Finite Group Databasebeta

← C2×#13079480 #15624439

Subgroups — C2×#13079480 #15624439

Order 2816.

2506 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623056C211yesmaximal, characteristic, complemented
2C2×#10623138C211yesmaximal, characteristic, complemented
3#13079480C2116yesmaximal, direct product factor
4C2×#10622498C211yesmaximal, characteristic, complemented
5C2×#10622479C211yesmaximal, characteristic, complemented
6C2×#10622616C211yesmaximal, characteristic, complemented
7C2×#10622478C211yesmaximal, characteristic, complemented
8C2×#10622395C211yesmaximal, characteristic, complemented
9C2×#10622496C211yesmaximal, characteristic, complemented
10C2×#10622388C211yesmaximal, characteristic, complemented
11C2×#10622345C211yesmaximal, characteristic, complemented
12C2×#10622386C211yesmaximal, characteristic, complemented
13C2×#10622386C211yesmaximal, characteristic, complemented
14C2×#10622649C211yesmaximal, characteristic, complemented
15C2×#10622340C211yesmaximal, characteristic, complemented
16C2×C11×#482C211yesmaximal, characteristic, complemented
17C22×D4×D11C2211yescharacteristic, complemented
18C22×#4339C2211yescharacteristic
19C23×D44C2211yescharacteristic, complemented
20C2×C11×#121C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic, complemented
22C2×#66993—21no—
23C2×#66991C2211yescharacteristic, complemented
24C2×#66990—21no—
25C22×#4323C2211yescharacteristic
26C22×#4323C2211yescharacteristic
27C2×#66983C2211yescharacteristic
28C22×D88C2211yescharacteristic
29C22×D88C2211yescharacteristic
30C22×#4313C2211yescharacteristic, complemented
31C22×C8×D11C2211yescharacteristic, complemented
32#10623138—24no—
33#10623138C2218yescomplemented
34#10623056—24no—
35#10623056C2218yescomplemented
36C2×#66948C2211yescharacteristic
37C2×#66948C2211yescharacteristic
38C2×#66948C2211yescharacteristic, complemented
39C2×#66948C2211yescharacteristic, complemented
40C2×#66948C2211yescharacteristic, complemented
41C2×#66945C2211yescharacteristic, complemented
42C2×#66938—21no—
43C2×#66935—21no—
44C2×#66935—21no—
45C2×#66935—21no—
46C2×#66928—21no—
47C2×#66927—21no—
48C11×#482C2218yescomplemented
49C2×C11×#107C2211yescharacteristic, complemented
50C2×C11×#106C2211yescharacteristic, complemented
51C2×C11×#102C2211yescharacteristic, complemented
52C2×C11×#102C2211yescharacteristic, complemented
53C2×C11×C22⋊C8C2211yescharacteristic, complemented
54C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
55C2×#66885C2211yescharacteristic, complemented
56C2×#66885C2211yescharacteristic, complemented
57C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
58C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
59#10622649C2218yescomplemented
60#10622616C2218yescomplemented
61C2×#66873C2211yescharacteristic, complemented
62C2×#66873C2211yescharacteristic, complemented
63C2×#66873C2211yescharacteristic, complemented
64C2×#66873C2211yescharacteristic, complemented
65C2×#66872C2211yescharacteristic, complemented
66C2×#66871C2211yescharacteristic, complemented
67#10622498C2218yescomplemented
68#10622496C2218yescomplemented
69#10622479C2218yescomplemented
70#10622478C2218yescomplemented
71#10622395C2218yescomplemented
72#10622388C2218yescomplemented
73#10622386C2218yescomplemented
74#10622386C2218yescomplemented
75#10622345C2218yescomplemented
76#10622340C2218yescomplemented
77C24×D11—21no—
78C24×D11—21no—
79C22×D4×C11—21no—
80C22×D4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C22×C22⋊D11D411yescharacteristic
86C22×C22⋊D11D411yescharacteristic
87C2×D4×D11—22no—
88C2×D4×D11—42no—
89C2×D4×D11—42no—
90C2×D4×D11C2314yescomplemented
91C2×#4339—42no—
92C2×#4339—42no—
93C2×#4339D414yes—
94C2×#4339C2314yes—
95C22×D44—21no—
96C22×D44—22no—
97C22×D44—21no—
98C22×D44—21no—
99C22×D44—21no—
100C22×D44—21no—
101C22×D44—21no—
102C22×D44—42no—
103C22×D44—42no—
104C22×D44D411yescharacteristic
105C22×D44C2311yescharacteristic
106C22×D44C2311yescharacteristic
107C22×D44C2311yescharacteristic
108C22×D44C2314yescomplemented
109C22×C4×D11C2311yescharacteristic
110C22×C4×D11C2311yescharacteristic
111C22×Dic22D411yescharacteristic
112C22×C8×C11C2311yescharacteristic
113C22×C8×C11C2311yescharacteristic
114C11×#121—22no—
115C11×#121C2314yes—
116C11×#117—22no—
117C11×#117C2314yescomplemented
118C2×C11×C4⋊C4C2311yescharacteristic
119C2×C11×C4⋊C4C2311yescharacteristic
120C2×C11×C4⋊C4C2311yescharacteristic
121C2×C11×C22⋊C4—21no—
122C2×C11×C22⋊C4—21no—
123C2×C42×C11—21no—
124C2×C22⋊Dic11—21no—
125#66993—28no—
126#66991—22no—
127#66991C2314yescomplemented
128#66990—28no—
129C2×#4323—42no—
130C2×#4323—42no—
131C2×#4323C2314yes—
132C2×#4323C2314yes—
133#66983—22no—
134#66983C2314yes—
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)⋊C4—21no—
141C2×(C2×D11)⋊C4—21no—
142C2×C4⋊Dic11C2311yescharacteristic
143C2×C4×Dic11—21no—
144C22×C11⋊C8C2311yescharacteristic
145C22×C11⋊C8C2311yescharacteristic
146C2×D88—42no—
147C2×D88—42no—
148C2×D88C2314yes—
149C2×D88C2314yes—
150C2×#4313—42no—
151C2×#4313C2314yescomplemented
152C2×C8×D11—42no—
153C2×C8×D11C2314yescomplemented
154#66948—22no—
155#66948—22no—
156#66948—22no—
157#66948—22no—
158#66948—22no—
159#66948C2314yes—
160#66948C2314yes—
161#66948C2314yescomplemented
162#66948C2314yescomplemented
163#66948C2314yescomplemented
164#66945—22no—
165#66945C2314yescomplemented
166#66938—28no—
167#66935—28no—
168#66935—28no—
169#66935—28no—
170#66928—28no—
171#66927—28no—
172C11×#107C2314yescomplemented
173C11×#106C2314yescomplemented
174C11×#102C2314yescomplemented
175C11×#102C2314yescomplemented
176C11×C22⋊C8C2314yescomplemented
177C22⋊(C11⋊C8)C2314yescomplemented
178#66885C2314yescomplemented
179#66885C2314yescomplemented
180(C2×D11)⋊C8C2314yescomplemented
181(C2×D11)⋊C8C2314yescomplemented
182#66873C2314yescomplemented
183#66873C2314yescomplemented
184#66873C2314yescomplemented
185#66873C2314yescomplemented
186#66872C2314yescomplemented
187#66871C2314yescomplemented
188C2×#3199—111nomaximal, Sylow
189C24×C11—21no—
190C24×C11C2×D411yescharacteristic
191C23×D11—21no—
192C23×D11—21no—
193C23×D11—21no—
194C23×D11—24no—
195C23×D11—24no—
196C23×D11—44no—
197C23×D11—44no—
198C23×D11—82no—
199C23×D11—82no—
200C23×D11—82no—
201C23×D11—82no—
202C23×D11C2×D411yescharacteristic
203C23×D11C2×D411yescharacteristic
204C2×D4×C11—24no—
205C2×D4×C11—21no—
206C2×D4×C11—22no—
207C2×D4×C11—22no—
208C2×D4×C11—82no—
209C2×D4×C11C2412yes—
210C22×C4×C11—22no—
211C22×C4×C11—22no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11C2×D411yescharacteristic
216C22×C4×C11C2×D412yes—
217C22×C4×C11C2412yes—
218C22×C4×C11C2411yescharacteristic
219C2×C22⋊D11—24no—
220C2×C22⋊D11—24no—
221C2×C22⋊D11—24no—
222C2×C22⋊D11—42no—
223C2×C22⋊D11—42no—
224C2×C22⋊D11—44no—
225C2×C22⋊D11—82no—
226C2×C22⋊D11—82no—
227C2×C22⋊D11C2×D414yes—
228C2×C22⋊D11C2×D414yes—
229C22×Dic11—21no—
230C22×Dic11C2×D411yescharacteristic
231C22×Dic11C2×D411yescharacteristic
232D4×D11—44no—
233D4×D11—44no—
234D4×D11—48no—
235#4339—48no—
236#4339—44no—
237#4339—44no—
238C2×D44—24no—
239C2×D44—24no—
240C2×D44—24no—
241C2×D44—24no—
242C2×D44—24no—
243C2×D44—24no—
244C2×D44—21no—
245C2×D44—21no—
246C2×D44—21no—
247C2×D44—22no—
248C2×D44—22no—
249C2×D44—22no—
250C2×D44—22no—
251C2×D44—22no—
252C2×D44—22no—
253C2×D44—42no—
254C2×D44—44no—
255C2×D44—44no—
256C2×D44—44no—
257C2×D44—48no—
258C2×D44—82no—
259C2×D44—82no—
260C2×D44—82no—
261C2×D44—82no—
262C2×D44—82no—
263C2×D44C2×D414yes—
264C2×D44C2412yes—
265C2×D44C2412yes—
266C2×D44C2412yes—
267C2×C4×D11—22no—
268C2×C4×D11—22no—
269C2×C4×D11—22no—
270C2×C4×D11—22no—
271C2×C4×D11C2×D412yes—
272C2×C4×D11C2×D412yes—
273C2×C4×D11C2412yes—
274C2×C4×D11C2412yes—
275C2×Dic22—42no—
276C2×Dic22C2×D414yes—
277C2×C8×C11—22no—
278C2×C8×C11—22no—
279C2×C8×C11C2412yes—
280C2×C8×C11C2412yes—
281C11×C4⋊C4—21no—
282C11×C4⋊C4—21no—
283C11×C4⋊C4—21no—
284C11×C4⋊C4C2412yes—
285C11×C4⋊C4C2412yes—
286C11×C4⋊C4C2412yes—
287C11×C22⋊C4—24no—
288C11×C22⋊C4—24no—
289C42×C11—24no—
290C22⋊Dic11—24no—
291#4323—44no—
292#4323—44no—
293(C2×D11)⋊C4—24no—
294(C2×D11)⋊C4—24no—
295(C2×D11)⋊C4—24no—
296(C2×D11)⋊C4—24no—
297(C2×D11)⋊C4—24no—
298(C2×D11)⋊C4—24no—
299(C2×D11)⋊C4—24no—
300C4⋊Dic11—21no—
301C4⋊Dic11C2412yes—
302C4×Dic11—24no—
303C2×C11⋊C8—22no—
304C2×C11⋊C8—22no—
305C2×C11⋊C8C2412yes—
306C2×C11⋊C8C2412yes—
307D88—44no—
308D88—44no—
309#4313—44no—
310C8×D11—44no—
311C2×#535—111no—
312C2×#535—111no—
313#3199—1116no—
314C2×#482—111no—
315C2×#482—111no—
316C2×#482—111no—
317C2×#482D1111yescharacteristic, complemented
318C2×#469—111no—
319C2×#469—111no—
320C2×#466—111no—
321C2×#466—111no—
322C2×#447—111no—
323C2×#447—111no—
324C2×#447—111no—
325C2×#447—111no—
326C2×#408—111no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—42no—
332C23×C11—42no—
333C23×C11—42no—
334C23×C11C22×D412yes—
335C23×C11C22×D411yescharacteristic
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—22no—
342C22×D11—22no—
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—48no—
346C22×D11—48no—
347C22×D11—42no—
348C22×D11—42no—
349C22×D11—42no—
350C22×D11—42no—
351C22×D11—42no—
352C22×D11—42no—
353C22×D11—42no—
354C22×D11—42no—
355C22×D11—42no—
356C22×D11—84no—
357C22×D11—84no—
358C22×D11—84no—
359C22×D11—84no—
360C22×D11—816no—
361C22×D11—816no—
362C22×D11C22×D412yes—
363C22×D11C22×D412yes—
364D4×C11—22no—
365D4×C11—22no—
366D4×C11—42no—
367D4×C11—84no—
368C2×C4×C11—22no—
369C2×C4×C11—24no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—42no—
376C2×C4×C11—42no—
377C2×C4×C11—42no—
378C2×C4×C11C22×D412yes—
379C2×C4×C11C22×D411yescharacteristic
380C2×C4×C11H(5,𝔽2)12yes—
381C2×C4×C11H(5,𝔽2)12yes—
382C2×C4×C11C2511yescharacteristic
383C22⋊D11—44no—
384C22⋊D11—44no—
385C22⋊D11—48no—
386C22⋊D11—84no—
387C22⋊D11—84no—
388C2×Dic11—22no—
389C2×Dic11—22no—
390C2×Dic11—22no—
391C2×Dic11—42no—
392C2×Dic11C22×D412yes—
393C2×Dic11C22×D412yes—
394D44—22no—
395D44—22no—
396D44—22no—
397D44—22no—
398D44—22no—
399D44—22no—
400D44—44no—
401D44—48no—
402D44—42no—
403D44—42no—
404D44—42no—
405D44—84no—
406D44—84no—
407D44—84no—
408D44—84no—
409D44—84no—
410C4×D11—24no—
411C4×D11—24no—
412C4×D11—22no—
413C4×D11—22no—
414C4×D11—22no—
415C4×D11—22no—
416Dic22—44no—
417C8×C11—22no—
418C8×C11—22no—
419C11⋊C8—22no—
420C11⋊C8—22no—
421C22×#41—111no—
422C23×D4—111no—
423C23×D4—111no—
424C22×D8—111no—
425C22×D8—111no—
426C22×D8—111no—
427C22×D8—111no—
428C22×M16—111no—
429C23×C8—111no—
430#535—118no—
431#535—118no—
432#535—224no—
433#535—224no—
434C2×#127—221no—
435C2×#127—221no—
436C2×#124—221no—
437C2×#124—221no—
438C2×#121—111no—
439C2×#121—111no—
440C2×#121—111no—
441C2×#121—111no—
442C2×#121—111no—
443C2×#121—111no—
444C2×#121—111no—
445C2×#121C2×D1111yescharacteristic
446C2×#120—221no—
447C2×#120—221no—
448C2×#120—221no—
449C2×#120—221no—
450C2×#117—111no—
451C2×#117C2×D1111yescharacteristic, complemented
452#482—118no—
453#482—118no—
454#482—118no—
455#482C2×D1118yescomplemented
456#469—118no—
457#469—118no—
458#466—118no—
459#466—118no—
460#447—118no—
461#447—118no—
462#447—118no—
463#447—118no—
464C2×#107—111no—
465C2×#107C2×D1111yescharacteristic, complemented
466C2×#106—111no—
467C2×#106C2×D1111yescharacteristic, complemented
468C2×#102—111no—
469C2×#102—111no—
470C2×#102—111no—
471C2×#102—111no—
472C2×#102—111no—
473C2×#102—111no—
474C2×#102C2×D1111yescharacteristic, complemented
475C2×#102C2×D1111yescharacteristic, complemented
476#408—118no—
477C2×C22⋊C8—111no—
478C2×C22⋊C8—111no—
479C2×C22⋊C8—111no—
480C2×C22⋊C8C2×D1111yescharacteristic, complemented
481C22×C11—22no—
482C22×C11—22no—
483C22×C11—22no—
484C22×C11—44no—
485C22×C11—42no—
486C22×C11—42no—
487C22×C11—42no—
488C22×C11—84no—
489C22×C11#53412yes—
490C22×C11#57612yes—
491C22×C11#57612yes—
492C22×C11C23×D411yescharacteristic
493C2×D11—22no—
494C2×D11—22no—
495C2×D11—22no—
496C2×D11—22no—
497C2×D11—22no—
498C2×D11—22no—
499C2×D11—44no—
500C2×D11—44no—
501C2×D11—42no—
502C2×D11—42no—
503C2×D11—42no—
504C2×D11—42no—
505C2×D11—42no—
506C2×D11—42no—
507C2×D11—42no—
508C2×D11—42no—
509C2×D11—42no—
510C2×D11—816no—
511C2×D11—816no—
512C2×D11—84no—
513C2×D11—84no—
514C2×D11—84no—
515C4×C11—22no—
516C4×C11—42no—
517C4×C11—42no—
518C4×C11—42no—
519C4×C11#53412yes—
520C4×C11C2×H(5,𝔽2)11yescharacteristic
521C4×C11C2×H(5,𝔽2)11yescharacteristic
522Dic11—22no—
523Dic11—22no—
524Dic11—42no—
525C25—221no—
526C25—221no—
527C2×#41—114no—
528C2×#41—114no—
529C2×#41—442no—
530C2×#41—442no—
531C22×Q8—111no—
532C22×D4—21no—
533C22×D4—111no—
534C22×D4—111no—
535C22×D4—114no—
536C22×D4—111no—
537C22×D4—111no—
538C22×D4—111no—
539C22×D4—111no—
540C22×D4—114no—
541C22×D4—221no—
542C22×D4—221no—
543C22×D4—221no—
544C22×D4—221no—
545C22×D4—221no—
546C22×D4—222no—
547C22×D4—221no—
548C22×D4—221no—
549C22×D4—221no—
550C22×D4—221no—
551C22×D4—222no—
552C22×D4—442no—
553C22×D4—442no—
554C22×D4—442no—
555C22×D4—442no—
556C22×D4C22×D1111yescharacteristic
557C23×C4—111no—
558C23×C4—111no—
559C23×C4C22×D1111yescharacteristic
560C2×D8—114no—
561C2×D8—114no—
562C2×D8—114no—
563C2×D8—114no—
564C2×D8—442no—
565C2×D8—442no—
566C2×D8—442no—
567C2×D8—442no—
568C2×M16—114no—
569C2×M16—442no—
570C22×C8—111no—
571C22×C8—111no—
572C22×C8—114no—
573C22×C8—442no—
574C22×C8C22×D1111yescharacteristic
575C22×C8C22×D1111yescharacteristic
576#127—228no—
577#127—228no—
578#124—228no—
579#124—228no—
580#121—22no—
581#121—114no—
582#121—114no—
583#121—114no—
584#121—114no—
585#121—114no—
586#121—114no—
587#121—114no—
588#121—222no—
589#121—222no—
590#121—222no—
591#121—222no—
592#121—222no—
593#121—222no—
594#121—222no—
595#121C22×D1114yes—
596#120—228no—
597#120—228no—
598#120—228no—
599#120—228no—
600#117—22no—
601#117—114no—
602#117—222no—
603#117C22×D1114yescomplemented
604C2×C4⋊C4—111no—
605C2×C4⋊C4C22×D1111yescharacteristic
606C2×C4⋊C4C22×D1111yescharacteristic
607C2×C4⋊C4C22×D1111yescharacteristic
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—221no—
611C2×C22⋊C4—221no—
612C2×C22⋊C4—221no—
613C2×C22⋊C4—221no—
614C2×C22⋊C4—221no—
615C2×C22⋊C4—221no—
616C2×C22⋊C4—221no—
617C2×C22⋊C4—221no—
618C2×C42—21no—
619C2×C42—221no—
620#107—114no—
621#107C22×D1114yescomplemented
622#106—114no—
623#106C22×D1114yescomplemented
624#102—114no—
625#102—114no—
626#102—114no—
627#102—114no—
628#102—114no—
629#102—114no—
630#102C22×D1114yescomplemented
631#102C22×D1114yescomplemented
632C22⋊C8—114no—
633C22⋊C8—114no—
634C22⋊C8—114no—
635C22⋊C8C22×D1114yescomplemented
636C2×C11—42no—
637C2×C11—82no—
638C2×C11#319914yescomplemented
639C2×C11C2×#53411yescharacteristic
640C2×C11C2×#57611yescharacteristic
641C2×C11C2×#57611yescharacteristic
642D11—42no—
643D11—42no—
644D11—82no—
645D11—82no—
646D11—82no—
647C24—21no—
648C24—111no—
649C24—111no—
650C24—224no—
651C24—221no—
652C24—221no—
653C24—221no—
654C24—224no—
655C24—444no—
656C24—444no—
657C24—882no—
658C24—882no—
659C24—882no—
660C24—882no—
661C24D4×D1111yescharacteristic
662#41—448no—
663#41—444no—
664#41—444no—
665C2×Q8—114no—
666C2×Q8—442no—
667C2×D4—24no—
668C2×D4—21no—
669C2×D4—22no—
670C2×D4—22no—
671C2×D4—82no—
672C2×D4—114no—
673C2×D4—114no—
674C2×D4—114no—
675C2×D4—112no—
676C2×D4—112no—
677C2×D4—112no—
678C2×D4—224no—
679C2×D4—224no—
680C2×D4—224no—
681C2×D4—224no—
682C2×D4—224no—
683C2×D4—224no—
684C2×D4—224no—
685C2×D4—224no—
686C2×D4—221no—
687C2×D4—221no—
688C2×D4—221no—
689C2×D4—224no—
690C2×D4—222no—
691C2×D4—222no—
692C2×D4—222no—
693C2×D4—222no—
694C2×D4—222no—
695C2×D4—222no—
696C2×D4—444no—
697C2×D4—444no—
698C2×D4—442no—
699C2×D4—444no—
700C2×D4—448no—
701C2×D4—444no—
702C2×D4—444no—
703C2×D4—448no—
704C2×D4—442no—
705C2×D4—442no—
706C2×D4—444no—
707C2×D4—882no—
708C2×D4—882no—
709C2×D4—882no—
710C2×D4—882no—
711C2×D4—882no—
712C2×D4—882no—
713C2×D4—882no—
714C2×D4C23×D1112yes—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—111no—
721C22×C4—111no—
722C22×C4—112no—
723C22×C4—112no—
724C22×C4—112no—
725C22×C4—112no—
726C22×C4—222no—
727C22×C4—222no—
728C22×C4—222no—
729C22×C4—222no—
730C22×C4—221no—
731C22×C4D4×D1112yes—
732C22×C4D4×D1111yescharacteristic
733C22×C4C23×D1112yes—
734C22×C4C23×D1111yescharacteristic
735D8—444no—
736D8—444no—
737D8—444no—
738D8—444no—
739M16—444no—
740C2×C8—22no—
741C2×C8—22no—
742C2×C8—112no—
743C2×C8—112no—
744C2×C8—222no—
745C2×C8—222no—
746C2×C8—444no—
747C2×C8C23×D1112yes—
748C2×C8C23×D1112yes—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—112no—
753C4⋊C4—221no—
754C4⋊C4C23×D1112yes—
755C4⋊C4C23×D1112yes—
756C4⋊C4C23×D1112yes—
757C22⋊C4—24no—
758C22⋊C4—24no—
759C22⋊C4—224no—
760C22⋊C4—224no—
761C22⋊C4—224no—
762C22⋊C4—224no—
763C22⋊C4—224no—
764C22⋊C4—224no—
765C22⋊C4—224no—
766C22⋊C4—224no—
767C42—24no—
768C42—224no—
769C11C2×#319911yescharacteristic, complemented, Sylow
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—42no—
775C23—42no—
776C23—42no—
777C23—112no—
778C23—112no—
779C23—222no—
780C23—222no—
781C23—222no—
782C23—222no—
783C23—222no—
784C23—222no—
785C23—222no—
786C23—222no—
787C23—222no—
788C23—448no—
789C23—448no—
790C23—442no—
791C23—442no—
792C23—442no—
793C23—442no—
794C23—442no—
795C23—442no—
796C23—442no—
797C23—442no—
798C23—442no—
799C23—884no—
800C23—884no—
801C23—884no—
802C23—884no—
803C23—8816no—
804C23—8816no—
805C23C2×D4×D1112yes—
806C23C2×D4×D1111yescharacteristic
807Q8—444no—
808D4—22no—
809D4—22no—
810D4—42no—
811D4—84no—
812D4—222no—
813D4—222no—
814D4—222no—
815D4—222no—
816D4—222no—
817D4—222no—
818D4—444no—
819D4—448no—
820D4—444no—
821D4—444no—
822D4—448no—
823D4—442no—
824D4—442no—
825D4—442no—
826D4—884no—
827D4—884no—
828D4—884no—
829D4—884no—
830D4—884no—
831D4—884no—
832D4—884no—
833C2×C4—22no—
834C2×C4—24no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—112no—
844C2×C4—112no—
845C2×C4—222no—
846C2×C4—222no—
847C2×C4—224no—
848C2×C4—224no—
849C2×C4—222no—
850C2×C4—222no—
851C2×C4—222no—
852C2×C4—222no—
853C2×C4—222no—
854C2×C4—442no—
855C2×C4C2×D4×D1112yes—
856C2×C4C2×D4×D1111yescharacteristic
857C2×C4#6704212yes—
858C2×C4#6704212yes—
859C2×C4C24×D1111yescharacteristic
860C8—22no—
861C8—22no—
862C8—222no—
863C8—222no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—44no—
868C22—42no—
869C22—42no—
870C22—42no—
871C22—84no—
872C22—222no—
873C22—222no—
874C22—222no—
875C22—222no—
876C22—222no—
877C22—222no—
878C22—444no—
879C22—444no—
880C22—442no—
881C22—442no—
882C22—442no—
883C22—442no—
884C22—442no—
885C22—442no—
886C22—442no—
887C22—442no—
888C22—442no—
889C22—8816no—
890C22—8816no—
891C22—884no—
892C22—884no—
893C22—884no—
894C22#1062318412yes—
895C22#1062330012yes—
896C22#1062330512yes—
897C22C22×D4×D1111yescharacteristic
898C4—22no—
899C4—42no—
900C4—42no—
901C4—42no—
902C4—222no—
903C4—222no—
904C4—442no—
905C4#1062318412yes—
906C4C2×#6704211yescharacteristic
907C4C2×#6704211yescharacteristic
908C2—42no—
909C2—82no—
910C2—442no—
911C2—442no—
912C2—882no—
913C2—882no—
914C2—882no—
915C2#1307948014yesdirect product factor
916C2C2×#1062318411yescharacteristic
917C2C2×#1062330011yescharacteristic
918C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#482C2
socleC23×C11C22×D4
hypercenterC2×#482D11
hypocenterC11C2×#3199
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#10623056C2semidirect
2. C2×#10623138C2semidirect
3. #13079480C2direct (N × H)
4. C2×#10622498C2semidirect
5. C2×#10622479C2semidirect
6. C2×#10622616C2semidirect
7. C2×#10622478C2semidirect
8. C2×#10622395C2semidirect
9. C2×#10622496C2semidirect
10. C2×#10622388C2semidirect
11. C2×#10622345C2semidirect
12. C2×#10622386C2semidirect
13. C2×#10622386C2semidirect
14. C2×#10622649C2semidirect
15. C2×#10622340C2semidirect
16. C2×C11×#482C2semidirect
17. C22×D4×D11C22semidirect
19. C23×D44C22semidirect
21. C2×C11×#117C22semidirect
23. C2×#66991C22semidirect
30. C22×#4313C22semidirect
31. C22×C8×D11C22semidirect
33. #10623138C22semidirect
35. #10623056C22semidirect
38. C2×#66948C22semidirect
39. C2×#66948C22semidirect
40. C2×#66948C22semidirect
41. C2×#66945C22semidirect
48. C11×#482C22semidirect
49. C2×C11×#107C22semidirect
50. C2×C11×#106C22semidirect
51. C2×C11×#102C22semidirect
52. C2×C11×#102C22semidirect
53. C2×C11×C22⋊C8C22semidirect
54. C2×C22⋊(C11⋊C8)C22semidirect
55. C2×#66885C22semidirect
56. C2×#66885C22semidirect
57. C2×(C2×D11)⋊C8C22semidirect
58. C2×(C2×D11)⋊C8C22semidirect
59. #10622649C22semidirect
60. #10622616C22semidirect
61. C2×#66873C22semidirect
62. C2×#66873C22semidirect
63. C2×#66873C22semidirect
64. C2×#66873C22semidirect
65. C2×#66872C22semidirect
66. C2×#66871C22semidirect
67. #10622498C22semidirect
68. #10622496C22semidirect
69. #10622479C22semidirect
70. #10622478C22semidirect
71. #10622395C22semidirect
72. #10622388C22semidirect
73. #10622386C22semidirect
74. #10622386C22semidirect
75. #10622345C22semidirect
76. #10622340C22semidirect
90. C2×D4×D11C23semidirect
108. C22×D44C23semidirect
117. C11×#117C23semidirect
127. #66991C23semidirect
151. C2×#4313C23semidirect
153. C2×C8×D11C23semidirect
161. #66948C23semidirect
162. #66948C23semidirect
163. #66948C23semidirect
165. #66945C23semidirect
172. C11×#107C23semidirect
173. C11×#106C23semidirect
174. C11×#102C23semidirect
175. C11×#102C23semidirect
176. C11×C22⋊C8C23semidirect
177. C22⋊(C11⋊C8)C23semidirect
178. #66885C23semidirect
179. #66885C23semidirect
180. (C2×D11)⋊C8C23semidirect
181. (C2×D11)⋊C8C23semidirect
182. #66873C23semidirect
183. #66873C23semidirect
184. #66873C23semidirect
185. #66873C23semidirect
186. #66872C23semidirect
187. #66871C23semidirect
317. C2×#482D11semidirect
451. C2×#117C2×D11semidirect
455. #482C2×D11semidirect
465. C2×#107C2×D11semidirect
467. C2×#106C2×D11semidirect
474. C2×#102C2×D11semidirect
475. C2×#102C2×D11semidirect
480. C2×C22⋊C8C2×D11semidirect
603. #117C22×D11semidirect
621. #107C22×D11semidirect
623. #106C22×D11semidirect
630. #102C22×D11semidirect
631. #102C22×D11semidirect
635. C22⋊C8C22×D11semidirect
638. C2×C11#3199semidirect
769. C11C2×#3199semidirect
915. C2#13079480direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230562
C2×#106231382
#130794802
C2×#106224982
C2×#106224792
C2×#106226162
C2×#106224782
C2×#106223952
C2×#106224962
C2×#106223882
C2×#106223452
C2×#106223862
C2×#106226492
C2×#106223402
C2×C11×#4822
C2×#319911