Finite Group Databasebeta

← #15622525

Subgroups — #15622525

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#13082365C211yesmaximal, characteristic, complemented
2D11×#518C211yesmaximal, characteristic, complemented
3#13078866C212yesmaximal, complemented
4#13078866C212yesmaximal, complemented
5#13078799C212yesmaximal, complemented
6#13078797C212yesmaximal, complemented
7#13078753C212yesmaximal, complemented
8#13078714C212yesmaximal, complemented
9#13078662C212yesmaximal, complemented
10#13078623C212yesmaximal, complemented
11#13078562C211yesmaximal, characteristic, complemented
12#13078527C211yesmaximal, characteristic, complemented
13#13078448C211yesmaximal, characteristic, complemented
14#13078447C211yesmaximal, characteristic, complemented
15#13078124C211yesmaximal, characteristic, complemented
16#13077841C211yesmaximal, characteristic
17C2×#10622782C211yesmaximal, characteristic, complemented
18#13077476C211yesmaximal, characteristic, complemented
19#13077471C211yesmaximal, characteristic, complemented
20#13077451C211yesmaximal, characteristic, complemented
21#13077449C211yesmaximal, characteristic, complemented
22#13077273C211yesmaximal, characteristic, complemented
23C11×#3042C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
26C22×C11×SD16C2211yescharacteristic
27C11×#536C2211yescharacteristic, complemented
28C11×#518C2211yescharacteristic
29#10623359C2211yescharacteristic
30#10623358C2211yescharacteristic, complemented
31C2×#67002C2211yescharacteristic
32C2×#66999C2211yescharacteristic
33#10623343C2211yescharacteristic, complemented
34C22×#4325C2211yescharacteristic
35#10623329C2211yescharacteristic
36#10623262C2212yescomplemented
37#10623259C2212yescomplemented
38#10623213C2212yescomplemented
39#10623211C2212yescomplemented
40#10623189—22no—
41#10623181—22no—
42#10623173—21no—
43#10623172—21no—
44#10623170—21no—
45#10623166—21no—
46#10623076—21no—
47#10623076—21no—
48#10623076C2212yes—
49#10623076C2212yes—
50C4×D4×D11—21no—
51C4×D4×D11—21no—
52C4×D4×D11C2212yes—
53C4×D4×D11C2212yes—
54#10623052C2211yescharacteristic
55#10623052C2211yescharacteristic
56D11×#117C2211yescharacteristic
57D11×#117C2211yescharacteristic
58#10623050C2211yescharacteristic, complemented
59#10623017—22no—
60C2×C22⋊C4×D11—22no—
61C11×#463C2212yescomplemented
62C11×#463C2212yescomplemented
63C11×#461C2212yescomplemented
64C11×#461C2212yescomplemented
65C11×#424C2211yescharacteristic, complemented
66C11×#419C2211yescharacteristic, complemented
67C11×#416C2211yescharacteristic, complemented
68#10622846C2211yescharacteristic, complemented
69#10622838C2211yescharacteristic, complemented
70#10622828C2211yescharacteristic
71C2×#66896C2211yescharacteristic
72#10622782C2212yes—
73#10622782C2212yes—
74#10622782C2212yes—
75#10622782C2212yes—
76#10622782C2212yes—
77#10622782C2212yes—
78#10622777C2212yescomplemented
79#10622777C2212yescomplemented
80#10622777C2212yescomplemented
81SD16×Dic11C2212yescomplemented
82SD16×Dic11C2212yescomplemented
83SD16×Dic11C2212yescomplemented
84#10622769C2212yes—
85#10622769C2212yes—
86#10622765C2212yescomplemented
87D8×Dic11C2212yescomplemented
88#10622744C2211yescharacteristic
89#10622739C2211yescharacteristic
90#10622735C2211yescharacteristic, complemented
91#10622734C2211yescharacteristic, complemented
92C2×#66885C2211yescharacteristic
93C2×(C2×D11)⋊C8C2211yescharacteristic
94#10622719C2211yescharacteristic, complemented
95#10622714C2211yescharacteristic, complemented
96#10622696C2212yescomplemented
97#10622696C2212yescomplemented
98#10622670C2212yescomplemented
99#10622670C2212yescomplemented
100#10622622C2212yescomplemented
101#10622622C2212yescomplemented
102#10622621C2212yescomplemented
103#10622620C2212yescomplemented
104#10622612C2211yescharacteristic, complemented
105#10622611C2211yescharacteristic, complemented
106#10622608C2211yescharacteristic, complemented
107#10622460C2212yescomplemented
108#10622460C2212yescomplemented
109#10622459C2212yescomplemented
110#10622455C2212yescomplemented
111#10622453C2212yescomplemented
112#10622453C2212yescomplemented
113#10622448C2212yescomplemented
114#10622446C2212yescomplemented
115#10622430C2212yescomplemented
116#10622430C2212yescomplemented
117#10622430C2212yescomplemented
118#10622428C2212yescomplemented
119#10622428C2211yescharacteristic, complemented
120#10622427C2212yescomplemented
121#10622427C2211yescharacteristic, complemented
122#10622422C2212yescomplemented
123#10622422C2211yescharacteristic, complemented
124#10622418C2212yescomplemented
125#10622418C2211yescharacteristic, complemented
126#10622401C2212yescomplemented
127#10622401C2212yescomplemented
128#10622401C2212yescomplemented
129#10622398C2212yescomplemented
130#10622397C2211yescharacteristic, complemented
131#10622392C2211yescharacteristic, complemented
132#10622390C2211yescharacteristic, complemented
133#10622387C2211yescharacteristic, complemented
134#10622369C2212yescomplemented
135C24×D11—21no—
136C2×C11×#41C2311yescharacteristic
137C22×Q8×C11C2311yescharacteristic
138C22×D4×C11C2311yescharacteristic
139C22×C22⋊D11—21no—
140C2×D4×D11—24no—
141C2×D4×D11—24no—
142C2×D4×D11—21no—
143C2×D4×D11—21no—
144C2×D4×D11C2312yes—
145C2×D4×D11C2312yes—
146C22×D44C2311yescharacteristic
147C22×C4×D11—22no—
148C22×C4×D11—22no—
149C22×C4×D11C2311yescharacteristic
150C11×AGL(1,ℤ/8)—24no—
151C2×C11×SD16—24no—
152C2×C11×SD16C2312yes—
153C2×C11×SD16C2312yes—
154C2×C11×SD16C2312yes—
155C2×C11×D8C2312yes—
156C2×C11×M16C2311yescharacteristic
157C22×C8×C11C2311yescharacteristic
158C11×C4⋊Q8C2312yescomplemented
159C11×#124C2312yescomplemented
160C11×#123—22no—
161C11×C22⋊Q8—21no—
162C11×C22⋊Q8—21no—
163C4×D4×C11—21no—
164C4×D4×C11—21no—
165C4×D4×C11C2312yes—
166C4×D4×C11C2312yes—
167C11×#117C2311yescharacteristic
168C11×#117C2311yescharacteristic
169C2×C11×C22⋊C4—22no—
170C2×C22⋊Dic11—22no—
171#67002—24no—
172#66999—21no—
173#66999—21no—
174#66999C2311yescharacteristic
175#66999C2312yes—
176#66999C2311yescharacteristic
177#66999C2312yes—
178Q8×Dic11—21no—
179Q8×Dic11—21no—
180Q8×Dic11C2312yescomplemented
181Q8×Dic11C2312yescomplemented
182Q8×Dic11C2312yescomplemented
183C2×#4325—24no—
184C2×#4325C2312yes—
185C2×#4325C2312yes—
186C2×#4325C2312yes—
187#66991C2311yescharacteristic
188#66991C2311yescharacteristic
189#66990—21no—
190#66988—21no—
191D4×Dic11—22no—
192D4×Dic11—21no—
193D4×Dic11—21no—
194D4×Dic11C2312yes—
195D4×Dic11C2312yes—
196D4×Dic11C2312yescomplemented
197C2×#4323C2312yes—
198C4×C22⋊D11—21no—
199C4×C22⋊D11—21no—
200C4×C22⋊D11—22no—
201C4×C22⋊D11—22no—
202C4×C22⋊D11—22no—
203C4×C22⋊D11—22no—
204C2×(C2×D11)⋊C4—21no—
205C2×(C2×D11)⋊C4—22no—
206C2×(C2×D11)⋊C4—22no—
207#66979—22no—
208#66979—21no—
209#66979C2311yescharacteristic
210#66979C2311yescharacteristic
211#66979C2311yescharacteristic
212C2×C4⋊Dic11—21no—
213C2×C4⋊Dic11C2311yescharacteristic
214C2×Dic11⋊C4—21no—
215C2×#4318C2311yescharacteristic
216C22×C11⋊C8C2311yescharacteristic
217#66951—22no—
218#66951—22no—
219#66950—22no—
220#66946—21no—
221#66946—21no—
222#66946C2312yes—
223#66946C2312yes—
224#66945—22no—
225#66945D411yescharacteristic
226#66945D411yescharacteristic
227#66945C2311yescharacteristic
228#66945C2311yescharacteristic
229C4⋊C4×D11D411yescharacteristic
230C4⋊C4×D11D411yescharacteristic
231C4⋊C4×D11C2311yescharacteristic
232C4⋊C4×D11C2311yescharacteristic
233#66943—21no—
234#66943—22no—
235#66942—22no—
236#66942—22no—
237#66941—21no—
238#66940—22no—
239#66939—22no—
240#66938—22no—
241#66936—22no—
242(C22⋊D11)⋊C4—22no—
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#66932—22no—
256#66932—22no—
257#66931—22no—
258#66931—22no—
259#66930—21no—
260#66930—22no—
261#66930D412yes—
262C4×D44—21no—
263C4×D44—21no—
264C4×D44C2312yes—
265C4×D44C2312yes—
266#66925—21no—
267#66925C2312yes—
268C42×D11—21no—
269C42×D11C2312yes—
270#66923C2312yescomplemented
271#66922C2312yescomplemented
272C11×C4⋊C8C2312yescomplemented
273C11×C4⋊C8C2312yescomplemented
274C11×#103C2311yescharacteristic, complemented
275C11×#103C2311yescharacteristic, complemented
276C11×#103C2312yescomplemented
277C11×#103C2312yescomplemented
278C11×#102C2311yescharacteristic, complemented
279C11×#102C2311yescharacteristic, complemented
280#66899C2311yescharacteristic, complemented
281#66899C2312yescomplemented
282#66899C2312yescomplemented
283#66899C2311yescharacteristic, complemented
284#66896C2312yes—
285#66896C2312yes—
286#66896C2312yes—
287#66896C2312yes—
288#66896C2311yescharacteristic, complemented
289#66896C2311yescharacteristic, complemented
290#66885C2312yes—
291#66885C2312yes—
292#66885C2312yes—
293#66885C2312yes—
294(C2×D11)⋊C8C2311yescharacteristic
295(C2×D11)⋊C8C2311yescharacteristic
296(C2×D11)⋊C8C2311yescharacteristic
297(C2×D11)⋊C8C2311yescharacteristic
298(C2×D11)⋊C8C2312yes—
299(C2×D11)⋊C8C2312yes—
300#66882C2312yescomplemented
301#66882C2311yescharacteristic, complemented
302#66882C2311yescharacteristic, complemented
303#66881C2312yescomplemented
304#66881C2311yescharacteristic, complemented
305#66881C2311yescharacteristic, complemented
306#66879C2312yescomplemented
307#66879C2312yescomplemented
308C8×Dic11C2312yescomplemented
309C8×Dic11C2312yescomplemented
310#66872C2312yescomplemented
311#66872C2311yescharacteristic, complemented
312#66872C2311yescharacteristic, complemented
313#66871C2312yescomplemented
314#66871C2311yescharacteristic, complemented
315#66871C2311yescharacteristic, complemented
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
327C11×#41—22no—
328C11×#41—22no—
329C2×Q8×C11—21no—
330C2×Q8×C11—22no—
331C2×Q8×C11—22no—
332C2×Q8×C11C2412yes—
333C2×Q8×C11C2411yescharacteristic
334C2×D4×C11—21no—
335C2×D4×C11—21no—
336C2×D4×C11—22no—
337C2×D4×C11#4114yes—
338C2×D4×C11C2411yescharacteristic
339C2×D4×C11C2412yes—
340C22×C4×C11—21no—
341C22×C4×C11—21no—
342C22×C4×C11—22no—
343C22×C4×C11—22no—
344C22×C4×C11C2411yescharacteristic
345C2×C22⋊D11—28no—
346C2×C22⋊D11—22no—
347C2×C22⋊D11—22no—
348C2×C22⋊D11—21no—
349C2×C22⋊D11—21no—
350C22×Dic11—22no—
351C22×Dic11—22no—
352C22×Dic11—22no—
353C22×Dic11—21no—
354C22×Dic11C2×D411yescharacteristic
355D4×D11—28no—
356D4×D11—28no—
357D4×D11—24no—
358D4×D11—24no—
359D4×D11—24no—
360D4×D11—24no—
361C2×D44—21no—
362C2×D44—22no—
363C2×D44#4114yes—
364C2×D44C2412yes—
365C2×C4×D11—22no—
366C2×C4×D11—22no—
367C2×C4×D11—21no—
368C2×C4×D11—21no—
369C2×C4×D11—22no—
370C2×C4×D11—22no—
371C2×C4×D11—22no—
372C2×C4×D11—22no—
373C2×C4×D11—84no—
374C2×C4×D11—84no—
375C2×C4×D11C2×D411yescharacteristic
376C2×C4×D11C2×D412yes—
377C2×C4×D11C2×D411yescharacteristic
378C2×C4×D11C2×D412yes—
379C2×C4×D11C2411yescharacteristic
380C2×C4×D11C2411yescharacteristic
381C2×Dic22—22no—
382C11×SD16—24no—
383C11×SD16—24no—
384C11×SD16—24no—
385C11×D8—24no—
386C11×M16—22no—
387C2×C8×C11—22no—
388C2×C8×C11C2411yescharacteristic
389C2×C8×C11C2412yes—
390C2×C8×C11C2411yescharacteristic
391C11×C4⋊C4—22no—
392C11×C4⋊C4—22no—
393C11×C4⋊C4C2×D411yescharacteristic
394C11×C4⋊C4C2×D411yescharacteristic
395C11×C4⋊C4C2411yescharacteristic
396C11×C4⋊C4C2411yescharacteristic
397C11×C22⋊C4—21no—
398C11×C22⋊C4—22no—
399C11×C22⋊C4—22no—
400C11×C22⋊C4—22no—
401C11×C22⋊C4—22no—
402C11×C22⋊C4C2×D412yes—
403C42×C11—21no—
404C42×C11C2412yes—
405C22⋊Dic11—21no—
406C22⋊Dic11—21no—
407C22⋊Dic11—22no—
408C22⋊Dic11—22no—
409C22⋊Dic11—22no—
410C22⋊Dic11—21no—
411C22⋊Dic11—21no—
412C22⋊Dic11C2×D412yes—
413#4325—24no—
414#4325—24no—
415#4325—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—22no—
422(C2×D11)⋊C4—22no—
423(C2×D11)⋊C4—21no—
424(C2×D11)⋊C4—21no—
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⋊Dic11—22no—
433C4⋊Dic11—21no—
434C4⋊Dic11C2×D411yescharacteristic
435C4⋊Dic11C2×D411yescharacteristic
436C4⋊Dic11C2411yescharacteristic
437C4⋊Dic11C2412yes—
438C4⋊Dic11C2411yescharacteristic
439C4⋊Dic11C2411yescharacteristic
440C4⋊Dic11C2411yescharacteristic
441Dic11⋊C4—21no—
442Dic11⋊C4—21no—
443Dic11⋊C4—22no—
444Dic11⋊C4—22no—
445Dic11⋊C4—21no—
446Dic11⋊C4—21no—
447Dic11⋊C4—22no—
448Dic11⋊C4—22no—
449Dic11⋊C4C2×D412yes—
450Dic11⋊C4C2×D412yes—
451C4×Dic11—21no—
452C4×Dic11—21no—
453C4×Dic11—22no—
454C4×Dic11—22no—
455C4×Dic11—22no—
456C4×Dic11—21no—
457C4×Dic11—21no—
458C4×Dic11C2×D412yes—
459C4×Dic11C2×D412yes—
460C4×Dic11C2412yes—
461#4318—22no—
462C2×C11⋊C8—22no—
463C2×C11⋊C8C2411yescharacteristic
464C2×C11⋊C8C2412yes—
465C2×C11⋊C8C2411yescharacteristic
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#3042D1111yescharacteristic, complemented
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—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—22no—
512Q8×C11—21no—
513Q8×C11—22no—
514Q8×C11—21no—
515Q8×C11—42no—
516D4×C11—24no—
517D4×C11—22no—
518D4×C11—21no—
519D4×C11—21no—
520D4×C11—42no—
521D4×C11C2×#4114yes—
522C2×C4×C11—22no—
523C2×C4×C11—21no—
524C2×C4×C11—21no—
525C2×C4×C11—21no—
526C2×C4×C11—42no—
527C2×C4×C11—42no—
528C2×C4×C11—82no—
529C2×C4×C11—82no—
530C2×C4×C11C22×D412yes—
531C2×C4×C11C22×D412yes—
532C2×C4×C11C22×D411yescharacteristic
533C2×C4×C11C2×#4112yes—
534C2×C4×C11C2×#4112yes—
535C2×C4×C11C2511yescharacteristic
536C22⋊D11—28no—
537C22⋊D11—28no—
538C22⋊D11—42no—
539C22⋊D11—81no—
540C2×Dic11—22no—
541C2×Dic11—21no—
542C2×Dic11—21no—
543C2×Dic11—21no—
544C2×Dic11—21no—
545C2×Dic11—22no—
546C2×Dic11—82no—
547C2×Dic11—82no—
548C2×Dic11—82no—
549C2×Dic11—81no—
550C2×Dic11C22×D412yes—
551C2×Dic11C22×D411yescharacteristic
552C2×Dic11C22×D412yes—
553C2×Dic11C22×D411yescharacteristic
554D44—24no—
555D44—22no—
556D44C2×#4114yes—
557C4×D11—24no—
558C4×D11—22no—
559C4×D11—22no—
560C4×D11—21no—
561C4×D11—21no—
562C4×D11—21no—
563C4×D11—21no—
564C4×D11—42no—
565C4×D11—42no—
566C4×D11—42no—
567C4×D11—82no—
568C4×D11—82no—
569C4×D11—82no—
570C4×D11—82no—
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×SD16C2×D1111yescharacteristic
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#536C2×D1111yescharacteristic, complemented
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—111no—
617#485—112no—
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#478—112no—
630#478—112no—
631#476—112no—
632#476—112no—
633#474—112no—
634#474—112no—
635#463—112no—
636#463—112no—
637#463C2×D1112yescomplemented
638#463C2×D1112yescomplemented
639#461—112no—
640#461—112no—
641#461C2×D1112yescomplemented
642#461C2×D1112yescomplemented
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#428—111no—
673#427—111no—
674#427—111no—
675#424—111no—
676#424C2×D1111yescharacteristic, complemented
677#419—111no—
678#419C2×D1111yescharacteristic, complemented
679#418—111no—
680#418—111no—
681#416—111no—
682#416C2×D1111yescharacteristic, complemented
683C2×#102—111no—
684C2×#102—111no—
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—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—41no—
716C4×C11—41no—
717C4×C11—42no—
718C4×C11—41no—
719C4×C11#52512yes—
720C4×C11C22×#4111yescharacteristic
721C4×C11C22×#4111yescharacteristic
722Dic11—22no—
723Dic11—21no—
724Dic11—21no—
725Dic11—22no—
726Dic11—41no—
727Dic11—42no—
728Dic11—41no—
729Dic11—41no—
730Dic11—41no—
731C25—221no—
732C2×#41C22×D1111yescharacteristic
733C22×Q8C22×D1111yescharacteristic
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—24no—
749C2×SD16—112no—
750C2×SD16—112no—
751C2×SD16—112no—
752C2×SD16—224no—
753C2×SD16C22×D1112yes—
754C2×SD16C22×D1112yes—
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—221no—
764C4⋊Q8C22×D1112yescomplemented
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—222no—
775#124C22×D1112yescomplemented
776#123—22no—
777#123—222no—
778#123—222no—
779#123—221no—
780C22⋊Q8—21no—
781C22⋊Q8—21no—
782C22⋊Q8—112no—
783C22⋊Q8—112no—
784C22⋊Q8—111no—
785C22⋊Q8—111no—
786C22⋊Q8—222no—
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—112no—
797C4×Q8—222no—
798C4×Q8—221no—
799C4×Q8—221no—
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—222no—
812C4×D4—222no—
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—221no—
822C4×D4—221no—
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—111no—
838#117—221no—
839#117—222no—
840#117—221no—
841#117—222no—
842#117—222no—
843#117—221no—
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—111no—
851C2×C4⋊C4—221no—
852C2×C4⋊C4—221no—
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#107—111no—
872#107—111no—
873#107—112no—
874#106—111no—
875#106—111no—
876#106—112no—
877#106—111no—
878#106—111no—
879#106—112no—
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#103C22×D1111yescharacteristic, complemented
889#103C22×D1111yescharacteristic, complemented
890#103C22×D1112yescomplemented
891#103C22×D1112yescomplemented
892#102—112no—
893#102—112no—
894#102—112no—
895#102—112no—
896#102—111no—
897#102—111no—
898#102—112no—
899#102—112no—
900#102—112no—
901#102—112no—
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#97—112no—
912C4×C8—112no—
913C4×C8—112no—
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—21no—
934C2×Q8—22no—
935C2×Q8—22no—
936C2×Q8—222no—
937C2×Q8C23×D1112yes—
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—221no—
956C2×D4—222no—
957C2×D4#434114yes—
958C2×D4C23×D1111yescharacteristic
959C2×D4C23×D1112yes—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—22no—
963C22×C4—22no—
964C22×C4—111no—
965C22×C4—112no—
966C22×C4—111no—
967C22×C4—111no—
968C22×C4—111no—
969C22×C4—111no—
970C22×C4—112no—
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—222no—
980C22×C4—221no—
981C22×C4—222no—
982C22×C4—222no—
983C22×C4—884no—
984C22×C4—884no—
985C22×C4C23×D1111yescharacteristic
986SD16—24no—
987SD16—24no—
988SD16—24no—
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—22no—
1005C4⋊C4—22no—
1006C4⋊C4—111no—
1007C4⋊C4—111no—
1008C4⋊C4—112no—
1009C4⋊C4—112no—
1010C4⋊C4—112no—
1011C4⋊C4—111no—
1012C4⋊C4—111no—
1013C4⋊C4—111no—
1014C4⋊C4—111no—
1015C4⋊C4—221no—
1016C4⋊C4—221no—
1017C4⋊C4—222no—
1018C4⋊C4—222no—
1019C4⋊C4—222no—
1020C4⋊C4—222no—
1021C4⋊C4—222no—
1022C4⋊C4—221no—
1023C4⋊C4—221no—
1024C4⋊C4—221no—
1025C4⋊C4—222no—
1026C4⋊C4—222no—
1027C4⋊C4—222no—
1028C4⋊C4D4×D1111yescharacteristic
1029C4⋊C4D4×D1111yescharacteristic
1030C4⋊C4C23×D1111yescharacteristic
1031C4⋊C4C23×D1111yescharacteristic
1032C22⋊C4—21no—
1033C22⋊C4—22no—
1034C22⋊C4—22no—
1035C22⋊C4—22no—
1036C22⋊C4—22no—
1037C22⋊C4—112no—
1038C22⋊C4—112no—
1039C22⋊C4—112no—
1040C22⋊C4—222no—
1041C22⋊C4—222no—
1042C22⋊C4—221no—
1043C22⋊C4—221no—
1044C22⋊C4—222no—
1045C22⋊C4—222no—
1046C22⋊C4—221no—
1047C22⋊C4—221no—
1048C22⋊C4—222no—
1049C22⋊C4—222no—
1050C22⋊C4—221no—
1051C22⋊C4—222no—
1052C22⋊C4—221no—
1053C22⋊C4—221no—
1054C22⋊C4—221no—
1055C22⋊C4—222no—
1056C22⋊C4—222no—
1057C22⋊C4D4×D1112yes—
1058C42—21no—
1059C42—112no—
1060C42—112no—
1061C42—112no—
1062C42—221no—
1063C42—221no—
1064C42—222no—
1065C42—222no—
1066C42—222no—
1067C42—221no—
1068C42—221no—
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—22no—
1094Q8—21no—
1095Q8—22no—
1096Q8—21no—
1097Q8—42no—
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×#434114yes—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—22no—
1115C2×C4—21no—
1116C2×C4—42no—
1117C2×C4—42no—
1118C2×C4—82no—
1119C2×C4—82no—
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—221no—
1135C2×C4—221no—
1136C2×C4—222no—
1137C2×C4—442no—
1138C2×C4—442no—
1139C2×C4—442no—
1140C2×C4—882no—
1141C2×C4—882no—
1142C2×C4—882no—
1143C2×C4—882no—
1144C2×C4—882no—
1145C2×C4—882no—
1146C2×C4—882no—
1147C2×C4—881no—
1148C2×C4C2×D4×D1112yes—
1149C2×C4C2×D4×D1112yes—
1150C2×C4C2×D4×D1111yescharacteristic
1151C2×C4C2×#434112yes—
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—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#1062313712yes—
1183C22C22×D4×D1111yescharacteristic
1184C4—22no—
1185C4—22no—
1186C4—41no—
1187C4—42no—
1188C4—41no—
1189C4—41no—
1190C4—221no—
1191C4—221no—
1192C4—222no—
1193C4—222no—
1194C4—441no—
1195C4—442no—
1196C4—441no—
1197C4—441no—
1198C4—441no—
1199C4#1062313712yes—
1200C4C22×#434111yescharacteristic
1201C4C2×#41×D1111yescharacteristic
1202C2—22no—
1203C2—44no—
1204C2—81no—
1205C2—222no—
1206C2—441no—
1207C2—444no—
1208C2C2×#1062313711yescharacteristic
1209C2D11×#57711yescharacteristic
1210C2#1308339411yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3042C2
socleC22×C11C23×D4
prime radical#13077841C2
hypercenter#3042D11
hypocenterC11#60579
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #3042

Complements

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

NH ≅ G/Ntype
1. #13082365C2semidirect
2. D11×#518C2semidirect
3. #13078866C2semidirect
4. #13078866C2semidirect
5. #13078799C2semidirect
6. #13078797C2semidirect
7. #13078753C2semidirect
8. #13078714C2semidirect
9. #13078662C2semidirect
10. #13078623C2semidirect
11. #13078562C2semidirect
12. #13078527C2semidirect
13. #13078448C2semidirect
14. #13078447C2semidirect
15. #13078124C2semidirect
17. C2×#10622782C2semidirect
18. #13077476C2semidirect
19. #13077471C2semidirect
20. #13077451C2semidirect
21. #13077449C2semidirect
22. #13077273C2semidirect
23. C11×#3042C2semidirect
27. C11×#536C22semidirect
30. #10623358C22semidirect
33. #10623343C22semidirect
36. #10623262C22semidirect
37. #10623259C22semidirect
38. #10623213C22semidirect
39. #10623211C22semidirect
58. #10623050C22semidirect
61. C11×#463C22semidirect
62. C11×#463C22semidirect
63. C11×#461C22semidirect
64. C11×#461C22semidirect
65. C11×#424C22semidirect
66. C11×#419C22semidirect
67. C11×#416C22semidirect
68. #10622846C22semidirect
69. #10622838C22semidirect
78. #10622777C22semidirect
79. #10622777C22semidirect
80. #10622777C22semidirect
81. SD16×Dic11C22semidirect
82. SD16×Dic11C22semidirect
83. SD16×Dic11C22semidirect
86. #10622765C22semidirect
87. D8×Dic11C22semidirect
90. #10622735C22semidirect
91. #10622734C22semidirect
94. #10622719C22semidirect
95. #10622714C22semidirect
96. #10622696C22semidirect
97. #10622696C22semidirect
98. #10622670C22semidirect
99. #10622670C22semidirect
100. #10622622C22semidirect
101. #10622622C22semidirect
102. #10622621C22semidirect
103. #10622620C22semidirect
104. #10622612C22semidirect
105. #10622611C22semidirect
106. #10622608C22semidirect
107. #10622460C22semidirect
108. #10622460C22semidirect
109. #10622459C22semidirect
110. #10622455C22semidirect
111. #10622453C22semidirect
112. #10622453C22semidirect
113. #10622448C22semidirect
114. #10622446C22semidirect
115. #10622430C22semidirect
116. #10622430C22semidirect
117. #10622430C22semidirect
118. #10622428C22semidirect
119. #10622428C22semidirect
120. #10622427C22semidirect
121. #10622427C22semidirect
122. #10622422C22semidirect
123. #10622422C22semidirect
124. #10622418C22semidirect
125. #10622418C22semidirect
126. #10622401C22semidirect
127. #10622401C22semidirect
128. #10622401C22semidirect
129. #10622398C22semidirect
130. #10622397C22semidirect
131. #10622392C22semidirect
132. #10622390C22semidirect
133. #10622387C22semidirect
134. #10622369C22semidirect
158. C11×C4⋊Q8C23semidirect
159. C11×#124C23semidirect
180. Q8×Dic11C23semidirect
181. Q8×Dic11C23semidirect
182. Q8×Dic11C23semidirect
196. D4×Dic11C23semidirect
270. #66923C23semidirect
271. #66922C23semidirect
272. C11×C4⋊C8C23semidirect
273. C11×C4⋊C8C23semidirect
274. C11×#103C23semidirect
275. C11×#103C23semidirect
276. C11×#103C23semidirect
277. C11×#103C23semidirect
278. C11×#102C23semidirect
279. C11×#102C23semidirect
280. #66899C23semidirect
281. #66899C23semidirect
282. #66899C23semidirect
283. #66899C23semidirect
288. #66896C23semidirect
289. #66896C23semidirect
300. #66882C23semidirect
301. #66882C23semidirect
302. #66882C23semidirect
303. #66881C23semidirect
304. #66881C23semidirect
305. #66881C23semidirect
306. #66879C23semidirect
307. #66879C23semidirect
308. C8×Dic11C23semidirect
309. C8×Dic11C23semidirect
310. #66872C23semidirect
311. #66872C23semidirect
312. #66872C23semidirect
313. #66871C23semidirect
314. #66871C23semidirect
315. #66871C23semidirect
316. C4⋊(C11⋊C8)C23semidirect
317. C4⋊(C11⋊C8)C23semidirect
481. #3042D11semidirect
592. #536C2×D11semidirect
637. #463C2×D11semidirect
638. #463C2×D11semidirect
641. #461C2×D11semidirect
642. #461C2×D11semidirect
676. #424C2×D11semidirect
678. #419C2×D11semidirect
682. #416C2×D11semidirect
764. C4⋊Q8C22×D11semidirect
775. #124C22×D11semidirect
882. C4⋊C8C22×D11semidirect
883. C4⋊C8C22×D11semidirect
888. #103C22×D11semidirect
889. #103C22×D11semidirect
890. #103C22×D11semidirect
891. #103C22×D11semidirect
902. #102C22×D11semidirect
903. #102C22×D11semidirect
1070. C11#60579semidirect

Maximal subgroups

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

subgroupindex
#130823652
D11×#5182
#130788662
#130787992
#130787972
#130787532
#130787142
#130786622
#130786232
#130785622
#130785272
#130784482
#130784472
#130781242
#130778412
C2×#106227822
#130774762
#130774712
#130774512
#130774492
#130772732
C11×#30422
#6057911