Finite Group Databasebeta

← #14774034

Subgroups — #14774034

Order 2816.

1302 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622777C211yesmaximal, characteristic, complemented
2C22×#66896C211yesmaximal, characteristic
3#13071625C211yesmaximal, characteristic, complemented
4D4×C22⋊Dic11C211yesmaximal, characteristic
5#13069499C211yesmaximal, characteristic, complemented
6#13069315C211yesmaximal, characteristic, complemented
7#13069238C211yesmaximal, characteristic, complemented
8#13069040C211yesmaximal, characteristic, complemented
9#13068973C211yesmaximal, characteristic, complemented
10#13068952C211yesmaximal, characteristic, complemented
11#13068865C211yesmaximal, characteristic, complemented
12#13068806C211yesmaximal, characteristic, complemented
13#13068443C211yesmaximal, characteristic, complemented
14#13068395C211yesmaximal, characteristic, complemented
15C2×C11×#450C211yesmaximal, characteristic
16C23×D4×C11C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C22×C22⋊Dic11—21no—
21C2×Q8×Dic11C2211yescharacteristic, complemented
22C2×D4×Dic11C2211yescharacteristic
23C2×D4×Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C23×C11⋊C8C2211yescharacteristic
26C11×#450C418yescomplemented
27C2×C11×#102C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C2×C11×C22⋊C8C2211yescharacteristic
30#10622860—21no—
31#10622843C2211yescharacteristic, complemented
32C2×#66899C2211yescharacteristic, complemented
33C2×#66899C2211yescharacteristic, complemented
34#10622834C2211yescharacteristic
35#10622834C2211yescharacteristic
36#10622833—21no—
37#10622833—21no—
38C2×#66896—24no—
39C2×#66896C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42C2×#66896C2211yescharacteristic
43#10622825C2211yescharacteristic
44C4×C22⋊Dic11C2211yescharacteristic
45#10622777—24no—
46C2×#66882C2211yescharacteristic, complemented
47C2×#66882C2211yescharacteristic, complemented
48C2×#66879C2211yescharacteristic, complemented
49C2×#66879C2211yescharacteristic, complemented
50#10622598—21no—
51#10622598C2211yescharacteristic, complemented
52#10622594—21no—
53C4⋊C4×Dic11C2211yescharacteristic, complemented
54#10622563—21no—
55C22⋊C4×Dic11—21no—
56#10622189C2211yescharacteristic, complemented
57#10622189C2211yescharacteristic, complemented
58#10622188C2211yescharacteristic, complemented
59#10622188C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61#10622167C2211yescharacteristic, complemented
62C25×C11—21no—
63C22×Q8×C11C2311yescharacteristic
64C22×D4×C11—22no—
65C22×D4×C11—22no—
66C22×D4×C11—21no—
67C22×D4×C11—22no—
68C22×D4×C11—41no—
69C22×D4×C11—41no—
70C22×D4×C11C2×C414yes—
71C22×D4×C11C2311yescharacteristic
72C22×D4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×Dic11—21no—
75C23×Dic11—21no—
76C23×Dic11—21no—
77C2×C11×SD16—22no—
78C2×C11×SD16—22no—
79C2×C11×SD16—41no—
80C2×C11×SD16—41no—
81C2×C11×SD16C2×C414yescomplemented
82C2×C11×SD16C2×C414yescomplemented
83C22×C8×C11C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C11×C22⋊Q8—22no—
86C11×C22⋊Q8C2×C414yescomplemented
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C22⋊C4—21no—
90C2×C22⋊Dic11—21no—
91C2×C22⋊Dic11—21no—
92C2×C22⋊Dic11—21no—
93C2×C22⋊Dic11—21no—
94C2×C22⋊Dic11—21no—
95C2×C22⋊Dic11—21no—
96C2×C22⋊Dic11—21no—
97C2×C22⋊Dic11—44no—
98C2×C22⋊Dic11D411yescharacteristic
99C2×C22⋊Dic11D411yescharacteristic
100Q8×Dic11—22no—
101Q8×Dic11—41no—
102D4×Dic11—22no—
103D4×Dic11—22no—
104D4×Dic11—41no—
105D4×Dic11—41no—
106C2×C4⋊Dic11—22no—
107C2×C4⋊Dic11—21no—
108C2×C4⋊Dic11—21no—
109C2×C4⋊Dic11—21no—
110C2×C4⋊Dic11—41no—
111C2×C4⋊Dic11C2311yescharacteristic
112C2×C4⋊Dic11C2311yescharacteristic
113C2×C4⋊Dic11C2311yescharacteristic
114C2×C4⋊Dic11C2311yescharacteristic
115C2×C4×Dic11—21no—
116C2×C4×Dic11—21no—
117C2×C4×Dic11C2311yescharacteristic
118C2×C4×Dic11C2311yescharacteristic
119C22×C11⋊C8—22no—
120C22×C11⋊C8—22no—
121C22×C11⋊C8—41no—
122C22×C11⋊C8C2311yescharacteristic
123C22×C11⋊C8C2311yescharacteristic
124C11×#102C2×C414yescomplemented
125C11×#102C2×C414yescomplemented
126C11×C22⋊C8C2×C414yescomplemented
127#66899—22no—
128#66899—41no—
129#66896—22no—
130#66896—22no—
131#66896—22no—
132#66896D414yes—
133C11⋊#95—21no—
134C11⋊#95—21no—
135C11⋊#95—21no—
136C11⋊#95—21no—
137C11⋊#95—21no—
138C11⋊#95D411yescharacteristic
139C11⋊#95D411yescharacteristic
140#66882—22no—
141#66882—41no—
142#66879—22no—
143#66879—41no—
144#22854—111nomaximal, Sylow
145C24×C11—21no—
146C24×C11—21no—
147C24×C11—24no—
148C24×C11—42no—
149C24×C11—42no—
150C24×C11—42no—
151C24×C11—42no—
152C24×C11—81no—
153C24×C11—81no—
154C24×C11C2×D411yescharacteristic
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×Q8×C11C22×C412yes—
161C2×D4×C11—28no—
162C2×D4×C11—24no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11—21no—
171C2×D4×C11—44no—
172C2×D4×C11—44no—
173C2×D4×C11—44no—
174C2×D4×C11—42no—
175C2×D4×C11—42no—
176C2×D4×C11C22×C412yes—
177C2×D4×C11C22×C412yes—
178C2×D4×C11C2×D412yes—
179C2×D4×C11#4112yes—
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×C11#4112yes—
189C22×C4×C11C2411yescharacteristic
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—21no—
193C22×Dic11—21no—
194C22×Dic11—42no—
195C22×Dic11—42no—
196C22×Dic11—42no—
197C22×Dic11—42no—
198C22×Dic11—42no—
199C22×Dic11—42no—
200C22×Dic11—81no—
201C22×Dic11—81no—
202C22×Dic11—81no—
203C22×Dic11C2×D411yescharacteristic
204C22×Dic11C2×D411yescharacteristic
205C22×Dic11C2×D411yescharacteristic
206C22×Dic11C2×D411yescharacteristic
207C11×SD16—28no—
208C11×SD16—44no—
209C2×C8×C11—21no—
210C2×C8×C11—21no—
211C2×C8×C11—21no—
212C2×C8×C11—21no—
213C2×C8×C11C22×C412yes—
214C2×C8×C11C22×C412yes—
215C11×C4⋊C4—24no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4C22×C412yes—
218C11×C22⋊C4—24no—
219C22⋊Dic11—22no—
220C22⋊Dic11—22no—
221C22⋊Dic11—42no—
222C22⋊Dic11—42no—
223C22⋊Dic11—42no—
224C22⋊Dic11—42no—
225C22⋊Dic11—42no—
226C22⋊Dic11—81no—
227C22⋊Dic11—81no—
228C4⋊Dic11—21no—
229C4⋊Dic11—21no—
230C4⋊Dic11—21no—
231C4⋊Dic11—21no—
232C4⋊Dic11—21no—
233C4⋊Dic11—21no—
234C4⋊Dic11—21no—
235C4⋊Dic11—42no—
236C4⋊Dic11—42no—
237C4⋊Dic11—81no—
238C4⋊Dic11C2×D412yes—
239C4×Dic11—21no—
240C4×Dic11—21no—
241C4×Dic11—21no—
242C4×Dic11—21no—
243C4×Dic11—42no—
244C4×Dic11—81no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8—21no—
248C2×C11⋊C8—21no—
249C2×C11⋊C8—21no—
250C2×C11⋊C8—44no—
251C2×C11⋊C8C2×D412yes—
252C2×#450D1111yescharacteristic
253C2×#440—111no—
254C22×#102—111no—
255#2360—111no—
256D4×C22⋊C4—111no—
257#1973—111no—
258#1936—111no—
259#1925—111no—
260#1892—111no—
261#1880—111no—
262#1877—111no—
263#1862—111no—
264#1852—111no—
265#1762—111no—
266#1752—111no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—22no—
272C23×C11—22no—
273C23×C11—22no—
274C23×C11—22no—
275C23×C11—48no—
276C23×C11—41no—
277C23×C11—41no—
278C23×C11—41no—
279C23×C11—41no—
280C23×C11—41no—
281C23×C11—41no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11—41no—
285C23×C11—41no—
286C23×C11—48no—
287C23×C11—84no—
288C23×C11—84no—
289C23×C11—84no—
290C23×C11—84no—
291C23×C11—84no—
292C23×C11C4×D412yes—
293C23×C11AGL(1,ℤ/8)12yes—
294C23×C11#13712yes—
295C23×C11C22×D411yescharacteristic
296Q8×C11—22no—
297Q8×C11—22no—
298Q8×C11—41no—
299Q8×C11—41no—
300D4×C11—22no—
301D4×C11—22no—
302D4×C11—22no—
303D4×C11—22no—
304D4×C11—22no—
305D4×C11—48no—
306D4×C11—41no—
307D4×C11—41no—
308D4×C11C4×D414yes—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11C4×D412yes—
322C2×C4×C11C23×C411yescharacteristic
323C2×C4×C11C22×D411yescharacteristic
324C2×C4×C11C2×#4111yescharacteristic
325C2×C4×C11C2×#4111yescharacteristic
326C2×C4×C11H(5,𝔽2)11yescharacteristic
327C2×C4×C11H(5,𝔽2)11yescharacteristic
328C2×Dic11—21no—
329C2×Dic11—21no—
330C2×Dic11—22no—
331C2×Dic11—21no—
332C2×Dic11—21no—
333C2×Dic11—21no—
334C2×Dic11—21no—
335C2×Dic11—21no—
336C2×Dic11—21no—
337C2×Dic11—21no—
338C2×Dic11—21no—
339C2×Dic11—21no—
340C2×Dic11—21no—
341C2×Dic11—41no—
342C2×Dic11—41no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11—41no—
346C2×Dic11—41no—
347C2×Dic11—41no—
348C2×Dic11—41no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—84no—
353C2×Dic11—84no—
354C2×Dic11—84no—
355C8×C11—22no—
356C8×C11—22no—
357C11⋊C8—22no—
358C11⋊C8—41no—
359C23×D4C2×D1111yescharacteristic
360C22×SD16C2×D1111yescharacteristic
361C22×SD16C2×D1111yescharacteristic
362C23×C8—111no—
363C2×C22⋊Q8C2×D1111yescharacteristic
364C2×C4×Q8—111no—
365C2×C4×D4—111no—
366C2×C4×D4—111no—
367C22×C4⋊C4—111no—
368C22×C22⋊C4—221no—
369#450Dic1118yescomplemented
370#440—224no—
371C2×#107—111no—
372C2×#107—111no—
373C2×#103—111no—
374C2×#103—111no—
375C2×#102—111no—
376C2×#102—111no—
377C2×#102—111no—
378C2×#102—111no—
379C2×#102—224no—
380C2×#102C2×D1111yescharacteristic
381C2×#102C2×D1111yescharacteristic
382C2×C22⋊C8C2×D1111yescharacteristic
383C2×#97—111no—
384C2×#97—111no—
385#391—111no—
386#390—111no—
387#390—111no—
388#389—111no—
389#389—221no—
390#387—221no—
391#386—221no—
392#386—221no—
393#385—221no—
394#380—111no—
395#379—221no—
396C4×C4⋊C4—111no—
397C4×C22⋊C4—111no—
398C4×C22⋊C4—221no—
399#340—111no—
400#340—111no—
401#340—111no—
402#340—111no—
403#336—111no—
404#336—111no—
405C22×C11—22no—
406C22×C11—22no—
407C22×C11—22no—
408C22×C11—22no—
409C22×C11—22no—
410C22×C11—22no—
411C22×C11—24no—
412C22×C11—42no—
413C22×C11—42no—
414C22×C11—42no—
415C22×C11—42no—
416C22×C11—42no—
417C22×C11—42no—
418C22×C11—42no—
419C22×C11—42no—
420C22×C11—42no—
421C22×C11—816no—
422C22×C11—81no—
423C22×C11—81no—
424C22×C11—81no—
425C22×C11—81no—
426C22×C11#44014yescomplemented
427C22×C11C2×C4×D411yescharacteristic
428C22×C11D4211yescharacteristic
429C22×C11#54611yescharacteristic
430C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
431C22×C11C2×#13711yescharacteristic
432C22×C11#57611yescharacteristic
433C22×C11#57711yescharacteristic
434C4×C11—22no—
435C4×C11—42no—
436C4×C11—42no—
437C4×C11C2×C4×D411yescharacteristic
438C4×C11#51811yescharacteristic
439C4×C11#54611yescharacteristic
440C4×C11#55111yescharacteristic
441Dic11—41no—
442Dic11—42no—
443Dic11—41no—
444Dic11—41no—
445Dic11—41no—
446Dic11—81no—
447Dic11—81no—
448Dic11—81no—
449C25—21no—
450C22×Q8C22×D1111yescharacteristic
451C22×D4—22no—
452C22×D4—22no—
453C22×D4—21no—
454C22×D4—22no—
455C22×D4—41no—
456C22×D4—41no—
457C22×D4C2×Dic1114yes—
458C22×D4C22×D1111yescharacteristic
459C22×D4C22×D1111yescharacteristic
460C23×C4—221no—
461C23×C4—221no—
462C23×C4—221no—
463C23×C4C22×D1111yescharacteristic
464C2×SD16—22no—
465C2×SD16—22no—
466C2×SD16—41no—
467C2×SD16—41no—
468C2×SD16C2×Dic1114yescomplemented
469C2×SD16C2×Dic1114yescomplemented
470C22×C8—111no—
471C22×C8—111no—
472C22×C8—222no—
473C22×C8—222no—
474C22×C8—441no—
475C22×C8C22×D1111yescharacteristic
476C22×C8C22×D1111yescharacteristic
477C22⋊Q8—22no—
478C22⋊Q8C2×Dic1114yescomplemented
479C4×Q8—222no—
480C4×Q8—441no—
481C4×D4—222no—
482C4×D4—222no—
483C4×D4—441no—
484C4×D4—441no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—111no—
487C2×C4⋊C4—111no—
488C2×C4⋊C4—111no—
489C2×C4⋊C4—111no—
490C2×C4⋊C4—222no—
491C2×C4⋊C4—221no—
492C2×C4⋊C4—221no—
493C2×C4⋊C4—221no—
494C2×C4⋊C4—441no—
495C2×C4⋊C4C22×D1111yescharacteristic
496C2×C22⋊C4—21no—
497C2×C22⋊C4—111no—
498C2×C22⋊C4—111no—
499C2×C22⋊C4—221no—
500C2×C22⋊C4—221no—
501C2×C22⋊C4—221no—
502C2×C22⋊C4—221no—
503C2×C22⋊C4—221no—
504C2×C22⋊C4—221no—
505C2×C22⋊C4—221no—
506C2×C22⋊C4—444no—
507C2×C42—111no—
508C2×C42—111no—
509C2×C42—221no—
510C2×C42—221no—
511#107—222no—
512#107—441no—
513#103—222no—
514#103—441no—
515#102—114no—
516#102—222no—
517#102—222no—
518#102—222no—
519#102C2×Dic1114yescomplemented
520#102C2×Dic1114yescomplemented
521C22⋊C8C2×Dic1114yescomplemented
522#97—222no—
523#97—441no—
524#95—111no—
525#95—111no—
526#95—221no—
527#95—221no—
528#95—221no—
529#95—221no—
530#95—221no—
531C2×C11—24no—
532C2×C11—44no—
533C2×C11—82no—
534C2×C11#235811yescharacteristic
535C2×C11C2×#44011yescharacteristic
536C2×C11#294611yescharacteristic
537C2×C11#326411yescharacteristic
538C2×C11#326611yescharacteristic
539C2×C11#331011yescharacteristic
540C2×C11#331411yescharacteristic
541C24—21no—
542C24—21no—
543C24—24no—
544C24—42no—
545C24—42no—
546C24—42no—
547C24—42no—
548C24—81no—
549C24—81no—
550C24D4×D1111yescharacteristic
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8C22×Dic1112yes—
557C2×D4—28no—
558C2×D4—24no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4D4×D1112yes—
573C2×D4#434112yes—
574C2×D4C22×Dic1112yes—
575C2×D4C22×Dic1112yes—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—111no—
583C22×C4—111no—
584C22×C4—111no—
585C22×C4—111no—
586C22×C4—221no—
587C22×C4—221no—
588C22×C4—221no—
589C22×C4—221no—
590C22×C4—442no—
591C22×C4—442no—
592C22×C4—442no—
593C22×C4—442no—
594C22×C4—442no—
595C22×C4—442no—
596C22×C4—881no—
597C22×C4—881no—
598C22×C4—881no—
599C22×C4D4×D1111yescharacteristic
600C22×C4#434112yes—
601C22×C4C22×Dic1112yes—
602C22×C4C23×D1111yescharacteristic
603SD16—28no—
604SD16—44no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—112no—
610C2×C8—221no—
611C2×C8—221no—
612C2×C8—221no—
613C2×C8—221no—
614C2×C8—221no—
615C2×C8—444no—
616C2×C8C22×Dic1112yes—
617C2×C8C22×Dic1112yes—
618C4⋊C4—24no—
619C4⋊C4—21no—
620C4⋊C4—112no—
621C4⋊C4—221no—
622C4⋊C4—221no—
623C4⋊C4—221no—
624C4⋊C4—221no—
625C4⋊C4—221no—
626C4⋊C4—221no—
627C4⋊C4—221no—
628C4⋊C4—442no—
629C4⋊C4—442no—
630C4⋊C4—881no—
631C4⋊C4C22×Dic1112yes—
632C22⋊C4—24no—
633C22⋊C4—222no—
634C22⋊C4—222no—
635C22⋊C4—442no—
636C22⋊C4—442no—
637C22⋊C4—442no—
638C22⋊C4—442no—
639C22⋊C4—442no—
640C22⋊C4—881no—
641C22⋊C4—881no—
642C42—221no—
643C42—221no—
644C42—221no—
645C42—221no—
646C42—442no—
647C42—881no—
648C11#2285411yescharacteristic, complemented, Sylow
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—48no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—48no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—84no—
670C23—84no—
671C23—84no—
672C23—84no—
673C23—84no—
674C23#6696712yes—
675C23#6696812yes—
676C23D4×Dic1112yes—
677C23C2×D4×D1111yescharacteristic
678Q8—22no—
679Q8—22no—
680Q8—41no—
681Q8—41no—
682D4—22no—
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—48no—
688D4—41no—
689D4—41no—
690D4D4×Dic1114yes—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—221no—
704C2×C4—221no—
705C2×C4—221no—
706C2×C4—221no—
707C2×C4—221no—
708C2×C4—221no—
709C2×C4—221no—
710C2×C4—221no—
711C2×C4—221no—
712C2×C4—221no—
713C2×C4—222no—
714C2×C4—221no—
715C2×C4—221no—
716C2×C4—441no—
717C2×C4—441no—
718C2×C4—441no—
719C2×C4—441no—
720C2×C4—441no—
721C2×C4—441no—
722C2×C4—441no—
723C2×C4—441no—
724C2×C4—441no—
725C2×C4—441no—
726C2×C4—441no—
727C2×C4—884no—
728C2×C4—884no—
729C2×C4—884no—
730C2×C4D4×Dic1112yes—
731C2×C4C2×D4×D1111yescharacteristic
732C2×C4C2×#434111yescharacteristic
733C2×C4C2×#434111yescharacteristic
734C2×C4#6703711yescharacteristic
735C2×C4#6703711yescharacteristic
736C2×C4C23×Dic1111yescharacteristic
737C8—22no—
738C8—22no—
739C8—222no—
740C8—441no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—24no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—816no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22#1062277714yescomplemented
763C22#1062312111yescharacteristic
764C22#1062312211yescharacteristic
765C22C2×#6696711yescharacteristic
766C22C2×#6696811yescharacteristic
767C22#1062330511yescharacteristic
768C22#1062330611yescharacteristic
769C22C2×D4×Dic1111yescharacteristic
770C4—22no—
771C4—42no—
772C4—42no—
773C4—441no—
774C4—442no—
775C4—441no—
776C4—441no—
777C4—441no—
778C4—881no—
779C4—881no—
780C4—881no—
781C4#1062311811yescharacteristic
782C4#1062312211yescharacteristic
783C4C2×D4×Dic1111yescharacteristic
784C4#1062332911yescharacteristic
785C2—24no—
786C2—44no—
787C2—82no—
788C2#1307160011yescharacteristic
789C2C2×#1062277711yescharacteristic
790C2#1307744911yescharacteristic
791C2#1308010011yescharacteristic
792C2#1308013011yescharacteristic
793C2#1308064111yescharacteristic
794C2#1308070111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#450C2
socleC23×C11C22×D4
prime radicalC23×D4×C11C22
cosocleC22×C4×C11C24
hypercenterC2×#450D11
hypocenterC11#22854
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
1. C2×#10622777C2semidirect
3. #13071625C2semidirect
5. #13069499C2semidirect
6. #13069315C2semidirect
7. #13069238C2semidirect
8. #13069040C2semidirect
9. #13068973C2semidirect
10. #13068952C2semidirect
11. #13068865C2semidirect
12. #13068806C2semidirect
13. #13068443C2semidirect
14. #13068395C2semidirect
21. C2×Q8×Dic11C22semidirect
26. C11×#450C4semidirect
31. #10622843C22semidirect
32. C2×#66899C22semidirect
33. C2×#66899C22semidirect
46. C2×#66882C22semidirect
47. C2×#66882C22semidirect
48. C2×#66879C22semidirect
49. C2×#66879C22semidirect
51. #10622598C22semidirect
53. C4⋊C4×Dic11C22semidirect
56. #10622189C22semidirect
57. #10622189C22semidirect
58. #10622188C22semidirect
59. #10622188C22semidirect
60. #10622167C22semidirect
61. #10622167C22semidirect
81. C2×C11×SD16C2×C4semidirect
82. C2×C11×SD16C2×C4semidirect
86. C11×C22⋊Q8C2×C4semidirect
124. C11×#102C2×C4semidirect
125. C11×#102C2×C4semidirect
126. C11×C22⋊C8C2×C4semidirect
369. #450Dic11semidirect
426. C22×C11#440semidirect
468. C2×SD16C2×Dic11semidirect
469. C2×SD16C2×Dic11semidirect
478. C22⋊Q8C2×Dic11semidirect
519. #102C2×Dic11semidirect
520. #102C2×Dic11semidirect
521. C22⋊C8C2×Dic11semidirect
648. C11#22854semidirect
762. C22#10622777semidirect

Maximal subgroups

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

subgroupindex
C2×#106227772
C22×#668962
#130716252
D4×C22⋊Dic112
#130694992
#130693152
#130692382
#130690402
#130689732
#130689522
#130688652
#130688062
#130684432
#130683952
C2×C11×#4502
#2285411