Finite Group Databasebeta

← #15631756

Subgroups — #15631756

Order 2816.

2116 conjugacy classes of subgroups.

The subgroup lattice has 1258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082540C211yesmaximal, characteristic, complemented
2#13082378C211yesmaximal, characteristic, complemented
3#13080831C212yesmaximal, complemented
4#13080816C212yesmaximal, complemented
5#13080756C212yesmaximal, complemented
6#13080711C212yesmaximal, complemented
7#13080636C212yesmaximal, complemented
8#13080591C212yesmaximal, complemented
9#13080465C212yesmaximal, complemented
10#13080450C212yesmaximal, complemented
11#13078604C211yesmaximal, characteristic, complemented
12#13078593C211yesmaximal, characteristic, complemented
13C2×#10622679C211yesmaximal, characteristic, complemented
14#13078285C211yesmaximal, characteristic, complemented
15#13078277C211yesmaximal, characteristic, complemented
16#13078065C211yesmaximal, characteristic, complemented
17#13077922C211yesmaximal, characteristic, complemented
18#13077922C211yesmaximal, characteristic, complemented
19C4×#66961C211yesmaximal, characteristic, complemented
20#13077362C211yesmaximal, characteristic, complemented
21#13077140C211yesmaximal, characteristic, complemented
22#13077140C211yesmaximal, characteristic, complemented
23C11×#3142C211yesmaximal, characteristic, complemented
24C2×#67042C2211yescharacteristic
25C2×#67042C2211yescharacteristic
26C11×#532C2211yescharacteristic
27C2×C11×#125C2211yescharacteristic, complemented
28#10623364C2211yescharacteristic
29#10623364C2211yescharacteristic
30C2×#67003C2211yescharacteristic, complemented
31C2×#67003C2211yescharacteristic, complemented
32C2×#66961C2211yescharacteristic
33C2×#66960C2211yescharacteristic, complemented
34C2×#66960C2211yescharacteristic, complemented
35#10623257C2212yes—
36#10623248C2212yes—
37#10623229—21no—
38#10623228—21no—
39#10623226C2212yescomplemented
40#10623226C2212yescomplemented
41#10623225C2212yescomplemented
42#10623225C2212yescomplemented
43#10623222—21no—
44#10623222—21no—
45#10623207C2212yes—
46#10623207C2212yes—
47#10623136—22no—
48D11×#121—22no—
49#10623082—21no—
50#10623081—21no—
51#10623081—21no—
52D4×D44—21no—
53#10623045—22no—
54#10623045—22no—
55#10623041C2211yescharacteristic, complemented
56#10623041C2211yescharacteristic, complemented
57#10623035C2211yescharacteristic, complemented
58#10623035C2211yescharacteristic, complemented
59#10623008C2211yescharacteristic
60C4×#4339C2211yescharacteristic, complemented
61C2×C4×D44C2211yescharacteristic
62C11×#491C2212yescomplemented
63C11×#490C2212yescomplemented
64C11×#488C2212yescomplemented
65C11×#488C2212yescomplemented
66C11×#417C2211yescharacteristic, complemented
67C11×#417C2211yescharacteristic, complemented
68C11×#417C2211yescharacteristic, complemented
69C11×#417C2211yescharacteristic, complemented
70C4×C11×M16C2211yescharacteristic, complemented
71#10622846C2211yescharacteristic, complemented
72#10622846C2211yescharacteristic, complemented
73#10622746C2211yescharacteristic, complemented
74#10622744C2211yescharacteristic
75#10622742C2211yescharacteristic, complemented
76#10622742C2211yescharacteristic, complemented
77#10622734C2211yescharacteristic, complemented
78#10622703C2211yescharacteristic, complemented
79#10622696C2211yescharacteristic, complemented
80#10622688C2211yescharacteristic, complemented
81#10622685C2211yescharacteristic, complemented
82#10622679C2212yescomplemented
83#10622679C2212yescomplemented
84#10622679C2212yescomplemented
85#10622679C2212yescomplemented
86#10622670C2211yescharacteristic, complemented
87#10622670C2211yescharacteristic, complemented
88#10622667C2211yescharacteristic, complemented
89#10622667C2211yescharacteristic, complemented
90C2×#66873C2211yescharacteristic
91C2×#66873C2211yescharacteristic
92C2×#66872C2211yescharacteristic, complemented
93C2×#66871C2211yescharacteristic, complemented
94C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
95#10622429C2212yescomplemented
96#10622428C2212yescomplemented
97#10622427C2212yescomplemented
98#10622426C2212yescomplemented
99#10622425C2212yescomplemented
100#10622424C2212yescomplemented
101#10622424C2212yescomplemented
102#10622423C2212yescomplemented
103#10622423C2212yescomplemented
104#10622422C2212yescomplemented
105#10622420C2212yescomplemented
106#10622418C2212yescomplemented
107#10622417C2212yescomplemented
108#10622417C2212yescomplemented
109#10622416C2212yescomplemented
110#10622416C2212yescomplemented
111#10622397C2212yescomplemented
112#10622395C2212yescomplemented
113#10622393C2212yescomplemented
114#10622392C2212yescomplemented
115#10622391C2212yescomplemented
116#10622390C2212yescomplemented
117#10622389C2212yescomplemented
118#10622389C2212yescomplemented
119#10622388C2212yescomplemented
120#10622387C2212yescomplemented
121#10622386C2212yescomplemented
122#10622386C2212yescomplemented
123#10622383C2212yescomplemented
124#10622383C2212yescomplemented
125D11×#102C2212yescomplemented
126D11×#102C2212yescomplemented
127#10622324C2212yescomplemented
128#10622323C2212yescomplemented
129#10622319C2212yescomplemented
130#10622319C2212yescomplemented
131C4×D88C2212yescomplemented
132C4×#4314C2212yescomplemented
133#10622301C2212yescomplemented
134C8×D44C2212yescomplemented
135C2×C11×#41C2311yescharacteristic
136C2×C11×#41C2311yescharacteristic
137#67042—24no—
138#67042—24no—
139#67042—42no—
140#67042—42no—
141C2×#4343C2312yes—
142C2×#4343C2312yes—
143C2×D4×D11—22no—
144C2×D4×D11—22no—
145C2×D4×D11—22no—
146C2×D4×D11C2312yes—
147C2×D4×D11C2312yes—
148C2×#4339—21no—
149C2×#4339—21no—
150C2×#4339C2311yescharacteristic
151C2×#4339C2311yescharacteristic
152C2×#4339C2311yescharacteristic
153C22×D44—21no—
154C22×D44—21no—
155C22×D44C2311yescharacteristic
156C22×C4×D11—21no—
157C2×C11×M16C2311yescharacteristic
158C2×C11×M16C2311yescharacteristic
159C11×C4⋊Q8C2311yescharacteristic
160C11×#127C2311yescharacteristic
161C11×#125—21no—
162C11×#125—21no—
163C11×#125C2312yes—
164C11×#125C2312yes—
165C11×#124C2311yescharacteristic
166C11×#124C2311yescharacteristic
167C11×#121—21no—
168C11×#121—21no—
169C4×D4×C11—21no—
170C4×D4×C11—21no—
171C2×C11×C4⋊C4—21no—
172C2×C11×C4⋊C4—21no—
173C2×C11×C4⋊C4C2311yescharacteristic
174C2×C11×C4⋊C4C2311yescharacteristic
175C2×C42×C11C2311yescharacteristic
176#67003—42no—
177#67003—42no—
178#66999C2312yes—
179#66999C2312yes—
180C2×#4326C2311yescharacteristic
181C2×#4326C2311yescharacteristic
182C2×#4325C2311yescharacteristic
183C2×#4325C2311yescharacteristic
184#66992—22no—
185#66992—22no—
186#66991—22no—
187#66991C2312yes—
188#66991C2312yes—
189#66990—22no—
190#66990—22no—
191C2×#4324C2311yescharacteristic
192C2×#4324C2311yescharacteristic
193C2×#4323C2311yescharacteristic
194C2×#4323C2311yescharacteristic
195#66983—22no—
196#66983—22no—
197#66983—21no—
198#66983—21no—
199#66983D412yes—
200#66983D412yes—
201C4×C22⋊D11—21no—
202C4×C22⋊D11—21no—
203C4×C22⋊D11—22no—
204C4×C22⋊D11—22no—
205C2×(C2×D11)⋊C4—21no—
206#66979C2311yescharacteristic
207C2×C4⋊Dic11C2311yescharacteristic
208#66977—21no—
209#66977—21no—
210C22×C11⋊C8C2311yescharacteristic
211C22×C11⋊C8C2311yescharacteristic
212#66961—24no—
213#66960—42no—
214#66960—42no—
215C2×D88C2312yes—
216C2×#4314C2312yes—
217C2×#4313C2312yes—
218C2×#4313C2312yes—
219C2×C8×D11C2312yes—
220C2×C8×D11C2312yes—
221#66951—22no—
222#66951—22no—
223#66951—22no—
224#66951—22no—
225#66950—21no—
226#66950—21no—
227#66950C2312yes—
228#66950C2312yes—
229#66948—22no—
230#66948—21no—
231#66948—21no—
232#66948—22no—
233#66948—22no—
234#66948C2312yes—
235#66948C2312yes—
236#66947—22no—
237#66947—22no—
238#66947—22no—
239#66947—22no—
240#66947—22no—
241#66947—22no—
242#66946—21no—
243#66946—21no—
244#66946—22no—
245#66946—22no—
246#66945—22no—
247#66945—22no—
248#66945C2312yes—
249#66945C2312yes—
250C4⋊C4×D11—22no—
251C4⋊C4×D11C2312yes—
252C4⋊C4×D11C2312yes—
253#66943—22no—
254#66943—22no—
255#66940—21no—
256#66940—21no—
257#66937—22no—
258#66937—22no—
259#66936—22no—
260#66936—22no—
261#66935—22no—
262#66935—22no—
263C22⋊C4×D11—22no—
264C22⋊C4×D11—22no—
265#66928D411yescharacteristic
266#66928D411yescharacteristic
267#66927D411yescharacteristic
268C4×D44—21no—
269C4×D44—21no—
270C4×D44C2312yes—
271C4×D44C2312yes—
272C4×D44C2312yes—
273C4×D44C2312yes—
274C4×D44C2311yescharacteristic
275C4×D44C2311yescharacteristic
276#66925—21no—
277C42×D11—21no—
278#66922D411yescharacteristic
279C4×Dic22C2311yescharacteristic
280C4×Dic22C2311yescharacteristic
281C11×#103C2312yes—
282C11×#103C2312yes—
283C11×#103C2312yes—
284C11×#103C2312yes—
285C11×#102C2312yes—
286C11×#102C2312yes—
287C11×#102C2312yes—
288C11×#102C2312yes—
289C11×#97C2312yes—
290C4×C8×C11C2312yes—
291#66899C2311yescharacteristic
292#66899C2311yescharacteristic
293#66899C2311yescharacteristic
294#66899C2311yescharacteristic
295#66896C2311yescharacteristic
296#66896C2311yescharacteristic
297#66896C2311yescharacteristic
298#66896C2311yescharacteristic
299#66885C2312yes—
300#66885C2312yes—
301#66885C2312yes—
302(C2×D11)⋊C8C2312yes—
303(C2×D11)⋊C8C2312yes—
304(C2×D11)⋊C8C2312yes—
305(C2×D11)⋊C8C2312yes—
306#66882C2312yes—
307#66881C2312yes—
308#66880C2312yes—
309#66873C2312yes—
310#66873C2312yes—
311#66873C2312yes—
312#66873C2312yes—
313#66872C2312yes—
314#66872C2312yes—
315#66871C2312yes—
316#66871C2312yes—
317C4⋊(C11⋊C8)C2311yescharacteristic
318C4⋊(C11⋊C8)C2311yescharacteristic
319C4⋊(C11⋊C8)C2311yescharacteristic
320C4⋊(C11⋊C8)C2311yescharacteristic
321#61201—111nomaximal, Sylow
322C23×D11—21no—
323C23×D11—22no—
324C23×D11—22no—
325C11×#41—22no—
326C11×#41—22no—
327C11×#41—22no—
328C11×#41—22no—
329C2×Q8×C11C2411yescharacteristic
330C2×Q8×C11C2411yescharacteristic
331C2×D4×C11—21no—
332C2×D4×C11—21no—
333C2×D4×C11—21no—
334C2×D4×C11—21no—
335C2×D4×C11C2411yescharacteristic
336C2×D4×C11C2411yescharacteristic
337C22×C4×C11—21no—
338C22×C4×C11—21no—
339C22×C4×C11—21no—
340C22×C4×C11—21no—
341C22×C4×C11C2×D411yescharacteristic
342C22×C4×C11C2×D411yescharacteristic
343C22×C4×C11C2411yescharacteristic
344C2×C22⋊D11—22no—
345C2×C22⋊D11—22no—
346C2×C22⋊D11—21no—
347C2×C22⋊D11—22no—
348C2×C22⋊D11—22no—
349C2×C22⋊D11C2×D412yes—
350C2×C22⋊D11C2×D412yes—
351C22×Dic11—21no—
352#4343—24no—
353#4343—24no—
354#4343—42no—
355#4343—42no—
356D4×D11—24no—
357D4×D11—24no—
358D4×D11—42no—
359D4×D11—42no—
360D4×D11—48no—
361D4×D11—48no—
362D4×D11—84no—
363#4339—22no—
364#4339—22no—
365#4339—22no—
366#4339—22no—
367#4339—22no—
368#4339—22no—
369#4339—44no—
370#4339—44no—
371C2×D44—22no—
372C2×D44—22no—
373C2×D44—22no—
374C2×D44—22no—
375C2×D44—21no—
376C2×D44—22no—
377C2×D44—44no—
378C2×D44—44no—
379C2×D44C2×D411yescharacteristic
380C2×D44C2×D411yescharacteristic
381C2×D44C2×D412yes—
382C2×D44C2×D412yes—
383C2×D44#4114yes—
384C2×D44C2411yescharacteristic
385C2×D44C2412yes—
386C2×C4×D11—22no—
387C2×C4×D11—22no—
388C2×C4×D11—22no—
389C2×C4×D11—22no—
390C2×C4×D11—21no—
391C2×C4×D11—22no—
392C2×C4×D11—21no—
393C2×C4×D11—21no—
394C2×C4×D11—22no—
395C2×C4×D11—82no—
396C2×C4×D11C2412yes—
397C2×C4×D11C2412yes—
398C2×Dic22C2×D411yescharacteristic
399C2×Dic22C2×D411yescharacteristic
400C2×Dic22C2411yescharacteristic
401C11×M16—22no—
402C11×M16—22no—
403C2×C8×C11C2412yes—
404C2×C8×C11C2412yes—
405C11×C4⋊C4—21no—
406C11×C4⋊C4—21no—
407C11×C4⋊C4—22no—
408C11×C4⋊C4—22no—
409C11×C4⋊C4—21no—
410C11×C4⋊C4—22no—
411C11×C4⋊C4—22no—
412C11×C4⋊C4—21no—
413C11×C4⋊C4C2412yes—
414C11×C4⋊C4C2412yes—
415C11×C22⋊C4—21no—
416C11×C22⋊C4—21no—
417C11×C22⋊C4—21no—
418C11×C22⋊C4—21no—
419C42×C11C2×D411yescharacteristic
420C42×C11C2×D411yescharacteristic
421C42×C11C2411yescharacteristic
422C42×C11C2411yescharacteristic
423C22⋊Dic11—22no—
424C22⋊Dic11—22no—
425C22⋊Dic11—21no—
426#4326—41no—
427#4326—41no—
428#4325—41no—
429#4325—41no—
430#4324—41no—
431#4324—41no—
432#4323—41no—
433#4323—41no—
434(C2×D11)⋊C4—22no—
435(C2×D11)⋊C4—22no—
436(C2×D11)⋊C4—22no—
437(C2×D11)⋊C4—22no—
438(C2×D11)⋊C4—22no—
439(C2×D11)⋊C4—22no—
440(C2×D11)⋊C4—22no—
441(C2×D11)⋊C4—22no—
442(C2×D11)⋊C4—21no—
443(C2×D11)⋊C4—21no—
444(C2×D11)⋊C4—22no—
445(C2×D11)⋊C4—22no—
446(C2×D11)⋊C4C2×D412yes—
447(C2×D11)⋊C4C2×D412yes—
448(C2×D11)⋊C4C2×D412yes—
449(C2×D11)⋊C4C2×D412yes—
450C4⋊Dic11—22no—
451C4⋊Dic11—22no—
452C4⋊Dic11—21no—
453C4⋊Dic11C2×D412yes—
454C4⋊Dic11C2×D412yes—
455C4⋊Dic11C2412yes—
456C4⋊Dic11C2411yescharacteristic
457C4⋊Dic11C2411yescharacteristic
458Dic11⋊C4—22no—
459Dic11⋊C4—22no—
460Dic11⋊C4—22no—
461Dic11⋊C4—22no—
462Dic11⋊C4—21no—
463Dic11⋊C4—21no—
464C4×Dic11—22no—
465C4×Dic11—22no—
466C4×Dic11—21no—
467C4×Dic11—21no—
468C4×Dic11—21no—
469C2×C11⋊C8—22no—
470C2×C11⋊C8—22no—
471C2×C11⋊C8C2411yescharacteristic
472C2×C11⋊C8C2411yescharacteristic
473C2×C11⋊C8C2411yescharacteristic
474C2×C11⋊C8C2411yescharacteristic
475D88—24no—
476#4314—24no—
477#4313—42no—
478#4313—42no—
479C8×D11—42no—
480C8×D11—42no—
481#3512—111no—
482#3496—111no—
483#3323—112no—
484#3322—112no—
485#3318—112no—
486#3315—112no—
487#3310—112no—
488#3307—112no—
489#3297—112no—
490#3296—112no—
491#3142D1111yescharacteristic, complemented
492#3099—111no—
493#3098—111no—
494C2×#478—111no—
495#3061—111no—
496#3060—111no—
497#3035—111no—
498#3012—111no—
499#3012—111no—
500C4×AGL(1,ℤ/8)—111no—
501#2935—111no—
502#2897—111no—
503#2897—111no—
504C23×C11—21no—
505C23×C11—21no—
506C23×C11C22×D411yescharacteristic
507C22×D11—22no—
508C22×D11—24no—
509C22×D11—21no—
510C22×D11—44no—
511C22×D11—44no—
512C22×D11—82no—
513C22×D11—82no—
514C22×D11—82no—
515C22×D11—82no—
516C22×D11—81no—
517C22×D11—81no—
518C22×D11C22×D412yes—
519C22×D11C22×D412yes—
520Q8×C11—21no—
521Q8×C11—21no—
522Q8×C11—21no—
523Q8×C11—21no—
524D4×C11—21no—
525D4×C11—21no—
526D4×C11—21no—
527D4×C11—21no—
528D4×C11—42no—
529D4×C11—42no—
530D4×C11—42no—
531D4×C11—81no—
532C2×C4×C11—22no—
533C2×C4×C11—22no—
534C2×C4×C11—21no—
535C2×C4×C11—21no—
536C2×C4×C11—41no—
537C2×C4×C11—41no—
538C2×C4×C11—42no—
539C2×C4×C11—42no—
540C2×C4×C11—81no—
541C2×C4×C11—81no—
542C2×C4×C11C22×D411yescharacteristic
543C2×C4×C11C22×D411yescharacteristic
544C2×C4×C11C22×D411yescharacteristic
545C2×C4×C11C22×D411yescharacteristic
546C2×C4×C11C22×D411yescharacteristic
547C2×C4×C11C2×#4112yes—
548C2×C4×C11H(5,𝔽2)12yes—
549C2×C4×C11C2511yescharacteristic
550C22⋊D11—24no—
551C22⋊D11—24no—
552C22⋊D11—44no—
553C22⋊D11—44no—
554C22⋊D11—42no—
555C22⋊D11—82no—
556C22⋊D11—82no—
557C2×Dic11—21no—
558C2×Dic11—21no—
559C2×Dic11—21no—
560C2×Dic11—22no—
561C2×Dic11—81no—
562C2×Dic11C22×D412yes—
563C2×Dic11C22×D412yes—
564D44—24no—
565D44—22no—
566D44—22no—
567D44—21no—
568D44—22no—
569D44—21no—
570D44—42no—
571D44—42no—
572D44—44no—
573D44—44no—
574D44—82no—
575D44—82no—
576D44C2×#4114yes—
577C4×D11—22no—
578C4×D11—22no—
579C4×D11—22no—
580C4×D11—22no—
581C4×D11—44no—
582C4×D11—44no—
583C4×D11—44no—
584C4×D11—42no—
585C4×D11—81no—
586C4×D11—81no—
587C4×D11—82no—
588C4×D11—82no—
589C4×D11—82no—
590Dic22—22no—
591Dic22—22no—
592Dic22—21no—
593Dic22—21no—
594C8×C11—22no—
595C8×C11—22no—
596C11⋊C8—21no—
597C11⋊C8—21no—
598C11⋊C8—21no—
599C11⋊C8—21no—
600C2×H(5,𝔽2)—111no—
601C2×H(5,𝔽2)—111no—
602C2×AGL(1,ℤ/8)—111no—
603C2×#135—111no—
604C2×#135—111no—
605C2×#131—111no—
606C2×#131—111no—
607#553—112no—
608#553—112no—
609#553—222no—
610#553—222no—
611#552—112no—
612#552—112no—
613#547—112no—
614#547—221no—
615#546—112no—
616#546—112no—
617#546—221no—
618#546—221no—
619D42—112no—
620D42—221no—
621#541—221no—
622#540—221no—
623#537—111no—
624#537—111no—
625#537—111no—
626#537—111no—
627#534—222no—
628#532—111no—
629#532C2×D1111yescharacteristic
630#529—221no—
631#529—221no—
632C2×#125C2×D1111yescharacteristic, complemented
633C2×#121—222no—
634#520—111no—
635#520—111no—
636C4×#41—111no—
637C2×C4×D4—111no—
638#491C2×D1112yescomplemented
639#490C2×D1112yescomplemented
640#488C2×D1112yescomplemented
641#488C2×D1112yescomplemented
642#485—112no—
643#485—112no—
644#484—112no—
645#483—112no—
646#482—112no—
647#482—112no—
648#481—112no—
649#480—112no—
650#478—112no—
651#478—112no—
652#478—112no—
653#478—112no—
654#470—112no—
655#469—112no—
656#468—112no—
657#468—112no—
658#467—112no—
659#466—112no—
660#465—112no—
661#465—112no—
662#464—111no—
663#464—111no—
664#463—111no—
665#463—111no—
666#462—111no—
667#461—111no—
668#460—111no—
669#459—111no—
670#452—112no—
671#452—112no—
672#450—112no—
673#450—112no—
674#449—112no—
675#449—112no—
676#447—112no—
677#447—112no—
678#442—112no—
679#440—112no—
680C4×SD16—112no—
681C4×D8—112no—
682#436—112no—
683#435—112no—
684#435—112no—
685C8×D4—112no—
686#428—111no—
687C2×#107—111no—
688C2×#106—111no—
689C2×C4⋊C8—111no—
690#418—111no—
691#418—112no—
692#418—112no—
693#417—111no—
694#417—112no—
695#417—112no—
696#417C2×D1111yescharacteristic, complemented
697#417C2×D1111yescharacteristic, complemented
698#417C2×D1111yescharacteristic, complemented
699#417C2×D1111yescharacteristic, complemented
700#416—111no—
701#416—111no—
702#416—112no—
703#416—112no—
704C2×#102—111no—
705C2×#102—111no—
706C2×#102—112no—
707C2×#102—112no—
708#408—111no—
709#408—111no—
710C4×M16C2×D1111yescharacteristic, complemented
711C22×C11—21no—
712C22×C11—21no—
713C22×C11—41no—
714C22×C11—41no—
715C22×C11—41no—
716C22×C11—41no—
717C22×C11—41no—
718C22×C11—41no—
719C22×C11#54612yes—
720C22×C11C23×D411yescharacteristic
721C2×D11—22no—
722C2×D11—22no—
723C2×D11—22no—
724C2×D11—22no—
725C2×D11—24no—
726C2×D11—22no—
727C2×D11—22no—
728C2×D11—42no—
729C2×D11—42no—
730C2×D11—41no—
731C2×D11—41no—
732C2×D11—41no—
733C2×D11—84no—
734C2×D11—164no—
735C2×D11—164no—
736C4×C11—21no—
737C4×C11—21no—
738C4×C11—21no—
739C4×C11—21no—
740C4×C11—42no—
741C4×C11—42no—
742C4×C11—41no—
743C4×C11—41no—
744C4×C11#54612yes—
745C4×C11C22×#4111yescharacteristic
746C4×C11C2×H(5,𝔽2)11yescharacteristic
747Dic11—22no—
748Dic11—22no—
749Dic11—41no—
750Dic11—42no—
751Dic11—41no—
752Dic11—41no—
753H(5,𝔽2)—224no—
754H(5,𝔽2)—224no—
755H(5,𝔽2)—442no—
756H(5,𝔽2)—442no—
757C2×#41—111no—
758C2×#41—111no—
759C2×#41—112no—
760C2×#41—112no—
761C2×#41—111no—
762C2×#41—221no—
763C2×#41—221no—
764C2×#41C22×D1111yescharacteristic
765C2×#41C22×D1111yescharacteristic
766C22×D4—112no—
767C22×D4—112no—
768C22×D4—111no—
769C22×D4—221no—
770C22×D4—221no—
771C22×D4—222no—
772C22×D4—222no—
773C22×D4—222no—
774C23×C4—221no—
775AGL(1,ℤ/8)—224no—
776#135—442no—
777#135—442no—
778C2×Q16—111no—
779C2×Q16—111no—
780C2×SD16—111no—
781C2×SD16—111no—
782C2×SD16—111no—
783C2×SD16—111no—
784C2×SD16—112no—
785C2×D8—111no—
786C2×D8—111no—
787C2×D8—112no—
788#131—442no—
789#131—442no—
790C2×M16—112no—
791C2×M16—112no—
792C2×M16C22×D1111yescharacteristic
793C2×M16C22×D1111yescharacteristic
794C22×C8—111no—
795C22×C8—111no—
796C22×C8—112no—
797C22×C8—112no—
798C4⋊Q8—111no—
799C4⋊Q8C22×D1111yescharacteristic
800#127—111no—
801#127C22×D1111yescharacteristic
802#126—222no—
803#126—222no—
804#126—222no—
805#126—222no—
806#125—21no—
807#125—21no—
808#125—222no—
809#125—222no—
810#125C22×D1112yes—
811#125C22×D1112yes—
812#124—111no—
813#124—111no—
814#124C22×D1111yescharacteristic
815#124C22×D1111yescharacteristic
816#123—222no—
817#123—222no—
818#123—222no—
819#123—222no—
820#123—222no—
821#123—222no—
822#123—222no—
823#123—222no—
824C22⋊Q8—112no—
825C22⋊Q8—112no—
826C22⋊Q8—112no—
827C22⋊Q8—112no—
828C22⋊Q8—221no—
829C22⋊Q8—221no—
830C22⋊Q8—221no—
831C22⋊Q8—221no—
832#121—21no—
833#121—21no—
834#121—112no—
835#121—112no—
836#121—112no—
837#121—112no—
838#121—112no—
839#121—112no—
840#121—222no—
841#121—222no—
842#121—222no—
843#121—221no—
844#121—221no—
845#121—222no—
846#121—222no—
847#121—222no—
848#121—221no—
849#121—221no—
850#121—222no—
851#121—222no—
852#121—222no—
853#121—222no—
854#120—222no—
855#120—222no—
856#120—222no—
857#120—222no—
858C4×Q8—111no—
859C4×Q8—111no—
860C4×Q8—221no—
861C4×Q8—221no—
862C4×D4—21no—
863C4×D4—21no—
864C4×D4—112no—
865C4×D4—112no—
866C4×D4—112no—
867C4×D4—112no—
868C4×D4—111no—
869C4×D4—111no—
870C4×D4—222no—
871C4×D4—222no—
872C4×D4—221no—
873C4×D4—221no—
874C4×D4—222no—
875C4×D4—222no—
876C4×D4—221no—
877C4×D4—221no—
878C4×D4—221no—
879C4×D4—221no—
880#117—111no—
881#117—112no—
882#117—112no—
883#117—222no—
884#117—222no—
885#117—221no—
886C2×C4⋊C4—21no—
887C2×C4⋊C4—21no—
888C2×C4⋊C4—111no—
889C2×C4⋊C4—112no—
890C2×C4⋊C4—112no—
891C2×C4⋊C4—222no—
892C2×C4⋊C4C22×D1111yescharacteristic
893C2×C4⋊C4C22×D1111yescharacteristic
894C2×C22⋊C4—222no—
895C2×C22⋊C4—222no—
896C2×C22⋊C4—221no—
897C2×C42—221no—
898C2×C42C22×D1111yescharacteristic
899#107—112no—
900#107—112no—
901#107—112no—
902#106—112no—
903#106—112no—
904#106—112no—
905C4⋊C8—111no—
906C4⋊C8—111no—
907C4⋊C8—111no—
908C4⋊C8—111no—
909#103—111no—
910#103—111no—
911#103—111no—
912#103—111no—
913#103—112no—
914#103C22×D1112yes—
915#103C22×D1112yes—
916#103C22×D1112yes—
917#103C22×D1112yes—
918#102—111no—
919#102—111no—
920#102—111no—
921#102—111no—
922#102—112no—
923#102—112no—
924#102—112no—
925#102—112no—
926#102—112no—
927#102—112no—
928#102—112no—
929#102C22×D1112yes—
930#102C22×D1112yes—
931#102C22×D1112yes—
932#102C22×D1112yes—
933C22⋊C8—112no—
934C22⋊C8—112no—
935C22⋊C8—112no—
936C22⋊C8—112no—
937#97C22×D1112yes—
938C4×C8C22×D1112yes—
939C2×C11—22no—
940C2×C11—81no—
941C2×C11—81no—
942C2×C11C2×#54611yescharacteristic
943C2×C11#358411yescharacteristic
944C2×C11#358511yescharacteristic
945D11—42no—
946D11—42no—
947D11—44no—
948D11—81no—
949C24—222no—
950C24—222no—
951C24—221no—
952#41—22no—
953#41—22no—
954#41—22no—
955#41—22no—
956#41—222no—
957#41—222no—
958#41—222no—
959#41—222no—
960#41—224no—
961#41—224no—
962#41—222no—
963#41—222no—
964#41—444no—
965#41—444no—
966#41—442no—
967#41—442no—
968C2×Q8—111no—
969C2×Q8—111no—
970C2×Q8—111no—
971C2×Q8C23×D1111yescharacteristic
972C2×Q8C23×D1111yescharacteristic
973C2×D4—21no—
974C2×D4—21no—
975C2×D4—21no—
976C2×D4—21no—
977C2×D4—112no—
978C2×D4—112no—
979C2×D4—111no—
980C2×D4—111no—
981C2×D4—112no—
982C2×D4—112no—
983C2×D4—114no—
984C2×D4—112no—
985C2×D4—111no—
986C2×D4—222no—
987C2×D4—222no—
988C2×D4—222no—
989C2×D4—222no—
990C2×D4—222no—
991C2×D4—222no—
992C2×D4—224no—
993C2×D4—224no—
994C2×D4—221no—
995C2×D4—222no—
996C2×D4—222no—
997C2×D4—221no—
998C2×D4—222no—
999C2×D4—444no—
1000C2×D4—444no—
1001C2×D4—442no—
1002C2×D4—442no—
1003C2×D4—448no—
1004C2×D4—448no—
1005C2×D4—884no—
1006C2×D4C23×D1111yescharacteristic
1007C2×D4C23×D1111yescharacteristic
1008C22×C4—21no—
1009C22×C4—21no—
1010C22×C4—21no—
1011C22×C4—21no—
1012C22×C4—112no—
1013C22×C4—112no—
1014C22×C4—222no—
1015C22×C4—222no—
1016C22×C4—222no—
1017C22×C4—222no—
1018C22×C4—221no—
1019C22×C4—221no—
1020C22×C4—222no—
1021C22×C4—221no—
1022C22×C4—221no—
1023C22×C4—222no—
1024C22×C4—882no—
1025C22×C4D4×D1111yescharacteristic
1026C22×C4D4×D1111yescharacteristic
1027C22×C4C23×D1111yescharacteristic
1028Q16—441no—
1029Q16—441no—
1030SD16—224no—
1031SD16—441no—
1032SD16—441no—
1033SD16—441no—
1034SD16—441no—
1035D8—224no—
1036D8—441no—
1037D8—441no—
1038M16—22no—
1039M16—22no—
1040M16—442no—
1041M16—442no—
1042C2×C8—111no—
1043C2×C8—111no—
1044C2×C8—111no—
1045C2×C8—111no—
1046C2×C8—222no—
1047C2×C8—222no—
1048C2×C8—442no—
1049C2×C8—442no—
1050C2×C8C23×D1112yes—
1051C2×C8C23×D1112yes—
1052C4⋊C4—22no—
1053C4⋊C4—22no—
1054C4⋊C4—22no—
1055C4⋊C4—22no—
1056C4⋊C4—21no—
1057C4⋊C4—21no—
1058C4⋊C4—21no—
1059C4⋊C4—21no—
1060C4⋊C4—112no—
1061C4⋊C4—112no—
1062C4⋊C4—111no—
1063C4⋊C4—111no—
1064C4⋊C4—112no—
1065C4⋊C4—222no—
1066C4⋊C4—222no—
1067C4⋊C4—222no—
1068C4⋊C4—222no—
1069C4⋊C4—222no—
1070C4⋊C4—222no—
1071C4⋊C4—221no—
1072C4⋊C4—221no—
1073C4⋊C4—221no—
1074C4⋊C4C23×D1112yes—
1075C4⋊C4C23×D1112yes—
1076C22⋊C4—21no—
1077C22⋊C4—21no—
1078C22⋊C4—21no—
1079C22⋊C4—21no—
1080C22⋊C4—112no—
1081C22⋊C4—112no—
1082C22⋊C4—112no—
1083C22⋊C4—112no—
1084C22⋊C4—222no—
1085C22⋊C4—222no—
1086C22⋊C4—222no—
1087C22⋊C4—222no—
1088C22⋊C4—222no—
1089C22⋊C4—222no—
1090C22⋊C4—222no—
1091C22⋊C4—222no—
1092C22⋊C4—222no—
1093C22⋊C4—222no—
1094C22⋊C4—221no—
1095C22⋊C4—222no—
1096C22⋊C4—222no—
1097C22⋊C4—221no—
1098C22⋊C4—221no—
1099C42—222no—
1100C42—222no—
1101C42—221no—
1102C42—221no—
1103C42—221no—
1104C42D4×D1111yescharacteristic
1105C42D4×D1111yescharacteristic
1106C42C23×D1111yescharacteristic
1107C42C23×D1111yescharacteristic
1108C11#6120111yescharacteristic, complemented, Sylow
1109C23—21no—
1110C23—21no—
1111C23—112no—
1112C23—112no—
1113C23—222no—
1114C23—224no—
1115C23—221no—
1116C23—444no—
1117C23—444no—
1118C23—881no—
1119C23—881no—
1120C23—882no—
1121C23—882no—
1122C23—882no—
1123C23—882no—
1124C23C2×D4×D1111yescharacteristic
1125Q8—21no—
1126Q8—21no—
1127Q8—21no—
1128Q8—21no—
1129Q8—222no—
1130Q8—222no—
1131Q8—221no—
1132Q8—221no—
1133D4—21no—
1134D4—21no—
1135D4—21no—
1136D4—21no—
1137D4—42no—
1138D4—42no—
1139D4—42no—
1140D4—81no—
1141D4—114no—
1142D4—224no—
1143D4—224no—
1144D4—221no—
1145D4—222no—
1146D4—221no—
1147D4—224no—
1148D4—222no—
1149D4—222no—
1150D4—442no—
1151D4—442no—
1152D4—444no—
1153D4—444no—
1154D4—444no—
1155D4—444no—
1156D4—442no—
1157D4—882no—
1158D4—882no—
1159D4—882no—
1160D4—882no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—81no—
1170C2×C4—81no—
1171C2×C4—112no—
1172C2×C4—112no—
1173C2×C4—222no—
1174C2×C4—222no—
1175C2×C4—222no—
1176C2×C4—222no—
1177C2×C4—221no—
1178C2×C4—221no—
1179C2×C4—221no—
1180C2×C4—222no—
1181C2×C4—444no—
1182C2×C4—444no—
1183C2×C4—444no—
1184C2×C4—442no—
1185C2×C4—882no—
1186C2×C4—881no—
1187C2×C4—881no—
1188C2×C4—882no—
1189C2×C4—882no—
1190C2×C4—881no—
1191C2×C4C2×D4×D1111yescharacteristic
1192C2×C4C2×D4×D1111yescharacteristic
1193C2×C4C2×D4×D1111yescharacteristic
1194C2×C4C2×D4×D1111yescharacteristic
1195C2×C4C2×D4×D1111yescharacteristic
1196C2×C4#41×D1112yes—
1197C2×C4#6704212yes—
1198C2×C4C24×D1111yescharacteristic
1199C8—22no—
1200C8—22no—
1201C8—221no—
1202C8—221no—
1203C8—221no—
1204C8—221no—
1205C22—21no—
1206C22—21no—
1207C22—41no—
1208C22—41no—
1209C22—41no—
1210C22—41no—
1211C22—41no—
1212C22—41no—
1213C22—222no—
1214C22—222no—
1215C22—222no—
1216C22—222no—
1217C22—224no—
1218C22—222no—
1219C22—222no—
1220C22—442no—
1221C22—442no—
1222C22—441no—
1223C22—441no—
1224C22—441no—
1225C22—884no—
1226C22—1764no—
1227C22—1764no—
1228C22#1062320712yes—
1229C22C22×D4×D1111yescharacteristic
1230C4—21no—
1231C4—21no—
1232C4—21no—
1233C4—21no—
1234C4—42no—
1235C4—41no—
1236C4—41no—
1237C4—42no—
1238C4—222no—
1239C4—222no—
1240C4—442no—
1241C4—441no—
1242C4—441no—
1243C4—441no—
1244C4#1062320712yes—
1245C4C2×#41×D1111yescharacteristic
1246C4C2×#6704211yescharacteristic
1247C2—22no—
1248C2—81no—
1249C2—81no—
1250C2—442no—
1251C2—442no—
1252C2—444no—
1253C2—881no—
1254C2C2×#1062320711yescharacteristic
1255C2#1308338911yescharacteristic
1256C2#1308339311yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3142C2
socleC22×C11C23×D4
hypercenter#3142D11
hypocenterC11#61201
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3142

Complements

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

NH ≅ G/Ntype
1. #13082540C2semidirect
2. #13082378C2semidirect
3. #13080831C2semidirect
4. #13080816C2semidirect
5. #13080756C2semidirect
6. #13080711C2semidirect
7. #13080636C2semidirect
8. #13080591C2semidirect
9. #13080465C2semidirect
10. #13080450C2semidirect
11. #13078604C2semidirect
12. #13078593C2semidirect
13. C2×#10622679C2semidirect
14. #13078285C2semidirect
15. #13078277C2semidirect
16. #13078065C2semidirect
17. #13077922C2semidirect
18. #13077922C2semidirect
19. C4×#66961C2semidirect
20. #13077362C2semidirect
21. #13077140C2semidirect
22. #13077140C2semidirect
23. C11×#3142C2semidirect
27. C2×C11×#125C22semidirect
30. C2×#67003C22semidirect
31. C2×#67003C22semidirect
33. C2×#66960C22semidirect
34. C2×#66960C22semidirect
39. #10623226C22semidirect
40. #10623226C22semidirect
41. #10623225C22semidirect
42. #10623225C22semidirect
55. #10623041C22semidirect
56. #10623041C22semidirect
57. #10623035C22semidirect
58. #10623035C22semidirect
60. C4×#4339C22semidirect
62. C11×#491C22semidirect
63. C11×#490C22semidirect
64. C11×#488C22semidirect
65. C11×#488C22semidirect
66. C11×#417C22semidirect
67. C11×#417C22semidirect
68. C11×#417C22semidirect
69. C11×#417C22semidirect
70. C4×C11×M16C22semidirect
71. #10622846C22semidirect
72. #10622846C22semidirect
73. #10622746C22semidirect
75. #10622742C22semidirect
76. #10622742C22semidirect
77. #10622734C22semidirect
78. #10622703C22semidirect
79. #10622696C22semidirect
80. #10622688C22semidirect
81. #10622685C22semidirect
82. #10622679C22semidirect
83. #10622679C22semidirect
84. #10622679C22semidirect
85. #10622679C22semidirect
86. #10622670C22semidirect
87. #10622670C22semidirect
88. #10622667C22semidirect
89. #10622667C22semidirect
92. C2×#66872C22semidirect
93. C2×#66871C22semidirect
94. C2×C4⋊(C11⋊C8)C22semidirect
95. #10622429C22semidirect
96. #10622428C22semidirect
97. #10622427C22semidirect
98. #10622426C22semidirect
99. #10622425C22semidirect
100. #10622424C22semidirect
101. #10622424C22semidirect
102. #10622423C22semidirect
103. #10622423C22semidirect
104. #10622422C22semidirect
105. #10622420C22semidirect
106. #10622418C22semidirect
107. #10622417C22semidirect
108. #10622417C22semidirect
109. #10622416C22semidirect
110. #10622416C22semidirect
111. #10622397C22semidirect
112. #10622395C22semidirect
113. #10622393C22semidirect
114. #10622392C22semidirect
115. #10622391C22semidirect
116. #10622390C22semidirect
117. #10622389C22semidirect
118. #10622389C22semidirect
119. #10622388C22semidirect
120. #10622387C22semidirect
121. #10622386C22semidirect
122. #10622386C22semidirect
123. #10622383C22semidirect
124. #10622383C22semidirect
125. D11×#102C22semidirect
126. D11×#102C22semidirect
127. #10622324C22semidirect
128. #10622323C22semidirect
129. #10622319C22semidirect
130. #10622319C22semidirect
131. C4×D88C22semidirect
132. C4×#4314C22semidirect
133. #10622301C22semidirect
134. C8×D44C22semidirect
491. #3142D11semidirect
632. C2×#125C2×D11semidirect
638. #491C2×D11semidirect
639. #490C2×D11semidirect
640. #488C2×D11semidirect
641. #488C2×D11semidirect
696. #417C2×D11semidirect
697. #417C2×D11semidirect
698. #417C2×D11semidirect
699. #417C2×D11semidirect
710. C4×M16C2×D11semidirect
1108. C11#61201semidirect

Maximal subgroups

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

subgroupindex
#130825402
#130823782
#130808312
#130808162
#130807562
#130807112
#130806362
#130805912
#130804652
#130804502
#130786042
#130785932
C2×#106226792
#130782852
#130782772
#130780652
#130779222
C4×#669612
#130773622
#130771402
C11×#31422
#6120111