Finite Group Databasebeta

← C11×#23399 #14600592

Subgroups — C11×#23399 #14600592

Order 2816.

2062 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#575C211yesmaximal, characteristic, complemented
2C11×#3449C211yesmaximal, characteristic, complemented
3C2×C11×#532C211yesmaximal, characteristic, complemented
4C22×C11×#104C211yesmaximal, characteristic, complemented
5C11×#2896C211yesmaximal, characteristic, complemented
6C2×C11×#413C211yesmaximal, characteristic, complemented
7C11×#2005C212yesmaximal, complemented
8C11×#2004C212yesmaximal, complemented
9C11×#2003C212yesmaximal, complemented
10C11×#2002C212yesmaximal, complemented
11C2×C11×#339C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C22×C11×#41C2211yescharacteristic
14C22×C11×#41C2211yescharacteristic
15C11×#575—24no—
16C11×#575—24no—
17C2×C11×#137—21no—
18C2×C11×#137C2212yes—
19C2×C11×AGL(1,ℤ/8)—21no—
20C2×C11×AGL(1,ℤ/8)C2212yes—
21C2×C11×#135—22no—
22C22×C11×M16C2211yescharacteristic
23C22×C11×M16C2211yescharacteristic
24C11×#537—22no—
25C11×#536—21no—
26C11×#536C2212yes—
27C11×#535—21no—
28C11×#535C2212yes—
29C11×#534—22no—
30C11×#532—24no—
31C11×#532—22no—
32C11×#532—24no—
33C2×C11×C4⋊Q8C2211yescharacteristic, complemented
34C2×C11×#127C2211yescharacteristic, complemented
35C2×C11×#124C2211yescharacteristic, complemented
36C2×C11×#124C2211yescharacteristic, complemented
37C11×#525—22no—
38C11×#525—22no—
39C2×C11×#121—22no—
40C2×C4×D4×C11—22no—
41C2×C11×#117C2211yescharacteristic
42C22×C42×C11C2211yescharacteristic
43C2×C11×#104—24no—
44C2×C11×#104C2212yes—
45C2×C11×#104C2212yes—
46C11×#419C2212yescomplemented
47C11×#418C2212yescomplemented
48C11×#417—22no—
49C11×#416—22no—
50C11×#413—24no—
51C2×C11×#101C2212yescomplemented
52C2×C11×#100C2212yescomplemented
53C11×#339C2212yescomplemented
54C11×#339C2212yescomplemented
55C2×C11×#41—21no—
56C2×C11×#41—21no—
57C2×C11×#41—22no—
58C2×C11×#41—22no—
59C2×C11×#41—22no—
60C2×C11×#41—21no—
61C2×C11×#41—21no—
62C2×C11×#41—21no—
63C2×C11×#41—21no—
64C2×C11×#41—22no—
65C2×C11×#41—22no—
66C2×C11×#41—21no—
67C2×C11×#41—21no—
68C2×C11×#41—22no—
69C2×C11×#41—21no—
70C2×C11×#41—21no—
71C2×C11×#41—22no—
72C2×C11×#41—22no—
73C2×C11×#41—22no—
74C2×C11×#41—22no—
75C2×C11×#41—22no—
76C2×C11×#41D412yescomplemented
77C2×C11×#41D414yescomplemented
78C2×C11×#41C2312yes—
79C22×Q8×C11D411yescharacteristic, complemented
80C22×Q8×C11C2311yescharacteristic
81C22×Q8×C11C2311yescharacteristic
82C22×D4×C11—22no—
83C22×D4×C11—21no—
84C22×D4×C11—21no—
85C22×D4×C11D412yes—
86C22×D4×C11D411yescharacteristic, complemented
87C22×D4×C11C2311yescharacteristic
88C22×D4×C11C2311yescharacteristic
89C23×C4×C11—21no—
90C23×C4×C11—21no—
91C23×C4×C11—21no—
92C23×C4×C11D412yes—
93C23×C4×C11C2311yescharacteristic
94C11×#137—28no—
95C11×#137—24no—
96C11×#137—24no—
97C11×AGL(1,ℤ/8)—28no—
98C11×AGL(1,ℤ/8)—24no—
99C11×AGL(1,ℤ/8)—24no—
100C11×#135—216no—
101C2×C11×Q16—22no—
102C2×C11×SD16—22no—
103C2×C11×SD16—22no—
104C2×C11×D8—22no—
105C2×C11×M16—21no—
106C2×C11×M16—22no—
107C2×C11×M16—21no—
108C2×C11×M16—22no—
109C2×C11×M16—22no—
110C2×C11×M16D414yescomplemented
111C2×C11×M16C2312yes—
112C2×C11×M16C2312yes—
113C22×C8×C11—21no—
114C22×C8×C11—21no—
115C11×C4⋊Q8—22no—
116C11×C4⋊Q8—22no—
117C11×C4⋊Q8—22no—
118C11×#127—22no—
119C11×#127—22no—
120C11×#127—22no—
121C11×#124—22no—
122C11×#124—22no—
123C11×#124—22no—
124C11×#124—22no—
125C11×#124—22no—
126C11×#124—22no—
127C11×#123—24no—
128C11×#123—24no—
129C11×C22⋊Q8—24no—
130C11×C22⋊Q8—24no—
131C11×#121—216no—
132C11×#121—24no—
133C11×#121—28no—
134C11×#121—24no—
135C11×#120—24no—
136C11×#120—24no—
137C4×D4×C11—216no—
138C4×D4×C11—28no—
139C11×#117—21no—
140C11×#117—21no—
141C11×#117D412yescomplemented
142C11×#117C2312yes—
143C2×C11×C4⋊C4—22no—
144C2×C11×C4⋊C4D412yescomplemented
145C2×C11×C22⋊C4—21no—
146C2×C11×C22⋊C4—22no—
147C2×C11×C22⋊C4—22no—
148C2×C42×C11—21no—
149C2×C42×C11—22no—
150C2×C42×C11—21no—
151C2×C42×C11D414yescomplemented
152C2×C42×C11C2311yescharacteristic
153C2×C42×C11C2311yescharacteristic
154C11×#104—24no—
155C11×#104—24no—
156C11×#103—24no—
157C11×#102—24no—
158C11×#101—24no—
159C11×#100—24no—
160#23399C1111yesmaximal, characteristic, direct product factor, Sylow
161C24×C11—21no—
162C24×C11—21no—
163C24×C11C2×D412yes—
164C24×C11C2×D411yescharacteristic
165C11×#41—24no—
166C11×#41—24no—
167C11×#41—24no—
168C11×#41—24no—
169C11×#41—24no—
170C11×#41—24no—
171C11×#41—22no—
172C11×#41—22no—
173C11×#41—22no—
174C11×#41—22no—
175C11×#41—42no—
176C11×#41—42no—
177C11×#41—42no—
178C11×#41—42no—
179C11×#41—42no—
180C11×#41—42no—
181C11×#41—42no—
182C11×#41—42no—
183C11×#41—42no—
184C11×#41—42no—
185C11×#41—42no—
186C11×#41—42no—
187C11×#41—42no—
188C11×#41—42no—
189C11×#41—42no—
190C11×#41—42no—
191C2×Q8×C11—21no—
192C2×Q8×C11—21no—
193C2×Q8×C11—21no—
194C2×Q8×C11—21no—
195C2×Q8×C11—21no—
196C2×Q8×C11—21no—
197C2×Q8×C11—21no—
198C2×Q8×C11—21no—
199C2×Q8×C11—22no—
200C2×Q8×C11—22no—
201C2×Q8×C11—21no—
202C2×Q8×C11—21no—
203C2×Q8×C11—21no—
204C2×Q8×C11—21no—
205C2×Q8×C11C2×D412yes—
206C2×Q8×C11C2×D412yes—
207C2×D4×C11—28no—
208C2×D4×C11—22no—
209C2×D4×C11—22no—
210C2×D4×C11—24no—
211C2×D4×C11—22no—
212C2×D4×C11—24no—
213C2×D4×C11—24no—
214C2×D4×C11—22no—
215C2×D4×C11—28no—
216C2×D4×C11—22no—
217C2×D4×C11—21no—
218C2×D4×C11—22no—
219C2×D4×C11—21no—
220C2×D4×C11—21no—
221C2×D4×C11—21no—
222C2×D4×C11—21no—
223C2×D4×C11—21no—
224C2×D4×C11—21no—
225C2×D4×C11—21no—
226C2×D4×C11—21no—
227C2×D4×C11—21no—
228C2×D4×C11—21no—
229C2×D4×C11—21no—
230C2×D4×C11—48no—
231C2×D4×C11—41no—
232C2×D4×C11—41no—
233C2×D4×C11—42no—
234C2×D4×C11—42no—
235C2×D4×C11—42no—
236C2×D4×C11C2×D412yes—
237C2×D4×C11C2×D412yes—
238C22×C4×C11—21no—
239C22×C4×C11—24no—
240C22×C4×C11—21no—
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11—22no—
244C22×C4×C11—24no—
245C22×C4×C11—24no—
246C22×C4×C11—22no—
247C22×C4×C11—22no—
248C22×C4×C11—22no—
249C22×C4×C11—24no—
250C22×C4×C11—22no—
251C22×C4×C11—44no—
252C22×C4×C11—41no—
253C22×C4×C11—41no—
254C22×C4×C11—42no—
255C22×C4×C11—42no—
256C22×C4×C11—42no—
257C22×C4×C11C2×D412yes—
258C22×C4×C11C2×D411yescharacteristic
259C22×C4×C11C2×D412yes—
260C22×C4×C11C2×D411yescharacteristic
261C22×C4×C11C2×D411yescharacteristic
262C22×C4×C11C2×D412yes—
263C22×C4×C11C2×D412yes—
264C22×C4×C11C2×D411yescharacteristic
265C22×C4×C11C2×D411yescharacteristic
266C22×C4×C11#4112yes—
267C22×C4×C11C2411yescharacteristic
268C11×Q16—28no—
269C11×SD16—28no—
270C11×SD16—28no—
271C11×D8—28no—
272C11×M16—24no—
273C11×M16—22no—
274C11×M16—22no—
275C11×M16—22no—
276C11×M16—42no—
277C11×M16C2×D414yes—
278C2×C8×C11—24no—
279C2×C8×C11—22no—
280C2×C8×C11—22no—
281C2×C8×C11—42no—
282C11×C4⋊C4—28no—
283C11×C4⋊C4—28no—
284C11×C4⋊C4—22no—
285C11×C4⋊C4C2×D414yes—
286C11×C22⋊C4—28no—
287C11×C22⋊C4—28no—
288C11×C22⋊C4—28no—
289C11×C22⋊C4—28no—
290C11×C22⋊C4—22no—
291C11×C22⋊C4—22no—
292C42×C11—24no—
293C42×C11—22no—
294C42×C11—21no—
295C42×C11—21no—
296C42×C11—22no—
297C42×C11C2×D412yes—
298C42×C11C2×D412yes—
299C2×#575C2×C1111yescharacteristic, complemented
300#3449C2×C1111yescharacteristic, complemented
301C2×#532C2×C1111yescharacteristic, complemented
302C22×#104C2×C1111yescharacteristic, complemented
303#2896C2×C1111yescharacteristic, complemented
304C2×#413C2×C1111yescharacteristic, complemented
305#2005C2×C1112yescomplemented
306#2004C2×C1112yescomplemented
307#2003C2×C1112yescomplemented
308#2002C2×C1112yescomplemented
309C2×#339C2×C1111yescharacteristic, complemented
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—42no—
316C23×C11—44no—
317C23×C11—44no—
318C23×C11—41no—
319C23×C11—41no—
320C23×C11—42no—
321C23×C11—82no—
322C23×C11#12011yescharacteristic
323C23×C11#12011yescharacteristic
324C23×C11#12012yes—
325C23×C11#12112yes—
326C23×C11C22×D411yescharacteristic
327Q8×C11—22no—
328Q8×C11—22no—
329Q8×C11—22no—
330Q8×C11—22no—
331Q8×C11—41no—
332Q8×C11—41no—
333Q8×C11—41no—
334Q8×C11—41no—
335Q8×C11—41no—
336Q8×C11—41no—
337Q8×C11—42no—
338D4×C11—22no—
339D4×C11—22no—
340D4×C11—22no—
341D4×C11—22no—
342D4×C11—416no—
343D4×C11—42no—
344D4×C11—42no—
345D4×C11—44no—
346D4×C11—44no—
347D4×C11—44no—
348D4×C11—44no—
349D4×C11—44no—
350D4×C11—41no—
351D4×C11—41no—
352D4×C11—41no—
353D4×C11—41no—
354D4×C11—41no—
355D4×C11—41no—
356D4×C11—42no—
357D4×C11—88no—
358C2×C4×C11—24no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—24no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—48no—
368C2×C4×C11—42no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11—42no—
372C2×C4×C11—42no—
373C2×C4×C11—42no—
374C2×C4×C11—44no—
375C2×C4×C11—44no—
376C2×C4×C11—44no—
377C2×C4×C11—44no—
378C2×C4×C11—44no—
379C2×C4×C11—82no—
380C2×C4×C11#12012yes—
381C2×C4×C11#12012yes—
382C2×C4×C11#12012yes—
383C2×C4×C11#12011yescharacteristic
384C2×C4×C11#12011yescharacteristic
385C2×C4×C11#12112yes—
386C2×C4×C11#12112yes—
387C2×C4×C11#12112yes—
388C2×C4×C11#12112yes—
389C2×C4×C11#12112yes—
390C2×C4×C11#12712yes—
391C2×C4×C11#12712yes—
392C2×C4×C11C22×D411yescharacteristic
393C2×C4×C11C22×D411yescharacteristic
394C2×C4×C11C22×D411yescharacteristic
395C2×C4×C11C22×D411yescharacteristic
396C2×C4×C11C22×D411yescharacteristic
397C2×C4×C11C2×#4111yescharacteristic
398C8×C11—24no—
399C8×C11—42no—
400C22×#41C22×C1111yescharacteristic
401C22×#41C22×C1111yescharacteristic
402C22×#41C22×C1111yescharacteristic
403#575—24no—
404#575—24no—
405C2×#137—21no—
406C2×#137C22×C1112yes—
407C2×AGL(1,ℤ/8)—21no—
408C2×AGL(1,ℤ/8)C22×C1112yes—
409C2×#135—22no—
410C22×M16C22×C1111yescharacteristic
411C22×M16C22×C1111yescharacteristic
412#537—22no—
413#536—21no—
414#536C22×C1112yes—
415#535—21no—
416#535C22×C1112yes—
417#534—22no—
418#532—24no—
419#532—22no—
420#532—24no—
421C2×C4⋊Q8C22×C1111yescharacteristic, complemented
422C2×#127C22×C1111yescharacteristic, complemented
423C2×#124C22×C1111yescharacteristic, complemented
424C2×#124C22×C1111yescharacteristic, complemented
425#525—22no—
426#525—22no—
427C2×#121—22no—
428C2×C4×D4—22no—
429C2×#117C22×C1111yescharacteristic
430C22×C42C22×C1111yescharacteristic
431C2×#104—24no—
432C2×#104C22×C1112yes—
433C2×#104C22×C1112yes—
434#419C22×C1112yescomplemented
435#418C22×C1112yescomplemented
436#417—22no—
437#416—22no—
438#413—24no—
439C2×#101C22×C1112yescomplemented
440C2×#100C22×C1112yescomplemented
441#339C22×C1112yescomplemented
442#339C22×C1112yescomplemented
443C22×C11—22no—
444C22×C11—22no—
445C22×C11—22no—
446C22×C11—42no—
447C22×C11—42no—
448C22×C11—44no—
449C22×C11—44no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—44no—
454C22×C11—44no—
455C22×C11—82no—
456C22×C11—82no—
457C22×C11—84no—
458C22×C11—82no—
459C22×C11#39212yes—
460C22×C11#39212yes—
461C22×C11C2×#12011yescharacteristic
462C22×C11C2×#12011yescharacteristic
463C22×C11C2×#12111yescharacteristic
464C4×C11—24no—
465C4×C11—42no—
466C4×C11—42no—
467C4×C11—42no—
468C4×C11—42no—
469C4×C11—44no—
470C4×C11#39212yes—
471C4×C11#39212yes—
472C4×C11C2×#12011yescharacteristic
473C4×C11C2×#12111yescharacteristic
474C4×C11C2×#12111yescharacteristic
475C4×C11C2×#12711yescharacteristic
476C2×#41—21no—
477C2×#41—21no—
478C2×#41—22no—
479C2×#41—21no—
480C2×#41—22no—
481C2×#41—22no—
482C2×#41—21no—
483C2×#41—21no—
484C2×#41—21no—
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—21no—
488C2×#41—21no—
489C2×#41—22no—
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—21no—
493C2×#41—21no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—22no—
497C2×#41D4×C1112yescomplemented
498C2×#41D4×C1114yescomplemented
499C2×#41C23×C1112yes—
500C22×Q8D4×C1111yescharacteristic, complemented
501C22×Q8C23×C1111yescharacteristic
502C22×Q8C23×C1111yescharacteristic
503C22×D4—22no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4D4×C1112yes—
507C22×D4D4×C1111yescharacteristic, complemented
508C22×D4C23×C1111yescharacteristic
509C22×D4C23×C1111yescharacteristic
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4D4×C1112yes—
514C23×C4C23×C1111yescharacteristic
515#137—28no—
516#137—24no—
517#137—24no—
518AGL(1,ℤ/8)—28no—
519AGL(1,ℤ/8)—24no—
520AGL(1,ℤ/8)—24no—
521#135—216no—
522C2×Q16—22no—
523C2×SD16—22no—
524C2×SD16—22no—
525C2×D8—22no—
526C2×M16—21no—
527C2×M16—22no—
528C2×M16—21no—
529C2×M16—22no—
530C2×M16—22no—
531C2×M16D4×C1114yescomplemented
532C2×M16C23×C1112yes—
533C2×M16C23×C1112yes—
534C22×C8—21no—
535C22×C8—21no—
536C4⋊Q8—22no—
537C4⋊Q8—22no—
538C4⋊Q8—22no—
539#127—22no—
540#127—22no—
541#127—22no—
542#124—22no—
543#124—22no—
544#124—22no—
545#124—22no—
546#124—22no—
547#124—22no—
548#123—24no—
549#123—24no—
550C22⋊Q8—24no—
551C22⋊Q8—24no—
552#121—216no—
553#121—24no—
554#121—28no—
555#121—24no—
556#120—24no—
557#120—24no—
558C4×D4—216no—
559C4×D4—28no—
560#117—21no—
561#117—21no—
562#117D4×C1112yescomplemented
563#117C23×C1112yes—
564C2×C4⋊C4—22no—
565C2×C4⋊C4D4×C1112yescomplemented
566C2×C22⋊C4—21no—
567C2×C22⋊C4—22no—
568C2×C22⋊C4—22no—
569C2×C42—21no—
570C2×C42—21no—
571C2×C42—22no—
572C2×C42D4×C1114yescomplemented
573C2×C42C23×C1111yescharacteristic
574C2×C42C23×C1111yescharacteristic
575#104—24no—
576#104—24no—
577#103—24no—
578#102—24no—
579#101—24no—
580#100—24no—
581C2×C11—21no—
582C2×C11—21no—
583C2×C11—22no—
584C2×C11—22no—
585C2×C11—82no—
586C2×C11—82no—
587C2×C11—82no—
588C2×C11C2×#39211yescharacteristic
589C2×C11#301812yes—
590C24—21no—
591C24—21no—
592C24C2×D4×C1112yes—
593C24C2×D4×C1111yescharacteristic
594#41—24no—
595#41—24no—
596#41—24no—
597#41—24no—
598#41—24no—
599#41—24no—
600#41—22no—
601#41—22no—
602#41—22no—
603#41—22no—
604#41—42no—
605#41—42no—
606#41—42no—
607#41—42no—
608#41—42no—
609#41—42no—
610#41—42no—
611#41—42no—
612#41—42no—
613#41—42no—
614#41—42no—
615#41—42no—
616#41—42no—
617#41—42no—
618#41—42no—
619#41—42no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8—21no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—22no—
629C2×Q8—22no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8—21no—
633C2×Q8—21no—
634C2×Q8C2×D4×C1112yes—
635C2×Q8C2×D4×C1112yes—
636C2×D4—28no—
637C2×D4—22no—
638C2×D4—22no—
639C2×D4—24no—
640C2×D4—22no—
641C2×D4—24no—
642C2×D4—24no—
643C2×D4—22no—
644C2×D4—28no—
645C2×D4—22no—
646C2×D4—21no—
647C2×D4—22no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—48no—
660C2×D4—41no—
661C2×D4—41no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4C2×D4×C1112yes—
666C2×D4C2×D4×C1112yes—
667C22×C4—21no—
668C22×C4—24no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—22no—
673C22×C4—24no—
674C22×C4—22no—
675C22×C4—24no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—24no—
679C22×C4—22no—
680C22×C4—44no—
681C22×C4—41no—
682C22×C4—41no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4C2×D4×C1112yes—
687C22×C4C2×D4×C1111yescharacteristic
688C22×C4C2×D4×C1111yescharacteristic
689C22×C4C2×D4×C1112yes—
690C22×C4C2×D4×C1111yescharacteristic
691C22×C4C2×D4×C1112yes—
692C22×C4C2×D4×C1112yes—
693C22×C4C2×D4×C1111yescharacteristic
694C22×C4C2×D4×C1111yescharacteristic
695C22×C4C11×#4112yes—
696C22×C4C24×C1111yescharacteristic
697Q16—28no—
698SD16—28no—
699SD16—28no—
700D8—28no—
701M16—24no—
702M16—22no—
703M16—22no—
704M16—22no—
705M16—42no—
706M16C2×D4×C1114yes—
707C2×C8—24no—
708C2×C8—22no—
709C2×C8—22no—
710C2×C8—42no—
711C4⋊C4—28no—
712C4⋊C4—28no—
713C4⋊C4—22no—
714C4⋊C4C2×D4×C1114yes—
715C22⋊C4—28no—
716C22⋊C4—28no—
717C22⋊C4—28no—
718C22⋊C4—28no—
719C22⋊C4—22no—
720C22⋊C4—22no—
721C42—24no—
722C42—22no—
723C42—21no—
724C42—21no—
725C42—22no—
726C42C2×D4×C1112yes—
727C42C2×D4×C1112yes—
728C11#2339911yescharacteristic, direct product factor, Sylow
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—42no—
735C23—44no—
736C23—44no—
737C23—41no—
738C23—41no—
739C23—42no—
740C23—82no—
741C23C11×#12011yescharacteristic
742C23C11×#12011yescharacteristic
743C23C11×#12012yes—
744C23C11×#12112yes—
745C23C22×D4×C1111yescharacteristic
746Q8—22no—
747Q8—22no—
748Q8—22no—
749Q8—22no—
750Q8—41no—
751Q8—41no—
752Q8—41no—
753Q8—41no—
754Q8—42no—
755Q8—41no—
756Q8—41no—
757D4—22no—
758D4—22no—
759D4—22no—
760D4—22no—
761D4—416no—
762D4—42no—
763D4—42no—
764D4—44no—
765D4—44no—
766D4—44no—
767D4—44no—
768D4—44no—
769D4—41no—
770D4—41no—
771D4—41no—
772D4—41no—
773D4—42no—
774D4—41no—
775D4—41no—
776D4—88no—
777C2×C4—24no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—24no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—48no—
787C2×C4—42no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—42no—
798C2×C4—82no—
799C2×C4C11×#12012yes—
800C2×C4C11×#12012yes—
801C2×C4C11×#12012yes—
802C2×C4C11×#12011yescharacteristic
803C2×C4C11×#12011yescharacteristic
804C2×C4C11×#12112yes—
805C2×C4C11×#12112yes—
806C2×C4C11×#12112yes—
807C2×C4C11×#12112yes—
808C2×C4C11×#12112yes—
809C2×C4C11×#12712yes—
810C2×C4C11×#12712yes—
811C2×C4C22×D4×C1111yescharacteristic
812C2×C4C22×D4×C1111yescharacteristic
813C2×C4C22×D4×C1111yescharacteristic
814C2×C4C22×D4×C1111yescharacteristic
815C2×C4C22×D4×C1111yescharacteristic
816C2×C4C2×C11×#4111yescharacteristic
817C8—24no—
818C8—42no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—42no—
823C22—42no—
824C22—44no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—44no—
830C22—44no—
831C22—82no—
832C22—82no—
833C22—84no—
834C22—82no—
835C22C11×#39212yes—
836C22C11×#39212yes—
837C22C2×C11×#12011yescharacteristic
838C22C2×C11×#12011yescharacteristic
839C22C2×C11×#12111yescharacteristic
840C4—24no—
841C4—42no—
842C4—42no—
843C4—42no—
844C4—42no—
845C4—44no—
846C4C11×#39212yes—
847C4C11×#39212yes—
848C4C2×C11×#12011yescharacteristic
849C4C2×C11×#12111yescharacteristic
850C4C2×C11×#12111yescharacteristic
851C4C2×C11×#12711yescharacteristic
852C2—21no—
853C2—21no—
854C2—22no—
855C2—22no—
856C2—82no—
857C2—82no—
858C2—82no—
859C2C2×C11×#39211yescharacteristic
860C2C11×#301812yes—
subgroupG/H
centerC2×C4×C11#120
commutator, Frattini, cosocleC22×C4C24×C11
socleC22×C11C2×#120
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#575C2semidirect
2. C11×#3449C2semidirect
3. C2×C11×#532C2semidirect
4. C22×C11×#104C2semidirect
5. C11×#2896C2semidirect
6. C2×C11×#413C2semidirect
7. C11×#2005C2semidirect
8. C11×#2004C2semidirect
9. C11×#2003C2semidirect
10. C11×#2002C2semidirect
11. C2×C11×#339C2semidirect
33. C2×C11×C4⋊Q8C22semidirect
34. C2×C11×#127C22semidirect
35. C2×C11×#124C22semidirect
36. C2×C11×#124C22semidirect
46. C11×#419C22semidirect
47. C11×#418C22semidirect
51. C2×C11×#101C22semidirect
52. C2×C11×#100C22semidirect
53. C11×#339C22semidirect
54. C11×#339C22semidirect
76. C2×C11×#41D4semidirect
77. C2×C11×#41D4semidirect
79. C22×Q8×C11D4semidirect
86. C22×D4×C11D4semidirect
110. C2×C11×M16D4semidirect
141. C11×#117D4semidirect
144. C2×C11×C4⋊C4D4semidirect
151. C2×C42×C11D4semidirect
160. #23399C11direct (N × H)
299. C2×#575C2×C11semidirect
300. #3449C2×C11semidirect
301. C2×#532C2×C11semidirect
302. C22×#104C2×C11semidirect
303. #2896C2×C11semidirect
304. C2×#413C2×C11semidirect
305. #2005C2×C11semidirect
306. #2004C2×C11semidirect
307. #2003C2×C11semidirect
308. #2002C2×C11semidirect
309. C2×#339C2×C11semidirect
421. C2×C4⋊Q8C22×C11semidirect
422. C2×#127C22×C11semidirect
423. C2×#124C22×C11semidirect
424. C2×#124C22×C11semidirect
434. #419C22×C11semidirect
435. #418C22×C11semidirect
439. C2×#101C22×C11semidirect
440. C2×#100C22×C11semidirect
441. #339C22×C11semidirect
442. #339C22×C11semidirect
497. C2×#41D4×C11semidirect
498. C2×#41D4×C11semidirect
500. C22×Q8D4×C11semidirect
507. C22×D4D4×C11semidirect
531. C2×M16D4×C11semidirect
562. #117D4×C11semidirect
565. C2×C4⋊C4D4×C11semidirect
572. C2×C42D4×C11semidirect
728. C11#23399direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5752
C11×#34492
C2×C11×#5322
C22×C11×#1042
C11×#28962
C2×C11×#4132
C11×#20052
C11×#20042
C11×#20032
C11×#20022
C2×C11×#3392
#2339911