Finite Group Databasebeta

← C2×#13080767 #15630454

Subgroups — C2×#13080767 #15630454

Order 2816.

2318 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623147C211yesmaximal, characteristic, complemented
2C2×#10623161C211yesmaximal, characteristic, complemented
3#13080767C2116yesmaximal, direct product factor
4C2×#10622408C211yesmaximal, characteristic, complemented
5C2×#10622658C211yesmaximal, characteristic, complemented
6C2×#10622498C211yesmaximal, characteristic, complemented
7C2×#10622503C211yesmaximal, characteristic, complemented
8C2×#10622388C211yesmaximal, characteristic, complemented
9C2×#10622778C211yesmaximal, characteristic, complemented
10C2×#10622785C211yesmaximal, characteristic, complemented
11C2×#10622649C211yesmaximal, characteristic, complemented
12C2×#10622398C211yesmaximal, characteristic, complemented
13C2×#10622740C211yesmaximal, characteristic, complemented
14C2×#10622744C211yesmaximal, characteristic, complemented
15C2×#10622417C211yesmaximal, characteristic, complemented
16C2×C11×#468C211yesmaximal, characteristic, complemented
17C22×#4343C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic, complemented
20C22×C11×M16C2211yescharacteristic
21C2×C11×C22⋊Q8C2211yescharacteristic
22C2×C11×#121C2211yescharacteristic
23C2×#67000C2211yescharacteristic
24C2×#66992—21no—
25C2×#66991C2211yescharacteristic, complemented
26C2×#66989—21no—
27C2×D4×Dic11C2211yescharacteristic, complemented
28C22×#4323C2211yescharacteristic
29C22×#4323C2211yescharacteristic
30C2×C4×C22⋊D11C2211yescharacteristic
31C2×#66979C2211yescharacteristic
32C22×C8×D11C2211yescharacteristic, complemented
33#10623161—24no—
34#10623161C2218yescomplemented
35#10623147—24no—
36#10623147C2218yescomplemented
37C2×#66948—21no—
38C2×#66948C2211yescharacteristic
39C2×#66947—21no—
40C2×#66946C2211yescharacteristic
41C2×#66945C2211yescharacteristic, complemented
42C2×#66941C2211yescharacteristic, complemented
43C2×#66938—21no—
44C2×#66935—21no—
45C2×C22⋊C4×D11—21no—
46C2×#66930—21no—
47C11×#468C2218yescomplemented
48C2×C11×#107C2211yescharacteristic, complemented
49C2×C11×#103C2211yescharacteristic, complemented
50C2×C11×#102C2211yescharacteristic, complemented
51C2×#66899C2211yescharacteristic, complemented
52C2×#66899C2211yescharacteristic, complemented
53C2×C22⋊(C11⋊C8)C2211yescharacteristic
54#10622785C2218yescomplemented
55#10622778C2218yescomplemented
56#10622744C2218yescomplemented
57#10622740C2218yescomplemented
58C2×#66885C2211yescharacteristic
59C2×#66885C2211yescharacteristic
60C2×#66885C2211yescharacteristic
61C2×#66885C2211yescharacteristic
62C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
63C2×#66879C2211yescharacteristic, complemented
64C2×Dic11⋊C8C2211yescharacteristic, complemented
65#10622658C2218yescomplemented
66#10622649C2218yescomplemented
67C2×#66873C2211yescharacteristic
68C2×#66873C2211yescharacteristic
69C2×#66872C2211yescharacteristic, complemented
70C2×#66871C2211yescharacteristic, complemented
71#10622503C2218yescomplemented
72#10622498C2218yescomplemented
73#10622417C2218yescomplemented
74#10622408C2218yescomplemented
75#10622398C2218yescomplemented
76#10622388C2218yescomplemented
77C24×D11—21no—
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11—21no—
80C22×D4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C22×C22⋊D11—21no—
83C22×C22⋊D11D411yescharacteristic
84C23×Dic11—21no—
85C2×#4343—22no—
86C2×#4343—24no—
87C2×#4343—42no—
88C2×#4343C2314yes—
89C22×D44—24no—
90C22×D44—21no—
91C22×D44—21no—
92C22×D44—22no—
93C22×D44—21no—
94C22×D44—42no—
95C22×D44C2311yescharacteristic
96C22×D44C2314yes—
97C22×D44C2311yescharacteristic
98C22×C4×D11—21no—
99C22×C4×D11—21no—
100C22×C4×D11C2311yescharacteristic
101C22×Dic22—21no—
102C2×C11×SD16—42no—
103C2×C11×SD16C2314yescomplemented
104C2×C11×M16—42no—
105C2×C11×M16C2314yes—
106C22×C8×C11C2311yescharacteristic
107C22×C8×C11C2311yescharacteristic
108C11×C22⋊Q8—22no—
109C11×C22⋊Q8C2314yes—
110C11×#121—22no—
111C11×#121C2314yes—
112C2×C11×C4⋊C4—21no—
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C22⋊Dic11—21no—
118C2×C22⋊Dic11—21no—
119C2×C22⋊Dic11—21no—
120C2×C22⋊Dic11D411yescharacteristic
121#67000—22no—
122#67000C2314yes—
123#66992—28no—
124#66991—22no—
125#66991C2314yescomplemented
126#66989—28no—
127D4×Dic11—22no—
128D4×Dic11C2314yescomplemented
129C2×#4323—24no—
130C2×#4323—42no—
131C2×#4323C2314yes—
132C2×#4323C2314yes—
133C4×C22⋊D11D414yes—
134C4×C22⋊D11C2314yes—
135C2×(C2×D11)⋊C4—21no—
136C2×(C2×D11)⋊C4—21no—
137C2×(C2×D11)⋊C4—21no—
138C2×(C2×D11)⋊C4—21no—
139C2×(C2×D11)⋊C4—21no—
140C2×(C2×D11)⋊C4D411yescharacteristic
141#66979—22no—
142#66979C2314yes—
143C2×C4⋊Dic11C2311yescharacteristic
144C2×C4⋊Dic11C2311yescharacteristic
145C2×Dic11⋊C4—21no—
146C2×Dic11⋊C4D411yescharacteristic
147C2×C4×Dic11—21no—
148C2×C4×Dic11—21no—
149C2×C4×Dic11C2311yescharacteristic
150C22×C11⋊C8C2311yescharacteristic
151C22×C11⋊C8C2311yescharacteristic
152C2×C8×D11—42no—
153C2×C8×D11C2314yescomplemented
154#66948—22no—
155#66948—28no—
156#66948C2314yes—
157#66947—28no—
158#66946—22no—
159#66946C2314yes—
160#66945—22no—
161#66945C2314yescomplemented
162#66941—22no—
163#66941C2314yescomplemented
164#66938—28no—
165#66935—28no—
166C22⋊C4×D11—28no—
167#66930—28no—
168C11×#107C2314yescomplemented
169C11×#103C2314yescomplemented
170C11×#102C2314yescomplemented
171#66899C2314yescomplemented
172#66899C2314yescomplemented
173C22⋊(C11⋊C8)C2314yes—
174#66885C2314yes—
175#66885C2314yes—
176#66885C2314yes—
177#66885C2314yes—
178(C2×D11)⋊C8C2314yescomplemented
179#66879C2314yescomplemented
180Dic11⋊C8C2314yescomplemented
181#66873C2314yes—
182#66873C2314yes—
183#66872C2314yescomplemented
184#66871C2314yescomplemented
185C2×#3319—111nomaximal, Sylow
186C24×C11—21no—
187C24×C11C2×D411yescharacteristic
188C23×D11—21no—
189C23×D11—21no—
190C23×D11—24no—
191C23×D11—44no—
192C23×D11—44no—
193C23×D11—82no—
194C23×D11C2×D411yescharacteristic
195C2×Q8×C11—21no—
196C2×Q8×C11—22no—
197C2×Q8×C11—22no—
198C2×Q8×C11C2412yes—
199C2×D4×C11—24no—
200C2×D4×C11—21no—
201C2×D4×C11—22no—
202C2×D4×C11—22no—
203C2×D4×C11—82no—
204C2×D4×C11C2412yes—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2×D412yes—
212C22×C4×C11C2412yes—
213C22×C4×C11C2411yescharacteristic
214C2×C22⋊D11—24no—
215C2×C22⋊D11—42no—
216C2×C22⋊D11—82no—
217C2×C22⋊D11C2×D414yes—
218C22×Dic11—24no—
219C22×Dic11—21no—
220C22×Dic11—21no—
221C22×Dic11—44no—
222C22×Dic11C2×D411yescharacteristic
223C22×Dic11C2×D411yescharacteristic
224C22×Dic11C2×D411yescharacteristic
225#4343—28no—
226#4343—44no—
227#4343—48no—
228C2×D44—24no—
229C2×D44—24no—
230C2×D44—28no—
231C2×D44—21no—
232C2×D44—24no—
233C2×D44—21no—
234C2×D44—22no—
235C2×D44—22no—
236C2×D44—22no—
237C2×D44—44no—
238C2×D44—44no—
239C2×D44—48no—
240C2×D44—44no—
241C2×D44—82no—
242C2×D44#4114yes—
243C2×D44C2412yes—
244C2×D44C2412yes—
245C2×C4×D11—24no—
246C2×C4×D11—24no—
247C2×C4×D11—22no—
248C2×C4×D11—22no—
249C2×C4×D11—44no—
250C2×C4×D11—82no—
251C2×C4×D11C2×D412yes—
252C2×C4×D11C2412yes—
253C2×Dic22—24no—
254C2×Dic22—82no—
255C11×SD16—44no—
256C11×M16—44no—
257C2×C8×C11—22no—
258C2×C8×C11—22no—
259C2×C8×C11C2412yes—
260C2×C8×C11C2412yes—
261C11×C4⋊C4—21no—
262C11×C4⋊C4—21no—
263C11×C4⋊C4—24no—
264C11×C4⋊C4C2412yes—
265C11×C4⋊C4C2412yes—
266C11×C22⋊C4—24no—
267C11×C22⋊C4—24no—
268C22⋊Dic11—24no—
269C22⋊Dic11—24no—
270C22⋊Dic11—24no—
271C22⋊Dic11C2×D414yes—
272#4323—28no—
273#4323—44no—
274(C2×D11)⋊C4—24no—
275(C2×D11)⋊C4—24no—
276(C2×D11)⋊C4—24no—
277(C2×D11)⋊C4—24no—
278(C2×D11)⋊C4—24no—
279(C2×D11)⋊C4C2×D414yes—
280C4⋊Dic11—21no—
281C4⋊Dic11—21no—
282C4⋊Dic11C2412yes—
283C4⋊Dic11C2412yes—
284Dic11⋊C4—24no—
285Dic11⋊C4C2×D414yes—
286C4×Dic11—24no—
287C4×Dic11—24no—
288C4×Dic11C2×D412yes—
289C4×Dic11C2412yes—
290C2×C11⋊C8—22no—
291C2×C11⋊C8—22no—
292C2×C11⋊C8C2412yes—
293C2×C11⋊C8C2412yes—
294C8×D11—44no—
295C2×#555—111no—
296C2×#546—111no—
297#3319—1116no—
298C2×#489—111no—
299C2×#485—111no—
300C2×#482—111no—
301C2×#474—111no—
302C2×#468D1111yescharacteristic, complemented
303C2×#466—111no—
304C2×#463—111no—
305C2×#449—111no—
306C2×#447—111no—
307C2×#442—111no—
308C2×#435—111no—
309C2×#418—111no—
310C2×#416—111no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—42no—
316C23×C11—42no—
317C23×C11—42no—
318C23×C11C22×D412yes—
319C23×C11C22×D411yescharacteristic
320C22×D11—22no—
321C22×D11—24no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—48no—
327C22×D11—42no—
328C22×D11—42no—
329C22×D11—48no—
330C22×D11—42no—
331C22×D11—42no—
332C22×D11—42no—
333C22×D11—84no—
334C22×D11—816no—
335C22×D11C22×D412yes—
336Q8×C11—22no—
337Q8×C11—22no—
338Q8×C11—42no—
339D4×C11—22no—
340D4×C11—22no—
341D4×C11—42no—
342D4×C11—84no—
343C2×C4×C11—22no—
344C2×C4×C11—24no—
345C2×C4×C11—22no—
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×C11—42no—
353C2×C4×C11C22×D412yes—
354C2×C4×C11C22×D411yescharacteristic
355C2×C4×C11C2×#4112yes—
356C2×C4×C11H(5,𝔽2)12yes—
357C2×C4×C11C2511yescharacteristic
358C22⋊D11—44no—
359C22⋊D11—84no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—48no—
366C2×Dic11—42no—
367C2×Dic11—42no—
368C2×Dic11C22×D412yes—
369C2×Dic11C22×D412yes—
370C2×Dic11C22×D412yes—
371D44—24no—
372D44—22no—
373D44—22no—
374D44—22no—
375D44—48no—
376D44—48no—
377D44—42no—
378D44—84no—
379D44C2×#4114yes—
380C4×D11—24no—
381C4×D11—22no—
382C4×D11—22no—
383C4×D11—48no—
384C4×D11—84no—
385Dic22—84no—
386C8×C11—22no—
387C8×C11—22no—
388C11⋊C8—22no—
389C11⋊C8—22no—
390C22×#41—111no—
391C23×D4—111no—
392C22×SD16C2×D1111yescharacteristic, complemented
393C22×D8—111no—
394C22×D8—111no—
395C22×M16C2×D1111yescharacteristic
396C23×C8—111no—
397#555—118no—
398#555—224no—
399#546—118no—
400#546—224no—
401C2×C4⋊Q8—111no—
402C2×#124—111no—
403C2×#124—221no—
404C2×#124—221no—
405C2×#123—221no—
406C2×C22⋊Q8C2×D1111yescharacteristic
407C2×#121—111no—
408C2×#121—111no—
409C2×#121—221no—
410C2×#121—221no—
411C2×#121C2×D1111yescharacteristic
412C2×#120—221no—
413C2×C4×D4—111no—
414C2×C4×D4—111no—
415C2×C4×D4—111no—
416C2×#117—111no—
417C2×#117—111no—
418C2×#117—221no—
419C22×C22⋊C4—221no—
420#489—118no—
421#485—118no—
422#482—118no—
423#474—118no—
424#468C2×D1118yescomplemented
425#466—118no—
426#463—118no—
427#449—118no—
428#447—118no—
429#442—118no—
430#435—118no—
431C2×#107—111no—
432C2×#107C2×D1111yescharacteristic, complemented
433C2×#106—111no—
434C2×C4⋊C8—111no—
435#418—118no—
436#416—118no—
437C2×#103—111no—
438C2×#103—111no—
439C2×#103C2×D1111yescharacteristic, complemented
440C2×#102—111no—
441C2×#102—111no—
442C2×#102—111no—
443C2×#102—111no—
444C2×#102—111no—
445C2×#102—111no—
446C2×#102C2×D1111yescharacteristic, complemented
447C2×C22⋊C8—111no—
448C2×C22⋊C8—111no—
449C2×#97—111no—
450C22×C11—22no—
451C22×C11—22no—
452C22×C11—22no—
453C22×C11—44no—
454C22×C11—42no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—84no—
458C22×C11#54612yes—
459C22×C11#57512yes—
460C22×C11#57612yes—
461C22×C11C23×D411yescharacteristic
462C2×D11—24no—
463C2×D11—22no—
464C2×D11—22no—
465C2×D11—22no—
466C2×D11—44no—
467C2×D11—48no—
468C2×D11—42no—
469C2×D11—42no—
470C2×D11—42no—
471C2×D11—42no—
472C2×D11—42no—
473C2×D11—816no—
474C2×D11—84no—
475C4×C11—22no—
476C4×C11—42no—
477C4×C11—42no—
478C4×C11—42no—
479C4×C11#54612yes—
480C4×C11C22×#4111yescharacteristic
481C4×C11C2×H(5,𝔽2)11yescharacteristic
482Dic11—22no—
483Dic11—22no—
484Dic11—22no—
485Dic11—42no—
486Dic11—42no—
487C25—221no—
488C2×#41—114no—
489C2×#41—222no—
490C2×#41—224no—
491C2×#41—442no—
492C22×Q8—221no—
493C22×Q8C22×D1111yescharacteristic
494C22×D4—21no—
495C22×D4—111no—
496C22×D4—111no—
497C22×D4—111no—
498C22×D4—114no—
499C22×D4—224no—
500C22×D4—221no—
501C22×D4—221no—
502C22×D4—221no—
503C22×D4—221no—
504C22×D4—222no—
505C22×D4—442no—
506C22×D4C22×D1111yescharacteristic
507C23×C4—111no—
508C23×C4—221no—
509C23×C4—221no—
510C23×C4—221no—
511C23×C4C22×D1111yescharacteristic
512C2×SD16—42no—
513C2×SD16C22×D1114yescomplemented
514C2×D8—114no—
515C2×D8—114no—
516C2×D8—224no—
517C2×D8—442no—
518C2×M16—42no—
519C2×M16C22×D1114yes—
520C22×C8—111no—
521C22×C8—111no—
522C22×C8—114no—
523C22×C8—442no—
524C22×C8C22×D1111yescharacteristic
525C22×C8C22×D1111yescharacteristic
526C4⋊Q8—114no—
527C4⋊Q8—222no—
528#124—114no—
529#124—222no—
530#124—228no—
531#124—228no—
532#123—228no—
533C22⋊Q8—22no—
534C22⋊Q8C22×D1114yes—
535#121—22no—
536#121—114no—
537#121—114no—
538#121—228no—
539#121—222no—
540#121—222no—
541#121—228no—
542#121C22×D1114yes—
543#120—228no—
544C4×D4—114no—
545C4×D4—114no—
546C4×D4—114no—
547C4×D4—114no—
548C4×D4—222no—
549C4×D4—222no—
550#117—114no—
551#117—114no—
552#117—228no—
553#117—222no—
554#117—222no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—111no—
557C2×C4⋊C4—111no—
558C2×C4⋊C4—111no—
559C2×C4⋊C4—221no—
560C2×C4⋊C4C22×D1111yescharacteristic
561C2×C4⋊C4C22×D1111yescharacteristic
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—111no—
565C2×C22⋊C4—111no—
566C2×C22⋊C4—228no—
567C2×C22⋊C4—221no—
568C2×C22⋊C4—221no—
569C2×C22⋊C4—221no—
570C2×C22⋊C4—221no—
571C2×C22⋊C4—221no—
572C2×C22⋊C4—221no—
573C2×C22⋊C4—221no—
574C2×C22⋊C4—221no—
575C2×C42—111no—
576C2×C42—221no—
577C2×C42—221no—
578#107—114no—
579#107C22×D1114yescomplemented
580#106—114no—
581C4⋊C8—114no—
582#103—114no—
583#103—114no—
584#103C22×D1114yescomplemented
585#102—114no—
586#102—114no—
587#102—114no—
588#102—114no—
589#102—114no—
590#102—114no—
591#102C22×D1114yescomplemented
592C22⋊C8—114no—
593C22⋊C8—114no—
594#97—114no—
595C2×C11—42no—
596C2×C11—82no—
597C2×C11#331914yescomplemented
598C2×C11C2×#54611yescharacteristic
599C2×C11C2×#57511yescharacteristic
600C2×C11C2×#57611yescharacteristic
601D11—42no—
602D11—44no—
603D11—82no—
604C24—21no—
605C24—111no—
606C24—221no—
607C24—221no—
608C24—224no—
609C24—444no—
610C24—444no—
611C24—882no—
612C24D4×D1111yescharacteristic
613#41—228no—
614#41—444no—
615#41—448no—
616C2×Q8—21no—
617C2×Q8—22no—
618C2×Q8—22no—
619C2×Q8—224no—
620C2×Q8—882no—
621C2×Q8C23×D1112yes—
622C2×D4—24no—
623C2×D4—21no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—82no—
627C2×D4—114no—
628C2×D4—114no—
629C2×D4—112no—
630C2×D4—112no—
631C2×D4—228no—
632C2×D4—224no—
633C2×D4—224no—
634C2×D4—224no—
635C2×D4—221no—
636C2×D4—224no—
637C2×D4—221no—
638C2×D4—222no—
639C2×D4—222no—
640C2×D4—222no—
641C2×D4—444no—
642C2×D4—448no—
643C2×D4—444no—
644C2×D4—444no—
645C2×D4—442no—
646C2×D4—882no—
647C2×D4—882no—
648C2×D4C23×D1112yes—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—111no—
655C22×C4—111no—
656C22×C4—111no—
657C22×C4—112no—
658C22×C4—112no—
659C22×C4—224no—
660C22×C4—224no—
661C22×C4—224no—
662C22×C4—222no—
663C22×C4—222no—
664C22×C4—221no—
665C22×C4—221no—
666C22×C4—444no—
667C22×C4—444no—
668C22×C4—882no—
669C22×C4D4×D1112yes—
670C22×C4D4×D1111yescharacteristic
671C22×C4C23×D1112yes—
672C22×C4C23×D1111yescharacteristic
673SD16—44no—
674D8—228no—
675D8—444no—
676M16—44no—
677C2×C8—22no—
678C2×C8—22no—
679C2×C8—112no—
680C2×C8—112no—
681C2×C8—222no—
682C2×C8—222no—
683C2×C8—444no—
684C2×C8C23×D1112yes—
685C2×C8C23×D1112yes—
686C4⋊C4—24no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—114no—
690C4⋊C4—112no—
691C4⋊C4—112no—
692C4⋊C4—224no—
693C4⋊C4—221no—
694C4⋊C4—221no—
695C4⋊C4C23×D1112yes—
696C4⋊C4C23×D1112yes—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—114no—
700C22⋊C4—114no—
701C22⋊C4—224no—
702C22⋊C4—224no—
703C22⋊C4—224no—
704C22⋊C4—224no—
705C22⋊C4—224no—
706C22⋊C4—224no—
707C22⋊C4—224no—
708C22⋊C4—224no—
709C42—112no—
710C42—112no—
711C42—224no—
712C42—224no—
713C11C2×#331911yescharacteristic, complemented, Sylow
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—112no—
722C23—222no—
723C23—222no—
724C23—222no—
725C23—224no—
726C23—222no—
727C23—222no—
728C23—448no—
729C23—448no—
730C23—442no—
731C23—442no—
732C23—442no—
733C23—442no—
734C23—442no—
735C23—884no—
736C23—8816no—
737C23C2×D4×D1112yes—
738C23C2×D4×D1111yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—42no—
742Q8—884no—
743D4—22no—
744D4—22no—
745D4—42no—
746D4—84no—
747D4—114no—
748D4—224no—
749D4—222no—
750D4—222no—
751D4—222no—
752D4—448no—
753D4—448no—
754D4—444no—
755D4—442no—
756D4—884no—
757D4—884no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—112no—
769C2×C4—112no—
770C2×C4—112no—
771C2×C4—222no—
772C2×C4—222no—
773C2×C4—222no—
774C2×C4—224no—
775C2×C4—222no—
776C2×C4—222no—
777C2×C4—222no—
778C2×C4—222no—
779C2×C4—448no—
780C2×C4—448no—
781C2×C4—442no—
782C2×C4—442no—
783C2×C4—884no—
784C2×C4C2×D4×D1112yes—
785C2×C4C2×D4×D1111yescharacteristic
786C2×C4#6703712yes—
787C2×C4#41×D1112yes—
788C2×C4C24×D1111yescharacteristic
789C8—22no—
790C8—22no—
791C8—222no—
792C8—222no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—44no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—84no—
801C22—222no—
802C22—224no—
803C22—222no—
804C22—222no—
805C22—444no—
806C22—448no—
807C22—442no—
808C22—442no—
809C22—442no—
810C22—442no—
811C22—442no—
812C22—8816no—
813C22—884no—
814C22#1062314112yes—
815C22#1062330512yes—
816C22#1062330812yes—
817C22C22×D4×D1111yescharacteristic
818C4—22no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—222no—
823C4—222no—
824C4—222no—
825C4—442no—
826C4—442no—
827C4#1062314112yes—
828C4C2×#6703711yescharacteristic
829C4C2×#41×D1111yescharacteristic
830C2—42no—
831C2—82no—
832C2—442no—
833C2—444no—
834C2—882no—
835C2#1308076714yesdirect product factor
836C2C2×#1062314111yescharacteristic
837C2C2×#1062330811yescharacteristic
838C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#468C2
socleC23×C11C22×D4
hypercenterC2×#468D11
hypocenterC11C2×#3319
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#10623147C2semidirect
2. C2×#10623161C2semidirect
3. #13080767C2direct (N × H)
4. C2×#10622408C2semidirect
5. C2×#10622658C2semidirect
6. C2×#10622498C2semidirect
7. C2×#10622503C2semidirect
8. C2×#10622388C2semidirect
9. C2×#10622778C2semidirect
10. C2×#10622785C2semidirect
11. C2×#10622649C2semidirect
12. C2×#10622398C2semidirect
13. C2×#10622740C2semidirect
14. C2×#10622744C2semidirect
15. C2×#10622417C2semidirect
16. C2×C11×#468C2semidirect
19. C22×C11×SD16C22semidirect
25. C2×#66991C22semidirect
27. C2×D4×Dic11C22semidirect
32. C22×C8×D11C22semidirect
34. #10623161C22semidirect
36. #10623147C22semidirect
41. C2×#66945C22semidirect
42. C2×#66941C22semidirect
47. C11×#468C22semidirect
48. C2×C11×#107C22semidirect
49. C2×C11×#103C22semidirect
50. C2×C11×#102C22semidirect
51. C2×#66899C22semidirect
52. C2×#66899C22semidirect
54. #10622785C22semidirect
55. #10622778C22semidirect
56. #10622744C22semidirect
57. #10622740C22semidirect
62. C2×(C2×D11)⋊C8C22semidirect
63. C2×#66879C22semidirect
64. C2×Dic11⋊C8C22semidirect
65. #10622658C22semidirect
66. #10622649C22semidirect
69. C2×#66872C22semidirect
70. C2×#66871C22semidirect
71. #10622503C22semidirect
72. #10622498C22semidirect
73. #10622417C22semidirect
74. #10622408C22semidirect
75. #10622398C22semidirect
76. #10622388C22semidirect
103. C2×C11×SD16C23semidirect
125. #66991C23semidirect
128. D4×Dic11C23semidirect
153. C2×C8×D11C23semidirect
161. #66945C23semidirect
163. #66941C23semidirect
168. C11×#107C23semidirect
169. C11×#103C23semidirect
170. C11×#102C23semidirect
171. #66899C23semidirect
172. #66899C23semidirect
178. (C2×D11)⋊C8C23semidirect
179. #66879C23semidirect
180. Dic11⋊C8C23semidirect
183. #66872C23semidirect
184. #66871C23semidirect
302. C2×#468D11semidirect
392. C22×SD16C2×D11semidirect
424. #468C2×D11semidirect
432. C2×#107C2×D11semidirect
439. C2×#103C2×D11semidirect
446. C2×#102C2×D11semidirect
513. C2×SD16C22×D11semidirect
579. #107C22×D11semidirect
584. #103C22×D11semidirect
591. #102C22×D11semidirect
597. C2×C11#3319semidirect
713. C11C2×#3319semidirect
835. C2#13080767direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231472
C2×#106231612
#130807672
C2×#106224082
C2×#106226582
C2×#106224982
C2×#106225032
C2×#106223882
C2×#106227782
C2×#106227852
C2×#106226492
C2×#106223982
C2×#106227402
C2×#106227442
C2×#106224172
C2×C11×#4682
C2×#331911