Finite Group Databasebeta

← #14769203

Subgroups — #14769203

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×#10623163C211yesmaximal, characteristic
2C2×(C22⋊D11)⋊C8C211yesmaximal, characteristic
3C22×#66874C211yesmaximal, characteristic, complemented
4C2×D11×#103C211yesmaximal, characteristic, complemented
5C4⋊C4×C22⋊D11C211yesmaximal, characteristic
6#13069537C211yesmaximal, characteristic, complemented
7#13069416C211yesmaximal, characteristic, complemented
8#13069040C211yesmaximal, characteristic, complemented
9#13069038C211yesmaximal, characteristic, complemented
10#13068922C211yesmaximal, characteristic, complemented
11#13068620C211yesmaximal, characteristic, complemented
12#13068552C211yesmaximal, characteristic, complemented
13#13068549C211yesmaximal, characteristic, complemented
14#13068435C211yesmaximal, characteristic, complemented
15C11×#1872C211yesmaximal, characteristic, complemented
16C22×Q8×D11C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C2×#66997C2211yescharacteristic
21C2×C4×C22⋊D11—21no—
22C2×C4×C22⋊D11C2211yescharacteristic
23C23×C11⋊C8C2211yescharacteristic
24C22×C8×D11C2211yescharacteristic
25#10623163—24no—
26#10623163C418yescomplemented
27C2×#66950C2211yescharacteristic
28C2×#66949—21no—
29C2×C4⋊C4×D11C2211yescharacteristic
30C2×#66941—21no—
31C2×#66940C2211yescharacteristic
32C2×(C22⋊D11)⋊C4—21no—
33C2×#66931—21no—
34C2×C11×#103C2211yescharacteristic
35C2×C11×#103C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39#10622825C2211yescharacteristic
40#10622823—21no—
41C2×(C2×D11)⋊C8C2211yescharacteristic
42C2×#66880C2211yescharacteristic
43C2×#66880C2211yescharacteristic
44C2×#66880C2211yescharacteristic
45C2×#66880C2211yescharacteristic
46C2×Dic11⋊C8C2211yescharacteristic
47C2×C8×Dic11C2211yescharacteristic
48#10622602—21no—
49#10622600C2211yescharacteristic
50#10622589C2211yescharacteristic
51C4⋊C4×Dic11C2211yescharacteristic
52#10622585—21no—
53C2×#66874—24no—
54C2×#66874C2211yescharacteristic
55C2×#66874C2211yescharacteristic
56C2×#66874C2211yescharacteristic
57C2×#66874C2211yescharacteristic
58D11×#103—24no—
59(C22⋊D11)⋊C8—24no—
60C11×#340C2211yescharacteristic
61C11×#340C2211yescharacteristic
62#10622167C2211yescharacteristic
63#10622167C2211yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C23×C4×C11—21no—
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11D411yescharacteristic
68C23×Dic11—21no—
69C2×Q8×D11—22no—
70C2×Q8×D11—22no—
71C2×Q8×D11—22no—
72C2×Q8×D11—41no—
73C2×Q8×D11—41no—
74C2×Q8×D11C2×C414yescomplemented
75C22×C4×D11—21no—
76C22×C4×D11—21no—
77C22×C4×D11C2311yescharacteristic
78C22×Dic22—22no—
79C22×Dic22—22no—
80C22×Dic22—21no—
81C22×Dic22—22no—
82C22×Dic22—21no—
83C22×Dic22—41no—
84C22×Dic22—41no—
85C22×Dic22C2×C414yescomplemented
86C22×Dic22C2311yescharacteristic
87C22×Dic22C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C22×C8×C11C2311yescharacteristic
90C11×C22⋊Q8—22no—
91C11×C22⋊Q8C2×C414yescomplemented
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—22no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—41no—
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C22⋊C4—21no—
100C2×C22⋊Dic11—21no—
101C2×C22⋊Dic11D411yescharacteristic
102#66997—22no—
103#66997C2×C414yescomplemented
104C4×C22⋊D11—44no—
105C4×C22⋊D11C2×C414yes—
106C4×C22⋊D11D414yes—
107C2×(C2×D11)⋊C4—21no—
108C2×(C2×D11)⋊C4—21no—
109C2×(C2×D11)⋊C4D411yescharacteristic
110C2×C4⋊Dic11—21no—
111C2×C4⋊Dic11C2311yescharacteristic
112C2×C4⋊Dic11C2311yescharacteristic
113C2×Dic11⋊C4—21no—
114C2×Dic11⋊C4—21no—
115C2×Dic11⋊C4—21no—
116C2×Dic11⋊C4—21no—
117C2×Dic11⋊C4—21no—
118C2×Dic11⋊C4—21no—
119C2×Dic11⋊C4D411yescharacteristic
120C2×C4×Dic11—21no—
121C2×C4×Dic11—21no—
122C2×C4×Dic11C2311yescharacteristic
123C22×C11⋊C8—22no—
124C22×C11⋊C8—22no—
125C22×C11⋊C8—41no—
126C22×C11⋊C8C2311yescharacteristic
127C22×C11⋊C8C2311yescharacteristic
128C2×C8×D11—22no—
129C2×C8×D11—22no—
130C2×C8×D11—41no—
131#66950—22no—
132#66950C2×C414yescomplemented
133#66949—28no—
134C4⋊C4×D11—22no—
135C4⋊C4×D11—41no—
136#66941—28no—
137#66940—22no—
138#66940C2×C414yescomplemented
139(C22⋊D11)⋊C4—28no—
140#66931—28no—
141C11×#103—22no—
142C11×#103—41no—
143C11×C22⋊C8—22no—
144#66899—22no—
145#66899—41no—
146C11⋊#95—21no—
147C11⋊#95—21no—
148C11⋊#95—21no—
149(C2×D11)⋊C8—22no—
150#66880—22no—
151#66880—22no—
152#66880—41no—
153#66880—41no—
154Dic11⋊C8—22no—
155C8×Dic11—22no—
156#66874—22no—
157#66874—22no—
158#66874—22no—
159#66874D414yescomplemented
160D4×#103—111nomaximal, Sylow
161C24×C11C2×D411yescharacteristic
162C23×D11C2×D411yescharacteristic
163C2×Q8×C11—21no—
164C2×Q8×C11—21no—
165C2×Q8×C11—21no—
166C2×Q8×C11—21no—
167C2×Q8×C11—21no—
168C2×Q8×C11C22×C412yes—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—42no—
178C22×C4×C11—42no—
179C22×C4×C11—81no—
180C22×C4×C11C22×C412yes—
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D412yes—
183C22×C4×C11C2411yescharacteristic
184C2×C22⋊D11C22⋊C414yes—
185C2×C22⋊D11SD1614yes—
186C2×C22⋊D11Q1614yes—
187C22×Dic11—24no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—42no—
193C22×Dic11—42no—
194C22×Dic11C2×D411yescharacteristic
195C22×Dic11C2×D411yescharacteristic
196C22×Dic11C2×D411yescharacteristic
197Q8×D11—28no—
198Q8×D11—44no—
199Q8×D11—44no—
200Q8×D11—44no—
201C2×C4×D11—24no—
202C2×C4×D11—21no—
203C2×C4×D11—21no—
204C2×C4×D11—21no—
205C2×C4×D11—21no—
206C2×C4×D11—42no—
207C2×C4×D11—42no—
208C2×C4×D11—42no—
209C2×C4×D11—42no—
210C2×C4×D11—81no—
211C2×C4×D11C22×C412yes—
212C2×C4×D11C2×D412yes—
213C2×Dic22—28no—
214C2×Dic22—24no—
215C2×Dic22—24no—
216C2×Dic22—21no—
217C2×Dic22—21no—
218C2×Dic22—21no—
219C2×Dic22—21no—
220C2×Dic22—21no—
221C2×Dic22—21no—
222C2×Dic22—21no—
223C2×Dic22—21no—
224C2×Dic22—44no—
225C2×Dic22—44no—
226C2×Dic22—44no—
227C2×Dic22—42no—
228C2×Dic22—42no—
229C2×Dic22—42no—
230C2×Dic22—42no—
231C2×Dic22C22×C412yes—
232C2×Dic22C22×C412yes—
233C2×Dic22C2×D412yes—
234C2×Dic22#4112yes—
235C2×C8×C11—21no—
236C2×C8×C11—21no—
237C2×C8×C11—21no—
238C2×C8×C11—21no—
239C2×C8×C11—21no—
240C2×C8×C11—21no—
241C11×C4⋊C4—24no—
242C11×C4⋊C4—21no—
243C11×C4⋊C4—21no—
244C11×C4⋊C4—21no—
245C11×C4⋊C4—21no—
246C11×C4⋊C4—42no—
247C11×C4⋊C4C22×C412yes—
248C11×C4⋊C4C2×D412yes—
249C11×C22⋊C4—24no—
250C22⋊Dic11—42no—
251C22⋊Dic11C22⋊C414yes—
252(C2×D11)⋊C4—24no—
253(C2×D11)⋊C4—42no—
254(C2×D11)⋊C4C22⋊C414yes—
255C4⋊Dic11—24no—
256C4⋊Dic11—21no—
257C4⋊Dic11—21no—
258C4⋊Dic11—21no—
259C4⋊Dic11—21no—
260Dic11⋊C4—24no—
261Dic11⋊C4—24no—
262Dic11⋊C4—24no—
263Dic11⋊C4—42no—
264Dic11⋊C4—42no—
265Dic11⋊C4—81no—
266Dic11⋊C4C22⋊C414yes—
267C4×Dic11—24no—
268C4×Dic11—42no—
269C4×Dic11C22×C412yes—
270C4×Dic11C2×D412yes—
271C2×C11⋊C8—21no—
272C2×C11⋊C8—21no—
273C2×C11⋊C8—21no—
274C2×C11⋊C8—21no—
275C2×C11⋊C8—21no—
276C2×C11⋊C8—44no—
277C2×C11⋊C8C2×D412yes—
278C8×D11—44no—
279C2×D4×Q8—111no—
280C2×C8×D4—111no—
281C22×#103—111no—
282C22×#103—111no—
283D4×C4⋊C4—111no—
284#1981—111no—
285#1956—111no—
286#1892—111no—
287#1892—111no—
288#1872—111no—
289#1872D1111yescharacteristic, complemented
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—41no—
312Q8×C11—41no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—84no—
332C2×C4×C11C2×C22⋊C412yes—
333C2×C4×C11C23×C411yescharacteristic
334C2×C4×C11C22×D411yescharacteristic
335C2×C4×C11C22×D411yescharacteristic
336C2×C4×C11C2×#4111yescharacteristic
337C2×C4×C11H(5,𝔽2)11yescharacteristic
338C2×C4×C11H(5,𝔽2)11yescharacteristic
339C22⋊D11#103116yescomplemented
340C2×Dic11—22no—
341C2×Dic11—21no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—21no—
345C2×Dic11—21no—
346C2×Dic11—21no—
347C2×Dic11—22no—
348C2×Dic11—48no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—41no—
353C2×Dic11—41no—
354C2×Dic11—41no—
355C2×Dic11—41no—
356C2×Dic11—41no—
357C2×Dic11C2×C22⋊C412yes—
358C2×Dic11C2×C22⋊C412yes—
359C2×Dic11C2×C22⋊C412yes—
360C2×Dic11C2×SD1612yes—
361C2×Dic11C2×Q1612yes—
362C4×D11—22no—
363C4×D11—22no—
364C4×D11—22no—
365C4×D11—22no—
366C4×D11—48no—
367C4×D11—84no—
368Dic22—22no—
369Dic22—22no—
370Dic22—22no—
371Dic22—22no—
372Dic22—22no—
373Dic22—48no—
374Dic22—48no—
375Dic22—41no—
376Dic22—41no—
377Dic22C4×D414yescomplemented
378C8×C11—41no—
379C8×C11—41no—
380C11⋊C8—22no—
381C11⋊C8—41no—
382C23×Q8—111no—
383C23×Q8—111no—
384C23×C8—111no—
385C23×C8—111no—
386D4×Q8—118no—
387D4×Q8—224no—
388C2×C4⋊Q8—111no—
389C2×C4⋊Q8—221no—
390C2×C22⋊Q8—111no—
391C2×C22⋊Q8—221no—
392C2×C22⋊Q8—221no—
393C2×C22⋊Q8C2×D1111yescharacteristic
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—111no—
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—111no—
412C2×#103—224no—
413C2×#103—224no—
414C2×#103C2×D1111yescharacteristic
415C2×#103C2×D1111yescharacteristic
416C2×C22⋊C8—111no—
417C2×C22⋊C8C2×D1111yescharacteristic
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#340C2×D1111yescharacteristic
429#340C2×D1111yescharacteristic
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—42no—
453C4×C11—42no—
454C4×C11—42no—
455C4×C11—81no—
456C4×C11C2×C4×D411yescharacteristic
457C4×C11#51811yescharacteristic
458C4×C11D4211yescharacteristic
459C4×C11#54611yescharacteristic
460Dic11—24no—
461Dic11—22no—
462Dic11—22no—
463Dic11—42no—
464Dic11—81no—
465Dic11—81no—
466Dic11C2×#10314yescomplemented
467C22×Q8—114no—
468C22×Q8—114no—
469C22×Q8—111no—
470C22×Q8—111no—
471C22×Q8—221no—
472C22×Q8—222no—
473C22×Q8—222no—
474C22×Q8—222no—
475C22×Q8—221no—
476C22×Q8—222no—
477C22×Q8—222no—
478C22×Q8—222no—
479C22×Q8—441no—
480C22×Q8—441no—
481C22×Q8—441no—
482C22×Q8—441no—
483C22×Q8C22×D1111yescharacteristic
484C22×D4—111no—
485C23×C4—21no—
486C23×C4—111no—
487C23×C4—221no—
488C23×C4—221no—
489C23×C4—221no—
490C23×C4C22×D1111yescharacteristic
491C22×C8—111no—
492C22×C8—111no—
493C22×C8—222no—
494C22×C8—222no—
495C22×C8—222no—
496C22×C8—222no—
497C22×C8—441no—
498C22×C8—441no—
499C22×C8C22×D1111yescharacteristic
500C22×C8C22×D1111yescharacteristic
501C4⋊Q8—114no—
502C4⋊Q8—222no—
503C4⋊Q8—228no—
504C22⋊Q8—22no—
505C22⋊Q8—114no—
506C22⋊Q8—228no—
507C22⋊Q8—228no—
508C22⋊Q8—222no—
509C22⋊Q8C4×D1114yescomplemented
510C4×Q8—114no—
511C4×Q8—222no—
512C4×D4—114no—
513C4×D4—114no—
514C4×D4—228no—
515C4×D4—444no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—22no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—41no—
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—222no—
528C2×C4⋊C4—221no—
529C2×C4⋊C4—221no—
530C2×C4⋊C4—221no—
531C2×C4⋊C4—441no—
532C2×C4⋊C4C22×D1111yescharacteristic
533C2×C4⋊C4C22×D1111yescharacteristic
534C2×C4⋊C4C22×D1111yescharacteristic
535C2×C22⋊C4—21no—
536C2×C22⋊C4—111no—
537C2×C22⋊C4—111no—
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—41no—
547#103—114no—
548#103—222no—
549#103—222no—
550#103—222no—
551#103—222no—
552#103—222no—
553#103—222no—
554#103—441no—
555#103—441no—
556#103—441no—
557C22⋊C8—22no—
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—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—112no—
580C2×Q8—112no—
581C2×Q8—112no—
582C2×Q8—112no—
583C2×Q8—224no—
584C2×Q8—228no—
585C2×Q8—224no—
586C2×Q8—221no—
587C2×Q8—221no—
588C2×Q8—221no—
589C2×Q8—221no—
590C2×Q8—228no—
591C2×Q8—221no—
592C2×Q8—221no—
593C2×Q8—221no—
594C2×Q8—221no—
595C2×Q8—442no—
596C2×Q8—442no—
597C2×Q8—444no—
598C2×Q8—444no—
599C2×Q8—444no—
600C2×Q8—442no—
601C2×Q8—442no—
602C2×Q8—444no—
603C2×Q8—444no—
604C2×Q8—444no—
605C2×Q8C2×C4×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—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—81no—
620C22×C4—111no—
621C22×C4—111no—
622C22×C4—111no—
623C22×C4—112no—
624C22×C4—112no—
625C22×C4—224no—
626C22×C4—221no—
627C22×C4—221no—
628C22×C4—221no—
629C22×C4—221no—
630C22×C4—221no—
631C22×C4—224no—
632C22×C4—221no—
633C22×C4—221no—
634C22×C4—221no—
635C22×C4—442no—
636C22×C4—442no—
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—21no—
652C2×C8—112no—
653C2×C8—221no—
654C2×C8—221no—
655C2×C8—221no—
656C2×C8—221no—
657C2×C8—221no—
658C2×C8—444no—
659C2×C8—444no—
660C4⋊C4—24no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—42no—
666C4⋊C4—114no—
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—442no—
676C4⋊C4—442no—
677C4⋊C4—881no—
678C4⋊C4C2×C4×D1112yes—
679C4⋊C4D4×D1112yes—
680C22⋊C4—24no—
681C22⋊C4—114no—
682C22⋊C4—114no—
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—41no—
709Q8—41no—
710Q8—114no—
711Q8—222no—
712Q8—222no—
713Q8—222no—
714Q8—222no—
715Q8—222no—
716Q8—448no—
717Q8—448no—
718Q8—441no—
719Q8—441no—
720D4—1116no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—84no—
740C2×C4—112no—
741C2×C4—112no—
742C2×C4—112no—
743C2×C4—112no—
744C2×C4—112no—
745C2×C4—222no—
746C2×C4—221no—
747C2×C4—221no—
748C2×C4—221no—
749C2×C4—222no—
750C2×C4—221no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—222no—
757C2×C4—448no—
758C2×C4—448no—
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×D4×D1111yescharacteristic
771C2×C4C2×D4×D1111yescharacteristic
772C2×C4#6703711yescharacteristic
773C2×C4#41×D1111yescharacteristic
774C2×C4#6704211yescharacteristic
775C8—41no—
776C8—41no—
777C8—222no—
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#1062312111yescharacteristic
795C22#1062318511yescharacteristic
796C22C2×SD16×D1111yescharacteristic
797C22C2×Q16×D1111yescharacteristic
798C22#1062330611yescharacteristic
799C22#1062331011yescharacteristic
800C4—22no—
801C4—42no—
802C4—42no—
803C4—42no—
804C4—81no—
805C4—114no—
806C4—222no—
807C4—224no—
808C4—222no—
809C4—442no—
810C4—881no—
811C4—881no—
812C4C4×D4×D1111yescharacteristic
813C4#1062307611yescharacteristic
814C4#1062314011yescharacteristic
815C4#1062314111yescharacteristic
816C2—24no—
817C2—224no—
818C2#1307143411yescharacteristic
819C2C2×D11×#10311yescharacteristic
820C2#1307714711yescharacteristic
821C2#1308031011yescharacteristic
822C2#1308036111yescharacteristic
823C2#1308047911yescharacteristic
824C2#1308049011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1872C2
socleC23×C11C22×D4
prime radicalC22×C22⋊D11D4
cosocleC22×C4×C11C24
hypercenter#1872D11
hypocenterC11D4×#103
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
3. C22×#66874C2semidirect
4. C2×D11×#103C2semidirect
6. #13069537C2semidirect
7. #13069416C2semidirect
8. #13069040C2semidirect
9. #13069038C2semidirect
10. #13068922C2semidirect
11. #13068620C2semidirect
12. #13068552C2semidirect
13. #13068549C2semidirect
14. #13068435C2semidirect
15. C11×#1872C2semidirect
26. #10623163C4semidirect
74. C2×Q8×D11C2×C4semidirect
85. C22×Dic22C2×C4semidirect
91. C11×C22⋊Q8C2×C4semidirect
103. #66997C2×C4semidirect
132. #66950C2×C4semidirect
138. #66940C2×C4semidirect
159. #66874D4semidirect
289. #1872D11semidirect
339. C22⋊D11#103semidirect
377. Dic22C4×D4semidirect
436. C22×C11C2×#103semidirect
450. C2×D11C2×#103semidirect
466. Dic11C2×#103semidirect
509. C22⋊Q8C4×D11semidirect
690. C11D4×#103semidirect
792. C22D11×#103semidirect

Maximal subgroups

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

subgroupindex
C2×#106231632
C2×(C22⋊D11)⋊C82
C22×#668742
C2×D11×#1032
C4⋊C4×C22⋊D112
#130695372
#130694162
#130690402
#130690382
#130689222
#130686202
#130685522
#130685492
#130684352
C11×#18722
D4×#10311