Finite Group Databasebeta

← C2×#13080936 #15630699

Subgroups — C2×#13080936 #15630699

Order 2816.

2426 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
1C2×#10623365C211yesmaximal, characteristic, complemented
2C2×#10623142C211yesmaximal, characteristic, complemented
3#13080936C2116yesmaximal, direct product factor
4C2×#10622373C211yesmaximal, characteristic, complemented
5C2×#10622348C211yesmaximal, characteristic, complemented
6C2×#10622390C211yesmaximal, characteristic, complemented
7C2×#10622404C211yesmaximal, characteristic, complemented
8C2×#10622652C211yesmaximal, characteristic, complemented
9C2×#10622772C211yesmaximal, characteristic, complemented
10C2×#10622763C211yesmaximal, characteristic, complemented
11C2×#10622785C211yesmaximal, characteristic, complemented
12C2×SD16×Dic11C211yesmaximal, characteristic, complemented
13C2×#10622342C211yesmaximal, characteristic, complemented
14C2×#10622845C211yesmaximal, characteristic, complemented
15C2×#10622416C211yesmaximal, characteristic, complemented
16C2×C11×#449C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C22×#4343C2211yescharacteristic
19C22×#4341—21no—
20C22×C11×SD16C2211yescharacteristic
21C22×C11×D8C2211yescharacteristic
22C2×C11×#121C2211yescharacteristic
23#10623365—24no—
24#10623365C2218yescomplemented
25C2×Q8×Dic11C2211yescharacteristic
26C2×#66993—21no—
27C2×#66993C2211yescharacteristic
28C2×#66991—21no—
29C2×#66991C2211yescharacteristic
30C2×#66991C2211yescharacteristic
31C2×#66988—21no—
32C2×D4×Dic11C2211yescharacteristic
33C22×#4323C2211yescharacteristic
34C2×#66983—21no—
35C2×#66983C2211yescharacteristic
36C2×C4×C22⋊D11—21no—
37C2×C4×C22⋊D11C2211yescharacteristic
38C22×C4⋊Dic11C2211yescharacteristic
39C22×#4318C2211yescharacteristic
40C22×#4313C2211yescharacteristic
41#10623142—24no—
42#10623142C2218yescomplemented
43C2×C4⋊C4×D11C2211yescharacteristic
44C2×#66941C2211yescharacteristic
45C2×#66936—21no—
46C2×#66931—21no—
47C11×#449C2218yescomplemented
48C2×C11×#103C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×C11×C22⋊C8C2211yescharacteristic
51#10622845C2218yescomplemented
52C2×#66899C2211yescharacteristic
53C2×#66899C2211yescharacteristic
54C2×#66896C2211yescharacteristic
55C2×#66896C2211yescharacteristic
56C2×#66896C2211yescharacteristic
57#10622785C2218yescomplemented
58SD16×Dic11C2218yescomplemented
59#10622772C2218yescomplemented
60#10622763C2218yescomplemented
61C2×#66885C2211yescharacteristic
62C2×#66885C2211yescharacteristic
63C2×(C2×D11)⋊C8C2211yescharacteristic
64C2×#66881C2211yescharacteristic
65C2×#66881C2211yescharacteristic
66C2×Dic11⋊C8C2211yescharacteristic
67C2×C8×Dic11C2211yescharacteristic
68#10622652C2218yescomplemented
69C2×#66873C2211yescharacteristic
70C2×#66872C2211yescharacteristic
71#10622416C2218yescomplemented
72#10622404C2218yescomplemented
73#10622390C2218yescomplemented
74#10622373C2218yescomplemented
75#10622348C2218yescomplemented
76#10622342C2218yescomplemented
77C2×C11×#41—22no—
78C2×C11×#41—24no—
79C2×C11×#41—42no—
80C2×C11×#41C2314yes—
81C22×Q8×C11C2311yescharacteristic
82C22×D4×C11—21no—
83C22×D4×C11—21no—
84C22×D4×C11C2311yescharacteristic
85C22×D4×C11C2311yescharacteristic
86C23×C4×C11—21no—
87C23×C4×C11C2311yescharacteristic
88C22×C22⋊D11—21no—
89C22×C22⋊D11—21no—
90C22×C22⋊D11—21no—
91C22×C22⋊D11—21no—
92C22×C22⋊D11—21no—
93C22×C22⋊D11D411yescharacteristic
94C23×Dic11—21no—
95C23×Dic11—21no—
96C2×#4343—22no—
97C2×#4343—24no—
98C2×#4343—42no—
99C2×#4343C2314yes—
100C2×#4341—28no—
101C2×#4341—48no—
102C22×D44—21no—
103C22×D44C2311yescharacteristic
104C22×C4×D11—21no—
105C22×C4×D11—21no—
106C22×C4×D11C2311yescharacteristic
107C22×Dic22—21no—
108C2×C11×SD16—24no—
109C2×C11×SD16C2314yes—
110C2×C11×D8—42no—
111C2×C11×D8C2314yes—
112C22×C8×C11C2311yescharacteristic
113C22×C8×C11C2311yescharacteristic
114C11×#121—22no—
115C11×#121C2314yes—
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C11×C22⋊C4—21no—
118C2×C22⋊Dic11—21no—
119C2×C22⋊Dic11—21no—
120C2×C22⋊Dic11—21no—
121C2×C22⋊Dic11D411yescharacteristic
122Q8×Dic11—22no—
123Q8×Dic11C2314yes—
124#66993—28no—
125#66993—22no—
126#66993C2314yes—
127#66991—22no—
128#66991—22no—
129#66991—28no—
130#66991C2314yes—
131#66991C2314yes—
132#66988—28no—
133D4×Dic11—22no—
134D4×Dic11C2314yes—
135C2×#4323—42no—
136C2×#4323C2314yes—
137#66983—22no—
138#66983—28no—
139#66983C2314yes—
140C4×C22⋊D11—28no—
141C4×C22⋊D11D414yes—
142C4×C22⋊D11C2314yes—
143C2×(C2×D11)⋊C4—21no—
144C2×(C2×D11)⋊C4D411yescharacteristic
145C2×C4⋊Dic11—21no—
146C2×C4⋊Dic11—22no—
147C2×C4⋊Dic11—21no—
148C2×C4⋊Dic11C2311yescharacteristic
149C2×C4⋊Dic11C2311yescharacteristic
150C2×C4⋊Dic11C2314yes—
151C2×C4⋊Dic11C2311yescharacteristic
152C2×Dic11⋊C4—21no—
153C2×Dic11⋊C4—21no—
154C2×Dic11⋊C4D411yescharacteristic
155C2×C4×Dic11—21no—
156C2×C4×Dic11C2311yescharacteristic
157C2×#4318—42no—
158C2×#4318C2314yes—
159C22×C11⋊C8C2311yescharacteristic
160C22×C11⋊C8C2311yescharacteristic
161C2×#4313—42no—
162C2×#4313C2314yes—
163C4⋊C4×D11—22no—
164C4⋊C4×D11C2314yes—
165#66941—22no—
166#66941C2314yes—
167#66936—28no—
168#66931—28no—
169C11×#103C2314yes—
170C11×#102C2314yes—
171C11×C22⋊C8C2314yes—
172#66899C2314yes—
173#66899C2314yes—
174#66896C2314yes—
175#66896C2314yes—
176#66896C2314yes—
177#66885C2314yes—
178#66885C2314yes—
179(C2×D11)⋊C8C2314yes—
180#66881C2314yes—
181#66881C2314yes—
182Dic11⋊C8C2314yes—
183C8×Dic11C2314yes—
184#66873C2314yes—
185#66872C2314yes—
186C2×#3332—111nomaximal, Sylow
187C24×C11—21no—
188C24×C11—21no—
189C24×C11C2×D411yescharacteristic
190C23×D11—21no—
191C23×D11C2×D411yescharacteristic
192C11×#41—28no—
193C11×#41—44no—
194C11×#41—48no—
195C2×Q8×C11—21no—
196C2×Q8×C11—22no—
197C2×Q8×C11#4114yescomplemented
198C2×Q8×C11C2412yes—
199C2×D4×C11—24no—
200C2×D4×C11—24no—
201C2×D4×C11—21no—
202C2×D4×C11—21no—
203C2×D4×C11—22no—
204C2×D4×C11—22no—
205C2×D4×C11—22no—
206C2×D4×C11—22no—
207C2×D4×C11—44no—
208C2×D4×C11—44no—
209C2×D4×C11C2412yes—
210C2×D4×C11C2412yes—
211C22×C4×C11—21no—
212C22×C4×C11—22no—
213C22×C4×C11—22no—
214C22×C4×C11—21no—
215C22×C4×C11—24no—
216C22×C4×C11—44no—
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D412yes—
219C22×C4×C11C2412yes—
220C22×C4×C11C2411yescharacteristic
221C2×C22⋊D11—24no—
222C2×C22⋊D11—24no—
223C2×C22⋊D11—24no—
224C2×C22⋊D11—24no—
225C2×C22⋊D11—24no—
226C2×C22⋊D11—24no—
227C2×C22⋊D11—44no—
228C2×C22⋊D11—44no—
229C2×C22⋊D11—82no—
230C2×C22⋊D11—82no—
231C2×C22⋊D11—82no—
232C2×C22⋊D11C2×D414yes—
233C22×Dic11—24no—
234C22×Dic11—21no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—24no—
238C22×Dic11—44no—
239C22×Dic11—44no—
240C22×Dic11C2×D411yescharacteristic
241C22×Dic11C2×D411yescharacteristic
242C22×Dic11C2×D411yescharacteristic
243#4343—28no—
244#4343—44no—
245#4343—48no—
246#4341—432no—
247C2×D44—24no—
248C2×D44—21no—
249C2×D44—22no—
250C2×D44—22no—
251C2×D44—44no—
252C2×D44C2412yes—
253C2×C4×D11—24no—
254C2×C4×D11—24no—
255C2×C4×D11—22no—
256C2×C4×D11—22no—
257C2×C4×D11—44no—
258C2×C4×D11—44no—
259C2×C4×D11C2×D412yes—
260C2×C4×D11C2412yes—
261C2×Dic22—24no—
262C2×Dic22—44no—
263C11×SD16—28no—
264C11×D8—44no—
265C2×C8×C11—22no—
266C2×C8×C11—22no—
267C2×C8×C11C2412yes—
268C2×C8×C11C2412yes—
269C11×C4⋊C4—21no—
270C11×C4⋊C4C2412yes—
271C11×C22⋊C4—24no—
272C22⋊Dic11—24no—
273C22⋊Dic11—24no—
274C22⋊Dic11—24no—
275C22⋊Dic11C2×D414yes—
276#4323—44no—
277(C2×D11)⋊C4—24no—
278(C2×D11)⋊C4C2×D414yes—
279C4⋊Dic11—24no—
280C4⋊Dic11—24no—
281C4⋊Dic11—21no—
282C4⋊Dic11—21no—
283C4⋊Dic11—21no—
284C4⋊Dic11C2412yes—
285C4⋊Dic11C2412yes—
286C4⋊Dic11C2412yes—
287Dic11⋊C4—24no—
288Dic11⋊C4—24no—
289Dic11⋊C4C2×D414yes—
290C4×Dic11—24no—
291C4×Dic11C2×D412yes—
292C4×Dic11C2412yes—
293#4318—44no—
294C2×C11⋊C8—22no—
295C2×C11⋊C8—22no—
296C2×C11⋊C8C2412yes—
297C2×C11⋊C8C2412yes—
298#4313—44no—
299C2×#550—111no—
300C2×#547—111no—
301#3332—1116no—
302C2×#486—111no—
303C2×#481—111no—
304C2×#481—111no—
305C2×#475—111no—
306C2×#469—111no—
307C2×#469—111no—
308C2×#459—111no—
309C2×#449—111no—
310C2×#449D1111yescharacteristic, complemented
311C2×C4×SD16—111no—
312C2×#436—111no—
313C2×#417—111no—
314C2×#417—111no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—42no—
321C23×C11—42no—
322C23×C11—42no—
323C23×C11—42no—
324C23×C11—42no—
325C23×C11—42no—
326C23×C11C22×D412yes—
327C23×C11C22×D411yescharacteristic
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—42no—
333C22×D11—42no—
334C22×D11—42no—
335C22×D11C22×D412yes—
336Q8×C11—24no—
337Q8×C11—22no—
338Q8×C11C2×#4114yescomplemented
339D4×C11—22no—
340D4×C11—22no—
341D4×C11—22no—
342D4×C11—22no—
343D4×C11—48no—
344D4×C11—48no—
345D4×C11—42no—
346D4×C11—42no—
347C2×C4×C11—24no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—24no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—48no—
355C2×C4×C11—42no—
356C2×C4×C11C22×D412yes—
357C2×C4×C11C22×D411yescharacteristic
358C2×C4×C11C2×#4112yes—
359C2×C4×C11H(5,𝔽2)12yes—
360C2×C4×C11C2511yescharacteristic
361C22⋊D11—28no—
362C22⋊D11—48no—
363C22⋊D11—48no—
364C22⋊D11—84no—
365C22⋊D11—84no—
366C22⋊D11—84no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—48no—
373C2×Dic11—42no—
374C2×Dic11—42no—
375C2×Dic11—42no—
376C2×Dic11—48no—
377C2×Dic11AGL(1,ℤ/8)14yes—
378C2×Dic11C22×D412yes—
379C2×Dic11C22×D412yes—
380C2×Dic11C22×D412yes—
381D44—22no—
382D44—22no—
383D44—48no—
384D44—42no—
385C4×D11—24no—
386C4×D11—22no—
387C4×D11—22no—
388C4×D11—48no—
389C4×D11—48no—
390Dic22—48no—
391C8×C11—22no—
392C8×C11—22no—
393C11⋊C8—22no—
394C11⋊C8—22no—
395C22×#41—111no—
396C22×#41—221no—
397C22×#41C2×D1111yescharacteristic
398C22×SD16C2×D1111yescharacteristic
399C22×D8—111no—
400C22×D8C2×D1111yescharacteristic
401C22×M16—111no—
402C22×M16—111no—
403#550—118no—
404#550—224no—
405#547—118no—
406#547—224no—
407C2×C4⋊Q8—111no—
408C2×#127—111no—
409C2×#127—221no—
410C2×#123—221no—
411C2×#123—221no—
412C2×C22⋊Q8—221no—
413C2×#121—111no—
414C2×#121—111no—
415C2×#121—111no—
416C2×#121—221no—
417C2×#121—221no—
418C2×#121C2×D1111yescharacteristic
419C2×C4×Q8—111no—
420C2×C4×D4—111no—
421C2×C4×D4—111no—
422C2×C4×D4—221no—
423C22×C4⋊C4—111no—
424C22×C4⋊C4—111no—
425#486—118no—
426#481—118no—
427#481—118no—
428#475—118no—
429#469—118no—
430#469—118no—
431#459—118no—
432#449—118no—
433#449C2×D1118yescomplemented
434C4×SD16—118no—
435#436—118no—
436C2×#106—111no—
437C2×#106—111no—
438C2×#106—111no—
439C2×C4⋊C8—111no—
440#417—118no—
441#417—118no—
442C2×#103—111no—
443C2×#103—111no—
444C2×#103C2×D1111yescharacteristic
445C2×#102—111no—
446C2×#102—111no—
447C2×#102—111no—
448C2×#102—111no—
449C2×#102—111no—
450C2×#102—111no—
451C2×#102C2×D1111yescharacteristic
452C2×C22⋊C8—111no—
453C2×C22⋊C8C2×D1111yescharacteristic
454C2×C4×C8—111no—
455C22×C11—22no—
456C22×C11—22no—
457C22×C11—22no—
458C22×C11—44no—
459C22×C11—42no—
460C22×C11—42no—
461C22×C11—42no—
462C22×C11—42no—
463C22×C11—42no—
464C22×C11—42no—
465C22×C11—84no—
466C22×C11—84no—
467C22×C11#54612yes—
468C22×C11C2×AGL(1,ℤ/8)12yes—
469C22×C11#57712yes—
470C22×C11C23×D411yescharacteristic
471C2×D11—22no—
472C2×D11—22no—
473C2×D11—22no—
474C2×D11—44no—
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—84no—
479C4×C11—22no—
480C4×C11—24no—
481C4×C11—42no—
482C4×C11#54612yes—
483C4×C11C22×#4111yescharacteristic
484C4×C11C2×H(5,𝔽2)11yescharacteristic
485Dic11—22no—
486Dic11—22no—
487Dic11—42no—
488Dic11—42no—
489Dic11—42no—
490Dic11C2×AGL(1,ℤ/8)14yes—
491C2×#41—22no—
492C2×#41—24no—
493C2×#41—42no—
494C2×#41—114no—
495C2×#41—222no—
496C2×#41—228no—
497C2×#41—224no—
498C2×#41—442no—
499C2×#41—448no—
500C2×#41C22×D1114yes—
501C22×Q8—221no—
502C22×Q8C22×D1111yescharacteristic
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—111no—
506C22×D4—111no—
507C22×D4—221no—
508C22×D4—221no—
509C22×D4—221no—
510C22×D4—221no—
511C22×D4—221no—
512C22×D4—221no—
513C22×D4C22×D1111yescharacteristic
514C22×D4C22×D1111yescharacteristic
515C23×C4—21no—
516C23×C4—111no—
517C23×C4—221no—
518C23×C4—221no—
519C23×C4—221no—
520C23×C4—221no—
521C23×C4C22×D1111yescharacteristic
522C2×SD16—24no—
523C2×SD16C22×D1114yes—
524C2×D8—42no—
525C2×D8—114no—
526C2×D8—442no—
527C2×D8C22×D1114yes—
528C2×M16—114no—
529C2×M16—114no—
530C2×M16—442no—
531C2×M16—442no—
532C22×C8—111no—
533C22×C8—111no—
534C22×C8C22×D1111yescharacteristic
535C22×C8C22×D1111yescharacteristic
536C4⋊Q8—114no—
537C4⋊Q8—222no—
538#127—114no—
539#127—222no—
540#127—228no—
541#123—228no—
542#123—228no—
543C22⋊Q8—228no—
544#121—22no—
545#121—114no—
546#121—114no—
547#121—114no—
548#121—228no—
549#121—228no—
550#121—222no—
551#121—222no—
552#121—222no—
553#121C22×D1114yes—
554C4×Q8—114no—
555C4×Q8—222no—
556C4×D4—114no—
557C4×D4—114no—
558C4×D4—114no—
559C4×D4—222no—
560C4×D4—228no—
561C2×C4⋊C4—111no—
562C2×C4⋊C4—111no—
563C2×C4⋊C4—111no—
564C2×C4⋊C4—114no—
565C2×C4⋊C4—111no—
566C2×C4⋊C4—114no—
567C2×C4⋊C4—222no—
568C2×C4⋊C4—221no—
569C2×C4⋊C4—221no—
570C2×C4⋊C4—221no—
571C2×C4⋊C4—221no—
572C2×C4⋊C4—222no—
573C2×C4⋊C4C22×D1111yescharacteristic
574C2×C22⋊C4—21no—
575C2×C22⋊C4—111no—
576C2×C22⋊C4—111no—
577C2×C22⋊C4—221no—
578C2×C22⋊C4—221no—
579C2×C22⋊C4—221no—
580C2×C22⋊C4—221no—
581C2×C42—111no—
582C2×C42—221no—
583#106—114no—
584#106—114no—
585#106—114no—
586C4⋊C8—114no—
587#103—114no—
588#103—114no—
589#103C22×D1114yes—
590#102—114no—
591#102—114no—
592#102—114no—
593#102—114no—
594#102—114no—
595#102—114no—
596#102C22×D1114yes—
597C22⋊C8—114no—
598C22⋊C8C22×D1114yes—
599C4×C8—114no—
600C2×C11—42no—
601C2×C11—82no—
602C2×C11—82no—
603C2×C11#333214yescomplemented
604C2×C11C2×#54611yescharacteristic
605C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
606C2×C11C2×#57711yescharacteristic
607D11—42no—
608D11—82no—
609C24—21no—
610C24—21no—
611C24—111no—
612C24—221no—
613C24D4×D1111yescharacteristic
614#41—28no—
615#41—44no—
616#41—48no—
617#41—228no—
618#41—444no—
619#41—448no—
620#41—4432no—
621C2×Q8—21no—
622C2×Q8—22no—
623C2×Q8—224no—
624C2×Q8—444no—
625C2×Q8#434114yescomplemented
626C2×Q8C23×D1112yes—
627C2×D4—24no—
628C2×D4—24no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—22no—
632C2×D4—22no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—44no—
636C2×D4—44no—
637C2×D4—114no—
638C2×D4—112no—
639C2×D4—224no—
640C2×D4—224no—
641C2×D4—224no—
642C2×D4—224no—
643C2×D4—224no—
644C2×D4—224no—
645C2×D4—224no—
646C2×D4—221no—
647C2×D4—222no—
648C2×D4—222no—
649C2×D4—444no—
650C2×D4—444no—
651C2×D4—444no—
652C2×D4—882no—
653C2×D4—882no—
654C2×D4—882no—
655C2×D4C23×D1112yes—
656C2×D4C23×D1112yes—
657C22×C4—21no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—21no—
661C22×C4—24no—
662C22×C4—44no—
663C22×C4—111no—
664C22×C4—111no—
665C22×C4—111no—
666C22×C4—112no—
667C22×C4—112no—
668C22×C4—224no—
669C22×C4—224no—
670C22×C4—224no—
671C22×C4—222no—
672C22×C4—222no—
673C22×C4—224no—
674C22×C4—221no—
675C22×C4—221no—
676C22×C4—221no—
677C22×C4—444no—
678C22×C4—444no—
679C22×C4—444no—
680C22×C4—444no—
681C22×C4D4×D1112yes—
682C22×C4D4×D1111yescharacteristic
683C22×C4C23×D1112yes—
684C22×C4C23×D1111yescharacteristic
685SD16—28no—
686D8—44no—
687D8—444no—
688M16—444no—
689M16—444no—
690C2×C8—22no—
691C2×C8—22no—
692C2×C8—112no—
693C2×C8—112no—
694C2×C8—222no—
695C2×C8—222no—
696C2×C8C23×D1112yes—
697C2×C8C23×D1112yes—
698C4⋊C4—21no—
699C4⋊C4—114no—
700C4⋊C4—112no—
701C4⋊C4—112no—
702C4⋊C4—112no—
703C4⋊C4—224no—
704C4⋊C4—224no—
705C4⋊C4—224no—
706C4⋊C4—221no—
707C4⋊C4—221no—
708C4⋊C4—224no—
709C4⋊C4—221no—
710C4⋊C4C23×D1112yes—
711C22⋊C4—24no—
712C22⋊C4—114no—
713C22⋊C4—114no—
714C22⋊C4—224no—
715C22⋊C4—224no—
716C22⋊C4—224no—
717C22⋊C4—224no—
718C42—112no—
719C42—112no—
720C42—224no—
721C11C2×#333211yescharacteristic, complemented, Sylow
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—112no—
734C23—222no—
735C23—222no—
736C23—222no—
737C23—222no—
738C23—442no—
739C23—442no—
740C23—442no—
741C23C2×D4×D1112yes—
742C23C2×D4×D1111yescharacteristic
743Q8—24no—
744Q8—22no—
745Q8—448no—
746Q8C2×#434114yescomplemented
747D4—22no—
748D4—22no—
749D4—22no—
750D4—22no—
751D4—48no—
752D4—48no—
753D4—42no—
754D4—42no—
755D4—228no—
756D4—222no—
757D4—222no—
758D4—448no—
759D4—448no—
760D4—448no—
761D4—442no—
762D4—884no—
763D4—884no—
764D4—884no—
765C2×C4—22no—
766C2×C4—24no—
767C2×C4—22no—
768C2×C4—24no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—48no—
773C2×C4—42no—
774C2×C4—114no—
775C2×C4—112no—
776C2×C4—112no—
777C2×C4—112no—
778C2×C4—222no—
779C2×C4—222no—
780C2×C4—224no—
781C2×C4—222no—
782C2×C4—222no—
783C2×C4—222no—
784C2×C4—222no—
785C2×C4—222no—
786C2×C4—448no—
787C2×C4—448no—
788C2×C4—448no—
789C2×C4—448no—
790C2×C4—442no—
791C2×C4—442no—
792C2×C4—442no—
793C2×C4C2×D4×D1112yes—
794C2×C4C2×D4×D1111yescharacteristic
795C2×C4C2×#434112yes—
796C2×C4#6703712yes—
797C2×C4C24×D1111yescharacteristic
798C8—22no—
799C8—22no—
800C8—222no—
801C8—222no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—44no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—84no—
813C22—84no—
814C22—222no—
815C22—222no—
816C22—222no—
817C22—444no—
818C22—442no—
819C22—442no—
820C22—442no—
821C22—884no—
822C22#1062312212yes—
823C22#1062330112yes—
824C22D11×AGL(1,ℤ/8)12yes—
825C22C22×D4×D1111yescharacteristic
826C4—22no—
827C4—24no—
828C4—42no—
829C4—114no—
830C4—222no—
831C4—222no—
832C4—442no—
833C4—442no—
834C4—442no—
835C4#1062312212yes—
836C4C22×#434111yescharacteristic
837C4C2×#6703711yescharacteristic
838C2—42no—
839C2—82no—
840C2—82no—
841C2—442no—
842C2—882no—
843C2#1308093614yesdirect product factor
844C2C2×#1062312211yescharacteristic
845C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
846C2C2×#1062330111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#449C2
socleC23×C11C22×D4
hypercenterC2×#449D11
hypocenterC11C2×#3332
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#10623365C2semidirect
2. C2×#10623142C2semidirect
3. #13080936C2direct (N × H)
4. C2×#10622373C2semidirect
5. C2×#10622348C2semidirect
6. C2×#10622390C2semidirect
7. C2×#10622404C2semidirect
8. C2×#10622652C2semidirect
9. C2×#10622772C2semidirect
10. C2×#10622763C2semidirect
11. C2×#10622785C2semidirect
12. C2×SD16×Dic11C2semidirect
13. C2×#10622342C2semidirect
14. C2×#10622845C2semidirect
15. C2×#10622416C2semidirect
16. C2×C11×#449C2semidirect
24. #10623365C22semidirect
42. #10623142C22semidirect
47. C11×#449C22semidirect
51. #10622845C22semidirect
57. #10622785C22semidirect
58. SD16×Dic11C22semidirect
59. #10622772C22semidirect
60. #10622763C22semidirect
68. #10622652C22semidirect
71. #10622416C22semidirect
72. #10622404C22semidirect
73. #10622390C22semidirect
74. #10622373C22semidirect
75. #10622348C22semidirect
76. #10622342C22semidirect
197. C2×Q8×C11#41semidirect
310. C2×#449D11semidirect
338. Q8×C11C2×#41semidirect
433. #449C2×D11semidirect
603. C2×C11#3332semidirect
625. C2×Q8#4341semidirect
721. C11C2×#3332semidirect
746. Q8C2×#4341semidirect
843. C2#13080936direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233652
C2×#106231422
#130809362
C2×#106223732
C2×#106223482
C2×#106223902
C2×#106224042
C2×#106226522
C2×#106227722
C2×#106227632
C2×#106227852
C2×SD16×Dic112
C2×#106223422
C2×#106228452
C2×#106224162
C2×C11×#4492
C2×#333211