Finite Group Databasebeta

← C2×#13080938 #15630701

Subgroups — C2×#13080938 #15630701

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×#10623130C211yesmaximal, characteristic, complemented
2C2×#10623142C211yesmaximal, characteristic, complemented
3#13080938C2116yesmaximal, direct product factor
4C2×#10622373C211yesmaximal, characteristic, complemented
5C2×#10622476C211yesmaximal, characteristic, complemented
6C2×#10622647C211yesmaximal, characteristic, complemented
7C2×#10622467C211yesmaximal, characteristic, complemented
8C2×#10622395C211yesmaximal, characteristic, complemented
9C2×#10622763C211yesmaximal, characteristic, complemented
10C2×#10622650C211yesmaximal, characteristic, complemented
11C2×#10622771C211yesmaximal, characteristic, complemented
12C2×#10622371C211yesmaximal, characteristic, complemented
13C2×#10622741C211yesmaximal, characteristic, complemented
14C2×#10622746C211yesmaximal, characteristic, complemented
15C2×#10622384C211yesmaximal, characteristic, complemented
16C2×C11×#469C211yesmaximal, characteristic, complemented
17C22×#4341—21no—
18C22×#4341C2211yescharacteristic
19C22×#4339C2211yescharacteristic
20C22×C11×D8C2211yescharacteristic
21C22×C11×M16C2211yescharacteristic
22C2×C11×#121C2211yescharacteristic
23C2×C11×#121C2211yescharacteristic
24C2×#66993—21no—
25C2×#66993C2211yescharacteristic
26C2×#66992—21no—
27C2×#66991C2211yescharacteristic
28C2×#66988—21no—
29C2×D4×Dic11C2211yescharacteristic
30C22×#4324C2211yescharacteristic
31C22×#4323C2211yescharacteristic
32C2×C4×C22⋊D11C2211yescharacteristic
33C22×C4⋊Dic11C2211yescharacteristic
34C22×#4313C2211yescharacteristic
35#10623142—24no—
36#10623142C2218yescomplemented
37#10623130—24no—
38#10623130C2218yescomplemented
39C2×#66948C2211yescharacteristic
40C2×C4⋊C4×D11C2211yescharacteristic
41C2×#66941C2211yescharacteristic
42C2×#66940C2211yescharacteristic
43C2×#66937—21no—
44C2×#66936—21no—
45C2×(C22⋊D11)⋊C4—21no—
46C2×#66931—21no—
47C11×#469C2218yescomplemented
48C2×C11×#106C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×#66896C2211yescharacteristic
52C2×#66896C2211yescharacteristic
53C2×C22⋊(C11⋊C8)C2211yescharacteristic
54#10622771C2218yescomplemented
55#10622763C2218yescomplemented
56#10622746C2218yescomplemented
57#10622741C2218yescomplemented
58C2×#66885C2211yescharacteristic
59C2×#66885C2211yescharacteristic
60C2×(C2×D11)⋊C8C2211yescharacteristic
61C2×#66880C2211yescharacteristic
62C2×#66880C2211yescharacteristic
63C2×Dic11⋊C8C2211yescharacteristic
64C2×C8×Dic11C2211yescharacteristic
65#10622650C2218yescomplemented
66#10622647C2218yescomplemented
67C2×#66874C2211yescharacteristic
68C2×#66873C2211yescharacteristic
69C2×#66872C2211yescharacteristic
70C2×#66872C2211yescharacteristic
71#10622476C2218yescomplemented
72#10622467C2218yescomplemented
73#10622395C2218yescomplemented
74#10622384C2218yescomplemented
75#10622373C2218yescomplemented
76#10622371C2218yescomplemented
77C22×D4×C11—21no—
78C22×D4×C11—21no—
79C22×D4×C11C2311yescharacteristic
80C22×D4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C22×C22⋊D11—21no—
87C22×C22⋊D11D411yescharacteristic
88C23×Dic11—21no—
89C23×Dic11—21no—
90C23×Dic11—21no—
91C2×#4341—28no—
92C2×#4341—22no—
93C2×#4341—24no—
94C2×#4341—42no—
95C2×#4341—48no—
96C2×#4341C2314yes—
97C2×#4339—22no—
98C2×#4339—24no—
99C2×#4339—42no—
100C2×#4339C2314yes—
101C22×D44—21no—
102C22×D44C2311yescharacteristic
103C22×C4×D11—21no—
104C22×C4×D11—21no—
105C22×C4×D11C2311yescharacteristic
106C22×Dic22—21no—
107C22×Dic22C2311yescharacteristic
108C2×C11×D8—42no—
109C2×C11×D8C2314yes—
110C2×C11×M16—42no—
111C2×C11×M16C2314yes—
112C22×C8×C11C2311yescharacteristic
113C22×C8×C11C2311yescharacteristic
114C11×#121—22no—
115C11×#121—22no—
116C11×#121C2314yes—
117C11×#121C2314yes—
118C2×C11×C4⋊C4C2311yescharacteristic
119C2×C11×C4⋊C4C2311yescharacteristic
120C2×C11×C22⋊C4—21no—
121C2×C11×C22⋊C4—21no—
122C2×C22⋊Dic11—21no—
123C2×C22⋊Dic11—21no—
124C2×C22⋊Dic11D411yescharacteristic
125#66993—28no—
126#66993—22no—
127#66993C2314yes—
128#66992—28no—
129#66991—22no—
130#66991C2314yes—
131#66988—28no—
132D4×Dic11—22no—
133D4×Dic11C2314yes—
134C2×#4324—24no—
135C2×#4324C2314yes—
136C2×#4323—42no—
137C2×#4323C2314yes—
138C4×C22⋊D11D414yes—
139C4×C22⋊D11C2314yes—
140C2×(C2×D11)⋊C4—21no—
141C2×(C2×D11)⋊C4D411yescharacteristic
142C2×C4⋊Dic11—21no—
143C2×C4⋊Dic11—22no—
144C2×C4⋊Dic11C2311yescharacteristic
145C2×C4⋊Dic11C2311yescharacteristic
146C2×C4⋊Dic11C2314yes—
147C2×Dic11⋊C4—21no—
148C2×Dic11⋊C4—21no—
149C2×Dic11⋊C4—21no—
150C2×Dic11⋊C4D411yescharacteristic
151C2×C4×Dic11—21no—
152C2×C4×Dic11C2311yescharacteristic
153C22×C11⋊C8C2311yescharacteristic
154C22×C11⋊C8C2311yescharacteristic
155C2×#4313—42no—
156C2×#4313C2314yes—
157#66948—22no—
158#66948C2314yes—
159C4⋊C4×D11—22no—
160C4⋊C4×D11C2314yes—
161#66941—22no—
162#66941C2314yes—
163#66940—22no—
164#66940C2314yes—
165#66937—28no—
166#66936—28no—
167(C22⋊D11)⋊C4—28no—
168#66931—28no—
169C11×#106C2314yes—
170C11×#102C2314yes—
171C11×#102C2314yes—
172#66896C2314yes—
173#66896C2314yes—
174C22⋊(C11⋊C8)C2314yes—
175#66885C2314yes—
176#66885C2314yes—
177(C2×D11)⋊C8C2314yes—
178#66880C2314yes—
179#66880C2314yes—
180Dic11⋊C8C2314yes—
181C8×Dic11C2314yes—
182#66874C2314yes—
183#66873C2314yes—
184#66872C2314yes—
185#66872C2314yes—
186C2×#3332—111nomaximal, Sylow
187C24×C11—21no—
188C24×C11—21no—
189C24×C11C2×D411yescharacteristic
190C23×D11—21no—
191C23×D11C2×D411yescharacteristic
192C2×D4×C11—24no—
193C2×D4×C11—24no—
194C2×D4×C11—21no—
195C2×D4×C11—21no—
196C2×D4×C11—22no—
197C2×D4×C11—22no—
198C2×D4×C11—22no—
199C2×D4×C11—22no—
200C2×D4×C11—44no—
201C2×D4×C11—82no—
202C2×D4×C11C2412yes—
203C2×D4×C11C2412yes—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D412yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2411yescharacteristic
212C2×C22⋊D11—24no—
213C2×C22⋊D11—24no—
214C2×C22⋊D11—24no—
215C2×C22⋊D11—24no—
216C2×C22⋊D11—24no—
217C2×C22⋊D11—24no—
218C2×C22⋊D11—44no—
219C2×C22⋊D11—44no—
220C2×C22⋊D11—44no—
221C2×C22⋊D11—44no—
222C2×C22⋊D11—82no—
223C2×C22⋊D11C2×D414yes—
224C22×Dic11—24no—
225C22×Dic11—24no—
226C22×Dic11—21no—
227C22×Dic11—21no—
228C22×Dic11—21no—
229C22×Dic11—24no—
230C22×Dic11—44no—
231C22×Dic11—44no—
232C22×Dic11—44no—
233C22×Dic11C2×D411yescharacteristic
234C22×Dic11C2×D411yescharacteristic
235C22×Dic11C2×D411yescharacteristic
236#4341—28no—
237#4341—44no—
238#4341—48no—
239#4341—432no—
240#4339—28no—
241#4339—44no—
242#4339—48no—
243C2×D44—24no—
244C2×D44—21no—
245C2×D44—22no—
246C2×D44—22no—
247C2×D44—82no—
248C2×D44C2412yes—
249C2×C4×D11—24no—
250C2×C4×D11—24no—
251C2×C4×D11—22no—
252C2×C4×D11—22no—
253C2×C4×D11—44no—
254C2×C4×D11—44no—
255C2×C4×D11C2×D412yes—
256C2×C4×D11C2412yes—
257C2×Dic22—24no—
258C2×Dic22—21no—
259C2×Dic22—22no—
260C2×Dic22—44no—
261C2×Dic22#4114yescomplemented
262C2×Dic22C2412yes—
263C11×D8—44no—
264C11×M16—44no—
265C2×C8×C11—22no—
266C2×C8×C11—22no—
267C2×C8×C11C2412yes—
268C2×C8×C11C2412yes—
269C11×C4⋊C4—21no—
270C11×C4⋊C4—21no—
271C11×C4⋊C4C2412yes—
272C11×C4⋊C4C2412yes—
273C11×C22⋊C4—24no—
274C11×C22⋊C4—24no—
275C22⋊Dic11—24no—
276C22⋊Dic11—24no—
277C22⋊Dic11C2×D414yes—
278#4324—28no—
279#4323—44no—
280(C2×D11)⋊C4—24no—
281(C2×D11)⋊C4C2×D414yes—
282C4⋊Dic11—24no—
283C4⋊Dic11—21no—
284C4⋊Dic11—21no—
285C4⋊Dic11C2412yes—
286C4⋊Dic11C2412yes—
287Dic11⋊C4—24no—
288Dic11⋊C4—24no—
289Dic11⋊C4—24no—
290Dic11⋊C4C2×D414yes—
291C4×Dic11—24no—
292C4×Dic11C2×D412yes—
293C4×Dic11C2412yes—
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×#469D1111yescharacteristic, complemented
308C2×#459—111no—
309C2×#449—111no—
310C2×#449—111no—
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—
336D4×C11—22no—
337D4×C11—22no—
338D4×C11—22no—
339D4×C11—22no—
340D4×C11—48no—
341D4×C11—42no—
342D4×C11—42no—
343D4×C11—84no—
344C2×C4×C11—22no—
345C2×C4×C11—24no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—42no—
351C2×C4×C11—42no—
352C2×C4×C11C22×D412yes—
353C2×C4×C11C22×D411yescharacteristic
354C2×C4×C11C2×#4112yes—
355C2×C4×C11H(5,𝔽2)12yes—
356C2×C4×C11C2511yescharacteristic
357C22⋊D11—28no—
358C22⋊D11—48no—
359C22⋊D11—48no—
360C22⋊D11—48no—
361C22⋊D11—48no—
362C22⋊D11—84no—
363C2×Dic11—24no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—48no—
370C2×Dic11—48no—
371C2×Dic11—42no—
372C2×Dic11—42no—
373C2×Dic11—48no—
374C2×Dic11AGL(1,ℤ/8)14yes—
375C2×Dic11C22×D412yes—
376C2×Dic11C22×D412yes—
377C2×Dic11C22×D412yes—
378D44—22no—
379D44—22no—
380D44—42no—
381D44—84no—
382C4×D11—24no—
383C4×D11—22no—
384C4×D11—22no—
385C4×D11—48no—
386C4×D11—48no—
387Dic22—24no—
388Dic22—22no—
389Dic22—48no—
390Dic22C2×#4114yescomplemented
391C8×C11—22no—
392C8×C11—22no—
393C11⋊C8—22no—
394C11⋊C8—22no—
395C22×#41—111no—
396C22×#41—111no—
397C22×#41—221no—
398C22×SD16—111no—
399C22×D8—111no—
400C22×D8C2×D1111yescharacteristic
401C22×M16—111no—
402C22×M16C2×D1111yescharacteristic
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—221no—
416C2×#121—221no—
417C2×#121C2×D1111yescharacteristic
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#469C2×D1118yescomplemented
431#459—118no—
432#449—118no—
433#449—118no—
434C4×SD16—118no—
435#436—118no—
436C2×#106—111no—
437C2×#106—111no—
438C2×#106C2×D1111yescharacteristic
439C2×C4⋊C8—111no—
440#417—118no—
441#417—118no—
442C2×#103—111no—
443C2×#103—111no—
444C2×#103—111no—
445C2×#102—111no—
446C2×#102—111no—
447C2×#102—111no—
448C2×#102—111no—
449C2×#102—111no—
450C2×#102C2×D1111yescharacteristic
451C2×#102C2×D1111yescharacteristic
452C2×C22⋊C8—111no—
453C2×C22⋊C8—111no—
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—42no—
481C4×C11—42no—
482C4×C11#54612yes—
483C4×C11C22×#4111yescharacteristic
484C4×C11C2×H(5,𝔽2)11yescharacteristic
485Dic11—24no—
486Dic11—22no—
487Dic11—22no—
488Dic11—42no—
489Dic11—42no—
490Dic11C2×AGL(1,ℤ/8)14yes—
491C2×#41—114no—
492C2×#41—114no—
493C2×#41—224no—
494C2×#41—222no—
495C2×#41—228no—
496C2×#41—222no—
497C2×#41—224no—
498C2×#41—442no—
499C2×#41—442no—
500C2×#41—448no—
501C22×Q8—111no—
502C22×Q8—221no—
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—111no—
516C23×C4—221no—
517C23×C4—221no—
518C23×C4—221no—
519C23×C4—221no—
520C23×C4—221no—
521C23×C4C22×D1111yescharacteristic
522C2×SD16—114no—
523C2×SD16—224no—
524C2×D8—42no—
525C2×D8—114no—
526C2×D8—442no—
527C2×D8C22×D1114yes—
528C2×M16—42no—
529C2×M16—114no—
530C2×M16—442no—
531C2×M16C22×D1114yes—
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—22no—
546#121—114no—
547#121—114no—
548#121—228no—
549#121—228no—
550#121—222no—
551#121—222no—
552#121C22×D1114yes—
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—114no—
566C2×C4⋊C4—222no—
567C2×C4⋊C4—221no—
568C2×C4⋊C4—221no—
569C2×C4⋊C4—221no—
570C2×C4⋊C4—221no—
571C2×C4⋊C4—222no—
572C2×C4⋊C4C22×D1111yescharacteristic
573C2×C4⋊C4C22×D1111yescharacteristic
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—111no—
577C2×C22⋊C4—111no—
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#106C22×D1114yes—
586C4⋊C8—114no—
587#103—114no—
588#103—114no—
589#103—114no—
590#102—114no—
591#102—114no—
592#102—114no—
593#102—114no—
594#102—114no—
595#102C22×D1114yes—
596#102C22×D1114yes—
597C22⋊C8—114no—
598C22⋊C8—114no—
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—228no—
615#41—228no—
616#41—444no—
617#41—448no—
618#41—444no—
619#41—448no—
620#41—4432no—
621C2×Q8—114no—
622C2×Q8—112no—
623C2×Q8—224no—
624C2×Q8—221no—
625C2×Q8—222no—
626C2×Q8—444no—
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—82no—
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—444no—
653C2×D4—882no—
654C2×D4—882no—
655C2×D4C23×D1112yes—
656C2×D4C23×D1112yes—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—111no—
662C22×C4—111no—
663C22×C4—111no—
664C22×C4—112no—
665C22×C4—112no—
666C22×C4—224no—
667C22×C4—224no—
668C22×C4—224no—
669C22×C4—221no—
670C22×C4—222no—
671C22×C4—222no—
672C22×C4—224no—
673C22×C4—221no—
674C22×C4—221no—
675C22×C4—224no—
676C22×C4—444no—
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—228no—
686D8—44no—
687D8—444no—
688M16—44no—
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—21no—
700C4⋊C4—114no—
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⋊C4C23×D1112yes—
710C4⋊C4C23×D1112yes—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—114no—
714C22⋊C4—114no—
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—114no—
744Q8—224no—
745Q8—222no—
746Q8—448no—
747D4—22no—
748D4—22no—
749D4—22no—
750D4—22no—
751D4—48no—
752D4—42no—
753D4—42no—
754D4—84no—
755D4—228no—
756D4—222no—
757D4—222no—
758D4—448no—
759D4—448no—
760D4—448no—
761D4—448no—
762D4—442no—
763D4—884no—
764D4—884no—
765C2×C4—22no—
766C2×C4—24no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—114no—
774C2×C4—112no—
775C2×C4—112no—
776C2×C4—112no—
777C2×C4—222no—
778C2×C4—222no—
779C2×C4—224no—
780C2×C4—222no—
781C2×C4—224no—
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—448no—
791C2×C4—442no—
792C2×C4—442no—
793C2×C4C2×D4×D1112yes—
794C2×C4C2×D4×D1111yescharacteristic
795C2×C4#6703712yes—
796C2×C4#41×D1112yes—
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#1062314112yes—
823C22D11×AGL(1,ℤ/8)12yes—
824C22#1062330612yes—
825C22C22×D4×D1111yescharacteristic
826C4—22no—
827C4—42no—
828C4—42no—
829C4—114no—
830C4—222no—
831C4—224no—
832C4—222no—
833C4—442no—
834C4—442no—
835C4#1062314112yes—
836C4C2×#6703711yescharacteristic
837C4C2×#41×D1111yescharacteristic
838C2—42no—
839C2—82no—
840C2—82no—
841C2—442no—
842C2—882no—
843C2#1308093814yesdirect product factor
844C2C2×#1062314111yescharacteristic
845C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
846C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#469C2
socleC23×C11C22×D4
hypercenterC2×#469D11
hypocenterC11C2×#3332
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#469

Complements

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

NH ≅ G/Ntype
1. C2×#10623130C2semidirect
2. C2×#10623142C2semidirect
3. #13080938C2direct (N × H)
4. C2×#10622373C2semidirect
5. C2×#10622476C2semidirect
6. C2×#10622647C2semidirect
7. C2×#10622467C2semidirect
8. C2×#10622395C2semidirect
9. C2×#10622763C2semidirect
10. C2×#10622650C2semidirect
11. C2×#10622771C2semidirect
12. C2×#10622371C2semidirect
13. C2×#10622741C2semidirect
14. C2×#10622746C2semidirect
15. C2×#10622384C2semidirect
16. C2×C11×#469C2semidirect
36. #10623142C22semidirect
38. #10623130C22semidirect
47. C11×#469C22semidirect
54. #10622771C22semidirect
55. #10622763C22semidirect
56. #10622746C22semidirect
57. #10622741C22semidirect
65. #10622650C22semidirect
66. #10622647C22semidirect
71. #10622476C22semidirect
72. #10622467C22semidirect
73. #10622395C22semidirect
74. #10622384C22semidirect
75. #10622373C22semidirect
76. #10622371C22semidirect
261. C2×Dic22#41semidirect
307. C2×#469D11semidirect
390. Dic22C2×#41semidirect
430. #469C2×D11semidirect
603. C2×C11#3332semidirect
721. C11C2×#3332semidirect
843. C2#13080938direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231302
C2×#106231422
#130809382
C2×#106223732
C2×#106224762
C2×#106226472
C2×#106224672
C2×#106223952
C2×#106227632
C2×#106226502
C2×#106227712
C2×#106223712
C2×#106227412
C2×#106227462
C2×#106223842
C2×C11×#4692
C2×#333211