Finite Group Databasebeta

← #14759367

Subgroups — #14759367

Order 2816.

1532 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D11C211yesmaximal, characteristic, complemented
2C2×#10622783C211yesmaximal, characteristic
3C2×#10622371C211yesmaximal, characteristic, complemented
4C2×SD16×Dic11C211yesmaximal, characteristic, complemented
5#13071132C211yesmaximal, characteristic
6#13068974C211yesmaximal, characteristic, complemented
7#13068930C211yesmaximal, characteristic
8#13068887C211yesmaximal, characteristic, complemented
9#13068884C211yesmaximal, characteristic, complemented
10#13068810C211yesmaximal, characteristic, complemented
11#13068549C211yesmaximal, characteristic, complemented
12#103×Dic11C211yesmaximal, characteristic, complemented
13#13068435C211yesmaximal, characteristic, complemented
14#13068373C211yesmaximal, characteristic, complemented
15C11×#1880C211yesmaximal, characteristic, complemented
16C22×Q8×D11C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C2×#66991C2211yescharacteristic
21C2×D4×Dic11C2211yescharacteristic
22C22×#4324C2211yescharacteristic
23C4×Q8×D11—24no—
24C4×Q8×D11—24no—
25C2×C4⋊C4×D11—21no—
26C2×C4⋊C4×D11C2211yescharacteristic
27C2×#66940—21no—
28C2×#66940C2211yescharacteristic
29C2×(C22⋊D11)⋊C4—21no—
30C2×C42×D11—21no—
31C2×C42×D11C2211yescharacteristic
32C2×C4×Dic22—21no—
33C2×C4×Dic22C2211yescharacteristic
34C2×C11×#103C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C11×#390C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40#10622783C418yescomplemented
41SD16×Dic11—24no—
42C2×(C2×D11)⋊C8C2211yescharacteristic
43C2×(C2×D11)⋊C8C2211yescharacteristic
44C2×#66881C2211yescharacteristic
45C2×#66880C2211yescharacteristic
46C2×#66880C2211yescharacteristic
47C2×C8×Dic11C2211yescharacteristic
48C2×C8×Dic11C2211yescharacteristic
49#10622600C2211yescharacteristic
50C4⋊C4×Dic11C2211yescharacteristic
51C2×#66874C2211yescharacteristic
52C2×#66872C2211yescharacteristic
53#10622569—21no—
54#10622558—21no—
55C22⋊C4×Dic11—21no—
56#10622541C2211yescharacteristic
57#10622371—24no—
58C11×#340C2211yescharacteristic
59C11×#336C2211yescharacteristic
60#10622189C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622167C2211yescharacteristic
63#10622162C2211yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C22×D4×C11C2311yescharacteristic
66C22×C22⋊D11—21no—
67C23×Dic11—21no—
68C2×Q8×D11—22no—
69C2×Q8×D11—22no—
70C2×Q8×D11—22no—
71C2×Q8×D11—22no—
72C2×Q8×D11—22no—
73C2×Q8×D11C2×C414yescomplemented
74C22×C4×D11—21no—
75C22×C4×D11—21no—
76C22×C4×D11D411yescharacteristic
77C22×C4×D11D411yescharacteristic
78C22×C4×D11C2311yescharacteristic
79C22×Dic22—21no—
80C22×Dic22C2311yescharacteristic
81C2×C11×SD16—22no—
82C2×C11×SD16—22no—
83C2×C11×SD16C2×C414yescomplemented
84C22×C8×C11C2311yescharacteristic
85C22×C8×C11C2311yescharacteristic
86C4×Q8×C11—22no—
87C4×Q8×C11—22no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C42×C11—21no—
94C2×C42×C11C2311yescharacteristic
95C2×C22⋊Dic11—21no—
96C2×C22⋊Dic11—21no—
97Q8×Dic11—22no—
98Q8×Dic11D414yescomplemented
99#66991—22no—
100#66991C2×C414yes—
101D4×Dic11—22no—
102D4×Dic11—22no—
103C2×#4324—22no—
104C2×#4324—22no—
105C2×#4324C2×C414yescomplemented
106C2×(C2×D11)⋊C4—21no—
107C2×C4⋊Dic11—21no—
108C2×C4⋊Dic11C2311yescharacteristic
109C2×C4⋊Dic11C2311yescharacteristic
110C2×C4⋊Dic11C2311yescharacteristic
111C2×Dic11⋊C4—21no—
112C2×Dic11⋊C4—21no—
113C2×Dic11⋊C4—21no—
114C2×Dic11⋊C4—21no—
115C2×C4×Dic11—21no—
116C2×C4×Dic11—21no—
117C2×C4×Dic11—21no—
118C2×C4×Dic11—21no—
119C2×C4×Dic11D411yescharacteristic
120C2×C4×Dic11D411yescharacteristic
121C2×C4×Dic11C2311yescharacteristic
122C22×C11⋊C8C2311yescharacteristic
123C22×C11⋊C8C2311yescharacteristic
124C4⋊C4×D11—28no—
125C4⋊C4×D11—22no—
126C4⋊C4×D11—22no—
127#66940—28no—
128#66940—22no—
129#66940D414yescomplemented
130(C22⋊D11)⋊C4—44no—
131C42×D11—28no—
132C42×D11—22no—
133C42×D11—22no—
134C4×Dic22—28no—
135C4×Dic22—22no—
136C4×Dic22—22no—
137C11×#103—22no—
138C11×#102—22no—
139#66899—22no—
140#66899C2×C414yescomplemented
141#66896—22no—
142C11⋊#95—21no—
143C11⋊#95—21no—
144C11⋊#95—21no—
145(C2×D11)⋊C8—22no—
146(C2×D11)⋊C8C2×C414yescomplemented
147#66881—22no—
148#66880—22no—
149#66880C2×C414yescomplemented
150C8×Dic11—22no—
151C8×Dic11—22no—
152#66874—22no—
153#66872—22no—
154C4×#448—111nomaximal, Sylow
155C24×C11—21no—
156C23×D11C2×D411yescharacteristic
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×Q8×C11C22×C412yes—
161C2×Q8×C11C2×D412yes—
162C2×Q8×C11#4112yes—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11—21no—
168C2×D4×C11C22×C412yes—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2411yescharacteristic
175C2×C22⋊D11—24no—
176C2×C22⋊D11—42no—
177C2×C22⋊D11—42no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11—21no—
182C22×Dic11—42no—
183C22×Dic11—42no—
184C22×Dic11—42no—
185C22×Dic11C2×D411yescharacteristic
186C22×Dic11C2×D411yescharacteristic
187C22×Dic11C2×D411yescharacteristic
188Q8×D11—28no—
189Q8×D11—28no—
190Q8×D11—28no—
191Q8×D11—28no—
192C2×C4×D11—24no—
193C2×C4×D11—24no—
194C2×C4×D11—22no—
195C2×C4×D11—22no—
196C2×C4×D11—24no—
197C2×C4×D11—22no—
198C2×C4×D11—24no—
199C2×C4×D11—22no—
200C2×C4×D11—21no—
201C2×C4×D11—21no—
202C2×C4×D11—21no—
203C2×C4×D11—21no—
204C2×C4×D11—41no—
205C2×C4×D11—42no—
206C2×C4×D11—42no—
207C2×C4×D11SD1614yescomplemented
208C2×C4×D11C22×C412yes—
209C2×C4×D11#4112yes—
210C2×Dic22—24no—
211C2×Dic22—24no—
212C2×Dic22—24no—
213C2×Dic22—21no—
214C2×Dic22—21no—
215C2×Dic22—21no—
216C2×Dic22C22×C412yes—
217C2×Dic22C2×D412yes—
218C2×Dic22#4112yes—
219C11×SD16—28no—
220C2×C8×C11—21no—
221C2×C8×C11—21no—
222C2×C8×C11—21no—
223C2×C8×C11—21no—
224C2×C8×C11—21no—
225C2×C8×C11C22×C412yes—
226C11×C4⋊C4—24no—
227C11×C4⋊C4—21no—
228C11×C4⋊C4—21no—
229C11×C4⋊C4—21no—
230C11×C4⋊C4C2×D412yes—
231C11×C22⋊C4—42no—
232C11×C22⋊C4—42no—
233C42×C11—24no—
234C42×C11—21no—
235C42×C11—21no—
236C22⋊Dic11—24no—
237C22⋊Dic11—42no—
238#4324—28no—
239(C2×D11)⋊C4—42no—
240C4⋊Dic11—24no—
241C4⋊Dic11—21no—
242C4⋊Dic11—21no—
243C4⋊Dic11—21no—
244C4⋊Dic11—21no—
245C4⋊Dic11C22×C412yes—
246C4⋊Dic11C2×D412yes—
247Dic11⋊C4—24no—
248Dic11⋊C4—24no—
249Dic11⋊C4—24no—
250Dic11⋊C4—42no—
251C4×Dic11—24no—
252C4×Dic11—22no—
253C4×Dic11—22no—
254C4×Dic11—24no—
255C4×Dic11—24no—
256C4×Dic11—42no—
257C4×Dic11C2×D412yes—
258C4×Dic11C2×D412yes—
259C2×C11⋊C8—21no—
260C2×C11⋊C8—21no—
261C2×C11⋊C8—21no—
262C2×C11⋊C8—21no—
263C2×C11⋊C8—21no—
264C2×C11⋊C8C22×C412yes—
265C22×C4×Q8—111no—
266C2×#448—111no—
267C2×C4×SD16—111no—
268C2×C4×SD16—111no—
269C4×#121—111no—
270#1880—111no—
271#1880D1111yescharacteristic, complemented
272#1874—111no—
273#1865—111no—
274#1865—111no—
275#1853—111no—
276#1787—111no—
277C4×#103—111no—
278C4×#103—111no—
279C4×C22⋊C8—111no—
280C23×C11—22no—
281C23×C11—41no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11—41no—
285C23×C11—41no—
286C23×C11—41no—
287C23×C11C22×D411yescharacteristic
288C22×D11—21no—
289C22×D11—21no—
290C22×D11—21no—
291C22×D11—21no—
292C22×D11C4×D412yes—
293C22×D11C2×SD1612yes—
294C22×D11#13512yes—
295Q8×C11—22no—
296Q8×C11—22no—
297Q8×C11—22no—
298Q8×C11C4×D414yescomplemented
299D4×C11—22no—
300D4×C11—22no—
301D4×C11—41no—
302D4×C11—41no—
303C2×C4×C11—22no—
304C2×C4×C11—21no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—22no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11C2×SD1612yes—
318C2×C4×C11C23×C411yescharacteristic
319C2×C4×C11C22×D411yescharacteristic
320C2×C4×C11C22×D411yescharacteristic
321C2×C4×C11C2×#4111yescharacteristic
322C2×C4×C11C2×#4111yescharacteristic
323C2×C4×C11C2×#4111yescharacteristic
324C22⋊D11—48no—
325C2×Dic11—22no—
326C2×Dic11—21no—
327C2×Dic11—22no—
328C2×Dic11—21no—
329C2×Dic11—22no—
330C2×Dic11—21no—
331C2×Dic11—21no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—41no—
335C2×Dic11—41no—
336C2×Dic11—41no—
337C2×Dic11—41no—
338C2×Dic11—41no—
339C2×Dic11—41no—
340C2×Dic11—41no—
341C2×Dic11—84no—
342C2×Dic11C4×D412yes—
343C2×Dic11#12012yes—
344C2×Dic11#12012yes—
345C2×Dic11C2×SD1612yes—
346C2×Dic11#13712yes—
347C4×D11—216no—
348C4×D11—22no—
349C4×D11—22no—
350C4×D11—22no—
351C4×D11—22no—
352C4×D11—28no—
353C4×D11—44no—
354C4×D11—48no—
355Dic22—216no—
356Dic22—22no—
357Dic22—22no—
358Dic22—22no—
359Dic22C4×D414yescomplemented
360C8×C11—22no—
361C8×C11—41no—
362C11⋊C8—22no—
363C11⋊C8—41no—
364C23×Q8—111no—
365C22×SD16—111no—
366C22×SD16C2×D1111yescharacteristic
367C2×#121—111no—
368C2×C4×Q8—111no—
369C2×C4×Q8—111no—
370C2×C4×Q8—111no—
371C2×C4×Q8—221no—
372C2×C4×Q8—221no—
373C2×C4×Q8—224no—
374C2×C4×Q8—224no—
375C2×C4×Q8C2×D1111yescharacteristic
376C2×C4×D4—111no—
377C2×C4×D4—221no—
378C22×C4⋊C4—111no—
379C22×C4⋊C4—221no—
380C22×C42—111no—
381C22×C42—221no—
382#448—118no—
383C4×SD16—224no—
384C4×SD16—224no—
385C2×#106—111no—
386C2×#106—111no—
387C2×#103—111no—
388C2×#103—111no—
389C2×#103—111no—
390C2×#103—111no—
391C2×#103—111no—
392C2×#103C2×D1111yescharacteristic
393C2×#102—111no—
394C2×#102C2×D1111yescharacteristic
395C2×C22⋊C8—111no—
396C2×C22⋊C8—111no—
397C2×C4×C8—111no—
398C2×C4×C8—111no—
399#390C2×D1111yescharacteristic
400#389—111no—
401#388—221no—
402#386—221no—
403#380—111no—
404C4×C4⋊C4—111no—
405C4×C22⋊C4—221no—
406#340—111no—
407#340—111no—
408#340—111no—
409#340C2×D1111yescharacteristic
410#336—111no—
411#336C2×D1111yescharacteristic
412C22×C11—42no—
413C22×C11—42no—
414C22×C11—42no—
415C22×C11—81no—
416C22×C11—81no—
417C22×C11—81no—
418C22×C11—81no—
419C22×C11C2×C4×D411yescharacteristic
420C22×C11C2×#12011yescharacteristic
421C22×C11#52511yescharacteristic
422C22×C11C22×SD1611yescharacteristic
423C22×C11C2×#13511yescharacteristic
424C22×C11C2×#13711yescharacteristic
425C22×C11#57511yescharacteristic
426C2×D11—22no—
427C2×D11—22no—
428C2×D11—22no—
429C2×D11—22no—
430C2×D11—22no—
431C2×D11—22no—
432C2×D11C4×SD1614yescomplemented
433C4×C11—22no—
434C4×C11—24no—
435C4×C11—41no—
436C4×C11—42no—
437C4×C11—81no—
438C4×C11C2×C4×D411yescharacteristic
439C4×C11C2×C4×D411yescharacteristic
440C4×C11#52511yescharacteristic
441C4×C11#52511yescharacteristic
442Dic11—22no—
443Dic11—22no—
444Dic11—24no—
445Dic11—42no—
446Dic11—42no—
447Dic11—81no—
448Dic11#44814yescomplemented
449C22×Q8—114no—
450C22×Q8—111no—
451C22×Q8—221no—
452C22×Q8—222no—
453C22×Q8—222no—
454C22×Q8—222no—
455C22×Q8—222no—
456C22×Q8—222no—
457C22×Q8C22×D1111yescharacteristic
458C22×D4—221no—
459C22×D4C22×D1111yescharacteristic
460C23×C4—111no—
461C23×C4—111no—
462C23×C4—111no—
463C23×C4—221no—
464C23×C4—221no—
465C23×C4—221no—
466C2×SD16—22no—
467C2×SD16—22no—
468C2×SD16—114no—
469C2×SD16—222no—
470C2×SD16—222no—
471C2×SD16C4×D1114yescomplemented
472C22×C8—111no—
473C22×C8—111no—
474C22×C8C22×D1111yescharacteristic
475C22×C8C22×D1111yescharacteristic
476#121—114no—
477#121—222no—
478C4×Q8—22no—
479C4×Q8—22no—
480C4×Q8—114no—
481C4×Q8—114no—
482C4×Q8—222no—
483C4×Q8—222no—
484C4×Q8—228no—
485C4×Q8—222no—
486C4×Q8—222no—
487C4×Q8—228no—
488C4×D4—222no—
489C4×D4—222no—
490C4×D4—444no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—111no—
493C2×C4⋊C4—111no—
494C2×C4⋊C4—111no—
495C2×C4⋊C4—222no—
496C2×C4⋊C4—228no—
497C2×C4⋊C4—221no—
498C2×C4⋊C4—221no—
499C2×C4⋊C4—221no—
500C2×C4⋊C4—221no—
501C2×C4⋊C4—222no—
502C2×C4⋊C4—221no—
503C2×C4⋊C4C22×D1111yescharacteristic
504C2×C4⋊C4C22×D1111yescharacteristic
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—221no—
508C2×C22⋊C4—221no—
509C2×C22⋊C4—221no—
510C2×C42—21no—
511C2×C42—111no—
512C2×C42—111no—
513C2×C42—111no—
514C2×C42—222no—
515C2×C42—222no—
516C2×C42—228no—
517C2×C42—221no—
518C2×C42—221no—
519C2×C42—221no—
520C2×C42—221no—
521C2×C42C22×D1111yescharacteristic
522#106—222no—
523#106—222no—
524#103—22no—
525#103—114no—
526#103—114no—
527#103—222no—
528#103—222no—
529#103—222no—
530#102—22no—
531#102—222no—
532C22⋊C8—114no—
533C22⋊C8—222no—
534C4×C8—222no—
535C4×C8—222no—
536#95—221no—
537#95—221no—
538#95—221no—
539C2×C11—82no—
540C2×C11C4×#12011yescharacteristic
541C2×C11C2×C4×SD1611yescharacteristic
542C2×C11C4×#13711yescharacteristic
543C2×C11C2×#44811yescharacteristic
544C2×C11#300211yescharacteristic
545C2×C11#310311yescharacteristic
546C2×C11#310811yescharacteristic
547D11—24no—
548C24—21no—
549C24—111no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—112no—
554C2×Q8—112no—
555C2×Q8—112no—
556C2×Q8—224no—
557C2×Q8—224no—
558C2×Q8—224no—
559C2×Q8—228no—
560C2×Q8—228no—
561C2×Q8—228no—
562C2×Q8—228no—
563C2×Q8—221no—
564C2×Q8—221no—
565C2×Q8—221no—
566C2×Q8C2×C4×D1112yes—
567C2×Q8D4×D1112yes—
568C2×Q8#434112yes—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—224no—
575C2×D4—442no—
576C2×D4—442no—
577C2×D4C2×C4×D1112yes—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—111no—
582C22×C4—111no—
583C22×C4—111no—
584C22×C4—114no—
585C22×C4—112no—
586C22×C4—112no—
587C22×C4—222no—
588C22×C4—222no—
589C22×C4—222no—
590C22×C4—224no—
591C22×C4—224no—
592C22×C4—224no—
593C22×C4—222no—
594C22×C4—224no—
595C22×C4—221no—
596C22×C4—221no—
597C22×C4—221no—
598C22×C4—221no—
599C22×C4—221no—
600C22×C4—221no—
601C22×C4—221no—
602C22×C4—221no—
603C22×C4—441no—
604C22×C4—442no—
605C22×C4—442no—
606C22×C4—442no—
607C22×C4—442no—
608C22×C4—442no—
609C22×C4D4×D1111yescharacteristic
610C22×C4D4×D1111yescharacteristic
611C22×C4C23×D1111yescharacteristic
612SD16—28no—
613SD16—228no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—112no—
620C2×C8—221no—
621C2×C8—221no—
622C2×C8—221no—
623C2×C8—221no—
624C2×C8—221no—
625C2×C8C2×C4×D1112yes—
626C4⋊C4—24no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—112no—
631C4⋊C4—112no—
632C4⋊C4—224no—
633C4⋊C4—224no—
634C4⋊C4—224no—
635C4⋊C4—224no—
636C4⋊C4—221no—
637C4⋊C4—221no—
638C4⋊C4—221no—
639C4⋊C4—221no—
640C4⋊C4—442no—
641C4⋊C4D4×D1112yes—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—224no—
645C22⋊C4—442no—
646C22⋊C4—442no—
647C42—24no—
648C42—21no—
649C42—21no—
650C42—112no—
651C42—112no—
652C42—222no—
653C42—222no—
654C42—224no—
655C42—224no—
656C42—224no—
657C42—442no—
658C11C4×#44811yescharacteristic, complemented, Sylow
659C23—22no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—112no—
667C23—112no—
668C23—112no—
669C23—221no—
670C23—221no—
671C23—221no—
672C23—221no—
673C23C2×D4×D1111yescharacteristic
674Q8—22no—
675Q8—22no—
676Q8—22no—
677Q8—114no—
678Q8—2216no—
679Q8—222no—
680Q8—222no—
681Q8—222no—
682Q8(C22⋊D11)⋊C414yescomplemented
683D4—22no—
684D4—22no—
685D4—41no—
686D4—41no—
687D4—448no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—112no—
703C2×C4—112no—
704C2×C4—112no—
705C2×C4—112no—
706C2×C4—112no—
707C2×C4—228no—
708C2×C4—2216no—
709C2×C4—221no—
710C2×C4—221no—
711C2×C4—222no—
712C2×C4—221no—
713C2×C4—222no—
714C2×C4—221no—
715C2×C4—222no—
716C2×C4—222no—
717C2×C4—222no—
718C2×C4—222no—
719C2×C4—222no—
720C2×C4—222no—
721C2×C4—222no—
722C2×C4—444no—
723C2×C4—448no—
724C2×C4—441no—
725C2×C4—441no—
726C2×C4—441no—
727C2×C4—441no—
728C2×C4—441no—
729C2×C4—441no—
730C2×C4—441no—
731C2×C4—884no—
732C2×C4SD16×D1112yes—
733C2×C4C22×C4×D1111yescharacteristic
734C2×C4C2×D4×D1111yescharacteristic
735C2×C4C2×D4×D1111yescharacteristic
736C2×C4C2×#434111yescharacteristic
737C2×C4#41×D1111yescharacteristic
738C2×C4#41×D1111yescharacteristic
739C8—22no—
740C8—41no—
741C8—222no—
742C8—441no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—114no—
751C22—222no—
752C22—222no—
753C22—222no—
754C22—222no—
755C22—222no—
756C22—222no—
757C22C4×D4×D1111yescharacteristic
758C22D11×#12011yescharacteristic
759C22#1062313711yescharacteristic
760C22C2×SD16×D1111yescharacteristic
761C22D11×#13511yescharacteristic
762C22#1062330411yescharacteristic
763C22D11×#13711yescharacteristic
764C4—24no—
765C4—22no—
766C4—41no—
767C4—42no—
768C4—81no—
769C4—114no—
770C4—222no—
771C4—224no—
772C4—222no—
773C4—442no—
774C4—442no—
775C4—881no—
776C4C2×(C22⋊D11)⋊C411yescharacteristic
777C4C4×D4×D1111yescharacteristic
778C4#1062313711yescharacteristic
779C4#1062318711yescharacteristic
780C2—82no—
781C2—224no—
782C2#1307112111yescharacteristic
783C2C4×SD16×D1111yescharacteristic
784C2#1307743811yescharacteristic
785C2D11×#44811yescharacteristic
786C2#1307783111yescharacteristic
787C2#1307864611yescharacteristic
788C2#1307869511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1880C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
cosocleC22×C4×C11C24
hypercenter#1880D11
hypocenterC11C4×#448
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1880

Complements

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

NH ≅ G/Ntype
1. C2×C4×Q8×D11C2semidirect
3. C2×#10622371C2semidirect
4. C2×SD16×Dic11C2semidirect
6. #13068974C2semidirect
8. #13068887C2semidirect
9. #13068884C2semidirect
10. #13068810C2semidirect
11. #13068549C2semidirect
12. #103×Dic11C2semidirect
13. #13068435C2semidirect
14. #13068373C2semidirect
15. C11×#1880C2semidirect
40. #10622783C4semidirect
73. C2×Q8×D11C2×C4semidirect
83. C2×C11×SD16C2×C4semidirect
98. Q8×Dic11D4semidirect
105. C2×#4324C2×C4semidirect
129. #66940D4semidirect
140. #66899C2×C4semidirect
146. (C2×D11)⋊C8C2×C4semidirect
149. #66880C2×C4semidirect
207. C2×C4×D11SD16semidirect
271. #1880D11semidirect
298. Q8×C11C4×D4semidirect
359. Dic22C4×D4semidirect
432. C2×D11C4×SD16semidirect
448. Dic11#448semidirect
471. C2×SD16C4×D11semidirect
658. C11C4×#448semidirect
682. Q8(C22⋊D11)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D112
C2×#106227832
C2×#106223712
C2×SD16×Dic112
#130711322
#130689742
#130689302
#130688872
#130688842
#130688102
#130685492
#103×Dic112
#130684352
#130683732
C11×#18802
C4×#44811