Finite Group Databasebeta

← #15622532

Subgroups — #15622532

Order 2816.

2214 conjugacy classes of subgroups.

The subgroup lattice has 1212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082371C211yesmaximal, characteristic, complemented
2D11×#518C211yesmaximal, characteristic, complemented
3#13078870C212yesmaximal, complemented
4#13078870C212yesmaximal, complemented
5#13078807C212yesmaximal, complemented
6#13078805C212yesmaximal, complemented
7#13078759C212yesmaximal, complemented
8#13078717C212yesmaximal, complemented
9#13078668C212yesmaximal, complemented
10#13078626C212yesmaximal, complemented
11#13078566C211yesmaximal, characteristic, complemented
12#13078533C211yesmaximal, characteristic, complemented
13#13078441C211yesmaximal, characteristic, complemented
14#13078129C211yesmaximal, characteristic, complemented
15#13078128C211yesmaximal, characteristic, complemented
16#13077845C211yesmaximal, characteristic
17C2×#10622389C211yesmaximal, characteristic, complemented
18#13077478C211yesmaximal, characteristic, complemented
19#13077474C211yesmaximal, characteristic, complemented
20#13077446C211yesmaximal, characteristic, complemented
21#13077442C211yesmaximal, characteristic, complemented
22#13077273C211yesmaximal, characteristic, complemented
23C11×#3081C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C11×#544C2211yescharacteristic, complemented
26C11×#518C2211yescharacteristic
27#10623329C2211yescharacteristic
28C22×#4324C2211yescharacteristic
29C2×#66985C2211yescharacteristic
30C2×#66961C2211yescharacteristic
31C22×#4314C2211yescharacteristic
32#10623264C2212yescomplemented
33#10623263—21no—
34#10623261—21no—
35#10623259C2212yescomplemented
36#10623228C2212yescomplemented
37#10623225—21no—
38#10623225—21no—
39#10623222C2212yescomplemented
40#10623173—22no—
41#10623168—22no—
42#10623076—21no—
43#10623076—21no—
44#10623076C2212yes—
45#10623076C2212yes—
46C4×D4×D11—21no—
47C4×D4×D11—21no—
48C4×D4×D11C2212yes—
49C4×D4×D11C2212yes—
50#10623057C2211yescharacteristic, complemented
51#10623055C2211yescharacteristic
52#10623052C2211yescharacteristic
53#10623052C2211yescharacteristic
54D11×#117C2211yescharacteristic
55D11×#117C2211yescharacteristic
56#10623047C2211yescharacteristic, complemented
57C2×#66950C2211yescharacteristic
58#10623035C2211yescharacteristic, complemented
59#10623017—22no—
60C2×C22⋊C4×D11—22no—
61C11×#478C2212yescomplemented
62C11×#478C2212yescomplemented
63C11×#476C2212yescomplemented
64C11×#474C2212yescomplemented
65C11×#428C2211yescharacteristic, complemented
66C11×#427C2211yescharacteristic, complemented
67C11×#424C2211yescharacteristic, complemented
68C11×#418C2211yescharacteristic
69C2×C11×#102C2211yescharacteristic
70#10622739C2211yescharacteristic
71#10622735C2211yescharacteristic, complemented
72#10622733C2211yescharacteristic, complemented
73#10622726C2211yescharacteristic, complemented
74C2×(C2×D11)⋊C8C2211yescharacteristic
75#10622714C2211yescharacteristic, complemented
76#10622700C2212yescomplemented
77#10622697C2212yescomplemented
78#10622679C2212yescomplemented
79#10622679C2212yescomplemented
80#10622632C2212yescomplemented
81#10622632C2212yescomplemented
82#10622629C2212yescomplemented
83#10622629C2212yescomplemented
84#10622617C2211yescharacteristic, complemented
85#10622615C2211yescharacteristic, complemented
86#10622614C2211yescharacteristic
87#10622612C2211yescharacteristic, complemented
88#10622611C2211yescharacteristic, complemented
89C2×#66873C2211yescharacteristic
90#10622577C2211yescharacteristic, complemented
91#10622502C2212yescomplemented
92#10622502C2212yescomplemented
93#10622502C2212yescomplemented
94#10622501C2211yescharacteristic, complemented
95#10622501C2212yescomplemented
96#10622498C2211yescharacteristic, complemented
97#10622497C2211yescharacteristic, complemented
98#10622497C2212yescomplemented
99#10622495C2211yescharacteristic, complemented
100#10622485C2212yescomplemented
101#10622482C2212yescomplemented
102#10622480C2211yescharacteristic, complemented
103#10622480C2212yescomplemented
104#10622479C2211yescharacteristic, complemented
105#10622476C2211yescharacteristic, complemented
106#10622475C2211yescharacteristic, complemented
107#10622475C2212yescomplemented
108#10622465C2212yescomplemented
109#10622465C2212yescomplemented
110#10622465C2212yescomplemented
111#10622457C2212yescomplemented
112#10622457C2212yescomplemented
113#10622454C2212yescomplemented
114#10622454C2212yescomplemented
115#10622453C2212yescomplemented
116#10622453C2212yescomplemented
117#10622448C2212yescomplemented
118#10622446C2212yescomplemented
119#10622398C2212yescomplemented
120#10622389C2212yes—
121#10622389C2212yes—
122#10622389C2212yes—
123#10622389C2212yes—
124#10622389C2212yes—
125#10622389C2212yes—
126#10622386C2212yes—
127#10622386C2212yes—
128#10622371C2212yescomplemented
129#10622371C2212yescomplemented
130#10622371C2212yescomplemented
131#10622370C2212yescomplemented
132#10622370C2212yescomplemented
133#10622370C2212yescomplemented
134#10622369C2212yescomplemented
135C24×D11—21no—
136C22×D4×C11C2311yescharacteristic
137C22×C22⋊D11—21no—
138C2×D4×D11—24no—
139C2×D4×D11—24no—
140C2×D4×D11—21no—
141C2×D4×D11—21no—
142C2×D4×D11C2312yes—
143C2×D4×D11C2312yes—
144C2×#4339C2311yescharacteristic
145C22×D44C2311yescharacteristic
146C22×C4×D11—22no—
147C22×C4×D11—22no—
148C22×C4×D11C2311yescharacteristic
149C22×Dic22C2311yescharacteristic
150C2×C11×M16C2311yescharacteristic
151C22×C8×C11C2311yescharacteristic
152C11×C4⋊Q8—21no—
153C11×C4⋊Q8C2312yescomplemented
154C11×#125—21no—
155C11×#125C2312yescomplemented
156C11×C22⋊Q8—22no—
157C4×D4×C11—21no—
158C4×D4×C11—21no—
159C4×D4×C11C2312yes—
160C4×D4×C11C2312yes—
161C11×#117C2311yescharacteristic
162C11×#117C2311yescharacteristic
163C11×#117C2311yescharacteristic
164C2×C11×C4⋊C4C2311yescharacteristic
165C2×C11×C22⋊C4—22no—
166C2×C22⋊Dic11—22no—
167#67000—22no—
168#66999—22no—
169#66999—22no—
170Q8×Dic11—22no—
171D4×Dic11—21no—
172D4×Dic11—21no—
173D4×Dic11C2312yes—
174D4×Dic11C2312yes—
175C2×#4324—24no—
176C2×#4324C2312yes—
177C2×#4324C2312yes—
178C2×#4324C2312yes—
179#66985—24no—
180C2×#4323C2312yes—
181C4×C22⋊D11—22no—
182C4×C22⋊D11—22no—
183C4×C22⋊D11—22no—
184C4×C22⋊D11—22no—
185C4×C22⋊D11—22no—
186C2×(C2×D11)⋊C4—21no—
187C2×(C2×D11)⋊C4—22no—
188C2×(C2×D11)⋊C4—22no—
189#66979C2311yescharacteristic
190#66979C2311yescharacteristic
191C2×C4⋊Dic11—21no—
192C2×#4318C2311yescharacteristic
193C22×C11⋊C8C2311yescharacteristic
194#66961—24no—
195C2×D88C2312yes—
196C2×#4314—24no—
197C2×#4314C2312yes—
198C2×#4314C2312yes—
199C2×#4314C2312yes—
200#66951—22no—
201#66951—22no—
202#66951—22no—
203#66951—22no—
204#66950—21no—
205#66950—21no—
206#66950—21no—
207#66950—21no—
208#66950C2311yescharacteristic
209#66950C2312yes—
210#66950C2312yes—
211#66950C2311yescharacteristic
212#66948C2311yescharacteristic
213#66948C2311yescharacteristic
214#66947—22no—
215#66947—22no—
216#66946—22no—
217#66946—21no—
218#66946—21no—
219#66946C2312yes—
220#66946C2312yes—
221#66946C2312yescomplemented
222#66945—22no—
223#66945—21no—
224#66945—22no—
225#66945D411yescharacteristic
226#66945D411yescharacteristic
227#66945C2311yescharacteristic
228#66945C2311yescharacteristic
229C4⋊C4×D11—21no—
230C4⋊C4×D11D411yescharacteristic
231C4⋊C4×D11D411yescharacteristic
232C4⋊C4×D11C2311yescharacteristic
233C4⋊C4×D11C2311yescharacteristic
234#66943—22no—
235#66943—22no—
236#66943—22no—
237#66940C2312yescomplemented
238#66940C2312yescomplemented
239#66940C2312yescomplemented
240#66939—21no—
241#66939—22no—
242#66935—21no—
243(C22⋊D11)⋊C4—22no—
244(C22⋊D11)⋊C4—22no—
245(C22⋊D11)⋊C4—22no—
246(C22⋊D11)⋊C4—22no—
247C22⋊C4×D11—21no—
248C22⋊C4×D11—22no—
249C22⋊C4×D11—22no—
250C22⋊C4×D11—22no—
251C22⋊C4×D11—22no—
252C22⋊C4×D11—22no—
253C22⋊C4×D11—22no—
254C22⋊C4×D11D412yes—
255#66930—21no—
256#66930—22no—
257#66930D412yes—
258#66928C2312yescomplemented
259C4×D44—21no—
260C4×D44—21no—
261C4×D44—21no—
262C4×D44—21no—
263C4×D44C2312yes—
264C4×D44C2312yes—
265#66925—21no—
266#66925C2312yes—
267C42×D11—21no—
268C42×D11C2312yes—
269#66922C2312yescomplemented
270C4×Dic22—21no—
271C4×Dic22—21no—
272C11×#107C2312yescomplemented
273C11×#107C2311yescharacteristic, complemented
274C11×#107C2311yescharacteristic, complemented
275C11×#106C2311yescharacteristic, complemented
276C11×#106C2311yescharacteristic, complemented
277C11×#106C2312yescomplemented
278C11×C4⋊C8C2312yescomplemented
279C11×C4⋊C8C2312yescomplemented
280C11×#102C2312yes—
281C11×#102C2312yes—
282C11×#102C2312yes—
283C11×#102C2312yes—
284#66885C2311yescharacteristic, complemented
285#66885C2311yescharacteristic, complemented
286(C2×D11)⋊C8C2311yescharacteristic
287(C2×D11)⋊C8C2311yescharacteristic
288(C2×D11)⋊C8C2311yescharacteristic
289(C2×D11)⋊C8C2311yescharacteristic
290(C2×D11)⋊C8C2312yes—
291(C2×D11)⋊C8C2312yes—
292#66880C2311yescharacteristic, complemented
293#66880C2311yescharacteristic, complemented
294#66880C2312yescomplemented
295#66880C2312yescomplemented
296#66879C2312yescomplemented
297#66879C2312yescomplemented
298C8×Dic11C2312yescomplemented
299C8×Dic11C2312yescomplemented
300#66874C2311yescharacteristic, complemented
301#66874C2312yescomplemented
302#66874C2312yescomplemented
303#66874C2311yescharacteristic, complemented
304#66873C2312yes—
305#66873C2312yes—
306#66873C2312yes—
307#66873C2312yes—
308#66873C2311yescharacteristic, complemented
309#66873C2311yescharacteristic, complemented
310#66872C2311yescharacteristic, complemented
311#66872C2312yescomplemented
312#66872C2311yescharacteristic, complemented
313#66871C2311yescharacteristic, complemented
314#66871C2311yescharacteristic, complemented
315#66871C2312yescomplemented
316C4⋊(C11⋊C8)C2312yescomplemented
317C4⋊(C11⋊C8)C2312yescomplemented
318#60579—111nomaximal, Sylow
319C24×C11—21no—
320C23×D11—28no—
321C23×D11—21no—
322C23×D11—22no—
323C23×D11—22no—
324C23×D11—82no—
325C23×D11—82no—
326C23×D11C2×D411yescharacteristic
327C2×Q8×C11—22no—
328C2×D4×C11—21no—
329C2×D4×C11—22no—
330C2×D4×C11#4114yes—
331C2×D4×C11C2412yes—
332C22×C4×C11—21no—
333C22×C4×C11—22no—
334C22×C4×C11—22no—
335C22×C4×C11C2411yescharacteristic
336C2×C22⋊D11—28no—
337C2×C22⋊D11—22no—
338C2×C22⋊D11—22no—
339C2×C22⋊D11—21no—
340C22×Dic11—22no—
341C22×Dic11—22no—
342C22×Dic11—21no—
343C22×Dic11C2×D411yescharacteristic
344D4×D11—28no—
345D4×D11—28no—
346D4×D11—24no—
347D4×D11—24no—
348D4×D11—24no—
349D4×D11—24no—
350#4339—22no—
351#4339—22no—
352C2×D44—21no—
353C2×D44—21no—
354C2×D44—21no—
355C2×D44—22no—
356C2×D44#4114yes—
357C2×D44C2411yescharacteristic
358C2×D44C2412yes—
359C2×C4×D11—22no—
360C2×C4×D11—22no—
361C2×C4×D11—22no—
362C2×C4×D11—21no—
363C2×C4×D11—21no—
364C2×C4×D11—21no—
365C2×C4×D11—22no—
366C2×C4×D11—22no—
367C2×C4×D11—22no—
368C2×C4×D11—22no—
369C2×C4×D11—84no—
370C2×C4×D11—84no—
371C2×C4×D11C2×D411yescharacteristic
372C2×C4×D11C2×D412yes—
373C2×C4×D11C2×D411yescharacteristic
374C2×C4×D11C2×D412yes—
375C2×C4×D11C2411yescharacteristic
376C2×C4×D11C2411yescharacteristic
377C2×Dic22—21no—
378C2×Dic22—22no—
379C2×Dic22—22no—
380C2×Dic22C2411yescharacteristic
381C2×Dic22C2412yes—
382C11×M16—22no—
383C2×C8×C11—22no—
384C2×C8×C11C2411yescharacteristic
385C2×C8×C11C2412yes—
386C2×C8×C11C2411yescharacteristic
387C11×C4⋊C4—22no—
388C11×C4⋊C4—22no—
389C11×C4⋊C4—22no—
390C11×C4⋊C4—21no—
391C11×C4⋊C4C2×D411yescharacteristic
392C11×C4⋊C4C2×D411yescharacteristic
393C11×C4⋊C4C2411yescharacteristic
394C11×C4⋊C4C2411yescharacteristic
395C11×C4⋊C4C2412yes—
396C11×C4⋊C4C2411yescharacteristic
397C11×C4⋊C4C2411yescharacteristic
398C11×C22⋊C4—21no—
399C11×C22⋊C4—21no—
400C11×C22⋊C4—22no—
401C11×C22⋊C4—22no—
402C11×C22⋊C4C2×D412yes—
403C42×C11—21no—
404C42×C11—21no—
405C42×C11C2412yes—
406C22⋊Dic11—22no—
407C22⋊Dic11—22no—
408C22⋊Dic11—21no—
409C22⋊Dic11C2×D412yes—
410#4324—24no—
411#4324—24no—
412#4324—24no—
413#4323—24no—
414(C2×D11)⋊C4—22no—
415(C2×D11)⋊C4—22no—
416(C2×D11)⋊C4—21no—
417(C2×D11)⋊C4—21no—
418(C2×D11)⋊C4—22no—
419(C2×D11)⋊C4—21no—
420(C2×D11)⋊C4—21no—
421(C2×D11)⋊C4—21no—
422(C2×D11)⋊C4—21no—
423(C2×D11)⋊C4—22no—
424(C2×D11)⋊C4—22no—
425(C2×D11)⋊C4—22no—
426(C2×D11)⋊C4—22no—
427(C2×D11)⋊C4—22no—
428(C2×D11)⋊C4—22no—
429(C2×D11)⋊C4C2×D412yes—
430(C2×D11)⋊C4C2×D412yes—
431C4⋊Dic11—21no—
432C4⋊Dic11—21no—
433C4⋊Dic11—22no—
434C4⋊Dic11—22no—
435C4⋊Dic11—22no—
436C4⋊Dic11—22no—
437C4⋊Dic11C2×D411yescharacteristic
438C4⋊Dic11C2×D411yescharacteristic
439C4⋊Dic11C2411yescharacteristic
440C4⋊Dic11C2411yescharacteristic
441Dic11⋊C4—22no—
442Dic11⋊C4—22no—
443Dic11⋊C4—21no—
444Dic11⋊C4—21no—
445Dic11⋊C4—22no—
446Dic11⋊C4C2×D412yes—
447Dic11⋊C4C2×D412yes—
448C4×Dic11—22no—
449C4×Dic11—22no—
450C4×Dic11—21no—
451C4×Dic11—21no—
452C4×Dic11—22no—
453C4×Dic11—21no—
454C4×Dic11C2×D412yes—
455C4×Dic11C2×D412yes—
456C4×Dic11C2412yes—
457#4318—22no—
458C2×C11⋊C8—22no—
459C2×C11⋊C8C2411yescharacteristic
460C2×C11⋊C8C2412yes—
461C2×C11⋊C8C2411yescharacteristic
462D88—24no—
463#4314—24no—
464#4314—24no—
465#4314—24no—
466#3495—111no—
467C2×#518—111no—
468#3123—112no—
469#3123—112no—
470#3118—112no—
471#3118—112no—
472#3114—112no—
473#3110—112no—
474#3105—112no—
475#3101—112no—
476#3095—111no—
477#3091—111no—
478#3081—111no—
479#3081D1111yescharacteristic, complemented
480#3042—111no—
481#3042—111no—
482#3003—111no—
483C2×#450—111no—
484#2949—111no—
485#2949—111no—
486#2946—111no—
487#2946—111no—
488#2924—111no—
489C23×C11—22no—
490C23×C11—24no—
491C23×C11—81no—
492C23×C11—81no—
493C23×C11C22×D411yescharacteristic
494C22×D11—28no—
495C22×D11—22no—
496C22×D11—22no—
497C22×D11—28no—
498C22×D11—24no—
499C22×D11—22no—
500C22×D11—21no—
501C22×D11—41no—
502C22×D11—44no—
503C22×D11—44no—
504C22×D11—82no—
505C22×D11—82no—
506C22×D11—816no—
507C22×D11—81no—
508C22×D11—81no—
509C22×D11C22×D411yescharacteristic
510C22×D11C22×D411yescharacteristic
511Q8×C11—82no—
512D4×C11—24no—
513D4×C11—22no—
514D4×C11C2×#4114yes—
515C2×C4×C11—21no—
516C2×C4×C11—21no—
517C2×C4×C11—22no—
518C2×C4×C11—21no—
519C2×C4×C11—21no—
520C2×C4×C11—82no—
521C2×C4×C11—82no—
522C2×C4×C11—81no—
523C2×C4×C11C22×D412yes—
524C2×C4×C11C22×D412yes—
525C2×C4×C11C22×D411yescharacteristic
526C2×C4×C11C2×#4112yes—
527C2×C4×C11C2×#4112yes—
528C2×C4×C11C2511yescharacteristic
529C22⋊D11—28no—
530C22⋊D11—28no—
531C22⋊D11—42no—
532C2×Dic11—22no—
533C2×Dic11—21no—
534C2×Dic11—22no—
535C2×Dic11—21no—
536C2×Dic11—21no—
537C2×Dic11—42no—
538C2×Dic11—82no—
539C2×Dic11—82no—
540C2×Dic11C22×D412yes—
541C2×Dic11C22×D411yescharacteristic
542C2×Dic11C22×D412yes—
543C2×Dic11C22×D411yescharacteristic
544D44—24no—
545D44—22no—
546D44—21no—
547D44—21no—
548D44—42no—
549D44—81no—
550D44C2×#4114yes—
551C4×D11—24no—
552C4×D11—22no—
553C4×D11—22no—
554C4×D11—21no—
555C4×D11—21no—
556C4×D11—21no—
557C4×D11—21no—
558C4×D11—42no—
559C4×D11—42no—
560C4×D11—42no—
561C4×D11—42no—
562C4×D11—82no—
563C4×D11—82no—
564C4×D11—82no—
565C4×D11—82no—
566C4×D11—82no—
567Dic22—22no—
568Dic22—21no—
569Dic22—22no—
570Dic22—21no—
571Dic22—42no—
572C8×C11—21no—
573C8×C11—21no—
574C8×C11—22no—
575C11⋊C8—21no—
576C11⋊C8—21no—
577C11⋊C8—22no—
578C23×D4—111no—
579C2×AGL(1,ℤ/8)—111no—
580C2×AGL(1,ℤ/8)—111no—
581C22×SD16—111no—
582C22×SD16—111no—
583#556—221no—
584#554—221no—
585#552—221no—
586#552—222no—
587#552—221no—
588#551—222no—
589#544C2×D1111yescharacteristic, complemented
590#542—112no—
591#541—112no—
592#536—111no—
593#533—112no—
594#529—112no—
595#525—111no—
596C2×C22⋊Q8—111no—
597#520—111no—
598#519—111no—
599#518—111no—
600#518—112no—
601#518—112no—
602#518—111no—
603#518—111no—
604#518—222no—
605#518—221no—
606#518—221no—
607#518C2×D1111yescharacteristic
608C2×C4×D4—112no—
609C2×C4×D4—112no—
610C2×C4×D4—221no—
611C2×C4×D4—221no—
612C2×#117—111no—
613C2×#117—111no—
614C22×C22⋊C4—222no—
615#485—111no—
616#485—112no—
617#485—111no—
618#485—112no—
619#484—111no—
620#484—112no—
621#483—111no—
622#483—112no—
623#482—111no—
624#482—111no—
625#481—111no—
626#480—111no—
627#478—112no—
628#478—112no—
629#478C2×D1112yescomplemented
630#478C2×D1112yescomplemented
631#476—112no—
632#476C2×D1112yescomplemented
633#474—112no—
634#474C2×D1112yescomplemented
635#463—112no—
636#463—112no—
637#463—112no—
638#463—112no—
639#461—112no—
640#461—112no—
641#461—112no—
642#461—112no—
643#450—112no—
644#450—112no—
645#450—112no—
646#450—112no—
647#450—112no—
648#450—112no—
649#447—112no—
650#447—112no—
651#442—112no—
652#442—112no—
653#440—112no—
654#440—112no—
655#440—112no—
656#440—112no—
657#440—112no—
658#440—112no—
659C4×SD16—112no—
660C4×SD16—112no—
661C4×SD16—112no—
662C4×SD16—112no—
663C4×SD16—112no—
664C4×SD16—112no—
665C4×D8—112no—
666C4×D8—112no—
667#433—112no—
668#433—112no—
669#432—112no—
670#431—112no—
671#428—111no—
672#428C2×D1111yescharacteristic, complemented
673#427—111no—
674#427C2×D1111yescharacteristic, complemented
675#424—111no—
676#424C2×D1111yescharacteristic, complemented
677#419—111no—
678#419—111no—
679#418—111no—
680#418C2×D1111yescharacteristic
681#416—111no—
682#416—111no—
683C2×#102—111no—
684C2×#102C2×D1111yescharacteristic
685#407—111no—
686C2×C22⋊C8—111no—
687#405—111no—
688#405—111no—
689C22×C11—21no—
690C22×C11—21no—
691C22×C11—24no—
692C22×C11—42no—
693C22×C11—42no—
694C22×C11—84no—
695C22×C11#52512yes—
696C22×C11C23×D411yescharacteristic
697C2×D11—21no—
698C2×D11—21no—
699C2×D11—21no—
700C2×D11—21no—
701C2×D11—24no—
702C2×D11—21no—
703C2×D11—44no—
704C2×D11—416no—
705C2×D11—42no—
706C2×D11—42no—
707C2×D11—41no—
708C2×D11—41no—
709C2×D11—41no—
710C2×D11—84no—
711C2×D11—88no—
712C2×D11#57712yes—
713C4×C11—22no—
714C4×C11—22no—
715C4×C11—41no—
716C4×C11—42no—
717C4×C11—41no—
718C4×C11—41no—
719C4×C11—41no—
720C4×C11#52512yes—
721C4×C11C22×#4111yescharacteristic
722C4×C11C22×#4111yescharacteristic
723Dic11—22no—
724Dic11—21no—
725Dic11—21no—
726Dic11—22no—
727Dic11—41no—
728Dic11—42no—
729Dic11—41no—
730Dic11—41no—
731C25—221no—
732C2×#41—111no—
733C22×Q8—111no—
734C22×D4—112no—
735C22×D4—112no—
736C22×D4—111no—
737C22×D4—221no—
738C22×D4—221no—
739C22×D4—221no—
740C22×D4—224no—
741C22×D4—224no—
742C22×D4C22×D1111yescharacteristic
743C23×C4—111no—
744C23×C4—222no—
745C23×C4—222no—
746AGL(1,ℤ/8)—224no—
747AGL(1,ℤ/8)—224no—
748C2×SD16—112no—
749C2×SD16—112no—
750C2×SD16—112no—
751C2×SD16—112no—
752C2×SD16—112no—
753C2×SD16—112no—
754C2×SD16—224no—
755C2×SD16—224no—
756C2×D8—112no—
757C2×D8—112no—
758C2×M16—111no—
759C2×M16C22×D1111yescharacteristic
760C22×C8—111no—
761C22×C8C22×D1111yescharacteristic
762C4⋊Q8—21no—
763C4⋊Q8—112no—
764C4⋊Q8C22×D1112yescomplemented
765#126—222no—
766#126—222no—
767#126—222no—
768#126—222no—
769#125—21no—
770#125—222no—
771#125—222no—
772#125—222no—
773#125C22×D1112yescomplemented
774#124—112no—
775#124—222no—
776#123—221no—
777#123—222no—
778#123—222no—
779#123—222no—
780C22⋊Q8—22no—
781C22⋊Q8—112no—
782C22⋊Q8—112no—
783C22⋊Q8—111no—
784C22⋊Q8—111no—
785C22⋊Q8—221no—
786C22⋊Q8—221no—
787C22⋊Q8—222no—
788C22⋊Q8—222no—
789C22⋊Q8—221no—
790C22⋊Q8—221no—
791#121—111no—
792#121—111no—
793#120—221no—
794C4×Q8—112no—
795C4×Q8—112no—
796C4×Q8—112no—
797C4×Q8—221no—
798C4×Q8—221no—
799C4×Q8—222no—
800C4×D4—21no—
801C4×D4—21no—
802C4×D4—112no—
803C4×D4—112no—
804C4×D4—112no—
805C4×D4—112no—
806C4×D4—112no—
807C4×D4—112no—
808C4×D4—112no—
809C4×D4—221no—
810C4×D4—221no—
811C4×D4—221no—
812C4×D4—221no—
813C4×D4—222no—
814C4×D4—222no—
815C4×D4—222no—
816C4×D4—222no—
817C4×D4—222no—
818C4×D4—222no—
819C4×D4—222no—
820C4×D4—222no—
821C4×D4—222no—
822C4×D4—222no—
823C4×D4—221no—
824C4×D4—221no—
825C4×D4—221no—
826C4×D4—221no—
827C4×D4C22×D1112yes—
828C4×D4C22×D1112yes—
829#117—111no—
830#117—111no—
831#117—111no—
832#117—112no—
833#117—112no—
834#117—111no—
835#117—111no—
836#117—111no—
837#117—221no—
838#117—222no—
839#117—222no—
840#117—221no—
841#117—221no—
842#117—222no—
843#117C22×D1111yescharacteristic
844#117C22×D1111yescharacteristic
845#117C22×D1111yescharacteristic
846C2×C4⋊C4—111no—
847C2×C4⋊C4—111no—
848C2×C4⋊C4—111no—
849C2×C4⋊C4—111no—
850C2×C4⋊C4—221no—
851C2×C4⋊C4—221no—
852C2×C4⋊C4C22×D1111yescharacteristic
853C2×C22⋊C4—22no—
854C2×C22⋊C4—112no—
855C2×C22⋊C4—222no—
856C2×C22⋊C4—222no—
857C2×C22⋊C4—222no—
858C2×C22⋊C4—222no—
859C2×C22⋊C4—222no—
860C2×C22⋊C4—221no—
861C2×C22⋊C4—222no—
862C2×C22⋊C4—222no—
863C2×C22⋊C4—222no—
864C2×C22⋊C4—221no—
865C2×C22⋊C4—222no—
866C2×C42—112no—
867C2×C42—221no—
868#107—111no—
869#107—111no—
870#107—112no—
871#107C22×D1111yescharacteristic, complemented
872#107C22×D1111yescharacteristic, complemented
873#107C22×D1112yescomplemented
874#106—111no—
875#106—111no—
876#106—112no—
877#106C22×D1111yescharacteristic, complemented
878#106C22×D1111yescharacteristic, complemented
879#106C22×D1112yescomplemented
880C4⋊C8—112no—
881C4⋊C8—112no—
882C4⋊C8C22×D1112yescomplemented
883C4⋊C8C22×D1112yescomplemented
884#103—111no—
885#103—111no—
886#103—112no—
887#103—112no—
888#103—111no—
889#103—111no—
890#103—112no—
891#103—112no—
892#102—111no—
893#102—111no—
894#102—112no—
895#102—112no—
896#102—112no—
897#102—112no—
898#102—111no—
899#102—111no—
900#102C22×D1112yes—
901#102C22×D1112yes—
902#102C22×D1112yes—
903#102C22×D1112yes—
904C22⋊C8—111no—
905C22⋊C8—111no—
906C22⋊C8—111no—
907C22⋊C8—111no—
908C22⋊C8—112no—
909C22⋊C8—112no—
910#97—112no—
911#97—112no—
912C4×C8—112no—
913C4×C8—112no—
914C2×C11—22no—
915C2×C11—44no—
916C2×C11C2×#52511yescharacteristic
917C2×C11C2×#57711yescharacteristic
918C2×C11#358511yescharacteristic
919D11—22no—
920D11—41no—
921D11—44no—
922D11—81no—
923C24—21no—
924C24—111no—
925C24—222no—
926C24—222no—
927C24—228no—
928C24—221no—
929C24—882no—
930C24—882no—
931#41—222no—
932#41—222no—
933C2×Q8—22no—
934C2×Q8—112no—
935C2×Q8—111no—
936C2×Q8—221no—
937C2×Q8—222no—
938C2×Q8—222no—
939C2×D4—21no—
940C2×D4—22no—
941C2×D4—114no—
942C2×D4—112no—
943C2×D4—111no—
944C2×D4—221no—
945C2×D4—221no—
946C2×D4—222no—
947C2×D4—222no—
948C2×D4—224no—
949C2×D4—224no—
950C2×D4—228no—
951C2×D4—228no—
952C2×D4—228no—
953C2×D4—224no—
954C2×D4—224no—
955C2×D4—221no—
956C2×D4—221no—
957C2×D4—222no—
958C2×D4#434314yes—
959C2×D4C23×D1112yes—
960C22×C4—21no—
961C22×C4—22no—
962C22×C4—22no—
963C22×C4—111no—
964C22×C4—112no—
965C22×C4—111no—
966C22×C4—111no—
967C22×C4—111no—
968C22×C4—111no—
969C22×C4—112no—
970C22×C4—222no—
971C22×C4—222no—
972C22×C4—222no—
973C22×C4—221no—
974C22×C4—221no—
975C22×C4—222no—
976C22×C4—222no—
977C22×C4—222no—
978C22×C4—222no—
979C22×C4—221no—
980C22×C4—221no—
981C22×C4—222no—
982C22×C4—222no—
983C22×C4—884no—
984C22×C4—884no—
985C22×C4C23×D1111yescharacteristic
986SD16—224no—
987SD16—224no—
988SD16—224no—
989SD16—224no—
990SD16—224no—
991SD16—224no—
992D8—224no—
993D8—224no—
994M16—22no—
995M16—222no—
996C2×C8—22no—
997C2×C8—111no—
998C2×C8—112no—
999C2×C8—111no—
1000C2×C8—222no—
1001C2×C8C23×D1111yescharacteristic
1002C2×C8C23×D1112yes—
1003C2×C8C23×D1111yescharacteristic
1004C4⋊C4—21no—
1005C4⋊C4—22no—
1006C4⋊C4—22no—
1007C4⋊C4—22no—
1008C4⋊C4—111no—
1009C4⋊C4—111no—
1010C4⋊C4—112no—
1011C4⋊C4—112no—
1012C4⋊C4—111no—
1013C4⋊C4—111no—
1014C4⋊C4—221no—
1015C4⋊C4—221no—
1016C4⋊C4—222no—
1017C4⋊C4—222no—
1018C4⋊C4—222no—
1019C4⋊C4—222no—
1020C4⋊C4—222no—
1021C4⋊C4—221no—
1022C4⋊C4—221no—
1023C4⋊C4—222no—
1024C4⋊C4—222no—
1025C4⋊C4D4×D1111yescharacteristic
1026C4⋊C4D4×D1111yescharacteristic
1027C4⋊C4C23×D1112yes—
1028C4⋊C4C23×D1111yescharacteristic
1029C4⋊C4C23×D1111yescharacteristic
1030C4⋊C4C23×D1111yescharacteristic
1031C4⋊C4C23×D1111yescharacteristic
1032C22⋊C4—21no—
1033C22⋊C4—21no—
1034C22⋊C4—22no—
1035C22⋊C4—22no—
1036C22⋊C4—112no—
1037C22⋊C4—112no—
1038C22⋊C4—112no—
1039C22⋊C4—222no—
1040C22⋊C4—222no—
1041C22⋊C4—221no—
1042C22⋊C4—222no—
1043C22⋊C4—221no—
1044C22⋊C4—221no—
1045C22⋊C4—221no—
1046C22⋊C4—222no—
1047C22⋊C4—222no—
1048C22⋊C4—221no—
1049C22⋊C4—221no—
1050C22⋊C4—222no—
1051C22⋊C4—222no—
1052C22⋊C4—221no—
1053C22⋊C4—222no—
1054C22⋊C4—222no—
1055C22⋊C4—222no—
1056C22⋊C4—222no—
1057C22⋊C4D4×D1112yes—
1058C42—21no—
1059C42—21no—
1060C42—112no—
1061C42—112no—
1062C42—112no—
1063C42—221no—
1064C42—221no—
1065C42—222no—
1066C42—222no—
1067C42—222no—
1068C42—221no—
1069C42C23×D1112yes—
1070C11#6057911yescharacteristic, complemented, Sylow
1071C23—22no—
1072C23—24no—
1073C23—81no—
1074C23—81no—
1075C23—111no—
1076C23—111no—
1077C23—222no—
1078C23—228no—
1079C23—228no—
1080C23—222no—
1081C23—222no—
1082C23—224no—
1083C23—221no—
1084C23—441no—
1085C23—444no—
1086C23—444no—
1087C23—881no—
1088C23—881no—
1089C23—882no—
1090C23—882no—
1091C23—8816no—
1092C23C2×D4×D1111yescharacteristic
1093Q8—82no—
1094Q8—222no—
1095Q8—221no—
1096Q8—222no—
1097Q8—221no—
1098Q8—442no—
1099D4—24no—
1100D4—22no—
1101D4—114no—
1102D4—228no—
1103D4—228no—
1104D4—224no—
1105D4—222no—
1106D4—221no—
1107D4—221no—
1108D4—442no—
1109D4—442no—
1110D4—881no—
1111D4C2×#434314yes—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—22no—
1117C2×C4—82no—
1118C2×C4—82no—
1119C2×C4—81no—
1120C2×C4—111no—
1121C2×C4—112no—
1122C2×C4—112no—
1123C2×C4—111no—
1124C2×C4—224no—
1125C2×C4—222no—
1126C2×C4—222no—
1127C2×C4—222no—
1128C2×C4—221no—
1129C2×C4—221no—
1130C2×C4—221no—
1131C2×C4—221no—
1132C2×C4—221no—
1133C2×C4—221no—
1134C2×C4—222no—
1135C2×C4—221no—
1136C2×C4—442no—
1137C2×C4—442no—
1138C2×C4—442no—
1139C2×C4—442no—
1140C2×C4—442no—
1141C2×C4—882no—
1142C2×C4—882no—
1143C2×C4—882no—
1144C2×C4—882no—
1145C2×C4—882no—
1146C2×C4—882no—
1147C2×C4—882no—
1148C2×C4C2×D4×D1112yes—
1149C2×C4C2×D4×D1112yes—
1150C2×C4C2×D4×D1111yescharacteristic
1151C2×C4C2×#434312yes—
1152C2×C4#41×D1112yes—
1153C2×C4C24×D1111yescharacteristic
1154C8—21no—
1155C8—21no—
1156C8—22no—
1157C8—221no—
1158C8—221no—
1159C8—222no—
1160C22—21no—
1161C22—21no—
1162C22—24no—
1163C22—42no—
1164C22—42no—
1165C22—84no—
1166C22—112no—
1167C22—221no—
1168C22—221no—
1169C22—221no—
1170C22—224no—
1171C22—221no—
1172C22—221no—
1173C22—444no—
1174C22—4416no—
1175C22—442no—
1176C22—442no—
1177C22—441no—
1178C22—441no—
1179C22—441no—
1180C22—884no—
1181C22—888no—
1182C22#1062315812yes—
1183C22C22×D4×D1111yescharacteristic
1184C4—22no—
1185C4—22no—
1186C4—41no—
1187C4—41no—
1188C4—41no—
1189C4—42no—
1190C4—41no—
1191C4—221no—
1192C4—221no—
1193C4—222no—
1194C4—222no—
1195C4—441no—
1196C4—442no—
1197C4—441no—
1198C4—441no—
1199C4#1062315812yes—
1200C4C22×#434311yescharacteristic
1201C4C2×#41×D1111yescharacteristic
1202C2—22no—
1203C2—44no—
1204C2—222no—
1205C2—441no—
1206C2—444no—
1207C2—881no—
1208C2C2×#1062315811yescharacteristic
1209C2D11×#57711yescharacteristic
1210C2#1308339111yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3081C2
socleC22×C11C23×D4
prime radical#13077845C2
hypercenter#3081D11
hypocenterC11#60579
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #3081

Complements

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

NH ≅ G/Ntype
1. #13082371C2semidirect
2. D11×#518C2semidirect
3. #13078870C2semidirect
4. #13078870C2semidirect
5. #13078807C2semidirect
6. #13078805C2semidirect
7. #13078759C2semidirect
8. #13078717C2semidirect
9. #13078668C2semidirect
10. #13078626C2semidirect
11. #13078566C2semidirect
12. #13078533C2semidirect
13. #13078441C2semidirect
14. #13078129C2semidirect
15. #13078128C2semidirect
17. C2×#10622389C2semidirect
18. #13077478C2semidirect
19. #13077474C2semidirect
20. #13077446C2semidirect
21. #13077442C2semidirect
22. #13077273C2semidirect
23. C11×#3081C2semidirect
25. C11×#544C22semidirect
32. #10623264C22semidirect
35. #10623259C22semidirect
36. #10623228C22semidirect
39. #10623222C22semidirect
50. #10623057C22semidirect
56. #10623047C22semidirect
58. #10623035C22semidirect
61. C11×#478C22semidirect
62. C11×#478C22semidirect
63. C11×#476C22semidirect
64. C11×#474C22semidirect
65. C11×#428C22semidirect
66. C11×#427C22semidirect
67. C11×#424C22semidirect
71. #10622735C22semidirect
72. #10622733C22semidirect
73. #10622726C22semidirect
75. #10622714C22semidirect
76. #10622700C22semidirect
77. #10622697C22semidirect
78. #10622679C22semidirect
79. #10622679C22semidirect
80. #10622632C22semidirect
81. #10622632C22semidirect
82. #10622629C22semidirect
83. #10622629C22semidirect
84. #10622617C22semidirect
85. #10622615C22semidirect
87. #10622612C22semidirect
88. #10622611C22semidirect
90. #10622577C22semidirect
91. #10622502C22semidirect
92. #10622502C22semidirect
93. #10622502C22semidirect
94. #10622501C22semidirect
95. #10622501C22semidirect
96. #10622498C22semidirect
97. #10622497C22semidirect
98. #10622497C22semidirect
99. #10622495C22semidirect
100. #10622485C22semidirect
101. #10622482C22semidirect
102. #10622480C22semidirect
103. #10622480C22semidirect
104. #10622479C22semidirect
105. #10622476C22semidirect
106. #10622475C22semidirect
107. #10622475C22semidirect
108. #10622465C22semidirect
109. #10622465C22semidirect
110. #10622465C22semidirect
111. #10622457C22semidirect
112. #10622457C22semidirect
113. #10622454C22semidirect
114. #10622454C22semidirect
115. #10622453C22semidirect
116. #10622453C22semidirect
117. #10622448C22semidirect
118. #10622446C22semidirect
119. #10622398C22semidirect
128. #10622371C22semidirect
129. #10622371C22semidirect
130. #10622371C22semidirect
131. #10622370C22semidirect
132. #10622370C22semidirect
133. #10622370C22semidirect
134. #10622369C22semidirect
153. C11×C4⋊Q8C23semidirect
155. C11×#125C23semidirect
221. #66946C23semidirect
237. #66940C23semidirect
238. #66940C23semidirect
239. #66940C23semidirect
258. #66928C23semidirect
269. #66922C23semidirect
272. C11×#107C23semidirect
273. C11×#107C23semidirect
274. C11×#107C23semidirect
275. C11×#106C23semidirect
276. C11×#106C23semidirect
277. C11×#106C23semidirect
278. C11×C4⋊C8C23semidirect
279. C11×C4⋊C8C23semidirect
284. #66885C23semidirect
285. #66885C23semidirect
292. #66880C23semidirect
293. #66880C23semidirect
294. #66880C23semidirect
295. #66880C23semidirect
296. #66879C23semidirect
297. #66879C23semidirect
298. C8×Dic11C23semidirect
299. C8×Dic11C23semidirect
300. #66874C23semidirect
301. #66874C23semidirect
302. #66874C23semidirect
303. #66874C23semidirect
308. #66873C23semidirect
309. #66873C23semidirect
310. #66872C23semidirect
311. #66872C23semidirect
312. #66872C23semidirect
313. #66871C23semidirect
314. #66871C23semidirect
315. #66871C23semidirect
316. C4⋊(C11⋊C8)C23semidirect
317. C4⋊(C11⋊C8)C23semidirect
479. #3081D11semidirect
589. #544C2×D11semidirect
629. #478C2×D11semidirect
630. #478C2×D11semidirect
632. #476C2×D11semidirect
634. #474C2×D11semidirect
672. #428C2×D11semidirect
674. #427C2×D11semidirect
676. #424C2×D11semidirect
764. C4⋊Q8C22×D11semidirect
773. #125C22×D11semidirect
871. #107C22×D11semidirect
872. #107C22×D11semidirect
873. #107C22×D11semidirect
877. #106C22×D11semidirect
878. #106C22×D11semidirect
879. #106C22×D11semidirect
882. C4⋊C8C22×D11semidirect
883. C4⋊C8C22×D11semidirect
1070. C11#60579semidirect

Maximal subgroups

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

subgroupindex
#130823712
D11×#5182
#130788702
#130788072
#130788052
#130787592
#130787172
#130786682
#130786262
#130785662
#130785332
#130784412
#130781292
#130781282
#130778452
C2×#106223892
#130774782
#130774742
#130774462
#130774422
#130772732
C11×#30812
#6057911