Finite Group Databasebeta

← #14769432

Subgroups — #14769432

Order 2816.

1582 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623365C211yesmaximal, characteristic
2C2×#10622741C211yesmaximal, characteristic, complemented
3C2×#10622416C211yesmaximal, characteristic, complemented
4C4⋊C4×C22⋊D11C211yesmaximal, characteristic, complemented
5#13069541C211yesmaximal, characteristic, complemented
6#13069420C211yesmaximal, characteristic, complemented
7#13069054C211yesmaximal, characteristic, complemented
8#13069051C211yesmaximal, characteristic, complemented
9#13068933C211yesmaximal, characteristic, complemented
10#13068930C211yesmaximal, characteristic, complemented
11#13068619C211yesmaximal, characteristic, complemented
12#13068556C211yesmaximal, characteristic, complemented
13#13068555C211yesmaximal, characteristic, complemented
14#103×Dic11C211yesmaximal, characteristic, complemented
15C2×C11×#417C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×#4343C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20#10623365—24no—
21#10623365C418yescomplemented
22C2×Q8×Dic11C2211yescharacteristic
23C2×#66993—21no—
24C2×#66993C2211yescharacteristic
25C2×#66991—21no—
26C2×#66991C2211yescharacteristic
27C2×#66983—21no—
28C2×#66983C2211yescharacteristic
29C2×C4×C22⋊D11—21no—
30C2×C4×C22⋊D11—21no—
31C2×C4×C22⋊D11C2211yescharacteristic
32C22×#4313C2211yescharacteristic
33C2×C4⋊C4×D11C2211yescharacteristic
34C11×#417—24no—
35C2×C11×#103C2211yescharacteristic
36C2×C11×#103C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×#102C2211yescharacteristic
39C2×#66899C2211yescharacteristic
40C2×#66899C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42C2×#66896C2211yescharacteristic
43#10622825C2211yescharacteristic
44#10622823—21no—
45C2×C22⋊(C11⋊C8)C2211yescharacteristic
46#10622741—24no—
47C2×#66885C2211yescharacteristic
48C2×#66885C2211yescharacteristic
49C2×(C2×D11)⋊C8C2211yescharacteristic
50C2×Dic11⋊C8C2211yescharacteristic
51C2×C8×Dic11C2211yescharacteristic
52#10622602—21no—
53#10622600C2211yescharacteristic
54#10622589C2211yescharacteristic
55C4⋊C4×Dic11C2211yescharacteristic
56#10622585—21no—
57C2×#66873C2211yescharacteristic
58C2×#66873C2211yescharacteristic
59#10622416—24no—
60#10622189C2211yescharacteristic
61#10622189C2211yescharacteristic
62#10622167C2211yescharacteristic
63#10622167C2211yescharacteristic
64C2×C11×#41—22no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—41no—
68C2×C11×#41—41no—
69C2×C11×#41C2×C414yescomplemented
70C22×Q8×C11C2311yescharacteristic
71C22×D4×C11—21no—
72C22×D4×C11C2311yescharacteristic
73C23×C4×C11—21no—
74C23×C4×C11—21no—
75C23×C4×C11C2311yescharacteristic
76C22×C22⋊D11—21no—
77C22×C22⋊D11—21no—
78C22×C22⋊D11—21no—
79C22×C22⋊D11—21no—
80C22×C22⋊D11D411yescharacteristic
81C2×#4343—22no—
82C2×#4343—22no—
83C2×#4343—22no—
84C2×#4343—41no—
85C2×#4343—41no—
86C2×#4343C2×C414yescomplemented
87C22×D44—21no—
88C22×D44C2311yescharacteristic
89C22×C4×D11—21no—
90C22×C4×D11—21no—
91C22×C4×D11C2311yescharacteristic
92C2×C11×M16—22no—
93C2×C11×M16—22no—
94C2×C11×M16—41no—
95C22×C8×C11C2311yescharacteristic
96C22×C8×C11C2311yescharacteristic
97C2×C11×C4⋊C4—22no—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4—41no—
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C22⋊Dic11—21no—
103C2×C22⋊Dic11—21no—
104C2×C22⋊Dic11D411yescharacteristic
105Q8×Dic11—22no—
106Q8×Dic11C2×C414yescomplemented
107#66993—28no—
108#66993—22no—
109#66993C2×C414yescomplemented
110#66991—22no—
111#66991—28no—
112#66991C2×C414yescomplemented
113#66983—22no—
114#66983—28no—
115#66983C2×C414yescomplemented
116C4×C22⋊D11—28no—
117C4×C22⋊D11—44no—
118C4×C22⋊D11C2×C414yes—
119C4×C22⋊D11D414yes—
120C2×(C2×D11)⋊C4—21no—
121C2×(C2×D11)⋊C4—21no—
122C2×(C2×D11)⋊C4D411yescharacteristic
123C2×C4⋊Dic11—21no—
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2311yescharacteristic
126C2×C4⋊Dic11C2311yescharacteristic
127C2×Dic11⋊C4—21no—
128C2×Dic11⋊C4—21no—
129C2×Dic11⋊C4—21no—
130C2×Dic11⋊C4D411yescharacteristic
131C2×C4×Dic11—21no—
132C2×C4×Dic11—21no—
133C2×C4×Dic11C2311yescharacteristic
134C22×C11⋊C8C2311yescharacteristic
135C22×C11⋊C8C2311yescharacteristic
136C2×#4313—22no—
137C2×#4313—22no—
138C2×#4313—41no—
139C4⋊C4×D11—22no—
140C4⋊C4×D11—41no—
141C11×#103—22no—
142C11×#103D414yescomplemented
143C11×#102—22no—
144C11×#102—22no—
145#66899—22no—
146#66899—22no—
147#66896—41no—
148#66896—41no—
149C11⋊#95—21no—
150C11⋊#95—21no—
151C11⋊#95—21no—
152C22⋊(C11⋊C8)—22no—
153#66885—22no—
154#66885—41no—
155(C2×D11)⋊C8—22no—
156Dic11⋊C8—22no—
157C8×Dic11—22no—
158#66873—22no—
159#66873—41no—
160#22432—111nomaximal, Sylow
161C24×C11—21no—
162C24×C11C2×D411yescharacteristic
163C23×D11—21no—
164C23×D11C2×D411yescharacteristic
165C11×#41—28no—
166C11×#41—44no—
167C11×#41—44no—
168C11×#41—44no—
169C2×Q8×C11—21no—
170C2×Q8×C11—21no—
171C2×Q8×C11—21no—
172C2×Q8×C11C22×C412yes—
173C2×Q8×C11C2×D412yes—
174C2×Q8×C11#4112yes—
175C2×D4×C11—24no—
176C2×D4×C11—21no—
177C2×D4×C11—21no—
178C2×D4×C11—21no—
179C2×D4×C11—21no—
180C2×D4×C11—21no—
181C2×D4×C11—42no—
182C2×D4×C11—42no—
183C2×D4×C11C22×C412yes—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—24no—
191C22×C4×C11—21no—
192C22×C4×C11—42no—
193C22×C4×C11—42no—
194C22×C4×C11—42no—
195C22×C4×C11—42no—
196C22×C4×C11—81no—
197C22×C4×C11C22×C412yes—
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2×D412yes—
200C22×C4×C11C2411yescharacteristic
201C2×C22⋊D11—24no—
202C2×C22⋊D11—24no—
203C2×C22⋊D11—22no—
204C2×C22⋊D11—22no—
205C2×C22⋊D11—24no—
206C2×C22⋊D11—24no—
207C2×C22⋊D11—42no—
208C2×C22⋊D11—42no—
209C2×C22⋊D11—81no—
210C2×C22⋊D11—81no—
211C2×C22⋊D11—81no—
212C2×C22⋊D11—81no—
213C2×C22⋊D11—81no—
214C2×C22⋊D11—81no—
215C2×C22⋊D11C22⋊C414yes—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11C2×D411yescharacteristic
220C22×Dic11C2×D411yescharacteristic
221C22×Dic11C2×D411yescharacteristic
222#4343—28no—
223#4343—44no—
224#4343—44no—
225#4343—44no—
226C2×D44—24no—
227C2×D44—21no—
228C2×D44—21no—
229C2×D44—21no—
230C2×D44—21no—
231C2×D44—21no—
232C2×D44—42no—
233C2×D44—42no—
234C2×D44C22×C412yes—
235C2×C4×D11—24no—
236C2×C4×D11—21no—
237C2×C4×D11—21no—
238C2×C4×D11—21no—
239C2×C4×D11—21no—
240C2×C4×D11—42no—
241C2×C4×D11—42no—
242C2×C4×D11—42no—
243C2×C4×D11—42no—
244C2×C4×D11—81no—
245C2×C4×D11C22×C412yes—
246C2×C4×D11C2×D412yes—
247C11×M16—44no—
248C2×C8×C11—21no—
249C2×C8×C11—21no—
250C2×C8×C11—21no—
251C2×C8×C11—21no—
252C2×C8×C11—21no—
253C2×C8×C11C2×D412yes—
254C11×C4⋊C4—21no—
255C11×C4⋊C4—21no—
256C11×C4⋊C4—21no—
257C11×C4⋊C4—42no—
258C11×C4⋊C4C2×D412yes—
259C22⋊Dic11—24no—
260C22⋊Dic11—42no—
261C22⋊Dic11C22⋊C414yes—
262(C2×D11)⋊C4—24no—
263(C2×D11)⋊C4—42no—
264(C2×D11)⋊C4C22⋊C414yes—
265C4⋊Dic11—24no—
266C4⋊Dic11—21no—
267C4⋊Dic11—21no—
268C4⋊Dic11—21no—
269C4⋊Dic11—21no—
270C4⋊Dic11—21no—
271C4⋊Dic11C22×C412yes—
272Dic11⋊C4—42no—
273Dic11⋊C4—42no—
274Dic11⋊C4—81no—
275Dic11⋊C4C22⋊C414yes—
276C4×Dic11—24no—
277C4×Dic11—42no—
278C4×Dic11C22×C412yes—
279C4×Dic11C2×D412yes—
280C2×C11⋊C8—21no—
281C2×C11⋊C8—21no—
282C2×C11⋊C8—21no—
283C2×C11⋊C8—21no—
284C2×C11⋊C8—21no—
285C2×C11⋊C8—21no—
286#4313—44no—
287C2×#550—111no—
288C2×#436—111no—
289C2×#417—111no—
290C2×#417D1111yescharacteristic, complemented
291D4×C4⋊C4—111no—
292#1982—111no—
293#1957—111no—
294#1895—111no—
295#1895—111no—
296#1874—111no—
297#1874—111no—
298#1803—111no—
299#1788—111no—
300#1788—111no—
301C4×#103—111no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—21no—
305C23×C11—21no—
306C23×C11—21no—
307C23×C11—21no—
308C23×C11—22no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—41no—
315C23×C11C2×C22⋊C412yes—
316C23×C11C22×D411yescharacteristic
317C22×D11—21no—
318C22×D11—21no—
319C22×D11—21no—
320C22×D11—21no—
321C22×D11—21no—
322C22×D11—21no—
323C22×D11—22no—
324C22×D11—41no—
325C22×D11—41no—
326C22×D11—41no—
327C22×D11—41no—
328C22×D11—41no—
329C22×D11—41no—
330C22×D11C2×C22⋊C412yes—
331Q8×C11—22no—
332Q8×C11—22no—
333Q8×C11—22no—
334Q8×C11C4×D414yescomplemented
335D4×C11—22no—
336D4×C11—22no—
337D4×C11—48no—
338D4×C11—41no—
339D4×C11—41no—
340C2×C4×C11—22no—
341C2×C4×C11—21no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—21no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—48no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—84no—
357C2×C4×C11C2×C22⋊C412yes—
358C2×C4×C11C23×C411yescharacteristic
359C2×C4×C11C22×D411yescharacteristic
360C2×C4×C11C22×D411yescharacteristic
361C2×C4×C11C2×#4111yescharacteristic
362C2×C4×C11H(5,𝔽2)11yescharacteristic
363C2×C4×C11H(5,𝔽2)11yescharacteristic
364C22⋊D11—28no—
365C22⋊D11—48no—
366C22⋊D11—84no—
367C22⋊D11—84no—
368C22⋊D11—84no—
369C2×Dic11—21no—
370C2×Dic11—21no—
371C2×Dic11—21no—
372C2×Dic11—21no—
373C2×Dic11—22no—
374C2×Dic11—41no—
375C2×Dic11—41no—
376C2×Dic11—41no—
377C2×Dic11—41no—
378C2×Dic11—41no—
379C2×Dic11—41no—
380C2×Dic11—41no—
381C2×Dic11—41no—
382C2×Dic11C2×C22⋊C412yes—
383C2×Dic11C2×C22⋊C412yes—
384C2×Dic11C2×C22⋊C412yes—
385C2×Dic11AGL(1,ℤ/8)12yes—
386C2×Dic11#13712yes—
387D44—22no—
388D44—22no—
389D44—48no—
390D44—41no—
391D44—41no—
392C4×D11—22no—
393C4×D11—22no—
394C4×D11—22no—
395C4×D11—22no—
396C4×D11—48no—
397C4×D11—84no—
398C8×C11—22no—
399C8×C11—41no—
400C11⋊C8—41no—
401C11⋊C8—41no—
402C22×#41—111no—
403C22×#41C2×D1111yescharacteristic
404C22×M16—111no—
405C22×M16C2×D1111yescharacteristic
406#550—118no—
407#550—224no—
408C2×#127—111no—
409C2×#127—221no—
410C2×#121—111no—
411C2×#121—111no—
412C2×#121—221no—
413C2×#121—221no—
414C2×C4×Q8—111no—
415C2×C4×D4—111no—
416C2×C4×D4—221no—
417C2×C4×D4—221no—
418C22×C4⋊C4—111no—
419C22×C4⋊C4C2×D1111yescharacteristic
420#436—224no—
421C2×C4⋊C8—111no—
422#417—24no—
423#417—224no—
424C2×#103—111no—
425C2×#103—111no—
426C2×#103C2×D1111yescharacteristic
427C2×#103C2×D1111yescharacteristic
428C2×#102—111no—
429C2×#102—111no—
430C2×#102—111no—
431C2×#102—111no—
432C2×#102—111no—
433C2×#102—111no—
434C2×#102C2×D1111yescharacteristic
435C2×#102C2×D1111yescharacteristic
436C2×C22⋊C8—111no—
437C2×C22⋊C8—111no—
438C2×C4×C8—111no—
439#389—221no—
440#385—221no—
441#385—221no—
442#384—111no—
443#380—111no—
444#380—111no—
445C4×C4⋊C4—111no—
446#340—111no—
447#340—111no—
448#340—111no—
449#340—111no—
450C22×C11—22no—
451C22×C11—22no—
452C22×C11—22no—
453C22×C11—41no—
454C22×C11—41no—
455C22×C11—41no—
456C22×C11—41no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—81no—
461C22×C11—81no—
462C22×C11—81no—
463C22×C11—81no—
464C22×C11C22×C22⋊C411yescharacteristic
465C22×C11D4211yescharacteristic
466C22×C11#54611yescharacteristic
467C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
468C22×C11C2×#13711yescharacteristic
469C22×C11#57611yescharacteristic
470C22×C11#57711yescharacteristic
471C2×D11—22no—
472C2×D11—22no—
473C2×D11—22no—
474C2×D11—41no—
475C2×D11—41no—
476C2×D11—41no—
477C2×D11—41no—
478C2×D11—42no—
479C2×D11—42no—
480C2×D11—42no—
481C2×D11—81no—
482C2×D11—81no—
483C2×D11—81no—
484C2×D11—81no—
485C4×C11—22no—
486C4×C11—24no—
487C4×C11—42no—
488C4×C11—81no—
489C4×C11C2×C4×D411yescharacteristic
490C4×C11#51811yescharacteristic
491C4×C11D4211yescharacteristic
492C4×C11#54611yescharacteristic
493Dic11—22no—
494Dic11—22no—
495Dic11—42no—
496Dic11—81no—
497Dic11—81no—
498Dic11#41714yescomplemented
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—114no—
505C2×#41—222no—
506C2×#41—222no—
507C2×#41—222no—
508C2×#41—441no—
509C2×#41—441no—
510C2×#41C4×D1114yescomplemented
511C22×Q8C22×D1111yescharacteristic
512C22×D4—21no—
513C22×D4—111no—
514C22×D4—111no—
515C22×D4—221no—
516C22×D4—221no—
517C22×D4—221no—
518C22×D4—221no—
519C22×D4—221no—
520C22×D4C22×D1111yescharacteristic
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—111no—
524C23×C4—221no—
525C23×C4—221no—
526C23×C4C22×D1111yescharacteristic
527C2×M16—22no—
528C2×M16—22no—
529C2×M16—41no—
530C2×M16—222no—
531C2×M16—222no—
532C2×M16—441no—
533C22×C8—111no—
534C22×C8—111no—
535C22×C8C22×D1111yescharacteristic
536C22×C8C22×D1111yescharacteristic
537#127—114no—
538#127—222no—
539#127—228no—
540#121—114no—
541#121—114no—
542#121—228no—
543#121—228no—
544#121—222no—
545#121—222no—
546C4×Q8—114no—
547C4×Q8—222no—
548C4×D4—114no—
549C4×D4—114no—
550C4×D4—228no—
551C4×D4—444no—
552C2×C4⋊C4—22no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—41no—
555C2×C4⋊C4—111no—
556C2×C4⋊C4—111no—
557C2×C4⋊C4—111no—
558C2×C4⋊C4—111no—
559C2×C4⋊C4—221no—
560C2×C4⋊C4—222no—
561C2×C4⋊C4—221no—
562C2×C4⋊C4—221no—
563C2×C4⋊C4—221no—
564C2×C4⋊C4—441no—
565C2×C4⋊C4C22×D1111yescharacteristic
566C2×C4⋊C4C22×D1111yescharacteristic
567C2×C22⋊C4—111no—
568C2×C22⋊C4—111no—
569C2×C22⋊C4—221no—
570C2×C22⋊C4—221no—
571C2×C22⋊C4—221no—
572C2×C22⋊C4—221no—
573C2×C42—111no—
574C2×C42—221no—
575C2×C42—221no—
576C4⋊C8—222no—
577#103—22no—
578#103—222no—
579#103—222no—
580#103C22⋊D1114yescomplemented
581#102—22no—
582#102—22no—
583#102—222no—
584#102—222no—
585#102—441no—
586#102—441no—
587#102—441no—
588#102—441no—
589C22⋊C8—222no—
590C22⋊C8—222no—
591C4×C8—222no—
592#95—221no—
593#95—221no—
594#95—221no—
595C2×C11—42no—
596C2×C11—82no—
597C2×C11D4×C22⋊C411yescharacteristic
598C2×C11C2×#41711yescharacteristic
599C2×C11#289711yescharacteristic
600C2×C11#327411yescharacteristic
601C2×C11#327811yescharacteristic
602C2×C11#333211yescharacteristic
603C2×C11#333311yescharacteristic
604D11—42no—
605D11—82no—
606C24—21no—
607C24—111no—
608C24—221no—
609C24D4×D1111yescharacteristic
610#41—28no—
611#41—44no—
612#41—44no—
613#41—44no—
614#41—228no—
615#41—444no—
616#41—444no—
617#41—444no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8C2×C4×D1112yes—
622C2×Q8#433912yes—
623C2×Q8C2×C22⋊D1112yes—
624C2×D4—24no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—114no—
633C2×D4—112no—
634C2×D4—224no—
635C2×D4—222no—
636C2×D4—222no—
637C2×D4—224no—
638C2×D4—224no—
639C2×D4—224no—
640C2×D4—224no—
641C2×D4—221no—
642C2×D4—221no—
643C2×D4—221no—
644C2×D4—221no—
645C2×D4—221no—
646C2×D4—442no—
647C2×D4—442no—
648C2×D4—442no—
649C2×D4—442no—
650C2×D4—881no—
651C2×D4—881no—
652C2×D4—881no—
653C2×D4—881no—
654C2×D4—881no—
655C2×D4—881no—
656C2×D4C2×C4×D1112yes—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—24no—
664C22×C4—21no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—42no—
669C22×C4—81no—
670C22×C4—111no—
671C22×C4—111no—
672C22×C4—111no—
673C22×C4—112no—
674C22×C4—112no—
675C22×C4—224no—
676C22×C4—221no—
677C22×C4—221no—
678C22×C4—221no—
679C22×C4—221no—
680C22×C4—221no—
681C22×C4—221no—
682C22×C4—221no—
683C22×C4—442no—
684C22×C4—442no—
685C22×C4—442no—
686C22×C4—442no—
687C22×C4—881no—
688C22×C4C2×C4×D1112yes—
689C22×C4D4×D1111yescharacteristic
690C22×C4D4×D1112yes—
691C22×C4C23×D1111yescharacteristic
692M16—44no—
693M16—444no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—221no—
700C2×C8—221no—
701C2×C8—221no—
702C2×C8—221no—
703C2×C8—221no—
704C2×C8—221no—
705C2×C8C2×C22⋊D1112yes—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—42no—
710C4⋊C4—114no—
711C4⋊C4—112no—
712C4⋊C4—224no—
713C4⋊C4—221no—
714C4⋊C4—221no—
715C4⋊C4—221no—
716C4⋊C4—221no—
717C4⋊C4—221no—
718C4⋊C4—442no—
719C4⋊C4—442no—
720C4⋊C4—881no—
721C4⋊C4C2×C22⋊D1112yes—
722C22⋊C4—114no—
723C22⋊C4—114no—
724C22⋊C4—224no—
725C22⋊C4—224no—
726C22⋊C4—442no—
727C22⋊C4—442no—
728C42—112no—
729C42—112no—
730C42—224no—
731C42—442no—
732C11#2243211yescharacteristic, complemented, Sylow
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—22no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—112no—
747C23—221no—
748C23—221no—
749C23—221no—
750C23—221no—
751C23—221no—
752C23—221no—
753C23—222no—
754C23—441no—
755C23—441no—
756C23—441no—
757C23—441no—
758C23—441no—
759C23—441no—
760C23C22⋊C4×D1112yes—
761C23C2×D4×D1111yescharacteristic
762Q8—22no—
763Q8—22no—
764Q8—22no—
765Q8C4×C22⋊D1114yescomplemented
766D4—22no—
767D4—22no—
768D4—48no—
769D4—41no—
770D4—41no—
771D4—228no—
772D4—222no—
773D4—222no—
774D4—448no—
775D4—448no—
776D4—441no—
777D4—441no—
778D4—884no—
779D4—884no—
780D4—884no—
781C2×C4—22no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—21no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—48no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—84no—
798C2×C4—112no—
799C2×C4—112no—
800C2×C4—112no—
801C2×C4—112no—
802C2×C4—112no—
803C2×C4—221no—
804C2×C4—221no—
805C2×C4—221no—
806C2×C4—221no—
807C2×C4—222no—
808C2×C4—222no—
809C2×C4—222no—
810C2×C4—222no—
811C2×C4—222no—
812C2×C4—448no—
813C2×C4—441no—
814C2×C4—441no—
815C2×C4—441no—
816C2×C4—441no—
817C2×C4—441no—
818C2×C4—441no—
819C2×C4—441no—
820C2×C4—441no—
821C2×C4—884no—
822C2×C4C22⋊C4×D1112yes—
823C2×C4C22×C4×D1111yescharacteristic
824C2×C4C2×#433911yescharacteristic
825C2×C4C2×D4×D1111yescharacteristic
826C2×C4#6703711yescharacteristic
827C2×C4#6703711yescharacteristic
828C2×C4C22×C22⋊D1111yescharacteristic
829C8—22no—
830C8—41no—
831C8—441no—
832C8—441no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—222no—
848C22—222no—
849C22—222no—
850C22—441no—
851C22—441no—
852C22—441no—
853C22—441no—
854C22—442no—
855C22—442no—
856C22—442no—
857C22—881no—
858C22—881no—
859C22—881no—
860C22—881no—
861C22C2×C22⋊C4×D1111yescharacteristic
862C22#1062302111yescharacteristic
863C22D11×AGL(1,ℤ/8)11yescharacteristic
864C22#1062330511yescharacteristic
865C22D11×#13711yescharacteristic
866C22#1062330911yescharacteristic
867C22D4×C22⋊D1111yescharacteristic
868C4—22no—
869C4—24no—
870C4—42no—
871C4—81no—
872C4—114no—
873C4—222no—
874C4—222no—
875C4—442no—
876C4—881no—
877C4—881no—
878C4#1062301711yescharacteristic
879C4#1062302111yescharacteristic
880C4C2×C4×C22⋊D1111yescharacteristic
881C4D4×C22⋊D1111yescharacteristic
882C2—42no—
883C2—82no—
884C2—442no—
885C2—882no—
886C2C22⋊C4×C22⋊D1111yescharacteristic
887C2D11×#41711yescharacteristic
888C2#1307714011yescharacteristic
889C2#1308023011yescharacteristic
890C2#1308027611yescharacteristic
891C2#1308093911yescharacteristic
892C2#1308095011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#417C2
socleC23×C11C22×D4
prime radicalC2×#10623365C2
cosocleC22×C4×C11C24
hypercenterC2×#417D11
hypocenterC11#22432
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C2×#10622741C2semidirect
3. C2×#10622416C2semidirect
4. C4⋊C4×C22⋊D11C2semidirect
5. #13069541C2semidirect
6. #13069420C2semidirect
7. #13069054C2semidirect
8. #13069051C2semidirect
9. #13068933C2semidirect
10. #13068930C2semidirect
11. #13068619C2semidirect
12. #13068556C2semidirect
13. #13068555C2semidirect
14. #103×Dic11C2semidirect
15. C2×C11×#417C2semidirect
21. #10623365C4semidirect
69. C2×C11×#41C2×C4semidirect
86. C2×#4343C2×C4semidirect
106. Q8×Dic11C2×C4semidirect
109. #66993C2×C4semidirect
112. #66991C2×C4semidirect
115. #66983C2×C4semidirect
142. C11×#103D4semidirect
290. C2×#417D11semidirect
334. Q8×C11C4×D4semidirect
498. Dic11#417semidirect
510. C2×#41C4×D11semidirect
580. #103C22⋊D11semidirect
732. C11#22432semidirect
765. Q8C4×C22⋊D11semidirect

Maximal subgroups

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

subgroupindex
C2×#106233652
C2×#106227412
C2×#106224162
C4⋊C4×C22⋊D112
#130695412
#130694202
#130690542
#130690512
#130689332
#130689302
#130686192
#130685562
#130685552
#103×Dic112
C2×C11×#4172
#2243211