Finite Group Databasebeta

← #14759507

Subgroups — #14759507

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×#10622831C211yesmaximal, characteristic
2C2×#10622631C211yesmaximal, characteristic, complemented
3C2×C4×#4324C211yesmaximal, characteristic, complemented
4#13071298C211yesmaximal, characteristic, complemented
5#13068950C211yesmaximal, characteristic, complemented
6#13068950C211yesmaximal, characteristic, complemented
7#13068928C211yesmaximal, characteristic, complemented
8#13068877C211yesmaximal, characteristic, complemented
9#13068863C211yesmaximal, characteristic, complemented
10#13068815C211yesmaximal, characteristic, complemented
11#13068547C211yesmaximal, characteristic
12#13068441C211yesmaximal, characteristic, complemented
13C4×#66896C211yesmaximal, characteristic, complemented
14#13068382C211yesmaximal, characteristic, complemented
15C2×C11×#518C211yesmaximal, characteristic
16C23×D4×C11C2211yescharacteristic
17C11×#518—24no—
18C11×#518—24no—
19C2×C4×D4×C11—21no—
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C2×C4×D4×C11C2211yescharacteristic
25C2×C11×#117C2211yescharacteristic
26C2×C11×#117C2211yescharacteristic
27C22×C11×C22⋊C4—21no—
28C22×C11×C22⋊C4—21no—
29C22×#4324C2211yescharacteristic
30C22×#4324C2211yescharacteristic
31C2×#66977C2211yescharacteristic
32C2×C4×Dic22C2211yescharacteristic, complemented
33#10622831C418yescomplemented
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40#10622825C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43#10622631—24no—
44C4×#4324—24no—
45#10622591—21no—
46#10622585—21no—
47C2×#66874C2211yescharacteristic, complemented
48C2×#66874C2211yescharacteristic, complemented
49C2×#66872C2211yescharacteristic, complemented
50C2×#66871C2211yescharacteristic, complemented
51#10622558—21no—
52#10622557—21no—
53C4×C4⋊Dic11C2211yescharacteristic, complemented
54#10622542C2211yescharacteristic, complemented
55#10622541C2211yescharacteristic, complemented
56C2×#66867C2211yescharacteristic, complemented
57C2×C4×C11⋊C8C2211yescharacteristic, complemented
58#10622167C2211yescharacteristic, complemented
59#10622167C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61#10622167C2211yescharacteristic, complemented
62#10622162C2211yescharacteristic, complemented
63#10622162C2211yescharacteristic, complemented
64C25×C11—21no—
65C22×D4×C11—22no—
66C22×D4×C11—22no—
67C22×D4×C11—22no—
68C22×D4×C11—22no—
69C22×D4×C11—21no—
70C22×D4×C11—22no—
71C22×D4×C11C2×C414yes—
72C22×D4×C11C2311yescharacteristic
73C22×D4×C11C2311yescharacteristic
74C23×C4×C11—21no—
75C23×C4×C11—21no—
76C23×C4×C11—21no—
77C23×C4×C11—21no—
78C23×C4×C11C2311yescharacteristic
79C22×Dic22C2311yescharacteristic
80C4×D4×C11—28no—
81C4×D4×C11—28no—
82C4×D4×C11—22no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11—22no—
87C4×D4×C11—22no—
88C4×D4×C11D414yes—
89C4×D4×C11D414yes—
90C11×#117—22no—
91C11×#117—22no—
92C11×#117—22no—
93C11×#117—22no—
94C2×C11×C4⋊C4D411yescharacteristic
95C2×C11×C4⋊C4D411yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C22⋊C4—28no—
99C2×C11×C22⋊C4—28no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4D411yescharacteristic
106C2×C11×C22⋊C4D411yescharacteristic
107C2×C42×C11—21no—
108C2×C42×C11C2311yescharacteristic
109C2×C42×C11C2311yescharacteristic
110C2×C22⋊Dic11—21no—
111C2×C22⋊Dic11—21no—
112C2×#4324—22no—
113C2×#4324—22no—
114C2×#4324—22no—
115C2×#4324—22no—
116C2×#4324C2×C414yescomplemented
117C2×#4324C2×C414yescomplemented
118C2×C4⋊Dic11C2311yescharacteristic
119C2×C4⋊Dic11C2311yescharacteristic
120C2×C4⋊Dic11C2311yescharacteristic
121#66977—22no—
122#66977C2×C414yescomplemented
123C2×Dic11⋊C4—21no—
124C2×Dic11⋊C4—21no—
125C2×Dic11⋊C4—21no—
126C2×C4×Dic11—21no—
127C2×C4×Dic11—21no—
128C22×C11⋊C8C2311yescharacteristic
129C22×C11⋊C8C2311yescharacteristic
130C22×C11⋊C8C2311yescharacteristic
131C22×C11⋊C8C2311yescharacteristic
132C4×Dic22—22no—
133C4×Dic22—22no—
134#66896—22no—
135#66896—22no—
136#66896—22no—
137#66896—22no—
138#66896C2×C414yescomplemented
139#66896C2×C414yescomplemented
140C11⋊#95—21no—
141C11⋊#95—21no—
142C11⋊#95—21no—
143C11⋊#95—21no—
144C11⋊#95—21no—
145C22⋊(C11⋊C8)—22no—
146C22⋊(C11⋊C8)C2×C414yescomplemented
147#66874—22no—
148#66874—22no—
149#66872—22no—
150#66871—22no—
151#66867—22no—
152C4×C11⋊C8—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×D4×C11—24no—
165C2×D4×C11—24no—
166C2×D4×C11—28no—
167C2×D4×C11—28no—
168C2×D4×C11—28no—
169C2×D4×C11—28no—
170C2×D4×C11—24no—
171C2×D4×C11—21no—
172C2×D4×C11—21no—
173C2×D4×C11—21no—
174C2×D4×C11—21no—
175C2×D4×C11—21no—
176C2×D4×C11—21no—
177C2×D4×C11C22×C412yes—
178C2×D4×C11C22×C412yes—
179C2×D4×C11C2×D412yes—
180C2×D4×C11C2×D412yes—
181C2×D4×C11#4112yes—
182C2×D4×C11#4112yes—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—24no—
190C22×C4×C11—24no—
191C22×C4×C11—24no—
192C22×C4×C11—24no—
193C22×C4×C11—81no—
194C22×C4×C11—81no—
195C22×C4×C11—81no—
196C22×C4×C11—81no—
197C22×C4×C11—81no—
198C22×C4×C11—81no—
199C22×C4×C11—81no—
200C22×C4×C11—81no—
201C22×C4×C11C22×C412yes—
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2×D411yescharacteristic
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11#4112yes—
208C22×C4×C11C2411yescharacteristic
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—21no—
213C2×Dic22—21no—
214C2×Dic22—21no—
215C2×Dic22—21no—
216C2×Dic22—21no—
217C2×Dic22—21no—
218C2×Dic22C22×C412yes—
219C11×C4⋊C4—22no—
220C11×C4⋊C4—22no—
221C11×C4⋊C4—21no—
222C11×C4⋊C4—21no—
223C11×C4⋊C4C2×D412yes—
224C11×C4⋊C4C2×D412yes—
225C11×C22⋊C4—24no—
226C11×C22⋊C4—24no—
227C11×C22⋊C4—24no—
228C11×C22⋊C4—22no—
229C11×C22⋊C4—22no—
230C11×C22⋊C4—24no—
231C11×C22⋊C4—24no—
232C42×C11—24no—
233C42×C11—21no—
234C42×C11—21no—
235C42×C11C2×D412yes—
236C42×C11C2×D412yes—
237C22⋊Dic11—24no—
238C22⋊Dic11—81no—
239#4324—28no—
240#4324—28no—
241C4⋊Dic11—21no—
242C4⋊Dic11—21no—
243C4⋊Dic11—21no—
244C4⋊Dic11—21no—
245C4⋊Dic11—21no—
246C4⋊Dic11C22×C412yes—
247Dic11⋊C4—24no—
248Dic11⋊C4—42no—
249Dic11⋊C4—81no—
250C4×Dic11—42no—
251C4×Dic11—81no—
252C2×C11⋊C8—21no—
253C2×C11⋊C8—21no—
254C2×C11⋊C8—21no—
255C2×C11⋊C8—21no—
256C2×C11⋊C8—21no—
257C2×C11⋊C8—21no—
258C2×C11⋊C8—21no—
259C2×C11⋊C8—21no—
260C2×C11⋊C8—21no—
261C2×C11⋊C8—21no—
262C2×C11⋊C8C22×C412yes—
263C2×C11⋊C8C22×C412yes—
264C2×#518D1111yescharacteristic
265C2×#450—111no—
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
308D4×C11—216no—
309D4×C11—22no—
310D4×C11—22no—
311D4×C11—22no—
312D4×C11—22no—
313D4×C11—22no—
314D4×C11—22no—
315D4×C11C4×D414yes—
316D4×C11C4×D414yes—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
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—21no—
328C2×C4×C11—21no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—21no—
334C2×C4×C11—21no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—84no—
340C2×C4×C11—84no—
341C2×C4×C11—84no—
342C2×C4×C11—84no—
343C2×C4×C11C4×D412yes—
344C2×C4×C11#12012yes—
345C2×C4×C11#12012yes—
346C2×C4×C11C23×C411yescharacteristic
347C2×C4×C11C22×D411yescharacteristic
348C2×C4×C11C22×D411yescharacteristic
349C2×C4×C11C2×#4111yescharacteristic
350C2×C4×C11C2×#4111yescharacteristic
351C2×C4×C11C2×#4111yescharacteristic
352C2×Dic11—22no—
353C2×Dic11—22no—
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—41no—
363C2×Dic11—41no—
364Dic22—22no—
365Dic22—22no—
366Dic22—41no—
367Dic22—41no—
368C11⋊C8—22no—
369C11⋊C8—22no—
370C11⋊C8—41no—
371C11⋊C8—41no—
372C23×D4C2×D1111yescharacteristic
373C22×SD16—111no—
374C22×SD16—111no—
375C2×C22⋊Q8—111no—
376#518—24no—
377#518—24no—
378C2×C4×Q8—111no—
379C2×C4×D4—21no—
380C2×C4×D4—21no—
381C2×C4×D4C2×D1111yescharacteristic
382C2×C4×D4C2×D1111yescharacteristic
383C2×C4×D4C2×D1111yescharacteristic
384C2×C4×D4C2×D1111yescharacteristic
385C2×#117C2×D1111yescharacteristic
386C2×#117C2×D1111yescharacteristic
387C22×C22⋊C4—21no—
388C22×C22⋊C4—21no—
389#450—118no—
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×#102—111no—
401C2×#102—111no—
402C2×C22⋊C8—111no—
403C2×C22⋊C8—111no—
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—42no—
436C22×C11—42no—
437C22×C11—41no—
438C22×C11—42no—
439C22×C11—42no—
440C22×C11—41no—
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—22no—
451C4×C11—22no—
452C4×C11—41no—
453C4×C11—42no—
454C4×C11—41no—
455C4×C11—42no—
456C4×C11C2×C4×D411yescharacteristic
457C4×C11C2×C4×D411yescharacteristic
458C4×C11#52511yescharacteristic
459C4×C11#52511yescharacteristic
460Dic11—42no—
461Dic11—42no—
462Dic11—81no—
463Dic11—81no—
464C25—21no—
465C22×Q8—111no—
466C22×D4—22no—
467C22×D4—22no—
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—22no—
471C22×D4—21no—
472C22×D4C4×D1114yes—
473C22×D4C22×D1111yescharacteristic
474C22×D4C22×D1111yescharacteristic
475C23×C4—21no—
476C23×C4—21no—
477C23×C4—21no—
478C23×C4—21no—
479C23×C4C22×D1111yescharacteristic
480C2×SD16—114no—
481C2×SD16—114no—
482C2×SD16—222no—
483C2×SD16—222no—
484C2×SD16—222no—
485C2×SD16—222no—
486C22×C8—111no—
487C22×C8—111no—
488C22×C8—111no—
489C22×C8—111no—
490C22⋊Q8—114no—
491C22⋊Q8—222no—
492C4×Q8—222no—
493C4×Q8—222no—
494C4×D4—28no—
495C4×D4—28no—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502C4×D4C22⋊D1114yes—
503C4×D4C22⋊D1114yes—
504#117—22no—
505#117—22no—
506#117—22no—
507#117—22no—
508C2×C4⋊C4—111no—
509C2×C4⋊C4—111no—
510C2×C4⋊C4—111no—
511C2×C4⋊C4—221no—
512C2×C4⋊C4—221no—
513C2×C4⋊C4—221no—
514C2×C4⋊C4C22⋊D1111yescharacteristic
515C2×C4⋊C4C22⋊D1111yescharacteristic
516C2×C4⋊C4C22×D1111yescharacteristic
517C2×C4⋊C4C22×D1111yescharacteristic
518C2×C22⋊C4—28no—
519C2×C22⋊C4—28no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—221no—
526C2×C22⋊C4—221no—
527C2×C22⋊C4C22⋊D1111yescharacteristic
528C2×C22⋊C4C22⋊D1111yescharacteristic
529C2×C42—21no—
530C2×C42—221no—
531C2×C42—221no—
532C2×C42C22×D1111yescharacteristic
533C2×C42C22×D1111yescharacteristic
534#107—222no—
535#106—222no—
536#103—222no—
537#103—222no—
538#102—114no—
539#102—114no—
540#102—222no—
541#102—222no—
542#102—222no—
543#102—222no—
544C22⋊C8—114no—
545C22⋊C8—222no—
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—
572C24C2×C22⋊D1111yescharacteristic
573C2×Q8—112no—
574C2×Q8—221no—
575C2×Q8—221no—
576C2×Q8—221no—
577C2×Q8—221no—
578C2×Q8—221no—
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×D4C2×C4×D1112yes—
593C2×D4C2×C4×D1112yes—
594C2×D4#433912yes—
595C2×D4#433912yes—
596C2×D4C2×C22⋊D1112yes—
597C2×D4C2×C22⋊D1112yes—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—81no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4—81no—
616C22×C4—221no—
617C22×C4—221no—
618C22×C4—221no—
619C22×C4—221no—
620C22×C4C2×C4×D1112yes—
621C22×C4#433912yes—
622C22×C4C2×C22⋊D1111yescharacteristic
623C22×C4C2×C22⋊D1111yescharacteristic
624C22×C4C2×C22⋊D1111yescharacteristic
625C22×C4C2×C22⋊D1111yescharacteristic
626C22×C4C2×C22⋊D1111yescharacteristic
627C22×C4C23×D1111yescharacteristic
628SD16—228no—
629SD16—228no—
630C2×C8—112no—
631C2×C8—112no—
632C2×C8—221no—
633C2×C8—221no—
634C2×C8—221no—
635C2×C8—221no—
636C2×C8—221no—
637C2×C8—221no—
638C2×C8—221no—
639C2×C8—221no—
640C2×C8—221no—
641C2×C8—221no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—112no—
647C4⋊C4—224no—
648C4⋊C4—221no—
649C4⋊C4—221no—
650C4⋊C4—221no—
651C4⋊C4—221no—
652C4⋊C4—221no—
653C4⋊C4—442no—
654C4⋊C4—881no—
655C4⋊C4C2×C22⋊D1112yes—
656C4⋊C4C2×C22⋊D1112yes—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—24no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—24no—
663C22⋊C4—24no—
664C22⋊C4—224no—
665C22⋊C4—881no—
666C42—24no—
667C42—21no—
668C42—21no—
669C42—442no—
670C42—881no—
671C42C2×C22⋊D1112yes—
672C42C2×C22⋊D1112yes—
673C11#2145911yescharacteristic, complemented, Sylow
674C23—216no—
675C23—22no—
676C23—22no—
677C23—21no—
678C23—22no—
679C23—22no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
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—
701C23C4×C22⋊D1112yes—
702C23C22×C22⋊D1111yescharacteristic
703Q8—222no—
704Q8—222no—
705Q8—441no—
706Q8—441no—
707D4—216no—
708D4—22no—
709D4—22no—
710D4—22no—
711D4—22no—
712D4—22no—
713D4—22no—
714D4C4×C22⋊D1114yes—
715D4C4×C22⋊D1114yes—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—84no—
739C2×C4—84no—
740C2×C4—84no—
741C2×C4—84no—
742C2×C4—222no—
743C2×C4—222no—
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—441no—
753C2×C4—441no—
754C2×C4C4×C22⋊D1112yes—
755C2×C4#6700612yes—
756C2×C4#6700612yes—
757C2×C4C22×C4×D1111yescharacteristic
758C2×C4C2×#433911yescharacteristic
759C2×C4C2×#433911yescharacteristic
760C2×C4C2×#433911yescharacteristic
761C2×C4C22×C22⋊D1111yescharacteristic
762C2×C4C22×C22⋊D1111yescharacteristic
763C8—222no—
764C8—222no—
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—
789C22C2×C4×C22⋊D1111yescharacteristic
790C22#1062332211yescharacteristic
791C22#1062336611yescharacteristic
792C22#1062336711yescharacteristic
793C22#1062336711yescharacteristic
794C22#1062336711yescharacteristic
795C22C2×#6700611yescharacteristic
796C4—22no—
797C4—22no—
798C4—22no—
799C4—41no—
800C4—42no—
801C4—41no—
802C4—42no—
803C4—442no—
804C4—442no—
805C4—881no—
806C4—881no—
807C4C2×C4×C22⋊D1111yescharacteristic
808C4C2×C4×C22⋊D1111yescharacteristic
809C4#1062332211yescharacteristic
810C4#1062332211yescharacteristic
811C2—42no—
812C2—44no—
813C2—44no—
814C2C4×#6700611yescharacteristic
815C2#1307744811yescharacteristic
816C2#1307747311yescharacteristic
817C2#1307789311yescharacteristic
818C2#1307792011yescharacteristic
819C2#1307880011yescharacteristic
820C2#1307886811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#518C2
socleC23×C11C22×D4
prime radicalC23×D4×C11C22
cosocleC22×C4×C11C24
hypercenterC2×#518D11
hypocenterC11#21459
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#518

Complements

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

NH ≅ G/Ntype
2. C2×#10622631C2semidirect
3. C2×C4×#4324C2semidirect
4. #13071298C2semidirect
5. #13068950C2semidirect
6. #13068950C2semidirect
7. #13068928C2semidirect
8. #13068877C2semidirect
9. #13068863C2semidirect
10. #13068815C2semidirect
12. #13068441C2semidirect
13. C4×#66896C2semidirect
14. #13068382C2semidirect
32. C2×C4×Dic22C22semidirect
33. #10622831C4semidirect
47. C2×#66874C22semidirect
48. C2×#66874C22semidirect
49. C2×#66872C22semidirect
50. C2×#66871C22semidirect
53. C4×C4⋊Dic11C22semidirect
54. #10622542C22semidirect
55. #10622541C22semidirect
56. C2×#66867C22semidirect
57. C2×C4×C11⋊C8C22semidirect
58. #10622167C22semidirect
59. #10622167C22semidirect
60. #10622167C22semidirect
61. #10622167C22semidirect
62. #10622162C22semidirect
63. #10622162C22semidirect
116. C2×#4324C2×C4semidirect
117. C2×#4324C2×C4semidirect
122. #66977C2×C4semidirect
138. #66896C2×C4semidirect
139. #66896C2×C4semidirect
146. C22⋊(C11⋊C8)C2×C4semidirect
673. C11#21459semidirect

Maximal subgroups

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

subgroupindex
C2×#106228312
C2×#106226312
C2×C4×#43242
#130712982
#130689502
#130689282
#130688772
#130688632
#130688152
#130685472
#130684412
C4×#668962
#130683822
C2×C11×#5182
#2145911