Finite Group Databasebeta

← C2×#13080939 #15630702

Subgroups — C2×#13080939 #15630702

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×#10623038C211yesmaximal, characteristic, complemented
3#13080939C2116yesmaximal, direct product factor
4C2×#10622373C211yesmaximal, characteristic, complemented
5C2×#10622581C211yesmaximal, characteristic, complemented
6C2×#10622390C211yesmaximal, characteristic, complemented
7C2×#10622404C211yesmaximal, characteristic, complemented
8C2×#10622748C211yesmaximal, characteristic, complemented
9C2×#10622395C211yesmaximal, characteristic, complemented
10C2×#10622399C211yesmaximal, characteristic, complemented
11C2×#10622424C211yesmaximal, characteristic, complemented
12C2×#10622851C211yesmaximal, characteristic, complemented
13C2×#10622401C211yesmaximal, characteristic, complemented
14C2×#10622741C211yesmaximal, characteristic, complemented
15C2×#10622416C211yesmaximal, characteristic, complemented
16C2×C11×#417C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C22×#4343C2211yescharacteristic
19C22×#4339—21no—
20C22×C11×M16C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22#10623365—24no—
23#10623365C2218yescomplemented
24C2×Q8×Dic11C2211yescharacteristic
25C22×#4325C2211yescharacteristic
26C2×#66993—21no—
27C2×#66993C2211yescharacteristic
28C2×#66991—21no—
29C2×#66991C2211yescharacteristic
30C22×#4323C2211yescharacteristic
31C2×#66983—21no—
32C2×#66983C2211yescharacteristic
33C2×#66983C2211yescharacteristic
34C2×#66982—21no—
35C2×C4×C22⋊D11—21no—
36C2×C4×C22⋊D11C2211yescharacteristic
37C22×D88C2211yescharacteristic
38C22×#4313C2211yescharacteristic
39C2×#66949—21no—
40#10623038—24no—
41#10623038C2218yescomplemented
42C2×#66948C2211yescharacteristic
43C2×#66947—21no—
44C2×#66946C2211yescharacteristic
45C2×C4⋊C4×D11C2211yescharacteristic
46C2×#66941C2211yescharacteristic
47C11×#417C2218yescomplemented
48C2×C11×#103C2211yescharacteristic
49C2×C11×#103C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52#10622851C2218yescomplemented
53C2×#66899C2211yescharacteristic
54C2×#66896C2211yescharacteristic
55C2×C22⋊(C11⋊C8)C2211yescharacteristic
56#10622748C2218yescomplemented
57#10622741C2218yescomplemented
58C2×#66885C2211yescharacteristic
59C2×#66885C2211yescharacteristic
60C2×(C2×D11)⋊C8C2211yescharacteristic
61C2×#66881C2211yescharacteristic
62C2×Dic11⋊C8C2211yescharacteristic
63C2×C8×Dic11C2211yescharacteristic
64#10622581C2218yescomplemented
65C2×#66873C2211yescharacteristic
66C2×#66873C2211yescharacteristic
67C2×#66872C2211yescharacteristic
68C2×#66872C2211yescharacteristic
69#10622424C2218yescomplemented
70#10622416C2218yescomplemented
71#10622404C2218yescomplemented
72#10622401C2218yescomplemented
73#10622399C2218yescomplemented
74#10622395C2218yescomplemented
75#10622390C2218yescomplemented
76#10622373C2218yescomplemented
77C2×C11×#41—22no—
78C2×C11×#41—24no—
79C2×C11×#41—42no—
80C2×C11×#41C2314yes—
81C22×Q8×C11C2311yescharacteristic
82C22×D4×C11—21no—
83C22×D4×C11C2311yescharacteristic
84C23×C4×C11—21no—
85C23×C4×C11—21no—
86C23×C4×C11C2311yescharacteristic
87C22×C22⋊D11—21no—
88C22×C22⋊D11—21no—
89C22×C22⋊D11—21no—
90C22×C22⋊D11—21no—
91C22×C22⋊D11—21no—
92C22×C22⋊D11D411yescharacteristic
93C2×#4343—22no—
94C2×#4343—24no—
95C2×#4343—42no—
96C2×#4343C2314yes—
97C2×#4339—28no—
98C2×#4339—48no—
99C22×D44—21no—
100C22×D44—21no—
101C22×D44C2311yescharacteristic
102C22×D44C2311yescharacteristic
103C22×C4×D11—21no—
104C22×C4×D11—21no—
105C22×C4×D11—21no—
106C22×C4×D11C2311yescharacteristic
107C22×Dic22—21no—
108C2×C11×M16—42no—
109C2×C11×M16C2314yes—
110C22×C8×C11C2311yescharacteristic
111C22×C8×C11C2311yescharacteristic
112C2×C11×C4⋊C4—21no—
113C2×C11×C4⋊C4—22no—
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C4⋊C4C2314yes—
117C2×C22⋊Dic11—21no—
118C2×C22⋊Dic11D411yescharacteristic
119Q8×Dic11—22no—
120Q8×Dic11C2314yes—
121C2×#4325—24no—
122C2×#4325C2314yes—
123#66993—28no—
124#66993—22no—
125#66993C2314yes—
126#66991—22no—
127#66991—28no—
128#66991C2314yes—
129C2×#4323—42no—
130C2×#4323C2314yes—
131#66983—22no—
132#66983—22no—
133#66983—28no—
134#66983C2314yes—
135#66983C2314yes—
136#66982—28no—
137C4×C22⋊D11—28no—
138C4×C22⋊D11D414yes—
139C4×C22⋊D11C2314yes—
140C2×(C2×D11)⋊C4—21no—
141C2×(C2×D11)⋊C4—21no—
142C2×(C2×D11)⋊C4—21no—
143C2×(C2×D11)⋊C4—21no—
144C2×(C2×D11)⋊C4D411yescharacteristic
145C2×C4⋊Dic11—21no—
146C2×C4⋊Dic11C2311yescharacteristic
147C2×C4⋊Dic11C2311yescharacteristic
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×D88—42no—
156C2×D88C2314yes—
157C2×#4313—42no—
158C2×#4313C2314yes—
159#66949—28no—
160#66948—22no—
161#66948C2314yes—
162#66947—28no—
163#66946—22no—
164#66946C2314yes—
165C4⋊C4×D11—22no—
166C4⋊C4×D11C2314yes—
167#66941—22no—
168#66941C2314yes—
169C11×#103C2314yes—
170C11×#103C2314yes—
171C11×#102C2314yes—
172C11×#102C2314yes—
173#66899C2314yes—
174#66896C2314yes—
175C22⋊(C11⋊C8)C2314yes—
176#66885C2314yes—
177#66885C2314yes—
178(C2×D11)⋊C8C2314yes—
179#66881C2314yes—
180Dic11⋊C8C2314yes—
181C8×Dic11C2314yes—
182#66873C2314yes—
183#66873C2314yes—
184#66872C2314yes—
185#66872C2314yes—
186C2×#3332—111nomaximal, Sylow
187C24×C11—21no—
188C24×C11C2×D411yescharacteristic
189C23×D11—21no—
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—21no—
201C2×D4×C11—22no—
202C2×D4×C11—22no—
203C2×D4×C11—44no—
204C2×D4×C11C2412yes—
205C22×C4×C11—21no—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—24no—
211C22×C4×C11—24no—
212C22×C4×C11—44no—
213C22×C4×C11—44no—
214C22×C4×C11C2×D411yescharacteristic
215C22×C4×C11C2×D412yes—
216C22×C4×C11C2412yes—
217C22×C4×C11C2411yescharacteristic
218C2×C22⋊D11—24no—
219C2×C22⋊D11—24no—
220C2×C22⋊D11—24no—
221C2×C22⋊D11—24no—
222C2×C22⋊D11—24no—
223C2×C22⋊D11—24no—
224C2×C22⋊D11—44no—
225C2×C22⋊D11—44no—
226C2×C22⋊D11—82no—
227C2×C22⋊D11—82no—
228C2×C22⋊D11—82no—
229C2×C22⋊D11C2×D414yes—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11C2×D411yescharacteristic
233C22×Dic11C2×D411yescharacteristic
234C22×Dic11C2×D411yescharacteristic
235#4343—28no—
236#4343—44no—
237#4343—48no—
238#4339—432no—
239C2×D44—24no—
240C2×D44—24no—
241C2×D44—21no—
242C2×D44—21no—
243C2×D44—22no—
244C2×D44—22no—
245C2×D44—22no—
246C2×D44—22no—
247C2×D44—44no—
248C2×D44—44no—
249C2×D44C2412yes—
250C2×D44C2412yes—
251C2×C4×D11—24no—
252C2×C4×D11—24no—
253C2×C4×D11—24no—
254C2×C4×D11—22no—
255C2×C4×D11—22no—
256C2×C4×D11—44no—
257C2×C4×D11—44no—
258C2×C4×D11—44no—
259C2×C4×D11C2×D412yes—
260C2×C4×D11C2412yes—
261C2×Dic22—24no—
262C2×Dic22—44no—
263C11×M16—44no—
264C2×C8×C11—22no—
265C2×C8×C11—22no—
266C2×C8×C11C2412yes—
267C2×C8×C11C2412yes—
268C11×C4⋊C4—21no—
269C11×C4⋊C4—21no—
270C11×C4⋊C4—24no—
271C11×C4⋊C4C2412yes—
272C11×C4⋊C4C2412yes—
273C22⋊Dic11—24no—
274C22⋊Dic11C2×D414yes—
275#4325—28no—
276#4323—44no—
277(C2×D11)⋊C4—24no—
278(C2×D11)⋊C4—24no—
279(C2×D11)⋊C4—24no—
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⋊C4C2×D414yes—
290C4×Dic11—24no—
291C4×Dic11C2×D412yes—
292C4×Dic11C2412yes—
293C2×C11⋊C8—22no—
294C2×C11⋊C8—22no—
295C2×C11⋊C8C2412yes—
296C2×C11⋊C8C2412yes—
297D88—44no—
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×#449—111no—
311C2×C4×SD16—111no—
312C2×#436—111no—
313C2×#417—111no—
314C2×#417D1111yescharacteristic, complemented
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—42no—
320C23×C11—42no—
321C23×C11—42no—
322C23×C11C22×D412yes—
323C23×C11C22×D411yescharacteristic
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—42no—
330C22×D11—42no—
331C22×D11—42no—
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—48no—
342D4×C11—42no—
343C2×C4×C11—24no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—24no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—48no—
352C2×C4×C11—48no—
353C2×C4×C11—42no—
354C2×C4×C11—42no—
355C2×C4×C11C22×D412yes—
356C2×C4×C11C22×D411yescharacteristic
357C2×C4×C11C2×#4112yes—
358C2×C4×C11H(5,𝔽2)12yes—
359C2×C4×C11C2511yescharacteristic
360C22⋊D11—28no—
361C22⋊D11—48no—
362C22⋊D11—48no—
363C22⋊D11—84no—
364C22⋊D11—84no—
365C22⋊D11—84no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—42no—
371C2×Dic11—42no—
372C2×Dic11AGL(1,ℤ/8)14yes—
373C2×Dic11C22×D412yes—
374C2×Dic11C22×D412yes—
375C2×Dic11C22×D412yes—
376D44—22no—
377D44—22no—
378D44—22no—
379D44—22no—
380D44—48no—
381D44—48no—
382D44—42no—
383D44—42no—
384C4×D11—24no—
385C4×D11—22no—
386C4×D11—22no—
387C4×D11—48no—
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×SD16—111no—
399C22×D8—111no—
400C22×D8—111no—
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—111no—
416C2×#121—111no—
417C2×#121—221no—
418C2×#121—221no—
419C2×C4×Q8—111no—
420C2×C4×D4—111no—
421C2×C4×D4—111no—
422C2×C4×D4—221no—
423C22×C4⋊C4—111no—
424C22×C4⋊C4C2×D1111yescharacteristic
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#449—118no—
434C4×SD16—118no—
435#436—118no—
436C2×#106—111no—
437C2×#106—111no—
438C2×#106—111no—
439C2×C4⋊C8—111no—
440#417—118no—
441#417C2×D1118yescomplemented
442C2×#103—111no—
443C2×#103C2×D1111yescharacteristic
444C2×#103C2×D1111yescharacteristic
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—84no—
463C22×C11#54612yes—
464C22×C11C2×AGL(1,ℤ/8)12yes—
465C22×C11#57712yes—
466C22×C11C23×D411yescharacteristic
467C2×D11—22no—
468C2×D11—22no—
469C2×D11—22no—
470C2×D11—44no—
471C2×D11—42no—
472C2×D11—42no—
473C2×D11—42no—
474C2×D11—42no—
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—84no—
478C2×D11—84no—
479C4×C11—22no—
480C4×C11—24no—
481C4×C11—42no—
482C4×C11—42no—
483C4×C11#54612yes—
484C4×C11C22×#4111yescharacteristic
485C4×C11C2×H(5,𝔽2)11yescharacteristic
486Dic11—22no—
487Dic11—22no—
488Dic11—42no—
489Dic11—42no—
490Dic11C2×AGL(1,ℤ/8)14yes—
491C2×#41—22no—
492C2×#41—24no—
493C2×#41—42no—
494C2×#41—114no—
495C2×#41—228no—
496C2×#41—222no—
497C2×#41—224no—
498C2×#41—448no—
499C2×#41—442no—
500C2×#41C22×D1114yes—
501C22×Q8—221no—
502C22×Q8C22×D1111yescharacteristic
503C22×D4—21no—
504C22×D4—111no—
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×D4—221no—
514C22×D4C22×D1111yescharacteristic
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—111no—
518C23×C4—221no—
519C23×C4—221no—
520C23×C4—221no—
521C23×C4C22×D1111yescharacteristic
522C2×SD16—114no—
523C2×SD16—224no—
524C2×D8—114no—
525C2×D8—114no—
526C2×D8—442no—
527C2×D8—442no—
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—114no—
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#121—222no—
554C4×Q8—114no—
555C4×Q8—222no—
556C4×D4—114no—
557C4×D4—114no—
558C4×D4—114no—
559C4×D4—222no—
560C4×D4—228no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—22no—
563C2×C4⋊C4—111no—
564C2×C4⋊C4—111no—
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⋊C4C22×D1111yescharacteristic
572C2×C4⋊C4C22×D1111yescharacteristic
573C2×C4⋊C4C22×D1114yes—
574C2×C22⋊C4—111no—
575C2×C22⋊C4—111no—
576C2×C22⋊C4—221no—
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#103C22×D1114yes—
589#103C22×D1114yes—
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#333214yescomplemented
603C2×C11C2×#54611yescharacteristic
604C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
605C2×C11C2×#57711yescharacteristic
606D11—42no—
607D11—82no—
608D11—82no—
609C24—21no—
610C24—111no—
611C24—221no—
612C24—221no—
613C24D4×D1111yescharacteristic
614#41—28no—
615#41—44no—
616#41—48no—
617#41—228no—
618#41—4432no—
619#41—444no—
620#41—448no—
621C2×Q8—21no—
622C2×Q8—22no—
623C2×Q8—224no—
624C2×Q8—444no—
625C2×Q8#433914yescomplemented
626C2×Q8C23×D1112yes—
627C2×D4—24no—
628C2×D4—22no—
629C2×D4—21no—
630C2×D4—22no—
631C2×D4—44no—
632C2×D4—114no—
633C2×D4—112no—
634C2×D4—112no—
635C2×D4—224no—
636C2×D4—224no—
637C2×D4—224no—
638C2×D4—224no—
639C2×D4—224no—
640C2×D4—224no—
641C2×D4—224no—
642C2×D4—224no—
643C2×D4—222no—
644C2×D4—222no—
645C2×D4—221no—
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×D4—882no—
656C2×D4C23×D1112yes—
657C22×C4—21no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—24no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—24no—
664C22×C4—44no—
665C22×C4—44no—
666C22×C4—111no—
667C22×C4—111no—
668C22×C4—111no—
669C22×C4—112no—
670C22×C4—112no—
671C22×C4—224no—
672C22×C4—224no—
673C22×C4—224no—
674C22×C4—222no—
675C22×C4—222no—
676C22×C4—221no—
677C22×C4—221no—
678C22×C4—444no—
679C22×C4—444no—
680C22×C4—444no—
681C22×C4D4×D1112yes—
682C22×C4D4×D1111yescharacteristic
683C22×C4C23×D1112yes—
684C22×C4C23×D1111yescharacteristic
685SD16—228no—
686D8—444no—
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—24no—
701C4⋊C4—114no—
702C4⋊C4—112no—
703C4⋊C4—112no—
704C4⋊C4—224no—
705C4⋊C4—224no—
706C4⋊C4—224no—
707C4⋊C4—221no—
708C4⋊C4—221no—
709C4⋊C4C23×D1112yes—
710C4⋊C4C23×D1112yes—
711C22⋊C4—114no—
712C22⋊C4—114no—
713C22⋊C4—224no—
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—42no—
727C23—42no—
728C23—42no—
729C23—112no—
730C23—222no—
731C23—222no—
732C23—222no—
733C23—222no—
734C23—222no—
735C23—442no—
736C23—442no—
737C23—442no—
738C23—442no—
739C23—442no—
740C23—442no—
741C23C2×D4×D1112yes—
742C23C2×D4×D1111yescharacteristic
743Q8—24no—
744Q8—22no—
745Q8—448no—
746Q8C2×#433914yescomplemented
747D4—22no—
748D4—22no—
749D4—48no—
750D4—42no—
751D4—228no—
752D4—222no—
753D4—222no—
754D4—222no—
755D4—222no—
756D4—448no—
757D4—448no—
758D4—448no—
759D4—448no—
760D4—442no—
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—22no—
773C2×C4—48no—
774C2×C4—48no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—114no—
778C2×C4—112no—
779C2×C4—112no—
780C2×C4—112no—
781C2×C4—222no—
782C2×C4—222no—
783C2×C4—224no—
784C2×C4—222no—
785C2×C4—222no—
786C2×C4—222no—
787C2×C4—222no—
788C2×C4—448no—
789C2×C4—448no—
790C2×C4—448no—
791C2×C4—442no—
792C2×C4—442no—
793C2×C4C2×#433912yes—
794C2×C4C2×D4×D1112yes—
795C2×C4C2×D4×D1111yescharacteristic
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—84no—
810C22—222no—
811C22—222no—
812C22—222no—
813C22—444no—
814C22—442no—
815C22—442no—
816C22—442no—
817C22—442no—
818C22—442no—
819C22—442no—
820C22—884no—
821C22—884no—
822C22#1062302112yes—
823C22D11×AGL(1,ℤ/8)12yes—
824C22#1062330912yes—
825C22C22×D4×D1111yescharacteristic
826C4—22no—
827C4—24no—
828C4—42no—
829C4—42no—
830C4—114no—
831C4—222no—
832C4—222no—
833C4—442no—
834C4—442no—
835C4#1062302112yes—
836C4C22×#433911yescharacteristic
837C4C2×#6703711yescharacteristic
838C2—42no—
839C2—82no—
840C2—442no—
841C2—882no—
842C2—882no—
843C2#1308093914yesdirect product factor
844C2C2×#1062302111yescharacteristic
845C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
846C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#417C2
socleC23×C11C22×D4
hypercenterC2×#417D11
hypocenterC11C2×#3332
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#10623365C2semidirect
2. C2×#10623038C2semidirect
3. #13080939C2direct (N × H)
4. C2×#10622373C2semidirect
5. C2×#10622581C2semidirect
6. C2×#10622390C2semidirect
7. C2×#10622404C2semidirect
8. C2×#10622748C2semidirect
9. C2×#10622395C2semidirect
10. C2×#10622399C2semidirect
11. C2×#10622424C2semidirect
12. C2×#10622851C2semidirect
13. C2×#10622401C2semidirect
14. C2×#10622741C2semidirect
15. C2×#10622416C2semidirect
16. C2×C11×#417C2semidirect
23. #10623365C22semidirect
41. #10623038C22semidirect
47. C11×#417C22semidirect
52. #10622851C22semidirect
56. #10622748C22semidirect
57. #10622741C22semidirect
64. #10622581C22semidirect
69. #10622424C22semidirect
70. #10622416C22semidirect
71. #10622404C22semidirect
72. #10622401C22semidirect
73. #10622399C22semidirect
74. #10622395C22semidirect
75. #10622390C22semidirect
76. #10622373C22semidirect
197. C2×Q8×C11#41semidirect
314. C2×#417D11semidirect
338. Q8×C11C2×#41semidirect
441. #417C2×D11semidirect
602. C2×C11#3332semidirect
625. C2×Q8#4339semidirect
721. C11C2×#3332semidirect
746. Q8C2×#4339semidirect
843. C2#13080939direct (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×#106230382
#130809392
C2×#106223732
C2×#106225812
C2×#106223902
C2×#106224042
C2×#106227482
C2×#106223952
C2×#106223992
C2×#106224242
C2×#106228512
C2×#106224012
C2×#106227412
C2×#106224162
C2×C11×#4172
C2×#333211