Finite Group Databasebeta

← #14960885

Subgroups — #14960885

Order 2816.

3282 conjugacy classes of subgroups.

The subgroup lattice has 1092 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076894C212yesmaximal, complemented
2#13075654C212yesmaximal, complemented
3#13075651C211yesmaximal, characteristic, complemented
4#13075176C212yesmaximal, complemented
5#13075011C212yesmaximal, complemented
6#13075005C212yesmaximal, complemented
7#13074999C212yesmaximal, complemented
8#13074940C212yesmaximal, complemented
9#13074836C211yesmaximal, characteristic, complemented
10#13074824C211yesmaximal, characteristic, complemented
11#13074420C211yesmaximal, characteristic, complemented
12#13074351C211yesmaximal, characteristic, complemented
13#13072855C212yesmaximal, complemented
14#13072745C212yesmaximal, complemented
15#13072157C212yesmaximal, complemented
16#13072085C212yesmaximal, complemented
17#13071278C212yesmaximal, complemented
18D11×#379C211yesmaximal, characteristic, complemented
19C11×#2736C211yesmaximal, characteristic, complemented
20C25×D11C2211yescharacteristic
21C2×#67006C2212yes—
22C2×#67000C2212yescomplemented
23C2×#66999C2211yescharacteristic, complemented
24C2×#66948C2211yescharacteristic, complemented
25C2×#66947C2212yescomplemented
26C2×#66937C2212yescomplemented
27C2×#66935C2212yes—
28C2×#66935C2212yes—
29C2×#66935C2212yes—
30C2×#66935C2212yes—
31C2×#66935C2212yes—
32C2×#66935C2212yes—
33C2×C22⋊C4×D11C2212yes—
34C2×C22⋊C4×D11C2212yes—
35C2×C22⋊C4×D11C2211yescharacteristic
36C2×C22⋊C4×D11C2211yescharacteristic
37C2×#66932C2212yescomplemented
38C2×C4×D44C2212yescomplemented
39C11×#397C2211yescharacteristic, complemented
40C11×#397C2212yescomplemented
41C11×#393C2212yescomplemented
42C11×#393C2211yescharacteristic, complemented
43C11×#388C2212yescomplemented
44C11×#388C2212yescomplemented
45C11×#388C2212yescomplemented
46C11×#379C2212yes—
47C11×#379C2211yescharacteristic
48#10622860C2211yescharacteristic
49#10622844C2211yescharacteristic, complemented
50#10622607C2212yescomplemented
51#10622607C2212yescomplemented
52#10622606C2211yescharacteristic, complemented
53#10622602C2212yescomplemented
54#10622601C2212yescomplemented
55#10622574C2212yescomplemented
56#10622574C2212yescomplemented
57#10622574C2212yescomplemented
58#10622573C2211yescharacteristic, complemented
59#10622572C2212yescomplemented
60#10622572C2212yescomplemented
61#10622570C2212yescomplemented
62#10622570C2212yescomplemented
63#10622569C2212yescomplemented
64#10622569C2212yescomplemented
65#10622568C2212yes—
66#10622568C2212yes—
67#10622568C2212yes—
68#10622568C2212yes—
69#10622568C2211yescharacteristic
70#10622568C2212yes—
71#10622568C2211yescharacteristic
72#10622568C2212yes—
73#10622568C2212yes—
74#10622568C2212yes—
75#10622565C2212yescomplemented
76#10622564C2212yescomplemented
77#10622562C2212yescomplemented
78#10622562C2211yescharacteristic, complemented
79#10622561C2212yescomplemented
80#10622558C2212yescomplemented
81#10622557C2212yescomplemented
82#10622553C2212yescomplemented
83#10622553C2212yescomplemented
84#10622552C2212yescomplemented
85#10622290C2211yescharacteristic, complemented
86#10622289C2212yescomplemented
87#10622288C2212yescomplemented
88#10622288C2212yescomplemented
89#10622287C2212yescomplemented
90#10622285C2212yescomplemented
91#10622285C2212yescomplemented
92#10622285C2212yescomplemented
93#10622284C2212yescomplemented
94#10622284C2211yescharacteristic, complemented
95#10622283C2212yescomplemented
96#10622283C2212yescomplemented
97#10622282C2212yescomplemented
98#10622282C2212yescomplemented
99#10622281C2212yescomplemented
100#10622280C2211yescharacteristic, complemented
101#10622280C2211yescharacteristic, complemented
102#10622279C2212yescomplemented
103#10622278C2212yescomplemented
104#10622278C2212yescomplemented
105#10622278C2212yescomplemented
106#10622278C2212yescomplemented
107C25×C11C2311yescharacteristic
108C24×D11—24no—
109C24×D11—44no—
110C24×D11—42no—
111C24×D11—42no—
112C24×D11—44no—
113C24×D11C2312yes—
114C24×D11C2311yescharacteristic
115C24×D11C2312yes—
116C24×D11C2311yescharacteristic
117C22×Q8×C11C2311yescharacteristic, complemented
118C22×C22⋊D11C2312yes—
119C22×C22⋊D11C2312yes—
120C22×C22⋊D11C2312yes—
121C22×D44C2312yes—
122C22×D44C2312yes—
123C22×D44C2312yes—
124C22×D44C2312yes—
125C22×D44C2311yescharacteristic, complemented
126C22×C4×D11C2312yes—
127C22×C4×D11C2311yescharacteristic
128C22×C4×D11C2311yescharacteristic
129C22×C4×D11C2312yescomplemented
130C2×C11×C4⋊C4C2312yescomplemented
131C2×C11×C4⋊C4C2311yescharacteristic, complemented
132C2×C11×C22⋊C4C2312yes—
133C2×C11×C22⋊C4C2312yes—
134C2×C11×C22⋊C4C2312yes—
135C2×C11×C22⋊C4C2311yescharacteristic
136C2×C11×C22⋊C4C2311yescharacteristic
137C2×C11×C22⋊C4C2312yes—
138C2×C11×C22⋊C4C2312yes—
139C2×C11×C22⋊C4C2312yes—
140C2×C11×C22⋊C4C2312yes—
141C2×C11×C22⋊C4C2312yes—
142C2×C42×C11C2312yescomplemented
143#67006—44no—
144C2×C22⋊Dic11C2312yes—
145C2×C22⋊Dic11C2312yes—
146C2×C22⋊Dic11C2312yes—
147C2×C22⋊Dic11C2311yescharacteristic
148C2×C22⋊Dic11C2311yescharacteristic
149C2×C22⋊Dic11C2312yes—
150C2×C22⋊Dic11C2312yes—
151#67000—44no—
152#66999—42no—
153C2×(C2×D11)⋊C4C2312yes—
154C2×(C2×D11)⋊C4C2312yes—
155C2×(C2×D11)⋊C4C2312yes—
156C2×(C2×D11)⋊C4C2312yes—
157C2×(C2×D11)⋊C4C2312yes—
158C2×(C2×D11)⋊C4C2312yes—
159C2×(C2×D11)⋊C4C2312yes—
160C2×(C2×D11)⋊C4C2312yes—
161C2×(C2×D11)⋊C4C2312yes—
162C2×(C2×D11)⋊C4C2312yes—
163C2×(C2×D11)⋊C4C2312yes—
164C2×(C2×D11)⋊C4C2311yescharacteristic
165C2×(C2×D11)⋊C4C2311yescharacteristic
166C2×(C2×D11)⋊C4C2312yes—
167C2×(C2×D11)⋊C4C2312yes—
168C2×(C2×D11)⋊C4C2312yes—
169C2×(C2×D11)⋊C4C2312yes—
170C2×(C2×D11)⋊C4C2312yes—
171C2×(C2×D11)⋊C4C2312yes—
172C2×(C2×D11)⋊C4C2312yescomplemented
173C2×(C2×D11)⋊C4C2312yescomplemented
174C2×(C2×D11)⋊C4C2312yescomplemented
175C2×(C2×D11)⋊C4C2312yescomplemented
176C2×(C2×D11)⋊C4C2312yescomplemented
177C2×(C2×D11)⋊C4C2312yescomplemented
178C2×C4⋊Dic11C2312yescomplemented
179C2×C4⋊Dic11C2312yescomplemented
180C2×C4⋊Dic11C2311yescharacteristic, complemented
181C2×Dic11⋊C4C2312yescomplemented
182C2×Dic11⋊C4C2312yescomplemented
183C2×Dic11⋊C4C2312yescomplemented
184C2×Dic11⋊C4C2312yescomplemented
185C2×Dic11⋊C4C2312yescomplemented
186C2×C4×Dic11C2312yescomplemented
187C2×C4×Dic11C2312yescomplemented
188#66948—42no—
189#66947—44no—
190#66937—44no—
191#66935—28no—
192#66935—44no—
193#66935—44no—
194#66935—44no—
195#66935—44no—
196#66935—44no—
197C22⋊C4×D11—44no—
198C22⋊C4×D11—44no—
199C22⋊C4×D11—42no—
200C22⋊C4×D11—42no—
201#66932—44no—
202C4×D44—44no—
203C11×#95C2312yescomplemented
204C11×#95C2312yescomplemented
205C11×#95C2312yescomplemented
206C11×#95C2311yescharacteristic, complemented
207C11×#95C2311yescharacteristic, complemented
208C11×#95C2312yescomplemented
209C11⋊#95C2312yescomplemented
210C11⋊#95C2312yescomplemented
211C11⋊#95C2312yescomplemented
212C11⋊#95C2312yescomplemented
213C11⋊#95C2312yescomplemented
214C11⋊#95C2311yescharacteristic, complemented
215C11⋊#95C2311yescharacteristic, complemented
216C11⋊#95C2312yescomplemented
217#36725—111nomaximal, Sylow
218C24×C11—22no—
219C24×C11—24no—
220C24×C11—41no—
221C24×C11—42no—
222C24×C11—41no—
223C24×C11C2411yescharacteristic
224C24×C11C2412yes—
225C23×D11—24no—
226C23×D11—24no—
227C23×D11—24no—
228C23×D11—22no—
229C23×D11—22no—
230C23×D11—22no—
231C23×D11—24no—
232C23×D11—24no—
233C23×D11—24no—
234C23×D11—24no—
235C23×D11—24no—
236C23×D11—24no—
237C23×D11—42no—
238C23×D11—42no—
239C23×D11—42no—
240C23×D11—42no—
241C23×D11—42no—
242C23×D11—42no—
243C23×D11—42no—
244C23×D11—42no—
245C23×D11—41no—
246C23×D11—42no—
247C23×D11—41no—
248C23×D11—432no—
249C23×D11—416no—
250C23×D11—416no—
251C23×D11—432no—
252C23×D11—416no—
253C23×D11#4114yes—
254C23×D11C2412yes—
255C23×D11C2411yescharacteristic
256C23×D11C2412yes—
257C23×D11C2411yescharacteristic
258C2×Q8×C11—41no—
259C2×Q8×C11—42no—
260C22×C4×C11C2412yes—
261C22×C4×C11C2412yes—
262C22×C4×C11C2412yes—
263C22×C4×C11C2412yes—
264C22×C4×C11C2411yescharacteristic
265C22×C4×C11C2411yescharacteristic
266C22×C4×C11C2412yes—
267C2×C22⋊D11—24no—
268C2×C22⋊D11—24no—
269C2×C22⋊D11—24no—
270C2×C22⋊D11—42no—
271C2×C22⋊D11—42no—
272C2×C22⋊D11—42no—
273C2×C22⋊D11—42no—
274C2×C22⋊D11—42no—
275C2×C22⋊D11—42no—
276C22×Dic11C2412yes—
277C22×Dic11C2412yes—
278C22×Dic11C2412yes—
279C22×Dic11C2412yes—
280C22×Dic11C2411yescharacteristic
281C22×Dic11C2411yescharacteristic
282C2×D44—24no—
283C2×D44—24no—
284C2×D44—24no—
285C2×D44—24no—
286C2×D44—24no—
287C2×D44—24no—
288C2×D44—42no—
289C2×D44—42no—
290C2×D44—42no—
291C2×D44—42no—
292C2×D44—42no—
293C2×D44—42no—
294C2×D44—42no—
295C2×D44—41no—
296C2×C4×D11—24no—
297C2×C4×D11—22no—
298C2×C4×D11—22no—
299C2×C4×D11—42no—
300C2×C4×D11—42no—
301C2×C4×D11—42no—
302C2×C4×D11—42no—
303C2×C4×D11—42no—
304C2×C4×D11—42no—
305C2×C4×D11—42no—
306C11×C4⋊C4—42no—
307C11×C4⋊C4—41no—
308C11×C22⋊C4—24no—
309C11×C22⋊C4—24no—
310C11×C22⋊C4—24no—
311C11×C22⋊C4—41no—
312C11×C22⋊C4—42no—
313C11×C22⋊C4—41no—
314C11×C22⋊C4—42no—
315C11×C22⋊C4—42no—
316C11×C22⋊C4—42no—
317C11×C22⋊C4—42no—
318C42×C11—42no—
319C22⋊Dic11—24no—
320C22⋊Dic11—24no—
321C22⋊Dic11—42no—
322C22⋊Dic11—41no—
323C22⋊Dic11—41no—
324C22⋊Dic11—42no—
325C22⋊Dic11—42no—
326(C2×D11)⋊C4—24no—
327(C2×D11)⋊C4—24no—
328(C2×D11)⋊C4—24no—
329(C2×D11)⋊C4—24no—
330(C2×D11)⋊C4—24no—
331(C2×D11)⋊C4—24no—
332(C2×D11)⋊C4—24no—
333(C2×D11)⋊C4—24no—
334(C2×D11)⋊C4—42no—
335(C2×D11)⋊C4—42no—
336(C2×D11)⋊C4—41no—
337(C2×D11)⋊C4—42no—
338(C2×D11)⋊C4—42no—
339(C2×D11)⋊C4—41no—
340(C2×D11)⋊C4—42no—
341(C2×D11)⋊C4—42no—
342(C2×D11)⋊C4—42no—
343(C2×D11)⋊C4—42no—
344(C2×D11)⋊C4—42no—
345(C2×D11)⋊C4—42no—
346(C2×D11)⋊C4—42no—
347(C2×D11)⋊C4—42no—
348(C2×D11)⋊C4—42no—
349(C2×D11)⋊C4—42no—
350(C2×D11)⋊C4—42no—
351C4⋊Dic11—42no—
352C4⋊Dic11—42no—
353C4⋊Dic11—41no—
354Dic11⋊C4—42no—
355Dic11⋊C4—42no—
356Dic11⋊C4—42no—
357Dic11⋊C4—42no—
358Dic11⋊C4—42no—
359C4×Dic11—42no—
360C4×Dic11—42no—
361#2846—112no—
362#2736D1111yescharacteristic, complemented
363#2735—111no—
364#2735—112no—
365#2697—112no—
366#2685—112no—
367#2685—112no—
368#2684—112no—
369#2678—112no—
370#2670—111no—
371#2668—111no—
372#2626—111no—
373#2617—111no—
374#2480—112no—
375#2472—112no—
376#2424—112no—
377#2418—112no—
378#2321—112no—
379C2×#379—111no—
380C23×C11—22no—
381C23×C11—21no—
382C23×C11—21no—
383C23×C11—22no—
384C23×C11—22no—
385C23×C11—22no—
386C23×C11—22no—
387C23×C11—22no—
388C23×C11—22no—
389C23×C11—22no—
390C23×C11—48no—
391C23×C11—44no—
392C23×C11—44no—
393C23×C11—48no—
394C23×C11—44no—
395C23×C11C2×#4112yes—
396C23×C11H(5,𝔽2)14yes—
397C23×C11C2511yescharacteristic
398C22×D11—22no—
399C22×D11—22no—
400C22×D11—216no—
401C22×D11—22no—
402C22×D11—22no—
403C22×D11—21no—
404C22×D11—21no—
405C22×D11—22no—
406C22×D11—22no—
407C22×D11—22no—
408C22×D11—22no—
409C22×D11—22no—
410C22×D11—22no—
411C22×D11—28no—
412C22×D11—22no—
413C22×D11—22no—
414C22×D11—22no—
415C22×D11—22no—
416C22×D11—22no—
417C22×D11—22no—
418C22×D11—22no—
419C22×D11—48no—
420C22×D11—48no—
421C22×D11—48no—
422C22×D11—48no—
423C22×D11—44no—
424C22×D11—48no—
425C22×D11—48no—
426C22×D11—48no—
427C22×D11—48no—
428C22×D11—48no—
429C22×D11—48no—
430C22×D11—48no—
431C22×D11—44no—
432C22×D11—44no—
433C22×D11—48no—
434C22×D11—48no—
435C22×D11—48no—
436C22×D11—44no—
437C22×D11—48no—
438C22×D11—4128no—
439C22×D11—48no—
440C22×D11—44no—
441C22×D11—48no—
442C22×D11C2×#4112yes—
443C22×D11C2×#4112yes—
444C22×D11H(5,𝔽2)14yes—
445C22×D11H(5,𝔽2)12yes—
446C22×D11H(5,𝔽2)12yes—
447Q8×C11—82no—
448C2×C4×C11—22no—
449C2×C4×C11—22no—
450C2×C4×C11—22no—
451C2×C4×C11—22no—
452C2×C4×C11—22no—
453C2×C4×C11—22no—
454C2×C4×C11—22no—
455C2×C4×C11—22no—
456C2×C4×C11—22no—
457C2×C4×C11—21no—
458C2×C4×C11—22no—
459C2×C4×C11—22no—
460C2×C4×C11—22no—
461C2×C4×C11—22no—
462C2×C4×C11—22no—
463C2×C4×C11—22no—
464C2×C4×C11—22no—
465C2×C4×C11—22no—
466C2×C4×C11—21no—
467C22⋊D11—84no—
468C22⋊D11—84no—
469C22⋊D11—84no—
470C2×Dic11—22no—
471C2×Dic11—22no—
472C2×Dic11—22no—
473C2×Dic11—22no—
474C2×Dic11—22no—
475C2×Dic11—21no—
476C2×Dic11—22no—
477C2×Dic11—22no—
478C2×Dic11—22no—
479C2×Dic11—22no—
480C2×Dic11—22no—
481C2×Dic11—22no—
482C2×Dic11—22no—
483C2×Dic11—22no—
484C2×Dic11—22no—
485C2×Dic11—21no—
486D44—48no—
487D44—84no—
488D44—84no—
489D44—84no—
490D44—82no—
491C4×D11—82no—
492C4×D11—84no—
493C4×D11—82no—
494C4×D11—84no—
495C26—111no—
496C2×#126—112no—
497C2×#124—112no—
498C2×#123—112no—
499C2×C22⋊Q8—111no—
500C2×#121—111no—
501C2×#121—112no—
502C2×#120—112no—
503C2×#120—112no—
504C2×#120—112no—
505C2×#120—112no—
506C2×#120—112no—
507C2×#120—112no—
508C2×#120—112no—
509C2×C4×D4—112no—
510C22×C22⋊C4—111no—
511C22×C22⋊C4—111no—
512C22×C22⋊C4—112no—
513C22×C22⋊C4—112no—
514#399—111no—
515#399—112no—
516#399—111no—
517#397—111no—
518#397—112no—
519#397—112no—
520#397—112no—
521#397—112no—
522#397C2×D1111yescharacteristic, complemented
523#397C2×D1112yescomplemented
524#396—112no—
525#396—112no—
526#396—112no—
527#396—112no—
528#394—112no—
529#394—112no—
530#394—112no—
531#394—112no—
532#394—112no—
533#394—112no—
534#394—112no—
535#394—112no—
536#393—111no—
537#393C2×D1111yescharacteristic, complemented
538#393C2×D1112yescomplemented
539#392—111no—
540#392—111no—
541#392—112no—
542#390—112no—
543#390—112no—
544#390—112no—
545#390—112no—
546#388—112no—
547#388—112no—
548#388—112no—
549#388—112no—
550#388—112no—
551#388—112no—
552#388—112no—
553#388—112no—
554#388—112no—
555#388C2×D1112yescomplemented
556#388C2×D1112yescomplemented
557#388C2×D1112yescomplemented
558#386—112no—
559#386—112no—
560#386—112no—
561#386—112no—
562#386—112no—
563#386—112no—
564#385—112no—
565#385—112no—
566#380—111no—
567#380—111no—
568#379—111no—
569#379—112no—
570#379—112no—
571#379—112no—
572#379—112no—
573#379—112no—
574#379—112no—
575#379—111no—
576#379—112no—
577#379—112no—
578#379—111no—
579#379C2×D1112yes—
580#379C2×D1111yescharacteristic
581C4×C22⋊C4—112no—
582C22×C11—22no—
583C22×C11—24no—
584C22×C11—24no—
585C22×C11—24no—
586C22×C11—24no—
587C22×C11—416no—
588C22×C11—42no—
589C22×C11—42no—
590C22×C11—42no—
591C22×C11—42no—
592C22×C11—41no—
593C22×C11—41no—
594C22×C11—42no—
595C22×C11C22×#4111yescharacteristic
596C22×C11C2×H(5,𝔽2)12yes—
597C22×C11C2×H(5,𝔽2)11yescharacteristic
598C22×C11C2×H(5,𝔽2)11yescharacteristic
599C22×C11C2×H(5,𝔽2)12yes—
600C2×D11—24no—
601C2×D11—24no—
602C2×D11—22no—
603C2×D11—22no—
604C2×D11—22no—
605C2×D11—24no—
606C2×D11—24no—
607C2×D11—24no—
608C2×D11—24no—
609C2×D11—432no—
610C2×D11—416no—
611C2×D11—432no—
612C2×D11—416no—
613C2×D11—42no—
614C2×D11—42no—
615C2×D11—42no—
616C2×D11—42no—
617C2×D11—42no—
618C2×D11—41no—
619C2×D11—41no—
620C2×D11—42no—
621C2×D11—42no—
622C2×D11—42no—
623C2×D11—42no—
624C2×D11—42no—
625C2×D11—42no—
626C2×D11—42no—
627C2×D11#53814yes—
628C4×C11—42no—
629C4×C11—42no—
630C4×C11—41no—
631C4×C11—42no—
632C4×C11—42no—
633C4×C11—41no—
634C4×C11—42no—
635Dic11—42no—
636Dic11—42no—
637Dic11—41no—
638Dic11—41no—
639Dic11—42no—
640Dic11—42no—
641C25—111no—
642C25—112no—
643C25—111no—
644C25—112no—
645C25—224no—
646C25—444no—
647C25—442no—
648C25—444no—
649C25—442no—
650C25C22×D1111yescharacteristic
651C22×Q8C22×D1111yescharacteristic, complemented
652C22×D4—112no—
653C22×D4—112no—
654C22×D4—112no—
655C22×D4—112no—
656C22×D4—112no—
657C22×D4—112no—
658C22×D4—112no—
659C22×D4—111no—
660C23×C4—112no—
661C23×C4—111no—
662C23×C4—111no—
663C23×C4—112no—
664#126—444no—
665#124—444no—
666#123—444no—
667C22⋊Q8—442no—
668#121—444no—
669#121—442no—
670#120—228no—
671#120—444no—
672#120—444no—
673#120—444no—
674#120—444no—
675#120—444no—
676#120—444no—
677C4×D4—444no—
678C2×C4⋊C4—112no—
679C2×C4⋊C4—112no—
680C2×C4⋊C4—111no—
681C2×C4⋊C4—112no—
682C2×C4⋊C4—112no—
683C2×C4⋊C4—112no—
684C2×C4⋊C4—112no—
685C2×C4⋊C4—112no—
686C2×C4⋊C4C22×D1111yescharacteristic, complemented
687C2×C4⋊C4C22×D1112yescomplemented
688C2×C22⋊C4—112no—
689C2×C22⋊C4—112no—
690C2×C22⋊C4—112no—
691C2×C22⋊C4—112no—
692C2×C22⋊C4—112no—
693C2×C22⋊C4—112no—
694C2×C22⋊C4—112no—
695C2×C22⋊C4—112no—
696C2×C22⋊C4—112no—
697C2×C22⋊C4—112no—
698C2×C22⋊C4—111no—
699C2×C22⋊C4—112no—
700C2×C22⋊C4—111no—
701C2×C22⋊C4—112no—
702C2×C22⋊C4—112no—
703C2×C22⋊C4—112no—
704C2×C22⋊C4—112no—
705C2×C22⋊C4—112no—
706C2×C22⋊C4—111no—
707C2×C22⋊C4—111no—
708C2×C22⋊C4—112no—
709C2×C22⋊C4—112no—
710C2×C22⋊C4—112no—
711C2×C22⋊C4—112no—
712C2×C22⋊C4—112no—
713C2×C22⋊C4—112no—
714C2×C22⋊C4—112no—
715C2×C22⋊C4—112no—
716C2×C22⋊C4—112no—
717C2×C22⋊C4—112no—
718C2×C22⋊C4—112no—
719C2×C22⋊C4—112no—
720C2×C22⋊C4—444no—
721C2×C22⋊C4—444no—
722C2×C22⋊C4—442no—
723C2×C22⋊C4—442no—
724C2×C22⋊C4C22×D1112yes—
725C2×C22⋊C4C22×D1112yes—
726C2×C22⋊C4C22×D1112yes—
727C2×C22⋊C4C22×D1111yescharacteristic
728C2×C22⋊C4C22×D1112yes—
729C2×C22⋊C4C22×D1111yescharacteristic
730C2×C22⋊C4C22×D1112yes—
731C2×C22⋊C4C22×D1112yes—
732C2×C22⋊C4C22×D1112yes—
733C2×C22⋊C4C22×D1112yes—
734C2×C42—112no—
735C2×C42—112no—
736C2×C42C22×D1112yescomplemented
737#95—112no—
738#95—111no—
739#95—111no—
740#95—112no—
741#95—112no—
742#95—112no—
743#95—112no—
744#95—112no—
745#95C22×D1112yescomplemented
746#95C22×D1111yescharacteristic, complemented
747#95C22×D1111yescharacteristic, complemented
748#95C22×D1112yescomplemented
749#95C22×D1112yescomplemented
750#95C22×D1112yescomplemented
751C2×C11—42no—
752C2×C11—44no—
753C2×C11C2×#53811yescharacteristic
754C2×C11#349012yes—
755C2×C11#353212yes—
756C2×C11#353211yescharacteristic
757C2×C11#353211yescharacteristic
758D11—24no—
759D11—42no—
760D11—44no—
761D11—82no—
762C24—22no—
763C24—24no—
764C24—41no—
765C24—42no—
766C24—41no—
767C24—111no—
768C24—111no—
769C24—112no—
770C24—114no—
771C24—112no—
772C24—222no—
773C24—222no—
774C24—224no—
775C24—224no—
776C24—224no—
777C24—224no—
778C24—224no—
779C24—224no—
780C24—224no—
781C24—224no—
782C24—222no—
783C24—224no—
784C24—442no—
785C24—442no—
786C24—442no—
787C24—442no—
788C24—442no—
789C24—441no—
790C24—441no—
791C24—442no—
792C24—442no—
793C24—442no—
794C24—442no—
795C24—4432no—
796C24—4416no—
797C24—4416no—
798C24—4432no—
799C24—4416no—
800C24C23×D1111yescharacteristic
801C24C23×D1112yes—
802C2×Q8—41no—
803C2×Q8—42no—
804C2×D4—224no—
805C2×D4—224no—
806C2×D4—224no—
807C2×D4—224no—
808C2×D4—224no—
809C2×D4—224no—
810C2×D4—224no—
811C2×D4—224no—
812C2×D4—224no—
813C2×D4—442no—
814C2×D4—442no—
815C2×D4—442no—
816C2×D4—442no—
817C2×D4—442no—
818C2×D4—442no—
819C2×D4—442no—
820C2×D4—441no—
821C2×D4—442no—
822C2×D4—442no—
823C2×D4—442no—
824C2×D4—442no—
825C2×D4—442no—
826C2×D4—442no—
827C22×C4—112no—
828C22×C4—112no—
829C22×C4—112no—
830C22×C4—112no—
831C22×C4—111no—
832C22×C4—111no—
833C22×C4—224no—
834C22×C4—222no—
835C22×C4—222no—
836C22×C4—442no—
837C22×C4—442no—
838C22×C4—442no—
839C22×C4—442no—
840C22×C4—442no—
841C22×C4—442no—
842C22×C4—442no—
843C22×C4C23×D1112yes—
844C22×C4C23×D1112yes—
845C22×C4C23×D1112yes—
846C22×C4C23×D1112yes—
847C22×C4C23×D1111yescharacteristic
848C22×C4C23×D1111yescharacteristic
849C22×C4C23×D1112yes—
850C4⋊C4—41no—
851C4⋊C4—42no—
852C4⋊C4—442no—
853C4⋊C4—442no—
854C4⋊C4—442no—
855C4⋊C4—441no—
856C4⋊C4—442no—
857C4⋊C4—442no—
858C4⋊C4—442no—
859C4⋊C4—442no—
860C22⋊C4—24no—
861C22⋊C4—24no—
862C22⋊C4—24no—
863C22⋊C4—41no—
864C22⋊C4—42no—
865C22⋊C4—41no—
866C22⋊C4—42no—
867C22⋊C4—42no—
868C22⋊C4—42no—
869C22⋊C4—42no—
870C22⋊C4—224no—
871C22⋊C4—224no—
872C22⋊C4—224no—
873C22⋊C4—224no—
874C22⋊C4—224no—
875C22⋊C4—224no—
876C22⋊C4—224no—
877C22⋊C4—224no—
878C22⋊C4—224no—
879C22⋊C4—224no—
880C22⋊C4—442no—
881C22⋊C4—442no—
882C22⋊C4—442no—
883C22⋊C4—441no—
884C22⋊C4—441no—
885C22⋊C4—442no—
886C22⋊C4—442no—
887C22⋊C4—442no—
888C22⋊C4—442no—
889C22⋊C4—442no—
890C22⋊C4—442no—
891C22⋊C4—442no—
892C22⋊C4—442no—
893C22⋊C4—442no—
894C22⋊C4—442no—
895C22⋊C4—442no—
896C22⋊C4—442no—
897C22⋊C4—442no—
898C22⋊C4—441no—
899C22⋊C4—441no—
900C22⋊C4—442no—
901C22⋊C4—442no—
902C42—42no—
903C42—442no—
904C42—442no—
905C11#3672511yescharacteristic, complemented, Sylow
906C23—22no—
907C23—22no—
908C23—22no—
909C23—21no—
910C23—21no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—44no—
917C23—48no—
918C23—44no—
919C23—48no—
920C23—44no—
921C23—112no—
922C23—112no—
923C23—112no—
924C23—112no—
925C23—114no—
926C23—228no—
927C23—2216no—
928C23—222no—
929C23—222no—
930C23—222no—
931C23—222no—
932C23—222no—
933C23—222no—
934C23—221no—
935C23—221no—
936C23—222no—
937C23—222no—
938C23—222no—
939C23—222no—
940C23—222no—
941C23—222no—
942C23—222no—
943C23—222no—
944C23—222no—
945C23—222no—
946C23—222no—
947C23—448no—
948C23—448no—
949C23—448no—
950C23—448no—
951C23—448no—
952C23—448no—
953C23—444no—
954C23—448no—
955C23—448no—
956C23—448no—
957C23—448no—
958C23—444no—
959C23—448no—
960C23—448no—
961C23—448no—
962C23—448no—
963C23—444no—
964C23—444no—
965C23—448no—
966C23—448no—
967C23—44128no—
968C23—448no—
969C23—444no—
970C23#41×D1112yes—
971C23#6704214yes—
972C23C24×D1111yescharacteristic
973Q8—82no—
974D4—448no—
975D4—884no—
976D4—884no—
977D4—884no—
978D4—882no—
979D4—884no—
980D4—884no—
981D4—884no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—222no—
1002C2×C4—222no—
1003C2×C4—222no—
1004C2×C4—222no—
1005C2×C4—222no—
1006C2×C4—222no—
1007C2×C4—222no—
1008C2×C4—222no—
1009C2×C4—222no—
1010C2×C4—222no—
1011C2×C4—222no—
1012C2×C4—222no—
1013C2×C4—222no—
1014C2×C4—221no—
1015C2×C4—222no—
1016C2×C4—221no—
1017C2×C4—884no—
1018C2×C4—882no—
1019C2×C4—882no—
1020C2×C4—884no—
1021C22—22no—
1022C22—24no—
1023C22—24no—
1024C22—24no—
1025C22—24no—
1026C22—416no—
1027C22—42no—
1028C22—42no—
1029C22—42no—
1030C22—41no—
1031C22—41no—
1032C22—42no—
1033C22—42no—
1034C22—114no—
1035C22—224no—
1036C22—222no—
1037C22—222no—
1038C22—224no—
1039C22—222no—
1040C22—224no—
1041C22—224no—
1042C22—224no—
1043C22—224no—
1044C22—4416no—
1045C22—4432no—
1046C22—4416no—
1047C22—4432no—
1048C22—442no—
1049C22—442no—
1050C22—442no—
1051C22—442no—
1052C22—441no—
1053C22—441no—
1054C22—442no—
1055C22—442no—
1056C22—442no—
1057C22—442no—
1058C22—442no—
1059C22—442no—
1060C22—442no—
1061C22—442no—
1062C22C2×#41×D1111yescharacteristic
1063C22C2×#6704212yes—
1064C22D11×H(5,𝔽2)11yescharacteristic
1065C22D11×H(5,𝔽2)11yescharacteristic
1066C22D11×H(5,𝔽2)12yes—
1067C4—42no—
1068C4—42no—
1069C4—42no—
1070C4—41no—
1071C4—41no—
1072C4—42no—
1073C4—42no—
1074C4—442no—
1075C4—442no—
1076C4—441no—
1077C4—442no—
1078C4—441no—
1079C4—442no—
1080C2—42no—
1081C2—44no—
1082C2—224no—
1083C2—442no—
1084C2—444no—
1085C2—882no—
1086C2D11×#53811yescharacteristic
1087C2#1308230012yes—
1088C2#1308276712yes—
1089C2#1308277211yescharacteristic
1090C2#1308277311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2736C2
hypercenter#2736D11
hypocenterC11#36725
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2736

Complements

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

NH ≅ G/Ntype
1. #13076894C2semidirect
2. #13075654C2semidirect
3. #13075651C2semidirect
4. #13075176C2semidirect
5. #13075011C2semidirect
6. #13075005C2semidirect
7. #13074999C2semidirect
8. #13074940C2semidirect
9. #13074836C2semidirect
10. #13074824C2semidirect
11. #13074420C2semidirect
12. #13074351C2semidirect
13. #13072855C2semidirect
14. #13072745C2semidirect
15. #13072157C2semidirect
16. #13072085C2semidirect
17. #13071278C2semidirect
18. D11×#379C2semidirect
19. C11×#2736C2semidirect
22. C2×#67000C22semidirect
23. C2×#66999C22semidirect
24. C2×#66948C22semidirect
25. C2×#66947C22semidirect
26. C2×#66937C22semidirect
37. C2×#66932C22semidirect
38. C2×C4×D44C22semidirect
39. C11×#397C22semidirect
40. C11×#397C22semidirect
41. C11×#393C22semidirect
42. C11×#393C22semidirect
43. C11×#388C22semidirect
44. C11×#388C22semidirect
45. C11×#388C22semidirect
49. #10622844C22semidirect
50. #10622607C22semidirect
51. #10622607C22semidirect
52. #10622606C22semidirect
53. #10622602C22semidirect
54. #10622601C22semidirect
55. #10622574C22semidirect
56. #10622574C22semidirect
57. #10622574C22semidirect
58. #10622573C22semidirect
59. #10622572C22semidirect
60. #10622572C22semidirect
61. #10622570C22semidirect
62. #10622570C22semidirect
63. #10622569C22semidirect
64. #10622569C22semidirect
75. #10622565C22semidirect
76. #10622564C22semidirect
77. #10622562C22semidirect
78. #10622562C22semidirect
79. #10622561C22semidirect
80. #10622558C22semidirect
81. #10622557C22semidirect
82. #10622553C22semidirect
83. #10622553C22semidirect
84. #10622552C22semidirect
85. #10622290C22semidirect
86. #10622289C22semidirect
87. #10622288C22semidirect
88. #10622288C22semidirect
89. #10622287C22semidirect
90. #10622285C22semidirect
91. #10622285C22semidirect
92. #10622285C22semidirect
93. #10622284C22semidirect
94. #10622284C22semidirect
95. #10622283C22semidirect
96. #10622283C22semidirect
97. #10622282C22semidirect
98. #10622282C22semidirect
99. #10622281C22semidirect
100. #10622280C22semidirect
101. #10622280C22semidirect
102. #10622279C22semidirect
103. #10622278C22semidirect
104. #10622278C22semidirect
105. #10622278C22semidirect
106. #10622278C22semidirect
117. C22×Q8×C11C23semidirect
125. C22×D44C23semidirect
129. C22×C4×D11C23semidirect
130. C2×C11×C4⋊C4C23semidirect
131. C2×C11×C4⋊C4C23semidirect
142. C2×C42×C11C23semidirect
172. C2×(C2×D11)⋊C4C23semidirect
173. C2×(C2×D11)⋊C4C23semidirect
174. C2×(C2×D11)⋊C4C23semidirect
175. C2×(C2×D11)⋊C4C23semidirect
176. C2×(C2×D11)⋊C4C23semidirect
177. C2×(C2×D11)⋊C4C23semidirect
178. C2×C4⋊Dic11C23semidirect
179. C2×C4⋊Dic11C23semidirect
180. C2×C4⋊Dic11C23semidirect
181. C2×Dic11⋊C4C23semidirect
182. C2×Dic11⋊C4C23semidirect
183. C2×Dic11⋊C4C23semidirect
184. C2×Dic11⋊C4C23semidirect
185. C2×Dic11⋊C4C23semidirect
186. C2×C4×Dic11C23semidirect
187. C2×C4×Dic11C23semidirect
203. C11×#95C23semidirect
204. C11×#95C23semidirect
205. C11×#95C23semidirect
206. C11×#95C23semidirect
207. C11×#95C23semidirect
208. C11×#95C23semidirect
209. C11⋊#95C23semidirect
210. C11⋊#95C23semidirect
211. C11⋊#95C23semidirect
212. C11⋊#95C23semidirect
213. C11⋊#95C23semidirect
214. C11⋊#95C23semidirect
215. C11⋊#95C23semidirect
216. C11⋊#95C23semidirect
362. #2736D11semidirect
522. #397C2×D11semidirect
523. #397C2×D11semidirect
537. #393C2×D11semidirect
538. #393C2×D11semidirect
555. #388C2×D11semidirect
556. #388C2×D11semidirect
557. #388C2×D11semidirect
651. C22×Q8C22×D11semidirect
686. C2×C4⋊C4C22×D11semidirect
687. C2×C4⋊C4C22×D11semidirect
736. C2×C42C22×D11semidirect
745. #95C22×D11semidirect
746. #95C22×D11semidirect
747. #95C22×D11semidirect
748. #95C22×D11semidirect
749. #95C22×D11semidirect
750. #95C22×D11semidirect
905. C11#36725semidirect

Maximal subgroups

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

subgroupindex
#130768942
#130756542
#130756512
#130751762
#130750112
#130750052
#130749992
#130749402
#130748362
#130748242
#130744202
#130743512
#130728552
#130727452
#130721572
#130720852
#130712782
D11×#3792
C11×#27362
#3672511