Finite Group Databasebeta

← #14759508

Subgroups — #14759508

Order 2816.

1560 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623329C211yesmaximal, characteristic
2C2×#10622777C211yesmaximal, characteristic, complemented
3C2×SD16×Dic11C211yesmaximal, characteristic, complemented
4#13071300C211yesmaximal, characteristic, complemented
5#13068952C211yesmaximal, characteristic, complemented
6#13068952C211yesmaximal, characteristic, complemented
7#13068929C211yesmaximal, characteristic, complemented
8#13068879C211yesmaximal, characteristic, complemented
9#13068865C211yesmaximal, characteristic, complemented
10#13068817C211yesmaximal, characteristic, complemented
11#13068547C211yesmaximal, characteristic
12#13068443C211yesmaximal, characteristic, complemented
13#102×Dic11C211yesmaximal, characteristic, complemented
14#13068384C211yesmaximal, characteristic, complemented
15C2×C11×#450C211yesmaximal, characteristic
16C23×D4×C11C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C22×C22⋊Dic11—21no—
21C22×C22⋊Dic11—21no—
22C2×Q8×Dic11C2211yescharacteristic, complemented
23#10623329—24no—
24#10623329—24no—
25C2×D4×Dic11—21no—
26C2×D4×Dic11—21no—
27C2×D4×Dic11C2211yescharacteristic
28C2×D4×Dic11C2211yescharacteristic
29C2×D4×Dic11C2211yescharacteristic
30C2×D4×Dic11C2211yescharacteristic
31C2×#66979C2211yescharacteristic
32C2×#66979C2211yescharacteristic
33C11×#450C418yescomplemented
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37#10622843C2211yescharacteristic, complemented
38C2×#66899C2211yescharacteristic, complemented
39C2×#66899C2211yescharacteristic, complemented
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42C2×#66896C2211yescharacteristic
43C2×#66896C2211yescharacteristic
44#10622825C2211yescharacteristic
45C2×C22⋊(C11⋊C8)C2211yescharacteristic
46#10622777—24no—
47SD16×Dic11—24no—
48C2×#66882C2211yescharacteristic, complemented
49C2×#66881C2211yescharacteristic, complemented
50C2×#66879C2211yescharacteristic, complemented
51C2×C8×Dic11C2211yescharacteristic, complemented
52#10622598—21no—
53#10622598C2211yescharacteristic, complemented
54#10622594—21no—
55C4⋊C4×Dic11C2211yescharacteristic, complemented
56#10622564—21no—
57#10622564—21no—
58#10622189C2211yescharacteristic, complemented
59#10622189C2211yescharacteristic, complemented
60#10622188C2211yescharacteristic, complemented
61#10622188C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63#10622167C2211yescharacteristic, complemented
64C25×C11—21no—
65C22×Q8×C11C2311yescharacteristic
66C22×D4×C11—22no—
67C22×D4×C11—22no—
68C22×D4×C11—22no—
69C22×D4×C11—22no—
70C22×D4×C11—21no—
71C22×D4×C11—22no—
72C22×D4×C11C2×C414yes—
73C22×D4×C11C2311yescharacteristic
74C22×D4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×Dic11—21no—
77C23×Dic11—21no—
78C23×Dic11—21no—
79C23×Dic11—21no—
80C2×C11×SD16—22no—
81C2×C11×SD16—22no—
82C2×C11×SD16—22no—
83C2×C11×SD16—22no—
84C2×C11×SD16C2×C414yescomplemented
85C2×C11×SD16C2×C414yescomplemented
86C22×C8×C11C2311yescharacteristic
87C22×C8×C11C2311yescharacteristic
88C11×C22⋊Q8—22no—
89C11×C22⋊Q8C2×C414yescomplemented
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C22⋊C4—21no—
93C2×C22⋊Dic11—28no—
94C2×C22⋊Dic11—28no—
95C2×C22⋊Dic11—21no—
96C2×C22⋊Dic11—21no—
97C2×C22⋊Dic11—21no—
98C2×C22⋊Dic11—21no—
99C2×C22⋊Dic11—21no—
100C2×C22⋊Dic11—21no—
101C2×C22⋊Dic11D411yescharacteristic
102C2×C22⋊Dic11D411yescharacteristic
103Q8×Dic11—22no—
104Q8×Dic11—22no—
105D4×Dic11—28no—
106D4×Dic11—28no—
107D4×Dic11—22no—
108D4×Dic11—22no—
109D4×Dic11—22no—
110D4×Dic11—22no—
111D4×Dic11—22no—
112D4×Dic11—22no—
113D4×Dic11D414yes—
114D4×Dic11D414yes—
115#66979—22no—
116#66979—22no—
117#66979—22no—
118#66979—22no—
119C2×C4⋊Dic11—21no—
120C2×C4⋊Dic11—21no—
121C2×C4⋊Dic11D411yescharacteristic
122C2×C4⋊Dic11D411yescharacteristic
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2311yescharacteristic
126C2×C4⋊Dic11C2311yescharacteristic
127C2×C4×Dic11—21no—
128C2×C4×Dic11—21no—
129C2×C4×Dic11—21no—
130C2×C4×Dic11C2311yescharacteristic
131C2×C4×Dic11C2311yescharacteristic
132C22×C11⋊C8C2311yescharacteristic
133C22×C11⋊C8C2311yescharacteristic
134C11×#102C2×C414yescomplemented
135C11×#102C2×C414yescomplemented
136C11×C22⋊C8C2×C414yescomplemented
137#66899—22no—
138#66899—22no—
139#66896—22no—
140#66896—22no—
141#66896—22no—
142#66896—22no—
143C11⋊#95—21no—
144C11⋊#95—21no—
145C11⋊#95—21no—
146C11⋊#95—21no—
147C11⋊#95—21no—
148C22⋊(C11⋊C8)—22no—
149#66882—22no—
150#66881—22no—
151#66879—22no—
152C8×Dic11—22no—
153#21459—111nomaximal, Sylow
154C24×C11—24no—
155C24×C11—24no—
156C24×C11—21no—
157C24×C11—21no—
158C24×C11—24no—
159C24×C11—81no—
160C24×C11—81no—
161C24×C11—81no—
162C24×C11—81no—
163C24×C11C2×D411yescharacteristic
164C2×Q8×C11—21no—
165C2×Q8×C11—21no—
166C2×Q8×C11—21no—
167C2×Q8×C11—21no—
168C2×Q8×C11—21no—
169C2×Q8×C11C22×C412yes—
170C2×D4×C11—24no—
171C2×D4×C11—24no—
172C2×D4×C11—28no—
173C2×D4×C11—28no—
174C2×D4×C11—28no—
175C2×D4×C11—28no—
176C2×D4×C11—24no—
177C2×D4×C11—21no—
178C2×D4×C11—21no—
179C2×D4×C11—21no—
180C2×D4×C11—21no—
181C2×D4×C11—21no—
182C2×D4×C11—21no—
183C2×D4×C11C22×C412yes—
184C2×D4×C11C22×C412yes—
185C2×D4×C11C2×D412yes—
186C2×D4×C11C2×D412yes—
187C2×D4×C11#4112yes—
188C2×D4×C11#4112yes—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11C22×C412yes—
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11#4112yes—
198C22×C4×C11C2411yescharacteristic
199C22×Dic11—24no—
200C22×Dic11—24no—
201C22×Dic11—24no—
202C22×Dic11—24no—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—81no—
208C22×Dic11—81no—
209C22×Dic11—81no—
210C22×Dic11—81no—
211C22×Dic11—81no—
212C22×Dic11—81no—
213C22×Dic11—81no—
214C22×Dic11—81no—
215C22×Dic11C2×D411yescharacteristic
216C22×Dic11C2×D411yescharacteristic
217C22×Dic11C2×D411yescharacteristic
218C22×Dic11C2×D411yescharacteristic
219C11×SD16—28no—
220C11×SD16—28no—
221C2×C8×C11—21no—
222C2×C8×C11—21no—
223C2×C8×C11—21no—
224C2×C8×C11—21no—
225C2×C8×C11C22×C412yes—
226C2×C8×C11C22×C412yes—
227C11×C4⋊C4—24no—
228C11×C4⋊C4—21no—
229C11×C4⋊C4C22×C412yes—
230C11×C22⋊C4—24no—
231C22⋊Dic11—24no—
232C22⋊Dic11—24no—
233C22⋊Dic11—24no—
234C22⋊Dic11—22no—
235C22⋊Dic11—22no—
236C22⋊Dic11—24no—
237C22⋊Dic11—24no—
238C22⋊Dic11—81no—
239C4⋊Dic11—22no—
240C4⋊Dic11—22no—
241C4⋊Dic11—21no—
242C4⋊Dic11—21no—
243C4⋊Dic11—21no—
244C4⋊Dic11—21no—
245C4⋊Dic11—21no—
246C4⋊Dic11—21no—
247C4⋊Dic11—42no—
248C4⋊Dic11—81no—
249C4⋊Dic11C2×D412yes—
250C4⋊Dic11C2×D412yes—
251C4×Dic11—24no—
252C4×Dic11—21no—
253C4×Dic11—21no—
254C4×Dic11—42no—
255C4×Dic11—81no—
256C4×Dic11C2×D412yes—
257C4×Dic11C2×D412yes—
258C2×C11⋊C8—21no—
259C2×C11⋊C8—21no—
260C2×C11⋊C8—21no—
261C2×C11⋊C8—21no—
262C2×C11⋊C8—21no—
263C2×C11⋊C8—21no—
264C2×#518—111no—
265C2×#450D1111yescharacteristic
266C2×#440—111no—
267C2×C4×SD16—111no—
268#2323—111no—
269#1877—111no—
270#1877—111no—
271#1873—111no—
272#1864—111no—
273#1862—111no—
274#1854—111no—
275#1786—111no—
276#1762—111no—
277C4×#102—111no—
278#1750—111no—
279C23×C11—216no—
280C23×C11—22no—
281C23×C11—22no—
282C23×C11—21no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—21no—
286C23×C11—22no—
287C23×C11—22no—
288C23×C11—21no—
289C23×C11—21no—
290C23×C11—21no—
291C23×C11—21no—
292C23×C11—41no—
293C23×C11—41no—
294C23×C11—41no—
295C23×C11—41no—
296C23×C11—41no—
297C23×C11—41no—
298C23×C11—41no—
299C23×C11—41no—
300C23×C11—84no—
301C23×C11—84no—
302C23×C11—84no—
303C23×C11—84no—
304C23×C11—84no—
305C23×C11—84no—
306C23×C11C4×D412yes—
307C23×C11C22×D411yescharacteristic
308Q8×C11—22no—
309Q8×C11—22no—
310Q8×C11—41no—
311Q8×C11—41no—
312D4×C11—216no—
313D4×C11—22no—
314D4×C11—22no—
315D4×C11—22no—
316D4×C11—22no—
317D4×C11—22no—
318D4×C11—22no—
319D4×C11C4×D414yes—
320D4×C11C4×D414yes—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11C4×D412yes—
334C2×C4×C11C23×C411yescharacteristic
335C2×C4×C11C22×D411yescharacteristic
336C2×C4×C11C22×D411yescharacteristic
337C2×C4×C11C2×#4111yescharacteristic
338C2×C4×C11C2×#4111yescharacteristic
339C2×C4×C11C2×#4111yescharacteristic
340C2×Dic11—21no—
341C2×Dic11—21no—
342C2×Dic11—21no—
343C2×Dic11—21no—
344C2×Dic11—21no—
345C2×Dic11—21no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—21no—
349C2×Dic11—21no—
350C2×Dic11—21no—
351C2×Dic11—21no—
352C2×Dic11—41no—
353C2×Dic11—41no—
354C2×Dic11—41no—
355C2×Dic11—41no—
356C2×Dic11—41no—
357C2×Dic11—41no—
358C2×Dic11—41no—
359C2×Dic11—41no—
360C2×Dic11—41no—
361C2×Dic11—41no—
362C2×Dic11—84no—
363C2×Dic11—84no—
364C2×Dic11—84no—
365C2×Dic11—84no—
366C2×Dic11#12012yes—
367C2×Dic11#12012yes—
368C8×C11—22no—
369C8×C11—22no—
370C11⋊C8—41no—
371C11⋊C8—41no—
372C23×D4C2×D1111yescharacteristic
373C22×SD16C2×D1111yescharacteristic
374C22×SD16C2×D1111yescharacteristic
375C2×C22⋊Q8C2×D1111yescharacteristic
376#518—224no—
377#518—224no—
378C2×C4×Q8—111no—
379C2×C4×D4—111no—
380C2×C4×D4—111no—
381C2×C4×D4—111no—
382C2×C4×D4—111no—
383C2×C4×D4—221no—
384C2×C4×D4—221no—
385C2×#117—111no—
386C2×#117—111no—
387C22×C22⋊C4—221no—
388C22×C22⋊C4—221no—
389#450Dic1118yescomplemented
390#440—224no—
391C4×SD16—224no—
392C2×#107—111no—
393C2×#106—111no—
394C2×#103—111no—
395C2×#103—111no—
396C2×#102—111no—
397C2×#102—111no—
398C2×#102—111no—
399C2×#102—111no—
400C2×#102C2×D1111yescharacteristic
401C2×#102C2×D1111yescharacteristic
402C2×C22⋊C8—111no—
403C2×C22⋊C8C2×D1111yescharacteristic
404C2×#97—111no—
405C2×C4×C8—111no—
406#391—111no—
407#389—111no—
408#389—221no—
409#388—221no—
410#388—221no—
411#387—221no—
412#380—111no—
413C4×C4⋊C4—111no—
414#340—111no—
415#340—111no—
416#340—111no—
417#340—111no—
418#336—111no—
419#336—111no—
420C22×C11—22no—
421C22×C11—22no—
422C22×C11—22no—
423C22×C11—24no—
424C22×C11—24no—
425C22×C11—41no—
426C22×C11—42no—
427C22×C11—42no—
428C22×C11—41no—
429C22×C11—42no—
430C22×C11—42no—
431C22×C11—42no—
432C22×C11—42no—
433C22×C11—42no—
434C22×C11—42no—
435C22×C11—41no—
436C22×C11—42no—
437C22×C11—42no—
438C22×C11—41no—
439C22×C11—42no—
440C22×C11—42no—
441C22×C11—816no—
442C22×C11C2×C4×D411yescharacteristic
443C22×C11C2×#12011yescharacteristic
444C22×C11#52511yescharacteristic
445C22×C11#57611yescharacteristic
446C22×C11#57711yescharacteristic
447C22×C11#57711yescharacteristic
448C22×C11#57711yescharacteristic
449C4×C11—22no—
450C4×C11—42no—
451C4×C11—42no—
452C4×C11C2×C4×D411yescharacteristic
453C4×C11C2×C4×D411yescharacteristic
454C4×C11#52511yescharacteristic
455C4×C11#52511yescharacteristic
456Dic11—22no—
457Dic11—22no—
458Dic11—41no—
459Dic11—42no—
460Dic11—41no—
461Dic11—42no—
462Dic11—81no—
463Dic11—81no—
464C25—21no—
465C22×Q8C22×D1111yescharacteristic
466C22×D4—22no—
467C22×D4—22no—
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—21no—
471C22×D4—22no—
472C22×D4C2×Dic1114yes—
473C22×D4C22×D1111yescharacteristic
474C22×D4C22×D1111yescharacteristic
475C23×C4—221no—
476C23×C4—221no—
477C23×C4—221no—
478C23×C4—221no—
479C23×C4C22×D1111yescharacteristic
480C2×SD16—22no—
481C2×SD16—22no—
482C2×SD16—22no—
483C2×SD16—22no—
484C2×SD16C2×Dic1114yescomplemented
485C2×SD16C2×Dic1114yescomplemented
486C22×C8—111no—
487C22×C8—111no—
488C22×C8C22×D1111yescharacteristic
489C22×C8C22×D1111yescharacteristic
490C22⋊Q8—22no—
491C22⋊Q8C2×Dic1114yescomplemented
492C4×Q8—222no—
493C4×Q8—222no—
494C4×D4—114no—
495C4×D4—114no—
496C4×D4—222no—
497C4×D4—222no—
498C4×D4—222no—
499C4×D4—222no—
500C4×D4—228no—
501C4×D4—228no—
502C4×D4—222no—
503C4×D4—222no—
504#117—222no—
505#117—222no—
506#117—222no—
507#117—222no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—111no—
510C2×C4⋊C4—111no—
511C2×C4⋊C4—111no—
512C2×C4⋊C4—111no—
513C2×C4⋊C4—111no—
514C2×C4⋊C4—111no—
515C2×C4⋊C4—221no—
516C2×C4⋊C4—221no—
517C2×C4⋊C4C22×D1111yescharacteristic
518C2×C22⋊C4—21no—
519C2×C22⋊C4—111no—
520C2×C22⋊C4—111no—
521C2×C22⋊C4—221no—
522C2×C22⋊C4—221no—
523C2×C22⋊C4—221no—
524C2×C22⋊C4—221no—
525C2×C22⋊C4—228no—
526C2×C22⋊C4—228no—
527C2×C22⋊C4—221no—
528C2×C22⋊C4—221no—
529C2×C42—111no—
530C2×C42—111no—
531C2×C42—221no—
532C2×C42—221no—
533C2×C42—221no—
534#107—222no—
535#106—222no—
536#103—222no—
537#103—222no—
538#102—222no—
539#102—222no—
540#102—222no—
541#102—222no—
542#102C2×Dic1114yescomplemented
543#102C2×Dic1114yescomplemented
544C22⋊C8—222no—
545C22⋊C8C2×Dic1114yescomplemented
546#97—222no—
547C4×C8—222no—
548#95—221no—
549#95—221no—
550#95—221no—
551#95—221no—
552#95—221no—
553C2×C11—42no—
554C2×C11—44no—
555C2×C11—44no—
556C2×C11C4×#12011yescharacteristic
557C2×C11#294611yescharacteristic
558C2×C11#294911yescharacteristic
559C2×C11#300911yescharacteristic
560C2×C11#301211yescharacteristic
561C2×C11#311811yescharacteristic
562C2×C11#312311yescharacteristic
563C24—24no—
564C24—24no—
565C24—21no—
566C24—21no—
567C24—24no—
568C24—81no—
569C24—81no—
570C24—81no—
571C24—81no—
572C24D4×D1111yescharacteristic
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8C22×Dic1112yes—
579C2×D4—24no—
580C2×D4—24no—
581C2×D4—28no—
582C2×D4—28no—
583C2×D4—28no—
584C2×D4—28no—
585C2×D4—24no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4D4×D1112yes—
593C2×D4D4×D1112yes—
594C2×D4#434112yes—
595C2×D4#434112yes—
596C2×D4C22×Dic1112yes—
597C2×D4C22×Dic1112yes—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—111no—
605C22×C4—111no—
606C22×C4—111no—
607C22×C4—111no—
608C22×C4—224no—
609C22×C4—224no—
610C22×C4—221no—
611C22×C4—221no—
612C22×C4—224no—
613C22×C4—224no—
614C22×C4—221no—
615C22×C4—221no—
616C22×C4—881no—
617C22×C4—881no—
618C22×C4—881no—
619C22×C4—881no—
620C22×C4—881no—
621C22×C4—881no—
622C22×C4—881no—
623C22×C4—881no—
624C22×C4D4×D1111yescharacteristic
625C22×C4#434112yes—
626C22×C4C22×Dic1112yes—
627C22×C4C23×D1111yescharacteristic
628SD16—28no—
629SD16—28no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—221no—
635C2×C8—221no—
636C2×C8—221no—
637C2×C8—221no—
638C2×C8—221no—
639C2×C8—221no—
640C2×C8C22×Dic1112yes—
641C2×C8C22×Dic1112yes—
642C4⋊C4—24no—
643C4⋊C4—21no—
644C4⋊C4—112no—
645C4⋊C4—112no—
646C4⋊C4—222no—
647C4⋊C4—222no—
648C4⋊C4—221no—
649C4⋊C4—221no—
650C4⋊C4—221no—
651C4⋊C4—221no—
652C4⋊C4—221no—
653C4⋊C4—221no—
654C4⋊C4—442no—
655C4⋊C4—881no—
656C4⋊C4C22×Dic1112yes—
657C22⋊C4—24no—
658C22⋊C4—222no—
659C22⋊C4—222no—
660C22⋊C4—224no—
661C22⋊C4—224no—
662C22⋊C4—224no—
663C22⋊C4—224no—
664C22⋊C4—224no—
665C22⋊C4—881no—
666C42—112no—
667C42—112no—
668C42—224no—
669C42—221no—
670C42—221no—
671C42—442no—
672C42—881no—
673C11#2145911yescharacteristic, complemented, Sylow
674C23—216no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—22no—
680C23—22no—
681C23—21no—
682C23—22no—
683C23—22no—
684C23—21no—
685C23—22no—
686C23—22no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—84no—
696C23—84no—
697C23—84no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23D4×Dic1112yes—
702C23C2×D4×D1111yescharacteristic
703Q8—22no—
704Q8—22no—
705Q8—41no—
706Q8—41no—
707D4—216no—
708D4—22no—
709D4—22no—
710D4—22no—
711D4—22no—
712D4—22no—
713D4—22no—
714D4D4×Dic1114yes—
715D4D4×Dic1114yes—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—112no—
729C2×C4—112no—
730C2×C4—221no—
731C2×C4—221no—
732C2×C4—221no—
733C2×C4—221no—
734C2×C4—221no—
735C2×C4—221no—
736C2×C4—221no—
737C2×C4—221no—
738C2×C4—222no—
739C2×C4—222no—
740C2×C4—221no—
741C2×C4—221no—
742C2×C4—441no—
743C2×C4—441no—
744C2×C4—441no—
745C2×C4—441no—
746C2×C4—441no—
747C2×C4—441no—
748C2×C4—441no—
749C2×C4—441no—
750C2×C4—441no—
751C2×C4—441no—
752C2×C4—884no—
753C2×C4—884no—
754C2×C4—884no—
755C2×C4—884no—
756C2×C4D4×Dic1112yes—
757C2×C4C2×D4×D1111yescharacteristic
758C2×C4C2×D4×D1111yescharacteristic
759C2×C4C2×#434111yescharacteristic
760C2×C4C2×#434111yescharacteristic
761C2×C4C2×#434111yescharacteristic
762C2×C4C23×Dic1111yescharacteristic
763C8—22no—
764C8—22no—
765C8—441no—
766C8—441no—
767C22—22no—
768C22—24no—
769C22—24no—
770C22—22no—
771C22—22no—
772C22—41no—
773C22—42no—
774C22—42no—
775C22—41no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—41no—
781C22—42no—
782C22—42no—
783C22—41no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—816no—
789C22#1062311711yescharacteristic
790C22D11×#12011yescharacteristic
791C22#1062329311yescharacteristic
792C22#1062329311yescharacteristic
793C22#1062330511yescharacteristic
794C22#1062330611yescharacteristic
795C22C2×D4×Dic1111yescharacteristic
796C4—22no—
797C4—42no—
798C4—42no—
799C4—222no—
800C4—222no—
801C4—441no—
802C4—442no—
803C4—441no—
804C4—442no—
805C4—881no—
806C4—881no—
807C4#1062311711yescharacteristic
808C4#1062311711yescharacteristic
809C4C2×D4×Dic1111yescharacteristic
810C4C2×D4×Dic1111yescharacteristic
811C2—42no—
812C2—44no—
813C2—44no—
814C2#120×Dic1111yescharacteristic
815C2#1307744911yescharacteristic
816C2#1307747611yescharacteristic
817C2#1307788811yescharacteristic
818C2#1307792111yescharacteristic
819C2#1307880111yescharacteristic
820C2#1307886211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#450C2
socleC23×C11C22×D4
prime radicalC23×D4×C11C22
cosocleC22×C4×C11C24
hypercenterC2×#450D11
hypocenterC11#21459
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
2. C2×#10622777C2semidirect
3. C2×SD16×Dic11C2semidirect
4. #13071300C2semidirect
5. #13068952C2semidirect
6. #13068952C2semidirect
7. #13068929C2semidirect
8. #13068879C2semidirect
9. #13068865C2semidirect
10. #13068817C2semidirect
12. #13068443C2semidirect
13. #102×Dic11C2semidirect
14. #13068384C2semidirect
22. C2×Q8×Dic11C22semidirect
33. C11×#450C4semidirect
37. #10622843C22semidirect
38. C2×#66899C22semidirect
39. C2×#66899C22semidirect
48. C2×#66882C22semidirect
49. C2×#66881C22semidirect
50. C2×#66879C22semidirect
51. C2×C8×Dic11C22semidirect
53. #10622598C22semidirect
55. C4⋊C4×Dic11C22semidirect
58. #10622189C22semidirect
59. #10622189C22semidirect
60. #10622188C22semidirect
61. #10622188C22semidirect
62. #10622167C22semidirect
63. #10622167C22semidirect
84. C2×C11×SD16C2×C4semidirect
85. C2×C11×SD16C2×C4semidirect
89. C11×C22⋊Q8C2×C4semidirect
134. C11×#102C2×C4semidirect
135. C11×#102C2×C4semidirect
136. C11×C22⋊C8C2×C4semidirect
389. #450Dic11semidirect
484. C2×SD16C2×Dic11semidirect
485. C2×SD16C2×Dic11semidirect
491. C22⋊Q8C2×Dic11semidirect
542. #102C2×Dic11semidirect
543. #102C2×Dic11semidirect
545. C22⋊C8C2×Dic11semidirect
673. C11#21459semidirect

Maximal subgroups

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

subgroupindex
C2×#106233292
C2×#106227772
C2×SD16×Dic112
#130713002
#130689522
#130689292
#130688792
#130688652
#130688172
#130685472
#130684432
#102×Dic112
#130683842
C2×C11×#4502
#2145911