⋊Q8—221no—
838#121—22no—
839#121—112no—
840#121—112no—
841#121—112no—
842#121—112no—
843#121—112no—
844#121—112no—
845#121—222no—
846#121—222no—
847#121—222no—
848#121—222no—
849#121—222no—
850#121—222no—
851#121—222no—
852#121—222no—
853#121—222no—
854#121—222no—
855#121—222no—
856#121C22×D1112yes—
857#121C22×D1112yes—
858C4×Q8—111no—
859C4×Q8—111no—
860C4×Q8—111no—
861C4×Q8—221no—
862C4×Q8—221no—
863C4×Q8C22×D1111yescharacteristic
864C4×D4—21no—
865C4×D4—111no—
866C4×D4—112no—
867C4×D4—111no—
868C4×D4—112no—
869C4×D4—111no—
870C4×D4—111no—
871C4×D4—111no—
872C4×D4—111no—
873C4×D4—221no—
874C4×D4—221no—
875C4×D4—221no—
876C4×D4—222no—
877C4×D4—222no—
878C4×D4—221no—
879C4×D4—221no—
880C4×D4C22×D1111yescharacteristic
881C4×D4C22×D1111yescharacteristic
882C2×C4⋊C4—111no—
883C2×C4⋊C4—112no—
884C2×C4⋊C4—111no—
885C2×C4⋊C4—112no—
886C2×C4⋊C4—112no—
887C2×C4⋊C4—112no—
888C2×C4⋊C4—111no—
889C2×C4⋊C4—222no—
890C2×C4⋊C4—222no—
891C2×C4⋊C4—221no—
892C2×C4⋊C4—221no—
893C2×C4⋊C4—222no—
894C2×C4⋊C4C22×D1112yes—
895C2×C22⋊C4—112no—
896C2×C22⋊C4—221no—
897C2×C22⋊C4—222no—
898C2×C22⋊C4—222no—
899C2×C42—111no—
900C2×C42—221no—
901#106—111no—
902#106—112no—
903#106—111no—
904#106—111no—
905#106—112no—
906#106—112no—
907#106C22×D1111yescharacteristic
908#106C22×D1112yes—
909C4⋊C8—112no—
910C4⋊C8—111no—
911C4⋊C8C22×D1111yescharacteristic
912#103—111no—
913#103—112no—
914#103—111no—
915#103—112no—
916#103—111no—
917#103—112no—
918#103C22×D1111yescharacteristic
919#103C22×D1112yes—
920#102—112no—
921#102—112no—
922#102—111no—
923#102—112no—
924#102—112no—
925#102—112no—
926#102—111no—
927#102—112no—
928#102—112no—
929#102—112no—
930#102—111no—
931#102—112no—
932#102C22×D1112yes—
933#102C22×D1112yes—
934#102C22×D1111yescharacteristic
935#102C22×D1112yes—
936C22⋊C8—112no—
937C22⋊C8—112no—
938C22⋊C8—112no—
939C22⋊C8C22×D1112yes—
940C4×C8—111no—
941C4×C8—111no—
942C4×C8—111no—
943C4×C8C22×D1111yescharacteristic
944C2×C11—42no—
945C2×C11—82no—
946C2×C11—81no—
947C2×C11C2×#54611yescharacteristic
948C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
949C2×C11C2×#57711yescharacteristic
950D11—42no—
951D11—82no—
952D11—81no—
953D11#333214yesdirect product factor
954C24—112no—
955C24—221no—
956C24—222no—
957#41—24no—
958#41—42no—
959#41—44no—
960#41—224no—
961#41—224no—
962#41—224no—
963#41—442no—
964#41—448no—
965#41—448no—
966#41—444no—
967#41—442no—
968#41—448no—
969#41—442no—
970#41—444no—
971#41—448no—
972#41—444no—
973C2×Q8—21no—
974C2×Q8—114no—
975C2×Q8—111no—
976C2×Q8—221no—
977C2×Q8—222no—
978C2×Q8—222no—
979C2×Q8—221no—
980C2×Q8—444no—
981C2×Q8C23×D1111yescharacteristic
982C2×D4—22no—
983C2×D4—22no—
984C2×D4—22no—
985C2×D4—21no—
986C2×D4—21no—
987C2×D4—112no—
988C2×D4—111no—
989C2×D4—112no—
990C2×D4—111no—
991C2×D4—222no—
992C2×D4—222no—
993C2×D4—222no—
994C2×D4—224no—
995C2×D4—222no—
996C2×D4—224no—
997C2×D4—222no—
998C2×D4—224no—
999C2×D4—221no—
1000C2×D4—222no—
1001C2×D4—222no—
1002C2×D4—222no—
1003C2×D4—222no—
1004C2×D4—222no—
1005C2×D4—222no—
1006C2×D4—222no—
1007C2×D4—222no—
1008C2×D4—222no—
1009C2×D4—221no—
1010C2×D4—221no—
1011C2×D4—444no—
1012C2×D4—448no—
1013C2×D4—448no—
1014C2×D4—882no—
1015C2×D4—884no—
1016C2×D4D4×D1111yescharacteristic
1017C2×D4C23×D1112yes—
1018C2×D4C23×D1111yescharacteristic
1019C22×C4—22no—
1020C22×C4—22no—
1021C22×C4—21no—
1022C22×C4—111no—
1023C22×C4—111no—
1024C22×C4—112no—
1025C22×C4—111no—
1026C22×C4—112no—
1027C22×C4—112no—
1028C22×C4—112no—
1029C22×C4—224no—
1030C22×C4—224no—
1031C22×C4—221no—
1032C22×C4—222no—
1033C22×C4—221no—
1034C22×C4—221no—
1035C22×C4—221no—
1036C22×C4—222no—
1037C22×C4—222no—
1038C22×C4—222no—
1039C22×C4—221no—
1040C22×C4—222no—
1041C22×C4—222no—
1042C22×C4—221no—
1043C22×C4—222no—
1044C22×C4—444no—
1045C22×C4—448no—
1046C22×C4—448no—
1047C22×C4C23×D1112yes—
1048SD16—22no—
1049SD16—222no—
1050SD16—222no—
1051SD16—222no—
1052D8—42no—
1053D8—442no—
1054D8—442no—
1055D8—442no—
1056M16—42no—
1057M16—442no—
1058M16—442no—
1059M16—442no—
1060C2×C8—111no—
1061C2×C8—111no—
1062C2×C8—112no—
1063C2×C8—222no—
1064C2×C8—224no—
1065C2×C8—222no—
1066C2×C8C23×D1111yescharacteristic
1067C2×C8C23×D1111yescharacteristic
1068C2×C8C23×D1112yes—
1069C4⋊C4—22no—
1070C4⋊C4—21no—
1071C4⋊C4—21no—
1072C4⋊C4—112no—
1073C4⋊C4—111no—
1074C4⋊C4—111no—
1075C4⋊C4—112no—
1076C4⋊C4—111no—
1077C4⋊C4—221no—
1078C4⋊C4—222no—
1079C4⋊C4—222no—
1080C4⋊C4—222no—
1081C4⋊C4—221no—
1082C4⋊C4—221no—
1083C4⋊C4—221no—
1084C4⋊C4—222no—
1085C4⋊C4—222no—
1086C4⋊C4—221no—
1087C4⋊C4—221no—
1088C4⋊C4D4×D1111yescharacteristic
1089C4⋊C4C23×D1111yescharacteristic
1090C4⋊C4C23×D1112yes—
1091C4⋊C4C23×D1111yescharacteristic
1092C22⋊C4—22no—
1093C22⋊C4—21no—
1094C22⋊C4—22no—
1095C22⋊C4—112no—
1096C22⋊C4—112no—
1097C22⋊C4—112no—
1098C22⋊C4—221no—
1099C22⋊C4—222no—
1100C22⋊C4—222no—
1101C22⋊C4—221no—
1102C22⋊C4—222no—
1103C22⋊C4—222no—
1104C22⋊C4—221no—
1105C22⋊C4—222no—
1106C22⋊C4—222no—
1107C22⋊C4D4×D1112yes—
1108C42—21no—
1109C42—111no—
1110C42—111no—
1111C42—111no—
1112C42—221no—
1113C42—221no—
1114C42—221no—
1115C42C23×D1111yescharacteristic
1116C11C2×#333211yescharacteristic, complemented, Sylow
1117C23—21no—
1118C23—22no—
1119C23—111no—
1120C23—112no—
1121C23—224no—
1122C23—224no—
1123C23—224no—
1124C23—221no—
1125C23—222no—
1126C23—444no—
1127C23—442no—
1128C23—442no—
1129C23—444no—
1130C23—444no—
1131C23—442no—
1132C23C2×D4×D1112yes—
1133Q8—21no—
1134Q8—42no—
1135Q8—112no—
1136Q8—224no—
1137Q8—221no—
1138Q8—444no—
1139Q8—442no—
1140Q8#41×D1112yescomplemented
1141D4—22no—
1142D4—21no—
1143D4—22no—
1144D4—21no—
1145D4—22no—
1146D4—44no—
1147D4—44no—
1148D4—42no—
1149D4—81no—
1150D4—82no—
1151D4—224no—
1152D4—222no—
1153D4—221no—
1154D4—222no—
1155D4—221no—
1156D4—222no—
1157D4—444no—
1158D4—444no—
1159D4—444no—
1160D4—442no—
1161D4—444no—
1162D4—444no—
1163D4—444no—
1164D4—444no—
1165D4—444no—
1166D4—442no—
1167D4—881no—
1168D4—882no—
1169D4—882no—
1170D4—882no—
1171D4—882no—
1172C2×C4—21no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—22no—
1178C2×C4—44no—
1179C2×C4—44no—
1180C2×C4—42no—
1181C2×C4—111no—
1182C2×C4—111no—
1183C2×C4—114no—
1184C2×C4—112no—
1185C2×C4—112no—
1186C2×C4—111no—
1187C2×C4—112no—
1188C2×C4—224no—
1189C2×C4—224no—
1190C2×C4—222no—
1191C2×C4—224no—
1192C2×C4—224no—
1193C2×C4—221no—
1194C2×C4—222no—
1195C2×C4—222no—
1196C2×C4—221no—
1197C2×C4—221no—
1198C2×C4—222no—
1199C2×C4—444no—
1200C2×C4—444no—
1201C2×C4—442no—
1202C2×C4—442no—
1203C2×C4—444no—
1204C2×C4—442no—
1205C2×C4—444no—
1206C2×C4—444no—
1207C2×C4—442no—
1208C2×C4—444no—
1209C2×C4—444no—
1210C2×C4—442no—
1211C2×C4C2×D4×D1111yescharacteristic
1212C2×C4C2×D4×D1112yes—
1213C2×C4C2×D4×D1111yescharacteristic
1214C2×C4C24×D1111yescharacteristic
1215C8—21no—
1216C8—21no—
1217C8—22no—
1218C8—221no—
1219C8—221no—
1220C8—222no—
1221C22—22no—
1222C22—22no—
1223C22—22no—
1224C22—42no—
1225C22—41no—
1226C22—41no—
1227C22—42no—
1228C22—42no—
1229C22—41no—
1230C22—112no—
1231C22—112no—
1232C22—112no—
1233C22—222no—
1234C22—222no—
1235C22—222no—
1236C22—448no—
1237C22—442no—
1238C22—441no—
1239C22—441no—
1240C22—442no—
1241C22—442no—
1242C22—441no—
1243C22—888no—
1244C22—884no—
1245C22C22×D4×D1111yescharacteristic
1246C4—22no—
1247C4—22no—
1248C4—21no—
1249C4—41no—
1250C4—42no—
1251C4—41no—
1252C4—112no—
1253C4—112no—
1254C4—222no—
1255C4—222no—
1256C4—221no—
1257C4—441no—
1258C4—442no—
1259C4—441no—
1260C4D11×AGL(1,ℤ/8)12yes—
1261C4C2×#41×D1111yescharacteristic
1262C4D11×H(5,𝔽2)11yescharacteristic
1263C2—42no—
1264C2—82no—
1265C2—81no—
1266C2—114no—
1267C2—442no—
1268C2—882no—
1269C2—881no—
1270C2D11×#54611yescharacteristic
1271C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
1272C2D11×#57711yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3332C2
socleC22×C11C23×D4
hypercenter#3332D11
hypocenterC11C2×#3332
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3332

Complements

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

NH ≅ G/Ntype
1. D11×#550C2semidirect
2. D11×#547C2semidirect
3. #13080946C2semidirect
4. #13080945C2semidirect
5. #13080944C2semidirect
6. #13080943C2semidirect
7. #13080942C2semidirect
8. #13080941C2semidirect
9. #13080940C2semidirect
10. #13080939C2semidirect
11. #13080938C2semidirect
12. #13080937C2semidirect
13. #13080936C2semidirect
14. D11×#486C2semidirect
15. D11×#481C2semidirect
16. D11×#475C2semidirect
17. D11×#469C2semidirect
18. D11×#459C2semidirect
19. D11×#449C2semidirect
20. C4×SD16×D11C2semidirect
21. D11×#436C2semidirect
22. D11×#417C2semidirect
23. C11×#3332C2semidirect
26. C11×#550C22semidirect
27. C11×#547C22semidirect
28. #10623365C22semidirect
33. #10623257C22semidirect
36. #10623249C22semidirect
43. #10623142C22semidirect
48. #10623130C22semidirect
49. #10623108C22semidirect
51. #10623086C22semidirect
53. #10623084C22semidirect
54. #10623082C22semidirect
58. #10623038C22semidirect
60. C11×#486C22semidirect
61. C11×#481C22semidirect
62. C11×#475C22semidirect
63. C11×#469C22semidirect
64. C11×#459C22semidirect
65. C11×#449C22semidirect
66. C4×C11×SD16C22semidirect
67. C11×#436C22semidirect
68. C11×#417C22semidirect
69. #10622851C22semidirect
70. #10622845C22semidirect
71. #10622785C22semidirect
72. SD16×Dic11C22semidirect
73. #10622772C22semidirect
74. #10622771C22semidirect
75. #10622763C22semidirect
76. #10622748C22semidirect
77. #10622746C22semidirect
78. #10622741C22semidirect
79. #10622707C22semidirect
80. #10622701C22semidirect
81. #10622685C22semidirect
82. #10622683C22semidirect
83. #10622652C22semidirect
84. #10622652C22semidirect
85. #10622650C22semidirect
86. #10622647C22semidirect
87. C4×#4325C22semidirect
88. #10622633C22semidirect
89. C4×#4324C22semidirect
90. #10622628C22semidirect
91. #10622625C22semidirect
92. #10622581C22semidirect
93. #10622579C22semidirect
94. #10622478C22semidirect
95. #10622476C22semidirect
96. #10622476C22semidirect
99. #10622467C22semidirect
100. #10622465C22semidirect
101. #10622464C22semidirect
102. #10622456C22semidirect
103. #10622451C22semidirect
105. #10622424C22semidirect
106. #10622416C22semidirect
107. #10622416C22semidirect
110. #10622404C22semidirect
111. #10622401C22semidirect
112. #10622399C22semidirect
113. #10622395C22semidirect
114. #10622395C22semidirect
115. #10622394C22semidirect
116. #10622390C22semidirect
117. #10622390C22semidirect
118. #10622384C22semidirect
119. #10622384C22semidirect
124. #10622373C22semidirect
125. #10622373C22semidirect
126. #10622371C22semidirect
127. #10622348C22semidirect
128. #10622347C22semidirect
129. #10622342C22semidirect
131. #10622307C22semidirect
132. C4×#4314C22semidirect
133. #10622301C22semidirect
359. Q8×D11#41semidirect
494. #3332D11direct (N × H)
522. Q8×C11C2×#41semidirect
601. Dic22C2×#41semidirect
621. #550C2×D11semidirect
630. #547C2×D11semidirect
649. #486C2×D11semidirect
657. #481C2×D11semidirect
663. #475C2×D11semidirect
671. #469C2×D11semidirect
677. #459C2×D11semidirect
685. #449C2×D11semidirect
693. C4×SD16C2×D11semidirect
699. #436C2×D11semidirect
710. #417C2×D11semidirect
953. D11#3332direct (N × H)
1116. C11C2×#3332semidirect
1140. Q8#41×D11semidirect

Maximal subgroups

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

subgroupindex
D11×#5502
D11×#5472
#130809462
#130809452
#130809442
#130809432
#130809422
#130809412
#130809402
#130809392
#130809382
#130809372
#130809362
D11×#4862
D11×#4812
D11×#4752
D11×#4692
D11×#4592
D11×#4492
C4×SD16×D112
D11×#4362
D11×#4172
C11×#33322
C2×#333211