Finite Group Databasebeta

← D11×#3098 #15621616

Subgroups — D11×#3098 #15621616

Order 2816.

2234 conjugacy classes of subgroups.

The subgroup lattice has 1262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#537C211yesmaximal, characteristic
2D11×#520C211yesmaximal, characteristic, complemented
3#13078599C211yesmaximal, characteristic, complemented
4#13078598C211yesmaximal, characteristic, complemented
5#13078597C212yesmaximal, complemented
6#13078596C211yesmaximal, characteristic, complemented
7#13078595C212yesmaximal, complemented
8#13078594C211yesmaximal, characteristic, complemented
9#13078593C211yesmaximal, characteristic, complemented
10#13078592C211yesmaximal, characteristic, complemented
11#13078591C212yesmaximal, complemented
12#13078590C211yesmaximal, characteristic, complemented
13#13078589C212yesmaximal, complemented
14D11×#484C212yesmaximal, complemented
15D11×#485C212yesmaximal, complemented
16D11×#482C212yesmaximal, complemented
17D11×#480C212yesmaximal, complemented
18D11×#428C211yesmaximal, characteristic, complemented
19C2×D11×#107C211yesmaximal, characteristic, complemented
20D11×#417C211yesmaximal, characteristic, complemented
21D11×#416C211yesmaximal, characteristic, complemented
22D11×#408C211yesmaximal, characteristic, complemented
23C11×#3098C211yesmaximal, characteristic, complemented
24C2×#41×D11C2211yescharacteristic
25C2×#41×D11C2211yescharacteristic
26C11×#537C2211yescharacteristic
27C11×#520C2211yescharacteristic, complemented
28#10623364C2211yescharacteristic
29#10623364C2211yescharacteristic
30#10623358C2211yescharacteristic, complemented
31C2×M16×D11C2211yescharacteristic
32C22×C8×D11C2211yescharacteristic
33#10623160—21no—
34#10623160C2212yes—
35D11×C22⋊Q8—21no—
36D11×C22⋊Q8C2212yes—
37#10623139—21no—
38#10623139C2212yes—
39D11×#121—21no—
40D11×#121—22no—
41D11×#121C2212yes—
42#10623128—22no—
43#10623105—21no—
44C4×Q8×D11—21no—
45#10623077—22no—
46#10623077—21no—
47C4×D4×D11—22no—
48C4×D4×D11—21no—
49#10623054C2212yescomplemented
50#10623054C2211yescharacteristic, complemented
51D11×#117C2211yescharacteristic
52D11×#117C2212yes—
53#10623041C2211yescharacteristic
54#10623035C2212yescomplemented
55#10623035C2211yescharacteristic, complemented
56C2×C4⋊C4×D11C2211yescharacteristic
57C2×C4⋊C4×D11C2211yescharacteristic
58C2×C4⋊C4×D11C2212yes—
59C11×#485C2212yescomplemented
60C11×#484C2212yescomplemented
61C11×#482C2212yescomplemented
62C11×#480C2212yescomplemented
63C11×#428C2211yescharacteristic, complemented
64C2×C11×#107C2211yescharacteristic, complemented
65C11×#417C2211yescharacteristic, complemented
66C11×#416C2211yescharacteristic, complemented
67C11×#408C2211yescharacteristic, complemented
68#10622847C2211yescharacteristic, complemented
69#10622846C2211yescharacteristic, complemented
70#10622845C2211yescharacteristic, complemented
71#10622746C2211yescharacteristic, complemented
72#10622742C2211yescharacteristic, complemented
73#10622734C2211yescharacteristic, complemented
74#10622726C2211yescharacteristic, complemented
75#10622723C2211yescharacteristic, complemented
76C2×#66882C2211yescharacteristic, complemented
77#10622658C2212yescomplemented
78#10622657C2212yescomplemented
79#10622648C2212yescomplemented
80#10622646C2212yescomplemented
81#10622616C2212yescomplemented
82#10622615C2211yescharacteristic, complemented
83#10622609C2212yescomplemented
84#10622608C2211yescharacteristic, complemented
85#10622583C2212yescomplemented
86#10622580C2212yescomplemented
87#10622579C2211yescharacteristic, complemented
88#10622577C2211yescharacteristic, complemented
89C2×#66871C2211yescharacteristic, complemented
90C2×#66871C2211yescharacteristic, complemented
91#10622501C2212yescomplemented
92#10622498C2212yescomplemented
93#10622497C2212yescomplemented
94#10622497C2212yescomplemented
95#10622495C2212yescomplemented
96#10622495C2212yescomplemented
97#10622494C2212yescomplemented
98D11×#107C2212yes—
99D11×#107C2212yes—
100D11×#107C2212yes—
101D11×#107C2212yescomplemented
102D11×#107C2212yescomplemented
103#10622480C2212yescomplemented
104#10622479C2212yescomplemented
105#10622474C2212yescomplemented
106D11×#106C2212yes—
107#10622428C2212yescomplemented
108#10622427C2212yescomplemented
109#10622422C2212yescomplemented
110#10622422C2212yescomplemented
111#10622417C2211yescharacteristic, complemented
112#10622417C2211yescharacteristic, complemented
113#10622416C2212yescomplemented
114D11×#103C2211yescharacteristic
115D11×#103C2211yescharacteristic
116D11×#103C2212yes—
117#10622397C2212yescomplemented
118#10622392C2212yescomplemented
119#10622387C2212yescomplemented
120#10622387C2212yescomplemented
121#10622385C2211yescharacteristic, complemented
122#10622385C2211yescharacteristic, complemented
123#10622384C2212yescomplemented
124D11×#102C2211yescharacteristic
125D11×#102C2211yescharacteristic
126D11×#102C2212yes—
127#10622350C2212yescomplemented
128#10622349C2212yescomplemented
129#10622340C2212yescomplemented
130#10622340C2212yescomplemented
131D11×C22⋊C8C2212yes—
132D11×C22⋊C8C2212yes—
133#10622336C2212yescomplemented
134#10622335C2212yescomplemented
135C2×C11×#41C2311yescharacteristic
136C2×C11×#41C2311yescharacteristic
137#41×D11—24no—
138#41×D11—24no—
139#41×D11—24no—
140#41×D11—24no—
141C2×#4343D411yescharacteristic
142C2×#4343C2311yescharacteristic
143C2×Q8×D11D411yescharacteristic
144C2×Q8×D11C2311yescharacteristic
145C2×#4341—21no—
146C2×#4341D412yes—
147C2×#4341D411yescharacteristic
148C2×#4341C2311yescharacteristic
149C2×D4×D11—21no—
150C2×D4×D11—22no—
151C2×D4×D11D412yes—
152C2×D4×D11D411yescharacteristic
153C2×D4×D11C2311yescharacteristic
154C2×#4339—21no—
155C2×#4339C2311yescharacteristic
156C2×#4339C2312yes—
157C2×#4339C2311yescharacteristic
158C22×C4×D11—22no—
159C22×C4×D11—21no—
160C22×C4×D11—21no—
161C22×C4×D11—21no—
162C22×C4×D11C2312yes—
163C22×C4×D11C2311yescharacteristic
164C2×C11×M16C2311yescharacteristic
165C22×C8×C11C2311yescharacteristic
166C11×C22⋊Q8—21no—
167C11×C22⋊Q8C2312yes—
168C11×#121—22no—
169C11×#121—21no—
170C11×#121C2312yes—
171C4×Q8×C11—21no—
172C4×D4×C11—21no—
173C4×D4×C11—22no—
174C11×#117C2311yescharacteristic
175C11×#117C2312yes—
176C2×C11×C4⋊C4C2311yescharacteristic
177C2×C11×C4⋊C4C2312yes—
178C2×C11×C4⋊C4C2311yescharacteristic
179#66999—21no—
180#66999C2312yes—
181Q8×Dic11—21no—
182#66992—22no—
183#66992—22no—
184#66992—22no—
185#66992—22no—
186#66991—21no—
187#66991—22no—
188#66991C2312yes—
189D4×Dic11—21no—
190D4×Dic11—22no—
191#66983—22no—
192#66983—21no—
193#66983C2312yes—
194C4×C22⋊D11—22no—
195C4×C22⋊D11—22no—
196C4×C22⋊D11—22no—
197#66979C2311yescharacteristic
198#66979C2312yes—
199C2×C4⋊Dic11C2311yescharacteristic
200C2×C4⋊Dic11C2311yescharacteristic
201C2×C4⋊Dic11C2312yes—
202#66977—21no—
203#66977C2312yes—
204C2×Dic11⋊C4—22no—
205C2×Dic11⋊C4—21no—
206C2×Dic11⋊C4—21no—
207C2×#4318C2311yescharacteristic
208C22×C11⋊C8C2311yescharacteristic
209M16×D11—24no—
210C2×#4313C2312yes—
211C2×C8×D11—24no—
212C2×C8×D11C2312yes—
213C2×C8×D11C2311yescharacteristic
214C2×C8×D11C2311yescharacteristic
215C2×C8×D11C2311yescharacteristic
216C2×C8×D11C2311yescharacteristic
217#66950—21no—
218#66950C2312yes—
219#66949—22no—
220#66949—22no—
221#66948—21no—
222#66948—22no—
223#66948C2312yes—
224#66946—22no—
225#66946—21no—
226#66945C2311yescharacteristic
227#66945C2312yes—
228#66945C2311yescharacteristic
229#66945C2312yes—
230C4⋊C4×D11—22no—
231C4⋊C4×D11—21no—
232C4⋊C4×D11—22no—
233C4⋊C4×D11—21no—
234C4⋊C4×D11—21no—
235C4⋊C4×D11—21no—
236C4⋊C4×D11—22no—
237C4⋊C4×D11C2311yescharacteristic
238C4⋊C4×D11C2312yes—
239C4⋊C4×D11C2312yes—
240C4⋊C4×D11C2312yes—
241C4⋊C4×D11C2311yescharacteristic
242C4⋊C4×D11C2312yes—
243C4⋊C4×D11C2312yes—
244C4⋊C4×D11C2312yes—
245#66940—22no—
246#66940—21no—
247#66937—22no—
248#66937—22no—
249#66937—22no—
250#66937—22no—
251(C22⋊D11)⋊C4—22no—
252(C22⋊D11)⋊C4—22no—
253(C22⋊D11)⋊C4—22no—
254C22⋊C4×D11—22no—
255C22⋊C4×D11—21no—
256C22⋊C4×D11—22no—
257C22⋊C4×D11—22no—
258#66931—22no—
259#66931—22no—
260#66930—22no—
261#66930—21no—
262C4×D44—22no—
263C4×D44—21no—
264#66925—22no—
265#66925—21no—
266C42×D11—22no—
267C42×D11—21no—
268C4×Dic22—22no—
269C4×Dic22—21no—
270C11×#107C2312yes—
271C11×#107C2312yes—
272C11×#107C2312yes—
273C11×#106C2312yes—
274C11×#103C2311yescharacteristic
275C11×#103C2311yescharacteristic
276C11×#103C2312yes—
277C11×#102C2312yes—
278C11×#102C2311yescharacteristic
279C11×#102C2311yescharacteristic
280C11×C22⋊C8C2312yes—
281C11×C22⋊C8C2312yes—
282#66899C2312yes—
283#66899C2311yescharacteristic
284#66899C2311yescharacteristic
285#66896C2312yes—
286#66896C2311yescharacteristic
287#66896C2311yescharacteristic
288C22⋊(C11⋊C8)C2312yes—
289C22⋊(C11⋊C8)C2312yes—
290#66885C2311yescharacteristic
291#66885C2311yescharacteristic
292#66885C2312yes—
293(C2×D11)⋊C8C2312yes—
294(C2×D11)⋊C8C2312yes—
295(C2×D11)⋊C8C2312yes—
296(C2×D11)⋊C8C2312yes—
297#66882C2312yes—
298#66882C2312yes—
299#66882C2312yes—
300#66881C2312yes—
301#66880C2311yescharacteristic
302#66880C2311yescharacteristic
303#66880C2312yes—
304#66874C2311yescharacteristic
305#66874C2311yescharacteristic
306#66874C2312yes—
307#66873C2311yescharacteristic
308#66873C2311yescharacteristic
309#66873C2312yes—
310#66872C2312yes—
311#66872C2312yes—
312#66871C2312yes—
313#66871C2312yes—
314#66871C2312yes—
315#66871C2312yes—
316#66871C2312yes—
317#66871C2312yes—
318C2×#3098—111nomaximal, Sylow
319C23×D11—21no—
320C23×D11C2×D412yes—
321C23×D11C2×D411yescharacteristic
322C11×#41—22no—
323C11×#41—22no—
324C11×#41—22no—
325C11×#41—22no—
326C2×Q8×C11C2×D411yescharacteristic
327C2×Q8×C11C2411yescharacteristic
328C2×D4×C11—21no—
329C2×D4×C11—22no—
330C2×D4×C11C2×D411yescharacteristic
331C2×D4×C11C2×D412yes—
332C2×D4×C11C2411yescharacteristic
333C22×C4×C11—22no—
334C22×C4×C11—21no—
335C22×C4×C11—21no—
336C22×C4×C11—21no—
337C22×C4×C11C2412yes—
338C22×C4×C11C2411yescharacteristic
339C2×C22⋊D11—21no—
340C2×C22⋊D11—21no—
341C2×C22⋊D11—22no—
342C2×C22⋊D11—21no—
343C2×C22⋊D11—22no—
344C2×C22⋊D11C2×D412yes—
345C2×C22⋊D11C2×D412yes—
346C2×C22⋊D11C2×D412yes—
347C22×Dic11—21no—
348C22×Dic11—22no—
349C22×Dic11—21no—
350C22×Dic11—21no—
351C22×Dic11C2×D412yes—
352C22×Dic11C2×D411yescharacteristic
353#4343—24no—
354#4343—22no—
355#4343—22no—
356Q8×D11—24no—
357Q8×D11—22no—
358Q8×D11—22no—
359#4341—28no—
360#4341—24no—
361#4341—22no—
362#4341—22no—
363#4341—44no—
364D4×D11—24no—
365D4×D11—28no—
366D4×D11—22no—
367D4×D11—22no—
368D4×D11—44no—
369D4×D11—84no—
370#4339—24no—
371#4339—24no—
372#4339—22no—
373#4339—22no—
374#4339—22no—
375#4339—22no—
376#4339—44no—
377C2×D44—21no—
378C2×D44—22no—
379C2×D44C2×D412yes—
380C2×D44C2×D411yescharacteristic
381C2×D44C2411yescharacteristic
382C2×C4×D11—24no—
383C2×C4×D11—24no—
384C2×C4×D11—21no—
385C2×C4×D11—21no—
386C2×C4×D11—22no—
387C2×C4×D11—21no—
388C2×C4×D11—22no—
389C2×C4×D11—21no—
390C2×C4×D11—22no—
391C2×C4×D11—22no—
392C2×C4×D11—22no—
393C2×C4×D11—22no—
394C2×C4×D11—21no—
395C2×C4×D11—44no—
396C2×C4×D11—82no—
397C2×C4×D11—82no—
398C2×C4×D11—84no—
399C2×C4×D11C2×D412yes—
400C2×C4×D11C2×D412yes—
401C2×C4×D11C2×D411yescharacteristic
402C2×C4×D11C2×D411yescharacteristic
403C2×C4×D11#4114yes—
404C2×C4×D11#4114yes—
405C2×C4×D11C2412yes—
406C2×C4×D11C2411yescharacteristic
407C2×C4×D11C2411yescharacteristic
408C2×Dic22—21no—
409C2×Dic22C2×D412yes—
410C2×Dic22C2×D411yescharacteristic
411C2×Dic22C2411yescharacteristic
412C11×M16—22no—
413C2×C8×C11—22no—
414C2×C8×C11C2412yes—
415C2×C8×C11C2411yescharacteristic
416C2×C8×C11C2411yescharacteristic
417C11×C4⋊C4—22no—
418C11×C4⋊C4—21no—
419C11×C4⋊C4—21no—
420C11×C4⋊C4—22no—
421C11×C4⋊C4C2412yes—
422C11×C4⋊C4C2412yes—
423C11×C4⋊C4C2411yescharacteristic
424C11×C4⋊C4C2411yescharacteristic
425C11×C22⋊C4—22no—
426C11×C22⋊C4—21no—
427C11×C22⋊C4—22no—
428C11×C22⋊C4—22no—
429C42×C11—22no—
430C42×C11—21no—
431C22⋊Dic11—22no—
432C22⋊Dic11—22no—
433C22⋊Dic11—21no—
434C22⋊Dic11—22no—
435(C2×D11)⋊C4—22no—
436(C2×D11)⋊C4—22no—
437(C2×D11)⋊C4—21no—
438(C2×D11)⋊C4—22no—
439(C2×D11)⋊C4—21no—
440(C2×D11)⋊C4—22no—
441(C2×D11)⋊C4—22no—
442(C2×D11)⋊C4—22no—
443C4⋊Dic11—22no—
444C4⋊Dic11—22no—
445C4⋊Dic11—21no—
446C4⋊Dic11—21no—
447C4⋊Dic11C2412yes—
448C4⋊Dic11C2411yescharacteristic
449C4⋊Dic11C2412yes—
450C4⋊Dic11C2411yescharacteristic
451Dic11⋊C4—22no—
452Dic11⋊C4—22no—
453Dic11⋊C4—22no—
454Dic11⋊C4—21no—
455Dic11⋊C4—22no—
456Dic11⋊C4—21no—
457Dic11⋊C4—22no—
458Dic11⋊C4—22no—
459Dic11⋊C4—22no—
460Dic11⋊C4—22no—
461C4×Dic11—22no—
462C4×Dic11—21no—
463C4×Dic11—22no—
464C4×Dic11—21no—
465C4×Dic11—22no—
466C4×Dic11—21no—
467#4318—22no—
468C2×C11⋊C8—22no—
469C2×C11⋊C8C2411yescharacteristic
470C2×C11⋊C8C2411yescharacteristic
471C2×C11⋊C8C2412yes—
472#4313—24no—
473C8×D11—22no—
474C8×D11—22no—
475C8×D11—22no—
476C8×D11—22no—
477C8×D11—24no—
478C2×#537—111no—
479C2×#520—111no—
480#3098—112no—
481#3098—112no—
482#3098—112no—
483#3098—112no—
484#3098—111no—
485#3098—111no—
486#3098—111no—
487#3098—111no—
488#3098—111no—
489#3098—111no—
490#3098—111no—
491#3098D1111yescharacteristic, direct product factor
492C2×#484—112no—
493C2×#485—112no—
494C2×#482—112no—
495C2×#480—112no—
496C2×#428—111no—
497C22×#107—111no—
498C2×#417—111no—
499C2×#416—111no—
500C2×#408—111no—
501C23×C11—21no—
502C23×C11C22×D412yes—
503C23×C11C22×D411yescharacteristic
504C22×D11—22no—
505C22×D11—22no—
506C22×D11—24no—
507C22×D11—24no—
508C22×D11—24no—
509C22×D11—21no—
510C22×D11—42no—
511C22×D11—42no—
512C22×D11—42no—
513C22×D11#12314yes—
514C22×D11C22×D412yes—
515C22×D11C22×D411yescharacteristic
516C22×D11C22×D411yescharacteristic
517Q8×C11—22no—
518Q8×C11—21no—
519Q8×C11—21no—
520D4×C11—24no—
521D4×C11—22no—
522D4×C11—21no—
523D4×C11—21no—
524D4×C11—42no—
525D4×C11—82no—
526C2×C4×C11—22no—
527C2×C4×C11—22no—
528C2×C4×C11—21no—
529C2×C4×C11—22no—
530C2×C4×C11—21no—
531C2×C4×C11—22no—
532C2×C4×C11—21no—
533C2×C4×C11—42no—
534C2×C4×C11—81no—
535C2×C4×C11—82no—
536C2×C4×C11—81no—
537C2×C4×C11C22×D412yes—
538C2×C4×C11C22×D411yescharacteristic
539C2×C4×C11C2×#4112yes—
540C2×C4×C11C2×#4112yes—
541C2×C4×C11C2511yescharacteristic
542C22⋊D11—24no—
543C22⋊D11—24no—
544C22⋊D11—24no—
545C22⋊D11—42no—
546C22⋊D11—42no—
547C22⋊D11—42no—
548C22⋊D11—82no—
549C22⋊D11—82no—
550C2×Dic11—24no—
551C2×Dic11—21no—
552C2×Dic11—22no—
553C2×Dic11—21no—
554C2×Dic11—22no—
555C2×Dic11—21no—
556C2×Dic11—42no—
557C2×Dic11—81no—
558C2×Dic11—82no—
559C2×Dic11—81no—
560C2×Dic11#12314yes—
561C2×Dic11C22×D412yes—
562C2×Dic11C22×D411yescharacteristic
563C2×Dic11C22×D411yescharacteristic
564D44—24no—
565D44—22no—
566D44—21no—
567D44—21no—
568D44—42no—
569D44—82no—
570C4×D11—24no—
571C4×D11—22no—
572C4×D11—22no—
573C4×D11—24no—
574C4×D11—42no—
575C4×D11—44no—
576C4×D11—42no—
577C4×D11—44no—
578C4×D11—42no—
579C4×D11—42no—
580C4×D11—42no—
581C4×D11—82no—
582C4×D11—82no—
583C4×D11—82no—
584C4×D11—82no—
585C4×D11#12314yes—
586C4×D11#12314yes—
587C4×D11C2×#4112yes—
588C4×D11C2×#4112yes—
589C4×D11C2×#4112yes—
590C4×D11C2×#4112yes—
591Dic22—22no—
592Dic22—24no—
593Dic22—21no—
594Dic22—21no—
595Dic22—42no—
596C8×C11—21no—
597C8×C11—21no—
598C8×C11—22no—
599C11⋊C8—21no—
600C11⋊C8—21no—
601C11⋊C8—22no—
602C22×#41—111no—
603C22×#41—111no—
604C22×M16—111no—
605C23×C8—111no—
606#537—111no—
607#537—111no—
608#537—112no—
609#537—112no—
610#537—111no—
611#537—222no—
612#537—221no—
613#537—221no—
614#537C2×D1111yescharacteristic
615C2×C22⋊Q8—112no—
616C2×C22⋊Q8—221no—
617C2×#121—112no—
618C2×#121—222no—
619C2×#121—221no—
620#520—111no—
621#520—111no—
622#520—112no—
623#520—112no—
624#520—111no—
625#520—221no—
626#520—222no—
627#520—221no—
628#520C2×D1111yescharacteristic, complemented
629C2×C4×Q8—221no—
630C2×C4×D4—221no—
631C2×C4×D4—222no—
632C2×#117—112no—
633C2×#117—111no—
634C22×C4⋊C4—112no—
635C22×C4⋊C4—111no—
636C22×C4⋊C4—111no—
637#485—112no—
638#485—112no—
639#485—112no—
640#485—112no—
641#485—112no—
642#485—112no—
643#485—112no—
644#485C2×D1112yescomplemented
645#484—112no—
646#484—112no—
647#484—112no—
648#484—112no—
649#484—112no—
650#484—112no—
651#484—112no—
652#484C2×D1112yescomplemented
653#482—112no—
654#482—112no—
655#482—112no—
656#482—112no—
657#482—112no—
658#482—112no—
659#482—112no—
660#482C2×D1112yescomplemented
661#480—112no—
662#480—112no—
663#480—112no—
664#480—112no—
665#480—112no—
666#480—112no—
667#480—112no—
668#480C2×D1112yescomplemented
669#428—111no—
670#428—111no—
671#428—111no—
672#428—112no—
673#428—112no—
674#428C2×D1111yescharacteristic, complemented
675C2×#107—111no—
676C2×#107—111no—
677C2×#107—111no—
678C2×#107—112no—
679C2×#107—112no—
680C2×#107—112no—
681C2×#107—112no—
682C2×#107—112no—
683C2×#107C2×D1111yescharacteristic, complemented
684C2×#106—112no—
685#417—111no—
686#417—111no—
687#417—111no—
688#417—112no—
689#417—112no—
690#417C2×D1111yescharacteristic, complemented
691#416—111no—
692#416—111no—
693#416—111no—
694#416—111no—
695#416—111no—
696#416—111no—
697#416—111no—
698#416C2×D1111yescharacteristic, complemented
699C2×#103—111no—
700C2×#103—112no—
701C2×#103—111no—
702C2×#102—111no—
703C2×#102—112no—
704C2×#102—111no—
705#408—111no—
706#408—111no—
707#408—111no—
708#408—112no—
709#408—112no—
710#408C2×D1111yescharacteristic, complemented
711C2×C22⋊C8—112no—
712C2×C22⋊C8—112no—
713C22×C11—21no—
714C22×C11—21no—
715C22×C11—22no—
716C22×C11—22no—
717C22×C11—22no—
718C22×C11—41no—
719C22×C11—41no—
720C22×C11—41no—
721C22×C11C2×#12312yes—
722C22×C11C23×D411yescharacteristic
723C2×D11—21no—
724C2×D11—21no—
725C2×D11—28no—
726C2×D11—22no—
727C2×D11—22no—
728C2×D11—22no—
729C2×D11—48no—
730C2×D11—41no—
731C2×D11—41no—
732C2×D11—41no—
733C2×D11—84no—
734C2×D11C2×#12312yes—
735C2×D11C2×#12312yes—
736C2×D11#57612yes—
737C2×D11#57812yes—
738C4×C11—22no—
739C4×C11—41no—
740C4×C11—42no—
741C4×C11—41no—
742C4×C11—42no—
743C4×C11—41no—
744C4×C11C2×#12312yes—
745C4×C11C22×#4111yescharacteristic
746C4×C11C22×#4111yescharacteristic
747Dic11—22no—
748Dic11—41no—
749Dic11—42no—
750Dic11—41no—
751Dic11—42no—
752Dic11—41no—
753Dic11C2×#12312yes—
754Dic11C2×#12312yes—
755C2×#41—111no—
756C2×#41—112no—
757C2×#41—111no—
758C2×#41—112no—
759C2×#41—111no—
760C2×#41—111no—
761C2×#41—111no—
762C2×#41—111no—
763C2×#41—221no—
764C2×#41—221no—
765C2×#41—224no—
766C2×#41—224no—
767C2×#41—224no—
768C2×#41—224no—
769C2×#41C22×D1111yescharacteristic
770C2×#41C22×D1111yescharacteristic
771C22×Q8—111no—
772C22×Q8—111no—
773C22×D4—111no—
774C22×D4—112no—
775C22×D4—111no—
776C22×D4—221no—
777C22×D4—222no—
778C23×C4—111no—
779C23×C4—112no—
780C23×C4—221no—
781C23×C4—221no—
782C23×C4—222no—
783C23×C4—221no—
784C2×M16—111no—
785C2×M16—112no—
786C2×M16—224no—
787C2×M16C22×D1111yescharacteristic
788C22×C8—111no—
789C22×C8—111no—
790C22×C8—111no—
791C22×C8—111no—
792C22×C8—111no—
793C22×C8—112no—
794C22×C8—224no—
795C22×C8C22×D1111yescharacteristic
796C22⋊Q8—21no—
797C22⋊Q8—112no—
798C22⋊Q8—112no—
799C22⋊Q8—112no—
800C22⋊Q8—222no—
801C22⋊Q8—222no—
802C22⋊Q8—222no—
803C22⋊Q8—222no—
804C22⋊Q8—221no—
805C22⋊Q8—221no—
806C22⋊Q8—221no—
807C22⋊Q8C22×D1112yes—
808#121—21no—
809#121—22no—
810#121—112no—
811#121—112no—
812#121—112no—
813#121—222no—
814#121—222no—
815#121—222no—
816#121—222no—
817#121—221no—
818#121—222no—
819#121—222no—
820#121—221no—
821#121—222no—
822#121—222no—
823#121—222no—
824#121—222no—
825#121—221no—
826#121—222no—
827#121C22×D1112yes—
828C4×Q8—21no—
829C4×Q8—222no—
830C4×Q8—221no—
831C4×Q8—222no—
832C4×Q8—221no—
833C4×Q8—221no—
834C4×D4—22no—
835C4×D4—21no—
836C4×D4—222no—
837C4×D4—221no—
838C4×D4—222no—
839C4×D4—222no—
840C4×D4—222no—
841C4×D4—222no—
842C4×D4—221no—
843C4×D4—222no—
844C4×D4—222no—
845C4×D4—222no—
846C4×D4—222no—
847C4×D4—221no—
848#117—111no—
849#117—112no—
850#117—111no—
851#117—111no—
852#117—112no—
853#117—112no—
854#117—221no—
855#117—222no—
856#117—221no—
857#117—222no—
858#117C22×D1111yescharacteristic
859#117C22×D1112yes—
860C2×C4⋊C4—111no—
861C2×C4⋊C4—112no—
862C2×C4⋊C4—111no—
863C2×C4⋊C4—111no—
864C2×C4⋊C4—112no—
865C2×C4⋊C4—112no—
866C2×C4⋊C4—112no—
867C2×C4⋊C4—112no—
868C2×C4⋊C4—112no—
869C2×C4⋊C4—112no—
870C2×C4⋊C4—111no—
871C2×C4⋊C4—221no—
872C2×C4⋊C4—222no—
873C2×C4⋊C4—221no—
874C2×C4⋊C4—222no—
875C2×C4⋊C4—221no—
876C2×C4⋊C4—221no—
877C2×C4⋊C4—222no—
878C2×C4⋊C4—221no—
879C2×C4⋊C4—222no—
880C2×C4⋊C4—221no—
881C2×C4⋊C4C22×D1111yescharacteristic
882C2×C4⋊C4C22×D1112yes—
883C2×C4⋊C4C22×D1111yescharacteristic
884C2×C22⋊C4—222no—
885C2×C22⋊C4—221no—
886C2×C22⋊C4—222no—
887C2×C22⋊C4—222no—
888C2×C42—221no—
889C2×C42—222no—
890#107—112no—
891#107—112no—
892#107—112no—
893#107—112no—
894#107—112no—
895#107—112no—
896#107—112no—
897#107—112no—
898#107—112no—
899#107C22×D1112yes—
900#107C22×D1112yes—
901#107C22×D1112yes—
902#106—112no—
903#106—112no—
904#106—112no—
905#106C22×D1112yes—
906#103—111no—
907#103—111no—
908#103—112no—
909#103—111no—
910#103—111no—
911#103—112no—
912#103—111no—
913#103—111no—
914#103—112no—
915#103C22×D1111yescharacteristic
916#103C22×D1111yescharacteristic
917#103C22×D1112yes—
918#102—111no—
919#102—111no—
920#102—112no—
921#102—111no—
922#102—111no—
923#102—112no—
924#102—111no—
925#102—111no—
926#102—112no—
927#102C22×D1111yescharacteristic
928#102C22×D1111yescharacteristic
929#102C22×D1112yes—
930C22⋊C8—112no—
931C22⋊C8—112no—
932C22⋊C8—112no—
933C22⋊C8—112no—
934C22⋊C8—112no—
935C22⋊C8—112no—
936C22⋊C8C22×D1112yes—
937C22⋊C8C22×D1112yes—
938C2×C11—22no—
939C2×C11—42no—
940C2×C11—81no—
941C2×C11C22×#12311yescharacteristic
942C2×C11C2×#57611yescharacteristic
943C2×C11C2×#57811yescharacteristic
944D11—22no—
945D11—42no—
946D11—81no—
947D11#309814yesdirect product factor
948C24—111no—
949C24—112no—
950C24—221no—
951#41—22no—
952#41—22no—
953#41—22no—
954#41—22no—
955#41—224no—
956#41—224no—
957#41—228no—
958#41—224no—
959#41—224no—
960#41—222no—
961#41—222no—
962#41—222no—
963#41—222no—
964#41—222no—
965#41—222no—
966#41—222no—
967#41—222no—
968#41—444no—
969#41—444no—
970C2×Q8—112no—
971C2×Q8—111no—
972C2×Q8—111no—
973C2×Q8—221no—
974C2×Q8—224no—
975C2×Q8—222no—
976C2×Q8—222no—
977C2×Q8D4×D1111yescharacteristic
978C2×Q8C23×D1111yescharacteristic
979C2×D4—21no—
980C2×D4—22no—
981C2×D4—112no—
982C2×D4—112no—
983C2×D4—112no—
984C2×D4—112no—
985C2×D4—111no—
986C2×D4—111no—
987C2×D4—221no—
988C2×D4—222no—
989C2×D4—224no—
990C2×D4—222no—
991C2×D4—222no—
992C2×D4—221no—
993C2×D4—228no—
994C2×D4—221no—
995C2×D4—221no—
996C2×D4—222no—
997C2×D4—222no—
998C2×D4—444no—
999C2×D4—884no—
1000C2×D4D4×D1112yes—
1001C2×D4D4×D1111yescharacteristic
1002C2×D4C23×D1111yescharacteristic
1003C22×C4—22no—
1004C22×C4—21no—
1005C22×C4—21no—
1006C22×C4—21no—
1007C22×C4—111no—
1008C22×C4—111no—
1009C22×C4—111no—
1010C22×C4—114no—
1011C22×C4—114no—
1012C22×C4—111no—
1013C22×C4—111no—
1014C22×C4—112no—
1015C22×C4—112no—
1016C22×C4—112no—
1017C22×C4—112no—
1018C22×C4—224no—
1019C22×C4—224no—
1020C22×C4—221no—
1021C22×C4—221no—
1022C22×C4—221no—
1023C22×C4—222no—
1024C22×C4—222no—
1025C22×C4—221no—
1026C22×C4—222no—
1027C22×C4—222no—
1028C22×C4—222no—
1029C22×C4—222no—
1030C22×C4—221no—
1031C22×C4—222no—
1032C22×C4—221no—
1033C22×C4—221no—
1034C22×C4—221no—
1035C22×C4—444no—
1036C22×C4—882no—
1037C22×C4—884no—
1038C22×C4—882no—
1039C22×C4C23×D1112yes—
1040C22×C4C23×D1111yescharacteristic
1041M16—22no—
1042M16—224no—
1043M16—222no—
1044C2×C8—22no—
1045C2×C8—112no—
1046C2×C8—111no—
1047C2×C8—111no—
1048C2×C8—222no—
1049C2×C8—222no—
1050C2×C8—222no—
1051C2×C8—222no—
1052C2×C8—224no—
1053C2×C8—222no—
1054C2×C8C23×D1112yes—
1055C2×C8C23×D1111yescharacteristic
1056C2×C8C23×D1111yescharacteristic
1057C4⋊C4—22no—
1058C4⋊C4—21no—
1059C4⋊C4—21no—
1060C4⋊C4—22no—
1061C4⋊C4—111no—
1062C4⋊C4—111no—
1063C4⋊C4—112no—
1064C4⋊C4—112no—
1065C4⋊C4—221no—
1066C4⋊C4—222no—
1067C4⋊C4—222no—
1068C4⋊C4—222no—
1069C4⋊C4—222no—
1070C4⋊C4—222no—
1071C4⋊C4—222no—
1072C4⋊C4—221no—
1073C4⋊C4—222no—
1074C4⋊C4—222no—
1075C4⋊C4—222no—
1076C4⋊C4—221no—
1077C4⋊C4—221no—
1078C4⋊C4—222no—
1079C4⋊C4C23×D1111yescharacteristic
1080C4⋊C4C23×D1111yescharacteristic
1081C4⋊C4C23×D1112yes—
1082C4⋊C4C23×D1112yes—
1083C22⋊C4—22no—
1084C22⋊C4—21no—
1085C22⋊C4—22no—
1086C22⋊C4—22no—
1087C22⋊C4—222no—
1088C22⋊C4—221no—
1089C22⋊C4—222no—
1090C22⋊C4—221no—
1091C22⋊C4—222no—
1092C22⋊C4—222no—
1093C22⋊C4—222no—
1094C22⋊C4—222no—
1095C22⋊C4—222no—
1096C22⋊C4—221no—
1097C22⋊C4—222no—
1098C22⋊C4—222no—
1099C42—22no—
1100C42—21no—
1101C42—221no—
1102C42—222no—
1103C42—221no—
1104C42—222no—
1105C42—222no—
1106C42—221no—
1107C11C2×#309811yescharacteristic, complemented, Sylow
1108C23—21no—
1109C23—111no—
1110C23—114no—
1111C23—111no—
1112C23—112no—
1113C23—222no—
1114C23—222no—
1115C23—224no—
1116C23—224no—
1117C23—224no—
1118C23—221no—
1119C23—442no—
1120C23—442no—
1121C23—442no—
1122C23C2×D4×D1112yes—
1123C23C2×D4×D1111yescharacteristic
1124Q8—22no—
1125Q8—21no—
1126Q8—21no—
1127Q8—224no—
1128Q8—222no—
1129Q8—221no—
1130Q8—221no—
1131Q8—442no—
1132D4—24no—
1133D4—22no—
1134D4—21no—
1135D4—21no—
1136D4—42no—
1137D4—82no—
1138D4—224no—
1139D4—224no—
1140D4—224no—
1141D4—224no—
1142D4—222no—
1143D4—221no—
1144D4—221no—
1145D4—442no—
1146D4—442no—
1147D4—442no—
1148D4—442no—
1149D4—882no—
1150D4—882no—
1151D4—882no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—21no—
1155C2×C4—22no—
1156C2×C4—21no—
1157C2×C4—22no—
1158C2×C4—21no—
1159C2×C4—42no—
1160C2×C4—81no—
1161C2×C4—82no—
1162C2×C4—81no—
1163C2×C4—114no—
1164C2×C4—111no—
1165C2×C4—111no—
1166C2×C4—114no—
1167C2×C4—114no—
1168C2×C4—112no—
1169C2×C4—112no—
1170C2×C4—112no—
1171C2×C4—112no—
1172C2×C4—112no—
1173C2×C4—224no—
1174C2×C4—224no—
1175C2×C4—224no—
1176C2×C4—222no—
1177C2×C4—222no—
1178C2×C4—221no—
1179C2×C4—221no—
1180C2×C4—222no—
1181C2×C4—222no—
1182C2×C4—221no—
1183C2×C4—442no—
1184C2×C4—442no—
1185C2×C4—444no—
1186C2×C4—442no—
1187C2×C4—444no—
1188C2×C4—442no—
1189C2×C4—442no—
1190C2×C4—442no—
1191C2×C4—882no—
1192C2×C4—882no—
1193C2×C4—882no—
1194C2×C4—882no—
1195C2×C4—881no—
1196C2×C4—882no—
1197C2×C4—881no—
1198C2×C4C2×D4×D1112yes—
1199C2×C4C2×D4×D1111yescharacteristic
1200C2×C4#41×D1112yes—
1201C2×C4#41×D1112yes—
1202C2×C4C24×D1111yescharacteristic
1203C8—21no—
1204C8—21no—
1205C8—22no—
1206C8—221no—
1207C8—221no—
1208C8—222no—
1209C22—21no—
1210C22—21no—
1211C22—22no—
1212C22—22no—
1213C22—22no—
1214C22—41no—
1215C22—41no—
1216C22—41no—
1217C22—112no—
1218C22—112no—
1219C22—112no—
1220C22—112no—
1221C22—228no—
1222C22—221no—
1223C22—221no—
1224C22—222no—
1225C22—222no—
1226C22—222no—
1227C22—448no—
1228C22—441no—
1229C22—441no—
1230C22—441no—
1231C22—884no—
1232C22D11×#12312yes—
1233C22C22×D4×D1111yescharacteristic
1234C4—22no—
1235C4—42no—
1236C4—41no—
1237C4—42no—
1238C4—41no—
1239C4—41no—
1240C4—112no—
1241C4—112no—
1242C4—222no—
1243C4—442no—
1244C4—441no—
1245C4—442no—
1246C4—441no—
1247C4—441no—
1248C4D11×#12312yes—
1249C4C2×#41×D1111yescharacteristic
1250C4C2×#41×D1111yescharacteristic
1251C2—22no—
1252C2—42no—
1253C2—81no—
1254C2—114no—
1255C2—222no—
1256C2—442no—
1257C2—881no—
1258C2C2×D11×#12311yescharacteristic
1259C2D11×#57611yescharacteristic
1260C2D11×#57811yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3098C2
socleC22×C11C23×D4
prime radicalD11×#537C2
hypercenter#3098D11
hypocenterC11C2×#3098
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3098

Complements

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

NH ≅ G/Ntype
2. D11×#520C2semidirect
3. #13078599C2semidirect
4. #13078598C2semidirect
5. #13078597C2semidirect
6. #13078596C2semidirect
7. #13078595C2semidirect
8. #13078594C2semidirect
9. #13078593C2semidirect
10. #13078592C2semidirect
11. #13078591C2semidirect
12. #13078590C2semidirect
13. #13078589C2semidirect
14. D11×#484C2semidirect
15. D11×#485C2semidirect
16. D11×#482C2semidirect
17. D11×#480C2semidirect
18. D11×#428C2semidirect
19. C2×D11×#107C2semidirect
20. D11×#417C2semidirect
21. D11×#416C2semidirect
22. D11×#408C2semidirect
23. C11×#3098C2semidirect
27. C11×#520C22semidirect
30. #10623358C22semidirect
49. #10623054C22semidirect
50. #10623054C22semidirect
54. #10623035C22semidirect
55. #10623035C22semidirect
59. C11×#485C22semidirect
60. C11×#484C22semidirect
61. C11×#482C22semidirect
62. C11×#480C22semidirect
63. C11×#428C22semidirect
64. C2×C11×#107C22semidirect
65. C11×#417C22semidirect
66. C11×#416C22semidirect
67. C11×#408C22semidirect
68. #10622847C22semidirect
69. #10622846C22semidirect
70. #10622845C22semidirect
71. #10622746C22semidirect
72. #10622742C22semidirect
73. #10622734C22semidirect
74. #10622726C22semidirect
75. #10622723C22semidirect
76. C2×#66882C22semidirect
77. #10622658C22semidirect
78. #10622657C22semidirect
79. #10622648C22semidirect
80. #10622646C22semidirect
81. #10622616C22semidirect
82. #10622615C22semidirect
83. #10622609C22semidirect
84. #10622608C22semidirect
85. #10622583C22semidirect
86. #10622580C22semidirect
87. #10622579C22semidirect
88. #10622577C22semidirect
89. C2×#66871C22semidirect
90. C2×#66871C22semidirect
91. #10622501C22semidirect
92. #10622498C22semidirect
93. #10622497C22semidirect
94. #10622497C22semidirect
95. #10622495C22semidirect
96. #10622495C22semidirect
97. #10622494C22semidirect
101. D11×#107C22semidirect
102. D11×#107C22semidirect
103. #10622480C22semidirect
104. #10622479C22semidirect
105. #10622474C22semidirect
107. #10622428C22semidirect
108. #10622427C22semidirect
109. #10622422C22semidirect
110. #10622422C22semidirect
111. #10622417C22semidirect
112. #10622417C22semidirect
113. #10622416C22semidirect
117. #10622397C22semidirect
118. #10622392C22semidirect
119. #10622387C22semidirect
120. #10622387C22semidirect
121. #10622385C22semidirect
122. #10622385C22semidirect
123. #10622384C22semidirect
127. #10622350C22semidirect
128. #10622349C22semidirect
129. #10622340C22semidirect
130. #10622340C22semidirect
133. #10622336C22semidirect
134. #10622335C22semidirect
491. #3098D11direct (N × H)
628. #520C2×D11semidirect
644. #485C2×D11semidirect
652. #484C2×D11semidirect
660. #482C2×D11semidirect
668. #480C2×D11semidirect
674. #428C2×D11semidirect
683. C2×#107C2×D11semidirect
690. #417C2×D11semidirect
698. #416C2×D11semidirect
710. #408C2×D11semidirect
947. D11#3098direct (N × H)
1107. C11C2×#3098semidirect

Maximal subgroups

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

subgroupindex
D11×#5372
D11×#5202
#130785992
#130785982
#130785972
#130785962
#130785952
#130785942
#130785932
#130785922
#130785912
#130785902
#130785892
D11×#4842
D11×#4852
D11×#4822
D11×#4802
D11×#4282
C2×D11×#1072
D11×#4172
D11×#4162
D11×#4082
C11×#30982
C2×#309811