Finite Group Databasebeta

← #14769313

Subgroups — #14769313

Order 2816.

1930 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622624C211yesmaximal, characteristic, complemented
2C2×#10622828C211yesmaximal, characteristic, complemented
3C22×#66896C211yesmaximal, characteristic, complemented
4#13071545C211yesmaximal, characteristic, complemented
5#13069544C211yesmaximal, characteristic, complemented
6#13069441C211yesmaximal, characteristic, complemented
7#13069055C211yesmaximal, characteristic, complemented
8#13069045C211yesmaximal, characteristic, complemented
9#13068939C211yesmaximal, characteristic, complemented
10#13068934C211yesmaximal, characteristic, complemented
11#13068626C211yesmaximal, characteristic, complemented
12#13068547C211yesmaximal, characteristic, complemented
13#13068547C211yesmaximal, characteristic, complemented
14#13068441C211yesmaximal, characteristic, complemented
15C2×D42×C11C211yesmaximal, characteristic
16C23×D4×C11—21no—
17C23×D4×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19D42×C11—24no—
20D42×C11C418yescomplemented
21C2×C11×#127C2211yescharacteristic
22C2×C11×#121—21no—
23C2×C11×#121C2211yescharacteristic
24C2×C11×#121C2211yescharacteristic
25C2×C11×#120—21no—
26C2×C11×#120—21no—
27C2×C4×D4×C11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C2×#66979C2211yescharacteristic, complemented
30C22×C4⋊Dic11C2211yescharacteristic, complemented
31C22×#4318C2211yescharacteristic, complemented
32C23×C11⋊C8C2211yescharacteristic, complemented
33#10622833—21no—
34#10622828—24no—
35C2×#66896—24no—
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40C2×#66896C2211yescharacteristic, complemented
41C2×#66896C2211yescharacteristic, complemented
42C2×#66896C2211yescharacteristic, complemented
43C2×#66896C2211yescharacteristic, complemented
44C2×#66896C2211yescharacteristic, complemented
45C2×#66896C2211yescharacteristic, complemented
46C2×#66896C2211yescharacteristic, complemented
47C2×#66896C2211yescharacteristic, complemented
48#10622825C2211yescharacteristic, complemented
49#10622825C2211yescharacteristic, complemented
50C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
51C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
52#10622624—24no—
53#10622594—21no—
54#10622564—21no—
55C22⋊C4×Dic11—21no—
56#10622549C2211yescharacteristic, complemented
57C4×C4⋊Dic11C2211yescharacteristic, complemented
58C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
59C2×#66867C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61#10622167C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63#10622167C2211yescharacteristic, complemented
64C25×C11—21no—
65C25×C11—21no—
66C22×D4×C11—22no—
67C22×D4×C11—22no—
68C22×D4×C11—22no—
69C22×D4×C11—22no—
70C22×D4×C11—21no—
71C22×D4×C11—21no—
72C22×D4×C11—28no—
73C22×D4×C11—21no—
74C22×D4×C11—21no—
75C22×D4×C11—21no—
76C22×D4×C11—22no—
77C22×D4×C11—22no—
78C22×D4×C11—21no—
79C22×D4×C11—41no—
80C22×D4×C11—41no—
81C22×D4×C11—41no—
82C22×D4×C11—41no—
83C22×D4×C11—44no—
84C22×D4×C11—44no—
85C22×D4×C11C2×C414yes—
86C22×D4×C11C2×C414yescomplemented
87C22×D4×C11D411yescharacteristic
88C22×D4×C11C2311yescharacteristic
89C22×D4×C11C2311yescharacteristic
90C22×D4×C11C2311yescharacteristic
91C23×C4×C11—21no—
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
94C23×Dic11—21no—
95C11×#127—22no—
96C11×#127C2×C414yescomplemented
97C11×#121—22no—
98C11×#121—22no—
99C11×#121—28no—
100C11×#121C2×C414yes—
101C11×#121C2×C414yescomplemented
102C11×#120—28no—
103C11×#120—28no—
104C4×D4×C11—22no—
105C4×D4×C11C2×C414yes—
106C4×D4×C11C2×C414yescomplemented
107C4×D4×C11D414yes—
108C2×C11×C4⋊C4D411yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4D411yescharacteristic
114C2×C11×C22⋊C4D411yescharacteristic
115C2×C42×C11C2311yescharacteristic
116C2×C22⋊Dic11—21no—
117C2×C22⋊Dic11—21no—
118C2×C22⋊Dic11—21no—
119#66979—22no—
120#66979—41no—
121C2×C4⋊Dic11—22no—
122C2×C4⋊Dic11—21no—
123C2×C4⋊Dic11—41no—
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2311yescharacteristic
126C2×C4⋊Dic11C2311yescharacteristic
127C2×C4⋊Dic11C2311yescharacteristic
128C2×C4×Dic11—21no—
129C2×C4×Dic11—21no—
130C2×#4318—22no—
131C2×#4318—22no—
132C2×#4318—41no—
133C22×C11⋊C8—22no—
134C22×C11⋊C8—22no—
135C22×C11⋊C8—41no—
136C22×C11⋊C8C2311yescharacteristic
137C22×C11⋊C8C2311yescharacteristic
138C22×C11⋊C8C2311yescharacteristic
139C22×C11⋊C8C2311yescharacteristic
140#66896—22no—
141#66896—22no—
142#66896—22no—
143#66896—22no—
144#66896—22no—
145#66896—22no—
146#66896—22no—
147#66896—41no—
148#66896—41no—
149#66896—41no—
150#66896—41no—
151#66896D414yescomplemented
152C11⋊#95—21no—
153C11⋊#95—21no—
154C11⋊#95—21no—
155C11⋊#95—21no—
156C11⋊#95—21no—
157C22⋊(C11⋊C8)—22no—
158C22⋊(C11⋊C8)—22no—
159C4⋊(C11⋊C8)—22no—
160#66867—22no—
161#22423—111nomaximal, Sylow
162C24×C11—21no—
163C24×C11—21no—
164C24×C11—21no—
165C24×C11—24no—
166C24×C11—24no—
167C24×C11—42no—
168C24×C11—42no—
169C24×C11—42no—
170C24×C11—42no—
171C24×C11—42no—
172C24×C11—42no—
173C24×C11—42no—
174C24×C11—42no—
175C24×C11—81no—
176C24×C11—81no—
177C24×C11—81no—
178C24×C11—81no—
179C24×C11C2×D411yescharacteristic
180C24×C11C2×D411yescharacteristic
181C2×D4×C11—22no—
182C2×D4×C11—22no—
183C2×D4×C11—28no—
184C2×D4×C11—28no—
185C2×D4×C11—24no—
186C2×D4×C11—24no—
187C2×D4×C11—24no—
188C2×D4×C11—24no—
189C2×D4×C11—24no—
190C2×D4×C11—24no—
191C2×D4×C11—21no—
192C2×D4×C11—21no—
193C2×D4×C11—21no—
194C2×D4×C11—21no—
195C2×D4×C11—21no—
196C2×D4×C11—21no—
197C2×D4×C11—21no—
198C2×D4×C11—21no—
199C2×D4×C11—21no—
200C2×D4×C11—21no—
201C2×D4×C11—21no—
202C2×D4×C11—21no—
203C2×D4×C11—21no—
204C2×D4×C11—44no—
205C2×D4×C11—44no—
206C2×D4×C11—44no—
207C2×D4×C11—44no—
208C2×D4×C11—44no—
209C2×D4×C11—44no—
210C2×D4×C11—42no—
211C2×D4×C11—42no—
212C2×D4×C11—42no—
213C2×D4×C11—42no—
214C2×D4×C11—42no—
215C2×D4×C11—42no—
216C2×D4×C11—432no—
217C2×D4×C11—42no—
218C2×D4×C11—42no—
219C2×D4×C11—42no—
220C2×D4×C11—42no—
221C2×D4×C11—81no—
222C2×D4×C11—81no—
223C2×D4×C11C22⋊C414yes—
224C2×D4×C11C22×C412yes—
225C2×D4×C11C22×C412yes—
226C2×D4×C11C22×C412yes—
227C2×D4×C11C2×D412yes—
228C2×D4×C11#4112yes—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—21no—
238C22×C4×C11—24no—
239C22×C4×C11—42no—
240C22×C4×C11—42no—
241C22×C4×C11C22×C412yes—
242C22×C4×C11C22×C412yes—
243C22×C4×C11C2×D411yescharacteristic
244C22×C4×C11C2×D411yescharacteristic
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2×D411yescharacteristic
247C22×C4×C11C2×D412yes—
248C22×C4×C11C2×D412yes—
249C22×C4×C11C2411yescharacteristic
250C22×Dic11—21no—
251C22×Dic11—21no—
252C22×Dic11—21no—
253C22×Dic11—21no—
254C22×Dic11—42no—
255C22×Dic11—42no—
256C22×Dic11—81no—
257C11×C4⋊C4—21no—
258C11×C4⋊C4C22⋊C414yes—
259C11×C4⋊C4C22×C412yes—
260C11×C22⋊C4—24no—
261C11×C22⋊C4—24no—
262C11×C22⋊C4—24no—
263C11×C22⋊C4C22⋊C414yes—
264C11×C22⋊C4C22⋊C414yes—
265C42×C11C22×C412yes—
266C42×C11C2×D412yes—
267C22⋊Dic11—42no—
268C22⋊Dic11—42no—
269C22⋊Dic11—81no—
270C4⋊Dic11—21no—
271C4⋊Dic11—21no—
272C4⋊Dic11—21no—
273C4⋊Dic11—21no—
274C4⋊Dic11—21no—
275C4⋊Dic11—21no—
276C4⋊Dic11—21no—
277C4⋊Dic11—42no—
278C4⋊Dic11C2×D412yescomplemented
279C4×Dic11—42no—
280C4×Dic11—81no—
281#4318—44no—
282C2×C11⋊C8—21no—
283C2×C11⋊C8—21no—
284C2×C11⋊C8—21no—
285C2×C11⋊C8—21no—
286C2×C11⋊C8—21no—
287C2×C11⋊C8—21no—
288C2×C11⋊C8—21no—
289C2×C11⋊C8—21no—
290C2×C11⋊C8—21no—
291C2×C11⋊C8—21no—
292C2×C11⋊C8—21no—
293C2×C11⋊C8—44no—
294C2×C11⋊C8C2×D412yescomplemented
295C2×D42D1111yescharacteristic
296C2×#435—111no—
297C2×#418—111no—
298C22×#102—111no—
299#2352—111no—
300#1982—111no—
301#1961—111no—
302#1895—111no—
303#1893—111no—
304#1875—111no—
305#1874—111no—
306#1804—111no—
307#1786—111no—
308#1786—111no—
309#1762—111no—
310C23×C11—21no—
311C23×C11—21no—
312C23×C11—21no—
313C23×C11—21no—
314C23×C11—22no—
315C23×C11—21no—
316C23×C11—22no—
317C23×C11—21no—
318C23×C11—22no—
319C23×C11—21no—
320C23×C11—21no—
321C23×C11—21no—
322C23×C11—21no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—48no—
326C23×C11—48no—
327C23×C11—48no—
328C23×C11—41no—
329C23×C11—41no—
330C23×C11—41no—
331C23×C11—41no—
332C23×C11—41no—
333C23×C11—41no—
334C23×C11—41no—
335C23×C11—41no—
336C23×C11—41no—
337C23×C11—41no—
338C23×C11—41no—
339C23×C11—41no—
340C23×C11—41no—
341C23×C11—41no—
342C23×C11—41no—
343C23×C11—41no—
344C23×C11—48no—
345C23×C11—84no—
346C23×C11—84no—
347C23×C11—84no—
348C23×C11—84no—
349C23×C11—84no—
350C23×C11—84no—
351C23×C11—84no—
352C23×C11—84no—
353C23×C11—84no—
354C23×C11—84no—
355C23×C11C2×C22⋊C412yes—
356C23×C11C2×C22⋊C412yes—
357C23×C11AGL(1,ℤ/8)12yes—
358C23×C11AGL(1,ℤ/8)12yes—
359C23×C11C22×D411yescharacteristic
360D4×C11—28no—
361D4×C11—22no—
362D4×C11—22no—
363D4×C11—22no—
364D4×C11—22no—
365D4×C11—22no—
366D4×C11—22no—
367D4×C11—22no—
368D4×C11—48no—
369D4×C11—48no—
370D4×C11—48no—
371D4×C11—48no—
372D4×C11—48no—
373D4×C11—41no—
374D4×C11—41no—
375D4×C11—41no—
376D4×C11—41no—
377D4×C11—84no—
378D4×C11C4×D414yes—
379C2×C4×C11—21no—
380C2×C4×C11—21no—
381C2×C4×C11—21no—
382C2×C4×C11—21no—
383C2×C4×C11—21no—
384C2×C4×C11—21no—
385C2×C4×C11—21no—
386C2×C4×C11—21no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—48no—
397C2×C4×C11—41no—
398C2×C4×C11—41no—
399C2×C4×C11C2×C22⋊C412yes—
400C2×C4×C11C2×C22⋊C412yes—
401C2×C4×C11C2×C22⋊C412yes—
402C2×C4×C11C2×C22⋊C412yes—
403C2×C4×C11C23×C411yescharacteristic
404C2×C4×C11C22×D411yescharacteristic
405C2×C4×C11C22×D411yescharacteristic
406C2×C4×C11C2×#4111yescharacteristic
407C2×C4×C11H(5,𝔽2)11yescharacteristic
408C2×C4×C11H(5,𝔽2)11yescharacteristic
409C2×Dic11—22no—
410C2×Dic11—41no—
411C2×Dic11—41no—
412C2×Dic11—41no—
413C2×Dic11—41no—
414C2×Dic11—41no—
415C2×Dic11—41no—
416C2×Dic11—41no—
417C2×Dic11—41no—
418C2×Dic11—41no—
419C2×Dic11—41no—
420C2×Dic11—41no—
421C2×Dic11—84no—
422C11⋊C8—22no—
423C11⋊C8—41no—
424C11⋊C8—41no—
425C11⋊C8—41no—
426C23×D4—21no—
427C23×D4C2×D1111yescharacteristic
428C23×D4C2×D1111yescharacteristic
429C22×M16—111no—
430C23×C8—111no—
431D42—24no—
432D42Dic1118yescomplemented
433C2×#127C2×D1111yescharacteristic
434C2×#121—21no—
435C2×#121C2×D1111yescharacteristic
436C2×#121C2×D1111yescharacteristic
437C2×#120—21no—
438C2×#120—21no—
439C2×C4×D4C2×D1111yescharacteristic
440C2×C4×D4C2×D1111yescharacteristic
441C2×#117—111no—
442C22×C4⋊C4—111no—
443#435—224no—
444C2×C4⋊C8—111no—
445#418—224no—
446C2×#102—111no—
447C2×#102—111no—
448C2×#102—111no—
449C2×#102—111no—
450C2×#102—111no—
451C2×#102—111no—
452C2×#102—111no—
453C2×#102—111no—
454C2×#102—111no—
455C2×#102—111no—
456C2×#102—111no—
457C2×#102—111no—
458C2×#102—224no—
459C2×C22⋊C8—111no—
460C2×C22⋊C8—111no—
461C2×#97—111no—
462#388—221no—
463#387—221no—
464#386—221no—
465#382—111no—
466#380—111no—
467#380—111no—
468C4×C4⋊C4—111no—
469C4×C22⋊C4—221no—
470#340—111no—
471#340—111no—
472#340—111no—
473#340—111no—
474C22×C11—22no—
475C22×C11—22no—
476C22×C11—22no—
477C22×C11—22no—
478C22×C11—22no—
479C22×C11—22no—
480C22×C11—22no—
481C22×C11—24no—
482C22×C11—22no—
483C22×C11—22no—
484C22×C11—42no—
485C22×C11—42no—
486C22×C11—41no—
487C22×C11—42no—
488C22×C11—41no—
489C22×C11—42no—
490C22×C11—41no—
491C22×C11—42no—
492C22×C11—41no—
493C22×C11—42no—
494C22×C11—42no—
495C22×C11—42no—
496C22×C11—42no—
497C22×C11—42no—
498C22×C11—42no—
499C22×C11—42no—
500C22×C11—816no—
501C22×C11—816no—
502C22×C11—81no—
503C22×C11—81no—
504C22×C11—81no—
505C22×C11—81no—
506C22×C11—81no—
507C22×C11—81no—
508C22×C11—81no—
509C22×C11—81no—
510C22×C11#41814yescomplemented
511C22×C11C22×C22⋊C411yescharacteristic
512C22×C11D4211yescharacteristic
513C22×C11#54611yescharacteristic
514C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
515C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
516C22×C11#57611yescharacteristic
517C22×C11#57711yescharacteristic
518C4×C11—22no—
519C4×C11—22no—
520C4×C11—22no—
521C4×C11—22no—
522C4×C11—42no—
523C4×C11C2×C4×D411yescharacteristic
524C4×C11#51811yescharacteristic
525C4×C11D4211yescharacteristic
526C4×C11#54611yescharacteristic
527Dic11—42no—
528Dic11—81no—
529Dic11—81no—
530Dic11—81no—
531C25—21no—
532C25—21no—
533C22×D4—22no—
534C22×D4—22no—
535C22×D4—22no—
536C22×D4—22no—
537C22×D4—21no—
538C22×D4—21no—
539C22×D4—28no—
540C22×D4—21no—
541C22×D4—21no—
542C22×D4—21no—
543C22×D4—22no—
544C22×D4—22no—
545C22×D4—21no—
546C22×D4—41no—
547C22×D4—41no—
548C22×D4—41no—
549C22×D4—41no—
550C22×D4—44no—
551C22×D4—44no—
552C22×D4C2×Dic1114yes—
553C22×D4C2×Dic1114yescomplemented
554C22×D4C22⋊D1111yescharacteristic
555C22×D4C22×D1111yescharacteristic
556C22×D4C22×D1111yescharacteristic
557C22×D4C22×D1111yescharacteristic
558C23×C4—21no—
559C23×C4—221no—
560C23×C4C22×D1111yescharacteristic
561C23×C4C22×D1111yescharacteristic
562C2×M16—222no—
563C2×M16—222no—
564C2×M16—441no—
565C22×C8—111no—
566C22×C8—111no—
567C22×C8—111no—
568C22×C8—111no—
569C22×C8—222no—
570C22×C8—222no—
571C22×C8—441no—
572#127—22no—
573#127C2×Dic1114yescomplemented
574#121—22no—
575#121—22no—
576#121—28no—
577#121C2×Dic1114yes—
578#121C2×Dic1114yescomplemented
579#120—28no—
580#120—28no—
581C4×D4—22no—
582C4×D4C2×Dic1114yes—
583C4×D4C2×Dic1114yescomplemented
584C4×D4C22⋊D1114yes—
585#117—222no—
586#117—441no—
587C2×C4⋊C4—111no—
588C2×C4⋊C4—111no—
589C2×C4⋊C4—111no—
590C2×C4⋊C4—111no—
591C2×C4⋊C4—222no—
592C2×C4⋊C4—221no—
593C2×C4⋊C4—441no—
594C2×C4⋊C4C22⋊D1111yescharacteristic
595C2×C4⋊C4C22×D1111yescharacteristic
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—221no—
600C2×C22⋊C4—221no—
601C2×C22⋊C4—221no—
602C2×C22⋊C4C22⋊D1111yescharacteristic
603C2×C22⋊C4C22⋊D1111yescharacteristic
604C2×C42—221no—
605C2×C42—221no—
606C2×C42C22×D1111yescharacteristic
607C4⋊C8—222no—
608#102—114no—
609#102—222no—
610#102—222no—
611#102—222no—
612#102—222no—
613#102—222no—
614#102—222no—
615#102—222no—
616#102—441no—
617#102—441no—
618#102—441no—
619#102—441no—
620C22⋊C8—222no—
621C22⋊C8—222no—
622#97—222no—
623#95—221no—
624#95—221no—
625#95—221no—
626#95—221no—
627#95—221no—
628C2×C11—24no—
629C2×C11—42no—
630C2×C11—44no—
631C2×C11—82no—
632C2×C11—82no—
633C2×C11D4×C22⋊C411yescharacteristic
634C2×C11C2×#41811yescharacteristic
635C2×C11#289711yescharacteristic
636C2×C11#326411yescharacteristic
637C2×C11#326511yescharacteristic
638C2×C11#331011yescharacteristic
639C2×C11#331811yescharacteristic
640C24—21no—
641C24—21no—
642C24—21no—
643C24—24no—
644C24—24no—
645C24—42no—
646C24—42no—
647C24—42no—
648C24—42no—
649C24—42no—
650C24—42no—
651C24—42no—
652C24—42no—
653C24—81no—
654C24—81no—
655C24—81no—
656C24—81no—
657C24C2×C22⋊D1111yescharacteristic
658C24C2×C22⋊D1111yescharacteristic
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—28no—
662C2×D4—28no—
663C2×D4—24no—
664C2×D4—24no—
665C2×D4—24no—
666C2×D4—24no—
667C2×D4—24no—
668C2×D4—24no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—44no—
686C2×D4—44no—
687C2×D4—44no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—432no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4C22⋊Dic1114yes—
702C2×D4D4×D1112yes—
703C2×D4#434112yes—
704C2×D4C22×Dic1112yes—
705C2×D4C22×Dic1112yes—
706C2×D4C22×Dic1112yes—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—24no—
717C22×C4—42no—
718C22×C4—42no—
719C22×C4—221no—
720C22×C4—221no—
721C22×C4—221no—
722C22×C4—221no—
723C22×C4—442no—
724C22×C4—442no—
725C22×C4—881no—
726C22×C4C22×Dic1112yes—
727C22×C4C22×Dic1112yes—
728C22×C4C2×C22⋊D1111yescharacteristic
729C22×C4C2×C22⋊D1111yescharacteristic
730C22×C4C2×C22⋊D1111yescharacteristic
731C22×C4C2×C22⋊D1111yescharacteristic
732C22×C4C2×C22⋊D1112yes—
733C22×C4C2×C22⋊D1112yes—
734C22×C4C23×D1111yescharacteristic
735M16—444no—
736C2×C8—112no—
737C2×C8—221no—
738C2×C8—221no—
739C2×C8—221no—
740C2×C8—221no—
741C2×C8—221no—
742C2×C8—221no—
743C2×C8—221no—
744C2×C8—221no—
745C2×C8—221no—
746C2×C8—221no—
747C2×C8—221no—
748C2×C8—444no—
749C4⋊C4—21no—
750C4⋊C4—112no—
751C4⋊C4—221no—
752C4⋊C4—221no—
753C4⋊C4—221no—
754C4⋊C4—221no—
755C4⋊C4—221no—
756C4⋊C4—221no—
757C4⋊C4—221no—
758C4⋊C4—442no—
759C4⋊C4C22⋊Dic1114yes—
760C4⋊C4C22×Dic1112yes—
761C22⋊C4—24no—
762C22⋊C4—24no—
763C22⋊C4—24no—
764C22⋊C4—442no—
765C22⋊C4—442no—
766C22⋊C4—881no—
767C22⋊C4C22⋊Dic1114yes—
768C22⋊C4C22⋊Dic1114yes—
769C42—442no—
770C42—881no—
771C42C22×Dic1112yes—
772C42C2×C22⋊D1112yes—
773C11#2242311yescharacteristic, complemented, Sylow
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—22no—
782C23—21no—
783C23—22no—
784C23—21no—
785C23—21no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—48no—
790C23—48no—
791C23—48no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—48no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—84no—
810C23—84no—
811C23—84no—
812C23—84no—
813C23—84no—
814C23—84no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23#6698512yes—
820C23#6698512yes—
821C23C2×C22⋊Dic1112yes—
822C23C2×C22⋊Dic1112yes—
823C23C22×C22⋊D1111yescharacteristic
824D4—28no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—22no—
832D4—48no—
833D4—48no—
834D4—48no—
835D4—48no—
836D4—48no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—84no—
842D4D4×Dic1114yes—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—48no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—222no—
864C2×C4—441no—
865C2×C4—441no—
866C2×C4—441no—
867C2×C4—441no—
868C2×C4—441no—
869C2×C4—441no—
870C2×C4—441no—
871C2×C4—441no—
872C2×C4—441no—
873C2×C4—441no—
874C2×C4—441no—
875C2×C4—884no—
876C2×C4C2×C22⋊Dic1112yes—
877C2×C4C2×C22⋊Dic1112yes—
878C2×C4C2×C22⋊Dic1112yes—
879C2×C4C2×C22⋊Dic1112yes—
880C2×C4C2×D4×D1111yescharacteristic
881C2×C4C2×#434111yescharacteristic
882C2×C4#6703711yescharacteristic
883C2×C4#6703711yescharacteristic
884C2×C4C23×Dic1111yescharacteristic
885C2×C4C22×C22⋊D1111yescharacteristic
886C8—222no—
887C8—441no—
888C8—441no—
889C8—441no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—22no—
897C22—24no—
898C22—22no—
899C22—22no—
900C22—41no—
901C22—42no—
902C22—41no—
903C22—42no—
904C22—41no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—41no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—816no—
917C22—816no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22#1062282814yescomplemented
927C22C2×#6698511yescharacteristic
928C22C2×#6698511yescharacteristic
929C22D4×C22⋊D1111yescharacteristic
930C22#1062333711yescharacteristic
931C22#1062336611yescharacteristic
932C22#1062336711yescharacteristic
933C22C22×C22⋊Dic1111yescharacteristic
934C4—22no—
935C4—22no—
936C4—22no—
937C4—22no—
938C4—42no—
939C4—442no—
940C4—881no—
941C4—881no—
942C4—881no—
943C4C2×D4×Dic1111yescharacteristic
944C4#1062332911yescharacteristic
945C4D4×C22⋊D1111yescharacteristic
946C4#1062333711yescharacteristic
947C2—24no—
948C2—42no—
949C2—44no—
950C2—82no—
951C2—82no—
952C2D4×C22⋊Dic1111yescharacteristic
953C2C2×#1062282811yescharacteristic
954C2#1307714211yescharacteristic
955C2#1308009211yescharacteristic
956C2#1308010711yescharacteristic
957C2#1308063711yescharacteristic
958C2#1308075711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×D42×C11C2
socleC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenterC2×D42D11
hypocenterC11#22423
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D42

Complements

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

NH ≅ G/Ntype
1. C2×#10622624C2semidirect
2. C2×#10622828C2semidirect
3. C22×#66896C2semidirect
4. #13071545C2semidirect
5. #13069544C2semidirect
6. #13069441C2semidirect
7. #13069055C2semidirect
8. #13069045C2semidirect
9. #13068939C2semidirect
10. #13068934C2semidirect
11. #13068626C2semidirect
12. #13068547C2semidirect
13. #13068547C2semidirect
14. #13068441C2semidirect
20. D42×C11C4semidirect
29. C2×#66979C22semidirect
30. C22×C4⋊Dic11C22semidirect
31. C22×#4318C22semidirect
32. C23×C11⋊C8C22semidirect
40. C2×#66896C22semidirect
41. C2×#66896C22semidirect
42. C2×#66896C22semidirect
43. C2×#66896C22semidirect
44. C2×#66896C22semidirect
45. C2×#66896C22semidirect
46. C2×#66896C22semidirect
47. C2×#66896C22semidirect
48. #10622825C22semidirect
49. #10622825C22semidirect
50. C2×C22⋊(C11⋊C8)C22semidirect
51. C2×C22⋊(C11⋊C8)C22semidirect
56. #10622549C22semidirect
57. C4×C4⋊Dic11C22semidirect
58. C2×C4⋊(C11⋊C8)C22semidirect
59. C2×#66867C22semidirect
60. #10622167C22semidirect
61. #10622167C22semidirect
62. #10622167C22semidirect
63. #10622167C22semidirect
86. C22×D4×C11C2×C4semidirect
96. C11×#127C2×C4semidirect
101. C11×#121C2×C4semidirect
106. C4×D4×C11C2×C4semidirect
151. #66896D4semidirect
278. C4⋊Dic11C2×D4semidirect
294. C2×C11⋊C8C2×D4semidirect
432. D42Dic11semidirect
510. C22×C11#418semidirect
553. C22×D4C2×Dic11semidirect
573. #127C2×Dic11semidirect
578. #121C2×Dic11semidirect
583. C4×D4C2×Dic11semidirect
773. C11#22423semidirect
926. C22#10622828semidirect

Maximal subgroups

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

subgroupindex
C2×#106226242
C2×#106228282
C22×#668962
#130715452
#130695442
#130694412
#130690552
#130690452
#130689392
#130689342
#130686262
#130685472
#130684412
C2×D42×C112
#2242311