Finite Group Databasebeta

← C2×#13078150 #15620693

Subgroups — C2×#13078150 #15620693

Order 2816.

2934 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66964C211yesmaximal, characteristic, complemented
2C22×#66965C211yesmaximal, characteristic, complemented
3C2×#10623246C211yesmaximal, characteristic, complemented
4C2×#10623077C211yesmaximal, characteristic, complemented
5#13078150C2116yesmaximal, direct product factor
6C2×#10622458C211yesmaximal, characteristic, complemented
7C2×#10622380C211yesmaximal, characteristic, complemented
8C2×#10622375C211yesmaximal, characteristic, complemented
9C2×#10622688C211yesmaximal, characteristic, complemented
10C2×#10622629C211yesmaximal, characteristic, complemented
11C2×#10622766C211yesmaximal, characteristic, complemented
12C2×#10622763C211yesmaximal, characteristic, complemented
13C2×#10622452C211yesmaximal, characteristic, complemented
14C2×#10622384C211yesmaximal, characteristic, complemented
15C2×D11×#102C211yesmaximal, characteristic, complemented
16C2×C11×#459C211yesmaximal, characteristic, complemented
17C22×#4341C2211yescharacteristic
18C22×#4341C2211yescharacteristic
19C22×D4×D11C2211yescharacteristic
20C22×C11×D8C2211yescharacteristic
21C22×C11×D8C2211yescharacteristic, complemented
22C2×C11×#127C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic, complemented
24C2×#66993C2211yescharacteristic
25C2×#66992—21no—
26C2×#66992—21no—
27C2×#66990—21no—
28C2×#66990—21no—
29C2×#66989C2211yescharacteristic
30C2×D4×Dic11C2211yescharacteristic, complemented
31C22×#4324C2211yescharacteristic
32C22×#4324C2211yescharacteristic, complemented
33C22×#4324C2211yescharacteristic, complemented
34C22×#4323C2211yescharacteristic
35C2×C4×C22⋊D11—21no—
36C22×Dic11⋊C4—21no—
37C2×#66965—28no—
38C2×#66965C2218yescomplemented
39C2×#66964—28no—
40C2×#66964C2218yescomplemented
41C22×Dic44C2211yescharacteristic, complemented
42C22×#4314C2211yescharacteristic
43C22×#4313C2211yescharacteristic
44C22×C8×D11C2211yescharacteristic
45#10623246—24no—
46#10623246C2218yescomplemented
47#10623077—24no—
48#10623077C2218yescomplemented
49C2×C4⋊C4×D11C2211yescharacteristic
50C2×#66940C2211yescharacteristic, complemented
51C2×(C22⋊D11)⋊C4—21no—
52C2×#66930—21no—
53C2×#66928C2211yescharacteristic
54C2×#66925C2211yescharacteristic
55C2×C4×Dic22C2211yescharacteristic, complemented
56C11×#459C2218yescomplemented
57C2×C11×C4⋊C8C2211yescharacteristic, complemented
58C2×C11×#102C2211yescharacteristic
59C2×C11×#102C2211yescharacteristic, complemented
60C2×#66896C2211yescharacteristic
61C2×#66896C2211yescharacteristic, complemented
62#10622766C2218yescomplemented
63#10622763C2218yescomplemented
64C2×#66885C2211yescharacteristic
65C2×#66880C2211yescharacteristic, complemented
66C2×Dic11⋊C8C2211yescharacteristic, complemented
67C2×Dic11⋊C8C2211yescharacteristic, complemented
68#10622688C2218yescomplemented
69#10622629C2218yescomplemented
70C2×#66874C2211yescharacteristic, complemented
71C2×#66873C2211yescharacteristic
72C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
73#10622458C2218yescomplemented
74#10622452C2218yescomplemented
75#10622384C2218yescomplemented
76D11×#102C2218yescomplemented
77#10622380C2218yescomplemented
78#10622375C2218yescomplemented
79C24×D11—21no—
80C22×D4×C11—21no—
81C22×D4×C11—21no—
82C22×D4×C11C2311yescharacteristic
83C22×D4×C11C2311yescharacteristic
84C22×D4×C11C2311yescharacteristic
85C23×C4×C11—21no—
86C22×C22⋊D11—21no—
87C22×C22⋊D11—21no—
88C22×C22⋊D11—21no—
89C22×C22⋊D11—21no—
90C22×C22⋊D11—21no—
91C23×Dic11—21no—
92C23×Dic11—21no—
93C23×Dic11—21no—
94C2×#4341—22no—
95C2×#4341—24no—
96C2×#4341—22no—
97C2×#4341—24no—
98C2×#4341—24no—
99C2×#4341D418yescomplemented
100C2×#4341C2314yes—
101C2×#4341C2314yes—
102C2×D4×D11—24no—
103C2×D4×D11—22no—
104C2×D4×D11—24no—
105C2×D4×D11C2314yes—
106C22×D44C2311yescharacteristic
107C22×C4×D11—21no—
108C22×C4×D11C2311yescharacteristic
109C22×Dic22C2311yescharacteristic
110C22×Dic22C2311yescharacteristic
111C2×C11×D8—24no—
112C2×C11×D8—24no—
113C2×C11×D8C2314yes—
114C2×C11×D8C2314yescomplemented
115C22×C8×C11C2311yescharacteristic
116C22×C8×C11C2311yescharacteristic
117C11×#127—22no—
118C11×#127C2314yes—
119C4×D4×C11—22no—
120C4×D4×C11C2314yescomplemented
121C2×C11×C4⋊C4C2311yescharacteristic
122C2×C11×C22⋊C4—21no—
123C2×C42×C11C2311yescharacteristic
124C2×C22⋊Dic11—21no—
125C2×C22⋊Dic11—21no—
126C2×C22⋊Dic11—21no—
127#66993—22no—
128#66993C2314yes—
129#66992—28no—
130#66992—28no—
131#66990—28no—
132#66990—28no—
133#66989—22no—
134#66989C2314yes—
135D4×Dic11—22no—
136D4×Dic11C2314yescomplemented
137C2×#4324—24no—
138C2×#4324—24no—
139C2×#4324—24no—
140C2×#4324C2314yes—
141C2×#4324C2314yescomplemented
142C2×#4324C2314yescomplemented
143C2×#4323—24no—
144C2×#4323C2314yes—
145C4×C22⋊D11—28no—
146C2×(C2×D11)⋊C4—21no—
147C2×(C2×D11)⋊C4—21no—
148C2×(C2×D11)⋊C4D411yescharacteristic
149C2×(C2×D11)⋊C4D411yescharacteristic
150C2×C4⋊Dic11C2311yescharacteristic
151C2×Dic11⋊C4—21no—
152C2×Dic11⋊C4—21no—
153C2×Dic11⋊C4—21no—
154C2×Dic11⋊C4—28no—
155C2×Dic11⋊C4D411yescharacteristic
156C2×Dic11⋊C4D411yescharacteristic
157C2×C4×Dic11—21no—
158C2×C4×Dic11—21no—
159C2×C4×Dic11C2311yescharacteristic
160C22×C11⋊C8C2311yescharacteristic
161C22×C11⋊C8C2311yescharacteristic
162#66965—232no—
163#66964—232no—
164C2×Dic44—24no—
165C2×Dic44C2314yescomplemented
166C2×#4314—24no—
167C2×#4314C2314yes—
168C2×#4313—24no—
169C2×#4313C2314yes—
170C2×C8×D11—24no—
171C2×C8×D11C2314yes—
172C4⋊C4×D11—22no—
173C4⋊C4×D11C2314yes—
174#66940—22no—
175#66940C2314yescomplemented
176(C22⋊D11)⋊C4—28no—
177#66930—28no—
178#66928—22no—
179#66928C2314yes—
180#66925D414yes—
181#66925C2314yes—
182C4×Dic22—22no—
183C4×Dic22C2314yescomplemented
184C11×C4⋊C8C2314yescomplemented
185C11×#102C2314yes—
186C11×#102C2314yescomplemented
187#66896C2314yes—
188#66896C2314yescomplemented
189#66885C2314yes—
190#66880C2314yescomplemented
191Dic11⋊C8C2314yescomplemented
192Dic11⋊C8C2314yescomplemented
193#66874C2314yescomplemented
194#66873C2314yes—
195C4⋊(C11⋊C8)C2314yescomplemented
196C2×#3045—111nomaximal, Sylow
197C24×C11—21no—
198C24×C11—21no—
199C24×C11—21no—
200C23×D11—21no—
201C23×D11—24no—
202C23×D11—44no—
203C23×D11—82no—
204C23×D11—82no—
205C23×D11C2×D411yescharacteristic
206C2×D4×C11—21no—
207C2×D4×C11—22no—
208C2×D4×C11—22no—
209C2×D4×C11—21no—
210C2×D4×C11—21no—
211C2×D4×C11—24no—
212C2×D4×C11—24no—
213C2×D4×C11—22no—
214C2×D4×C11—22no—
215C2×D4×C11—22no—
216C2×D4×C11—82no—
217C2×D4×C11—82no—
218C2×D4×C11C2×D414yes—
219C2×D4×C11C2412yes—
220C2×D4×C11C2412yes—
221C2×D4×C11C2412yes—
222C22×C4×C11—21no—
223C22×C4×C11—24no—
224C22×C4×C11—82no—
225C22×C4×C11C2×D411yescharacteristic
226C22×C4×C11C2×D411yescharacteristic
227C22×C4×C11C2411yescharacteristic
228C2×C22⋊D11—24no—
229C2×C22⋊D11—24no—
230C2×C22⋊D11—24no—
231C2×C22⋊D11—28no—
232C2×C22⋊D11—24no—
233C2×C22⋊D11—24no—
234C2×C22⋊D11—44no—
235C2×C22⋊D11—44no—
236C2×C22⋊D11—82no—
237C2×C22⋊D11—82no—
238C22×Dic11—28no—
239C22×Dic11—24no—
240C22×Dic11—24no—
241C22×Dic11—24no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11—21no—
245C22×Dic11—44no—
246C22×Dic11—82no—
247C22×Dic11C2×D411yescharacteristic
248C22×Dic11C2×D411yescharacteristic
249C22×Dic11C2×D411yescharacteristic
250#4341—216no—
251#4341—28no—
252#4341—28no—
253#4341—28no—
254#4341—48no—
255#4341C2×D4116yescomplemented
256D4×D11—28no—
257D4×D11—28no—
258D4×D11—48no—
259C2×D44—21no—
260C2×D44—22no—
261C2×D44—22no—
262C2×D44C2412yes—
263C2×C4×D11—24no—
264C2×C4×D11—82no—
265C2×C4×D11C2×D414yes—
266C2×C4×D11C2×D412yes—
267C2×C4×D11#4114yes—
268C2×C4×D11C2412yes—
269C2×Dic22—21no—
270C2×Dic22—22no—
271C2×Dic22—21no—
272C2×Dic22—22no—
273C2×Dic22—22no—
274C2×Dic22C2×D414yes—
275C2×Dic22C2412yes—
276C2×Dic22C2412yes—
277C11×D8—28no—
278C11×D8—28no—
279C2×C8×C11—22no—
280C2×C8×C11—22no—
281C2×C8×C11C2412yes—
282C2×C8×C11C2412yes—
283C11×C4⋊C4—21no—
284C11×C4⋊C4C2412yes—
285C11×C22⋊C4—24no—
286C42×C11C2×D412yes—
287C42×C11C2412yes—
288C22⋊Dic11—24no—
289C22⋊Dic11—24no—
290C22⋊Dic11—24no—
291#4324—28no—
292#4324—28no—
293#4324—28no—
294#4323—28no—
295(C2×D11)⋊C4—24no—
296(C2×D11)⋊C4—24no—
297(C2×D11)⋊C4C2×D414yes—
298(C2×D11)⋊C4C2×D414yes—
299C4⋊Dic11—21no—
300C4⋊Dic11C2412yes—
301Dic11⋊C4—24no—
302Dic11⋊C4—24no—
303Dic11⋊C4—24no—
304Dic11⋊C4C2×D414yes—
305Dic11⋊C4C2×D414yes—
306C4×Dic11—24no—
307C4×Dic11—24no—
308C4×Dic11C2×D412yes—
309C4×Dic11C2412yes—
310C2×C11⋊C8—22no—
311C2×C11⋊C8—22no—
312C2×C11⋊C8C2412yes—
313C2×C11⋊C8C2412yes—
314Dic44—28no—
315#4314—28no—
316#4313—28no—
317C8×D11—28no—
318C22×AGL(1,ℤ/8)—111no—
319C22×#135—111no—
320C2×#535—111no—
321C2×#520—111no—
322#3045—1116no—
323C2×#464—111no—
324C2×#464—111no—
325C2×#460—111no—
326C2×#460—111no—
327C2×#463—111no—
328C2×#463—111no—
329C2×#459—111no—
330C2×#459D1111yescharacteristic, complemented
331C2×#424—111no—
332C2×#417—111no—
333C22×#102—111no—
334C23×C11—24no—
335C23×C11—22no—
336C23×C11—22no—
337C23×C11—22no—
338C23×C11—42no—
339C23×C11—42no—
340C23×C11—42no—
341C23×C11—42no—
342C23×C11—42no—
343C23×C11—42no—
344C23×C11—42no—
345C23×C11—42no—
346C23×C11C22×D411yescharacteristic
347C22×D11—22no—
348C22×D11—22no—
349C22×D11—22no—
350C22×D11—42no—
351C22×D11—42no—
352C22×D11—42no—
353C22×D11—48no—
354C22×D11—84no—
355C22×D11—84no—
356C22×D11—816no—
357C22×D11#12114yes—
358C22×D11C22×D412yes—
359D4×C11—24no—
360D4×C11—22no—
361D4×C11—22no—
362D4×C11—22no—
363D4×C11—22no—
364D4×C11—22no—
365D4×C11—42no—
366D4×C11—42no—
367D4×C11—84no—
368D4×C11—84no—
369D4×C11C22×D414yes—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—42no—
374C2×C4×C11—84no—
375C2×C4×C11C22×D412yes—
376C2×C4×C11C22×D412yes—
377C2×C4×C11C22×D411yescharacteristic
378C2×C4×C11C22×D412yes—
379C2×C4×C11C2×#4112yes—
380C2×C4×C11C2511yescharacteristic
381C22⋊D11—216no—
382C22⋊D11—48no—
383C22⋊D11—48no—
384C22⋊D11—84no—
385C22⋊D11—84no—
386C2×Dic11—24no—
387C2×Dic11—22no—
388C2×Dic11—22no—
389C2×Dic11—22no—
390C2×Dic11—216no—
391C2×Dic11—22no—
392C2×Dic11—22no—
393C2×Dic11—42no—
394C2×Dic11—42no—
395C2×Dic11—48no—
396C2×Dic11—84no—
397C2×Dic11#12114yes—
398C2×Dic11C22×D412yes—
399C2×Dic11C22×D412yes—
400C2×Dic11C22×D412yes—
401D44—22no—
402D44—22no—
403D44—42no—
404C4×D11—84no—
405C4×D11#12118yes—
406C4×D11C22×D414yes—
407C4×D11C2×#4114yes—
408Dic22—24no—
409Dic22—22no—
410Dic22—22no—
411Dic22—22no—
412Dic22—42no—
413Dic22C22×D414yes—
414C8×C11—22no—
415C8×C11—22no—
416C11⋊C8—22no—
417C11⋊C8—22no—
418C22×#41—111no—
419C22×#41—111no—
420C23×D4—111no—
421C2×AGL(1,ℤ/8)—118no—
422C2×AGL(1,ℤ/8)—228no—
423C2×#135—118no—
424C2×#135—228no—
425C22×Q16—111no—
426C22×SD16—111no—
427C22×SD16—111no—
428C22×SD16—111no—
429C22×SD16—111no—
430C22×D8—111no—
431C22×D8C2×D1111yescharacteristic
432C22×D8C2×D1111yescharacteristic, complemented
433C22×M16—111no—
434C23×C8—111no—
435#535—118no—
436#535—224no—
437C2×#127—111no—
438C2×#127C2×D1111yescharacteristic
439C2×#124—111no—
440C2×#124—111no—
441C2×#121—221no—
442C2×#121—221no—
443C2×#120—221no—
444C2×#120—221no—
445#520—118no—
446#520—224no—
447C2×C4×Q8—111no—
448C2×C4×Q8—111no—
449C2×C4×D4—111no—
450C2×C4×D4—221no—
451C2×C4×D4—221no—
452C2×C4×D4C2×D1111yescharacteristic, complemented
453C2×#117—111no—
454C2×#117—221no—
455C22×C4⋊C4—111no—
456C22×C4⋊C4—221no—
457#464—118no—
458#464—118no—
459#463—118no—
460#463—118no—
461#460—118no—
462#460—118no—
463#459—118no—
464#459C2×D1118yescomplemented
465#424—118no—
466C2×C4⋊C8—111no—
467C2×C4⋊C8—111no—
468C2×C4⋊C8—111no—
469C2×C4⋊C8C2×D1111yescharacteristic, complemented
470#417—118no—
471C2×#103—111no—
472C2×#103—111no—
473C2×#102—111no—
474C2×#102—111no—
475C2×#102—111no—
476C2×#102—111no—
477C2×#102—118no—
478C2×#102C2×D1111yescharacteristic
479C2×#102C2×D1111yescharacteristic, complemented
480C22×C11—24no—
481C22×C11—48no—
482C22×C11—42no—
483C22×C11—42no—
484C22×C11—42no—
485C22×C11—42no—
486C22×C11—42no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11—42no—
490C22×C11—84no—
491C22×C11—84no—
492C22×C11C2×#12112yes—
493C22×C11#57612yes—
494C22×C11#57712yes—
495C22×C11C23×D411yescharacteristic
496C2×D11—28no—
497C2×D11—22no—
498C2×D11—22no—
499C2×D11—42no—
500C2×D11—42no—
501C2×D11—42no—
502C2×D11—816no—
503C2×D11—84no—
504C2×D11C2×#12114yes—
505C4×C11—22no—
506C4×C11—22no—
507C4×C11—42no—
508C4×C11C2×#12112yes—
509C4×C11C23×D411yescharacteristic
510C4×C11C22×#4111yescharacteristic
511Dic11—24no—
512Dic11—22no—
513Dic11—22no—
514Dic11—42no—
515Dic11—42no—
516Dic11C2×#12114yes—
517C25—221no—
518C2×#41—118no—
519C2×#41—114no—
520C2×#41—114no—
521C2×#41—222no—
522C2×#41—224no—
523C2×#41—222no—
524C2×#41—224no—
525C2×#41—224no—
526C22×Q8—111no—
527C22×Q8—111no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—114no—
531C22×D4—111no—
532C22×D4—224no—
533C22×D4—224no—
534C22×D4—222no—
535C22×D4—221no—
536C22×D4—221no—
537C22×D4—221no—
538C22×D4—221no—
539C22×D4—221no—
540C22×D4C22×D1111yescharacteristic
541C22×D4C22×D1111yescharacteristic
542C22×D4C22×D1111yescharacteristic
543C23×C4—21no—
544C23×C4—111no—
545C23×C4—221no—
546C23×C4—221no—
547C23×C4—221no—
548C23×C4—221no—
549AGL(1,ℤ/8)—2232no—
550#135—2232no—
551C2×Q16—114no—
552C2×Q16—224no—
553C2×SD16—114no—
554C2×SD16—114no—
555C2×SD16—114no—
556C2×SD16—114no—
557C2×SD16—224no—
558C2×SD16—224no—
559C2×SD16—224no—
560C2×SD16—224no—
561C2×D8—24no—
562C2×D8—24no—
563C2×D8—114no—
564C2×D8—224no—
565C2×D8C22×D1114yes—
566C2×D8C22×D1114yescomplemented
567C2×M16—114no—
568C2×M16—224no—
569C22×C8—111no—
570C22×C8—111no—
571C22×C8—114no—
572C22×C8—224no—
573C22×C8C22×D1111yescharacteristic
574C22×C8C22×D1111yescharacteristic
575#127—22no—
576#127—114no—
577#127—222no—
578#127C22×D1114yes—
579#124—114no—
580#124—114no—
581#124—222no—
582#124—222no—
583#121—228no—
584#121—228no—
585#120—228no—
586#120—228no—
587C4×Q8—114no—
588C4×Q8—114no—
589C4×Q8—222no—
590C4×Q8—222no—
591C4×D4—22no—
592C4×D4—114no—
593C4×D4—222no—
594C4×D4—228no—
595C4×D4—228no—
596C4×D4C22×D1114yescomplemented
597#117—114no—
598#117—114no—
599#117—228no—
600C2×C4⋊C4—111no—
601C2×C4⋊C4—111no—
602C2×C4⋊C4—111no—
603C2×C4⋊C4—114no—
604C2×C4⋊C4—222no—
605C2×C4⋊C4—228no—
606C2×C4⋊C4—221no—
607C2×C4⋊C4—221no—
608C2×C4⋊C4—221no—
609C2×C4⋊C4C22×D1111yescharacteristic
610C2×C22⋊C4—21no—
611C2×C22⋊C4—111no—
612C2×C22⋊C4—111no—
613C2×C22⋊C4—221no—
614C2×C22⋊C4—221no—
615C2×C22⋊C4—221no—
616C2×C22⋊C4—221no—
617C2×C22⋊C4—221no—
618C2×C42—111no—
619C2×C42—221no—
620C2×C42—221no—
621C2×C42C22×D1111yescharacteristic
622C4⋊C8—114no—
623C4⋊C8—114no—
624C4⋊C8—114no—
625C4⋊C8C22×D1114yescomplemented
626#103—114no—
627#103—114no—
628#102—114no—
629#102—114no—
630#102—114no—
631#102—114no—
632#102C22×D1114yes—
633#102C22×D1114yescomplemented
634C2×C11—44no—
635C2×C11—82no—
636C2×C11—82no—
637C2×C11#304514yescomplemented
638C2×C11C22×#12111yescharacteristic
639C2×C11C2×#57611yescharacteristic
640C2×C11C2×#57711yescharacteristic
641D11—24no—
642D11—82no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—111no—
647C24—224no—
648C24—221no—
649C24—444no—
650C24—882no—
651C24—882no—
652#41—1116no—
653#41—2216no—
654#41—228no—
655#41—228no—
656#41—228no—
657#41—448no—
658C2×Q8—114no—
659C2×Q8—112no—
660C2×Q8—112no—
661C2×Q8—221no—
662C2×Q8—221no—
663C2×Q8—222no—
664C2×Q8—222no—
665C2×Q8—222no—
666C2×D4—21no—
667C2×D4—22no—
668C2×D4—22no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—24no—
672C2×D4—24no—
673C2×D4—22no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—82no—
677C2×D4—82no—
678C2×D4—112no—
679C2×D4—228no—
680C2×D4—228no—
681C2×D4—224no—
682C2×D4—224no—
683C2×D4—224no—
684C2×D4—224no—
685C2×D4—228no—
686C2×D4—224no—
687C2×D4—222no—
688C2×D4—221no—
689C2×D4—222no—
690C2×D4—448no—
691C2×D4—444no—
692C2×D4—444no—
693C2×D4—882no—
694C2×D4—882no—
695C2×D4D4×D1114yes—
696C2×D4C23×D1112yes—
697C2×D4C23×D1112yes—
698C2×D4C23×D1112yes—
699C22×C4—21no—
700C22×C4—24no—
701C22×C4—82no—
702C22×C4—111no—
703C22×C4—112no—
704C22×C4—114no—
705C22×C4—114no—
706C22×C4—112no—
707C22×C4—111no—
708C22×C4—111no—
709C22×C4—224no—
710C22×C4—224no—
711C22×C4—228no—
712C22×C4—224no—
713C22×C4—224no—
714C22×C4—221no—
715C22×C4—221no—
716C22×C4—221no—
717C22×C4—444no—
718C22×C4—882no—
719C22×C4—882no—
720C22×C4D4×D1111yescharacteristic
721C22×C4D4×D1111yescharacteristic
722C22×C4C23×D1111yescharacteristic
723Q16—228no—
724SD16—228no—
725SD16—228no—
726SD16—228no—
727SD16—228no—
728D8—28no—
729D8—28no—
730D8—228no—
731M16—228no—
732C2×C8—22no—
733C2×C8—22no—
734C2×C8—112no—
735C2×C8—112no—
736C2×C8—228no—
737C2×C8—222no—
738C2×C8—222no—
739C2×C8C23×D1112yes—
740C2×C8C23×D1112yes—
741C4⋊C4—21no—
742C4⋊C4—114no—
743C4⋊C4—114no—
744C4⋊C4—112no—
745C4⋊C4—224no—
746C4⋊C4—224no—
747C4⋊C4—221no—
748C4⋊C4—224no—
749C4⋊C4C23×D1112yes—
750C22⋊C4—24no—
751C22⋊C4—114no—
752C22⋊C4—114no—
753C22⋊C4—224no—
754C22⋊C4—224no—
755C22⋊C4—224no—
756C22⋊C4—224no—
757C22⋊C4—224no—
758C42—112no—
759C42—112no—
760C42—224no—
761C42—224no—
762C42D4×D1112yes—
763C42C23×D1112yes—
764C11C2×#304511yescharacteristic, complemented, Sylow
765C23—24no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—42no—
776C23—42no—
777C23—114no—
778C23—112no—
779C23—222no—
780C23—222no—
781C23—222no—
782C23—448no—
783C23—442no—
784C23—442no—
785C23—442no—
786C23—884no—
787C23—884no—
788C23—8816no—
789C23C2×D4×D1111yescharacteristic
790Q8—114no—
791Q8—224no—
792Q8—222no—
793Q8—222no—
794Q8—222no—
795Q8—442no—
796D4—24no—
797D4—22no—
798D4—22no—
799D4—22no—
800D4—22no—
801D4—22no—
802D4—42no—
803D4—42no—
804D4—84no—
805D4—84no—
806D4—2216no—
807D4—222no—
808D4—222no—
809D4—448no—
810D4—448no—
811D4—442no—
812D4—884no—
813D4—884no—
814D4C2×D4×D1114yes—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—42no—
819C2×C4—84no—
820C2×C4—114no—
821C2×C4—112no—
822C2×C4—118no—
823C2×C4—114no—
824C2×C4—114no—
825C2×C4—112no—
826C2×C4—112no—
827C2×C4—2216no—
828C2×C4—222no—
829C2×C4—222no—
830C2×C4—224no—
831C2×C4—222no—
832C2×C4—222no—
833C2×C4—222no—
834C2×C4—448no—
835C2×C4—442no—
836C2×C4—442no—
837C2×C4—884no—
838C2×C4—884no—
839C2×C4C2×D4×D1112yes—
840C2×C4C2×D4×D1112yes—
841C2×C4C2×D4×D1111yescharacteristic
842C2×C4C2×D4×D1112yes—
843C2×C4#41×D1112yes—
844C2×C4C24×D1111yescharacteristic
845C8—22no—
846C8—22no—
847C8—222no—
848C8—222no—
849C22—24no—
850C22—48no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—84no—
860C22—84no—
861C22—114no—
862C22—228no—
863C22—222no—
864C22—222no—
865C22—442no—
866C22—442no—
867C22—442no—
868C22—8816no—
869C22—884no—
870C22D11×#12112yes—
871C22#1062328812yes—
872C22#1062330612yes—
873C22C22×D4×D1111yescharacteristic
874C4—22no—
875C4—22no—
876C4—42no—
877C4—114no—
878C4—222no—
879C4—224no—
880C4—222no—
881C4—442no—
882C4—442no—
883C4D11×#12112yes—
884C4C22×D4×D1111yescharacteristic
885C4C2×#41×D1111yescharacteristic
886C2—44no—
887C2—82no—
888C2—82no—
889C2—224no—
890C2—882no—
891C2#1307815014yesdirect product factor
892C2C2×D11×#12111yescharacteristic
893C2C2×#1062328811yescharacteristic
894C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#459C2
socleC23×C11C22×D4
hypercenterC2×#459D11
hypocenterC11C2×#3045
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C22×#66964C2semidirect
2. C22×#66965C2semidirect
3. C2×#10623246C2semidirect
4. C2×#10623077C2semidirect
5. #13078150C2direct (N × H)
6. C2×#10622458C2semidirect
7. C2×#10622380C2semidirect
8. C2×#10622375C2semidirect
9. C2×#10622688C2semidirect
10. C2×#10622629C2semidirect
11. C2×#10622766C2semidirect
12. C2×#10622763C2semidirect
13. C2×#10622452C2semidirect
14. C2×#10622384C2semidirect
15. C2×D11×#102C2semidirect
16. C2×C11×#459C2semidirect
21. C22×C11×D8C22semidirect
23. C2×C4×D4×C11C22semidirect
30. C2×D4×Dic11C22semidirect
32. C22×#4324C22semidirect
33. C22×#4324C22semidirect
38. C2×#66965C22semidirect
40. C2×#66964C22semidirect
41. C22×Dic44C22semidirect
46. #10623246C22semidirect
48. #10623077C22semidirect
50. C2×#66940C22semidirect
55. C2×C4×Dic22C22semidirect
56. C11×#459C22semidirect
57. C2×C11×C4⋊C8C22semidirect
59. C2×C11×#102C22semidirect
61. C2×#66896C22semidirect
62. #10622766C22semidirect
63. #10622763C22semidirect
65. C2×#66880C22semidirect
66. C2×Dic11⋊C8C22semidirect
67. C2×Dic11⋊C8C22semidirect
68. #10622688C22semidirect
69. #10622629C22semidirect
70. C2×#66874C22semidirect
72. C2×C4⋊(C11⋊C8)C22semidirect
73. #10622458C22semidirect
74. #10622452C22semidirect
75. #10622384C22semidirect
76. D11×#102C22semidirect
77. #10622380C22semidirect
78. #10622375C22semidirect
99. C2×#4341D4semidirect
114. C2×C11×D8C23semidirect
120. C4×D4×C11C23semidirect
136. D4×Dic11C23semidirect
141. C2×#4324C23semidirect
142. C2×#4324C23semidirect
165. C2×Dic44C23semidirect
175. #66940C23semidirect
183. C4×Dic22C23semidirect
184. C11×C4⋊C8C23semidirect
186. C11×#102C23semidirect
188. #66896C23semidirect
190. #66880C23semidirect
191. Dic11⋊C8C23semidirect
192. Dic11⋊C8C23semidirect
193. #66874C23semidirect
195. C4⋊(C11⋊C8)C23semidirect
255. #4341C2×D4semidirect
330. C2×#459D11semidirect
432. C22×D8C2×D11semidirect
452. C2×C4×D4C2×D11semidirect
464. #459C2×D11semidirect
469. C2×C4⋊C8C2×D11semidirect
479. C2×#102C2×D11semidirect
566. C2×D8C22×D11semidirect
596. C4×D4C22×D11semidirect
625. C4⋊C8C22×D11semidirect
633. #102C22×D11semidirect
637. C2×C11#3045semidirect
764. C11C2×#3045semidirect
891. C2#13078150direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669642
C22×#669652
C2×#106232462
C2×#106230772
#130781502
C2×#106224582
C2×#106223802
C2×#106223752
C2×#106226882
C2×#106226292
C2×#106227662
C2×#106227632
C2×#106224522
C2×#106223842
C2×D11×#1022
C2×C11×#4592
C2×#304511