Finite Group Databasebeta

← #15618024

Subgroups — #15618024

Order 2816.

2734 conjugacy classes of subgroups.

The subgroup lattice has 1232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623301C211yesmaximal, characteristic
2C4×#67043C211yesmaximal, characteristic, complemented
3C4×#67042C211yesmaximal, characteristic, complemented
4#13077492C211yesmaximal, characteristic, complemented
5#13077488C212yesmaximal, complemented
6#13077474C211yesmaximal, characteristic, complemented
7#13077472C212yesmaximal, complemented
8#13077462C211yesmaximal, characteristic, complemented
9#13077458C212yesmaximal, complemented
10#13077451C211yesmaximal, characteristic, complemented
11#13077445C212yesmaximal, complemented
12C4×#67004C211yesmaximal, characteristic, complemented
13#13077432C212yesmaximal, complemented
14#13077427C212yesmaximal, complemented
15C4×#67002C211yesmaximal, characteristic, complemented
16#13077411C212yesmaximal, complemented
17C2×#10622323C211yesmaximal, characteristic, complemented
18D11×#440C212yesmaximal, complemented
19#13077213C211yesmaximal, characteristic, complemented
20#13077145C211yesmaximal, characteristic, complemented
21#13077138C211yesmaximal, characteristic, complemented
22#13077041C211yesmaximal, characteristic, complemented
23C11×#2943C211yesmaximal, characteristic, complemented
24C2×#67043C2211yescharacteristic
25C2×#67042C2211yescharacteristic
26C2×C11×#135C2211yescharacteristic
27C4×C11×#41C2211yescharacteristic
28C4×C11×#41C2211yescharacteristic, complemented
29#10623358C2211yescharacteristic
30#10623358C2211yescharacteristic, complemented
31C2×#67004C2211yescharacteristic
32C2×#67002C2211yescharacteristic
33#10623301C4116yescomplemented
34C2×#66971C2212yes—
35C2×#66969C2212yes—
36C2×SD16×D11C2212yes—
37C2×#66964C2212yes—
38C22×#4314C2211yescharacteristic
39C2×#66954C2211yescharacteristic
40C2×#66954C2211yescharacteristic
41#10623105C2212yes—
42C4×#4343C2212yes—
43#10623103C2212yescomplemented
44C4×Q8×D11C2212yescomplemented
45#10623077—22no—
46#10623077C2212yescomplemented
47#10623076—22no—
48#10623076C2212yes—
49C4×D4×D11—22no—
50C4×D4×D11C2212yes—
51C4×#4341—22no—
52C4×#4341C2212yescomplemented
53#10623054—21no—
54#10623054—21no—
55#10623054C2211yescharacteristic
56#10623054C2211yescharacteristic
57#10623052—21no—
58#10623052C2211yescharacteristic
59#10623047—21no—
60#10623047C2211yescharacteristic, complemented
61C4×#4339—21no—
62C4×#4339—21no—
63C4×#4339C2211yescharacteristic
64C2×C4×D44—21no—
65C2×C4×D44C2211yescharacteristic
66C2×C4×Dic22—21no—
67C2×C4×Dic22C2211yescharacteristic, complemented
68C11×#442C2211yescharacteristic, complemented
69C11×#442C2211yescharacteristic, complemented
70C11×#441C2211yescharacteristic, complemented
71C11×#441C2211yescharacteristic, complemented
72C11×#440C2211yescharacteristic, complemented
73C11×#440C2211yescharacteristic, complemented
74C11×#440C2211yescharacteristic, complemented
75C11×#440C2211yescharacteristic, complemented
76C11×#427C2211yescharacteristic, complemented
77C11×#416C2211yescharacteristic
78C11×#416C2211yescharacteristic, complemented
79C2×C11×#97C2211yescharacteristic, complemented
80#10622845C2211yescharacteristic
81#10622845C2211yescharacteristic, complemented
82Q16×Dic11C2212yescomplemented
83#10622777C2212yescomplemented
84#10622777C2212yescomplemented
85D8×Dic11C2212yescomplemented
86C2×#66885C2211yescharacteristic
87C2×#66882C2211yescharacteristic, complemented
88C2×#66880C2211yescharacteristic, complemented
89#10622714C2211yescharacteristic, complemented
90#10622714C2211yescharacteristic, complemented
91#10622643C2212yescomplemented
92C4×#4326C2212yescomplemented
93#10622639C2212yescomplemented
94C4×#4325C2212yescomplemented
95#10622631C2212yescomplemented
96C4×#4324C2212yescomplemented
97#10622627C2212yescomplemented
98C4×#4323C2212yescomplemented
99#10622617C2211yescharacteristic, complemented
100#10622614C2211yescharacteristic
101#10622608C2211yescharacteristic, complemented
102#10622608C2211yescharacteristic, complemented
103C4×#4318C2211yescharacteristic, complemented
104#10622502C2212yescomplemented
105#10622502C2212yescomplemented
106#10622493C2212yescomplemented
107D11×#107C2212yescomplemented
108#10622474C2212yescomplemented
109#10622474C2212yescomplemented
110#10622465C2212yescomplemented
111#10622465C2212yescomplemented
112#10622430C2212yescomplemented
113#10622417C2212yes—
114#10622416C2212yes—
115#10622415C2212yescomplemented
116D11×#103C2212yescomplemented
117#10622403C2212yescomplemented
118#10622402C2212yescomplemented
119#10622401C2212yescomplemented
120#10622398C2212yescomplemented
121#10622385C2212yescomplemented
122#10622384C2212yescomplemented
123#10622383C2212yes—
124D11×#102C2212yes—
125#10622371C2212yescomplemented
126#10622370C2212yescomplemented
127#10622369C2212yescomplemented
128#10622323C2212yescomplemented
129#10622323C2212yescomplemented
130#10622323C2212yescomplemented
131#10622323C2212yescomplemented
132#10622321C2212yescomplemented
133#10622321C2212yescomplemented
134#10622320C2212yescomplemented
135D11×#97C2212yescomplemented
136C2×C11×#41C2311yescharacteristic
137C2×C11×#41C2311yescharacteristic
138#67043—24no—
139#67043C2×C418yescomplemented
140#67042—24no—
141#67042C2×C418yescomplemented
142C2×#4343C2312yes—
143C2×Q8×D11C2312yes—
144C2×#4341—22no—
145C2×#4341C2312yes—
146C2×D4×D11—22no—
147C2×D4×D11C2312yes—
148C2×#4339—21no—
149C2×#4339—21no—
150C2×#4339C2311yescharacteristic
151C22×D44—21no—
152C22×D44C2311yescharacteristic
153C22×C4×D11—21no—
154C22×C4×D11—22no—
155C22×Dic22—21no—
156C22×Dic22C2311yescharacteristic
157C11×#135C2×C418yescomplemented
158C2×C11×Q16C2311yescharacteristic
159C2×C11×SD16C2311yescharacteristic
160C2×C11×SD16C2311yescharacteristic
161C2×C11×D8C2311yescharacteristic
162C22×C8×C11C2311yescharacteristic
163C22×C8×C11C2311yescharacteristic
164C4×Q8×C11C2311yescharacteristic
165C4×Q8×C11C2311yescharacteristic
166C4×Q8×C11C2311yescharacteristic
167C4×Q8×C11C2311yescharacteristic
168C4×D4×C11—21no—
169C4×D4×C11—21no—
170C4×D4×C11—21no—
171C4×D4×C11—21no—
172C4×D4×C11C2311yescharacteristic
173C4×D4×C11C2311yescharacteristic
174C4×D4×C11C2311yescharacteristic
175C4×D4×C11C2311yescharacteristic
176C11×#117—21no—
177C11×#117—21no—
178C11×#117C2311yescharacteristic
179C11×#117C2311yescharacteristic
180C2×C42×C11—21no—
181C2×C42×C11—21no—
182C2×C42×C11C2311yescharacteristic
183#67004C2×C418yescomplemented
184#67002C2×C418yescomplemented
185Q8×Dic11C2312yes—
186Q8×Dic11C2312yes—
187C2×#4326C2312yes—
188C2×#4325C2312yes—
189D4×Dic11—22no—
190D4×Dic11—22no—
191D4×Dic11C2312yes—
192D4×Dic11C2312yes—
193C2×#4324C2312yes—
194C2×#4323C2312yes—
195C4×C22⋊D11—22no—
196C4×C22⋊D11—22no—
197C4×C22⋊D11—22no—
198C4×C22⋊D11—22no—
199C4×C22⋊D11D412yes—
200C4×C22⋊D11D412yes—
201C2×(C2×D11)⋊C4—21no—
202C2×(C2×D11)⋊C4—22no—
203#66979—21no—
204#66979—21no—
205#66979C2311yescharacteristic
206C2×C4⋊Dic11—21no—
207C2×C4⋊Dic11—21no—
208C2×C4⋊Dic11C2311yescharacteristic
209C2×C4⋊Dic11C2311yescharacteristic
210C2×Dic11⋊C4—21no—
211C2×Dic11⋊C4—22no—
212C2×C4×Dic11—21no—
213C2×C4×Dic11—22no—
214C2×#4318C2311yescharacteristic
215C2×#4318C2311yescharacteristic
216#66971C2×C4116yescomplemented
217#66969C2×C4116yescomplemented
218SD16×D11C2×C4116yescomplemented
219#66964C2×C4116yescomplemented
220C2×#4314C2×C418yescomplemented
221C2×#4314C2312yes—
222C2×#4314C2312yes—
223#66954—24no—
224#66954C2×C418yescomplemented
225C2×#4313C2312yes—
226C2×#4313C2312yes—
227C2×C8×D11C2312yes—
228C2×C8×D11C2312yes—
229#66946—22no—
230#66946—22no—
231#66946C2312yes—
232#66946C2312yes—
233#66945—22no—
234#66945—22no—
235#66945C2312yes—
236#66945C2312yes—
237C4⋊C4×D11—22no—
238C4⋊C4×D11—22no—
239C4⋊C4×D11C2312yes—
240C4⋊C4×D11C2312yes—
241#66940—22no—
242#66940—22no—
243#66940C2312yes—
244#66940C2312yes—
245(C22⋊D11)⋊C4—22no—
246(C22⋊D11)⋊C4—22no—
247(C22⋊D11)⋊C4—22no—
248(C22⋊D11)⋊C4—22no—
249(C22⋊D11)⋊C4—22no—
250(C22⋊D11)⋊C4—22no—
251C22⋊C4×D11—22no—
252C22⋊C4×D11—22no—
253C22⋊C4×D11—22no—
254#66930—22no—
255#66930—22no—
256#66930—22no—
257C4×D44—21no—
258C4×D44—21no—
259C4×D44—22no—
260C4×D44—21no—
261C4×D44—21no—
262C4×D44—22no—
263C4×D44—21no—
264C4×D44—21no—
265C4×D44D411yescharacteristic
266C4×D44D411yescharacteristic
267C4×D44C2312yes—
268C4×D44C2312yes—
269#66925—22no—
270#66925—22no—
271#66925C2312yes—
272C42×D11—22no—
273C42×D11—22no—
274C42×D11C2312yes—
275C4×Dic22—21no—
276C4×Dic22—21no—
277C4×Dic22—21no—
278C4×Dic22—21no—
279C4×Dic22—21no—
280C4×Dic22—21no—
281C4×Dic22—22no—
282C4×Dic22—22no—
283C4×Dic22D411yescharacteristic
284C4×Dic22D411yescharacteristic
285C4×Dic22C2312yes—
286C4×Dic22C2312yes—
287C11×#107C2311yescharacteristic
288C11×#107C2311yescharacteristic
289C11×#106C2311yescharacteristic
290C11×#106C2311yescharacteristic
291C11×#103C2311yescharacteristic
292C11×#103C2311yescharacteristic
293C11×#103C2311yescharacteristic
294C11×#103C2311yescharacteristic
295C11×#102C2311yescharacteristic
296C11×#102C2311yescharacteristic
297C11×#102C2311yescharacteristic
298C11×#102C2311yescharacteristic
299C11×#97C2311yescharacteristic
300C11×#97C2311yescharacteristic
301C11×#97C2311yescharacteristic
302C11×#97C2311yescharacteristic
303#66899C2312yes—
304#66899C2312yes—
305#66896C2312yes—
306#66896C2312yes—
307#66885C2312yes—
308#66885C2312yes—
309#66882C2312yes—
310#66882C2312yes—
311#66880C2312yes—
312#66880C2312yes—
313#66879C2312yes—
314#66879C2312yes—
315C8×Dic11C2312yes—
316C8×Dic11C2312yes—
317#66874C2312yes—
318#66874C2312yes—
319#66873C2312yes—
320#66873C2312yes—
321#66872C2312yes—
322#66872C2312yes—
323#66871C2312yes—
324#66871C2312yes—
325#66867C2312yes—
326C4×C11⋊C8C2312yes—
327#60174—111nomaximal, Sylow
328C23×D11—21no—
329C23×D11—22no—
330C11×#41—22no—
331C11×#41—22no—
332C11×#41C22×C414yes—
333C11×#41C22×C414yescomplemented
334C2×Q8×C11C2411yescharacteristic
335C2×Q8×C11C2411yescharacteristic
336C2×D4×C11—21no—
337C2×D4×C11—21no—
338C2×D4×C11C2411yescharacteristic
339C2×D4×C11C2411yescharacteristic
340C22×C4×C11—21no—
341C22×C4×C11—21no—
342C22×C4×C11—21no—
343C22×C4×C11—21no—
344C22×C4×C11—21no—
345C22×C4×C11—21no—
346C22×C4×C11C2×D411yescharacteristic
347C22×C4×C11C2×D411yescharacteristic
348C22×C4×C11C2411yescharacteristic
349C2×C22⋊D11—22no—
350C2×C22⋊D11—22no—
351C2×C22⋊D11C2×D412yes—
352C22×Dic11—22no—
353C22×Dic11—22no—
354C22×Dic11—22no—
355C22×Dic11—21no—
356C22×Dic11—21no—
357C22×Dic11—21no—
358#4343—24no—
359#4343C22×C418yes—
360Q8×D11—24no—
361Q8×D11C22×C418yescomplemented
362#4341—216no—
363#4341—24no—
364#4341C22×C418yescomplemented
365D4×D11—216no—
366D4×D11—24no—
367D4×D11C22×C418yes—
368#4339—28no—
369#4339—28no—
370#4339C22×C414yes—
371#4339#4114yes—
372C2×D44—28no—
373C2×D44—22no—
374C2×D44—21no—
375C2×D44—22no—
376C2×D44C22×C414yes—
377C2×D44C2×D411yescharacteristic
378C2×D44C2412yes—
379C2×C4×D11—22no—
380C2×C4×D11—22no—
381C2×C4×D11—22no—
382C2×C4×D11—22no—
383C2×C4×D11—22no—
384C2×C4×D11—22no—
385C2×C4×D11—22no—
386C2×C4×D11—22no—
387C2×C4×D11—82no—
388C2×C4×D11—84no—
389C2×C4×D11C2×D412yes—
390C2×C4×D11C2×D412yes—
391C2×C4×D11C2412yes—
392C2×Dic22—22no—
393C2×Dic22—28no—
394C2×Dic22—21no—
395C2×Dic22—22no—
396C2×Dic22C22×C414yescomplemented
397C2×Dic22C2×D411yescharacteristic
398C2×Dic22C2412yes—
399C11×Q16C22×C414yescomplemented
400C11×SD16C22×C414yescomplemented
401C11×SD16C22×C414yescomplemented
402C11×D8C22×C414yescomplemented
403C2×C8×C11—22no—
404C2×C8×C11C22×C414yescomplemented
405C2×C8×C11C2411yescharacteristic
406C2×C8×C11C2411yescharacteristic
407C2×C8×C11C2411yescharacteristic
408C2×C8×C11C2411yescharacteristic
409C11×C4⋊C4—21no—
410C11×C4⋊C4—21no—
411C11×C4⋊C4—21no—
412C11×C4⋊C4—21no—
413C11×C4⋊C4C2411yescharacteristic
414C11×C4⋊C4C2411yescharacteristic
415C11×C4⋊C4C2411yescharacteristic
416C11×C4⋊C4C2411yescharacteristic
417C11×C22⋊C4—21no—
418C11×C22⋊C4—21no—
419C11×C22⋊C4—21no—
420C11×C22⋊C4—21no—
421C11×C22⋊C4—21no—
422C11×C22⋊C4—21no—
423C42×C11—21no—
424C42×C11—21no—
425C42×C11—21no—
426C42×C11—21no—
427C42×C11—21no—
428C42×C11—21no—
429C42×C11C2×D411yescharacteristic
430C42×C11C2×D411yescharacteristic
431C42×C11C2411yescharacteristic
432C42×C11C2411yescharacteristic
433C22⋊Dic11—22no—
434C22⋊Dic11—22no—
435C22⋊Dic11C2×D412yes—
436#4326C22×C418yescomplemented
437#4325C22×C418yescomplemented
438#4324C22×C418yescomplemented
439#4323C22×C418yescomplemented
440(C2×D11)⋊C4—22no—
441(C2×D11)⋊C4—22no—
442(C2×D11)⋊C4—22no—
443(C2×D11)⋊C4—22no—
444(C2×D11)⋊C4—22no—
445(C2×D11)⋊C4—22no—
446(C2×D11)⋊C4C2×D412yes—
447(C2×D11)⋊C4C2×D412yes—
448C4⋊Dic11—22no—
449C4⋊Dic11—22no—
450C4⋊Dic11—21no—
451C4⋊Dic11—21no—
452C4⋊Dic11C2×D411yescharacteristic
453C4⋊Dic11C2×D411yescharacteristic
454C4⋊Dic11C2412yes—
455C4⋊Dic11C2412yes—
456Dic11⋊C4—22no—
457Dic11⋊C4—22no—
458Dic11⋊C4—22no—
459Dic11⋊C4—22no—
460Dic11⋊C4—22no—
461Dic11⋊C4—22no—
462Dic11⋊C4C2×D412yes—
463Dic11⋊C4C2×D412yes—
464C4×Dic11—22no—
465C4×Dic11—22no—
466C4×Dic11—22no—
467C4×Dic11—22no—
468C4×Dic11—22no—
469C4×Dic11—22no—
470C4×Dic11—22no—
471C4×Dic11—22no—
472C4×Dic11C2×D412yes—
473C4×Dic11C2×D412yes—
474C4×Dic11C2412yes—
475#4318—22no—
476#4318C22×C414yescomplemented
477C2×C11⋊C8C2412yes—
478C2×C11⋊C8C2412yes—
479#4314C22×C418yescomplemented
480#4314C22×C418yescomplemented
481#4313—24no—
482#4313C22×C418yescomplemented
483C8×D11—24no—
484C8×D11C22×C418yescomplemented
485C2×#577—111no—
486C4×2−1+4—111no—
487C4×H(5,𝔽2)—111no—
488#2951—112no—
489#2951—111no—
490#2949—112no—
491#2949—111no—
492#2947—112no—
493#2947—111no—
494#2946—112no—
495#2946—111no—
496C4×#137—112no—
497C4×#137—111no—
498C4×AGL(1,ℤ/8)—112no—
499C4×AGL(1,ℤ/8)—111no—
500#2943—112no—
501#2943D1111yescharacteristic, complemented
502C2×#440—112no—
503C2×#440—111no—
504#2913—111no—
505#2898—111no—
506#2897—111no—
507#2875—111no—
508C23×C11—21no—
509C23×C11—21no—
510C23×C11C22×D411yescharacteristic
511C22×D11—22no—
512C22×D11—24no—
513C22×D11—28no—
514C22×D11—82no—
515C22×D11—82no—
516C22×D11—81no—
517C22×D11—81no—
518C22×D11C22×D412yes—
519Q8×C11—21no—
520Q8×C11—21no—
521Q8×C11C23×C412yes—
522Q8×C11C23×C412yes—
523D4×C11—24no—
524D4×C11—24no—
525D4×C11—21no—
526D4×C11—21no—
527D4×C11C23×C412yes—
528D4×C11C23×C412yes—
529C2×C4×C11—21no—
530C2×C4×C11—21no—
531C2×C4×C11—24no—
532C2×C4×C11—24no—
533C2×C4×C11—21no—
534C2×C4×C11—21no—
535C2×C4×C11—21no—
536C2×C4×C11—21no—
537C2×C4×C11—41no—
538C2×C4×C11—41no—
539C2×C4×C11—42no—
540C2×C4×C11—42no—
541C2×C4×C11—81no—
542C2×C4×C11—81no—
543C2×C4×C11C23×C412yes—
544C2×C4×C11C22×D411yescharacteristic
545C2×C4×C11C22×D411yescharacteristic
546C2×C4×C11C22×D411yescharacteristic
547C2×C4×C11C22×D411yescharacteristic
548C2×C4×C11C22×D411yescharacteristic
549C2×C4×C11C2×#4112yes—
550C2×C4×C11C2511yescharacteristic
551C22⋊D11—28no—
552C22⋊D11—28no—
553C22⋊D11C4×D418yes—
554C2×Dic11—24no—
555C2×Dic11—22no—
556C2×Dic11—28no—
557C2×Dic11—22no—
558C2×Dic11—22no—
559C2×Dic11—82no—
560C2×Dic11—82no—
561C2×Dic11—81no—
562C2×Dic11—81no—
563C2×Dic11C22×D412yes—
564C2×Dic11C22×D412yes—
565C2×Dic11C22×D412yes—
566D44—28no—
567D44—24no—
568D44—22no—
569D44C4×D414yes—
570D44C23×C414yes—
571C4×D11—28no—
572C4×D11—28no—
573C4×D11—42no—
574C4×D11—42no—
575C4×D11—44no—
576C4×D11—82no—
577C4×D11—82no—
578C4×D11—82no—
579C4×D11—82no—
580C4×D11—82no—
581C4×D11C23×C414yes—
582C4×D11C2×#4114yes—
583Dic22—24no—
584Dic22—22no—
585Dic22—28no—
586Dic22C4×D414yes—
587Dic22C23×C414yes—
588C8×C11—21no—
589C8×C11—21no—
590C8×C11C23×C412yes—
591C8×C11C23×C412yes—
592C11⋊C8—22no—
593C11⋊C8C23×C414yes—
594C2×2−1+4—111no—
595C2×H(5,𝔽2)—111no—
596#577—1116no—
597C2×#137—111no—
598C2×#137—112no—
599C2×AGL(1,ℤ/8)—111no—
600C2×AGL(1,ℤ/8)—112no—
601C2×#135—112no—
602C2×#135C2×D1111yescharacteristic
603C22×SD16—112no—
604C22×SD16—111no—
605C2×#131—111no—
606C2×#131—111no—
607#520—111no—
608#520—111no—
609#520—111no—
610#520—111no—
611#520—112no—
612#520—112no—
613#520—221no—
614#520—221no—
615#520—222no—
616#519—112no—
617#519—111no—
618#519—221no—
619#518—112no—
620#518—111no—
621#518—221no—
622#518—222no—
623C4×#41—111no—
624C4×#41—112no—
625C4×#41—112no—
626C4×#41—221no—
627C4×#41—221no—
628C4×#41—222no—
629C4×#41C2×D1111yescharacteristic
630C4×#41C2×D1111yescharacteristic, complemented
631C2×C4×Q8—112no—
632C2×C4×Q8—111no—
633C2×C4×Q8—221no—
634C2×C4×D4—112no—
635C2×C4×D4—111no—
636C2×C4×D4—221no—
637C2×C4×D4—222no—
638#442—112no—
639#442—112no—
640#442C2×D1111yescharacteristic, complemented
641#442C2×D1111yescharacteristic, complemented
642#441—112no—
643#441—112no—
644#441C2×D1111yescharacteristic, complemented
645#441C2×D1111yescharacteristic, complemented
646#440—112no—
647#440—112no—
648#440—112no—
649#440—112no—
650#440—112no—
651#440—112no—
652#440—112no—
653#440—112no—
654#440—112no—
655#440—112no—
656#440—112no—
657#440—112no—
658#440C2×D1111yescharacteristic, complemented
659#440C2×D1111yescharacteristic, complemented
660#440C2×D1111yescharacteristic, complemented
661#440C2×D1111yescharacteristic, complemented
662C4×Q16—112no—
663C4×Q16—112no—
664C4×Q16—112no—
665C4×SD16—112no—
666C4×SD16—112no—
667C4×SD16—112no—
668C4×SD16—112no—
669C4×SD16—112no—
670C4×SD16—112no—
671C4×D8—112no—
672C4×D8—112no—
673C4×D8—112no—
674#428—111no—
675#428—111no—
676#428—112no—
677#428—112no—
678#427—112no—
679#427C2×D1111yescharacteristic, complemented
680C2×#107—111no—
681C2×#107—112no—
682#419—111no—
683#419—112no—
684#418—111no—
685#418—112no—
686#417—111no—
687#417—111no—
688#417—112no—
689#417—112no—
690#416—112no—
691#416—112no—
692#416C2×D1111yescharacteristic
693#416C2×D1111yescharacteristic, complemented
694C2×#103—111no—
695C2×#103—112no—
696C2×#102—111no—
697C2×#102—112no—
698#405—111no—
699#405—111no—
700#405—112no—
701#405—112no—
702C4×M16—111no—
703C4×M16—112no—
704C2×#97—112no—
705C2×#97C2×D1111yescharacteristic, complemented
706C22×C11—21no—
707C22×C11—21no—
708C22×C11—22no—
709C22×C11—22no—
710C22×C11—41no—
711C22×C11—41no—
712C22×C11—41no—
713C22×C11—41no—
714C22×C11C2×C4×D412yes—
715C22×C11C23×D411yescharacteristic
716C2×D11—22no—
717C2×D11—22no—
718C2×D11—24no—
719C2×D11—42no—
720C2×D11—42no—
721C2×D11—88no—
722C2×D11—84no—
723C2×D11C2×C4×D414yes—
724C4×C11—21no—
725C4×C11—21no—
726C4×C11—21no—
727C4×C11—21no—
728C4×C11—22no—
729C4×C11—22no—
730C4×C11—41no—
731C4×C11—41no—
732C4×C11—41no—
733C4×C11—41no—
734C4×C11C2×C4×D412yes—
735C4×C11C24×C411yescharacteristic
736C4×C11C22×#4111yescharacteristic
737Dic11—22no—
738Dic11—22no—
739Dic11—24no—
740Dic11—42no—
741Dic11—42no—
742Dic11C2×C4×D414yes—
7432−1+4—118no—
7442−1+4—224no—
745H(5,𝔽2)—118no—
746H(5,𝔽2)—224no—
747C2×#41—111no—
748C2×#41—112no—
749C2×#41—112no—
750C2×#41—221no—
751C2×#41—221no—
752C2×#41—222no—
753C2×#41C22×D1111yescharacteristic
754C2×#41C22×D1111yescharacteristic
755C22×Q8—112no—
756C22×Q8—111no—
757C22×Q8—221no—
758C22×D4—112no—
759C22×D4—111no—
760C22×D4—221no—
761C22×D4—222no—
762C23×C4—222no—
763C23×C4—221no—
764#137—118no—
765#137—1116no—
766AGL(1,ℤ/8)—118no—
767AGL(1,ℤ/8)—1116no—
768#135—1116no—
769#135C4×D1118yescomplemented
770C2×Q16—112no—
771C2×Q16C22×D1111yescharacteristic
772C2×SD16—112no—
773C2×SD16—112no—
774C2×SD16—1116no—
775C2×SD16—118no—
776C2×SD16—112no—
777C2×SD16—112no—
778C2×SD16C22×D1111yescharacteristic
779C2×SD16C22×D1111yescharacteristic
780C2×D8—112no—
781C2×D8C22×D1111yescharacteristic
782#131—118no—
783#131—224no—
784C2×M16—111no—
785C2×M16—111no—
786C2×M16—112no—
787C2×M16—112no—
788C22×C8—112no—
789C22×C8—112no—
790C22×C8C22×D1111yescharacteristic
791C22×C8C22×D1111yescharacteristic
792C4×Q8—111no—
793C4×Q8—111no—
794C4×Q8—112no—
795C4×Q8—112no—
796C4×Q8—112no—
797C4×Q8—112no—
798C4×Q8—112no—
799C4×Q8—112no—
800C4×Q8—222no—
801C4×Q8—221no—
802C4×Q8—222no—
803C4×Q8—221no—
804C4×Q8—221no—
805C4×Q8—221no—
806C4×Q8—222no—
807C4×Q8—222no—
808C4×Q8—221no—
809C4×Q8—221no—
810C4×Q8C22×D1111yescharacteristic
811C4×Q8C22×D1111yescharacteristic
812C4×Q8C22×D1111yescharacteristic
813C4×Q8C22×D1111yescharacteristic
814C4×D4—21no—
815C4×D4—21no—
816C4×D4—21no—
817C4×D4—21no—
818C4×D4—112no—
819C4×D4—112no—
820C4×D4—112no—
821C4×D4—112no—
822C4×D4—112no—
823C4×D4—112no—
824C4×D4—111no—
825C4×D4—111no—
826C4×D4—112no—
827C4×D4—112no—
828C4×D4—222no—
829C4×D4—221no—
830C4×D4—221no—
831C4×D4—222no—
832C4×D4—221no—
833C4×D4—221no—
834C4×D4—222no—
835C4×D4—222no—
836C4×D4—222no—
837C4×D4—222no—
838C4×D4—222no—
839C4×D4—222no—
840C4×D4—222no—
841C4×D4—222no—
842C4×D4—222no—
843C4×D4—222no—
844C4×D4—222no—
845C4×D4—222no—
846C4×D4—222no—
847C4×D4—222no—
848C4×D4—221no—
849C4×D4—221no—
850C4×D4C22×D1111yescharacteristic
851C4×D4C22×D1111yescharacteristic
852C4×D4C22×D1111yescharacteristic
853C4×D4C22×D1111yescharacteristic
854#117—21no—
855#117—21no—
856#117—111no—
857#117—112no—
858#117—112no—
859#117—112no—
860#117—222no—
861#117—222no—
862#117—222no—
863#117—222no—
864#117—222no—
865#117—222no—
866#117—222no—
867#117—221no—
868#117—221no—
869#117C22×D1111yescharacteristic
870#117C22×D1111yescharacteristic
871C2×C4⋊C4—111no—
872C2×C4⋊C4—111no—
873C2×C4⋊C4—112no—
874C2×C4⋊C4—112no—
875C2×C4⋊C4—222no—
876C2×C4⋊C4—222no—
877C2×C4⋊C4—221no—
878C2×C4⋊C4—222no—
879C2×C4⋊C4—221no—
880C2×C4⋊C4—221no—
881C2×C22⋊C4—222no—
882C2×C22⋊C4—222no—
883C2×C22⋊C4—222no—
884C2×C22⋊C4—222no—
885C2×C22⋊C4—221no—
886C2×C42—21no—
887C2×C42—21no—
888C2×C42—112no—
889C2×C42—222no—
890C2×C42—222no—
891C2×C42—222no—
892C2×C42—221no—
893C2×C42C22×D1111yescharacteristic
894#107—112no—
895#107—112no—
896#107—112no—
897#107—112no—
898#107C22×D1111yescharacteristic
899#107C22×D1111yescharacteristic
900#106—112no—
901#106—112no—
902#106C22×D1111yescharacteristic
903#106C22×D1111yescharacteristic
904#103—112no—
905#103—112no—
906#103—112no—
907#103—112no—
908#103—112no—
909#103—112no—
910#103C22×D1111yescharacteristic
911#103C22×D1111yescharacteristic
912#103C22×D1111yescharacteristic
913#103C22×D1111yescharacteristic
914#102—112no—
915#102—112no—
916#102—112no—
917#102—112no—
918#102—112no—
919#102—112no—
920#102C22×D1111yescharacteristic
921#102C22×D1111yescharacteristic
922#102C22×D1111yescharacteristic
923#102C22×D1111yescharacteristic
924#97—112no—
925#97—112no—
926#97—112no—
927#97C22×D1111yescharacteristic
928#97C22×D1111yescharacteristic
929#97C22×D1111yescharacteristic
930#97C22×D1111yescharacteristic
931C4×C8—112no—
932C4×C8—112no—
933C4×C8—112no—
934C2×C11—22no—
935C2×C11—42no—
936C2×C11—42no—
937C2×C11C22×C4×D411yescharacteristic
938C2×C11#358511yescharacteristic
939C2×C11#358611yescharacteristic
940D11—24no—
941D11—44no—
942C24—222no—
943C24—221no—
944#41—22no—
945#41—22no—
946#41—114no—
947#41—114no—
948#41—118no—
949#41—118no—
950#41—228no—
951#41—228no—
952#41—224no—
953#41—224no—
954#41—2216no—
955#41C2×C4×D1114yes—
956#41C2×C4×D1114yescomplemented
957C2×Q8—111no—
958C2×Q8—118no—
959C2×Q8—114no—
960C2×Q8—112no—
961C2×Q8—222no—
962C2×Q8—228no—
963C2×Q8—224no—
964C2×Q8—221no—
965C2×Q8—222no—
966C2×Q8C23×D1111yescharacteristic
967C2×Q8C23×D1111yescharacteristic
968C2×D4—21no—
969C2×D4—21no—
970C2×D4—112no—
971C2×D4—118no—
972C2×D4—114no—
973C2×D4—111no—
974C2×D4—112no—
975C2×D4—228no—
976C2×D4—222no—
977C2×D4—224no—
978C2×D4—222no—
979C2×D4—2216no—
980C2×D4—222no—
981C2×D4—221no—
982C2×D4—222no—
983C2×D4C23×D1111yescharacteristic
984C2×D4C23×D1111yescharacteristic
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—112no—
992C22×C4—112no—
993C22×C4—112no—
994C22×C4—222no—
995C22×C4—222no—
996C22×C4—222no—
997C22×C4—222no—
998C22×C4—222no—
999C22×C4—222no—
1000C22×C4—222no—
1001C22×C4—222no—
1002C22×C4—222no—
1003C22×C4—221no—
1004C22×C4—221no—
1005C22×C4—221no—
1006C22×C4—222no—
1007C22×C4—222no—
1008C22×C4—882no—
1009C22×C4—884no—
1010C22×C4D4×D1111yescharacteristic
1011C22×C4D4×D1111yescharacteristic
1012C22×C4C23×D1111yescharacteristic
1013Q16—118no—
1014Q16C2×C4×D1114yescomplemented
1015SD16—118no—
1016SD16—118no—
1017SD16—118no—
1018SD16—118no—
1019SD16C2×C4×D1114yescomplemented
1020SD16C2×C4×D1114yescomplemented
1021D8—118no—
1022D8C2×C4×D1114yescomplemented
1023M16—114no—
1024M16—118no—
1025M16—224no—
1026M16—222no—
1027C2×C8—22no—
1028C2×C8—112no—
1029C2×C8—118no—
1030C2×C8—112no—
1031C2×C8—224no—
1032C2×C8C2×C4×D1114yescomplemented
1033C2×C8C23×D1111yescharacteristic
1034C2×C8C23×D1111yescharacteristic
1035C2×C8C23×D1111yescharacteristic
1036C2×C8C23×D1111yescharacteristic
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—112no—
1042C4⋊C4—111no—
1043C4⋊C4—112no—
1044C4⋊C4—111no—
1045C4⋊C4—112no—
1046C4⋊C4—112no—
1047C4⋊C4—222no—
1048C4⋊C4—222no—
1049C4⋊C4—222no—
1050C4⋊C4—222no—
1051C4⋊C4—222no—
1052C4⋊C4—222no—
1053C4⋊C4—221no—
1054C4⋊C4—221no—
1055C4⋊C4—222no—
1056C4⋊C4—222no—
1057C4⋊C4C23×D1111yescharacteristic
1058C4⋊C4C23×D1111yescharacteristic
1059C4⋊C4C23×D1111yescharacteristic
1060C4⋊C4C23×D1111yescharacteristic
1061C22⋊C4—21no—
1062C22⋊C4—21no—
1063C22⋊C4—21no—
1064C22⋊C4—21no—
1065C22⋊C4—21no—
1066C22⋊C4—21no—
1067C22⋊C4—112no—
1068C22⋊C4—112no—
1069C22⋊C4—112no—
1070C22⋊C4—222no—
1071C22⋊C4—222no—
1072C22⋊C4—222no—
1073C22⋊C4—222no—
1074C22⋊C4—222no—
1075C22⋊C4—222no—
1076C22⋊C4—222no—
1077C22⋊C4—222no—
1078C42—21no—
1079C42—21no—
1080C42—21no—
1081C42—21no—
1082C42—21no—
1083C42—21no—
1084C42—112no—
1085C42—112no—
1086C42—112no—
1087C42—222no—
1088C42—222no—
1089C42—222no—
1090C42—222no—
1091C42—222no—
1092C42—222no—
1093C42—222no—
1094C42—222no—
1095C42D4×D1111yescharacteristic
1096C42D4×D1111yescharacteristic
1097C42C23×D1111yescharacteristic
1098C42C23×D1111yescharacteristic
1099C11#6017411yescharacteristic, complemented, Sylow
1100C23—21no—
1101C23—21no—
1102C23—112no—
1103C23—228no—
1104C23—222no—
1105C23—224no—
1106C23—881no—
1107C23—881no—
1108C23—882no—
1109C23—882no—
1110C23C2×D4×D1111yescharacteristic
1111Q8—21no—
1112Q8—21no—
1113Q8—114no—
1114Q8—114no—
1115Q8—228no—
1116Q8—224no—
1117Q8—222no—
1118Q8C22×C4×D1112yes—
1119Q8C22×C4×D1112yes—
1120D4—24no—
1121D4—24no—
1122D4—21no—
1123D4—21no—
1124D4—118no—
1125D4—114no—
1126D4—114no—
1127D4—228no—
1128D4—228no—
1129D4—228no—
1130D4—224no—
1131D4—222no—
1132D4C22×C4×D1112yes—
1133D4C22×C4×D1112yes—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—42no—
1145C2×C4—42no—
1146C2×C4—81no—
1147C2×C4—81no—
1148C2×C4—112no—
1149C2×C4—114no—
1150C2×C4—114no—
1151C2×C4—112no—
1152C2×C4—112no—
1153C2×C4—228no—
1154C2×C4—228no—
1155C2×C4—228no—
1156C2×C4—224no—
1157C2×C4—222no—
1158C2×C4—222no—
1159C2×C4—222no—
1160C2×C4—442no—
1161C2×C4—442no—
1162C2×C4—444no—
1163C2×C4—882no—
1164C2×C4—882no—
1165C2×C4—882no—
1166C2×C4—882no—
1167C2×C4—882no—
1168C2×C4—882no—
1169C2×C4—882no—
1170C2×C4—881no—
1171C2×C4—881no—
1172C2×C4C22×C4×D1112yes—
1173C2×C4C2×D4×D1111yescharacteristic
1174C2×C4C2×D4×D1111yescharacteristic
1175C2×C4C2×D4×D1111yescharacteristic
1176C2×C4C2×D4×D1111yescharacteristic
1177C2×C4C2×D4×D1111yescharacteristic
1178C2×C4#41×D1112yes—
1179C2×C4C24×D1111yescharacteristic
1180C8—21no—
1181C8—21no—
1182C8—114no—
1183C8—222no—
1184C8C22×C4×D1112yes—
1185C8C22×C4×D1112yes—
1186C22—21no—
1187C22—21no—
1188C22—22no—
1189C22—22no—
1190C22—41no—
1191C22—41no—
1192C22—41no—
1193C22—41no—
1194C22—114no—
1195C22—222no—
1196C22—222no—
1197C22—224no—
1198C22—442no—
1199C22—442no—
1200C22—884no—
1201C22—888no—
1202C22C4×D4×D1112yes—
1203C22C22×D4×D1111yescharacteristic
1204C4—21no—
1205C4—21no—
1206C4—21no—
1207C4—21no—
1208C4—22no—
1209C4—22no—
1210C4—41no—
1211C4—41no—
1212C4—41no—
1213C4—41no—
1214C4—114no—
1215C4—222no—
1216C4—222no—
1217C4—224no—
1218C4—442no—
1219C4—442no—
1220C4C4×D4×D1112yes—
1221C4C23×C4×D1111yescharacteristic
1222C4C2×#41×D1111yescharacteristic
1223C2—22no—
1224C2—42no—
1225C2—42no—
1226C2—224no—
1227C2—444no—
1228C2C2×C4×D4×D1111yescharacteristic
1229C2#1308339311yescharacteristic
1230C2#1308340011yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
FittingC11×#2943C2
socleC22×C11C23×D4
prime radicalC2×#10623301C2
cosocleC2×C4×C11C25
hypercenter#2943D11
hypocenterC11#60174
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2943

Complements

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

NH ≅ G/Ntype
2. C4×#67043C2semidirect
3. C4×#67042C2semidirect
4. #13077492C2semidirect
5. #13077488C2semidirect
6. #13077474C2semidirect
7. #13077472C2semidirect
8. #13077462C2semidirect
9. #13077458C2semidirect
10. #13077451C2semidirect
11. #13077445C2semidirect
12. C4×#67004C2semidirect
13. #13077432C2semidirect
14. #13077427C2semidirect
15. C4×#67002C2semidirect
16. #13077411C2semidirect
17. C2×#10622323C2semidirect
18. D11×#440C2semidirect
19. #13077213C2semidirect
20. #13077145C2semidirect
21. #13077138C2semidirect
22. #13077041C2semidirect
23. C11×#2943C2semidirect
28. C4×C11×#41C22semidirect
30. #10623358C22semidirect
33. #10623301C4semidirect
43. #10623103C22semidirect
44. C4×Q8×D11C22semidirect
46. #10623077C22semidirect
52. C4×#4341C22semidirect
60. #10623047C22semidirect
67. C2×C4×Dic22C22semidirect
68. C11×#442C22semidirect
69. C11×#442C22semidirect
70. C11×#441C22semidirect
71. C11×#441C22semidirect
72. C11×#440C22semidirect
73. C11×#440C22semidirect
74. C11×#440C22semidirect
75. C11×#440C22semidirect
76. C11×#427C22semidirect
78. C11×#416C22semidirect
79. C2×C11×#97C22semidirect
81. #10622845C22semidirect
82. Q16×Dic11C22semidirect
83. #10622777C22semidirect
84. #10622777C22semidirect
85. D8×Dic11C22semidirect
87. C2×#66882C22semidirect
88. C2×#66880C22semidirect
89. #10622714C22semidirect
90. #10622714C22semidirect
91. #10622643C22semidirect
92. C4×#4326C22semidirect
93. #10622639C22semidirect
94. C4×#4325C22semidirect
95. #10622631C22semidirect
96. C4×#4324C22semidirect
97. #10622627C22semidirect
98. C4×#4323C22semidirect
99. #10622617C22semidirect
101. #10622608C22semidirect
102. #10622608C22semidirect
103. C4×#4318C22semidirect
104. #10622502C22semidirect
105. #10622502C22semidirect
106. #10622493C22semidirect
107. D11×#107C22semidirect
108. #10622474C22semidirect
109. #10622474C22semidirect
110. #10622465C22semidirect
111. #10622465C22semidirect
112. #10622430C22semidirect
115. #10622415C22semidirect
116. D11×#103C22semidirect
117. #10622403C22semidirect
118. #10622402C22semidirect
119. #10622401C22semidirect
120. #10622398C22semidirect
121. #10622385C22semidirect
122. #10622384C22semidirect
125. #10622371C22semidirect
126. #10622370C22semidirect
127. #10622369C22semidirect
128. #10622323C22semidirect
129. #10622323C22semidirect
130. #10622323C22semidirect
131. #10622323C22semidirect
132. #10622321C22semidirect
133. #10622321C22semidirect
134. #10622320C22semidirect
135. D11×#97C22semidirect
139. #67043C2×C4semidirect
141. #67042C2×C4semidirect
157. C11×#135C2×C4semidirect
183. #67004C2×C4semidirect
184. #67002C2×C4semidirect
216. #66971C2×C4semidirect
217. #66969C2×C4semidirect
218. SD16×D11C2×C4semidirect
219. #66964C2×C4semidirect
220. C2×#4314C2×C4semidirect
224. #66954C2×C4semidirect
333. C11×#41C22×C4semidirect
361. Q8×D11C22×C4semidirect
364. #4341C22×C4semidirect
396. C2×Dic22C22×C4semidirect
399. C11×Q16C22×C4semidirect
400. C11×SD16C22×C4semidirect
401. C11×SD16C22×C4semidirect
402. C11×D8C22×C4semidirect
404. C2×C8×C11C22×C4semidirect
436. #4326C22×C4semidirect
437. #4325C22×C4semidirect
438. #4324C22×C4semidirect
439. #4323C22×C4semidirect
476. #4318C22×C4semidirect
479. #4314C22×C4semidirect
480. #4314C22×C4semidirect
482. #4313C22×C4semidirect
484. C8×D11C22×C4semidirect
501. #2943D11semidirect
630. C4×#41C2×D11semidirect
640. #442C2×D11semidirect
641. #442C2×D11semidirect
644. #441C2×D11semidirect
645. #441C2×D11semidirect
658. #440C2×D11semidirect
659. #440C2×D11semidirect
660. #440C2×D11semidirect
661. #440C2×D11semidirect
679. #427C2×D11semidirect
693. #416C2×D11semidirect
705. C2×#97C2×D11semidirect
769. #135C4×D11semidirect
956. #41C2×C4×D11semidirect
1014. Q16C2×C4×D11semidirect
1019. SD16C2×C4×D11semidirect
1020. SD16C2×C4×D11semidirect
1022. D8C2×C4×D11semidirect
1032. C2×C8C2×C4×D11semidirect
1099. C11#60174semidirect

Maximal subgroups

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

subgroupindex
C2×#106233012
C4×#670432
C4×#670422
#130774922
#130774882
#130774742
#130774722
#130774622
#130774582
#130774512
#130774452
C4×#670042
#130774322
#130774272
C4×#670022
#130774112
C2×#106223232
D11×#4402
#130772132
#130771452
#130771382
#130770412
C11×#29432
#6017411