Finite Group Databasebeta

← #15639568

Subgroups — #15639568

Order 2816.

2224 conjugacy classes of subgroups.

The subgroup lattice has 1256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082855C211yesmaximal, characteristic, complemented
2#13080817C212yesmaximal, complemented
3#13080757C212yesmaximal, complemented
4#13080622C212yesmaximal, complemented
5#13080518C212yesmaximal, complemented
6D4×#4323C212yesmaximal, complemented
7#13080236C212yesmaximal, complemented
8#13080112C212yesmaximal, complemented
9#13080097C212yesmaximal, complemented
10#13079666C212yesmaximal, complemented
11#13079462C212yesmaximal, complemented
12#13079413C211yesmaximal, characteristic, complemented
13#13079364C211yesmaximal, characteristic, complemented
14#13078815C212yesmaximal, complemented
15#13077884C212yesmaximal, complemented
16#13077868C211yesmaximal, characteristic, complemented
17C2×#10622851C211yesmaximal, characteristic, complemented
18#13077664C211yesmaximal, characteristic, complemented
19C11×#3488C211yesmaximal, characteristic, complemented
20C2×C11×H(5,𝔽2)C2211yescharacteristic, complemented
21C22×C11×#41C2211yescharacteristic, complemented
22C11×#550C2212yescomplemented
23C11×#548C2212yescomplemented
24C11×#546—22no—
25C11×#546C2212yescomplemented
26D42×C11—22no—
27D42×C11C2212yescomplemented
28C11×#537—21no—
29C11×#537C2211yescharacteristic, complemented
30C11×#535—21no—
31C11×#535C2211yescharacteristic, complemented
32C11×#525—21no—
33C11×#525C2211yescharacteristic
34C2×C11×#121—21no—
35C2×C11×#121C2211yescharacteristic, complemented
36C11×#520C2211yescharacteristic, complemented
37#10623361C2212yescomplemented
38C2×#67002C2211yescharacteristic, complemented
39C2×#67002C2212yescomplemented
40C2×#67002C2211yescharacteristic, complemented
41C22×#4325C2211yescharacteristic, complemented
42C22×#4323C2212yescomplemented
43C22×#4323C2211yescharacteristic, complemented
44C2×#66983C2211yescharacteristic, complemented
45C2×#66983C2211yescharacteristic, complemented
46#10623197—22no—
47#10623175—21no—
48#10623175—21no—
49#10623136—21no—
50#10623136—21no—
51#10623121—22no—
52#10623096C2212yescomplemented
53#10623096C2212yescomplemented
54D4×D44C2212yescomplemented
55D4×D44C2212yescomplemented
56#10623066C2212yescomplemented
57#10622851C2212yescomplemented
58#10622851C2212yescomplemented
59#10622851C2212yescomplemented
60#10622851C2212yescomplemented
61#10622851C2212yescomplemented
62#10622851C2212yescomplemented
63#10622851C2212yescomplemented
64#10622851C2212yescomplemented
65#10622847C2212yescomplemented
66#10622846C2212yescomplemented
67#10622845C2211yescharacteristic, complemented
68#10622845C2211yescharacteristic, complemented
69#10622840C2212yescomplemented
70C2×#66899C2211yescharacteristic, complemented
71#10622830C2212yescomplemented
72#10622830C2212yescomplemented
73#10622830C2212yescomplemented
74#10622830C2212yescomplemented
75#10622830C2212yescomplemented
76#10622828C2212yescomplemented
77C2×#66896C2211yescharacteristic, complemented
78#10622820C2211yescharacteristic, complemented
79C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
80#10622686C2212yescomplemented
81#10622685C2212yescomplemented
82#10622685C2212yescomplemented
83#10622684C2212yescomplemented
84#10622671C2212yescomplemented
85#10622670C2212yescomplemented
86#10622670C2212yescomplemented
87#10622669C2212yescomplemented
88#10622662C2212yescomplemented
89#10622661C2212yescomplemented
90#10622659C2212yescomplemented
91#10622658C2212yescomplemented
92#10622652C2212yescomplemented
93#10622652C2212yescomplemented
94#10622652C2212yescomplemented
95#10622651C2212yescomplemented
96#10622651C2212yescomplemented
97#10622651C2212yescomplemented
98#10622649C2212yescomplemented
99#10622649C2212yescomplemented
100#10622649C2212yescomplemented
101#10622648C2212yescomplemented
102#10622647C2212yescomplemented
103#10622646C2212yescomplemented
104#10622640C2212yescomplemented
105#10622639C2212yescomplemented
106C4×#4325C2212yescomplemented
107#10622635C2212yescomplemented
108#10622628C2212yescomplemented
109#10622627C2212yescomplemented
110C4×#4323C2212yescomplemented
111#10622625C2212yescomplemented
112#10622624C2212yescomplemented
113#10622624C2212yescomplemented
114D4×C11⋊C8C2212yescomplemented
115#10622622C2212yescomplemented
116#10622613C2212yescomplemented
117#10622581C2212yescomplemented
118#10622580C2212yescomplemented
119C11×H(5,𝔽2)—42no—
120C11×H(5,𝔽2)—42no—
121C2×C11×#41—21no—
122C2×C11×#41—21no—
123C2×C11×#41—21no—
124C2×C11×#41—42no—
125C2×C11×#41—42no—
126C2×C11×#41C2311yescharacteristic
127C2×C11×#41C2311yescharacteristic
128C2×C11×#41C2311yescharacteristic
129C2×C11×#41C2312yes—
130C2×C11×#41C2311yescharacteristic
131C2×C11×#41C2311yescharacteristic
132C22×Q8×C11C2311yescharacteristic
133C22×D4×C11—21no—
134C22×D4×C11—21no—
135C22×D4×C11—21no—
136C22×D4×C11—22no—
137C22×D4×C11—22no—
138C22×D4×C11C2311yescharacteristic
139C22×D4×C11C2312yes—
140C22×D4×C11C2311yescharacteristic
141C23×C4×C11—21no—
142C23×C4×C11C2311yescharacteristic
143C22×C22⋊D11—21no—
144C22×C22⋊D11—21no—
145C2×D4×D11—22no—
146C2×D4×D11—22no—
147C22×D44C2311yescharacteristic
148C22×D44C2311yescharacteristic
149C22×D44C2312yes—
150C11×#127—22no—
151C11×#127C2312yes—
152C11×#124—22no—
153C11×#124C2312yes—
154C11×#123—22no—
155C11×#123D412yes—
156C11×C22⋊Q8—21no—
157C11×C22⋊Q8—22no—
158C11×C22⋊Q8D411yescharacteristic
159C11×C22⋊Q8D411yescharacteristic
160C11×C22⋊Q8C2312yes—
161C11×#121—21no—
162C11×#121—22no—
163C11×#121—22no—
164C11×#121—21no—
165C11×#121—21no—
166C11×#121—21no—
167C11×#121—21no—
168C11×#121—22no—
169C11×#121—22no—
170C11×#121—22no—
171C11×#121—22no—
172C11×#121D411yescharacteristic
173C11×#121D411yescharacteristic
174C11×#121C2312yes—
175C11×#121C2312yes—
176C11×#121C2312yes—
177C11×#120—22no—
178C11×#120—22no—
179C11×#120—22no—
180C11×#120—22no—
181C11×#120D412yes—
182C4×Q8×C11C2312yes—
183C4×D4×C11—22no—
184C4×D4×C11—22no—
185C4×D4×C11—22no—
186C4×D4×C11C2312yes—
187C4×D4×C11C2312yes—
188C4×D4×C11C2312yes—
189C11×#117—21no—
190C11×#117C2311yescharacteristic
191C2×C11×C4⋊C4—21no—
192C2×C11×C4⋊C4C2311yescharacteristic
193C2×C11×C22⋊C4—21no—
194C2×C11×C22⋊C4—22no—
195#67002—42no—
196#67002—44no—
197#67002—42no—
198#67000—22no—
199C2×#4325—42no—
200C2×#4325C2312yes—
201C2×#4325C2312yes—
202C2×#4325C2312yes—
203C2×#4325C2312yes—
204#66993—22no—
205#66992—22no—
206#66992—22no—
207#66990—22no—
208#66990—22no—
209C2×#4323—42no—
210C2×#4323—44no—
211C2×#4323C2312yes—
212C2×#4323C2312yes—
213C2×#4323C2312yes—
214C2×#4323C2312yes—
215C2×#4323C2312yes—
216C2×#4323C2312yes—
217C2×#4323C2312yes—
218C2×#4323C2312yes—
219#66983—21no—
220#66983—21no—
221#66983—21no—
222#66983—21no—
223#66983C2312yes—
224#66983C2312yes—
225#66983C2312yes—
226#66983C2312yes—
227#66983C2312yes—
228#66983C2312yes—
229C2×(C2×D11)⋊C4—21no—
230C2×(C2×D11)⋊C4—21no—
231#66979C2312yes—
232C2×C4⋊Dic11C2311yescharacteristic
233C2×C4⋊Dic11C2311yescharacteristic
234C2×#4318C2311yescharacteristic
235C2×#4318C2311yescharacteristic
236C2×#4318C2312yes—
237C22×C11⋊C8C2311yescharacteristic
238C22×C11⋊C8C2312yes—
239C22×C11⋊C8C2311yescharacteristic
240#66951—22no—
241#66951—22no—
242#66948—22no—
243#66948—22no—
244#66947—22no—
245#66947—22no—
246#66937—22no—
247#66937—22no—
248#66936—22no—
249#66936—22no—
250#66935—22no—
251#66935—22no—
252#66935—22no—
253#66935—22no—
254(C22⋊D11)⋊C4—22no—
255(C22⋊D11)⋊C4—22no—
256#66927C2312yes—
257C4×D44C2312yes—
258C4×D44C2312yes—
259#66923C2312yes—
260#66899C2312yes—
261#66899C2312yes—
262#66899C2312yes—
263#66899C2312yes—
264#66896C2312yes—
265#66896C2312yes—
266#66896C2312yes—
267#66896C2312yes—
268#66896C2312yes—
269#66896C2312yes—
270#66896C2312yes—
271#66896C2312yes—
272C22⋊(C11⋊C8)C2312yes—
273C22⋊(C11⋊C8)C2312yes—
274C22⋊(C11⋊C8)C2312yes—
275C22⋊(C11⋊C8)C2312yes—
276C22⋊(C11⋊C8)C2312yes—
277C22⋊(C11⋊C8)C2312yes—
278#66873C2312yes—
279#66873C2312yes—
280#66873C2312yes—
281#66873C2312yes—
282#66872C2312yes—
283#66872C2312yes—
284#66871C2312yes—
285#66871C2312yes—
286C4⋊(C11⋊C8)C2312yes—
287C4⋊(C11⋊C8)C2312yes—
288#66867C2312yes—
289C4×C11⋊C8C2312yes—
290#61617—111nomaximal, Sylow
291C24×C11—21no—
292C24×C11—22no—
293C24×C11—21no—
294C24×C11C2×D411yescharacteristic
295C23×D11—21no—
296C23×D11—21no—
297C23×D11—22no—
298C11×#41—22no—
299C11×#41—22no—
300C11×#41—22no—
301C11×#41—24no—
302C11×#41—22no—
303C11×#41—41no—
304C11×#41—41no—
305C11×#41—41no—
306C11×#41—41no—
307C11×#41—41no—
308C11×#41—41no—
309C11×#41—42no—
310C11×#41—44no—
311C11×#41—44no—
312C11×#41—44no—
313C2×Q8×C11—21no—
314C2×Q8×C11—22no—
315C2×Q8×C11—41no—
316C2×Q8×C11C2×D411yescharacteristic
317C2×Q8×C11C2411yescharacteristic
318C2×Q8×C11C2411yescharacteristic
319C2×D4×C11—21no—
320C2×D4×C11—22no—
321C2×D4×C11—24no—
322C2×D4×C11—22no—
323C2×D4×C11—21no—
324C2×D4×C11—21no—
325C2×D4×C11—22no—
326C2×D4×C11—21no—
327C2×D4×C11—22no—
328C2×D4×C11—22no—
329C2×D4×C11—21no—
330C2×D4×C11—22no—
331C2×D4×C11—21no—
332C2×D4×C11—22no—
333C2×D4×C11—22no—
334C2×D4×C11—41no—
335C2×D4×C11—42no—
336C2×D4×C11—41no—
337C2×D4×C11—41no—
338C2×D4×C11—44no—
339C2×D4×C11—44no—
340C2×D4×C11—48no—
341C2×D4×C11—84no—
342C2×D4×C11—82no—
343C2×D4×C11C2×D412yes—
344C2×D4×C11C2×D411yescharacteristic
345C2×D4×C11C2×D412yes—
346C2×D4×C11C2×D412yes—
347C2×D4×C11C2412yes—
348C2×D4×C11C2411yescharacteristic
349C2×D4×C11C2411yescharacteristic
350C22×C4×C11—21no—
351C22×C4×C11—21no—
352C22×C4×C11—21no—
353C22×C4×C11—21no—
354C22×C4×C11—21no—
355C22×C4×C11—22no—
356C22×C4×C11—21no—
357C22×C4×C11—22no—
358C22×C4×C11—41no—
359C22×C4×C11—41no—
360C22×C4×C11—44no—
361C22×C4×C11C2×D411yescharacteristic
362C22×C4×C11C2×D411yescharacteristic
363C22×C4×C11C2×D411yescharacteristic
364C22×C4×C11C2411yescharacteristic
365C22×C4×C11C2411yescharacteristic
366C22×C4×C11C2412yes—
367C22×C4×C11C2411yescharacteristic
368C2×C22⋊D11—22no—
369C2×C22⋊D11—22no—
370C2×C22⋊D11—22no—
371C2×C22⋊D11—22no—
372C2×C22⋊D11—22no—
373C2×C22⋊D11—22no—
374C2×C22⋊D11—82no—
375C2×C22⋊D11—82no—
376C22×Dic11—21no—
377C22×Dic11—21no—
378D4×D11—84no—
379D4×D11—84no—
380C2×D44—22no—
381C2×D44—22no—
382C2×D44—21no—
383C2×D44—21no—
384C2×D44—22no—
385C2×D44—41no—
386C2×D44—42no—
387C2×D44—41no—
388C2×D44—41no—
389C2×D44—41no—
390C2×D44—42no—
391C2×D44C2412yes—
392C2×D44C2412yes—
393C2×C4×D11—22no—
394C2×C4×D11—22no—
395C11×C4⋊C4—21no—
396C11×C4⋊C4—22no—
397C11×C4⋊C4—22no—
398C11×C4⋊C4C2×D411yescharacteristic
399C11×C4⋊C4C2×D411yescharacteristic
400C11×C4⋊C4C2×D412yes—
401C11×C4⋊C4C2×D412yes—
402C11×C4⋊C4C2412yes—
403C11×C22⋊C4—22no—
404C11×C22⋊C4—22no—
405C11×C22⋊C4—22no—
406C11×C22⋊C4—22no—
407C11×C22⋊C4—22no—
408C11×C22⋊C4—22no—
409C11×C22⋊C4—22no—
410C11×C22⋊C4C2×D412yes—
411C11×C22⋊C4C2×D412yes—
412C11×C22⋊C4C2×D412yes—
413C11×C22⋊C4C2×D412yes—
414C11×C22⋊C4C2×D412yes—
415C42×C11—22no—
416C42×C11C2412yes—
417C22⋊Dic11—22no—
418#4325—24no—
419#4325—24no—
420#4325—42no—
421#4325—42no—
422#4323—24no—
423#4323—24no—
424#4323—42no—
425#4323—42no—
426#4323—42no—
427#4323—42no—
428#4323—42no—
429#4323—42no—
430(C2×D11)⋊C4—22no—
431(C2×D11)⋊C4—22no—
432(C2×D11)⋊C4—22no—
433(C2×D11)⋊C4—22no—
434(C2×D11)⋊C4—22no—
435(C2×D11)⋊C4—22no—
436(C2×D11)⋊C4—22no—
437(C2×D11)⋊C4—22no—
438C4⋊Dic11—21no—
439C4⋊Dic11—21no—
440C4⋊Dic11C2412yes—
441C4⋊Dic11C2412yes—
442Dic11⋊C4—22no—
443Dic11⋊C4—22no—
444C4×Dic11—22no—
445#4318—41no—
446#4318—41no—
447#4318—42no—
448C2×C11⋊C8—41no—
449C2×C11⋊C8—42no—
450C2×C11⋊C8—41no—
451C2×C11⋊C8C2412yes—
452C2×C11⋊C8C2412yes—
453C2×C11⋊C8C2412yes—
454C2×C11⋊C8C2412yes—
455#3537—111no—
456#3488D1111yescharacteristic, complemented
457#3322—112no—
458#3318—112no—
459#3309—112no—
460#3301—112no—
461D4×D8—112no—
462#3274—112no—
463#3265—112no—
464#3264—112no—
465#3220—112no—
466#3198—112no—
467#3192—111no—
468#3186—111no—
469#3119—112no—
470#3008—112no—
471#3006—111no—
472C2×#449—111no—
473#2976—111no—
474C23×C11—21no—
475C23×C11—22no—
476C23×C11—22no—
477C23×C11—21no—
478C23×C11—41no—
479C23×C11—41no—
480C23×C11—42no—
481C23×C11—44no—
482C23×C11—42no—
483C23×C11—42no—
484C23×C11—81no—
485C23×C11—81no—
486C23×C11—82no—
487C23×C11—82no—
488C23×C11—81no—
489C23×C11C22×D412yes—
490C23×C11C22×D411yescharacteristic
491C23×C11C22×D411yescharacteristic
492C23×C11C22×D411yescharacteristic
493C22×D11—22no—
494C22×D11—22no—
495C22×D11—42no—
496C22×D11—42no—
497C22×D11—81no—
498C22×D11—81no—
499C22×D11—82no—
500C22×D11—82no—
501C22×D11—82no—
502C22×D11—81no—
503C22×D11—81no—
504Q8×C11—21no—
505Q8×C11—21no—
506Q8×C11—21no—
507Q8×C11—41no—
508Q8×C11—42no—
509Q8×C11H(5,𝔽2)12yes—
510D4×C11—24no—
511D4×C11—24no—
512D4×C11—21no—
513D4×C11—22no—
514D4×C11—21no—
515D4×C11—22no—
516D4×C11—21no—
517D4×C11—42no—
518D4×C11—41no—
519D4×C11—42no—
520D4×C11—44no—
521D4×C11—42no—
522D4×C11—44no—
523D4×C11—42no—
524D4×C11—42no—
525D4×C11—42no—
526D4×C11—42no—
527D4×C11—44no—
528D4×C11—82no—
529D4×C11—82no—
530D4×C11—82no—
531D4×C11—82no—
532D4×C11H(5,𝔽2)12yes—
533C2×C4×C11—24no—
534C2×C4×C11—21no—
535C2×C4×C11—21no—
536C2×C4×C11—21no—
537C2×C4×C11—22no—
538C2×C4×C11—21no—
539C2×C4×C11—21no—
540C2×C4×C11—22no—
541C2×C4×C11—21no—
542C2×C4×C11—21no—
543C2×C4×C11—22no—
544C2×C4×C11—21no—
545C2×C4×C11—41no—
546C2×C4×C11—41no—
547C2×C4×C11—41no—
548C2×C4×C11—42no—
549C2×C4×C11—44no—
550C2×C4×C11—42no—
551C2×C4×C11—42no—
552C2×C4×C11—42no—
553C2×C4×C11—82no—
554C2×C4×C11—81no—
555C2×C4×C11C22×D412yes—
556C2×C4×C11C22×D412yes—
557C2×C4×C11C22×D412yes—
558C2×C4×C11C22×D411yescharacteristic
559C2×C4×C11C22×D411yescharacteristic
560C2×C4×C11C22×D411yescharacteristic
561C2×C4×C11C2511yescharacteristic
562C22⋊D11—44no—
563C22⋊D11—44no—
564C22⋊D11—82no—
565C22⋊D11—82no—
566C22⋊D11—82no—
567C22⋊D11—82no—
568C2×Dic11—22no—
569C2×Dic11—22no—
570C2×Dic11—81no—
571C2×Dic11—81no—
572D44—22no—
573D44—22no—
574D44—22no—
575D44—22no—
576D44—81no—
577D44—82no—
578D44—81no—
579D44—82no—
580D44—82no—
581C4×D11—82no—
582C4×D11—82no—
583C11⋊C8—22no—
584C11⋊C8—22no—
585C11⋊C8—22no—
586C11⋊C8—22no—
587C2×H(5,𝔽2)C2×D1111yescharacteristic, complemented
588C22×#41C2×D1111yescharacteristic, complemented
589C2×AGL(1,ℤ/8)—111no—
590C2×AGL(1,ℤ/8)—111no—
591C2×AGL(1,ℤ/8)—112no—
592C22×SD16—111no—
593C22×D8—111no—
594C22×D8—112no—
595#560—222no—
596#553—112no—
597#553—112no—
598#550C2×D1112yescomplemented
599#548C2×D1112yescomplemented
600#546—22no—
601#546C2×D1112yescomplemented
602D42—22no—
603D42—112no—
604D42—112no—
605D42—222no—
606D42C2×D1112yescomplemented
607#540—112no—
608#538—221no—
609#538—221no—
610#537—21no—
611#537C2×D1111yescharacteristic, complemented
612#535—21no—
613#535—112no—
614#535C2×D1111yescharacteristic, complemented
615#534—221no—
616#534—221no—
617#525—21no—
618#525C2×D1111yescharacteristic
619C2×#121—21no—
620C2×#121—111no—
621C2×#121—111no—
622C2×#121C2×D1111yescharacteristic, complemented
623#520C2×D1111yescharacteristic, complemented
624#496—112no—
625#493—112no—
626#490—112no—
627#488—112no—
628#485—112no—
629#482—112no—
630#481—112no—
631#481—112no—
632#480—112no—
633#480—112no—
634#479—112no—
635#478—112no—
636#469—112no—
637#469—112no—
638#469—112no—
639#468—112no—
640#466—112no—
641#466—112no—
642#466—112no—
643#465—112no—
644#463—112no—
645#463—112no—
646#460—112no—
647#459—112no—
648#459—112no—
649#459—112no—
650#450—112no—
651#449—112no—
652#449—112no—
653#449—112no—
654#449—112no—
655#449—112no—
656#449—112no—
657#449—112no—
658#449—112no—
659#448—112no—
660#447—112no—
661#447—112no—
662#447—112no—
663#447—112no—
664#447—112no—
665#447—112no—
666#447—112no—
667#447—112no—
668#442—112no—
669#440—112no—
670C4×SD16—112no—
671C4×D8—112no—
672#436—112no—
673#435—112no—
674#435—112no—
675C8×D4—112no—
676#433—112no—
677#418—112no—
678#417—111no—
679#417—111no—
680#416—112no—
681C2×#103—111no—
682C2×#102—111no—
683#408—112no—
684#407—111no—
685C2×C22⋊C8—111no—
686C22×C11—21no—
687C22×C11—21no—
688C22×C11—21no—
689C22×C11—22no—
690C22×C11—21no—
691C22×C11—21no—
692C22×C11—22no—
693C22×C11—21no—
694C22×C11—22no—
695C22×C11—21no—
696C22×C11—22no—
697C22×C11—21no—
698C22×C11—41no—
699C22×C11—41no—
700C22×C11—41no—
701C22×C11—42no—
702C22×C11—41no—
703C22×C11—42no—
704C22×C11—42no—
705C22×C11—41no—
706C22×C11—82no—
707C22×C11—84no—
708C22×C11—164no—
709C22×C11—162no—
710C22×C11#57612yes—
711C22×C11C23×D411yescharacteristic
712C2×D11—42no—
713C2×D11—42no—
714C2×D11—42no—
715C2×D11—42no—
716C2×D11—42no—
717C2×D11—42no—
718C2×D11—162no—
719C2×D11—162no—
720C2×D11—164no—
721C4×C11—22no—
722C4×C11—21no—
723C4×C11—22no—
724C4×C11—21no—
725C4×C11—22no—
726C4×C11—21no—
727C4×C11—22no—
728C4×C11—41no—
729C4×C11—42no—
730C4×C11C2×H(5,𝔽2)11yescharacteristic
731C4×C11C2×H(5,𝔽2)11yescharacteristic
732Dic11—42no—
733Dic11—42no—
734H(5,𝔽2)—42no—
735H(5,𝔽2)—42no—
736C2×#41—21no—
737C2×#41—21no—
738C2×#41—21no—
739C2×#41—42no—
740C2×#41—42no—
741C2×#41C22×D1111yescharacteristic
742C2×#41C22×D1111yescharacteristic
743C2×#41C22×D1112yes—
744C2×#41C22×D1111yescharacteristic
745C2×#41C22×D1111yescharacteristic
746C2×#41C22×D1111yescharacteristic
747C22×Q8C22×D1111yescharacteristic
748C22×D4—21no—
749C22×D4—21no—
750C22×D4—21no—
751C22×D4—22no—
752C22×D4—22no—
753C22×D4—111no—
754C22×D4—111no—
755C22×D4—112no—
756C22×D4—221no—
757C22×D4—221no—
758C22×D4—222no—
759C22×D4—222no—
760C22×D4C22×D1111yescharacteristic
761C22×D4C22×D1112yes—
762C22×D4C22×D1111yescharacteristic
763C23×C4—21no—
764C23×C4C22×D1111yescharacteristic
765AGL(1,ℤ/8)—442no—
766AGL(1,ℤ/8)—444no—
767AGL(1,ℤ/8)—442no—
768C2×SD16—112no—
769C2×SD16—112no—
770C2×SD16—112no—
771C2×SD16—112no—
772C2×SD16—442no—
773C2×D8—112no—
774C2×D8—112no—
775C2×D8—112no—
776C2×D8—112no—
777C2×D8—112no—
778C2×D8—112no—
779C2×D8—112no—
780C2×D8—112no—
781C2×D8—442no—
782C2×D8—444no—
783C2×M16—111no—
784C2×M16—111no—
785C2×M16—112no—
786C22×C8—111no—
787C22×C8—112no—
788C22×C8—111no—
789#127—22no—
790#127—112no—
791#127—222no—
792#127C22×D1112yes—
793#126—222no—
794#126—222no—
795#125—112no—
796#124—22no—
797#124—222no—
798#124C22×D1112yes—
799#123—22no—
800#123—222no—
801#123—222no—
802#123—222no—
803#123—222no—
804#123C22⋊D1112yes—
805C22⋊Q8—21no—
806C22⋊Q8—22no—
807C22⋊Q8C22⋊D1111yescharacteristic
808C22⋊Q8C22⋊D1111yescharacteristic
809C22⋊Q8C22×D1112yes—
810#121—21no—
811#121—22no—
812#121—22no—
813#121—21no—
814#121—21no—
815#121—21no—
816#121—21no—
817#121—22no—
818#121—22no—
819#121—22no—
820#121—22no—
821#121—112no—
822#121—112no—
823#121—112no—
824#121—112no—
825#121—112no—
826#121—112no—
827#121—222no—
828#121—222no—
829#121—221no—
830#121—221no—
831#121—221no—
832#121—221no—
833#121—222no—
834#121—222no—
835#121—222no—
836#121—222no—
837#121C22⋊D1111yescharacteristic
838#121C22⋊D1111yescharacteristic
839#121C22×D1112yes—
840#121C22×D1112yes—
841#121C22×D1112yes—
842#120—22no—
843#120—22no—
844#120—22no—
845#120—22no—
846#120—222no—
847#120—222no—
848#120—222no—
849#120—222no—
850#120—222no—
851#120—222no—
852#120C22⋊D1112yes—
853C4×Q8C22×D1112yes—
854C4×D4—22no—
855C4×D4—22no—
856C4×D4—22no—
857C4×D4—112no—
858C4×D4—112no—
859C4×D4—222no—
860C4×D4—222no—
861C4×D4C22×D1112yes—
862C4×D4C22×D1112yes—
863C4×D4C22×D1112yes—
864#117—21no—
865#117—112no—
866#117C22×D1111yescharacteristic
867C2×C4⋊C4—21no—
868C2×C4⋊C4—111no—
869C2×C4⋊C4—111no—
870C2×C4⋊C4C22×D1111yescharacteristic
871C2×C22⋊C4—21no—
872C2×C22⋊C4—22no—
873C2×C22⋊C4—221no—
874C2×C22⋊C4—221no—
875#107—112no—
876#107—112no—
877#106—112no—
878#106—112no—
879C4⋊C8—112no—
880C4⋊C8—112no—
881#103—112no—
882#103—112no—
883#103—112no—
884#103—112no—
885#102—112no—
886#102—112no—
887#102—112no—
888#102—112no—
889#102—112no—
890#102—112no—
891#102—112no—
892#102—112no—
893#102—112no—
894#102—112no—
895#102—112no—
896#102—112no—
897C22⋊C8—112no—
898C22⋊C8—112no—
899C22⋊C8—112no—
900C22⋊C8—112no—
901C22⋊C8—112no—
902C22⋊C8—112no—
903#97—112no—
904C4×C8—112no—
905C2×C11—22no—
906C2×C11—41no—
907C2×C11—42no—
908C2×C11—41no—
909C2×C11—42no—
910C2×C11—81no—
911C2×C11—82no—
912C2×C11#348411yescharacteristic
913C2×C11C2×#57611yescharacteristic
914C2×C11#358511yescharacteristic
915D11—82no—
916D11—82no—
917C24—21no—
918C24—22no—
919C24—21no—
920C24—221no—
921C24—221no—
922C24—222no—
923C24C2×C22⋊D1111yescharacteristic
924#41—22no—
925#41—22no—
926#41—22no—
927#41—24no—
928#41—22no—
929#41—41no—
930#41—41no—
931#41—41no—
932#41—41no—
933#41—41no—
934#41—41no—
935#41—42no—
936#41—44no—
937#41—44no—
938#41—44no—
939C2×Q8—21no—
940C2×Q8—22no—
941C2×Q8—41no—
942C2×Q8C2×C22⋊D1111yescharacteristic
943C2×Q8C23×D1111yescharacteristic
944C2×Q8C23×D1111yescharacteristic
945C2×D4—21no—
946C2×D4—22no—
947C2×D4—24no—
948C2×D4—22no—
949C2×D4—21no—
950C2×D4—21no—
951C2×D4—22no—
952C2×D4—21no—
953C2×D4—22no—
954C2×D4—22no—
955C2×D4—21no—
956C2×D4—22no—
957C2×D4—21no—
958C2×D4—22no—
959C2×D4—22no—
960C2×D4—41no—
961C2×D4—42no—
962C2×D4—41no—
963C2×D4—41no—
964C2×D4—44no—
965C2×D4—44no—
966C2×D4—48no—
967C2×D4—84no—
968C2×D4—82no—
969C2×D4—112no—
970C2×D4—112no—
971C2×D4—222no—
972C2×D4—222no—
973C2×D4—222no—
974C2×D4—222no—
975C2×D4—222no—
976C2×D4—222no—
977C2×D4—221no—
978C2×D4—221no—
979C2×D4—222no—
980C2×D4—222no—
981C2×D4—222no—
982C2×D4—441no—
983C2×D4—442no—
984C2×D4—441no—
985C2×D4—441no—
986C2×D4—441no—
987C2×D4—442no—
988C2×D4—884no—
989C2×D4—884no—
990C2×D4—882no—
991C2×D4—882no—
992C2×D4C2×C22⋊D1112yes—
993C2×D4C2×C22⋊D1112yes—
994C2×D4C2×C22⋊D1111yescharacteristic
995C2×D4C2×C22⋊D1112yes—
996C2×D4C23×D1112yes—
997C2×D4C23×D1111yescharacteristic
998C2×D4C23×D1111yescharacteristic
999C22×C4—21no—
1000C22×C4—21no—
1001C22×C4—21no—
1002C22×C4—21no—
1003C22×C4—21no—
1004C22×C4—22no—
1005C22×C4—21no—
1006C22×C4—22no—
1007C22×C4—41no—
1008C22×C4—41no—
1009C22×C4—44no—
1010C22×C4—221no—
1011C22×C4—221no—
1012C22×C4—222no—
1013C22×C4—222no—
1014C22×C4C2×C22⋊D1111yescharacteristic
1015C22×C4C2×C22⋊D1111yescharacteristic
1016C22×C4C2×C22⋊D1111yescharacteristic
1017C22×C4C23×D1111yescharacteristic
1018C22×C4C23×D1111yescharacteristic
1019C22×C4C23×D1111yescharacteristic
1020C22×C4C23×D1112yes—
1021SD16—224no—
1022SD16—224no—
1023SD16—442no—
1024SD16—442no—
1025D8—224no—
1026D8—224no—
1027D8—442no—
1028D8—442no—
1029D8—442no—
1030D8—442no—
1031D8—442no—
1032D8—442no—
1033M16—441no—
1034M16—442no—
1035M16—441no—
1036C2×C8—112no—
1037C2×C8—112no—
1038C2×C8—112no—
1039C2×C8—112no—
1040C2×C8—441no—
1041C2×C8—442no—
1042C2×C8—441no—
1043C4⋊C4—21no—
1044C4⋊C4—22no—
1045C4⋊C4—22no—
1046C4⋊C4—112no—
1047C4⋊C4—112no—
1048C4⋊C4—221no—
1049C4⋊C4—221no—
1050C4⋊C4—222no—
1051C4⋊C4—222no—
1052C4⋊C4C2×C22⋊D1111yescharacteristic
1053C4⋊C4C2×C22⋊D1111yescharacteristic
1054C4⋊C4C2×C22⋊D1112yes—
1055C4⋊C4C2×C22⋊D1112yes—
1056C4⋊C4C23×D1112yes—
1057C22⋊C4—22no—
1058C22⋊C4—22no—
1059C22⋊C4—22no—
1060C22⋊C4—22no—
1061C22⋊C4—22no—
1062C22⋊C4—22no—
1063C22⋊C4—22no—
1064C22⋊C4—222no—
1065C22⋊C4—222no—
1066C22⋊C4—222no—
1067C22⋊C4—222no—
1068C22⋊C4—222no—
1069C22⋊C4—222no—
1070C22⋊C4—222no—
1071C22⋊C4—222no—
1072C22⋊C4—222no—
1073C22⋊C4C2×C22⋊D1112yes—
1074C22⋊C4C2×C22⋊D1112yes—
1075C22⋊C4C2×C22⋊D1112yes—
1076C22⋊C4C2×C22⋊D1112yes—
1077C22⋊C4C2×C22⋊D1112yes—
1078C42—22no—
1079C42—222no—
1080C42C23×D1112yes—
1081C11#6161711yescharacteristic, complemented, Sylow
1082C23—21no—
1083C23—22no—
1084C23—22no—
1085C23—21no—
1086C23—41no—
1087C23—41no—
1088C23—42no—
1089C23—44no—
1090C23—42no—
1091C23—42no—
1092C23—81no—
1093C23—81no—
1094C23—82no—
1095C23—82no—
1096C23—81no—
1097C23—222no—
1098C23—222no—
1099C23—442no—
1100C23—442no—
1101C23—881no—
1102C23—881no—
1103C23—882no—
1104C23—881no—
1105C23—882no—
1106C23—881no—
1107C23—882no—
1108C23C22×C22⋊D1112yes—
1109C23C22×C22⋊D1111yescharacteristic
1110C23C22×C22⋊D1111yescharacteristic
1111C23C22×C22⋊D1111yescharacteristic
1112Q8—21no—
1113Q8—21no—
1114Q8—21no—
1115Q8—41no—
1116Q8—42no—
1117Q8#6703712yes—
1118D4—24no—
1119D4—24no—
1120D4—21no—
1121D4—22no—
1122D4—21no—
1123D4—22no—
1124D4—21no—
1125D4—41no—
1126D4—42no—
1127D4—42no—
1128D4—44no—
1129D4—42no—
1130D4—44no—
1131D4—42no—
1132D4—42no—
1133D4—42no—
1134D4—42no—
1135D4—44no—
1136D4—82no—
1137D4—82no—
1138D4—82no—
1139D4—82no—
1140D4—222no—
1141D4—222no—
1142D4—222no—
1143D4—222no—
1144D4—444no—
1145D4—444no—
1146D4—881no—
1147D4—882no—
1148D4—881no—
1149D4—882no—
1150D4—882no—
1151D4—882no—
1152D4—882no—
1153D4—882no—
1154D4—882no—
1155D4#6703712yes—
1156C2×C4—24no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—22no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—22no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—22no—
1167C2×C4—21no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—42no—
1172C2×C4—44no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—82no—
1177C2×C4—81no—
1178C2×C4—222no—
1179C2×C4—222no—
1180C2×C4—882no—
1181C2×C4—882no—
1182C2×C4—881no—
1183C2×C4—881no—
1184C2×C4C22×C22⋊D1112yes—
1185C2×C4C22×C22⋊D1112yes—
1186C2×C4C22×C22⋊D1112yes—
1187C2×C4C22×C22⋊D1111yescharacteristic
1188C2×C4C22×C22⋊D1111yescharacteristic
1189C2×C4C22×C22⋊D1111yescharacteristic
1190C2×C4C24×D1111yescharacteristic
1191C8—222no—
1192C8—222no—
1193C8—222no—
1194C8—222no—
1195C22—21no—
1196C22—21no—
1197C22—21no—
1198C22—22no—
1199C22—21no—
1200C22—21no—
1201C22—22no—
1202C22—21no—
1203C22—22no—
1204C22—21no—
1205C22—21no—
1206C22—22no—
1207C22—41no—
1208C22—41no—
1209C22—41no—
1210C22—42no—
1211C22—41no—
1212C22—42no—
1213C22—42no—
1214C22—41no—
1215C22—82no—
1216C22—84no—
1217C22—164no—
1218C22—162no—
1219C22—442no—
1220C22—442no—
1221C22—442no—
1222C22—442no—
1223C22—442no—
1224C22—442no—
1225C22—1762no—
1226C22—1762no—
1227C22—1764no—
1228C22#1062336612yes—
1229C22C23×C22⋊D1111yescharacteristic
1230C4—22no—
1231C4—21no—
1232C4—22no—
1233C4—21no—
1234C4—22no—
1235C4—21no—
1236C4—22no—
1237C4—41no—
1238C4—42no—
1239C4—442no—
1240C4—442no—
1241C4C2×#6703711yescharacteristic
1242C4C2×#6703711yescharacteristic
1243C2—22no—
1244C2—41no—
1245C2—41no—
1246C2—42no—
1247C2—42no—
1248C2—81no—
1249C2—82no—
1250C2—882no—
1251C2—882no—
1252C2#1308225111yescharacteristic
1253C2C2×#1062336611yescharacteristic
1254C2#1308339511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3488C2
socleC22×C11C23×D4
hypercenter#3488D11
hypocenterC11#61617
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #525 ◁ #3488

Complements

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

NH ≅ G/Ntype
1. #13082855C2semidirect
2. #13080817C2semidirect
3. #13080757C2semidirect
4. #13080622C2semidirect
5. #13080518C2semidirect
6. D4×#4323C2semidirect
7. #13080236C2semidirect
8. #13080112C2semidirect
9. #13080097C2semidirect
10. #13079666C2semidirect
11. #13079462C2semidirect
12. #13079413C2semidirect
13. #13079364C2semidirect
14. #13078815C2semidirect
15. #13077884C2semidirect
16. #13077868C2semidirect
17. C2×#10622851C2semidirect
18. #13077664C2semidirect
19. C11×#3488C2semidirect
20. C2×C11×H(5,𝔽2)C22semidirect
21. C22×C11×#41C22semidirect
22. C11×#550C22semidirect
23. C11×#548C22semidirect
25. C11×#546C22semidirect
27. D42×C11C22semidirect
29. C11×#537C22semidirect
31. C11×#535C22semidirect
35. C2×C11×#121C22semidirect
36. C11×#520C22semidirect
37. #10623361C22semidirect
38. C2×#67002C22semidirect
39. C2×#67002C22semidirect
40. C2×#67002C22semidirect
41. C22×#4325C22semidirect
42. C22×#4323C22semidirect
43. C22×#4323C22semidirect
44. C2×#66983C22semidirect
45. C2×#66983C22semidirect
52. #10623096C22semidirect
53. #10623096C22semidirect
54. D4×D44C22semidirect
55. D4×D44C22semidirect
56. #10623066C22semidirect
57. #10622851C22semidirect
58. #10622851C22semidirect
59. #10622851C22semidirect
60. #10622851C22semidirect
61. #10622851C22semidirect
62. #10622851C22semidirect
63. #10622851C22semidirect
64. #10622851C22semidirect
65. #10622847C22semidirect
66. #10622846C22semidirect
67. #10622845C22semidirect
68. #10622845C22semidirect
69. #10622840C22semidirect
70. C2×#66899C22semidirect
71. #10622830C22semidirect
72. #10622830C22semidirect
73. #10622830C22semidirect
74. #10622830C22semidirect
75. #10622830C22semidirect
76. #10622828C22semidirect
77. C2×#66896C22semidirect
78. #10622820C22semidirect
79. C2×C22⋊(C11⋊C8)C22semidirect
80. #10622686C22semidirect
81. #10622685C22semidirect
82. #10622685C22semidirect
83. #10622684C22semidirect
84. #10622671C22semidirect
85. #10622670C22semidirect
86. #10622670C22semidirect
87. #10622669C22semidirect
88. #10622662C22semidirect
89. #10622661C22semidirect
90. #10622659C22semidirect
91. #10622658C22semidirect
92. #10622652C22semidirect
93. #10622652C22semidirect
94. #10622652C22semidirect
95. #10622651C22semidirect
96. #10622651C22semidirect
97. #10622651C22semidirect
98. #10622649C22semidirect
99. #10622649C22semidirect
100. #10622649C22semidirect
101. #10622648C22semidirect
102. #10622647C22semidirect
103. #10622646C22semidirect
104. #10622640C22semidirect
105. #10622639C22semidirect
106. C4×#4325C22semidirect
107. #10622635C22semidirect
108. #10622628C22semidirect
109. #10622627C22semidirect
110. C4×#4323C22semidirect
111. #10622625C22semidirect
112. #10622624C22semidirect
113. #10622624C22semidirect
114. D4×C11⋊C8C22semidirect
115. #10622622C22semidirect
116. #10622613C22semidirect
117. #10622581C22semidirect
118. #10622580C22semidirect
456. #3488D11semidirect
587. C2×H(5,𝔽2)C2×D11semidirect
588. C22×#41C2×D11semidirect
598. #550C2×D11semidirect
599. #548C2×D11semidirect
601. #546C2×D11semidirect
606. D42C2×D11semidirect
611. #537C2×D11semidirect
614. #535C2×D11semidirect
622. C2×#121C2×D11semidirect
623. #520C2×D11semidirect
1081. C11#61617semidirect

Maximal subgroups

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

subgroupindex
#130828552
#130808172
#130807572
#130806222
#130805182
D4×#43232
#130802362
#130801122
#130800972
#130796662
#130794622
#130794132
#130793642
#130788152
#130778842
#130778682
C2×#106228512
#130776642
C11×#34882
#6161711