Finite Group Databasebeta

← #103×C22⋊D11 #14769201

Subgroups — #103×C22⋊D11 #14769201

Order 2816.

1530 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C22⋊D11C211yesmaximal, characteristic
2C2×C8×C22⋊D11C211yesmaximal, characteristic
3C2×D11×#103C211yesmaximal, characteristic, complemented
4C4⋊C4×C22⋊D11C211yesmaximal, characteristic
5#13069537C211yesmaximal, characteristic, complemented
6#13069416C211yesmaximal, characteristic, complemented
7#13069039C211yesmaximal, characteristic, complemented
8#13069036C211yesmaximal, characteristic, complemented
9#13068923C211yesmaximal, characteristic, complemented
10#13068920C211yesmaximal, characteristic, complemented
11#13068619C211yesmaximal, characteristic, complemented
12#13068551C211yesmaximal, characteristic, complemented
13#13068549C211yesmaximal, characteristic, complemented
14#103×Dic11C211yesmaximal, characteristic, complemented
15C22×C11×#103C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic
17C22×Q8×D11C2211yescharacteristic
18C23×C8×C11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20Q8×C22⋊D11—24no—
21Q8×C22⋊D11C418yescomplemented
22C2×#66999—21no—
23C2×#66999C2211yescharacteristic
24C2×Q8×Dic11C2211yescharacteristic
25C2×#66997—21no—
26C2×#66997C2211yescharacteristic
27C2×C4×C22⋊D11—21no—
28C2×C4×C22⋊D11—21no—
29C2×C4×C22⋊D11C2211yescharacteristic
30C2×#66977—21no—
31C2×#66977C2211yescharacteristic
32C22×C8×D11C2211yescharacteristic
33C2×C4⋊C4×D11C2211yescharacteristic
34C2×C11×#103—24no—
35C2×C11×#103C2211yescharacteristic
36C2×C11×#103C2211yescharacteristic
37C2×C11×#103C2211yescharacteristic
38C2×C11×#103C2211yescharacteristic
39C2×#66899C2211yescharacteristic
40C2×#66899C2211yescharacteristic
41C2×#66899C2211yescharacteristic
42C2×#66899C2211yescharacteristic
43#10622825C2211yescharacteristic
44#10622823—21no—
45C2×C22⋊(C11⋊C8)C2211yescharacteristic
46C8×C22⋊D11—24no—
47C2×(C2×D11)⋊C8C2211yescharacteristic
48C2×#66880C2211yescharacteristic
49C2×#66880C2211yescharacteristic
50C2×Dic11⋊C8C2211yescharacteristic
51C2×C8×Dic11C2211yescharacteristic
52#10622602—21no—
53#10622600C2211yescharacteristic
54#10622589C2211yescharacteristic
55C4⋊C4×Dic11C2211yescharacteristic
56#10622585—21no—
57C2×#66874C2211yescharacteristic
58C2×#66874C2211yescharacteristic
59D11×#103—24no—
60#10622189C2211yescharacteristic
61#10622189C2211yescharacteristic
62#10622167C2211yescharacteristic
63#10622167C2211yescharacteristic
64C22×Q8×C11—21no—
65C22×Q8×C11—22no—
66C22×Q8×C11—22no—
67C22×Q8×C11—22no—
68C22×Q8×C11—41no—
69C22×Q8×C11—41no—
70C22×Q8×C11C2×C414yescomplemented
71C22×Q8×C11C2311yescharacteristic
72C22×Q8×C11C2311yescharacteristic
73C23×C4×C11—21no—
74C23×C4×C11—21no—
75C23×C4×C11C2311yescharacteristic
76C22×C22⋊D11D411yescharacteristic
77C2×Q8×D11—22no—
78C2×Q8×D11—22no—
79C2×Q8×D11—22no—
80C2×Q8×D11—41no—
81C2×Q8×D11—41no—
82C2×Q8×D11C2×C414yescomplemented
83C22×C4×D11—21no—
84C22×C4×D11—21no—
85C22×C4×D11C2311yescharacteristic
86C22×Dic22—21no—
87C22×Dic22C2311yescharacteristic
88C22×C8×C11—22no—
89C22×C8×C11—22no—
90C22×C8×C11—41no—
91C22×C8×C11C2311yescharacteristic
92C22×C8×C11C2311yescharacteristic
93C2×C11×C4⋊C4—22no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—41no—
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C22⋊Dic11—21no—
99C2×C22⋊Dic11—21no—
100C2×C22⋊Dic11D411yescharacteristic
101#66999—22no—
102#66999—28no—
103#66999C2×C414yescomplemented
104Q8×Dic11—22no—
105Q8×Dic11C2×C414yescomplemented
106#66997—28no—
107#66997—22no—
108#66997C2×C414yescomplemented
109C4×C22⋊D11—28no—
110C4×C22⋊D11—44no—
111C4×C22⋊D11C2×C414yes—
112C4×C22⋊D11D414yes—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4D411yescharacteristic
116C2×C4⋊Dic11—21no—
117C2×C4⋊Dic11C2311yescharacteristic
118C2×C4⋊Dic11C2311yescharacteristic
119C2×C4⋊Dic11C2311yescharacteristic
120#66977—22no—
121#66977—28no—
122#66977C2×C414yescomplemented
123C2×Dic11⋊C4—21no—
124C2×Dic11⋊C4—21no—
125C2×Dic11⋊C4—21no—
126C2×Dic11⋊C4—21no—
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×C8×D11—22no—
137C2×C8×D11—22no—
138C2×C8×D11—41no—
139C4⋊C4×D11—22no—
140C4⋊C4×D11—41no—
141C11×#103—22no—
142C11×#103—22no—
143C11×#103—22no—
144C11×#103D414yescomplemented
145#66899—22no—
146#66899—22no—
147#66899—41no—
148#66899—41no—
149C11⋊#95—21no—
150C11⋊#95—21no—
151C11⋊#95—21no—
152C22⋊(C11⋊C8)—22no—
153(C2×D11)⋊C8—22no—
154#66880—22no—
155#66880—41no—
156Dic11⋊C8—22no—
157C8×Dic11—22no—
158#66874—22no—
159#66874—41no—
160D4×#103—111nomaximal, Sylow
161C24×C11C2×D411yescharacteristic
162C23×D11C2×D411yescharacteristic
163C2×Q8×C11—24no—
164C2×Q8×C11—21no—
165C2×Q8×C11—21no—
166C2×Q8×C11—21no—
167C2×Q8×C11—21no—
168C2×Q8×C11—28no—
169C2×Q8×C11—21no—
170C2×Q8×C11—21no—
171C2×Q8×C11—21no—
172C2×Q8×C11—21no—
173C2×Q8×C11—42no—
174C2×Q8×C11—42no—
175C2×Q8×C11—44no—
176C2×Q8×C11—44no—
177C2×Q8×C11—44no—
178C2×Q8×C11C22×C412yes—
179C2×Q8×C11C22×C412yes—
180C2×Q8×C11C2×D412yes—
181C2×Q8×C11#4112yes—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—24no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—42no—
192C22×C4×C11—42no—
193C22×C4×C11—42no—
194C22×C4×C11—42no—
195C22×C4×C11—81no—
196C22×C4×C11C22×C412yes—
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D412yes—
199C22×C4×C11C2411yescharacteristic
200C2×C22⋊D11C22⋊C414yes—
201C2×C22⋊D11SD1614yes—
202C2×C22⋊D11Q1614yes—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11C2×D411yescharacteristic
208C22×Dic11C2×D411yescharacteristic
209C22×Dic11C2×D411yescharacteristic
210Q8×D11—28no—
211Q8×D11—44no—
212Q8×D11—44no—
213Q8×D11—44no—
214C2×C4×D11—24no—
215C2×C4×D11—21no—
216C2×C4×D11—21no—
217C2×C4×D11—21no—
218C2×C4×D11—21no—
219C2×C4×D11—42no—
220C2×C4×D11—42no—
221C2×C4×D11—42no—
222C2×C4×D11—42no—
223C2×C4×D11—81no—
224C2×C4×D11C22×C412yes—
225C2×C4×D11C2×D412yes—
226C2×Dic22—24no—
227C2×Dic22—21no—
228C2×Dic22—21no—
229C2×Dic22—21no—
230C2×Dic22—21no—
231C2×Dic22—21no—
232C2×Dic22—42no—
233C2×Dic22—42no—
234C2×Dic22C22×C412yes—
235C2×C8×C11—21no—
236C2×C8×C11—21no—
237C2×C8×C11—21no—
238C2×C8×C11—21no—
239C2×C8×C11—21no—
240C2×C8×C11—44no—
241C2×C8×C11C2×D412yes—
242C11×C4⋊C4—21no—
243C11×C4⋊C4—21no—
244C11×C4⋊C4—21no—
245C11×C4⋊C4—42no—
246C11×C4⋊C4C2×D412yes—
247C22⋊Dic11—24no—
248C22⋊Dic11—42no—
249C22⋊Dic11C22⋊C414yes—
250(C2×D11)⋊C4—24no—
251(C2×D11)⋊C4—42no—
252(C2×D11)⋊C4C22⋊C414yes—
253C4⋊Dic11—24no—
254C4⋊Dic11—21no—
255C4⋊Dic11—21no—
256C4⋊Dic11—21no—
257C4⋊Dic11—21no—
258C4⋊Dic11—21no—
259C4⋊Dic11C22×C412yes—
260Dic11⋊C4—24no—
261Dic11⋊C4—24no—
262Dic11⋊C4—24no—
263Dic11⋊C4—24no—
264Dic11⋊C4—42no—
265Dic11⋊C4—42no—
266Dic11⋊C4—81no—
267Dic11⋊C4C22⋊C414yes—
268C4×Dic11—24no—
269C4×Dic11—42no—
270C4×Dic11C22×C412yes—
271C4×Dic11C2×D412yes—
272C2×C11⋊C8—21no—
273C2×C11⋊C8—21no—
274C2×C11⋊C8—21no—
275C2×C11⋊C8—21no—
276C2×C11⋊C8—21no—
277C2×C11⋊C8—21no—
278C8×D11—44no—
279C2×D4×Q8—111no—
280C2×C8×D4—111no—
281C22×#103—111no—
282C22×#103D1111yescharacteristic, complemented
283D4×C4⋊C4—111no—
284#1981—111no—
285#1956—111no—
286#1892—111no—
287#1892—111no—
288#1872—111no—
289#1872—111no—
290#1803—111no—
291#1787—111no—
292#1787—111no—
293C4×#103—111no—
294C23×C11—21no—
295C23×C11—21no—
296C23×C11—21no—
297C23×C11—21no—
298C23×C11C2×C22⋊C412yes—
299C23×C11C2×SD1612yes—
300C23×C11C2×Q1612yes—
301C23×C11C22×D411yescharacteristic
302C22×D11—21no—
303C22×D11—21no—
304C22×D11—21no—
305C22×D11—21no—
306C22×D11C2×C22⋊C412yes—
307C22×D11C2×SD1612yes—
308C22×D11C2×Q1612yes—
309Q8×C11—22no—
310Q8×C11—22no—
311Q8×C11—22no—
312Q8×C11—22no—
313Q8×C11—22no—
314Q8×C11—48no—
315Q8×C11—41no—
316Q8×C11—41no—
317Q8×C11C4×D414yescomplemented
318C2×C4×C11—22no—
319C2×C4×C11—21no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
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—48no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11—84no—
338C2×C4×C11C2×C22⋊C412yes—
339C2×C4×C11C23×C411yescharacteristic
340C2×C4×C11C22×D411yescharacteristic
341C2×C4×C11C22×D411yescharacteristic
342C2×C4×C11C2×#4111yescharacteristic
343C2×C4×C11H(5,𝔽2)11yescharacteristic
344C2×C4×C11H(5,𝔽2)11yescharacteristic
345C22⋊D11#103116yesdirect product factor
346C2×Dic11—21no—
347C2×Dic11—21no—
348C2×Dic11—21no—
349C2×Dic11—21no—
350C2×Dic11—22no—
351C2×Dic11—22no—
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×Dic11C2×C22⋊C412yes—
363C2×Dic11C2×C22⋊C412yes—
364C2×Dic11C2×C22⋊C412yes—
365C2×Dic11C2×SD1612yes—
366C2×Dic11C2×Q1612yes—
367C4×D11—22no—
368C4×D11—22no—
369C4×D11—22no—
370C4×D11—22no—
371C4×D11—48no—
372C4×D11—84no—
373Dic22—22no—
374Dic22—22no—
375Dic22—48no—
376Dic22—41no—
377Dic22—41no—
378C8×C11—22no—
379C8×C11—41no—
380C11⋊C8—41no—
381C11⋊C8—41no—
382C23×Q8—111no—
383C23×Q8C2×D1111yescharacteristic
384C23×C8—111no—
385C23×C8C2×D1111yescharacteristic
386D4×Q8—118no—
387D4×Q8—224no—
388C2×C4⋊Q8—111no—
389C2×C4⋊Q8—221no—
390C2×C22⋊Q8—111no—
391C2×C22⋊Q8—111no—
392C2×C22⋊Q8—221no—
393C2×C22⋊Q8—221no—
394C2×C4×Q8—111no—
395C2×C4×D4—111no—
396C2×C4×D4—221no—
397C2×C4×D4—221no—
398C22×C4⋊C4—111no—
399C22×C4⋊C4C2×D1111yescharacteristic
400C8×D4—224no—
401C2×C4⋊C8—111no—
402C2×#103—24no—
403C2×#103—111no—
404C2×#103—111no—
405C2×#103—111no—
406C2×#103—111no—
407C2×#103—111no—
408C2×#103—111no—
409C2×#103—111no—
410C2×#103—111no—
411C2×#103—224no—
412C2×#103C2×D1111yescharacteristic
413C2×#103C2×D1111yescharacteristic
414C2×#103C2×D1111yescharacteristic
415C2×#103C2×D1111yescharacteristic
416C2×C22⋊C8—111no—
417C2×C22⋊C8—111no—
418C2×C4×C8—111no—
419#389—221no—
420#385—221no—
421#385—221no—
422#384—111no—
423#380—111no—
424#380—111no—
425C4×C4⋊C4—111no—
426#340—111no—
427#340—111no—
428#340—111no—
429#340—111no—
430C22×C11—22no—
431C22×C11—22no—
432C22×C11—22no—
433C22×C11—22no—
434C22×C11—22no—
435C22×C11—22no—
436C22×C11C2×#10314yescomplemented
437C22×C11C22×C22⋊C411yescharacteristic
438C22×C11D4211yescharacteristic
439C22×C11#54611yescharacteristic
440C22×C11C22×SD1611yescharacteristic
441C22×C11C22×Q1611yescharacteristic
442C22×C11#57711yescharacteristic
443C22×C11#57811yescharacteristic
444C2×D11—22no—
445C2×D11—22no—
446C2×D11—22no—
447C2×D11—22no—
448C2×D11—22no—
449C2×D11—22no—
450C2×D11C2×#10314yescomplemented
451C4×C11—22no—
452C4×C11—24no—
453C4×C11—42no—
454C4×C11—42no—
455C4×C11—81no—
456C4×C11C2×C4×D411yescharacteristic
457C4×C11#51811yescharacteristic
458C4×C11D4211yescharacteristic
459C4×C11#54611yescharacteristic
460Dic11—22no—
461Dic11—22no—
462Dic11—42no—
463Dic11—42no—
464Dic11—81no—
465Dic11—81no—
466Dic11C2×#10314yescomplemented
467C22×Q8—21no—
468C22×Q8—22no—
469C22×Q8—22no—
470C22×Q8—22no—
471C22×Q8—41no—
472C22×Q8—41no—
473C22×Q8—114no—
474C22×Q8—111no—
475C22×Q8—221no—
476C22×Q8—222no—
477C22×Q8—222no—
478C22×Q8—222no—
479C22×Q8—441no—
480C22×Q8—441no—
481C22×Q8C4×D1114yescomplemented
482C22×Q8C22×D1111yescharacteristic
483C22×Q8C22×D1111yescharacteristic
484C22×D4—111no—
485C23×C4—21no—
486C23×C4—21no—
487C23×C4—111no—
488C23×C4—221no—
489C23×C4—221no—
490C23×C4C22×D1111yescharacteristic
491C22×C8—22no—
492C22×C8—22no—
493C22×C8—41no—
494C22×C8—111no—
495C22×C8—111no—
496C22×C8—222no—
497C22×C8—222no—
498C22×C8—441no—
499C22×C8C22×D1111yescharacteristic
500C22×C8C22×D1111yescharacteristic
501C4⋊Q8—114no—
502C4⋊Q8—222no—
503C4⋊Q8—228no—
504C22⋊Q8—114no—
505C22⋊Q8—114no—
506C22⋊Q8—228no—
507C22⋊Q8—228no—
508C22⋊Q8—222no—
509C22⋊Q8—222no—
510C4×Q8—114no—
511C4×Q8—222no—
512C4×D4—114no—
513C4×D4—114no—
514C4×D4—228no—
515C4×D4—444no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—41no—
519C2×C4⋊C4—111no—
520C2×C4⋊C4—111no—
521C2×C4⋊C4—111no—
522C2×C4⋊C4—111no—
523C2×C4⋊C4—221no—
524C2×C4⋊C4—221no—
525C2×C4⋊C4—221no—
526C2×C4⋊C4—221no—
527C2×C4⋊C4—221no—
528C2×C4⋊C4—222no—
529C2×C4⋊C4—221no—
530C2×C4⋊C4—221no—
531C2×C4⋊C4—221no—
532C2×C4⋊C4—441no—
533C2×C4⋊C4C22×D1111yescharacteristic
534C2×C4⋊C4C22×D1111yescharacteristic
535C2×C22⋊C4—111no—
536C2×C22⋊C4—111no—
537C2×C22⋊C4—221no—
538C2×C22⋊C4—221no—
539C2×C22⋊C4—221no—
540C2×C22⋊C4—221no—
541C2×C42—111no—
542C2×C42—221no—
543C2×C42—221no—
544C4⋊C8—222no—
545#103—22no—
546#103—22no—
547#103—22no—
548#103—222no—
549#103—222no—
550#103—222no—
551#103—222no—
552#103—441no—
553#103—441no—
554#103—441no—
555#103—441no—
556#103C22⋊D1114yesdirect product factor
557C22⋊C8—222no—
558C22⋊C8—222no—
559C4×C8—222no—
560#95—221no—
561#95—221no—
562#95—221no—
563C2×C11—24no—
564C2×C11D4×C22⋊C411yescharacteristic
565C2×C11C22×#10311yescharacteristic
566C2×C11#289811yescharacteristic
567C2×C11D4×SD1611yescharacteristic
568C2×C11D4×Q1611yescharacteristic
569C2×C11#329811yescharacteristic
570C2×C11#329911yescharacteristic
571D11—24no—
572C24—111no—
573C24D4×D1111yescharacteristic
574C2×Q8—24no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—28no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—42no—
585C2×Q8—42no—
586C2×Q8—44no—
587C2×Q8—44no—
588C2×Q8—44no—
589C2×Q8—112no—
590C2×Q8—224no—
591C2×Q8—221no—
592C2×Q8—228no—
593C2×Q8—221no—
594C2×Q8—221no—
595C2×Q8—221no—
596C2×Q8—221no—
597C2×Q8—442no—
598C2×Q8—442no—
599C2×Q8—444no—
600C2×Q8—444no—
601C2×Q8—444no—
602C2×Q8C2×C4×D1112yes—
603C2×Q8C2×C4×D1112yes—
604C2×Q8#433912yes—
605C2×Q8C2×C22⋊D1112yes—
606C2×D4—114no—
607C2×D4—114no—
608C2×D4—114no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—24no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—81no—
623C22×C4—111no—
624C22×C4—111no—
625C22×C4—111no—
626C22×C4—112no—
627C22×C4—112no—
628C22×C4—224no—
629C22×C4—221no—
630C22×C4—221no—
631C22×C4—221no—
632C22×C4—221no—
633C22×C4—221no—
634C22×C4—221no—
635C22×C4—221no—
636C22×C4—221no—
637C22×C4—442no—
638C22×C4—442no—
639C22×C4—442no—
640C22×C4—442no—
641C22×C4—881no—
642C22×C4C2×C4×D1112yes—
643C22×C4D4×D1111yescharacteristic
644C22×C4D4×D1112yes—
645C22×C4C23×D1111yescharacteristic
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—44no—
652C2×C8—221no—
653C2×C8—221no—
654C2×C8—221no—
655C2×C8—221no—
656C2×C8—221no—
657C2×C8—221no—
658C2×C8—444no—
659C2×C8C2×C22⋊D1112yes—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—42no—
664C4⋊C4—114no—
665C4⋊C4—112no—
666C4⋊C4—224no—
667C4⋊C4—224no—
668C4⋊C4—224no—
669C4⋊C4—224no—
670C4⋊C4—224no—
671C4⋊C4—221no—
672C4⋊C4—221no—
673C4⋊C4—221no—
674C4⋊C4—221no—
675C4⋊C4—221no—
676C4⋊C4—442no—
677C4⋊C4—442no—
678C4⋊C4—881no—
679C4⋊C4C2×C22⋊D1112yes—
680C22⋊C4—114no—
681C22⋊C4—114no—
682C22⋊C4—224no—
683C22⋊C4—224no—
684C22⋊C4—442no—
685C22⋊C4—442no—
686C42—112no—
687C42—112no—
688C42—224no—
689C42—442no—
690C11D4×#10311yescharacteristic, complemented, Sylow
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—112no—
696C23—112no—
697C23—112no—
698C23—221no—
699C23—221no—
700C23—221no—
701C23—221no—
702C23C22⋊C4×D1112yes—
703C23SD16×D1112yes—
704C23Q16×D1112yes—
705C23C2×D4×D1111yescharacteristic
706Q8—22no—
707Q8—22no—
708Q8—22no—
709Q8—22no—
710Q8—22no—
711Q8—48no—
712Q8—41no—
713Q8—41no—
714Q8—222no—
715Q8—222no—
716Q8—448no—
717Q8—441no—
718Q8—441no—
719Q8C4×C22⋊D1114yescomplemented
720D4—1116no—
721C2×C4—22no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—48no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—84no—
741C2×C4—112no—
742C2×C4—112no—
743C2×C4—112no—
744C2×C4—112no—
745C2×C4—112no—
746C2×C4—221no—
747C2×C4—221no—
748C2×C4—221no—
749C2×C4—221no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—448no—
757C2×C4—441no—
758C2×C4—441no—
759C2×C4—441no—
760C2×C4—441no—
761C2×C4—441no—
762C2×C4—441no—
763C2×C4—441no—
764C2×C4—441no—
765C2×C4—441no—
766C2×C4—441no—
767C2×C4—884no—
768C2×C4C22⋊C4×D1112yes—
769C2×C4C22×C4×D1111yescharacteristic
770C2×C4C2×#433911yescharacteristic
771C2×C4C2×D4×D1111yescharacteristic
772C2×C4#6703711yescharacteristic
773C2×C4#6703711yescharacteristic
774C2×C4C22×C22⋊D1111yescharacteristic
775C8—22no—
776C8—41no—
777C8—441no—
778C8—441no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—114no—
786C22—222no—
787C22—222no—
788C22—222no—
789C22—222no—
790C22—222no—
791C22—222no—
792C22D11×#10314yescomplemented
793C22C2×C22⋊C4×D1111yescharacteristic
794C22#1062302111yescharacteristic
795C22C2×SD16×D1111yescharacteristic
796C22#1062329311yescharacteristic
797C22C2×Q16×D1111yescharacteristic
798C22#1062329711yescharacteristic
799C22D4×C22⋊D1111yescharacteristic
800C4—22no—
801C4—24no—
802C4—42no—
803C4—42no—
804C4—81no—
805C4—114no—
806C4—222no—
807C4—222no—
808C4—442no—
809C4—442no—
810C4—881no—
811C4—881no—
812C4#1062301711yescharacteristic
813C4#1062302111yescharacteristic
814C4C2×C4×C22⋊D1111yescharacteristic
815C4D4×C22⋊D1111yescharacteristic
816C2—24no—
817C2—224no—
818C2C22⋊C4×C22⋊D1111yescharacteristic
819C2C2×D11×#10311yescharacteristic
820C2#1307714411yescharacteristic
821C2SD16×C22⋊D1111yescharacteristic
822C2Q16×C22⋊D1111yescharacteristic
823C2#1308047711yescharacteristic
824C2#1308048811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#103C2
socleC23×C11C22×D4
prime radicalC22×C22⋊D11D4
cosocleC22×C4×C11C24
hypercenterC22×#103D11
hypocenterC11D4×#103
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
3. C2×D11×#103C2semidirect
5. #13069537C2semidirect
6. #13069416C2semidirect
7. #13069039C2semidirect
8. #13069036C2semidirect
9. #13068923C2semidirect
10. #13068920C2semidirect
11. #13068619C2semidirect
12. #13068551C2semidirect
13. #13068549C2semidirect
14. #103×Dic11C2semidirect
15. C22×C11×#103C2semidirect
21. Q8×C22⋊D11C4semidirect
70. C22×Q8×C11C2×C4semidirect
82. C2×Q8×D11C2×C4semidirect
103. #66999C2×C4semidirect
105. Q8×Dic11C2×C4semidirect
108. #66997C2×C4semidirect
122. #66977C2×C4semidirect
144. C11×#103D4semidirect
282. C22×#103D11semidirect
317. Q8×C11C4×D4semidirect
345. C22⋊D11#103direct (N × H)
436. C22×C11C2×#103semidirect
450. C2×D11C2×#103semidirect
466. Dic11C2×#103semidirect
481. C22×Q8C4×D11semidirect
556. #103C22⋊D11direct (N × H)
690. C11D4×#103semidirect
719. Q8C4×C22⋊D11semidirect
792. C22D11×#103semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C22⋊D112
C2×C8×C22⋊D112
C2×D11×#1032
C4⋊C4×C22⋊D112
#130695372
#130694162
#130690392
#130690362
#130689232
#130689202
#130686192
#130685512
#130685492
#103×Dic112
C22×C11×#1032
D4×#10311