Finite Group Databasebeta

← #15620165

Subgroups — #15620165

Order 2816.

5098 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4339C211yesmaximal, characteristic, complemented
2C2×#10623353C212yesmaximal, complemented
3#13077874C214yesmaximal, complemented
4#13077866C214yesmaximal, complemented
5#13077856C214yesmaximal, complemented
6#13077849C212yesmaximal, complemented
7#13077842C212yesmaximal, complemented
8#13077832C218yesmaximal, complemented
9#13077133C212yesmaximal, complemented
10C2×#10622820C211yesmaximal, characteristic, complemented
11C2×C11×#525C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic, complemented
13C24×C4×C11C2211yescharacteristic
14C23×C22⋊D11—21no—
15C22×#4339—22no—
16C22×#4339—21no—
17C22×#4339—22no—
18C22×#4339—21no—
19C22×#4339—216no—
20C22×#4339C2214yes—
21C22×#4339C2212yes—
22C22×#4339C2214yescomplemented
23C22×#4339C2212yescomplemented
24C23×D44C2211yescharacteristic, complemented
25C23×C4×D11—21no—
26C23×Dic22C2211yescharacteristic, complemented
27C11×#525—22no—
28C11×#525—21no—
29C11×#525—21no—
30C11×#525C2212yes—
31C11×#525C2212yescomplemented
32C11×#525C2214yescomplemented
33C2×C11×#123—21no—
34C2×C11×C22⋊Q8C2212yescomplemented
35C2×C11×#121C2212yescomplemented
36C2×C11×#120—21no—
37C2×C4×D4×C11—22no—
38C2×C11×#117C2211yescharacteristic, complemented
39C2×#67004C2214yescomplemented
40#10623353—216no—
41C2×#67003C2218yescomplemented
42C2×#67002C2214yescomplemented
43C2×#66995C2214yescomplemented
44C2×#66985C2214yescomplemented
45C22×#4318C2212yescomplemented
46#10622820C2212yescomplemented
47#10622820C2214yescomplemented
48#10622820C2212yescomplemented
49C2×C22⋊(C11⋊C8)C2214yescomplemented
50#10622663C2218yescomplemented
51#10622660C22116yescomplemented
52#10622659C2218yescomplemented
53#10622653C2218yescomplemented
54#10622650C22116yescomplemented
55#10622649C2218yescomplemented
56#10622617C2214yescomplemented
57#10622615C2218yescomplemented
58#10622614C2214yescomplemented
59#10622579C2218yescomplemented
60C25×C11D411yescharacteristic
61C24×D11—21no—
62C2×C11×#41—21no—
63C2×C11×#41—21no—
64C2×C11×#41—28no—
65C2×C11×#41C2312yes—
66C2×C11×#41C2312yescomplemented
67C22×Q8×C11C2311yescharacteristic, complemented
68C22×D4×C11—22no—
69C22×D4×C11—21no—
70C22×D4×C11C2311yescharacteristic, complemented
71C23×C4×C11—28no—
72C23×C4×C11—21no—
73C23×C4×C11D412yes—
74C23×C4×C11D411yescharacteristic
75C23×C4×C11D411yescharacteristic
76C23×C4×C11D412yes—
77C23×C4×C11D411yescharacteristic
78C23×C4×C11C2312yes—
79C23×C4×C11C2312yes—
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C22×C22⋊D11—216no—
84C22×C22⋊D11—24no—
85C22×C22⋊D11—22no—
86C22×C22⋊D11—24no—
87C22×C22⋊D11—22no—
88C23×Dic11—21no—
89C2×#4339—216no—
90C2×#4339—232no—
91C2×#4339—232no—
92C2×#4339—216no—
93C2×#4339—28no—
94C2×#4339—24no—
95C2×#4339—24no—
96C2×#4339—22no—
97C2×#4339—22no—
98C2×#4339—24no—
99C2×#4339—24no—
100C2×#4339—24no—
101C2×#4339—232no—
102C2×#4339—232no—
103C2×#4339—28no—
104C2×#4339—28no—
105C2×#4339D4116yescomplemented
106C2×#4339C2318yes—
107C2×#4339C2314yes—
108C2×#4339C2314yes—
109C22×D44—22no—
110C22×D44—21no—
111C22×D44—28no—
112C22×D44C2314yes—
113C22×D44C2312yes—
114C22×C4×D11—216no—
115C22×C4×D11—24no—
116C22×C4×D11—22no—
117C22×C4×D11—24no—
118C22×C4×D11—22no—
119C22×Dic22—22no—
120C22×Dic22—21no—
121C22×Dic22—28no—
122C22×Dic22C2314yes—
123C22×Dic22C2312yes—
124C11×#123—22no—
125C11×#123—22no—
126C11×#123—24no—
127C11×C22⋊Q8—22no—
128C11×C22⋊Q8—22no—
129C11×C22⋊Q8C2314yes—
130C11×C22⋊Q8C2314yescomplemented
131C11×#121—22no—
132C11×#121—22no—
133C11×#121C2314yes—
134C11×#121C2314yescomplemented
135C11×#120—22no—
136C11×#120—22no—
137C11×#120—24no—
138C4×D4×C11—24no—
139C4×D4×C11—24no—
140C4×D4×C11—24no—
141C4×D4×C11—24no—
142C11×#117—21no—
143C11×#117—21no—
144C11×#117C2312yes—
145C11×#117C2312yescomplemented
146C2×C11×C4⋊C4—22no—
147C2×C11×C4⋊C4C2312yescomplemented
148C2×C11×C22⋊C4—21no—
149C2×C11×C22⋊C4—22no—
150C2×C11×C22⋊C4—22no—
151C2×C42×C11—21no—
152#67004—216no—
153#67003—232no—
154#67002—216no—
155C2×#4326C2318yescomplemented
156#66995—216no—
157C2×#4325C2318yescomplemented
158C2×#4324C2318yescomplemented
159#66985—216no—
160C2×#4323C2318yescomplemented
161C2×#4318—28no—
162C2×#4318C2314yes—
163C2×#4318C2314yescomplemented
164C22×C11⋊C8C2314yescomplemented
165C22⋊(C11⋊C8)C2318yes—
166C22⋊(C11⋊C8)C2318yescomplemented
167#66874C23116yescomplemented
168#66873C23116yescomplemented
169#60359—111nomaximal, Sylow
170C24×C11—24no—
171C24×C11—21no—
172C24×C11—44no—
173C24×C11C2×D411yescharacteristic
174C24×C11C2×D412yes—
175C24×C11C2×D412yes—
176C24×C11C2×D411yescharacteristic
177C24×C11C2×D411yescharacteristic
178C23×D11—28no—
179C23×D11—24no—
180C23×D11—22no—
181C23×D11—48no—
182C11×#41—28no—
183C11×#41—28no—
184C11×#41—44no—
185C11×#41—44no—
186C2×Q8×C11—21no—
187C2×Q8×C11—24no—
188C2×Q8×C11C2412yes—
189C2×D4×C11—24no—
190C2×D4×C11—24no—
191C2×D4×C11—22no—
192C2×D4×C11—22no—
193C2×D4×C11—24no—
194C2×D4×C11—21no—
195C2×D4×C11—48no—
196C2×D4×C11—44no—
197C2×D4×C11C2412yes—
198C22×C4×C11—24no—
199C22×C4×C11—24no—
200C22×C4×C11—24no—
201C22×C4×C11—28no—
202C22×C4×C11—28no—
203C22×C4×C11—24no—
204C22×C4×C11—24no—
205C22×C4×C11—28no—
206C22×C4×C11—28no—
207C22×C4×C11—22no—
208C22×C4×C11—21no—
209C22×C4×C11—22no—
210C22×C4×C11—22no—
211C22×C4×C11—44no—
212C22×C4×C11C2×D412yes—
213C22×C4×C11C2×D412yes—
214C22×C4×C11C2×D412yes—
215C22×C4×C11C2×D412yes—
216C22×C4×C11C2×D412yes—
217C22×C4×C11C2×D412yes—
218C22×C4×C11C2×D412yes—
219C22×C4×C11C2×D411yescharacteristic
220C22×C4×C11C2×D411yescharacteristic
221C22×C4×C11C2×D412yes—
222C22×C4×C11C2×D411yescharacteristic
223C22×C4×C11C2×D411yescharacteristic
224C22×C4×C11C2×D411yescharacteristic
225C22×C4×C11C2×D418yes—
226C22×C4×C11C2412yes—
227C22×C4×C11C2412yes—
228C22×C4×C11C2411yescharacteristic
229C22×C4×C11C2411yescharacteristic
230C22×C4×C11C2411yescharacteristic
231C2×C22⋊D11—232no—
232C2×C22⋊D11—232no—
233C2×C22⋊D11—216no—
234C2×C22⋊D11—216no—
235C2×C22⋊D11—28no—
236C2×C22⋊D11—24no—
237C2×C22⋊D11—24no—
238C22×Dic11—28no—
239C22×Dic11—22no—
240C22×Dic11—24no—
241#4339—232no—
242#4339—232no—
243#4339—232no—
244#4339—232no—
245#4339—232no—
246#4339—216no—
247#4339—216no—
248#4339—216no—
249#4339—216no—
250#4339—28no—
251#4339—28no—
252#4339C2×D4116yes—
253#4339C2×D4116yescomplemented
254C2×D44—28no—
255C2×D44—216no—
256C2×D44—216no—
257C2×D44—24no—
258C2×D44—24no—
259C2×D44—22no—
260C2×D44C2×D418yescomplemented
261C2×D44C2414yes—
262C2×C4×D11—216no—
263C2×C4×D11—232no—
264C2×C4×D11—232no—
265C2×C4×D11—216no—
266C2×C4×D11—28no—
267C2×C4×D11—24no—
268C2×C4×D11—24no—
269C2×Dic22—28no—
270C2×Dic22—216no—
271C2×Dic22—216no—
272C2×Dic22—24no—
273C2×Dic22—24no—
274C2×Dic22—22no—
275C2×Dic22C2×D418yescomplemented
276C2×Dic22C2414yes—
277C11×C4⋊C4—24no—
278C11×C4⋊C4—24no—
279C11×C4⋊C4—22no—
280C11×C4⋊C4C2414yes—
281C11×C22⋊C4—22no—
282C11×C22⋊C4—22no—
283C11×C22⋊C4—24no—
284C11×C22⋊C4—24no—
285C11×C22⋊C4—24no—
286C11×C22⋊C4—24no—
287C42×C11—22no—
288C42×C11—22no—
289#4326—216no—
290#4325—216no—
291#4324—216no—
292#4323—216no—
293#4318—28no—
294#4318—28no—
295C2×C11⋊C8—28no—
296C2×C11⋊C8C2418yes—
297C23×#41—111no—
298C2×#575—112no—
299C2×#525D1111yescharacteristic, complemented
300#3007—114no—
301#3006—114no—
302#3005—114no—
303#3004—112no—
304#3003—112no—
305#3002—118no—
306#2896—112no—
307C2×#407—111no—
308C23×C11—22no—
309C23×C11—24no—
310C23×C11—24no—
311C23×C11—24no—
312C23×C11—22no—
313C23×C11—24no—
314C23×C11—24no—
315C23×C11—22no—
316C23×C11—42no—
317C23×C11—42no—
318C23×C11—42no—
319C23×C11—42no—
320C23×C11—416no—
321C23×C11—44no—
322C23×C11—42no—
323C23×C11#12014yes—
324C23×C11C22×D412yes—
325C23×C11C22×D411yescharacteristic
326C23×C11C22×D411yescharacteristic
327C23×C11C22×D411yescharacteristic
328C23×C11C22×D412yes—
329C22×D11—216no—
330C22×D11—28no—
331C22×D11—24no—
332C22×D11—432no—
333C22×D11—48no—
334C22×D11—48no—
335C22×D11—48no—
336Q8×C11—24no—
337Q8×C11—42no—
338D4×C11—24no—
339D4×C11—48no—
340D4×C11—44no—
341D4×C11—44no—
342D4×C11—48no—
343D4×C11—42no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—24no—
347C2×C4×C11—24no—
348C2×C4×C11—24no—
349C2×C4×C11—24no—
350C2×C4×C11—24no—
351C2×C4×C11—24no—
352C2×C4×C11—24no—
353C2×C4×C11—24no—
354C2×C4×C11—24no—
355C2×C4×C11—24no—
356C2×C4×C11—24no—
357C2×C4×C11—22no—
358C2×C4×C11—44no—
359C2×C4×C11—42no—
360C2×C4×C11—44no—
361C2×C4×C11—44no—
362C2×C4×C11#12014yes—
363C2×C4×C11#12014yes—
364C2×C4×C11#12014yes—
365C2×C4×C11C22×D414yes—
366C2×C4×C11C22×D414yes—
367C2×C4×C11C22×D414yes—
368C2×C4×C11C22×D412yes—
369C2×C4×C11C22×D412yes—
370C2×C4×C11C22×D411yescharacteristic
371C2×C4×C11C22×D411yescharacteristic
372C2×C4×C11C22×D411yescharacteristic
373C2×C4×C11C2511yescharacteristic
374C22⋊D11—232no—
375C22⋊D11—216no—
376C22⋊D11—216no—
377C2×Dic11—216no—
378C2×Dic11—28no—
379C2×Dic11—24no—
380D44—216no—
381D44—28no—
382D44—24no—
383D44C22×D418yes—
384C4×D11—232no—
385C4×D11—216no—
386C4×D11—216no—
387Dic22—216no—
388Dic22—28no—
389Dic22—24no—
390Dic22C22×D418yes—
391C11⋊C8—28no—
392C22×#41—112no—
393C22×#41—114no—
394C22×#41—112no—
395C22×#41—114no—
396C22×#41—2216no—
397C22×#41—222no—
398C22×#41—221no—
399C22×#41—222no—
400C22×#41—221no—
401C22×#41C2×D1111yescharacteristic, complemented
402C23×Q8—111no—
403C23×D4—111no—
404C23×D4—221no—
405C24×C4—221no—
406C24×C4C2×D1111yescharacteristic
407#575—2216no—
408C2×#137—114no—
409C2×#137—114no—
410C2×AGL(1,ℤ/8)—114no—
411C2×AGL(1,ℤ/8)—114no—
412C2×#135—118no—
413C22×M16—112no—
414#525—22no—
415#525—21no—
416#525—21no—
417#525C2×D1112yes—
418#525C2×D1112yescomplemented
419#525C2×D1114yescomplemented
420C2×#123—21no—
421C2×C22⋊Q8C2×D1112yescomplemented
422C2×#121C2×D1112yescomplemented
423C2×#120—21no—
424C2×C4×D4—22no—
425C2×#117C2×D1111yescharacteristic, complemented
426#452—1116no—
427#451—118no—
428#450—118no—
429#449—1116no—
430#448—118no—
431#447—118no—
432#419—114no—
433#418—114no—
434#417—118no—
435#416—118no—
436#407—112no—
437#407—112no—
438#407—114no—
439C2×C22⋊C8—114no—
440C22×C11—28no—
441C22×C11—22no—
442C22×C11—22no—
443C22×C11—22no—
444C22×C11—22no—
445C22×C11—22no—
446C22×C11—22no—
447C22×C11—22no—
448C22×C11—22no—
449C22×C11—44no—
450C22×C11—48no—
451C22×C11—48no—
452C22×C11—44no—
453C22×C11—42no—
454C22×C11—44no—
455C22×C11—84no—
456C22×C11C2×#12012yes—
457C22×C11C2×#12012yes—
458C22×C11C2×#12012yes—
459C22×C11#57514yescomplemented
460C22×C11C23×D411yescharacteristic
461C2×D11—28no—
462C2×D11—416no—
463C2×D11—432no—
464C2×D11—48no—
465C4×C11—22no—
466C4×C11—22no—
467C4×C11—42no—
468C4×C11—44no—
469C4×C11C2×#12012yes—
470C4×C11C2×#12012yes—
471C4×C11C2×#12012yes—
472C4×C11C23×D412yes—
473Dic11—28no—
474C25—221no—
475C25C22⋊D1111yescharacteristic
476C2×#41—21no—
477C2×#41—21no—
478C2×#41—28no—
479C2×#41—1116no—
480C2×#41—114no—
481C2×#41—114no—
482C2×#41—118no—
483C2×#41—228no—
484C2×#41—228no—
485C2×#41—2232no—
486C2×#41—2232no—
487C2×#41—2216no—
488C2×#41—2232no—
489C2×#41—2232no—
490C2×#41—2216no—
491C2×#41—228no—
492C2×#41—224no—
493C2×#41—224no—
494C2×#41—224no—
495C2×#41—224no—
496C2×#41—222no—
497C2×#41—224no—
498C2×#41—222no—
499C2×#41C22×D1112yes—
500C2×#41C22×D1112yescomplemented
501C22×Q8—112no—
502C22×Q8—114no—
503C22×Q8—228no—
504C22×Q8—222no—
505C22×Q8—221no—
506C22×Q8C22×D1111yescharacteristic, complemented
507C22×D4—22no—
508C22×D4—21no—
509C22×D4—112no—
510C22×D4—114no—
511C22×D4—228no—
512C22×D4—2216no—
513C22×D4—224no—
514C22×D4—224no—
515C22×D4—222no—
516C22×D4—222no—
517C22×D4—222no—
518C22×D4—221no—
519C22×D4C22×D1111yescharacteristic, complemented
520C23×C4—28no—
521C23×C4—21no—
522C23×C4—2216no—
523C23×C4—221no—
524C23×C4—224no—
525C23×C4—222no—
526C23×C4—224no—
527C23×C4—222no—
528C23×C4C22⋊D1112yes—
529C23×C4C22⋊D1111yescharacteristic
530C23×C4C22⋊D1111yescharacteristic
531C23×C4C22⋊D1112yes—
532C23×C4C22⋊D1111yescharacteristic
533C23×C4C22×D1112yes—
534C23×C4C22×D1111yescharacteristic
535C23×C4C22×D1112yes—
536C23×C4C22×D1111yescharacteristic
537C23×C4C22×D1111yescharacteristic
538#137—2216no—
539#137—2216no—
540AGL(1,ℤ/8)—2216no—
541AGL(1,ℤ/8)—2216no—
542#135—2232no—
543C2×Q16—118no—
544C2×SD16—118no—
545C2×SD16—118no—
546C2×D8—118no—
547C2×M16—114no—
548C2×M16—114no—
549C2×M16—228no—
550C22×C8—114no—
551#123—22no—
552#123—22no—
553#123—24no—
554C22⋊Q8—22no—
555C22⋊Q8—22no—
556C22⋊Q8C22×D1114yes—
557C22⋊Q8C22×D1114yescomplemented
558#121—22no—
559#121—22no—
560#121C22×D1114yes—
561#121C22×D1114yescomplemented
562#120—22no—
563#120—22no—
564#120—24no—
565C4×D4—24no—
566C4×D4—24no—
567C4×D4—24no—
568C4×D4—24no—
569#117—21no—
570#117—21no—
571#117C22×D1112yes—
572#117C22×D1112yescomplemented
573C2×C4⋊C4—22no—
574C2×C4⋊C4C22×D1112yescomplemented
575C2×C22⋊C4—21no—
576C2×C22⋊C4—22no—
577C2×C22⋊C4—22no—
578C2×C42—21no—
579#103—1116no—
580#102—1116no—
581C22⋊C8—118no—
582C22⋊C8—118no—
583C2×C11—22no—
584C2×C11—24no—
585C2×C11—22no—
586C2×C11—22no—
587C2×C11—42no—
588C2×C11—82no—
589C2×C11C22×#12011yescharacteristic
590C2×C11C2×#57512yes—
591D11—48no—
592C24—24no—
593C24—21no—
594C24—44no—
595C24—228no—
596C24—224no—
597C24—222no—
598C24—448no—
599C24C2×C22⋊D1111yescharacteristic
600C24C2×C22⋊D1112yes—
601C24C2×C22⋊D1112yes—
602C24C2×C22⋊D1111yescharacteristic
603C24C2×C22⋊D1111yescharacteristic
604#41—28no—
605#41—28no—
606#41—44no—
607#41—44no—
608#41—1116no—
609#41—1116no—
610#41—2216no—
611#41—2216no—
612#41—2232no—
613#41—2232no—
614#41—2232no—
615#41—2232no—
616#41—2232no—
617#41—2216no—
618#41—2216no—
619#41—228no—
620#41—228no—
621C2×Q8—21no—
622C2×Q8—24no—
623C2×Q8—118no—
624C2×Q8—114no—
625C2×Q8—2216no—
626C2×Q8—228no—
627C2×Q8—2216no—
628C2×Q8—224no—
629C2×Q8—224no—
630C2×Q8—222no—
631C2×Q8C23×D1112yes—
632C2×D4—24no—
633C2×D4—24no—
634C2×D4—22no—
635C2×D4—22no—
636C2×D4—24no—
637C2×D4—21no—
638C2×D4—48no—
639C2×D4—44no—
640C2×D4—118no—
641C2×D4—114no—
642C2×D4—2216no—
643C2×D4—228no—
644C2×D4—2216no—
645C2×D4—2232no—
646C2×D4—2232no—
647C2×D4—2216no—
648C2×D4—2216no—
649C2×D4—228no—
650C2×D4—224no—
651C2×D4—224no—
652C2×D4—224no—
653C2×D4—224no—
654C2×D4—222no—
655C2×D4C23×D1112yes—
656C22×C4—24no—
657C22×C4—24no—
658C22×C4—24no—
659C22×C4—28no—
660C22×C4—28no—
661C22×C4—24no—
662C22×C4—24no—
663C22×C4—28no—
664C22×C4—28no—
665C22×C4—22no—
666C22×C4—21no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—44no—
670C22×C4—2216no—
671C22×C4—2232no—
672C22×C4—2232no—
673C22×C4—228no—
674C22×C4—224no—
675C22×C4—222no—
676C22×C4—2216no—
677C22×C4—228no—
678C22×C4—224no—
679C22×C4—224no—
680C22×C4D4×D1118yes—
681C22×C4C2×C22⋊D1112yes—
682C22×C4C2×C22⋊D1112yes—
683C22×C4C2×C22⋊D1112yes—
684C22×C4C2×C22⋊D1112yes—
685C22×C4C2×C22⋊D1112yes—
686C22×C4C2×C22⋊D1111yescharacteristic
687C22×C4C2×C22⋊D1111yescharacteristic
688C22×C4C2×C22⋊D1112yes—
689C22×C4C2×C22⋊D1112yes—
690C22×C4C2×C22⋊D1112yes—
691C22×C4C2×C22⋊D1111yescharacteristic
692C22×C4C2×C22⋊D1111yescharacteristic
693C22×C4C2×C22⋊D1111yescharacteristic
694C22×C4C23×D1112yes—
695C22×C4C23×D1112yes—
696C22×C4C23×D1111yescharacteristic
697C22×C4C23×D1111yescharacteristic
698C22×C4C23×D1111yescharacteristic
699Q16—2216no—
700SD16—2216no—
701SD16—2216no—
702D8—2216no—
703M16—228no—
704M16—228no—
705C2×C8—118no—
706C2×C8—228no—
707C4⋊C4—24no—
708C4⋊C4—24no—
709C4⋊C4—22no—
710C4⋊C4C23×D1114yes—
711C22⋊C4—22no—
712C22⋊C4—22no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—24no—
716C22⋊C4—24no—
717C42—22no—
718C42—22no—
719C11#6035911yescharacteristic, complemented, Sylow
720C23—22no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—22no—
725C23—24no—
726C23—24no—
727C23—22no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—416no—
733C23—44no—
734C23—42no—
735C23—2216no—
736C23—228no—
737C23—224no—
738C23—4432no—
739C23—448no—
740C23—448no—
741C23—448no—
742C23#6699014yes—
743C23C22×C22⋊D1112yes—
744C23C22×C22⋊D1111yescharacteristic
745C23C22×C22⋊D1111yescharacteristic
746C23C22×C22⋊D1111yescharacteristic
747C23C22×C22⋊D1112yes—
748Q8—24no—
749Q8—42no—
750Q8—118no—
751Q8—2216no—
752Q8—228no—
753Q8—224no—
754D4—24no—
755D4—48no—
756D4—44no—
757D4—44no—
758D4—48no—
759D4—42no—
760D4—118no—
761D4—2216no—
762D4—2232no—
763D4—2216no—
764D4—2216no—
765D4—228no—
766D4—224no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—22no—
781C2×C4—44no—
782C2×C4—42no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—2232no—
786C2×C4—2216no—
787C2×C4—228no—
788C2×C4—224no—
789C2×C4—2216no—
790C2×C4—2216no—
791C2×C4#6699014yes—
792C2×C4#6699014yes—
793C2×C4#6699014yes—
794C2×C4C2×D4×D1114yes—
795C2×C4C2×D4×D1114yes—
796C2×C4C2×D4×D1114yes—
797C2×C4C22×C22⋊D1112yes—
798C2×C4C22×C22⋊D1112yes—
799C2×C4C22×C22⋊D1111yescharacteristic
800C2×C4C22×C22⋊D1111yescharacteristic
801C2×C4C22×C22⋊D1111yescharacteristic
802C2×C4C24×D1111yescharacteristic
803C8—228no—
804C22—28no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—44no—
814C22—48no—
815C22—48no—
816C22—44no—
817C22—44no—
818C22—42no—
819C22—84no—
820C22—228no—
821C22—4416no—
822C22—4432no—
823C22—448no—
824C22C2×#6699012yes—
825C22C2×#6699012yes—
826C22C2×#6699012yes—
827C22#1062335314yescomplemented
828C22C23×C22⋊D1111yescharacteristic
829C4—22no—
830C4—22no—
831C4—44no—
832C4—42no—
833C4—228no—
834C4C2×#6699012yes—
835C4C2×#6699012yes—
836C4C2×#6699012yes—
837C4C22×D4×D1112yes—
838C2—22no—
839C2—24no—
840C2—22no—
841C2—22no—
842C2—42no—
843C2—82no—
844C2—448no—
845C2C22×#6699011yescharacteristic
846C2C2×#1062335312yes—
subgroupG/H
centerC2×C4C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#525C2
socleC22×C11C23×D4
hypercenterC2×#525D11
hypocenterC11#60359
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C23×#4339C2semidirect
2. C2×#10623353C2semidirect
3. #13077874C2semidirect
4. #13077866C2semidirect
5. #13077856C2semidirect
6. #13077849C2semidirect
7. #13077842C2semidirect
8. #13077832C2semidirect
9. #13077133C2semidirect
10. C2×#10622820C2semidirect
11. C2×C11×#525C2semidirect
12. C22×C11×#41C22semidirect
22. C22×#4339C22semidirect
23. C22×#4339C22semidirect
24. C23×D44C22semidirect
26. C23×Dic22C22semidirect
31. C11×#525C22semidirect
32. C11×#525C22semidirect
34. C2×C11×C22⋊Q8C22semidirect
35. C2×C11×#121C22semidirect
38. C2×C11×#117C22semidirect
39. C2×#67004C22semidirect
41. C2×#67003C22semidirect
42. C2×#67002C22semidirect
43. C2×#66995C22semidirect
44. C2×#66985C22semidirect
45. C22×#4318C22semidirect
46. #10622820C22semidirect
47. #10622820C22semidirect
48. #10622820C22semidirect
49. C2×C22⋊(C11⋊C8)C22semidirect
50. #10622663C22semidirect
51. #10622660C22semidirect
52. #10622659C22semidirect
53. #10622653C22semidirect
54. #10622650C22semidirect
55. #10622649C22semidirect
56. #10622617C22semidirect
57. #10622615C22semidirect
58. #10622614C22semidirect
59. #10622579C22semidirect
66. C2×C11×#41C23semidirect
67. C22×Q8×C11C23semidirect
70. C22×D4×C11C23semidirect
105. C2×#4339D4semidirect
130. C11×C22⋊Q8C23semidirect
134. C11×#121C23semidirect
145. C11×#117C23semidirect
147. C2×C11×C4⋊C4C23semidirect
155. C2×#4326C23semidirect
157. C2×#4325C23semidirect
158. C2×#4324C23semidirect
160. C2×#4323C23semidirect
163. C2×#4318C23semidirect
164. C22×C11⋊C8C23semidirect
166. C22⋊(C11⋊C8)C23semidirect
167. #66874C23semidirect
168. #66873C23semidirect
253. #4339C2×D4semidirect
260. C2×D44C2×D4semidirect
275. C2×Dic22C2×D4semidirect
299. C2×#525D11semidirect
401. C22×#41C2×D11semidirect
418. #525C2×D11semidirect
419. #525C2×D11semidirect
421. C2×C22⋊Q8C2×D11semidirect
422. C2×#121C2×D11semidirect
425. C2×#117C2×D11semidirect
459. C22×C11#575semidirect
500. C2×#41C22×D11semidirect
506. C22×Q8C22×D11semidirect
519. C22×D4C22×D11semidirect
557. C22⋊Q8C22×D11semidirect
561. #121C22×D11semidirect
572. #117C22×D11semidirect
574. C2×C4⋊C4C22×D11semidirect
719. C11#60359semidirect
827. C22#10623353semidirect

Maximal subgroups

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

subgroupindex
C23×#43392
C2×#106233532
#130778742
#130778662
#130778562
#130778492
#130778422
#130778322
#130771332
C2×#106228202
C2×C11×#5252
#6035911