Finite Group Databasebeta

← #15622531

Subgroups — #15622531

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#13082369C211yesmaximal, characteristic, complemented
2D11×#518C211yesmaximal, characteristic, complemented
3#13078867C212yesmaximal, complemented
4#13078865C212yesmaximal, complemented
5#13078798C212yesmaximal, complemented
6#13078796C212yesmaximal, complemented
7#13078752C212yesmaximal, complemented
8#13078713C212yesmaximal, complemented
9#13078661C212yesmaximal, complemented
10#13078622C212yesmaximal, complemented
11#13078566C211yesmaximal, characteristic, complemented
12#13078527C211yesmaximal, characteristic, complemented
13#13078445C211yesmaximal, characteristic, complemented
14#13078443C211yesmaximal, characteristic, complemented
15#13078131C211yesmaximal, characteristic, complemented
16#13078130C211yesmaximal, characteristic, complemented
17#13077841C211yesmaximal, characteristic
18C2×#10622389C211yesmaximal, characteristic, complemented
19#13077477C211yesmaximal, characteristic, complemented
20#13077473C211yesmaximal, characteristic, complemented
21#13077444C211yesmaximal, characteristic, complemented
22#13077271C211yesmaximal, characteristic, complemented
23C11×#2946C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
26C11×#520C2211yescharacteristic, complemented
27C11×#518C2211yescharacteristic
28#10623359C2211yescharacteristic
29#10623356C2211yescharacteristic, complemented
30C2×#67002C2211yescharacteristic
31#10623329C2211yescharacteristic
32C22×#4324C2211yescharacteristic
33C22×#4314C2211yescharacteristic
34#10623114C2212yescomplemented
35#10623109C2212yescomplemented
36#10623092C2212yescomplemented
37#10623088C2212yescomplemented
38#10623087—22no—
39#10623076—21no—
40#10623076—21no—
41#10623076C2212yes—
42#10623076C2212yes—
43C4×D4×D11—21no—
44C4×D4×D11—21no—
45C4×D4×D11C2212yes—
46C4×D4×D11C2212yes—
47#10623072—22no—
48#10623064—21no—
49#10623060—21no—
50#10623052C2211yescharacteristic
51#10623052C2211yescharacteristic
52D11×#117C2211yescharacteristic
53D11×#117C2211yescharacteristic
54#10623047C2211yescharacteristic, complemented
55#10623044—21no—
56#10623042—21no—
57C2×#66950C2211yescharacteristic
58#10623031C2211yescharacteristic, complemented
59#10623017—22no—
60C2×C22⋊C4×D11—22no—
61C11×#442C2212yescomplemented
62C11×#440C2212yescomplemented
63C4×C11×SD16C2212yescomplemented
64C4×C11×D8C2212yescomplemented
65C11×#428C2211yescharacteristic, complemented
66C11×#416C2211yescharacteristic, complemented
67C2×C11×#102C2211yescharacteristic
68C11×#405C2211yescharacteristic, complemented
69#10622846C2211yescharacteristic, complemented
70#10622828C2211yescharacteristic
71#10622782C2212yes—
72#10622782C2212yes—
73#10622775C2212yescomplemented
74#10622775C2212yescomplemented
75#10622769C2212yes—
76#10622769C2212yes—
77#10622766C2212yescomplemented
78#10622766C2212yescomplemented
79#10622744C2211yescharacteristic
80#10622739C2211yescharacteristic
81#10622733C2211yescharacteristic, complemented
82#10622732C2211yescharacteristic, complemented
83C2×(C2×D11)⋊C8C2211yescharacteristic
84#10622719C2211yescharacteristic, complemented
85#10622715C2211yescharacteristic, complemented
86#10622639C2212yescomplemented
87C4×#4325C2212yescomplemented
88#10622631C2212yescomplemented
89#10622631C2212yescomplemented
90C4×#4324C2212yescomplemented
91C4×#4324C2212yescomplemented
92#10622627C2212yescomplemented
93C4×#4323C2212yescomplemented
94#10622617C2211yescharacteristic, complemented
95#10622611C2211yescharacteristic, complemented
96#10622610C2211yescharacteristic, complemented
97C2×#66873C2211yescharacteristic
98#10622577C2211yescharacteristic, complemented
99#10622504C2212yescomplemented
100#10622503C2212yescomplemented
101#10622501C2212yescomplemented
102#10622497C2212yescomplemented
103#10622484C2212yescomplemented
104#10622483C2212yescomplemented
105#10622480C2212yescomplemented
106#10622475C2212yescomplemented
107#10622431C2212yescomplemented
108#10622431C2212yescomplemented
109#10622428C2211yescharacteristic, complemented
110#10622427C2211yescharacteristic, complemented
111#10622422C2211yescharacteristic, complemented
112#10622418C2211yescharacteristic, complemented
113#10622400C2212yescomplemented
114#10622400C2212yescomplemented
115#10622397C2211yescharacteristic, complemented
116#10622392C2211yescharacteristic, complemented
117#10622390C2211yescharacteristic, complemented
118#10622389C2212yes—
119#10622389C2212yes—
120#10622389C2212yes—
121#10622389C2212yes—
122#10622387C2211yescharacteristic, complemented
123#10622379C2212yescomplemented
124#10622376C2212yescomplemented
125#10622374C2212yescomplemented
126#10622372C2212yescomplemented
127#10622323C2212yescomplemented
128#10622323C2212yescomplemented
129#10622322C2212yescomplemented
130#10622318C2212yescomplemented
131C4×#4314C2212yescomplemented
132C4×#4314C2212yescomplemented
133#10622303C2212yescomplemented
134#10622298C2212yescomplemented
135C24×D11—21no—
136C2×C11×#41C2311yescharacteristic
137C22×D4×C11C2311yescharacteristic
138C22×C22⋊D11—21no—
139C2×D4×D11—24no—
140C2×D4×D11—24no—
141C2×D4×D11—21no—
142C2×D4×D11—21no—
143C2×D4×D11C2312yes—
144C2×D4×D11C2312yes—
145C22×D44C2311yescharacteristic
146C22×C4×D11—22no—
147C22×C4×D11—22no—
148C22×C4×D11C2311yescharacteristic
149C22×Dic22C2311yescharacteristic
150C11×AGL(1,ℤ/8)—24no—
151C2×C11×SD16C2312yes—
152C2×C11×D8C2312yes—
153C2×C11×M16C2311yescharacteristic
154C22×C8×C11C2311yescharacteristic
155C4×Q8×C11C2312yescomplemented
156C4×D4×C11—21no—
157C4×D4×C11—21no—
158C4×D4×C11—22no—
159C4×D4×C11C2312yes—
160C4×D4×C11C2312yes—
161C4×D4×C11C2312yescomplemented
162C11×#117—21no—
163C11×#117C2311yescharacteristic
164C11×#117C2311yescharacteristic
165C2×C11×C4⋊C4—21no—
166C2×C11×C4⋊C4C2311yescharacteristic
167C2×C11×C22⋊C4—22no—
168C2×C22⋊Dic11—22no—
169#67002—24no—
170#66999C2311yescharacteristic
171#66999C2311yescharacteristic
172#66997C2312yescomplemented
173C2×#4325C2312yes—
174#66991C2311yescharacteristic
175#66991C2311yescharacteristic
176#66990—21no—
177#66989C2312yescomplemented
178#66988—21no—
179#66988—22no—
180D4×Dic11—21no—
181D4×Dic11—21no—
182D4×Dic11C2312yes—
183D4×Dic11C2312yes—
184C2×#4324—24no—
185C2×#4324C2312yes—
186C2×#4324C2312yes—
187C2×#4323C2312yes—
188#66982—22no—
189C4×C22⋊D11—21no—
190C4×C22⋊D11—22no—
191C4×C22⋊D11—21no—
192C4×C22⋊D11—22no—
193C4×C22⋊D11—22no—
194C4×C22⋊D11—22no—
195C4×C22⋊D11—22no—
196C2×(C2×D11)⋊C4—21no—
197C2×(C2×D11)⋊C4—22no—
198C2×(C2×D11)⋊C4—22no—
199#66979—22no—
200#66979C2311yescharacteristic
201#66979C2311yescharacteristic
202#66979C2311yescharacteristic
203C2×C4⋊Dic11—21no—
204#66977—22no—
205#66977—21no—
206#66977—21no—
207#66977—22no—
208C2×#4318C2311yescharacteristic
209C22×C11⋊C8C2311yescharacteristic
210C2×#4314—24no—
211C2×#4314C2312yes—
212C2×#4314C2312yes—
213#66951—22no—
214#66950—21no—
215#66950—21no—
216#66950C2312yes—
217#66950C2312yes—
218#66949—22no—
219#66946—21no—
220#66946—21no—
221#66946C2312yes—
222#66946C2312yes—
223#66945D411yescharacteristic
224#66945D411yescharacteristic
225#66945C2311yescharacteristic
226#66945C2311yescharacteristic
227C4⋊C4×D11D411yescharacteristic
228C4⋊C4×D11D411yescharacteristic
229C4⋊C4×D11C2311yescharacteristic
230C4⋊C4×D11C2311yescharacteristic
231#66943—21no—
232#66943C2312yescomplemented
233#66942—22no—
234#66942—22no—
235#66941—21no—
236#66941C2312yescomplemented
237#66940—21no—
238#66940—21no—
239#66938—22no—
240#66936—22no—
241(C22⋊D11)⋊C4—22no—
242(C22⋊D11)⋊C4—22no—
243(C22⋊D11)⋊C4—22no—
244(C22⋊D11)⋊C4—22no—
245C22⋊C4×D11—21no—
246C22⋊C4×D11—22no—
247C22⋊C4×D11—22no—
248C22⋊C4×D11—22no—
249C22⋊C4×D11—22no—
250C22⋊C4×D11—22no—
251C22⋊C4×D11—22no—
252C22⋊C4×D11D412yes—
253#66932—22no—
254#66932—22no—
255#66930—21no—
256#66930—22no—
257#66930D412yes—
258#66929—22no—
259C4×D44—21no—
260C4×D44—21no—
261C4×D44C2312yes—
262C4×D44C2312yes—
263#66925—21no—
264#66925—22no—
265#66925C2312yes—
266C42×D11—21no—
267C42×D11C2312yes—
268#66923—22no—
269C4×Dic22—22no—
270C4×Dic22C2312yescomplemented
271C4×Dic22C2312yescomplemented
272C11×#107C2312yescomplemented
273C11×#106C2312yescomplemented
274C11×#103C2311yescharacteristic, complemented
275C11×#103C2311yescharacteristic, complemented
276C11×#102C2312yes—
277C11×#102C2312yes—
278C11×#102C2311yescharacteristic, complemented
279C11×#102C2311yescharacteristic, complemented
280C11×#97C2312yescomplemented
281C4×C8×C11C2312yescomplemented
282#66899C2311yescharacteristic, complemented
283#66899C2311yescharacteristic, complemented
284#66896C2312yes—
285#66896C2312yes—
286#66896C2311yescharacteristic, complemented
287#66896C2311yescharacteristic, complemented
288#66885C2312yes—
289#66885C2312yes—
290(C2×D11)⋊C8C2311yescharacteristic
291(C2×D11)⋊C8C2311yescharacteristic
292(C2×D11)⋊C8C2311yescharacteristic
293(C2×D11)⋊C8C2311yescharacteristic
294(C2×D11)⋊C8C2312yes—
295(C2×D11)⋊C8C2312yes—
296#66882C2311yescharacteristic, complemented
297#66882C2311yescharacteristic, complemented
298#66881C2311yescharacteristic, complemented
299#66881C2311yescharacteristic, complemented
300#66880C2312yescomplemented
301#66880C2312yescomplemented
302Dic11⋊C8C2312yescomplemented
303Dic11⋊C8C2312yescomplemented
304Dic11⋊C8C2312yescomplemented
305Dic11⋊C8C2312yescomplemented
306#66874C2312yescomplemented
307#66874C2312yescomplemented
308#66873C2312yes—
309#66873C2312yes—
310#66872C2312yescomplemented
311#66872C2311yescharacteristic, complemented
312#66872C2311yescharacteristic, complemented
313#66871C2312yescomplemented
314#66871C2311yescharacteristic, complemented
315#66871C2311yescharacteristic, complemented
316#66867C2312yescomplemented
317C4×C11⋊C8C2312yescomplemented
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
327C11×#41—22no—
328C11×#41—22no—
329C2×Q8×C11C2411yescharacteristic
330C2×D4×C11—21no—
331C2×D4×C11—21no—
332C2×D4×C11—22no—
333C2×D4×C11#4114yes—
334C2×D4×C11C2411yescharacteristic
335C2×D4×C11C2412yes—
336C22×C4×C11—21no—
337C22×C4×C11—21no—
338C22×C4×C11—22no—
339C22×C4×C11—22no—
340C22×C4×C11—22no—
341C22×C4×C11C2411yescharacteristic
342C2×C22⋊D11—28no—
343C2×C22⋊D11—22no—
344C2×C22⋊D11—22no—
345C2×C22⋊D11—21no—
346C2×C22⋊D11—21no—
347C22×Dic11—22no—
348C22×Dic11—22no—
349C22×Dic11—21no—
350C22×Dic11C2×D411yescharacteristic
351D4×D11—28no—
352D4×D11—28no—
353D4×D11—24no—
354D4×D11—24no—
355D4×D11—24no—
356D4×D11—24no—
357C2×D44—21no—
358C2×D44—22no—
359C2×D44#4114yes—
360C2×D44C2412yes—
361C2×C4×D11—22no—
362C2×C4×D11—22no—
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—22no—
378C2×Dic22—21no—
379C2×Dic22—22no—
380C2×Dic22—22no—
381C2×Dic22C2412yes—
382C11×SD16—24no—
383C11×D8—24no—
384C11×M16—22no—
385C2×C8×C11—22no—
386C2×C8×C11C2412yes—
387C2×C8×C11C2411yescharacteristic
388C2×C8×C11C2411yescharacteristic
389C11×C4⋊C4—21no—
390C11×C4⋊C4—22no—
391C11×C4⋊C4C2×D411yescharacteristic
392C11×C4⋊C4C2×D411yescharacteristic
393C11×C4⋊C4C2412yes—
394C11×C4⋊C4C2411yescharacteristic
395C11×C4⋊C4C2411yescharacteristic
396C11×C22⋊C4—21no—
397C11×C22⋊C4—22no—
398C11×C22⋊C4—22no—
399C11×C22⋊C4—22no—
400C11×C22⋊C4C2×D412yes—
401C42×C11—22no—
402C42×C11—21no—
403C42×C11C2412yes—
404C22⋊Dic11—21no—
405C22⋊Dic11—21no—
406C22⋊Dic11—22no—
407C22⋊Dic11—22no—
408C22⋊Dic11—22no—
409C22⋊Dic11—22no—
410C22⋊Dic11—21no—
411C22⋊Dic11—21no—
412C22⋊Dic11C2×D412yes—
413#4325—24no—
414#4324—24no—
415#4324—24no—
416#4323—24no—
417(C2×D11)⋊C4—22no—
418(C2×D11)⋊C4—22no—
419(C2×D11)⋊C4—21no—
420(C2×D11)⋊C4—21no—
421(C2×D11)⋊C4—21no—
422(C2×D11)⋊C4—22no—
423(C2×D11)⋊C4—21no—
424(C2×D11)⋊C4—22no—
425(C2×D11)⋊C4—22no—
426(C2×D11)⋊C4—22no—
427(C2×D11)⋊C4C2×D412yes—
428(C2×D11)⋊C4C2×D412yes—
429C4⋊Dic11—22no—
430C4⋊Dic11—22no—
431C4⋊Dic11—22no—
432C4⋊Dic11C2×D411yescharacteristic
433C4⋊Dic11C2×D411yescharacteristic
434C4⋊Dic11C2411yescharacteristic
435C4⋊Dic11C2411yescharacteristic
436C4⋊Dic11C2411yescharacteristic
437C4⋊Dic11C2411yescharacteristic
438Dic11⋊C4—21no—
439Dic11⋊C4—22no—
440Dic11⋊C4—21no—
441Dic11⋊C4—22no—
442Dic11⋊C4—21no—
443Dic11⋊C4—21no—
444Dic11⋊C4—22no—
445Dic11⋊C4—22no—
446Dic11⋊C4—22no—
447Dic11⋊C4—22no—
448Dic11⋊C4C2×D412yes—
449Dic11⋊C4C2×D412yes—
450C4×Dic11—21no—
451C4×Dic11—21no—
452C4×Dic11—22no—
453C4×Dic11—22no—
454C4×Dic11—21no—
455C4×Dic11—21no—
456C4×Dic11C2×D412yes—
457C4×Dic11C2×D412yes—
458C4×Dic11C2412yes—
459#4318—22no—
460C2×C11⋊C8—22no—
461C2×C11⋊C8C2411yescharacteristic
462C2×C11⋊C8C2412yes—
463C2×C11⋊C8C2411yescharacteristic
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#3081—111no—
480#3042—111no—
481#3042—111no—
482#3003—111no—
483C2×#450—111no—
484#2949—111no—
485#2949—111no—
486#2946—111no—
487#2946D1111yescharacteristic, complemented
488#2924—111no—
489C23×C11—22no—
490C23×C11—24no—
491C23×C11—21no—
492C23×C11—81no—
493C23×C11—81no—
494C23×C11C22×D411yescharacteristic
495C22×D11—28no—
496C22×D11—22no—
497C22×D11—22no—
498C22×D11—28no—
499C22×D11—24no—
500C22×D11—22no—
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—21no—
512Q8×C11—21no—
513D4×C11—24no—
514D4×C11—22no—
515D4×C11—21no—
516D4×C11—21no—
517D4×C11—42no—
518D4×C11C2×#4114yes—
519C2×C4×C11—21no—
520C2×C4×C11—21no—
521C2×C4×C11—21no—
522C2×C4×C11—22no—
523C2×C4×C11—42no—
524C2×C4×C11—82no—
525C2×C4×C11—82no—
526C2×C4×C11—82no—
527C2×C4×C11—81no—
528C2×C4×C11C22×D412yes—
529C2×C4×C11C22×D412yes—
530C2×C4×C11C22×D411yescharacteristic
531C2×C4×C11C2×#4112yes—
532C2×C4×C11C2×#4112yes—
533C2×C4×C11C2511yescharacteristic
534C22⋊D11—28no—
535C22⋊D11—28no—
536C22⋊D11—42no—
537C22⋊D11—81no—
538C2×Dic11—22no—
539C2×Dic11—21no—
540C2×Dic11—21no—
541C2×Dic11—22no—
542C2×Dic11—21no—
543C2×Dic11—21no—
544C2×Dic11—42no—
545C2×Dic11—82no—
546C2×Dic11—82no—
547C2×Dic11C22×D411yescharacteristic
548C2×Dic11C22×D411yescharacteristic
549C2×Dic11C22×D412yes—
550C2×Dic11C22×D412yes—
551D44—24no—
552D44—22no—
553D44C2×#4114yes—
554C4×D11—24no—
555C4×D11—22no—
556C4×D11—22no—
557C4×D11—21no—
558C4×D11—21no—
559C4×D11—21no—
560C4×D11—21no—
561C4×D11—42no—
562C4×D11—42no—
563C4×D11—42no—
564C4×D11—82no—
565C4×D11—82no—
566C4×D11—82no—
567C4×D11—82no—
568Dic22—22no—
569Dic22—22no—
570Dic22—42no—
571Dic22—82no—
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)C2×D1111yescharacteristic
581C22×SD16—111no—
582C22×SD16—111no—
583#556—221no—
584#554—221no—
585#552—221no—
586#552—221no—
587#552—222no—
588#551—222no—
589#544—111no—
590#542—112no—
591#541—112no—
592#536—111no—
593#533—112no—
594#529—112no—
595#525—111no—
596C2×C22⋊Q8—111no—
597#520C2×D1111yescharacteristic, complemented
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—112no—
616#485—112no—
617#485—111no—
618#485—111no—
619#484—112no—
620#484—111no—
621#483—112no—
622#483—111no—
623#482—111no—
624#482—111no—
625#481—111no—
626#480—111no—
627#478—112no—
628#478—112no—
629#478—112no—
630#478—112no—
631#476—112no—
632#476—112no—
633#474—112no—
634#474—112no—
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#442C2×D1112yescomplemented
653#440—112no—
654#440—112no—
655#440—112no—
656#440—112no—
657#440—112no—
658#440C2×D1112yescomplemented
659C4×SD16—112no—
660C4×SD16—112no—
661C4×SD16—112no—
662C4×SD16—112no—
663C4×SD16—112no—
664C4×SD16C2×D1112yescomplemented
665C4×D8—112no—
666C4×D8C2×D1112yescomplemented
667#433—112no—
668#433—112no—
669#432—112no—
670#431—112no—
671#428—111no—
672#428C2×D1111yescharacteristic, complemented
673#427—111no—
674#427—111no—
675#424—111no—
676#424—111no—
677#419—111no—
678#419—111no—
679#418—111no—
680#418—111no—
681#416—111no—
682#416C2×D1111yescharacteristic, complemented
683C2×#102—111no—
684C2×#102C2×D1111yescharacteristic
685#407—111no—
686C2×C22⋊C8—111no—
687#405—111no—
688#405C2×D1111yescharacteristic, complemented
689C22×C11—21no—
690C22×C11—21no—
691C22×C11—24no—
692C22×C11—42no—
693C22×C11—42no—
694C22×C11—41no—
695C22×C11—41no—
696C22×C11—41no—
697C22×C11—84no—
698C22×C11#52512yes—
699C22×C11C23×D411yescharacteristic
700C2×D11—21no—
701C2×D11—21no—
702C2×D11—21no—
703C2×D11—21no—
704C2×D11—24no—
705C2×D11—21no—
706C2×D11—44no—
707C2×D11—416no—
708C2×D11—42no—
709C2×D11—42no—
710C2×D11—84no—
711C2×D11—88no—
712C2×D11#57712yes—
713C4×C11—22no—
714C4×C11—22no—
715C4×C11—42no—
716C4×C11—41no—
717C4×C11—41no—
718C4×C11—41no—
719C4×C11#52512yes—
720C4×C11C22×#4111yescharacteristic
721C4×C11C22×#4111yescharacteristic
722Dic11—22no—
723Dic11—21no—
724Dic11—21no—
725Dic11—22no—
726Dic11—41no—
727Dic11—41no—
728Dic11—42no—
729Dic11—41no—
730Dic11—41no—
731C25—221no—
732C2×#41C22×D1111yescharacteristic
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)—24no—
747AGL(1,ℤ/8)—224no—
748C2×SD16—112no—
749C2×SD16—112no—
750C2×SD16—112no—
751C2×SD16—112no—
752C2×SD16—112no—
753C2×SD16—224no—
754C2×SD16—224no—
755C2×SD16C22×D1112yes—
756C2×D8—112no—
757C2×D8C22×D1112yes—
758C2×M16—111no—
759C2×M16C22×D1111yescharacteristic
760C22×C8—111no—
761C22×C8C22×D1111yescharacteristic
762C4⋊Q8—112no—
763C4⋊Q8—112no—
764C4⋊Q8—221no—
765#126—222no—
766#126—222no—
767#126—222no—
768#126—222no—
769#125—112no—
770#125—222no—
771#125—222no—
772#125—222no—
773#125—221no—
774#124—112no—
775#124—222no—
776#123—222no—
777#123—222no—
778#123—222no—
779#123—221no—
780C22⋊Q8—111no—
781C22⋊Q8—111no—
782C22⋊Q8—112no—
783C22⋊Q8—112no—
784C22⋊Q8—222no—
785C22⋊Q8—221no—
786C22⋊Q8—221no—
787C22⋊Q8—222no—
788C22⋊Q8—221no—
789C22⋊Q8—221no—
790C22⋊Q8—222no—
791#121—111no—
792#121—111no—
793#120—221no—
794C4×Q8—112no—
795C4×Q8—112no—
796C4×Q8—222no—
797C4×Q8—221no—
798C4×Q8—221no—
799C4×Q8C22×D1112yescomplemented
800C4×D4—21no—
801C4×D4—21no—
802C4×D4—22no—
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—222no—
812C4×D4—222no—
813C4×D4—222no—
814C4×D4—222no—
815C4×D4—222no—
816C4×D4—222no—
817C4×D4—222no—
818C4×D4—222no—
819C4×D4—221no—
820C4×D4—221no—
821C4×D4—221no—
822C4×D4—221no—
823C4×D4—222no—
824C4×D4—221no—
825C4×D4—221no—
826C4×D4C22×D1112yes—
827C4×D4C22×D1112yes—
828C4×D4C22×D1112yescomplemented
829#117—21no—
830#117—111no—
831#117—111no—
832#117—111no—
833#117—112no—
834#117—112no—
835#117—111no—
836#117—111no—
837#117—111no—
838#117—111no—
839#117—221no—
840#117—222no—
841#117—222no—
842#117—221no—
843#117—222no—
844#117C22×D1111yescharacteristic
845#117C22×D1111yescharacteristic
846C2×C4⋊C4—21no—
847C2×C4⋊C4—111no—
848C2×C4⋊C4—111no—
849C2×C4⋊C4—111no—
850C2×C4⋊C4—111no—
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—111no—
871#107—111no—
872#107—112no—
873#107C22×D1112yescomplemented
874#106—111no—
875#106—111no—
876#106—111no—
877#106—111no—
878#106—112no—
879#106C22×D1112yescomplemented
880C4⋊C8—112no—
881C4⋊C8—112no—
882C4⋊C8—112no—
883C4⋊C8—112no—
884#103—111no—
885#103—111no—
886#103—112no—
887#103—112no—
888#103—112no—
889#103—112no—
890#103C22×D1111yescharacteristic, complemented
891#103C22×D1111yescharacteristic, complemented
892#102—112no—
893#102—112no—
894#102—111no—
895#102—111no—
896#102—112no—
897#102—112no—
898#102—112no—
899#102—112no—
900#102C22×D1112yes—
901#102C22×D1112yes—
902#102C22×D1111yescharacteristic, complemented
903#102C22×D1111yescharacteristic, complemented
904C22⋊C8—111no—
905C22⋊C8—111no—
906C22⋊C8—111no—
907C22⋊C8—111no—
908C22⋊C8—112no—
909C22⋊C8—112no—
910#97—112no—
911#97C22×D1112yescomplemented
912C4×C8—112no—
913C4×C8C22×D1112yescomplemented
914C2×C11—22no—
915C2×C11—44no—
916C2×C11—81no—
917C2×C11C2×#52511yescharacteristic
918C2×C11C2×#57711yescharacteristic
919C2×C11#358511yescharacteristic
920D11—22no—
921D11—41no—
922D11—44no—
923C24—21no—
924C24—111no—
925C24—222no—
926C24—222no—
927C24—228no—
928C24—221no—
929C24—882no—
930C24—882no—
931#41—22no—
932#41—22no—
933C2×Q8—112no—
934C2×Q8—222no—
935C2×Q8—221no—
936C2×Q8—222no—
937C2×Q8—222no—
938C2×Q8C23×D1111yescharacteristic
939C2×D4—21no—
940C2×D4—21no—
941C2×D4—22no—
942C2×D4—114no—
943C2×D4—112no—
944C2×D4—222no—
945C2×D4—222no—
946C2×D4—224no—
947C2×D4—224no—
948C2×D4—228no—
949C2×D4—228no—
950C2×D4—228no—
951C2×D4—224no—
952C2×D4—224no—
953C2×D4—221no—
954C2×D4—221no—
955C2×D4—222no—
956C2×D4—221no—
957C2×D4#433914yes—
958C2×D4C23×D1111yescharacteristic
959C2×D4C23×D1112yes—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—22no—
963C22×C4—22no—
964C22×C4—22no—
965C22×C4—111no—
966C22×C4—112no—
967C22×C4—111no—
968C22×C4—111no—
969C22×C4—111no—
970C22×C4—111no—
971C22×C4—112no—
972C22×C4—222no—
973C22×C4—222no—
974C22×C4—221no—
975C22×C4—221no—
976C22×C4—222no—
977C22×C4—222no—
978C22×C4—222no—
979C22×C4—222no—
980C22×C4—221no—
981C22×C4—222no—
982C22×C4—222no—
983C22×C4—884no—
984C22×C4—884no—
985C22×C4C23×D1111yescharacteristic
986SD16—24no—
987SD16—224no—
988SD16—224no—
989SD16—224no—
990SD16—224no—
991SD16—224no—
992D8—24no—
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—112no—
1007C4⋊C4—111no—
1008C4⋊C4—111no—
1009C4⋊C4—112no—
1010C4⋊C4—111no—
1011C4⋊C4—111no—
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⋊C4—222no—
1026C4⋊C4—222no—
1027C4⋊C4D4×D1111yescharacteristic
1028C4⋊C4D4×D1111yescharacteristic
1029C4⋊C4C23×D1112yes—
1030C4⋊C4C23×D1111yescharacteristic
1031C4⋊C4C23×D1111yescharacteristic
1032C22⋊C4—21no—
1033C22⋊C4—22no—
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—221no—
1043C22⋊C4—222no—
1044C22⋊C4—222no—
1045C22⋊C4—221no—
1046C22⋊C4—221no—
1047C22⋊C4—222no—
1048C22⋊C4—222no—
1049C22⋊C4—221no—
1050C22⋊C4—222no—
1051C22⋊C4—221no—
1052C22⋊C4—222no—
1053C22⋊C4—221no—
1054C22⋊C4—221no—
1055C22⋊C4—222no—
1056C22⋊C4—222no—
1057C22⋊C4D4×D1112yes—
1058C42—21no—
1059C42—22no—
1060C42—112no—
1061C42—112no—
1062C42—112no—
1063C42—221no—
1064C42—221no—
1065C42—221no—
1066C42—221no—
1067C42—222no—
1068C42—222no—
1069C42C23×D1112yes—
1070C11#6057911yescharacteristic, complemented, Sylow
1071C23—22no—
1072C23—24no—
1073C23—21no—
1074C23—81no—
1075C23—81no—
1076C23—111no—
1077C23—111no—
1078C23—222no—
1079C23—228no—
1080C23—228no—
1081C23—222no—
1082C23—222no—
1083C23—224no—
1084C23—441no—
1085C23—444no—
1086C23—444no—
1087C23—881no—
1088C23—881no—
1089C23—882no—
1090C23—882no—
1091C23—8816no—
1092C23C2×D4×D1111yescharacteristic
1093Q8—21no—
1094Q8—21no—
1095Q8—222no—
1096Q8—222no—
1097Q8—442no—
1098Q8—882no—
1099D4—24no—
1100D4—21no—
1101D4—22no—
1102D4—21no—
1103D4—42no—
1104D4—114no—
1105D4—228no—
1106D4—228no—
1107D4—224no—
1108D4—222no—
1109D4—442no—
1110D4—881no—
1111D4C2×#433914yes—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—22no—
1116C2×C4—42no—
1117C2×C4—82no—
1118C2×C4—82no—
1119C2×C4—82no—
1120C2×C4—81no—
1121C2×C4—111no—
1122C2×C4—112no—
1123C2×C4—112no—
1124C2×C4—111no—
1125C2×C4—224no—
1126C2×C4—222no—
1127C2×C4—222no—
1128C2×C4—222no—
1129C2×C4—221no—
1130C2×C4—221no—
1131C2×C4—221no—
1132C2×C4—221no—
1133C2×C4—221no—
1134C2×C4—221no—
1135C2×C4—221no—
1136C2×C4—221no—
1137C2×C4—222no—
1138C2×C4—442no—
1139C2×C4—442no—
1140C2×C4—442no—
1141C2×C4—442no—
1142C2×C4—882no—
1143C2×C4—882no—
1144C2×C4—882no—
1145C2×C4—882no—
1146C2×C4—882no—
1147C2×C4—882no—
1148C2×C4C2×#433912yes—
1149C2×C4C2×D4×D1112yes—
1150C2×C4C2×D4×D1112yes—
1151C2×C4C2×D4×D1111yescharacteristic
1152C2×C4#41×D1112yes—
1153C2×C4C24×D1111yescharacteristic
1154C8—22no—
1155C8—21no—
1156C8—21no—
1157C8—221no—
1158C8—221no—
1159C8—222no—
1160C22—21no—
1161C22—21no—
1162C22—24no—
1163C22—42no—
1164C22—42no—
1165C22—41no—
1166C22—41no—
1167C22—41no—
1168C22—84no—
1169C22—112no—
1170C22—221no—
1171C22—221no—
1172C22—221no—
1173C22—224no—
1174C22—221no—
1175C22—221no—
1176C22—444no—
1177C22—4416no—
1178C22—442no—
1179C22—442no—
1180C22—884no—
1181C22—888no—
1182C22#1062307812yes—
1183C22C22×D4×D1111yescharacteristic
1184C4—22no—
1185C4—22no—
1186C4—41no—
1187C4—41no—
1188C4—41no—
1189C4—42no—
1190C4—221no—
1191C4—221no—
1192C4—222no—
1193C4—222no—
1194C4—442no—
1195C4—441no—
1196C4—441no—
1197C4—441no—
1198C4—441no—
1199C4#1062307812yes—
1200C4C22×#433911yescharacteristic
1201C4C2×#41×D1111yescharacteristic
1202C2—22no—
1203C2—44no—
1204C2—81no—
1205C2—222no—
1206C2—441no—
1207C2—444no—
1208C2C2×#1062307811yescharacteristic
1209C2D11×#57711yescharacteristic
1210C2#1308339111yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#2946C2
socleC22×C11C23×D4
prime radical#13077841C2
hypercenter#2946D11
hypocenterC11#60579
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #2946

Complements

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

NH ≅ G/Ntype
1. #13082369C2semidirect
2. D11×#518C2semidirect
3. #13078867C2semidirect
4. #13078865C2semidirect
5. #13078798C2semidirect
6. #13078796C2semidirect
7. #13078752C2semidirect
8. #13078713C2semidirect
9. #13078661C2semidirect
10. #13078622C2semidirect
11. #13078566C2semidirect
12. #13078527C2semidirect
13. #13078445C2semidirect
14. #13078443C2semidirect
15. #13078131C2semidirect
16. #13078130C2semidirect
18. C2×#10622389C2semidirect
19. #13077477C2semidirect
20. #13077473C2semidirect
21. #13077444C2semidirect
22. #13077271C2semidirect
23. C11×#2946C2semidirect
26. C11×#520C22semidirect
29. #10623356C22semidirect
34. #10623114C22semidirect
35. #10623109C22semidirect
36. #10623092C22semidirect
37. #10623088C22semidirect
54. #10623047C22semidirect
58. #10623031C22semidirect
61. C11×#442C22semidirect
62. C11×#440C22semidirect
63. C4×C11×SD16C22semidirect
64. C4×C11×D8C22semidirect
65. C11×#428C22semidirect
66. C11×#416C22semidirect
68. C11×#405C22semidirect
69. #10622846C22semidirect
73. #10622775C22semidirect
74. #10622775C22semidirect
77. #10622766C22semidirect
78. #10622766C22semidirect
81. #10622733C22semidirect
82. #10622732C22semidirect
84. #10622719C22semidirect
85. #10622715C22semidirect
86. #10622639C22semidirect
87. C4×#4325C22semidirect
88. #10622631C22semidirect
89. #10622631C22semidirect
90. C4×#4324C22semidirect
91. C4×#4324C22semidirect
92. #10622627C22semidirect
93. C4×#4323C22semidirect
94. #10622617C22semidirect
95. #10622611C22semidirect
96. #10622610C22semidirect
98. #10622577C22semidirect
99. #10622504C22semidirect
100. #10622503C22semidirect
101. #10622501C22semidirect
102. #10622497C22semidirect
103. #10622484C22semidirect
104. #10622483C22semidirect
105. #10622480C22semidirect
106. #10622475C22semidirect
107. #10622431C22semidirect
108. #10622431C22semidirect
109. #10622428C22semidirect
110. #10622427C22semidirect
111. #10622422C22semidirect
112. #10622418C22semidirect
113. #10622400C22semidirect
114. #10622400C22semidirect
115. #10622397C22semidirect
116. #10622392C22semidirect
117. #10622390C22semidirect
122. #10622387C22semidirect
123. #10622379C22semidirect
124. #10622376C22semidirect
125. #10622374C22semidirect
126. #10622372C22semidirect
127. #10622323C22semidirect
128. #10622323C22semidirect
129. #10622322C22semidirect
130. #10622318C22semidirect
131. C4×#4314C22semidirect
132. C4×#4314C22semidirect
133. #10622303C22semidirect
134. #10622298C22semidirect
155. C4×Q8×C11C23semidirect
161. C4×D4×C11C23semidirect
172. #66997C23semidirect
177. #66989C23semidirect
232. #66943C23semidirect
236. #66941C23semidirect
270. C4×Dic22C23semidirect
271. C4×Dic22C23semidirect
272. C11×#107C23semidirect
273. C11×#106C23semidirect
274. C11×#103C23semidirect
275. C11×#103C23semidirect
278. C11×#102C23semidirect
279. C11×#102C23semidirect
280. C11×#97C23semidirect
281. C4×C8×C11C23semidirect
282. #66899C23semidirect
283. #66899C23semidirect
286. #66896C23semidirect
287. #66896C23semidirect
296. #66882C23semidirect
297. #66882C23semidirect
298. #66881C23semidirect
299. #66881C23semidirect
300. #66880C23semidirect
301. #66880C23semidirect
302. Dic11⋊C8C23semidirect
303. Dic11⋊C8C23semidirect
304. Dic11⋊C8C23semidirect
305. Dic11⋊C8C23semidirect
306. #66874C23semidirect
307. #66874C23semidirect
310. #66872C23semidirect
311. #66872C23semidirect
312. #66872C23semidirect
313. #66871C23semidirect
314. #66871C23semidirect
315. #66871C23semidirect
316. #66867C23semidirect
317. C4×C11⋊C8C23semidirect
487. #2946D11semidirect
597. #520C2×D11semidirect
652. #442C2×D11semidirect
658. #440C2×D11semidirect
664. C4×SD16C2×D11semidirect
666. C4×D8C2×D11semidirect
672. #428C2×D11semidirect
682. #416C2×D11semidirect
688. #405C2×D11semidirect
799. C4×Q8C22×D11semidirect
828. C4×D4C22×D11semidirect
873. #107C22×D11semidirect
879. #106C22×D11semidirect
890. #103C22×D11semidirect
891. #103C22×D11semidirect
902. #102C22×D11semidirect
903. #102C22×D11semidirect
911. #97C22×D11semidirect
913. 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
#130823692
D11×#5182
#130788672
#130788652
#130787982
#130787962
#130787522
#130787132
#130786612
#130786222
#130785662
#130785272
#130784452
#130784432
#130781312
#130781302
#130778412
C2×#106223892
#130774772
#130774732
#130774442
#130772712
C11×#29462
#6057911