Finite Group Databasebeta

← #14769259

Subgroups — #14769259

Order 2816.

1670 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623161C211yesmaximal, characteristic
2C2×#10622724C211yesmaximal, characteristic, complemented
3C2×#10622416C211yesmaximal, characteristic, complemented
4C22×#66885C211yesmaximal, characteristic, complemented
5#13071512C211yesmaximal, characteristic, complemented
6#13069545C211yesmaximal, characteristic, complemented
7#13069429C211yesmaximal, characteristic, complemented
8#13069053C211yesmaximal, characteristic, complemented
9#13068932C211yesmaximal, characteristic, complemented
10#13068924C211yesmaximal, characteristic, complemented
11#13068615C211yesmaximal, characteristic, complemented
12#13068555C211yesmaximal, characteristic, complemented
13#13068546C211yesmaximal, characteristic, complemented
14#13068440C211yesmaximal, characteristic, complemented
15C11×#1892C211yesmaximal, characteristic, complemented
16C22×#4343C2211yescharacteristic
17C23×D44C2211yescharacteristic
18C23×C8×C11C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×#67000C2211yescharacteristic
21C2×C4×C22⋊D11C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C22×#4313C2211yescharacteristic, complemented
24#10623161—24no—
25#10623161C418yescomplemented
26C2×#66948—21no—
27C2×#66948C2211yescharacteristic
28C2×#66947—21no—
29C2×#66946C2211yescharacteristic
30C2×C4⋊C4×D11C2211yescharacteristic, complemented
31C2×#66935—21no—
32C2×(C22⋊D11)⋊C4—21no—
33C2×C22⋊C4×D11—21no—
34C2×C11×#103C2211yescharacteristic, complemented
35C2×C11×#103C2211yescharacteristic, complemented
36C11×#380C2211yescharacteristic
37C2×#66899C2211yescharacteristic, complemented
38C2×#66899C2211yescharacteristic, complemented
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40C2×#66885—24no—
41C2×#66885C2211yescharacteristic
42C2×#66885C2211yescharacteristic
43C2×#66885C2211yescharacteristic
44C2×#66885C2211yescharacteristic
45#10622724—24no—
46C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
47C2×#66879C2211yescharacteristic, complemented
48C2×Dic11⋊C8C2211yescharacteristic, complemented
49#10622600C2211yescharacteristic, complemented
50#10622589C2211yescharacteristic, complemented
51C4⋊C4×Dic11C2211yescharacteristic, complemented
52C2×#66873C2211yescharacteristic
53C2×#66873C2211yescharacteristic
54C2×#66873C2211yescharacteristic
55C2×#66873C2211yescharacteristic
56#10622559—21no—
57#10622416—24no—
58#10622281—21no—
59#10622260—21no—
60C11×#340C2211yescharacteristic, complemented
61C11×#340C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63#10622167C2211yescharacteristic, complemented
64C24×D11—21no—
65C22×Q8×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11D411yescharacteristic
68C23×Dic11—21no—
69C2×#4343—22no—
70C2×#4343—22no—
71C2×#4343—22no—
72C2×#4343—41no—
73C2×#4343—41no—
74C2×#4343C2×C414yescomplemented
75C22×D44—22no—
76C22×D44—22no—
77C22×D44—21no—
78C22×D44—21no—
79C22×D44—22no—
80C22×D44—21no—
81C22×D44—41no—
82C22×D44—41no—
83C22×D44C2×C414yescomplemented
84C22×D44C2311yescharacteristic
85C22×D44C2311yescharacteristic
86C22×C4×D11—21no—
87C22×C4×D11—21no—
88C22×C4×D11—21no—
89C22×C4×D11C2311yescharacteristic
90C22×C8×C11—22no—
91C22×C8×C11—22no—
92C22×C8×C11—41no—
93C22×C8×C11C2311yescharacteristic
94C22×C8×C11C2311yescharacteristic
95C11×C22⋊Q8—22no—
96C11×C22⋊Q8C2×C414yescomplemented
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C22⋊Dic11D411yescharacteristic
104#67000—22no—
105#67000C2×C414yescomplemented
106C4×C22⋊D11C2×C414yes—
107C4×C22⋊D11D414yes—
108C2×(C2×D11)⋊C4—21no—
109C2×(C2×D11)⋊C4—21no—
110C2×(C2×D11)⋊C4—21no—
111C2×(C2×D11)⋊C4—21no—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4D411yescharacteristic
114C2×C4⋊Dic11—22no—
115C2×C4⋊Dic11—21no—
116C2×C4⋊Dic11—41no—
117C2×C4⋊Dic11C2311yescharacteristic
118C2×C4⋊Dic11C2311yescharacteristic
119C2×Dic11⋊C4—21no—
120C2×Dic11⋊C4—21no—
121C2×Dic11⋊C4—21no—
122C2×Dic11⋊C4D411yescharacteristic
123C2×C4×Dic11—21no—
124C2×C4×Dic11C2311yescharacteristic
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127C2×#4313—22no—
128C2×#4313—22no—
129C2×#4313—41no—
130#66948—22no—
131#66948—28no—
132#66948C2×C414yescomplemented
133#66947—28no—
134#66946—22no—
135#66946C2×C414yescomplemented
136C4⋊C4×D11—22no—
137C4⋊C4×D11—41no—
138#66935—28no—
139(C22⋊D11)⋊C4—44no—
140C22⋊C4×D11—28no—
141C11×#103—22no—
142C11×#103—41no—
143C11×#95—21no—
144#66899—22no—
145#66899—41no—
146C11⋊#95—21no—
147C11⋊#95—21no—
148C22⋊(C11⋊C8)—22no—
149#66885—22no—
150#66885—22no—
151#66885—22no—
152#66885D414yescomplemented
153(C2×D11)⋊C8—22no—
154#66879—22no—
155Dic11⋊C8—22no—
156#66873—22no—
157#66873—22no—
158#66873—41no—
159#66873—41no—
160#22419—111nomaximal, Sylow
161C24×C11C2×D411yescharacteristic
162C23×D11—21no—
163C23×D11—21no—
164C23×D11—24no—
165C23×D11—42no—
166C23×D11—42no—
167C23×D11—42no—
168C23×D11—42no—
169C23×D11—81no—
170C23×D11—81no—
171C23×D11C2×D411yescharacteristic
172C2×Q8×C11—21no—
173C2×Q8×C11—21no—
174C2×Q8×C11—21no—
175C2×Q8×C11—21no—
176C2×Q8×C11—21no—
177C2×Q8×C11C22×C412yes—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11C22×C412yes—
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D412yes—
189C22×C4×C11C2411yescharacteristic
190C2×C22⋊D11—22no—
191C2×C22⋊D11—22no—
192C2×C22⋊D11C22⋊C414yes—
193C22×Dic11—21no—
194C22×Dic11—21no—
195C22×Dic11—42no—
196C22×Dic11—42no—
197C22×Dic11—81no—
198C22×Dic11C2×D411yescharacteristic
199C22×Dic11C2×D411yescharacteristic
200C22×Dic11C2×D411yescharacteristic
201#4343—28no—
202#4343—44no—
203#4343—44no—
204#4343—44no—
205C2×D44—24no—
206C2×D44—24no—
207C2×D44—28no—
208C2×D44—24no—
209C2×D44—21no—
210C2×D44—21no—
211C2×D44—21no—
212C2×D44—21no—
213C2×D44—21no—
214C2×D44—21no—
215C2×D44—21no—
216C2×D44—21no—
217C2×D44—42no—
218C2×D44—42no—
219C2×D44—44no—
220C2×D44—44no—
221C2×D44—44no—
222C2×D44—42no—
223C2×D44—42no—
224C2×D44—81no—
225C2×D44—81no—
226C2×D44C22×C412yes—
227C2×D44C22×C412yes—
228C2×D44C2×D412yes—
229C2×D44#4112yes—
230C2×C4×D11—24no—
231C2×C4×D11—24no—
232C2×C4×D11—21no—
233C2×C4×D11—21no—
234C2×C4×D11—21no—
235C2×C4×D11—21no—
236C2×C4×D11—42no—
237C2×C4×D11—42no—
238C2×C4×D11—42no—
239C2×C4×D11—42no—
240C2×C4×D11—81no—
241C2×C4×D11—81no—
242C2×C4×D11—81no—
243C2×C4×D11C22×C412yes—
244C2×C4×D11C2×D412yes—
245C2×C8×C11—21no—
246C2×C8×C11—21no—
247C2×C8×C11—21no—
248C2×C8×C11—21no—
249C2×C8×C11—21no—
250C2×C8×C11—44no—
251C2×C8×C11C2×D412yes—
252C11×C4⋊C4—24no—
253C11×C4⋊C4—21no—
254C11×C4⋊C4—21no—
255C11×C4⋊C4—21no—
256C11×C4⋊C4—21no—
257C11×C4⋊C4—21no—
258C11×C4⋊C4C22×C412yes—
259C11×C22⋊C4—24no—
260C11×C22⋊C4—42no—
261C22⋊Dic11C22⋊C414yes—
262(C2×D11)⋊C4—24no—
263(C2×D11)⋊C4—24no—
264(C2×D11)⋊C4—24no—
265(C2×D11)⋊C4—24no—
266(C2×D11)⋊C4—42no—
267(C2×D11)⋊C4C22⋊C414yes—
268C4⋊Dic11—21no—
269C4⋊Dic11—21no—
270C4⋊Dic11—21no—
271C4⋊Dic11—42no—
272C4⋊Dic11C2×D412yes—
273Dic11⋊C4—42no—
274Dic11⋊C4—42no—
275Dic11⋊C4—81no—
276Dic11⋊C4C22⋊C414yes—
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×#546—111no—
288C2×#435—111no—
289C2×#417—111no—
290C22×#102—111no—
291D4×C4⋊C4—111no—
292#1983—111no—
293#1959—111no—
294#1895—111no—
295#1892D1111yescharacteristic, complemented
296#1874—111no—
297#1872—111no—
298#1802—111no—
299#1788—111no—
300#1786—111no—
301#1762—111no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—21no—
305C23×C11—21no—
306C23×C11C2×C22⋊C412yes—
307C23×C11AGL(1,ℤ/8)12yes—
308C23×C11#13712yes—
309C23×C11C22×D411yescharacteristic
310C22×D11—22no—
311C22×D11—21no—
312C22×D11—22no—
313C22×D11—21no—
314C22×D11—22no—
315C22×D11—21no—
316C22×D11—21no—
317C22×D11—21no—
318C22×D11—21no—
319C22×D11—22no—
320C22×D11—48no—
321C22×D11—41no—
322C22×D11—41no—
323C22×D11—41no—
324C22×D11—41no—
325C22×D11—41no—
326C22×D11—41no—
327C22×D11—41no—
328C22×D11—41no—
329C22×D11—41no—
330C22×D11—41no—
331C22×D11—48no—
332C22×D11—84no—
333C22×D11—84no—
334C22×D11—84no—
335C22×D11—84no—
336C22×D11—84no—
337C22×D11C2×C22⋊C412yes—
338Q8×C11—22no—
339Q8×C11—22no—
340Q8×C11—41no—
341Q8×C11—41no—
342C2×C4×C11—21no—
343C2×C4×C11—21no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
359C2×C4×C11—41no—
360C2×C4×C11C2×C22⋊C412yes—
361C2×C4×C11C23×C411yescharacteristic
362C2×C4×C11C22×D411yescharacteristic
363C2×C4×C11C22×D411yescharacteristic
364C2×C4×C11C2×#4111yescharacteristic
365C2×C4×C11H(5,𝔽2)11yescharacteristic
366C2×C4×C11H(5,𝔽2)11yescharacteristic
367C22⋊D11—28no—
368C2×Dic11—21no—
369C2×Dic11—21no—
370C2×Dic11—21no—
371C2×Dic11—21no—
372C2×Dic11—21no—
373C2×Dic11—21no—
374C2×Dic11—22no—
375C2×Dic11—41no—
376C2×Dic11—41no—
377C2×Dic11—41no—
378C2×Dic11—41no—
379C2×Dic11—41no—
380C2×Dic11—84no—
381C2×Dic11C2×C22⋊C412yes—
382C2×Dic11C2×C22⋊C412yes—
383C2×Dic11C2×C22⋊C412yes—
384D44—22no—
385D44—22no—
386D44—22no—
387D44—22no—
388D44—22no—
389D44—48no—
390D44—48no—
391D44—41no—
392D44—41no—
393D44—84no—
394D44C4×D414yescomplemented
395C4×D11—22no—
396C4×D11—22no—
397C4×D11—22no—
398C4×D11—22no—
399C4×D11—48no—
400C4×D11—84no—
401C4×D11—84no—
402C8×C11—22no—
403C8×C11—41no—
404C11⋊C8—41no—
405C11⋊C8—41no—
406C22×#41—111no—
407C23×D4—111no—
408C22×M16—111no—
409C23×C8C2×D1111yescharacteristic
410#546—118no—
411#546—224no—
412C2×#124—111no—
413C2×#123—221no—
414C2×C22⋊Q8C2×D1111yescharacteristic
415C2×#121—111no—
416C2×#121—221no—
417C2×#120—221no—
418C2×C4×D4—111no—
419C2×C4×D4—111no—
420C2×C4×D4—221no—
421C22×C4⋊C4—111no—
422C22×C4⋊C4—111no—
423C22×C22⋊C4—221no—
424#435—224no—
425C2×C4⋊C8—111no—
426#417—224no—
427C2×#103—111no—
428C2×#103—111no—
429C2×#103C2×D1111yescharacteristic, complemented
430C2×#103C2×D1111yescharacteristic, complemented
431C2×#102—111no—
432C2×#102—111no—
433C2×#102—111no—
434C2×#102—111no—
435C2×#102—111no—
436C2×#102—111no—
437C2×#102—111no—
438C2×#102—111no—
439C2×#102—224no—
440C2×C22⋊C8—111no—
441C2×C22⋊C8—111no—
442C2×#97—111no—
443#389—221no—
444#385—221no—
445#385—221no—
446#384—111no—
447#380—111no—
448#380C2×D1111yescharacteristic
449C4×C4⋊C4—111no—
450#340—111no—
451#340—111no—
452#340C2×D1111yescharacteristic, complemented
453#340C2×D1111yescharacteristic, complemented
454C22×C11—22no—
455C22×C11—22no—
456C22×C11—22no—
457C22×C11—22no—
458C22×C11—22no—
459C22×C11—22no—
460C22×C11#41714yescomplemented
461C22×C11C22×C22⋊C411yescharacteristic
462C22×C11D4211yescharacteristic
463C22×C11#54611yescharacteristic
464C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
465C22×C11C2×#13711yescharacteristic
466C22×C11#57611yescharacteristic
467C22×C11#57711yescharacteristic
468C2×D11—24no—
469C2×D11—22no—
470C2×D11—22no—
471C2×D11—22no—
472C2×D11—42no—
473C2×D11—42no—
474C2×D11—41no—
475C2×D11—42no—
476C2×D11—41no—
477C2×D11—42no—
478C2×D11—41no—
479C2×D11—42no—
480C2×D11—41no—
481C2×D11—42no—
482C2×D11—42no—
483C2×D11—42no—
484C2×D11—42no—
485C2×D11—816no—
486C2×D11—81no—
487C2×D11—81no—
488C2×D11—81no—
489C2×D11—81no—
490C4×C11—22no—
491C4×C11—42no—
492C4×C11—42no—
493C4×C11—81no—
494C4×C11—81no—
495C4×C11C2×C4×D411yescharacteristic
496C4×C11#51811yescharacteristic
497C4×C11D4211yescharacteristic
498C4×C11#54611yescharacteristic
499Dic11—22no—
500Dic11—22no—
501Dic11—22no—
502Dic11—42no—
503Dic11—81no—
504C25—221no—
505C2×#41—114no—
506C2×#41—222no—
507C2×#41—222no—
508C2×#41—222no—
509C2×#41—441no—
510C2×#41—441no—
511C22×Q8C22×D1111yescharacteristic
512C22×D4—111no—
513C22×D4—114no—
514C22×D4—111no—
515C22×D4—111no—
516C22×D4—222no—
517C22×D4—222no—
518C22×D4—221no—
519C22×D4—221no—
520C22×D4—221no—
521C22×D4—222no—
522C22×D4—441no—
523C22×D4—441no—
524C23×C4—111no—
525C23×C4—221no—
526C23×C4—221no—
527C23×C4—221no—
528C23×C4—221no—
529C23×C4C22×D1111yescharacteristic
530C2×M16—222no—
531C2×M16—222no—
532C2×M16—441no—
533C22×C8—22no—
534C22×C8—22no—
535C22×C8—41no—
536C22×C8—111no—
537C22×C8—111no—
538C22×C8C22×D1111yescharacteristic
539C22×C8C22×D1111yescharacteristic
540#124—114no—
541#124—222no—
542#123—228no—
543C22⋊Q8—22no—
544C22⋊Q8C4×D1114yescomplemented
545#121—114no—
546#121—228no—
547#121—222no—
548#120—228no—
549C4×D4—114no—
550C4×D4—114no—
551C4×D4—114no—
552C4×D4—222no—
553C4×D4—444no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—111no—
556C2×C4⋊C4—111no—
557C2×C4⋊C4—111no—
558C2×C4⋊C4—222no—
559C2×C4⋊C4—222no—
560C2×C4⋊C4—221no—
561C2×C4⋊C4—221no—
562C2×C4⋊C4—221no—
563C2×C4⋊C4—221no—
564C2×C4⋊C4—441no—
565C2×C4⋊C4—441no—
566C2×C4⋊C4C22×D1111yescharacteristic
567C2×C4⋊C4C22×D1111yescharacteristic
568C2×C4⋊C4C22×D1111yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—111no—
572C2×C22⋊C4—111no—
573C2×C22⋊C4—228no—
574C2×C22⋊C4—221no—
575C2×C22⋊C4—221no—
576C2×C22⋊C4—221no—
577C2×C22⋊C4—221no—
578C2×C22⋊C4—221no—
579C2×C42—111no—
580C2×C42—221no—
581C4⋊C8—222no—
582#103—22no—
583#103—41no—
584#103—222no—
585#103—441no—
586#102—114no—
587#102—222no—
588#102—222no—
589#102—222no—
590#102—222no—
591#102—222no—
592#102—441no—
593#102—441no—
594C22⋊C8—222no—
595C22⋊C8—222no—
596#97—222no—
597#95—21no—
598#95—221no—
599#95—221no—
600C2×C11—24no—
601C2×C11D4×C22⋊C411yescharacteristic
602C2×C11C2×#41711yescharacteristic
603C2×C11#289711yescharacteristic
604C2×C11#326411yescharacteristic
605C2×C11#326611yescharacteristic
606C2×C11#330611yescharacteristic
607C2×C11#331411yescharacteristic
608D11—42no—
609D11—44no—
610D11—82no—
611C24—111no—
612C24—221no—
613C24—221no—
614C24—224no—
615C24—442no—
616C24—442no—
617C24—442no—
618C24—442no—
619C24—881no—
620C24—881no—
621C24D4×D1111yescharacteristic
622#41—228no—
623#41—444no—
624#41—444no—
625#41—444no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8C2×C4×D1112yes—
632C2×D4—114no—
633C2×D4—112no—
634C2×D4—112no—
635C2×D4—112no—
636C2×D4—112no—
637C2×D4—228no—
638C2×D4—224no—
639C2×D4—224no—
640C2×D4—222no—
641C2×D4—222no—
642C2×D4—224no—
643C2×D4—221no—
644C2×D4—221no—
645C2×D4—221no—
646C2×D4—221no—
647C2×D4—221no—
648C2×D4—221no—
649C2×D4—221no—
650C2×D4—221no—
651C2×D4—444no—
652C2×D4—444no—
653C2×D4—444no—
654C2×D4—442no—
655C2×D4—442no—
656C2×D4—442no—
657C2×D4—442no—
658C2×D4—881no—
659C2×D4—881no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—111no—
669C22×C4—111no—
670C22×C4—111no—
671C22×C4—112no—
672C22×C4—112no—
673C22×C4—224no—
674C22×C4—224no—
675C22×C4—221no—
676C22×C4—221no—
677C22×C4—221no—
678C22×C4—221no—
679C22×C4—221no—
680C22×C4—221no—
681C22×C4—442no—
682C22×C4—442no—
683C22×C4—442no—
684C22×C4—442no—
685C22×C4—442no—
686C22×C4—442no—
687C22×C4—881no—
688C22×C4—881no—
689C22×C4—881no—
690C22×C4—881no—
691C22×C4C2×C4×D1112yes—
692C22×C4D4×D1111yescharacteristic
693C22×C4D4×D1112yes—
694C22×C4C23×D1111yescharacteristic
695M16—444no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—44no—
702C2×C8—221no—
703C2×C8—221no—
704C2×C8—221no—
705C2×C8—221no—
706C2×C8—221no—
707C2×C8—221no—
708C2×C8D4×D1112yes—
709C4⋊C4—24no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—114no—
716C4⋊C4—112no—
717C4⋊C4—221no—
718C4⋊C4—221no—
719C4⋊C4—221no—
720C4⋊C4—442no—
721C4⋊C4—442no—
722C4⋊C4—442no—
723C4⋊C4—881no—
724C4⋊C4C2×C4×D1112yes—
725C22⋊C4—24no—
726C22⋊C4—42no—
727C22⋊C4—114no—
728C22⋊C4—114no—
729C22⋊C4—224no—
730C22⋊C4—224no—
731C22⋊C4—224no—
732C22⋊C4—224no—
733C22⋊C4—442no—
734C42—112no—
735C42—112no—
736C42—442no—
737C11#2241911yescharacteristic, complemented, Sylow
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—112no—
743C23—222no—
744C23—221no—
745C23—221no—
746C23—221no—
747C23—221no—
748C23—221no—
749C23—222no—
750C23—221no—
751C23—222no—
752C23—222no—
753C23—448no—
754C23—441no—
755C23—441no—
756C23—441no—
757C23—441no—
758C23—441no—
759C23—441no—
760C23—441no—
761C23—441no—
762C23—441no—
763C23—441no—
764C23—448no—
765C23—884no—
766C23—884no—
767C23—884no—
768C23—884no—
769C23—884no—
770C23C22⋊C4×D1112yes—
771C23#6696712yes—
772C23#6697112yes—
773C23C2×D4×D1111yescharacteristic
774Q8—22no—
775Q8—22no—
776Q8—41no—
777Q8—41no—
778D4—114no—
779D4—228no—
780D4—222no—
781D4—222no—
782D4—222no—
783D4—222no—
784D4—222no—
785D4—448no—
786D4—448no—
787D4—441no—
788D4—441no—
789D4—884no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—112no—
809C2×C4—112no—
810C2×C4—112no—
811C2×C4—221no—
812C2×C4—221no—
813C2×C4—221no—
814C2×C4—221no—
815C2×C4—221no—
816C2×C4—221no—
817C2×C4—222no—
818C2×C4—222no—
819C2×C4—222no—
820C2×C4—222no—
821C2×C4—222no—
822C2×C4—448no—
823C2×C4—441no—
824C2×C4—441no—
825C2×C4—441no—
826C2×C4—441no—
827C2×C4—441no—
828C2×C4—884no—
829C2×C4—884no—
830C2×C4—884no—
831C2×C4C22⋊C4×D1112yes—
832C2×C4C22×C4×D1111yescharacteristic
833C2×C4C2×D4×D1111yescharacteristic
834C2×C4C2×D4×D1111yescharacteristic
835C2×C4#6703711yescharacteristic
836C2×C4#41×D1111yescharacteristic
837C2×C4#6704211yescharacteristic
838C8—22no—
839C8—41no—
840C8—441no—
841C8—441no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—222no—
849C22—224no—
850C22—222no—
851C22—222no—
852C22—441no—
853C22—442no—
854C22—441no—
855C22—442no—
856C22—441no—
857C22—442no—
858C22—441no—
859C22—442no—
860C22—442no—
861C22—442no—
862C22—442no—
863C22—442no—
864C22—442no—
865C22—8816no—
866C22—881no—
867C22—881no—
868C22—881no—
869C22—881no—
870C22#1062241614yescomplemented
871C22C2×C22⋊C4×D1111yescharacteristic
872C22#1062314011yescharacteristic
873C22#1062314111yescharacteristic
874C22C2×#6696711yescharacteristic
875C22C2×#6697111yescharacteristic
876C22#1062330011yescharacteristic
877C22#1062330111yescharacteristic
878C4—22no—
879C4—42no—
880C4—42no—
881C4—81no—
882C4—81no—
883C4—222no—
884C4—222no—
885C4—222no—
886C4—442no—
887C4—881no—
888C4C4×D4×D1111yescharacteristic
889C4#1062307611yescharacteristic
890C4#1062312111yescharacteristic
891C4#1062318511yescharacteristic
892C2—24no—
893C2—442no—
894C2—444no—
895C2—882no—
896C2#1307143411yescharacteristic
897C2C2×#1062241611yescharacteristic
898C2#1307713811yescharacteristic
899C2#1308009311yescharacteristic
900C2#1308012311yescharacteristic
901C2#1308058311yescharacteristic
902C2#1308070311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1892C2
socleC23×C11C22×D4
prime radicalC2×#10623161C2
cosocleC22×C4×C11C24
hypercenter#1892D11
hypocenterC11#22419
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1892

Complements

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

NH ≅ G/Ntype
2. C2×#10622724C2semidirect
3. C2×#10622416C2semidirect
4. C22×#66885C2semidirect
5. #13071512C2semidirect
6. #13069545C2semidirect
7. #13069429C2semidirect
8. #13069053C2semidirect
9. #13068932C2semidirect
10. #13068924C2semidirect
11. #13068615C2semidirect
12. #13068555C2semidirect
13. #13068546C2semidirect
14. #13068440C2semidirect
15. C11×#1892C2semidirect
23. C22×#4313C22semidirect
25. #10623161C4semidirect
30. C2×C4⋊C4×D11C22semidirect
34. C2×C11×#103C22semidirect
35. C2×C11×#103C22semidirect
37. C2×#66899C22semidirect
38. C2×#66899C22semidirect
46. C2×(C2×D11)⋊C8C22semidirect
47. C2×#66879C22semidirect
48. C2×Dic11⋊C8C22semidirect
49. #10622600C22semidirect
50. #10622589C22semidirect
51. C4⋊C4×Dic11C22semidirect
60. C11×#340C22semidirect
61. C11×#340C22semidirect
62. #10622167C22semidirect
63. #10622167C22semidirect
74. C2×#4343C2×C4semidirect
83. C22×D44C2×C4semidirect
96. C11×C22⋊Q8C2×C4semidirect
105. #67000C2×C4semidirect
132. #66948C2×C4semidirect
135. #66946C2×C4semidirect
152. #66885D4semidirect
295. #1892D11semidirect
394. D44C4×D4semidirect
429. C2×#103C2×D11semidirect
430. C2×#103C2×D11semidirect
452. #340C2×D11semidirect
453. #340C2×D11semidirect
460. C22×C11#417semidirect
544. C22⋊Q8C4×D11semidirect
737. C11#22419semidirect
870. C22#10622416semidirect

Maximal subgroups

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

subgroupindex
C2×#106231612
C2×#106227242
C2×#106224162
C22×#668852
#130715122
#130695452
#130694292
#130690532
#130689322
#130689242
#130686152
#130685552
#130685462
#130684402
C11×#18922
#2241911