Finite Group Databasebeta

← D4×#66870 #14769092

Subgroups — D4×#66870 #14769092

Order 2816.

2102 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C22⋊D11C211yesmaximal, characteristic
2C22×#66870C212yesmaximal, complemented
3D4×C22⋊Dic11C211yesmaximal, characteristic, complemented
4#13069452C211yesmaximal, characteristic, complemented
5#13069451C211yesmaximal, characteristic, complemented
6#13069069C212yesmaximal, complemented
7#13069067C212yesmaximal, complemented
8#13068601C211yesmaximal, characteristic, complemented
9#13068530C212yesmaximal, complemented
10C4×#66870C211yesmaximal, characteristic, complemented
11D4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C23×C22⋊D11C2212yes—
14C22×D4×D11C411yescharacteristic, complemented
15C2×C4×D4×C11—21no—
16C22×C11×C22⋊C4C2212yescomplemented
17C2×#67006C2212yes—
18C22×C22⋊Dic11C2212yescomplemented
19C2×#66993C411yescharacteristic, complemented
20C2×#66992C412yescomplemented
21D4×C22⋊D11—21no—
22D4×C22⋊D11—22no—
23D4×C22⋊D11—21no—
24D4×C22⋊D11—21no—
25D4×C22⋊D11—22no—
26D4×C22⋊D11—21no—
27C2×#66991C411yescharacteristic, complemented
28C2×#66990C412yescomplemented
29C2×D4×Dic11—21no—
30C2×D4×Dic11C411yescharacteristic, complemented
31C2×#66983C2211yescharacteristic
32C2×C4×C22⋊D11C2211yescharacteristic
33C11×#390—21no—
34C11×#386—22no—
35C11×#380C2211yescharacteristic, complemented
36C11×#379C2212yescomplemented
37C4×C11×C22⋊C4C2211yescharacteristic, complemented
38#10622860C2212yescomplemented
39#10622834—21no—
40#10622833—22no—
41#10622825C2211yescharacteristic, complemented
42C4×C22⋊Dic11C2211yescharacteristic, complemented
43C2×#66870—28no—
44C2×#66870C2212yes—
45C2×#66870C2211yescharacteristic
46C2×#66870C2211yescharacteristic
47C2×#66870C2212yescomplemented
48C2×#66870C2212yescomplemented
49C2×#66870C2212yescomplemented
50C2×#66870C2212yescomplemented
51#10622165C2211yescharacteristic, complemented
52#10622165C2212yescomplemented
53#10622165C2211yescharacteristic, complemented
54C25×C11C2312yes—
55C24×D11C2×C412yescomplemented
56C22×D4×C11—44no—
57C22×D4×C11C2×C411yescharacteristic
58C22×D4×C11C2×C412yes—
59C22×D4×C11C2×C411yescharacteristic
60C22×D4×C11D411yescharacteristic
61C22×D4×C11D412yes—
62C22×D4×C11D411yescharacteristic
63C22×D4×C11D411yescharacteristic
64C22×D4×C11D412yes—
65C22×D4×C11D411yescharacteristic
66C23×C4×C11—22no—
67C23×C4×C11C2311yescharacteristic
68C22×C22⋊D11—22no—
69C22×C22⋊D11—22no—
70C22×C22⋊D11—22no—
71C22×C22⋊D11—22no—
72C22×C22⋊D11—24no—
73C22×C22⋊D11—24no—
74C22×C22⋊D11—42no—
75C22×C22⋊D11—42no—
76C22×C22⋊D11C2×C412yescomplemented
77C22×C22⋊D11C2×C412yescomplemented
78C22×C22⋊D11C2×C412yescomplemented
79C22×C22⋊D11C2×C412yescomplemented
80C22×C22⋊D11C2312yes—
81C22×C22⋊D11C2311yescharacteristic
82C23×Dic11—22no—
83C23×Dic11C2×C412yescomplemented
84C2×D4×D11—22no—
85C2×D4×D11—21no—
86C2×D4×D11—21no—
87C2×D4×D11—44no—
88C22×D44C2×C411yescharacteristic, complemented
89C22×C4×D11C2×C411yescharacteristic, complemented
90C4×D4×C11—44no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C22⋊C4—24no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—22no—
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4—42no—
97C2×C11×C22⋊C4C2312yes—
98C2×C11×C22⋊C4C2311yescharacteristic
99C2×C11×C22⋊C4C2311yescharacteristic
100C2×C42×C11—21no—
101#67006—22no—
102#67006—22no—
103#67006—22no—
104#67006—22no—
105C2×C22⋊Dic11—24no—
106C2×C22⋊Dic11—22no—
107C2×C22⋊Dic11—22no—
108C2×C22⋊Dic11—22no—
109C2×C22⋊Dic11—42no—
110C2×C22⋊Dic11C2×C412yescomplemented
111C2×C22⋊Dic11C2×C412yescomplemented
112C2×C22⋊Dic11C2311yescharacteristic
113C2×C22⋊Dic11C2312yes—
114C2×C22⋊Dic11C2311yescharacteristic
115C2×C22⋊Dic11C2311yescharacteristic
116#66993—21no—
117#66993—21no—
118#66993—22no—
119#66992—22no—
120#66992—22no—
121#66992—22no—
122#66992—22no—
123#66991—21no—
124#66991—21no—
125#66991—22no—
126#66990—22no—
127#66990—22no—
128#66990—22no—
129#66990—22no—
130D4×Dic11—22no—
131D4×Dic11—21no—
132D4×Dic11—21no—
133D4×Dic11—44no—
134#66983—21no—
135#66983—21no—
136#66983—21no—
137#66983—21no—
138C4×C22⋊D11—21no—
139C4×C22⋊D11—21no—
140C4×C22⋊D11—21no—
141C4×C22⋊D11—21no—
142C2×(C2×D11)⋊C4C2×C411yescharacteristic, complemented
143C2×(C2×D11)⋊C4C2×C412yescomplemented
144C2×C4⋊Dic11—21no—
145C2×C4⋊Dic11C2×C411yescharacteristic, complemented
146C2×Dic11⋊C4C2×C411yescharacteristic, complemented
147C2×C4×Dic11—21no—
148C2×C4×Dic11C2×C411yescharacteristic, complemented
149C11×#95—21no—
150C11×#95—21no—
151C11⋊#95—21no—
152C11⋊#95—21no—
153#66870—24no—
154#66870—22no—
155#66870—24no—
156#66870—24no—
157#66870—42no—
158#66870—42no—
159#66870D414yesdirect product factor
160D4×#99—111nomaximal, Sylow
161C24×C11—22no—
162C24×C11—22no—
163C24×C11—22no—
164C24×C11—22no—
165C24×C11—44no—
166C24×C11—82no—
167C24×C11C22×C412yes—
168C24×C11C22×C412yes—
169C24×C11C2×D412yes—
170C24×C11C2×D412yes—
171C24×C11C2×D412yes—
172C24×C11C2×D412yes—
173C24×C11C2411yescharacteristic
174C23×D11—22no—
175C23×D11—22no—
176C23×D11—24no—
177C23×D11—42no—
178C23×D11—44no—
179C23×D11—82no—
180C23×D11C22×C412yes—
181C23×D11C22×C411yescharacteristic
182C2×D4×C11—24no—
183C2×D4×C11—24no—
184C2×D4×C11—24no—
185C2×D4×C11—42no—
186C2×D4×C11—42no—
187C2×D4×C11—42no—
188C2×D4×C11—44no—
189C2×D4×C11—44no—
190C2×D4×C11—44no—
191C2×D4×C11C22⋊C412yes—
192C2×D4×C11C22⋊C411yescharacteristic
193C2×D4×C11C22⋊C412yes—
194C2×D4×C11C22⋊C412yes—
195C2×D4×C11C22⋊C411yescharacteristic
196C2×D4×C11C22⋊C411yescharacteristic
197C2×D4×C11C22⋊C412yes—
198C2×D4×C11C22⋊C412yes—
199C2×D4×C11C22⋊C412yes—
200C2×D4×C11C22⋊C411yescharacteristic
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—22no—
204C22×C4×C11—42no—
205C22×C4×C11—44no—
206C22×C4×C11—44no—
207C22×C4×C11—82no—
208C22×C4×C11C22×C411yescharacteristic
209C22×C4×C11C22×C411yescharacteristic
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2×D411yescharacteristic
214C2×C22⋊D11—24no—
215C2×C22⋊D11—22no—
216C2×C22⋊D11—22no—
217C2×C22⋊D11—22no—
218C2×C22⋊D11—22no—
219C2×C22⋊D11—22no—
220C2×C22⋊D11—22no—
221C2×C22⋊D11—22no—
222C2×C22⋊D11—22no—
223C2×C22⋊D11—21no—
224C2×C22⋊D11—21no—
225C2×C22⋊D11—22no—
226C2×C22⋊D11—22no—
227C2×C22⋊D11—22no—
228C2×C22⋊D11—22no—
229C2×C22⋊D11—21no—
230C2×C22⋊D11—21no—
231C2×C22⋊D11—22no—
232C2×C22⋊D11—22no—
233C2×C22⋊D11—24no—
234C2×C22⋊D11—42no—
235C2×C22⋊D11—42no—
236C2×C22⋊D11—44no—
237C2×C22⋊D11—44no—
238C2×C22⋊D11—44no—
239C2×C22⋊D11—44no—
240C2×C22⋊D11—44no—
241C2×C22⋊D11—44no—
242C2×C22⋊D11—44no—
243C2×C22⋊D11—44no—
244C2×C22⋊D11—44no—
245C2×C22⋊D11—82no—
246C2×C22⋊D11C2×D412yes—
247C2×C22⋊D11#4112yes—
248C22×Dic11—24no—
249C22×Dic11—22no—
250C22×Dic11—22no—
251C22×Dic11—21no—
252C22×Dic11—21no—
253C22×Dic11—22no—
254C22×Dic11—42no—
255C22×Dic11—44no—
256C22×Dic11—44no—
257C22×Dic11—82no—
258C22×Dic11C22×C412yes—
259C22×Dic11C22×C411yescharacteristic
260C22×Dic11C22×C411yescharacteristic
261C22×Dic11C22×C411yescharacteristic
262D4×D11—48no—
263D4×D11—44no—
264D4×D11—44no—
265C2×D44—21no—
266C2×D44—21no—
267C2×D44—42no—
268C2×C4×D11—21no—
269C2×C4×D11—21no—
270C2×C4×D11—42no—
271C11×C4⋊C4—42no—
272C11×C22⋊C4—21no—
273C11×C22⋊C4—22no—
274C11×C22⋊C4—21no—
275C11×C22⋊C4—21no—
276C11×C22⋊C4—22no—
277C11×C22⋊C4—44no—
278C11×C22⋊C4—44no—
279C11×C22⋊C4—82no—
280C11×C22⋊C4C2×D412yescomplemented
281C42×C11—42no—
282C22⋊Dic11—22no—
283C22⋊Dic11—22no—
284C22⋊Dic11—22no—
285C22⋊Dic11—22no—
286C22⋊Dic11—21no—
287C22⋊Dic11—21no—
288C22⋊Dic11—22no—
289C22⋊Dic11—21no—
290C22⋊Dic11—21no—
291C22⋊Dic11—21no—
292C22⋊Dic11—22no—
293C22⋊Dic11—44no—
294C22⋊Dic11—44no—
295C22⋊Dic11—82no—
296C22⋊Dic11C2×D412yescomplemented
297(C2×D11)⋊C4—21no—
298(C2×D11)⋊C4—21no—
299(C2×D11)⋊C4—22no—
300(C2×D11)⋊C4—22no—
301C4⋊Dic11—21no—
302C4⋊Dic11—21no—
303C4⋊Dic11—42no—
304Dic11⋊C4—21no—
305Dic11⋊C4—21no—
306C4×Dic11—21no—
307C4×Dic11—21no—
308C4×Dic11—42no—
309C2×D42—111no—
310C22×#99—112no—
311D4×C22⋊C4—111no—
312D4×C22⋊C4D1111yescharacteristic, complemented
313#1964—111no—
314#1964—111no—
315#1898—112no—
316#1898—112no—
317#1799—111no—
318#1781—112no—
319C4×#99—111no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—24no—
327C23×C11—24no—
328C23×C11—24no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—42no—
336C23×C11—41no—
337C23×C11—42no—
338C23×C11—42no—
339C23×C11—41no—
340C23×C11—42no—
341C23×C11—42no—
342C23×C11—42no—
343C23×C11—42no—
344C23×C11—42no—
345C23×C11—42no—
346C23×C11—84no—
347C23×C11—84no—
348C23×C11—84no—
349C23×C11—84no—
350C23×C11C2×C22⋊C412yes—
351C23×C11C2×C22⋊C412yes—
352C23×C11C2×C22⋊C412yes—
353C23×C11C2×C22⋊C412yes—
354C23×C11C23×C411yescharacteristic
355C23×C11C22×D411yescharacteristic
356C23×C11C22×D411yescharacteristic
357C23×C11C22×D411yescharacteristic
358C23×C11C2×#4111yescharacteristic
359C23×C11H(5,𝔽2)11yescharacteristic
360C23×C11H(5,𝔽2)11yescharacteristic
361C22×D11—21no—
362C22×D11—21no—
363C22×D11—22no—
364C22×D11—22no—
365C22×D11—22no—
366C22×D11—44no—
367C22×D11—44no—
368C22×D11—41no—
369C22×D11—41no—
370C22×D11—44no—
371C22×D11—44no—
372C22×D11—42no—
373C22×D11—42no—
374C22×D11—82no—
375C22×D11—82no—
376C22×D11—88no—
377C22×D11—88no—
378C22×D11C4×D412yescomplemented
379D4×C11—24no—
380D4×C11—24no—
381D4×C11—24no—
382D4×C11—22no—
383D4×C11—22no—
384D4×C11—22no—
385D4×C11—42no—
386D4×C11—42no—
387D4×C11—42no—
388D4×C11#9914yescomplemented
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—41no—
398C2×C4×C11—41no—
399C2×C4×C11—42no—
400C2×C4×C11—41no—
401C2×C4×C11—42no—
402C2×C4×C11—42no—
403C2×C4×C11—41no—
404C2×C4×C11—88no—
405C2×C4×C11C2×C22⋊C411yescharacteristic
406C2×C4×C11C2×C22⋊C411yescharacteristic
407C2×C4×C11C2×C22⋊C411yescharacteristic
408C2×C4×C11C2×C22⋊C411yescharacteristic
409C22⋊D11—22no—
410C22⋊D11—22no—
411C22⋊D11—22no—
412C22⋊D11—22no—
413C22⋊D11—44no—
414C22⋊D11—44no—
415C22⋊D11—44no—
416C22⋊D11—44no—
417C22⋊D11—44no—
418C22⋊D11—42no—
419C22⋊D11—42no—
420C22⋊D11—42no—
421C22⋊D11—42no—
422C22⋊D11—44no—
423C22⋊D11—82no—
424C22⋊D11—82no—
425C2×Dic11—21no—
426C2×Dic11—21no—
427C2×Dic11—21no—
428C2×Dic11—21no—
429C2×Dic11—22no—
430C2×Dic11—22no—
431C2×Dic11—22no—
432C2×Dic11—22no—
433C2×Dic11—44no—
434C2×Dic11—44no—
435C2×Dic11—41no—
436C2×Dic11—41no—
437C2×Dic11—41no—
438C2×Dic11—41no—
439C2×Dic11—41no—
440C2×Dic11—42no—
441C2×Dic11—41no—
442C2×Dic11—42no—
443C2×Dic11—42no—
444C2×Dic11—41no—
445C2×Dic11—88no—
446C2×Dic11C4×D412yescomplemented
447D44—42no—
448D44—42no—
449C4×D11—42no—
450C4×D11—42no—
451C23×D4—112no—
452C23×D4—111no—
453C23×D4C2×D1111yescharacteristic
454D42—221no—
455D42—222no—
456D42—221no—
457D42—221no—
458D42—222no—
459D42—221no—
460C2×#127—111no—
461C2×#121—111no—
462C2×#121—112no—
463C2×#121—111no—
464C2×#120—112no—
465C2×#120—112no—
466C2×C4×D4—21no—
467C2×C4×D4—111no—
468C2×C4×D4—111no—
469C2×C4×D4—221no—
470C22×C22⋊C4—112no—
471C22×C22⋊C4C2×D1112yescomplemented
472C2×#99—111no—
473C2×#99—112no—
474C2×#99—112no—
475C2×#99—112no—
476C2×#99—111no—
477C2×#99—112no—
478C2×#99—112no—
479C2×#99—228no—
480#390—21no—
481#390—221no—
482#386—22no—
483#386—222no—
484#380—111no—
485#380C2×D1111yescharacteristic, complemented
486#379—112no—
487#379C2×D1112yescomplemented
488C4×C22⋊C4—111no—
489C4×C22⋊C4C2×D1111yescharacteristic, complemented
490#342—112no—
491#342—111no—
492#342—111no—
493C22×C11—22no—
494C22×C11—21no—
495C22×C11—21no—
496C22×C11—21no—
497C22×C11—21no—
498C22×C11—21no—
499C22×C11—22no—
500C22×C11—21no—
501C22×C11—22no—
502C22×C11—22no—
503C22×C11—22no—
504C22×C11—22no—
505C22×C11—22no—
506C22×C11—22no—
507C22×C11—22no—
508C22×C11—22no—
509C22×C11—22no—
510C22×C11—41no—
511C22×C11—41no—
512C22×C11—41no—
513C22×C11—41no—
514C22×C11—44no—
515C22×C11—44no—
516C22×C11—44no—
517C22×C11—44no—
518C22×C11—44no—
519C22×C11—44no—
520C22×C11—82no—
521C22×C11—82no—
522C22×C11—82no—
523C22×C11—82no—
524C22×C11—82no—
525C22×C11—82no—
526C22×C11C2×#9914yescomplemented
527C22×C11C22×C22⋊C411yescharacteristic
528C22×C11C2×C4×D411yescharacteristic
529C22×C11#51811yescharacteristic
530C22×C11D4211yescharacteristic
531C22×C11D4211yescharacteristic
532C22×C11#54611yescharacteristic
533C22×C11#54611yescharacteristic
534C2×D11—22no—
535C2×D11—42no—
536C2×D11—41no—
537C2×D11—41no—
538C2×D11—42no—
539C2×D11—42no—
540C2×D11—42no—
541C2×D11—42no—
542C2×D11—88no—
543C2×D11—88no—
544C2×D11—82no—
545C2×D11—82no—
546C4×C11—21no—
547C4×C11—21no—
548C4×C11—21no—
549C4×C11—42no—
550C4×C11—81no—
551C4×C11—82no—
552C4×C11C2×#9912yescomplemented
553Dic11—22no—
554Dic11—42no—
555Dic11—42no—
556Dic11—41no—
557Dic11—41no—
558Dic11—81no—
559Dic11—82no—
560C25—112no—
561C25C22×D1112yes—
562C22×D4—44no—
563C22×D4—111no—
564C22×D4—112no—
565C22×D4—112no—
566C22×D4—112no—
567C22×D4—112no—
568C22×D4—112no—
569C22×D4—111no—
570C22×D4—224no—
571C22×D4—224no—
572C22×D4—222no—
573C22×D4—222no—
574C22×D4—222no—
575C22×D4—222no—
576C22×D4—222no—
577C22×D4—221no—
578C22×D4—221no—
579C22×D4—444no—
580C22×D4—442no—
581C22×D4—442no—
582C22×D4C4×D1111yescharacteristic
583C22×D4C4×D1112yes—
584C22×D4C4×D1111yescharacteristic
585C22×D4D4411yescharacteristic
586C22×D4D4412yes—
587C22×D4D4411yescharacteristic
588C22×D4C22⋊D1111yescharacteristic
589C22×D4C22⋊D1112yes—
590C22×D4C22⋊D1111yescharacteristic
591C23×C4—22no—
592C23×C4—112no—
593C23×C4—111no—
594C23×C4—222no—
595C23×C4C22×D1111yescharacteristic
596#127—221no—
597#127—221no—
598#127—222no—
599#121—221no—
600#121—221no—
601#121—222no—
602#121—222no—
603#121—222no—
604#121—222no—
605#121—222no—
606#121—221no—
607#121—221no—
608#121—221no—
609#121—221no—
610#120—222no—
611#120—222no—
612#120—222no—
613#120—222no—
614#120—222no—
615#120—222no—
616#120—222no—
617#120—222no—
618C4×D4—44no—
619C4×D4—222no—
620C4×D4—221no—
621C4×D4—221no—
622C4×D4—221no—
623C4×D4—221no—
624C4×D4—221no—
625C4×D4—221no—
626C4×D4—444no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—111no—
629C2×C4⋊C4—111no—
630C2×C4⋊C4—221no—
631C2×C22⋊C4—24no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—42no—
636C2×C22⋊C4—111no—
637C2×C22⋊C4—112no—
638C2×C22⋊C4—112no—
639C2×C22⋊C4—111no—
640C2×C22⋊C4—111no—
641C2×C22⋊C4—112no—
642C2×C22⋊C4—112no—
643C2×C22⋊C4—111no—
644C2×C22⋊C4—224no—
645C2×C22⋊C4—222no—
646C2×C22⋊C4—222no—
647C2×C22⋊C4—222no—
648C2×C22⋊C4—442no—
649C2×C22⋊C4C22×D1112yes—
650C2×C22⋊C4C22×D1111yescharacteristic
651C2×C22⋊C4C22×D1111yescharacteristic
652C2×C42—21no—
653C2×C42—111no—
654C2×C42—221no—
655#99—114no—
656#99—224no—
657#99—222no—
658#99—224no—
659#99—224no—
660#99—442no—
661#99—442no—
662#95—21no—
663#95—21no—
664#95—221no—
665#95—221no—
666C2×C11—21no—
667C2×C11—21no—
668C2×C11—21no—
669C2×C11—21no—
670C2×C11—21no—
671C2×C11—21no—
672C2×C11—24no—
673C2×C11—42no—
674C2×C11—42no—
675C2×C11—42no—
676C2×C11D4×C22⋊C411yescharacteristic
677C2×C11C22×#9911yescharacteristic
678C2×C11#288311yescharacteristic
679D11—42no—
680D11—82no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—44no—
686C24—82no—
687C24—111no—
688C24—112no—
689C24—224no—
690C24—222no—
691C24—222no—
692C24—442no—
693C24—444no—
694C24—882no—
695C24C2×C4×D1112yes—
696C24C2×C4×D1112yes—
697C24C2×D4412yes—
698C24C2×D4412yes—
699C24C2×C22⋊D1112yes—
700C24C2×C22⋊D1112yes—
701C24C23×D1111yescharacteristic
702C2×D4—24no—
703C2×D4—24no—
704C2×D4—24no—
705C2×D4—42no—
706C2×D4—42no—
707C2×D4—42no—
708C2×D4—44no—
709C2×D4—44no—
710C2×D4—44no—
711C2×D4—112no—
712C2×D4—112no—
713C2×D4—224no—
714C2×D4—221no—
715C2×D4—221no—
716C2×D4—221no—
717C2×D4—221no—
718C2×D4—224no—
719C2×D4—222no—
720C2×D4—222no—
721C2×D4—222no—
722C2×D4—222no—
723C2×D4—222no—
724C2×D4—222no—
725C2×D4—222no—
726C2×D4—222no—
727C2×D4—222no—
728C2×D4—222no—
729C2×D4—222no—
730C2×D4—222no—
731C2×D4—222no—
732C2×D4—222no—
733C2×D4—221no—
734C2×D4—221no—
735C2×D4—442no—
736C2×D4—442no—
737C2×D4—442no—
738C2×D4—448no—
739C2×D4—444no—
740C2×D4—444no—
741C2×D4—444no—
742C2×D4—444no—
743C2×D4—444no—
744C2×D4—444no—
745C2×D4—444no—
746C2×D4—444no—
747C2×D4—444no—
748C2×D4—444no—
749C2×D4—444no—
750C2×D4—882no—
751C2×D4(C2×D11)⋊C412yes—
752C2×D4(C2×D11)⋊C411yescharacteristic
753C2×D4(C2×D11)⋊C412yes—
754C2×D4(C2×D11)⋊C412yes—
755C2×D4(C2×D11)⋊C411yescharacteristic
756C2×D4(C2×D11)⋊C411yescharacteristic
757C2×D4(C2×D11)⋊C412yes—
758C2×D4(C2×D11)⋊C412yes—
759C2×D4(C2×D11)⋊C412yes—
760C2×D4(C2×D11)⋊C411yescharacteristic
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—22no—
764C22×C4—42no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4—82no—
768C22×C4—111no—
769C22×C4—112no—
770C22×C4—111no—
771C22×C4—111no—
772C22×C4—224no—
773C22×C4—222no—
774C22×C4—222no—
775C22×C4—221no—
776C22×C4—221no—
777C22×C4—221no—
778C22×C4—221no—
779C22×C4—222no—
780C22×C4—442no—
781C22×C4—442no—
782C22×C4—444no—
783C22×C4—444no—
784C22×C4—882no—
785C22×C4C2×C4×D1111yescharacteristic
786C22×C4C2×C4×D1111yescharacteristic
787C22×C4C2×D4411yescharacteristic
788C22×C4C2×D4411yescharacteristic
789C22×C4C2×C22⋊D1111yescharacteristic
790C22×C4C2×C22⋊D1111yescharacteristic
791C4⋊C4—42no—
792C4⋊C4—221no—
793C4⋊C4—221no—
794C4⋊C4—221no—
795C4⋊C4—221no—
796C4⋊C4—442no—
797C22⋊C4—21no—
798C22⋊C4—22no—
799C22⋊C4—22no—
800C22⋊C4—21no—
801C22⋊C4—21no—
802C22⋊C4—44no—
803C22⋊C4—44no—
804C22⋊C4—82no—
805C22⋊C4—112no—
806C22⋊C4—222no—
807C22⋊C4—222no—
808C22⋊C4—222no—
809C22⋊C4—222no—
810C22⋊C4—221no—
811C22⋊C4—221no—
812C22⋊C4—221no—
813C22⋊C4—221no—
814C22⋊C4—221no—
815C22⋊C4—222no—
816C22⋊C4—222no—
817C22⋊C4—222no—
818C22⋊C4—221no—
819C22⋊C4—221no—
820C22⋊C4—222no—
821C22⋊C4—444no—
822C22⋊C4—444no—
823C22⋊C4—882no—
824C22⋊C4D4×D1112yescomplemented
825C42—42no—
826C42—221no—
827C42—221no—
828C42—442no—
829C11D4×#9911yescharacteristic, complemented, Sylow
830C23—22no—
831C23—22no—
832C23—22no—
833C23—24no—
834C23—24no—
835C23—24no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—41no—
846C23—42no—
847C23—42no—
848C23—41no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—84no—
857C23—84no—
858C23—84no—
859C23—84no—
860C23—112no—
861C23—221no—
862C23—221no—
863C23—222no—
864C23—222no—
865C23—222no—
866C23—444no—
867C23—444no—
868C23—441no—
869C23—441no—
870C23—444no—
871C23—442no—
872C23—442no—
873C23—444no—
874C23—882no—
875C23—882no—
876C23—888no—
877C23—888no—
878C23C2×(C2×D11)⋊C412yes—
879C23C2×(C2×D11)⋊C412yes—
880C23C2×(C2×D11)⋊C412yes—
881C23C2×(C2×D11)⋊C412yes—
882C23C22×C4×D1111yescharacteristic
883C23C22×D4411yescharacteristic
884C23C2×D4×D1111yescharacteristic
885C23#6703711yescharacteristic
886C23#41×D1111yescharacteristic
887C23#6704211yescharacteristic
888C23C22×C22⋊D1111yescharacteristic
889D4—24no—
890D4—24no—
891D4—24no—
892D4—22no—
893D4—22no—
894D4—22no—
895D4—42no—
896D4—42no—
897D4—42no—
898D4—222no—
899D4—222no—
900D4—222no—
901D4—222no—
902D4—442no—
903D4—444no—
904D4—444no—
905D4—444no—
906D4—444no—
907D4—444no—
908D4—442no—
909D4—444no—
910D4—442no—
911D4—442no—
912D4—442no—
913D4—442no—
914D4—882no—
915D4—882no—
916D4#6687014yesdirect product factor
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—42no—
928C2×C4—41no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—41no—
932C2×C4—88no—
933C2×C4—112no—
934C2×C4—221no—
935C2×C4—221no—
936C2×C4—221no—
937C2×C4—222no—
938C2×C4—221no—
939C2×C4—222no—
940C2×C4—222no—
941C2×C4—222no—
942C2×C4—442no—
943C2×C4—444no—
944C2×C4—444no—
945C2×C4—441no—
946C2×C4—441no—
947C2×C4—442no—
948C2×C4—441no—
949C2×C4—441no—
950C2×C4—441no—
951C2×C4—442no—
952C2×C4—441no—
953C2×C4—442no—
954C2×C4—442no—
955C2×C4—441no—
956C2×C4—888no—
957C2×C4C2×(C2×D11)⋊C411yescharacteristic
958C2×C4C2×(C2×D11)⋊C411yescharacteristic
959C2×C4C2×(C2×D11)⋊C411yescharacteristic
960C2×C4C2×(C2×D11)⋊C411yescharacteristic
961C22—22no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—21no—
966C22—21no—
967C22—21no—
968C22—22no—
969C22—22no—
970C22—22no—
971C22—22no—
972C22—22no—
973C22—22no—
974C22—22no—
975C22—22no—
976C22—22no—
977C22—22no—
978C22—41no—
979C22—41no—
980C22—41no—
981C22—41no—
982C22—44no—
983C22—44no—
984C22—44no—
985C22—44no—
986C22—44no—
987C22—44no—
988C22—82no—
989C22—82no—
990C22—82no—
991C22—82no—
992C22—82no—
993C22—82no—
994C22—222no—
995C22—442no—
996C22—442no—
997C22—441no—
998C22—441no—
999C22—442no—
1000C22—442no—
1001C22—442no—
1002C22—888no—
1003C22—882no—
1004C22—882no—
1005C22—888no—
1006C22C2×#6687014yescomplemented
1007C22C4×D4×D1111yescharacteristic
1008C22#1062307611yescharacteristic
1009C22D4×D4411yescharacteristic
1010C22#1062308511yescharacteristic
1011C22C22×(C2×D11)⋊C411yescharacteristic
1012C22D4×C22⋊D1111yescharacteristic
1013C22#1062336011yescharacteristic
1014C4—21no—
1015C4—21no—
1016C4—21no—
1017C4—42no—
1018C4—82no—
1019C4—81no—
1020C4—222no—
1021C4—442no—
1022C4—442no—
1023C4—441no—
1024C4—441no—
1025C4—882no—
1026C4—881no—
1027C4C2×#6687012yescomplemented
1028C2—21no—
1029C2—21no—
1030C2—21no—
1031C2—21no—
1032C2—21no—
1033C2—21no—
1034C2—24no—
1035C2—42no—
1036C2—42no—
1037C2—42no—
1038C2—442no—
1039C2—882no—
1040C2D4×(C2×D11)⋊C411yescharacteristic
1041C2C22×#6687011yescharacteristic
1042C2#1307707611yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingD4×C11×C22⋊C4C2
socleC22×C11C22×C22⋊C4
prime radicalC2×D4×C22⋊D11C2
cosocleC24×C11C24
hypercenterD4×C22⋊C4D11
hypocenterC11D4×#99
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×D4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×#66870C2semidirect
3. D4×C22⋊Dic11C2semidirect
4. #13069452C2semidirect
5. #13069451C2semidirect
6. #13069069C2semidirect
7. #13069067C2semidirect
8. #13068601C2semidirect
9. #13068530C2semidirect
10. C4×#66870C2semidirect
11. D4×C11×C22⋊C4C2semidirect
14. C22×D4×D11C4semidirect
16. C22×C11×C22⋊C4C22semidirect
18. C22×C22⋊Dic11C22semidirect
19. C2×#66993C4semidirect
20. C2×#66992C4semidirect
27. C2×#66991C4semidirect
28. C2×#66990C4semidirect
30. C2×D4×Dic11C4semidirect
35. C11×#380C22semidirect
36. C11×#379C22semidirect
37. C4×C11×C22⋊C4C22semidirect
38. #10622860C22semidirect
41. #10622825C22semidirect
42. C4×C22⋊Dic11C22semidirect
47. C2×#66870C22semidirect
48. C2×#66870C22semidirect
49. C2×#66870C22semidirect
50. C2×#66870C22semidirect
51. #10622165C22semidirect
52. #10622165C22semidirect
53. #10622165C22semidirect
55. C24×D11C2×C4semidirect
76. C22×C22⋊D11C2×C4semidirect
77. C22×C22⋊D11C2×C4semidirect
78. C22×C22⋊D11C2×C4semidirect
79. C22×C22⋊D11C2×C4semidirect
83. C23×Dic11C2×C4semidirect
88. C22×D44C2×C4semidirect
89. C22×C4×D11C2×C4semidirect
110. C2×C22⋊Dic11C2×C4semidirect
111. C2×C22⋊Dic11C2×C4semidirect
142. C2×(C2×D11)⋊C4C2×C4semidirect
143. C2×(C2×D11)⋊C4C2×C4semidirect
145. C2×C4⋊Dic11C2×C4semidirect
146. C2×Dic11⋊C4C2×C4semidirect
148. C2×C4×Dic11C2×C4semidirect
159. #66870D4direct (N × H)
280. C11×C22⋊C4C2×D4semidirect
296. C22⋊Dic11C2×D4semidirect
312. D4×C22⋊C4D11semidirect
378. C22×D11C4×D4semidirect
388. D4×C11#99semidirect
446. C2×Dic11C4×D4semidirect
471. C22×C22⋊C4C2×D11semidirect
485. #380C2×D11semidirect
487. #379C2×D11semidirect
489. C4×C22⋊C4C2×D11semidirect
526. C22×C11C2×#99semidirect
552. C4×C11C2×#99semidirect
824. C22⋊C4D4×D11semidirect
829. C11D4×#99semidirect
916. D4#66870direct (N × H)
1006. C22C2×#66870semidirect
1027. C4C2×#66870semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C22⋊D112
C22×#668702
D4×C22⋊Dic112
#130694522
#130694512
#130690692
#130690672
#130686012
#130685302
C4×#668702
D4×C11×C22⋊C42
D4×#9911