Finite Group Databasebeta

← #14769370

Subgroups — #14769370

Order 2816.

1606 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623085C211yesmaximal, characteristic
2C2×#10622451C211yesmaximal, characteristic, complemented
3C2×#10622384C211yesmaximal, characteristic, complemented
4C2×#10622383C211yesmaximal, characteristic, complemented
5#13071542C211yesmaximal, characteristic, complemented
6#13069546C211yesmaximal, characteristic, complemented
7#13069425C211yesmaximal, characteristic, complemented
8#13069053C211yesmaximal, characteristic, complemented
9#13069048C211yesmaximal, characteristic, complemented
10#13068932C211yesmaximal, characteristic, complemented
11#13068927C211yesmaximal, characteristic, complemented
12#13068553C211yesmaximal, characteristic, complemented
13#13068545C211yesmaximal, characteristic, complemented
14C4×#66896C211yesmaximal, characteristic, complemented
15C11×#1804C211yesmaximal, characteristic, complemented
16C22×#4341C2211yescharacteristic
17C22×D4×D11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×#66983—21no—
20C22×(C2×D11)⋊C4—21no—
21C22×#4313C2211yescharacteristic
22C22×#4313C2211yescharacteristic, complemented
23#10623085—24no—
24#10623085C418yescomplemented
25C2×#66950C2211yescharacteristic
26C2×#66948C2211yescharacteristic
27C2×#66945C2211yescharacteristic
28C2×C4⋊C4×D11C2211yescharacteristic, complemented
29C2×#66939—21no—
30C2×#66935—21no—
31C2×#66928C2211yescharacteristic
32C2×C4×D44C2211yescharacteristic
33C2×C11×C4⋊C8C2211yescharacteristic, complemented
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C11×#382C2211yescharacteristic, complemented
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39C2×#66885C2211yescharacteristic
40C2×#66885C2211yescharacteristic
41C2×(C2×D11)⋊C8C2211yescharacteristic
42C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
43C2×#66880C2211yescharacteristic, complemented
44C2×#66880C2211yescharacteristic, complemented
45#10622600C2211yescharacteristic
46#10622600C2211yescharacteristic, complemented
47C2×#66874C2211yescharacteristic, complemented
48C2×#66874C2211yescharacteristic, complemented
49C2×#66873C2211yescharacteristic
50C2×#66873C2211yescharacteristic
51C4×C4⋊Dic11C2211yescharacteristic, complemented
52C2×C4×C11⋊C8C2211yescharacteristic, complemented
53#10622451—24no—
54#10622384—24no—
55#10622383—24no—
56#10622282—21no—
57#10622279—21no—
58#10622278—21no—
59#10622267—21no—
60C11×#340C2211yescharacteristic, complemented
61C11×#340C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63#10622167C2211yescharacteristic, complemented
64C24×D11—21no—
65C22×D4×C11C2311yescharacteristic
66C23×C4×C11—21no—
67C22×C22⋊D11—21no—
68C22×C22⋊D11—21no—
69C23×Dic11—21no—
70C2×#4341—22no—
71C2×#4341—22no—
72C2×#4341—22no—
73C2×#4341—41no—
74C2×#4341—41no—
75C2×#4341C2×C414yes—
76C2×D4×D11—22no—
77C2×D4×D11—22no—
78C2×D4×D11—22no—
79C2×D4×D11—41no—
80C2×D4×D11—41no—
81C2×D4×D11C2×C414yescomplemented
82C22×D44—21no—
83C22×D44D411yescharacteristic
84C22×D44C2311yescharacteristic
85C22×C4×D11—21no—
86C22×C4×D11C2311yescharacteristic
87C22×C4×D11C2311yescharacteristic
88C22×Dic22C2311yescharacteristic
89C22×C8×C11C2311yescharacteristic
90C22×C8×C11C2311yescharacteristic
91C4×D4×C11—22no—
92C4×D4×C11C2×C414yescomplemented
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C22⋊C4—21no—
97C2×C42×C11C2311yescharacteristic
98#66983—28no—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4—21no—
101C2×(C2×D11)⋊C4—21no—
102C2×(C2×D11)⋊C4—21no—
103C2×(C2×D11)⋊C4—28no—
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107C2×(C2×D11)⋊C4D411yescharacteristic
108C2×(C2×D11)⋊C4D411yescharacteristic
109C2×C4⋊Dic11—21no—
110C2×C4⋊Dic11D411yescharacteristic
111C2×C4⋊Dic11C2311yescharacteristic
112C2×C4⋊Dic11C2311yescharacteristic
113C2×Dic11⋊C4—21no—
114C2×C4×Dic11—21no—
115C2×C4×Dic11—21no—
116C22×C11⋊C8C2311yescharacteristic
117C22×C11⋊C8C2311yescharacteristic
118C2×#4313—22no—
119C2×#4313—22no—
120C2×#4313—22no—
121C2×#4313—22no—
122C2×#4313—41no—
123C2×#4313—41no—
124#66950—22no—
125#66950C2×C414yescomplemented
126#66948—22no—
127#66948C2×C414yes—
128#66945—22no—
129#66945—41no—
130C4⋊C4×D11—22no—
131C4⋊C4×D11—41no—
132#66939—28no—
133#66935—28no—
134#66928—22no—
135#66928C2×C414yescomplemented
136C4×D44C2×C414yes—
137C4×D44D414yes—
138C11×C4⋊C8—22no—
139C11×#102—22no—
140C11×#102—22no—
141C11×#95—21no—
142C11×#95—21no—
143#66896—22no—
144#66896D414yescomplemented
145C11⋊#95—21no—
146C11⋊#95—21no—
147C11⋊#95—21no—
148#66885—22no—
149#66885—41no—
150(C2×D11)⋊C8—22no—
151(C2×D11)⋊C8—22no—
152#66880—22no—
153#66880—41no—
154#66874—22no—
155#66874—41no—
156#66873—22no—
157#66873—41no—
158C4×C11⋊C8—22no—
159#22427—111nomaximal, Sylow
160C24×C11—21no—
161C23×D11—21no—
162C23×D11—24no—
163C23×D11—42no—
164C23×D11—42no—
165C23×D11—42no—
166C23×D11—42no—
167C23×D11—81no—
168C23×D11—81no—
169C23×D11C2×D411yescharacteristic
170C23×D11C2×D411yescharacteristic
171C2×D4×C11—21no—
172C2×D4×C11—21no—
173C2×D4×C11—21no—
174C2×D4×C11C22×C412yes—
175C2×D4×C11C2×D412yes—
176C2×D4×C11#4112yes—
177C22×C4×C11—21no—
178C22×C4×C11—24no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—81no—
182C22×C4×C11—81no—
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2411yescharacteristic
186C2×C22⋊D11—24no—
187C2×C22⋊D11—24no—
188C2×C22⋊D11—42no—
189C2×C22⋊D11—42no—
190C2×C22⋊D11—42no—
191C2×C22⋊D11—42no—
192C22×Dic11—24no—
193C22×Dic11—21no—
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11—42no—
197C22×Dic11—42no—
198C22×Dic11C2×D411yescharacteristic
199C22×Dic11C2×D411yescharacteristic
200#4341—28no—
201#4341—44no—
202#4341—44no—
203#4341—44no—
204D4×D11—28no—
205D4×D11—44no—
206D4×D11—44no—
207D4×D11—44no—
208C2×D44—24no—
209C2×D44—21no—
210C2×D44—21no—
211C2×D44—21no—
212C2×D44—21no—
213C2×D44—21no—
214C2×D44—41no—
215C2×D44—41no—
216C2×D44—81no—
217C2×D44—81no—
218C2×D44C22⋊C414yes—
219C2×D44C22×C412yes—
220C2×C4×D11—21no—
221C2×C4×D11—21no—
222C2×C4×D11—21no—
223C2×C4×D11—21no—
224C2×C4×D11—21no—
225C2×C4×D11—21no—
226C2×C4×D11—21no—
227C2×C4×D11—21no—
228C2×C4×D11—42no—
229C2×C4×D11—42no—
230C2×C4×D11—81no—
231C2×C4×D11C22×C412yes—
232C2×C4×D11C22×C412yes—
233C2×C4×D11C2×D412yes—
234C2×C4×D11C2×D412yes—
235C2×Dic22—21no—
236C2×Dic22—21no—
237C2×Dic22—21no—
238C2×Dic22—21no—
239C2×Dic22—21no—
240C2×Dic22C22×C412yes—
241C2×C8×C11—21no—
242C2×C8×C11—21no—
243C2×C8×C11—21no—
244C2×C8×C11—21no—
245C2×C8×C11—21no—
246C2×C8×C11—21no—
247C11×C4⋊C4—21no—
248C11×C4⋊C4—21no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4—21no—
251C11×C4⋊C4—21no—
252C11×C4⋊C4C22×C412yes—
253C11×C22⋊C4—24no—
254C42×C11C22×C412yes—
255C42×C11C2×D412yes—
256(C2×D11)⋊C4—24no—
257(C2×D11)⋊C4—24no—
258(C2×D11)⋊C4—24no—
259(C2×D11)⋊C4—24no—
260(C2×D11)⋊C4—42no—
261(C2×D11)⋊C4—42no—
262(C2×D11)⋊C4—81no—
263(C2×D11)⋊C4C22⋊C414yes—
264(C2×D11)⋊C4C22⋊C414yes—
265C4⋊Dic11—24no—
266C4⋊Dic11—21no—
267C4⋊Dic11—21no—
268C4⋊Dic11—21no—
269C4⋊Dic11C22⋊C414yes—
270C4⋊Dic11C2×D412yes—
271Dic11⋊C4—42no—
272C4×Dic11—42no—
273C4×Dic11—81no—
274C2×C11⋊C8—21no—
275C2×C11⋊C8—21no—
276C2×C11⋊C8—21no—
277C2×C11⋊C8—21no—
278C2×C11⋊C8—21no—
279C2×C11⋊C8C2×D412yes—
280#4313—44no—
281#4313—44no—
282C2×#546—111no—
283C2×#436—111no—
284C2×#417—111no—
285C2×#418—111no—
286#2352—111no—
287#1983—111no—
288#1958—111no—
289#1895—111no—
290#1894—111no—
291#1874—111no—
292#1873—111no—
293#1804D1111yescharacteristic, complemented
294#1788—111no—
295#1786—111no—
296C4×#102—111no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—41no—
301C23×C11—41no—
302C23×C11—41no—
303C23×C11—41no—
304C23×C11C22×D411yescharacteristic
305C22×D11—21no—
306C22×D11—21no—
307C22×D11—21no—
308C22×D11—21no—
309C22×D11—21no—
310C22×D11—21no—
311C22×D11—21no—
312C22×D11—21no—
313C22×D11—21no—
314C22×D11—21no—
315C22×D11—21no—
316C22×D11—21no—
317C22×D11—22no—
318C22×D11—48no—
319C22×D11—48no—
320C22×D11—41no—
321C22×D11—41no—
322C22×D11—41no—
323C22×D11—41no—
324C22×D11—41no—
325C22×D11—41no—
326C22×D11—84no—
327C22×D11—84no—
328C22×D11—84no—
329C22×D11—84no—
330C22×D11—84no—
331C22×D11C2×C22⋊C412yes—
332C22×D11C2×C22⋊C412yes—
333D4×C11—22no—
334D4×C11—22no—
335D4×C11—22no—
336D4×C11C4×D414yes—
337C2×C4×C11—21no—
338C2×C4×C11—21no—
339C2×C4×C11—21no—
340C2×C4×C11—21no—
341C2×C4×C11—22no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11—84no—
351C2×C4×C11C2×C22⋊C412yes—
352C2×C4×C11C2×C22⋊C412yes—
353C2×C4×C11C23×C411yescharacteristic
354C2×C4×C11C22×D411yescharacteristic
355C2×C4×C11C22×D411yescharacteristic
356C2×C4×C11C2×#4111yescharacteristic
357C2×C4×C11H(5,𝔽2)11yescharacteristic
358C2×C4×C11H(5,𝔽2)11yescharacteristic
359C22⋊D11—48no—
360C22⋊D11—48no—
361C2×Dic11—21no—
362C2×Dic11—21no—
363C2×Dic11—21no—
364C2×Dic11—21no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—48no—
368C2×Dic11—41no—
369C2×Dic11—41no—
370C2×Dic11—41no—
371C2×Dic11—41no—
372C2×Dic11—41no—
373C2×Dic11—41no—
374C2×Dic11—41no—
375C2×Dic11C2×C22⋊C412yes—
376C2×Dic11C2×C22⋊C412yes—
377D44—22no—
378D44—22no—
379D44—44no—
380D44—41no—
381D44—41no—
382D44—84no—
383C4×D11—22no—
384C4×D11—22no—
385C4×D11—22no—
386C4×D11—22no—
387C4×D11—22no—
388C4×D11—22no—
389C4×D11—22no—
390C4×D11—22no—
391C4×D11—84no—
392Dic22—22no—
393Dic22—22no—
394Dic22—41no—
395Dic22—41no—
396C8×C11—41no—
397C8×C11—41no—
398C11⋊C8—22no—
399C11⋊C8—41no—
400C22×#41—111no—
401C23×D4—111no—
402C22×M16—111no—
403C22×M16—111no—
404#546—118no—
405#546—224no—
406C2×#124—111no—
407C2×#123—221no—
408C2×C22⋊Q8—111no—
409C2×#121—111no—
410C2×#121—221no—
411C2×#120—221no—
412C2×C4×D4—111no—
413C2×C4×D4C2×D1111yescharacteristic
414C2×#117—111no—
415C22×C4⋊C4—111no—
416C22×C22⋊C4—221no—
417#436—224no—
418C2×C4⋊C8C2×D1111yescharacteristic, complemented
419#418—224no—
420#417—224no—
421C2×#103—111no—
422C2×#103—111no—
423C2×#103—111no—
424C2×#103—111no—
425C2×#102—111no—
426C2×#102—111no—
427C2×#102—111no—
428C2×#102—111no—
429C2×#102—111no—
430C2×#102—111no—
431C2×#102C2×D1111yescharacteristic
432C2×#102C2×D1111yescharacteristic
433C2×C22⋊C8—111no—
434C2×C22⋊C8—111no—
435C2×C4×C8—111no—
436#388—221no—
437#387—221no—
438#386—221no—
439#382C2×D1111yescharacteristic, complemented
440#380—111no—
441#380—111no—
442C4×C4⋊C4—111no—
443C4×C22⋊C4—221no—
444#340—111no—
445#340—111no—
446#340C2×D1111yescharacteristic, complemented
447#340C2×D1111yescharacteristic, complemented
448C22×C11—24no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11C22×C22⋊C411yescharacteristic
456C22×C11D4211yescharacteristic
457C22×C11#54611yescharacteristic
458C22×C11#57511yescharacteristic
459C22×C11#57511yescharacteristic
460C22×C11#57611yescharacteristic
461C22×C11#57711yescharacteristic
462C2×D11—22no—
463C2×D11—22no—
464C2×D11—22no—
465C2×D11—22no—
466C2×D11—22no—
467C2×D11—22no—
468C2×D11—41no—
469C2×D11—41no—
470C2×D11—41no—
471C2×D11—41no—
472C2×D11—41no—
473C2×D11—41no—
474C2×D11—41no—
475C2×D11—41no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—42no—
479C2×D11—816no—
480C2×D11—81no—
481C2×D11—81no—
482C2×D11—81no—
483C2×D11—81no—
484C4×C11—22no—
485C4×C11—22no—
486C4×C11—42no—
487C4×C11—81no—
488C4×C11—81no—
489C4×C11C2×C4×D411yescharacteristic
490C4×C11#51811yescharacteristic
491C4×C11D4211yescharacteristic
492C4×C11#54611yescharacteristic
493Dic11—22no—
494Dic11—22no—
495Dic11—42no—
496Dic11—42no—
497Dic11—81no—
498C25—221no—
499C2×#41—114no—
500C2×#41—222no—
501C2×#41—222no—
502C2×#41—222no—
503C2×#41—441no—
504C2×#41—441no—
505C22×Q8—111no—
506C22×D4—114no—
507C22×D4—111no—
508C22×D4—111no—
509C22×D4—221no—
510C22×D4—222no—
511C22×D4—221no—
512C22×D4—222no—
513C22×D4—222no—
514C22×D4—221no—
515C22×D4—441no—
516C22×D4—441no—
517C22×D4C22×D1111yescharacteristic
518C23×C4—21no—
519C23×C4—111no—
520C23×C4—111no—
521C23×C4—221no—
522C23×C4—221no—
523C2×M16—222no—
524C2×M16—222no—
525C2×M16—222no—
526C2×M16—222no—
527C2×M16—441no—
528C2×M16—441no—
529C22×C8—111no—
530C22×C8—111no—
531C22×C8C22×D1111yescharacteristic
532C22×C8C22×D1111yescharacteristic
533#124—114no—
534#124—222no—
535#123—228no—
536C22⋊Q8—114no—
537C22⋊Q8—222no—
538#121—114no—
539#121—228no—
540#121—222no—
541#120—228no—
542C4×D4—22no—
543C4×D4—114no—
544C4×D4—114no—
545C4×D4C4×D1114yescomplemented
546#117—222no—
547#117—441no—
548C2×C4⋊C4—111no—
549C2×C4⋊C4—111no—
550C2×C4⋊C4—111no—
551C2×C4⋊C4—222no—
552C2×C4⋊C4—221no—
553C2×C4⋊C4—221no—
554C2×C4⋊C4—441no—
555C2×C4⋊C4C22×D1111yescharacteristic
556C2×C4⋊C4C22×D1111yescharacteristic
557C2×C4⋊C4C22×D1111yescharacteristic
558C2×C22⋊C4—21no—
559C2×C22⋊C4—111no—
560C2×C22⋊C4—111no—
561C2×C22⋊C4—228no—
562C2×C22⋊C4—221no—
563C2×C22⋊C4—221no—
564C2×C22⋊C4—221no—
565C2×C22⋊C4—221no—
566C2×C22⋊C4—221no—
567C2×C22⋊C4—221no—
568C2×C22⋊C4—221no—
569C2×C42—221no—
570C2×C42—221no—
571C2×C42C22×D1111yescharacteristic
572C4⋊C8—22no—
573#103—222no—
574#103—222no—
575#103—441no—
576#103—441no—
577#102—22no—
578#102—22no—
579#102—114no—
580#102—222no—
581#102—222no—
582#102—222no—
583#102—441no—
584#102—441no—
585C22⋊C8—222no—
586C22⋊C8—222no—
587C4×C8—222no—
588#95—21no—
589#95—21no—
590#95—221no—
591#95—221no—
592#95—221no—
593C2×C11—44no—
594C2×C11D4×C22⋊C411yescharacteristic
595C2×C11#289611yescharacteristic
596C2×C11#289711yescharacteristic
597C2×C11#327311yescharacteristic
598C2×C11#327511yescharacteristic
599C2×C11#332211yescharacteristic
600C2×C11#332311yescharacteristic
601D11—42no—
602D11—42no—
603D11—82no—
604C24—21no—
605C24—111no—
606C24—111no—
607C24—224no—
608C24—221no—
609C24—442no—
610C24—442no—
611C24—442no—
612C24—442no—
613C24—881no—
614C24—881no—
615#41—228no—
616#41—444no—
617#41—444no—
618#41—444no—
619C2×Q8—112no—
620C2×Q8—221no—
621C2×Q8—221no—
622C2×Q8—221no—
623C2×Q8—221no—
624C2×Q8—221no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—114no—
629C2×D4—112no—
630C2×D4—224no—
631C2×D4—224no—
632C2×D4—228no—
633C2×D4—224no—
634C2×D4—221no—
635C2×D4—221no—
636C2×D4—221no—
637C2×D4—221no—
638C2×D4—221no—
639C2×D4—441no—
640C2×D4—441no—
641C2×D4—444no—
642C2×D4—444no—
643C2×D4—444no—
644C2×D4—442no—
645C2×D4—442no—
646C2×D4—442no—
647C2×D4—442no—
648C2×D4—881no—
649C2×D4—881no—
650C2×D4C2×C4×D1112yes—
651C2×D4D4×D1112yes—
652C2×D4#434312yes—
653C22×C4—21no—
654C22×C4—24no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—81no—
658C22×C4—81no—
659C22×C4—111no—
660C22×C4—111no—
661C22×C4—112no—
662C22×C4—112no—
663C22×C4—112no—
664C22×C4—112no—
665C22×C4—224no—
666C22×C4—221no—
667C22×C4—221no—
668C22×C4—221no—
669C22×C4—221no—
670C22×C4—221no—
671C22×C4—221no—
672C22×C4—221no—
673C22×C4—221no—
674C22×C4—221no—
675C22×C4—221no—
676C22×C4—221no—
677C22×C4—442no—
678C22×C4—442no—
679C22×C4—442no—
680C22×C4—442no—
681C22×C4—881no—
682C22×C4D4×D1111yescharacteristic
683C22×C4D4×D1111yescharacteristic
684C22×C4C23×D1111yescharacteristic
685M16—444no—
686M16—444no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—112no—
694C2×C8—221no—
695C2×C8—221no—
696C2×C8—221no—
697C2×C8—221no—
698C2×C8—221no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—114no—
705C4⋊C4—112no—
706C4⋊C4—224no—
707C4⋊C4—221no—
708C4⋊C4—221no—
709C4⋊C4—221no—
710C4⋊C4—442no—
711C4⋊C4C2×C4×D1112yes—
712C22⋊C4—24no—
713C22⋊C4—114no—
714C22⋊C4—114no—
715C22⋊C4—224no—
716C22⋊C4—224no—
717C22⋊C4—224no—
718C22⋊C4—224no—
719C22⋊C4—442no—
720C22⋊C4—442no—
721C22⋊C4—881no—
722C42—442no—
723C42—881no—
724C42C2×C4×D1112yes—
725C42D4×D1112yes—
726C11#2242711yescharacteristic, complemented, Sylow
727C23—22no—
728C23—22no—
729C23—22no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—112no—
735C23—112no—
736C23—221no—
737C23—221no—
738C23—221no—
739C23—221no—
740C23—221no—
741C23—221no—
742C23—221no—
743C23—221no—
744C23—221no—
745C23—221no—
746C23—221no—
747C23—221no—
748C23—222no—
749C23—448no—
750C23—448no—
751C23—441no—
752C23—441no—
753C23—441no—
754C23—441no—
755C23—441no—
756C23—441no—
757C23—884no—
758C23—884no—
759C23—884no—
760C23—884no—
761C23—884no—
762C23C2×D4×D1111yescharacteristic
763Q8—222no—
764Q8—222no—
765Q8—441no—
766Q8—441no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—222no—
771D4—222no—
772D4—444no—
773D4—448no—
774D4—448no—
775D4—441no—
776D4—441no—
777D4—884no—
778D4#6694614yes—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—84no—
793C2×C4—112no—
794C2×C4—112no—
795C2×C4—221no—
796C2×C4—221no—
797C2×C4—221no—
798C2×C4—221no—
799C2×C4—222no—
800C2×C4—222no—
801C2×C4—222no—
802C2×C4—222no—
803C2×C4—222no—
804C2×C4—222no—
805C2×C4—222no—
806C2×C4—222no—
807C2×C4—222no—
808C2×C4—222no—
809C2×C4—448no—
810C2×C4—441no—
811C2×C4—441no—
812C2×C4—441no—
813C2×C4—441no—
814C2×C4—441no—
815C2×C4—441no—
816C2×C4—441no—
817C2×C4—884no—
818C2×C4C22⋊C4×D1112yes—
819C2×C4C22⋊C4×D1112yes—
820C2×C4C22×C4×D1111yescharacteristic
821C2×C4C2×D4×D1111yescharacteristic
822C2×C4C2×D4×D1111yescharacteristic
823C2×C4C2×#434311yescharacteristic
824C2×C4#6704211yescharacteristic
825C2×C4#6704211yescharacteristic
826C8—41no—
827C8—41no—
828C8—222no—
829C8—441no—
830C22—24no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—222no—
838C22—222no—
839C22—222no—
840C22—222no—
841C22—222no—
842C22—222no—
843C22—441no—
844C22—441no—
845C22—441no—
846C22—441no—
847C22—441no—
848C22—441no—
849C22—441no—
850C22—441no—
851C22—442no—
852C22—442no—
853C22—442no—
854C22—8816no—
855C22—881no—
856C22—881no—
857C22—881no—
858C22—881no—
859C22C2×C22⋊C4×D1111yescharacteristic
860C22#1062314011yescharacteristic
861C22#1062316111yescharacteristic
862C22#1062329911yescharacteristic
863C22#1062329911yescharacteristic
864C22#1062330511yescharacteristic
865C22#1062330611yescharacteristic
866C4—22no—
867C4—22no—
868C4—42no—
869C4—81no—
870C4—81no—
871C4—222no—
872C4—222no—
873C4—442no—
874C4—442no—
875C4—881no—
876C4C2×#6694611yescharacteristic
877C4#1062305211yescharacteristic
878C4#1062314011yescharacteristic
879C4#1062316111yescharacteristic
880C2—44no—
881C2—442no—
882C2—442no—
883C2—882no—
884C2#1307143611yescharacteristic
885C2#1307713111yescharacteristic
886C2#1307714111yescharacteristic
887C2#1308022211yescharacteristic
888C2#1308025311yescharacteristic
889C2#1308081411yescharacteristic
890C2#1308082911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1804C2
socleC23×C11C22×D4
prime radicalC2×#10623085C2
cosocleC22×C4×C11C24
hypercenter#1804D11
hypocenterC11#22427
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
2. C2×#10622451C2semidirect
3. C2×#10622384C2semidirect
4. C2×#10622383C2semidirect
5. #13071542C2semidirect
6. #13069546C2semidirect
7. #13069425C2semidirect
8. #13069053C2semidirect
9. #13069048C2semidirect
10. #13068932C2semidirect
11. #13068927C2semidirect
12. #13068553C2semidirect
13. #13068545C2semidirect
14. C4×#66896C2semidirect
15. C11×#1804C2semidirect
22. C22×#4313C22semidirect
24. #10623085C4semidirect
28. C2×C4⋊C4×D11C22semidirect
33. C2×C11×C4⋊C8C22semidirect
36. C11×#382C22semidirect
42. C2×(C2×D11)⋊C8C22semidirect
43. C2×#66880C22semidirect
44. C2×#66880C22semidirect
46. #10622600C22semidirect
47. C2×#66874C22semidirect
48. C2×#66874C22semidirect
51. C4×C4⋊Dic11C22semidirect
52. C2×C4×C11⋊C8C22semidirect
60. C11×#340C22semidirect
61. C11×#340C22semidirect
62. #10622167C22semidirect
63. #10622167C22semidirect
81. C2×D4×D11C2×C4semidirect
92. C4×D4×C11C2×C4semidirect
125. #66950C2×C4semidirect
135. #66928C2×C4semidirect
144. #66896D4semidirect
293. #1804D11semidirect
418. C2×C4⋊C8C2×D11semidirect
439. #382C2×D11semidirect
446. #340C2×D11semidirect
447. #340C2×D11semidirect
545. C4×D4C4×D11semidirect
726. C11#22427semidirect

Maximal subgroups

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

subgroupindex
C2×#106230852
C2×#106224512
C2×#106223842
C2×#106223832
#130715422
#130695462
#130694252
#130690532
#130690482
#130689322
#130689272
#130685532
#130685452
C4×#668962
C11×#18042
#2242711