Finite Group Databasebeta

← D11×#3329 #15630662

Subgroups — D11×#3329 #15630662

Order 2816.

2146 conjugacy classes of subgroups.

The subgroup lattice has 1206 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#555C211yesmaximal, characteristic
2D4×Q8×D11C211yesmaximal, characteristic, complemented
3#13080913C211yesmaximal, characteristic, complemented
4#13080912C211yesmaximal, characteristic, complemented
5#13080911C211yesmaximal, characteristic, complemented
6#13080910C211yesmaximal, characteristic, complemented
7#13080909C211yesmaximal, characteristic, complemented
8#13080908C212yesmaximal, complemented
9#13080907C211yesmaximal, characteristic, complemented
10#13080906C212yesmaximal, complemented
11#13080905C212yesmaximal, complemented
12#13080904C211yesmaximal, characteristic, complemented
13#13080903C212yesmaximal, complemented
14D11×#487C211yesmaximal, characteristic, complemented
15D11×#485C212yesmaximal, complemented
16D11×#477C211yesmaximal, characteristic, complemented
17D11×#468C212yesmaximal, complemented
18D11×#461C211yesmaximal, characteristic, complemented
19D11×#448C212yesmaximal, complemented
20C4×SD16×D11C211yesmaximal, characteristic, complemented
21D11×#436C211yesmaximal, characteristic, complemented
22D11×#419C212yesmaximal, complemented
23C11×#3329C211yesmaximal, characteristic, complemented
24C22×Q8×D11C2212yes—
25C11×#555C2211yescharacteristic
26D4×Q8×C11C2211yescharacteristic, complemented
27Q8×C22⋊D11C2212yescomplemented
28C2×SD16×D11C2211yescharacteristic
29C2×SD16×D11C2212yes—
30C2×M16×D11C2212yes—
31#10623265C2211yescharacteristic
32#10623258—21no—
33#10623258C2211yescharacteristic, complemented
34D11×C4⋊Q8—21no—
35D11×C4⋊Q8C2211yescharacteristic
36D11×C4⋊Q8C2211yescharacteristic
37D11×#124—22no—
38#10623201—22no—
39#10623163—22no—
40#10623163C2212yescomplemented
41D11×C22⋊Q8—22no—
42D11×C22⋊Q8C2212yes—
43#10623147—21no—
44#10623147C2212yes—
45D11×#121—21no—
46D11×#121C2212yes—
47Q8×D44C2211yescharacteristic, complemented
48C4×Q8×D11C2211yescharacteristic
49#10623094C2211yescharacteristic
50#10623094C2211yescharacteristic
51C4×D4×D11—21no—
52C4×D4×D11C2211yescharacteristic
53C4×D4×D11C2211yescharacteristic
54D4×Dic22—21no—
55D4×Dic22C2211yescharacteristic, complemented
56#10623063—21no—
57#10623063C2212yes—
58D11×#117—21no—
59D11×#117C2212yes—
60C11×#487C2211yescharacteristic, complemented
61C11×#485C2212yescomplemented
62C11×#477C2211yescharacteristic, complemented
63C11×#468C2212yescomplemented
64C11×#461C2211yescharacteristic, complemented
65C11×#448C2212yescomplemented
66C4×C11×SD16C2211yescharacteristic, complemented
67C11×#436C2211yescharacteristic, complemented
68C11×#419C2212yescomplemented
69#10622840C2212yescomplemented
70#10622838C2212yescomplemented
71#10622787C2212yescomplemented
72#10622783C2212yescomplemented
73#10622783C2212yescomplemented
74#10622775C2212yescomplemented
75SD16×Dic11C2211yescharacteristic, complemented
76#10622747C2212yescomplemented
77#10622741C2212yescomplemented
78#10622733C2212yescomplemented
79#10622706C2211yescharacteristic, complemented
80#10622704C2211yescharacteristic, complemented
81#10622696C2211yescharacteristic, complemented
82#10622694C2211yescharacteristic, complemented
83#10622662C2212yescomplemented
84#10622658C2212yescomplemented
85#10622655C2212yescomplemented
86#10622653C2212yescomplemented
87C4×#4325C2211yescharacteristic, complemented
88#10622634C2211yescharacteristic, complemented
89#10622632C2211yescharacteristic, complemented
90C4×#4324C2211yescharacteristic, complemented
91#10622625C2211yescharacteristic, complemented
92#10622617C2212yescomplemented
93#10622609C2212yescomplemented
94#10622501C2212yescomplemented
95#10622499C2212yescomplemented
96D11×#107C2212yes—
97#10622488C2212yescomplemented
98#10622480C2212yescomplemented
99D11×#106C2211yescharacteristic
100#10622465C2211yescharacteristic, complemented
101#10622463C2211yescharacteristic, complemented
102#10622454C2211yescharacteristic, complemented
103#10622451C2211yescharacteristic, complemented
104D11×C4⋊C8C2211yescharacteristic
105#10622431C2212yescomplemented
106#10622428C2212yescomplemented
107#10622427C2212yescomplemented
108#10622425C2212yescomplemented
109#10622419C2212yescomplemented
110#10622419C2212yescomplemented
111#10622415C2212yescomplemented
112#10622415C2212yescomplemented
113#10622415C2212yescomplemented
114#10622415C2212yescomplemented
115D11×#103C2212yes—
116D11×#103C2212yes—
117D11×#103C2212yes—
118D11×#103C2211yescharacteristic
119D11×#103C2212yes—
120#10622407C2212yescomplemented
121#10622405C2212yescomplemented
122#10622405C2212yescomplemented
123#10622401C2211yescharacteristic, complemented
124#10622393C2212yescomplemented
125D11×#102C2211yescharacteristic
126#10622371C2211yescharacteristic, complemented
127#10622351C2212yescomplemented
128#10622342C2212yescomplemented
129D11×C22⋊C8C2212yes—
130#10622336C2212yescomplemented
131C4×#4314C2211yescharacteristic, complemented
132#10622301C2211yescharacteristic, complemented
133C4×C8×D11C2211yescharacteristic
134#10622294C2211yescharacteristic, complemented
135C22×Q8×C11C2312yes—
136C2×Q8×D11—22no—
137C2×Q8×D11—22no—
138C2×Q8×D11—21no—
139C2×Q8×D11—28no—
140C2×Q8×D11—44no—
141C2×Q8×D11C2312yes—
142C2×Q8×D11C2312yes—
143C2×Q8×D11C2312yes—
144C2×Q8×D11C2311yescharacteristic
145C2×D4×D11—22no—
146C2×D4×D11D411yescharacteristic
147C2×D4×D11C2311yescharacteristic
148C22×C4×D11—22no—
149C22×C4×D11—21no—
150C22×C4×D11C2312yes—
151C22×Dic22—22no—
152C22×Dic22C2312yes—
153C2×C11×SD16C2311yescharacteristic
154C2×C11×SD16C2312yes—
155C2×C11×M16C2312yes—
156C11×C4⋊Q8—21no—
157C11×C4⋊Q8C2311yescharacteristic
158C11×C4⋊Q8C2311yescharacteristic
159C11×#124—22no—
160C11×C22⋊Q8—22no—
161C11×C22⋊Q8C2312yes—
162C11×#121—21no—
163C11×#121C2312yes—
164C4×Q8×C11C2311yescharacteristic
165C4×D4×C11—21no—
166C4×D4×C11C2311yescharacteristic
167C4×D4×C11C2311yescharacteristic
168C11×#117—21no—
169C11×#117C2312yes—
170#67000—22no—
171#66999—22no—
172#66999C2312yes—
173Q8×Dic11C2311yescharacteristic
174#66997—22no—
175#66997—21no—
176#66997C2312yes—
177C2×#4325C2311yescharacteristic
178C2×#4325C2312yes—
179#66992—22no—
180#66992—22no—
181#66991—21no—
182#66991C2312yes—
183#66989—22no—
184D4×Dic11—21no—
185D4×Dic11D411yescharacteristic
186D4×Dic11C2311yescharacteristic
187C2×#4324C2311yescharacteristic
188C2×#4324C2312yes—
189#66983—21no—
190#66983C2312yes—
191C4×C22⋊D11—22no—
192C4×C22⋊D11—21no—
193C4×C22⋊D11C2312yes—
194#66979—21no—
195#66979C2312yes—
196#66977—22no—
197#66977C2312yes—
198C2×#4318C2312yes—
199SD16×D11—24no—
200SD16×D11—44no—
201M16×D11—44no—
202C2×#4314C2311yescharacteristic
203C2×#4314C2312yes—
204C2×#4313C2312yes—
205C2×#4313C2312yes—
206C2×C8×D11C2311yescharacteristic
207C2×C8×D11C2312yes—
208C2×C8×D11C2311yescharacteristic
209#66950—22no—
210#66950C2312yes—
211#66949—22no—
212#66949—22no—
213#66949—22no—
214#66948—21no—
215#66948C2312yes—
216#66946—21no—
217#66946D411yescharacteristic
218#66946C2311yescharacteristic
219#66945—21no—
220#66945—21no—
221#66945C2312yes—
222#66945C2312yes—
223C4⋊C4×D11—21no—
224C4⋊C4×D11—22no—
225C4⋊C4×D11—21no—
226C4⋊C4×D11—21no—
227C4⋊C4×D11—21no—
228C4⋊C4×D11D411yescharacteristic
229C4⋊C4×D11C2311yescharacteristic
230C4⋊C4×D11C2311yescharacteristic
231C4⋊C4×D11C2312yes—
232#66941—21no—
233#66941—21no—
234#66941—22no—
235#66941—21no—
236#66941—21no—
237#66941—21no—
238#66941C2312yes—
239#66940—21no—
240#66940C2311yescharacteristic
241#66938—22no—
242#66938—22no—
243#66938—22no—
244#66938—22no—
245#66937—22no—
246#66937—22no—
247(C22⋊D11)⋊C4—22no—
248(C22⋊D11)⋊C4—21no—
249(C22⋊D11)⋊C4D412yes—
250C22⋊C4×D11—22no—
251C22⋊C4×D11—22no—
252C22⋊C4×D11—22no—
253C22⋊C4×D11—21no—
254C22⋊C4×D11D412yes—
255#66931—22no—
256#66931—22no—
257#66931—22no—
258#66930—22no—
259#66930—22no—
260#66928—22no—
261C4×D44—21no—
262C4×D44C2311yescharacteristic
263C4×D44C2311yescharacteristic
264#66925—22no—
265#66925—22no—
266C42×D11—21no—
267C42×D11—22no—
268C42×D11C2311yescharacteristic
269#66922—21no—
270#66922C2311yescharacteristic
271#66922C2311yescharacteristic
272C4×Dic22—21no—
273C4×Dic22C2311yescharacteristic
274C11×#107C2312yes—
275C11×#106C2311yescharacteristic
276C11×C4⋊C8C2311yescharacteristic
277C11×#103C2311yescharacteristic
278C11×#103C2312yes—
279C11×#103C2312yes—
280C11×#103C2312yes—
281C11×#103C2312yes—
282C11×#102C2311yescharacteristic
283C11×C22⋊C8C2312yes—
284C4×C8×C11C2311yescharacteristic
285#66899C2311yescharacteristic
286#66899C2312yes—
287#66899C2312yes—
288#66899C2312yes—
289#66899C2312yes—
290#66896C2311yescharacteristic
291C22⋊(C11⋊C8)C2312yes—
292#66885C2311yescharacteristic
293(C2×D11)⋊C8C2312yes—
294(C2×D11)⋊C8C2312yes—
295#66882C2312yes—
296#66881C2311yescharacteristic
297#66880C2311yescharacteristic
298#66880C2312yes—
299#66880C2312yes—
300#66880C2312yes—
301#66880C2312yes—
302Dic11⋊C8C2312yes—
303C8×Dic11C2311yescharacteristic
304C8×Dic11C2311yescharacteristic
305#66874C2311yescharacteristic
306#66874C2312yes—
307#66874C2312yes—
308#66874C2312yes—
309#66874C2312yes—
310#66873C2311yescharacteristic
311#66872C2311yescharacteristic
312#66872C2311yescharacteristic
313#66871C2312yes—
314#66871C2312yes—
315C4⋊(C11⋊C8)C2311yescharacteristic
316C4×C11⋊C8C2311yescharacteristic
317C2×#3329—111nomaximal, Sylow
318C23×D11—21no—
319C23×D11C2×D412yes—
320C2×Q8×C11—22no—
321C2×Q8×C11—21no—
322C2×Q8×C11—24no—
323C2×Q8×C11—42no—
324C2×Q8×C11C2412yes—
325C2×Q8×C11C2411yescharacteristic
326C2×D4×C11—22no—
327C2×D4×C11C2×D411yescharacteristic
328C2×D4×C11C2411yescharacteristic
329C22×C4×C11—22no—
330C22×C4×C11—21no—
331C22×C4×C11C2412yes—
332C2×C22⋊D11—21no—
333C2×C22⋊D11—22no—
334C2×C22⋊D11—22no—
335C2×C22⋊D11C2×D412yes—
336C22×Dic11—21no—
337C22×Dic11—22no—
338C22×Dic11C2×D412yes—
339Q8×D11—22no—
340Q8×D11—24no—
341Q8×D11—24no—
342Q8×D11—24no—
343Q8×D11—24no—
344Q8×D11—42no—
345Q8×D11—42no—
346Q8×D11—48no—
347Q8×D11—48no—
348Q8×D11—82no—
349Q8×D11#4114yes—
350D4×D11—24no—
351D4×D11—22no—
352D4×D11—22no—
353D4×D11—84no—
354C2×D44—22no—
355C2×D44C2×D411yescharacteristic
356C2×D44C2411yescharacteristic
357C2×C4×D11—24no—
358C2×C4×D11—24no—
359C2×C4×D11—21no—
360C2×C4×D11—21no—
361C2×C4×D11—21no—
362C2×C4×D11—21no—
363C2×C4×D11—22no—
364C2×C4×D11—22no—
365C2×C4×D11—22no—
366C2×C4×D11—22no—
367C2×C4×D11—21no—
368C2×C4×D11—48no—
369C2×C4×D11—44no—
370C2×C4×D11C2×D412yes—
371C2×C4×D11C2×D411yescharacteristic
372C2×C4×D11C2×D412yes—
373C2×C4×D11C2×D411yescharacteristic
374C2×C4×D11C2412yes—
375C2×C4×D11C2411yescharacteristic
376C2×Dic22—21no—
377C2×Dic22—24no—
378C2×Dic22—22no—
379C2×Dic22—22no—
380C2×Dic22—22no—
381C2×Dic22—22no—
382C2×Dic22—22no—
383C2×Dic22—21no—
384C2×Dic22—42no—
385C2×Dic22—48no—
386C2×Dic22C2412yes—
387C2×Dic22C2411yescharacteristic
388C11×SD16—22no—
389C11×SD16—42no—
390C11×M16—42no—
391C2×C8×C11C2411yescharacteristic
392C2×C8×C11C2411yescharacteristic
393C2×C8×C11C2412yes—
394C11×C4⋊C4—21no—
395C11×C4⋊C4—21no—
396C11×C4⋊C4—21no—
397C11×C4⋊C4—21no—
398C11×C4⋊C4—22no—
399C11×C4⋊C4C2×D411yescharacteristic
400C11×C4⋊C4C2411yescharacteristic
401C11×C4⋊C4C2412yes—
402C11×C4⋊C4C2411yescharacteristic
403C11×C22⋊C4—22no—
404C11×C22⋊C4—22no—
405C11×C22⋊C4—22no—
406C11×C22⋊C4—21no—
407C11×C22⋊C4C2×D412yes—
408C42×C11—21no—
409C42×C11—22no—
410C42×C11C2411yescharacteristic
411C22⋊Dic11—22no—
412C22⋊Dic11—21no—
413C22⋊Dic11—22no—
414C22⋊Dic11—22no—
415C22⋊Dic11C2×D412yes—
416#4325—22no—
417#4325—42no—
418#4324—22no—
419#4324—42no—
420(C2×D11)⋊C4—22no—
421(C2×D11)⋊C4—21no—
422(C2×D11)⋊C4—22no—
423(C2×D11)⋊C4—22no—
424(C2×D11)⋊C4—22no—
425(C2×D11)⋊C4—22no—
426(C2×D11)⋊C4—22no—
427(C2×D11)⋊C4—21no—
428(C2×D11)⋊C4C2×D412yes—
429(C2×D11)⋊C4C2×D412yes—
430C4⋊Dic11—21no—
431C4⋊Dic11—22no—
432C4⋊Dic11—21no—
433C4⋊Dic11—21no—
434C4⋊Dic11—21no—
435C4⋊Dic11C2×D411yescharacteristic
436C4⋊Dic11C2411yescharacteristic
437C4⋊Dic11C2412yes—
438C4⋊Dic11C2411yescharacteristic
439Dic11⋊C4—21no—
440Dic11⋊C4—21no—
441Dic11⋊C4—21no—
442Dic11⋊C4—22no—
443Dic11⋊C4—22no—
444Dic11⋊C4—22no—
445Dic11⋊C4—22no—
446Dic11⋊C4—22no—
447Dic11⋊C4—21no—
448Dic11⋊C4—22no—
449Dic11⋊C4C2×D412yes—
450C4×Dic11—22no—
451C4×Dic11—22no—
452C4×Dic11—21no—
453C4×Dic11—21no—
454C4×Dic11—21no—
455C4×Dic11—22no—
456C4×Dic11C2×D411yescharacteristic
457C4×Dic11C2×D411yescharacteristic
458C4×Dic11C2411yescharacteristic
459#4318—42no—
460C2×C11⋊C8C2411yescharacteristic
461C2×C11⋊C8C2411yescharacteristic
462C2×C11⋊C8C2412yes—
463#4314—22no—
464#4314—42no—
465#4313—42no—
466#4313—42no—
467C8×D11—22no—
468C8×D11—22no—
469C8×D11—24no—
470C2×#555—111no—
471C2×D4×Q8—111no—
472#3329—111no—
473#3329—112no—
474#3329—111no—
475#3329—112no—
476#3329—111no—
477#3329—112no—
478#3329—111no—
479#3329—111no—
480#3329—112no—
481#3329—111no—
482#3329—111no—
483#3329D1111yescharacteristic, direct product factor
484C2×#487—111no—
485C2×#485—112no—
486C2×#477—111no—
487C2×#468—112no—
488C2×#461—111no—
489C2×#448—112no—
490C2×C4×SD16—111no—
491C2×#436—111no—
492C2×#419—112no—
493C23×C11—21no—
494C23×C11C22×D412yes—
495C22×D11—24no—
496C22×D11—24no—
497C22×D11—24no—
498C22×D11—21no—
499C22×D11—42no—
500C22×D11—42no—
501C22×D11—42no—
502C22×D11C22×D412yes—
503C22×D11C22×D411yescharacteristic
504Q8×C11—21no—
505Q8×C11—22no—
506Q8×C11—22no—
507Q8×C11—44no—
508Q8×C11—81no—
509Q8×C11C2×#4112yes—
510D4×C11—22no—
511D4×C11—21no—
512D4×C11—21no—
513D4×C11—82no—
514C2×C4×C11—21no—
515C2×C4×C11—22no—
516C2×C4×C11—22no—
517C2×C4×C11—21no—
518C2×C4×C11—21no—
519C2×C4×C11—22no—
520C2×C4×C11—22no—
521C2×C4×C11—44no—
522C2×C4×C11—42no—
523C2×C4×C11C22×D412yes—
524C2×C4×C11C22×D411yescharacteristic
525C2×C4×C11C22×D411yescharacteristic
526C2×C4×C11C2511yescharacteristic
527C22⋊D11—24no—
528C22⋊D11—42no—
529C22⋊D11—82no—
530C22⋊D11—82no—
531C2×Dic11—21no—
532C2×Dic11—24no—
533C2×Dic11—21no—
534C2×Dic11—21no—
535C2×Dic11—22no—
536C2×Dic11—22no—
537C2×Dic11—44no—
538C2×Dic11—42no—
539C2×Dic11C22×D412yes—
540C2×Dic11C22×D411yescharacteristic
541C2×Dic11C22×D411yescharacteristic
542C2×Dic11C22×D411yescharacteristic
543D44—22no—
544D44—21no—
545D44—21no—
546D44—82no—
547C4×D11—24no—
548C4×D11—24no—
549C4×D11—22no—
550C4×D11—22no—
551C4×D11—22no—
552C4×D11—24no—
553C4×D11—44no—
554C4×D11—44no—
555C4×D11—44no—
556C4×D11—42no—
557C4×D11—42no—
558C4×D11—44no—
559C4×D11—42no—
560C4×D11—42no—
561C4×D11#13714yes—
562C4×D11C2×#4112yes—
563C4×D11H(5,𝔽2)12yes—
564Dic22—21no—
565Dic22—24no—
566Dic22—22no—
567Dic22—22no—
568Dic22—44no—
569Dic22—44no—
570Dic22—44no—
571Dic22—44no—
572Dic22—82no—
573Dic22—81no—
574Dic22C2×#4112yes—
575C8×C11—21no—
576C8×C11—21no—
577C8×C11—22no—
578C11⋊C8—21no—
579C11⋊C8—21no—
580C11⋊C8—22no—
581C23×Q8—112no—
582C22×SD16—111no—
583C22×SD16—112no—
584C22×M16—112no—
585#555—111no—
586#555—112no—
587#555—111no—
588#555—111no—
589#555—112no—
590#555—221no—
591#555—221no—
592#555—222no—
593#555C2×D1111yescharacteristic
594D4×Q8—112no—
595D4×Q8—111no—
596D4×Q8—112no—
597D4×Q8—111no—
598D4×Q8—111no—
599D4×Q8—221no—
600D4×Q8—222no—
601D4×Q8—221no—
602D4×Q8C2×D1111yescharacteristic, complemented
603C2×C4⋊Q8—111no—
604C2×C4⋊Q8—111no—
605C2×C4⋊Q8—221no—
606C2×#124—222no—
607C2×C22⋊Q8—112no—
608C2×C22⋊Q8—222no—
609C2×#121—112no—
610C2×#121—221no—
611C2×C4×Q8—111no—
612C2×C4×D4—111no—
613C2×C4×D4—111no—
614C2×C4×D4—221no—
615C2×#117—112no—
616C2×#117—221no—
617#487—111no—
618#487—111no—
619#487—112no—
620#487—112no—
621#487—111no—
622#487C2×D1111yescharacteristic, complemented
623#485—112no—
624#485—112no—
625#485—112no—
626#485—112no—
627#485—112no—
628#485—112no—
629#485—112no—
630#485C2×D1112yescomplemented
631#477—111no—
632#477—111no—
633#477—112no—
634#477—111no—
635#477—112no—
636#477C2×D1111yescharacteristic, complemented
637#468—112no—
638#468—112no—
639#468—112no—
640#468—112no—
641#468—112no—
642#468—112no—
643#468—112no—
644#468C2×D1112yescomplemented
645#461—112no—
646#461—111no—
647#461—111no—
648#461—111no—
649#461—112no—
650#461C2×D1111yescharacteristic, complemented
651#448—112no—
652#448—112no—
653#448—112no—
654#448—112no—
655#448—112no—
656#448—112no—
657#448—112no—
658#448C2×D1112yescomplemented
659C4×SD16—111no—
660C4×SD16—111no—
661C4×SD16—111no—
662C4×SD16—111no—
663C4×SD16—111no—
664C4×SD16—111no—
665C4×SD16—111no—
666C4×SD16C2×D1111yescharacteristic, complemented
667#436—112no—
668#436—111no—
669#436—111no—
670#436—112no—
671#436—111no—
672#436C2×D1111yescharacteristic, complemented
673C2×#107—112no—
674C2×#106—111no—
675C2×C4⋊C8—111no—
676#419—112no—
677#419—112no—
678#419—112no—
679#419—112no—
680#419—112no—
681#419—112no—
682#419—112no—
683#419C2×D1112yescomplemented
684C2×#103—112no—
685C2×#103—112no—
686C2×#103—112no—
687C2×#103—112no—
688C2×#103—111no—
689C2×#102—111no—
690C2×C22⋊C8—112no—
691C2×C4×C8—111no—
692C22×C11—22no—
693C22×C11—22no—
694C22×C11—22no—
695C22×C11—41no—
696C22×C11—41no—
697C22×C11—41no—
698C22×C11C23×D411yescharacteristic
699C2×D11—22no—
700C2×D11—22no—
701C2×D11—22no—
702C2×D11—48no—
703C2×D11—41no—
704C2×D11—41no—
705C2×D11—41no—
706C2×D11—84no—
707C2×D11#54612yes—
708C2×D11C2×#13712yes—
709C2×D11#57712yes—
710C4×C11—22no—
711C4×C11—22no—
712C4×C11—21no—
713C4×C11—42no—
714C4×C11—41no—
715C4×C11—42no—
716C4×C11—41no—
717C4×C11C2×#13712yes—
718C4×C11C22×#4111yescharacteristic
719C4×C11C2×H(5,𝔽2)11yescharacteristic
720Dic11—22no—
721Dic11—22no—
722Dic11—21no—
723Dic11—42no—
724Dic11—41no—
725Dic11—42no—
726Dic11—41no—
727Dic11#54612yes—
728Dic11C2×#13712yes—
729C22×Q8—111no—
730C22×Q8—112no—
731C22×Q8—112no—
732C22×Q8—112no—
733C22×Q8—112no—
734C22×Q8—222no—
735C22×Q8—222no—
736C22×Q8—222no—
737C22×Q8—221no—
738C22×Q8—228no—
739C22×Q8—444no—
740C22×Q8C22×D1112yes—
741C22×D4—111no—
742C22×D4—111no—
743C22×D4—222no—
744C23×C4—112no—
745C23×C4—221no—
746C23×C4—222no—
747C2×SD16—111no—
748C2×SD16—111no—
749C2×SD16—112no—
750C2×SD16—112no—
751C2×SD16—111no—
752C2×SD16—112no—
753C2×SD16—224no—
754C2×SD16—444no—
755C2×SD16C22×D1111yescharacteristic
756C2×SD16C22×D1112yes—
757C2×M16—112no—
758C2×M16—112no—
759C2×M16—112no—
760C2×M16—444no—
761C2×M16C22×D1112yes—
762C22×C8—111no—
763C22×C8—112no—
764C22×C8—111no—
765C4⋊Q8—21no—
766C4⋊Q8—112no—
767C4⋊Q8—112no—
768C4⋊Q8—111no—
769C4⋊Q8—111no—
770C4⋊Q8—221no—
771C4⋊Q8—221no—
772C4⋊Q8—221no—
773C4⋊Q8—221no—
774C4⋊Q8—221no—
775C4⋊Q8—222no—
776C4⋊Q8—221no—
777C4⋊Q8—222no—
778C4⋊Q8—221no—
779C4⋊Q8C22×D1111yescharacteristic
780C4⋊Q8C22×D1111yescharacteristic
781#124—22no—
782#124—222no—
783#124—222no—
784#124—222no—
785#124—222no—
786#124—222no—
787#124—222no—
788#124—222no—
789C22⋊Q8—22no—
790C22⋊Q8—112no—
791C22⋊Q8—112no—
792C22⋊Q8—112no—
793C22⋊Q8—222no—
794C22⋊Q8—222no—
795C22⋊Q8—222no—
796C22⋊Q8—222no—
797C22⋊Q8—222no—
798C22⋊Q8—222no—
799C22⋊Q8—222no—
800C22⋊Q8—222no—
801C22⋊Q8—222no—
802C22⋊Q8C22×D1112yes—
803#121—21no—
804#121—112no—
805#121—112no—
806#121—112no—
807#121—222no—
808#121—222no—
809#121—221no—
810#121—221no—
811#121—222no—
812#121—222no—
813#121—221no—
814#121C22×D1112yes—
815C4×Q8—111no—
816C4×Q8—111no—
817C4×Q8—111no—
818C4×Q8—221no—
819C4×Q8—221no—
820C4×Q8C22×D1111yescharacteristic
821C4×D4—21no—
822C4×D4—111no—
823C4×D4—112no—
824C4×D4—111no—
825C4×D4—112no—
826C4×D4—111no—
827C4×D4—111no—
828C4×D4—111no—
829C4×D4—111no—
830C4×D4—221no—
831C4×D4—221no—
832C4×D4—221no—
833C4×D4—222no—
834C4×D4—221no—
835C4×D4—222no—
836C4×D4—221no—
837C4×D4C22×D1111yescharacteristic
838C4×D4C22×D1111yescharacteristic
839#117—21no—
840#117—112no—
841#117—112no—
842#117—112no—
843#117—222no—
844#117—222no—
845#117—222no—
846#117—222no—
847#117—221no—
848#117—221no—
849#117—221no—
850#117C22×D1112yes—
851C2×C4⋊C4—111no—
852C2×C4⋊C4—111no—
853C2×C4⋊C4—112no—
854C2×C4⋊C4—111no—
855C2×C4⋊C4—221no—
856C2×C4⋊C4—221no—
857C2×C4⋊C4—221no—
858C2×C4⋊C4—222no—
859C2×C4⋊C4—221no—
860C2×C22⋊C4—112no—
861C2×C22⋊C4—222no—
862C2×C22⋊C4—221no—
863C2×C22⋊C4—222no—
864C2×C22⋊C4—222no—
865C2×C42—111no—
866C2×C42—222no—
867C2×C42—221no—
868#107—112no—
869#107—112no—
870#107—112no—
871#107C22×D1112yes—
872#106—111no—
873#106—111no—
874#106—111no—
875#106C22×D1111yescharacteristic
876C4⋊C8—112no—
877C4⋊C8—111no—
878C4⋊C8C22×D1111yescharacteristic
879#103—111no—
880#103—112no—
881#103—112no—
882#103—112no—
883#103—112no—
884#103—111no—
885#103—112no—
886#103—112no—
887#103—112no—
888#103—112no—
889#103—111no—
890#103—112no—
891#103—112no—
892#103—112no—
893#103—112no—
894#103C22×D1111yescharacteristic
895#103C22×D1112yes—
896#103C22×D1112yes—
897#103C22×D1112yes—
898#103C22×D1112yes—
899#102—111no—
900#102—111no—
901#102—111no—
902#102C22×D1111yescharacteristic
903C22⋊C8—112no—
904C22⋊C8—112no—
905C22⋊C8—112no—
906C22⋊C8C22×D1112yes—
907C4×C8—111no—
908C4×C8—111no—
909C4×C8—111no—
910C4×C8C22×D1111yescharacteristic
911C2×C11—42no—
912C2×C11—81no—
913C2×C11C2×#54611yescharacteristic
914C2×C11C22×#13711yescharacteristic
915C2×C11C2×#57711yescharacteristic
916D11—42no—
917D11—81no—
918D11#332914yesdirect product factor
919C24—112no—
920C24—221no—
921C2×Q8—22no—
922C2×Q8—21no—
923C2×Q8—24no—
924C2×Q8—42no—
925C2×Q8—114no—
926C2×Q8—111no—
927C2×Q8—112no—
928C2×Q8—221no—
929C2×Q8—222no—
930C2×Q8—222no—
931C2×Q8—222no—
932C2×Q8—222no—
933C2×Q8—224no—
934C2×Q8—222no—
935C2×Q8—224no—
936C2×Q8—224no—
937C2×Q8—222no—
938C2×Q8—221no—
939C2×Q8—224no—
940C2×Q8—224no—
941C2×Q8—442no—
942C2×Q8—448no—
943C2×Q8—448no—
944C2×Q8—442no—
945C2×Q8—442no—
946C2×Q8—448no—
947C2×Q8—882no—
948C2×Q8C23×D1112yes—
949C2×Q8C23×D1111yescharacteristic
950C2×D4—22no—
951C2×D4—112no—
952C2×D4—111no—
953C2×D4—111no—
954C2×D4—222no—
955C2×D4—224no—
956C2×D4—222no—
957C2×D4—222no—
958C2×D4—221no—
959C2×D4—222no—
960C2×D4—222no—
961C2×D4—884no—
962C2×D4D4×D1111yescharacteristic
963C2×D4C23×D1111yescharacteristic
964C22×C4—22no—
965C22×C4—21no—
966C22×C4—111no—
967C22×C4—111no—
968C22×C4—112no—
969C22×C4—111no—
970C22×C4—112no—
971C22×C4—112no—
972C22×C4—112no—
973C22×C4—224no—
974C22×C4—224no—
975C22×C4—221no—
976C22×C4—221no—
977C22×C4—221no—
978C22×C4—221no—
979C22×C4—222no—
980C22×C4—222no—
981C22×C4—222no—
982C22×C4—222no—
983C22×C4—221no—
984C22×C4—222no—
985C22×C4—221no—
986C22×C4—444no—
987C22×C4—448no—
988C22×C4C23×D1112yes—
989SD16—22no—
990SD16—42no—
991SD16—222no—
992SD16—222no—
993SD16—222no—
994SD16—442no—
995SD16—442no—
996SD16—442no—
997M16—42no—
998M16—442no—
999M16—442no—
1000M16—442no—
1001C2×C8—111no—
1002C2×C8—111no—
1003C2×C8—112no—
1004C2×C8—222no—
1005C2×C8—224no—
1006C2×C8—222no—
1007C2×C8C23×D1111yescharacteristic
1008C2×C8C23×D1111yescharacteristic
1009C2×C8C23×D1112yes—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—22no—
1015C4⋊C4—112no—
1016C4⋊C4—111no—
1017C4⋊C4—111no—
1018C4⋊C4—111no—
1019C4⋊C4—112no—
1020C4⋊C4—221no—
1021C4⋊C4—222no—
1022C4⋊C4—221no—
1023C4⋊C4—222no—
1024C4⋊C4—222no—
1025C4⋊C4—221no—
1026C4⋊C4—221no—
1027C4⋊C4—222no—
1028C4⋊C4—222no—
1029C4⋊C4—222no—
1030C4⋊C4—221no—
1031C4⋊C4—221no—
1032C4⋊C4—221no—
1033C4⋊C4—222no—
1034C4⋊C4—221no—
1035C4⋊C4D4×D1111yescharacteristic
1036C4⋊C4C23×D1111yescharacteristic
1037C4⋊C4C23×D1111yescharacteristic
1038C4⋊C4C23×D1112yes—
1039C22⋊C4—22no—
1040C22⋊C4—22no—
1041C22⋊C4—22no—
1042C22⋊C4—21no—
1043C22⋊C4—112no—
1044C22⋊C4—112no—
1045C22⋊C4—112no—
1046C22⋊C4—222no—
1047C22⋊C4—221no—
1048C22⋊C4—222no—
1049C22⋊C4—222no—
1050C22⋊C4—222no—
1051C22⋊C4—222no—
1052C22⋊C4—222no—
1053C22⋊C4—221no—
1054C22⋊C4—222no—
1055C22⋊C4—222no—
1056C22⋊C4—222no—
1057C22⋊C4—221no—
1058C22⋊C4D4×D1112yes—
1059C42—22no—
1060C42—21no—
1061C42—111no—
1062C42—111no—
1063C42—111no—
1064C42—222no—
1065C42—222no—
1066C42—221no—
1067C42—221no—
1068C42—222no—
1069C42—221no—
1070C42C23×D1111yescharacteristic
1071C11C2×#332911yescharacteristic, complemented, Sylow
1072C23—21no—
1073C23—111no—
1074C23—112no—
1075C23—224no—
1076C23—224no—
1077C23—224no—
1078C23—221no—
1079C23—442no—
1080C23—442no—
1081C23—442no—
1082C23C2×D4×D1112yes—
1083Q8—21no—
1084Q8—22no—
1085Q8—22no—
1086Q8—44no—
1087Q8—81no—
1088Q8—112no—
1089Q8—224no—
1090Q8—221no—
1091Q8—222no—
1092Q8—222no—
1093Q8—444no—
1094Q8—444no—
1095Q8—444no—
1096Q8—444no—
1097Q8—881no—
1098Q8—882no—
1099Q8#41×D1112yes—
1100D4—22no—
1101D4—21no—
1102D4—21no—
1103D4—82no—
1104D4—224no—
1105D4—222no—
1106D4—221no—
1107D4—221no—
1108D4—442no—
1109D4—882no—
1110D4—882no—
1111D4—882no—
1112C2×C4—21no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—44no—
1120C2×C4—42no—
1121C2×C4—111no—
1122C2×C4—111no—
1123C2×C4—114no—
1124C2×C4—112no—
1125C2×C4—112no—
1126C2×C4—111no—
1127C2×C4—112no—
1128C2×C4—224no—
1129C2×C4—224no—
1130C2×C4—222no—
1131C2×C4—224no—
1132C2×C4—224no—
1133C2×C4—221no—
1134C2×C4—222no—
1135C2×C4—222no—
1136C2×C4—221no—
1137C2×C4—221no—
1138C2×C4—222no—
1139C2×C4—222no—
1140C2×C4—444no—
1141C2×C4—442no—
1142C2×C4—444no—
1143C2×C4—444no—
1144C2×C4—442no—
1145C2×C4—444no—
1146C2×C4—442no—
1147C2×C4—442no—
1148C2×C4—444no—
1149C2×C4—442no—
1150C2×C4C2×D4×D1112yes—
1151C2×C4C2×D4×D1111yescharacteristic
1152C2×C4C2×D4×D1111yescharacteristic
1153C2×C4C24×D1111yescharacteristic
1154C8—21no—
1155C8—21no—
1156C8—22no—
1157C8—221no—
1158C8—221no—
1159C8—222no—
1160C22—22no—
1161C22—22no—
1162C22—22no—
1163C22—41no—
1164C22—41no—
1165C22—41no—
1166C22—112no—
1167C22—112no—
1168C22—112no—
1169C22—222no—
1170C22—222no—
1171C22—222no—
1172C22—448no—
1173C22—441no—
1174C22—441no—
1175C22—441no—
1176C22—884no—
1177C22C22×D4×D1111yescharacteristic
1178C4—22no—
1179C4—22no—
1180C4—21no—
1181C4—42no—
1182C4—41no—
1183C4—42no—
1184C4—41no—
1185C4—112no—
1186C4—112no—
1187C4—222no—
1188C4—222no—
1189C4—221no—
1190C4—442no—
1191C4—441no—
1192C4—442no—
1193C4—441no—
1194C4D11×#13712yes—
1195C4C2×#41×D1111yescharacteristic
1196C4D11×H(5,𝔽2)11yescharacteristic
1197C2—42no—
1198C2—81no—
1199C2—114no—
1200C2—442no—
1201C2—881no—
1202C2D11×#54611yescharacteristic
1203C2C2×D11×#13711yescharacteristic
1204C2D11×#57711yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3329C2
socleC22×C11C23×D4
prime radicalD11×#555C2
hypercenter#3329D11
hypocenterC11C2×#3329
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3329

Complements

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

NH ≅ G/Ntype
2. D4×Q8×D11C2semidirect
3. #13080913C2semidirect
4. #13080912C2semidirect
5. #13080911C2semidirect
6. #13080910C2semidirect
7. #13080909C2semidirect
8. #13080908C2semidirect
9. #13080907C2semidirect
10. #13080906C2semidirect
11. #13080905C2semidirect
12. #13080904C2semidirect
13. #13080903C2semidirect
14. D11×#487C2semidirect
15. D11×#485C2semidirect
16. D11×#477C2semidirect
17. D11×#468C2semidirect
18. D11×#461C2semidirect
19. D11×#448C2semidirect
20. C4×SD16×D11C2semidirect
21. D11×#436C2semidirect
22. D11×#419C2semidirect
23. C11×#3329C2semidirect
26. D4×Q8×C11C22semidirect
27. Q8×C22⋊D11C22semidirect
33. #10623258C22semidirect
40. #10623163C22semidirect
47. Q8×D44C22semidirect
55. D4×Dic22C22semidirect
60. C11×#487C22semidirect
61. C11×#485C22semidirect
62. C11×#477C22semidirect
63. C11×#468C22semidirect
64. C11×#461C22semidirect
65. C11×#448C22semidirect
66. C4×C11×SD16C22semidirect
67. C11×#436C22semidirect
68. C11×#419C22semidirect
69. #10622840C22semidirect
70. #10622838C22semidirect
71. #10622787C22semidirect
72. #10622783C22semidirect
73. #10622783C22semidirect
74. #10622775C22semidirect
75. SD16×Dic11C22semidirect
76. #10622747C22semidirect
77. #10622741C22semidirect
78. #10622733C22semidirect
79. #10622706C22semidirect
80. #10622704C22semidirect
81. #10622696C22semidirect
82. #10622694C22semidirect
83. #10622662C22semidirect
84. #10622658C22semidirect
85. #10622655C22semidirect
86. #10622653C22semidirect
87. C4×#4325C22semidirect
88. #10622634C22semidirect
89. #10622632C22semidirect
90. C4×#4324C22semidirect
91. #10622625C22semidirect
92. #10622617C22semidirect
93. #10622609C22semidirect
94. #10622501C22semidirect
95. #10622499C22semidirect
97. #10622488C22semidirect
98. #10622480C22semidirect
100. #10622465C22semidirect
101. #10622463C22semidirect
102. #10622454C22semidirect
103. #10622451C22semidirect
105. #10622431C22semidirect
106. #10622428C22semidirect
107. #10622427C22semidirect
108. #10622425C22semidirect
109. #10622419C22semidirect
110. #10622419C22semidirect
111. #10622415C22semidirect
112. #10622415C22semidirect
113. #10622415C22semidirect
114. #10622415C22semidirect
120. #10622407C22semidirect
121. #10622405C22semidirect
122. #10622405C22semidirect
123. #10622401C22semidirect
124. #10622393C22semidirect
126. #10622371C22semidirect
127. #10622351C22semidirect
128. #10622342C22semidirect
130. #10622336C22semidirect
131. C4×#4314C22semidirect
132. #10622301C22semidirect
134. #10622294C22semidirect
483. #3329D11direct (N × H)
602. D4×Q8C2×D11semidirect
622. #487C2×D11semidirect
630. #485C2×D11semidirect
636. #477C2×D11semidirect
644. #468C2×D11semidirect
650. #461C2×D11semidirect
658. #448C2×D11semidirect
666. C4×SD16C2×D11semidirect
672. #436C2×D11semidirect
683. #419C2×D11semidirect
918. D11#3329direct (N × H)
1071. C11C2×#3329semidirect

Maximal subgroups

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

subgroupindex
D11×#5552
D4×Q8×D112
#130809132
#130809122
#130809112
#130809102
#130809092
#130809082
#130809072
#130809062
#130809052
#130809042
#130809032
D11×#4872
D11×#4852
D11×#4772
D11×#4682
D11×#4612
D11×#4482
C4×SD16×D112
D11×#4362
D11×#4192
C11×#33292
C2×#332911