Finite Group Databasebeta

← C2×#13080845 #15630600

Subgroups — C2×#13080845 #15630600

Order 2816.

2566 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623064C211yesmaximal, characteristic, complemented
2C2×#10623140C211yesmaximal, characteristic
3#13080845C2116yesmaximal, direct product factor
4C2×#10622373C211yesmaximal, characteristic, complemented
5C2×#10622479C211yesmaximal, characteristic, complemented
6C2×#10622503C211yesmaximal, characteristic, complemented
7C2×#10622499C211yesmaximal, characteristic, complemented
8C2×#10622655C211yesmaximal, characteristic, complemented
9C2×#10622375C211yesmaximal, characteristic, complemented
10C2×#10622344C211yesmaximal, characteristic, complemented
11C2×#10622389C211yesmaximal, characteristic, complemented
12C2×#10622465C211yesmaximal, characteristic, complemented
13C2×#10622342C211yesmaximal, characteristic, complemented
14C2×#10622614C211yesmaximal, characteristic, complemented
15C2×#10622383C211yesmaximal, characteristic, complemented
16C2×C11×#482C211yesmaximal, characteristic, complemented
17C22×D4×D11—21no—
18C22×D4×D11C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic, complemented
22C2×#66993C2211yescharacteristic
23C2×#66990—21no—
24C22×#4324C2211yescharacteristic, complemented
25C2×C4×C22⋊D11C2211yescharacteristic
26C2×#66977C2211yescharacteristic, complemented
27C22×#4318C2211yescharacteristic, complemented
28C22×#4314C2211yescharacteristic
29C22×#4314C2211yescharacteristic, complemented
30C22×#4313C2211yescharacteristic, complemented
31#10623140—24no—
32#10623140C2218yes—
33#10623064—24no—
34#10623064C2218yescomplemented
35C2×#66950C2211yescharacteristic, complemented
36C2×#66948C2211yescharacteristic
37C2×#66946C2211yescharacteristic
38C2×#66945C2211yescharacteristic, complemented
39C2×#66941C2211yescharacteristic, complemented
40C2×#66940C2211yescharacteristic, complemented
41C2×#66938—21no—
42C2×#66937—21no—
43C2×#66935—21no—
44C2×#66932—21no—
45C2×#66929—21no—
46C2×C4×Dic22—21no—
47C11×#482C2218yescomplemented
48C2×C11×#107C2211yescharacteristic, complemented
49C2×C11×#106C2211yescharacteristic, complemented
50C2×C11×#102C2211yescharacteristic, complemented
51C2×C11×#102C2211yescharacteristic, complemented
52C2×C11×C22⋊C8C2211yescharacteristic, complemented
53C2×#66896C2211yescharacteristic, complemented
54C2×#66885C2211yescharacteristic
55C2×#66885C2211yescharacteristic, complemented
56C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
57C2×Dic11⋊C8C2211yescharacteristic, complemented
58C2×C8×Dic11C2211yescharacteristic, complemented
59#10622655C2218yescomplemented
60#10622614C2218yescomplemented
61C2×#66874C2211yescharacteristic, complemented
62C2×#66873C2211yescharacteristic
63C2×#66873C2211yescharacteristic
64C2×#66873C2211yescharacteristic, complemented
65C2×#66873C2211yescharacteristic, complemented
66C2×#66871C2211yescharacteristic, complemented
67#10622503C2218yescomplemented
68#10622499C2218yescomplemented
69#10622479C2218yescomplemented
70#10622465C2218yescomplemented
71#10622389C2218yescomplemented
72#10622383C2218yescomplemented
73#10622375C2218yescomplemented
74#10622373C2218yescomplemented
75#10622344C2218yescomplemented
76#10622342C2218yescomplemented
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
86C2×D4×D11—28no—
87C2×D4×D11—24no—
88C2×D4×D11—22no—
89C2×D4×D11—42no—
90C2×D4×D11—48no—
91C2×D4×D11C2314yes—
92C22×D44—24no—
93C22×D44—21no—
94C22×D44—21no—
95C22×D44—22no—
96C22×D44—42no—
97C22×D44C2311yescharacteristic
98C22×D44C2314yes—
99C22×D44C2311yescharacteristic
100C22×C4×D11—21no—
101C22×C4×D11C2311yescharacteristic
102C22×Dic22—21no—
103C22×Dic22C2311yescharacteristic
104C22×C8×C11C2311yescharacteristic
105C22×C8×C11C2311yescharacteristic
106C11×#121—22no—
107C11×#121C2314yes—
108C11×#117—22no—
109C11×#117C2314yescomplemented
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4—21no—
115C2×C42×C11—21no—
116C2×C22⋊Dic11—21no—
117C2×C22⋊Dic11D411yescharacteristic
118#66993—22no—
119#66993C2314yes—
120#66990—28no—
121C2×#4324—42no—
122C2×#4324C2314yescomplemented
123C4×C22⋊D11D414yes—
124C4×C22⋊D11C2314yes—
125C2×(C2×D11)⋊C4—21no—
126C2×(C2×D11)⋊C4—21no—
127C2×(C2×D11)⋊C4—21no—
128C2×(C2×D11)⋊C4—21no—
129C2×(C2×D11)⋊C4D411yescharacteristic
130C2×C4⋊Dic11—21no—
131C2×C4⋊Dic11C2311yescharacteristic
132#66977—22no—
133#66977C2314yescomplemented
134C2×Dic11⋊C4—21no—
135C2×Dic11⋊C4—21no—
136C2×Dic11⋊C4—21no—
137C2×Dic11⋊C4D411yescharacteristic
138C2×C4×Dic11—21no—
139C2×C4×Dic11—21no—
140C2×C4×Dic11C2311yescharacteristic
141C2×#4318—42no—
142C2×#4318C2314yescomplemented
143C22×C11⋊C8C2311yescharacteristic
144C22×C11⋊C8C2311yescharacteristic
145C2×#4314—24no—
146C2×#4314—42no—
147C2×#4314C2314yes—
148C2×#4314C2314yescomplemented
149C2×#4313—42no—
150C2×#4313C2314yescomplemented
151#66950—22no—
152#66950C2314yescomplemented
153#66948—22no—
154#66948C2314yes—
155#66946—22no—
156#66946C2314yes—
157#66945—22no—
158#66945C2314yescomplemented
159#66941—22no—
160#66941C2314yescomplemented
161#66940—22no—
162#66940C2314yescomplemented
163#66938—28no—
164#66937—28no—
165#66935—28no—
166#66932—28no—
167#66929—28no—
168C4×Dic22—28no—
169C11×#107C2314yescomplemented
170C11×#106C2314yescomplemented
171C11×#102C2314yescomplemented
172C11×#102C2314yescomplemented
173C11×C22⋊C8C2314yescomplemented
174#66896C2314yescomplemented
175#66885C2314yes—
176#66885C2314yescomplemented
177(C2×D11)⋊C8C2314yescomplemented
178Dic11⋊C8C2314yescomplemented
179C8×Dic11C2314yescomplemented
180#66874C2314yescomplemented
181#66873C2314yes—
182#66873C2314yes—
183#66873C2314yescomplemented
184#66873C2314yescomplemented
185#66871C2314yescomplemented
186C2×#3324—111nomaximal, Sylow
187C24×C11—21no—
188C24×C11C2×D411yescharacteristic
189C23×D11—21no—
190C23×D11—21no—
191C23×D11—24no—
192C23×D11—24no—
193C23×D11—44no—
194C23×D11—44no—
195C23×D11—44no—
196C23×D11—44no—
197C23×D11—82no—
198C23×D11—82no—
199C23×D11C2×D411yescharacteristic
200C2×D4×C11—24no—
201C2×D4×C11—21no—
202C2×D4×C11—22no—
203C2×D4×C11—22no—
204C2×D4×C11—44no—
205C2×D4×C11C2412yes—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2×D412yes—
213C22×C4×C11C2412yes—
214C22×C4×C11C2411yescharacteristic
215C2×C22⋊D11—24no—
216C2×C22⋊D11—24no—
217C2×C22⋊D11—24no—
218C2×C22⋊D11—24no—
219C2×C22⋊D11—44no—
220C2×C22⋊D11—44no—
221C2×C22⋊D11—82no—
222C2×C22⋊D11C2×D414yes—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11C2×D411yescharacteristic
226C22×Dic11C2×D411yescharacteristic
227C22×Dic11C2×D411yescharacteristic
228D4×D11—28no—
229D4×D11—44no—
230D4×D11—48no—
231D4×D11—432no—
232C2×D44—24no—
233C2×D44—28no—
234C2×D44—21no—
235C2×D44—24no—
236C2×D44—21no—
237C2×D44—22no—
238C2×D44—22no—
239C2×D44—22no—
240C2×D44—44no—
241C2×D44—44no—
242C2×D44—48no—
243C2×D44—44no—
244C2×D44#4114yes—
245C2×D44C2412yes—
246C2×D44C2412yes—
247C2×C4×D11—24no—
248C2×C4×D11—22no—
249C2×C4×D11—22no—
250C2×C4×D11—44no—
251C2×C4×D11C2×D412yes—
252C2×C4×D11C2412yes—
253C2×Dic22—24no—
254C2×Dic22—21no—
255C2×Dic22—22no—
256C2×Dic22—22no—
257C2×Dic22—44no—
258C2×Dic22C2412yes—
259C2×C8×C11—22no—
260C2×C8×C11—22no—
261C2×C8×C11C2412yes—
262C2×C8×C11C2412yes—
263C11×C4⋊C4—21no—
264C11×C4⋊C4—21no—
265C11×C4⋊C4—21no—
266C11×C4⋊C4C2412yes—
267C11×C4⋊C4C2412yes—
268C11×C4⋊C4C2412yes—
269C11×C22⋊C4—24no—
270C11×C22⋊C4—24no—
271C42×C11—24no—
272C22⋊Dic11—24no—
273C22⋊Dic11C2×D414yes—
274#4324—44no—
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—24no—
281C4⋊Dic11—21no—
282C4⋊Dic11C2412yes—
283Dic11⋊C4—24no—
284Dic11⋊C4—24no—
285Dic11⋊C4—24no—
286Dic11⋊C4C2×D414yes—
287C4×Dic11—24no—
288C4×Dic11—24no—
289C4×Dic11C2×D412yes—
290C4×Dic11C2412yes—
291#4318—44no—
292C2×C11⋊C8—22no—
293C2×C11⋊C8—22no—
294C2×C11⋊C8C2412yes—
295C2×C11⋊C8C2412yes—
296#4314—28no—
297#4314—44no—
298#4313—44no—
299C2×#556—111no—
300C2×D42—111no—
301#3324—1116no—
302C2×#486—111no—
303C2×#482—111no—
304C2×#482D1111yescharacteristic, complemented
305C2×#474—111no—
306C2×#468—111no—
307C2×#468—111no—
308C2×#460—111no—
309C2×#450—111no—
310C2×#450—111no—
311C2×C4×SD16—111no—
312C2×#436—111no—
313C2×#418—111no—
314C2×#418—111no—
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—24no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—48no—
331C22×D11—48no—
332C22×D11—48no—
333C22×D11—42no—
334C22×D11—42no—
335C22×D11—48no—
336C22×D11—42no—
337C22×D11—42no—
338C22×D11—42no—
339C22×D11—84no—
340C22×D11—84no—
341C22×D11—816no—
342C22×D11—816no—
343C22×D11C22×D412yes—
344D4×C11—22no—
345D4×C11—22no—
346D4×C11—48no—
347D4×C11—42no—
348C2×C4×C11—22no—
349C2×C4×C11—24no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—42no—
356C2×C4×C11—42no—
357C2×C4×C11—42no—
358C2×C4×C11C22×D412yes—
359C2×C4×C11C22×D411yescharacteristic
360C2×C4×C11C2×#4112yes—
361C2×C4×C11H(5,𝔽2)12yes—
362C2×C4×C11C2511yescharacteristic
363C22⋊D11—28no—
364C22⋊D11—48no—
365C22⋊D11—48no—
366C22⋊D11—84no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—42no—
372C2×Dic11—42no—
373C2×Dic11AGL(1,ℤ/8)14yes—
374C2×Dic11C22×D412yes—
375C2×Dic11C22×D412yes—
376C2×Dic11C22×D412yes—
377D44—24no—
378D44—22no—
379D44—22no—
380D44—22no—
381D44—48no—
382D44—48no—
383D44—42no—
384D44C2×#4114yes—
385C4×D11—24no—
386C4×D11—22no—
387C4×D11—22no—
388C4×D11—48no—
389Dic22—22no—
390Dic22—22no—
391Dic22—42no—
392Dic22—48no—
393C8×C11—22no—
394C8×C11—22no—
395C11⋊C8—22no—
396C11⋊C8—22no—
397C23×D4—111no—
398C23×D4—111no—
399C23×D4—221no—
400C22×SD16—111no—
401C22×SD16—111no—
402C22×SD16—111no—
403C22×M16—111no—
404C22×M16—111no—
405#556—118no—
406#556—224no—
407D42—118no—
408D42—224no—
409C2×C4⋊Q8—111no—
410C2×#127—111no—
411C2×#126—221no—
412C2×#126—221no—
413C2×#124—221no—
414C2×C22⋊Q8—111no—
415C2×C22⋊Q8—111no—
416C2×#121—111no—
417C2×#121—221no—
418C2×#121C2×D1111yescharacteristic
419C2×#120—221no—
420C2×#120—221no—
421C2×C4×Q8—111no—
422C2×C4×Q8—221no—
423C2×C4×D4—111no—
424C2×C4×D4—111no—
425C2×#117—111no—
426C2×#117C2×D1111yescharacteristic, complemented
427#486—118no—
428#482—118no—
429#482C2×D1118yescomplemented
430#474—118no—
431#468—118no—
432#468—118no—
433#460—118no—
434#450—118no—
435#450—118no—
436C4×SD16—118no—
437#436—118no—
438C2×#107—111no—
439C2×#107C2×D1111yescharacteristic, complemented
440C2×#106C2×D1111yescharacteristic, complemented
441C2×C4⋊C8—111no—
442#418—118no—
443#418—118no—
444C2×#103—111no—
445C2×#102—111no—
446C2×#102—111no—
447C2×#102—111no—
448C2×#102—111no—
449C2×#102—111no—
450C2×#102—111no—
451C2×#102—111no—
452C2×#102C2×D1111yescharacteristic, complemented
453C2×#102C2×D1111yescharacteristic, complemented
454C2×C22⋊C8—111no—
455C2×C22⋊C8C2×D1111yescharacteristic, complemented
456C2×C4×C8—111no—
457C22×C11—22no—
458C22×C11—22no—
459C22×C11—22no—
460C22×C11—44no—
461C22×C11—42no—
462C22×C11—42no—
463C22×C11—42no—
464C22×C11—84no—
465C22×C11#54612yes—
466C22×C11C2×AGL(1,ℤ/8)12yes—
467C22×C11#57712yes—
468C22×C11C23×D411yescharacteristic
469C2×D11—24no—
470C2×D11—22no—
471C2×D11—22no—
472C2×D11—22no—
473C2×D11—42no—
474C2×D11—44no—
475C2×D11—48no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—42no—
479C2×D11—42no—
480C2×D11—816no—
481C2×D11—816no—
482C2×D11—84no—
483C4×C11—22no—
484C4×C11—42no—
485C4×C11—42no—
486C4×C11—42no—
487C4×C11#54612yes—
488C4×C11C22×#4111yescharacteristic
489C4×C11C2×H(5,𝔽2)11yescharacteristic
490Dic11—22no—
491Dic11—22no—
492Dic11—42no—
493Dic11—42no—
494Dic11C2×AGL(1,ℤ/8)14yes—
495C25—221no—
496C25—221no—
497C22×Q8—111no—
498C22×Q8—221no—
499C22×D4—21no—
500C22×D4—111no—
501C22×D4—114no—
502C22×D4—111no—
503C22×D4—111no—
504C22×D4—114no—
505C22×D4—224no—
506C22×D4—221no—
507C22×D4—222no—
508C22×D4—221no—
509C22×D4—221no—
510C22×D4—221no—
511C22×D4—224no—
512C22×D4—228no—
513C22×D4—221no—
514C22×D4—222no—
515C22×D4—442no—
516C22×D4—442no—
517C22×D4—448no—
518C22×D4C22×D1111yescharacteristic
519C23×C4—111no—
520C23×C4—221no—
521C23×C4C22×D1111yescharacteristic
522C2×SD16—114no—
523C2×SD16—114no—
524C2×SD16—114no—
525C2×SD16—224no—
526C2×SD16—442no—
527C2×SD16—442no—
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#126—228no—
541#126—228no—
542#124—228no—
543C22⋊Q8—114no—
544C22⋊Q8—114no—
545C22⋊Q8—222no—
546C22⋊Q8—222no—
547#121—22no—
548#121—114no—
549#121—228no—
550#121—222no—
551#121C22×D1114yes—
552#120—228no—
553#120—228no—
554C4×Q8—114no—
555C4×Q8—228no—
556C4×Q8—222no—
557C4×D4—114no—
558C4×D4—114no—
559C4×D4—114no—
560C4×D4—222no—
561#117—22no—
562#117—114no—
563#117—222no—
564#117C22×D1114yescomplemented
565C2×C4⋊C4—111no—
566C2×C4⋊C4—111no—
567C2×C4⋊C4—221no—
568C2×C4⋊C4—221no—
569C2×C4⋊C4—221no—
570C2×C4⋊C4—221no—
571C2×C4⋊C4C22×D1111yescharacteristic
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×C22⋊C4—221no—
582C2×C22⋊C4—221no—
583C2×C42—21no—
584C2×C42—111no—
585C2×C42—221no—
586C2×C42—221no—
587#107—114no—
588#107C22×D1114yescomplemented
589#106C22×D1114yescomplemented
590C4⋊C8—114no—
591#103—114no—
592#102—114no—
593#102—114no—
594#102—114no—
595#102—114no—
596#102—114no—
597#102—114no—
598#102—114no—
599#102C22×D1114yescomplemented
600#102C22×D1114yescomplemented
601C22⋊C8—114no—
602C22⋊C8C22×D1114yescomplemented
603C4×C8—114no—
604C2×C11—42no—
605C2×C11—82no—
606C2×C11#332414yescomplemented
607C2×C11C2×#54611yescharacteristic
608C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
609C2×C11C2×#57711yescharacteristic
610D11—42no—
611D11—44no—
612D11—82no—
613C24—21no—
614C24—111no—
615C24—224no—
616C24—221no—
617C24—221no—
618C24—224no—
619C24—444no—
620C24—444no—
621C24—444no—
622C24—444no—
623C24—882no—
624C24—882no—
625C24D4×D1111yescharacteristic
626C2×Q8—112no—
627C2×Q8—224no—
628C2×Q8—221no—
629C2×Q8—222no—
630C2×Q8—222no—
631C2×Q8—444no—
632C2×D4—24no—
633C2×D4—21no—
634C2×D4—22no—
635C2×D4—22no—
636C2×D4—44no—
637C2×D4—114no—
638C2×D4—114no—
639C2×D4—112no—
640C2×D4—112no—
641C2×D4—228no—
642C2×D4—224no—
643C2×D4—224no—
644C2×D4—224no—
645C2×D4—224no—
646C2×D4—224no—
647C2×D4—228no—
648C2×D4—221no—
649C2×D4—224no—
650C2×D4—221no—
651C2×D4—222no—
652C2×D4—222no—
653C2×D4—222no—
654C2×D4—444no—
655C2×D4—448no—
656C2×D4—444no—
657C2×D4—444no—
658C2×D4—444no—
659C2×D4—444no—
660C2×D4—448no—
661C2×D4—444no—
662C2×D4—4432no—
663C2×D4—882no—
664C2×D4C23×D1112yes—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—111no—
671C22×C4—111no—
672C22×C4—111no—
673C22×C4—112no—
674C22×C4—112no—
675C22×C4—224no—
676C22×C4—222no—
677C22×C4—222no—
678C22×C4—221no—
679C22×C4—221no—
680C22×C4—444no—
681C22×C4D4×D1112yes—
682C22×C4D4×D1111yescharacteristic
683C22×C4C23×D1112yes—
684C22×C4C23×D1111yescharacteristic
685SD16—228no—
686SD16—444no—
687SD16—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—21no—
700C4⋊C4—21no—
701C4⋊C4—114no—
702C4⋊C4—112no—
703C4⋊C4—224no—
704C4⋊C4—224no—
705C4⋊C4—224no—
706C4⋊C4—221no—
707C4⋊C4—224no—
708C4⋊C4C23×D1112yes—
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—
718C22⋊C4—224no—
719C22⋊C4—224no—
720C42—24no—
721C42—112no—
722C42—112no—
723C42—224no—
724C42—224no—
725C11C2×#332411yescharacteristic, complemented, Sylow
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—112no—
734C23—222no—
735C23—222no—
736C23—222no—
737C23—224no—
738C23—222no—
739C23—222no—
740C23—448no—
741C23—448no—
742C23—448no—
743C23—448no—
744C23—442no—
745C23—442no—
746C23—442no—
747C23—442no—
748C23—442no—
749C23—884no—
750C23—884no—
751C23—8816no—
752C23—8816no—
753C23C2×D4×D1112yes—
754C23C2×D4×D1111yescharacteristic
755Q8—222no—
756Q8—222no—
757Q8—448no—
758Q8—442no—
759D4—22no—
760D4—22no—
761D4—48no—
762D4—42no—
763D4—114no—
764D4—228no—
765D4—224no—
766D4—222no—
767D4—222no—
768D4—222no—
769D4—448no—
770D4—448no—
771D4—448no—
772D4—448no—
773D4—442no—
774D4—884no—
775C2×C4—22no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—114no—
786C2×C4—112no—
787C2×C4—112no—
788C2×C4—112no—
789C2×C4—222no—
790C2×C4—222no—
791C2×C4—224no—
792C2×C4—222no—
793C2×C4—222no—
794C2×C4—222no—
795C2×C4—222no—
796C2×C4—448no—
797C2×C4—442no—
798C2×C4—442no—
799C2×C4C2×D4×D1112yes—
800C2×C4C2×D4×D1111yescharacteristic
801C2×C4#41×D1112yes—
802C2×C4#6704212yes—
803C2×C4C24×D1111yescharacteristic
804C8—22no—
805C8—22no—
806C8—222no—
807C8—222no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—44no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—84no—
816C22—222no—
817C22—224no—
818C22—222no—
819C22—222no—
820C22—444no—
821C22—448no—
822C22—442no—
823C22—442no—
824C22—442no—
825C22—442no—
826C22—442no—
827C22—8816no—
828C22—8816no—
829C22—884no—
830C22#1062318512yes—
831C22#1062330112yes—
832C22D11×AGL(1,ℤ/8)12yes—
833C22C22×D4×D1111yescharacteristic
834C4—22no—
835C4—42no—
836C4—42no—
837C4—42no—
838C4—114no—
839C4—222no—
840C4—222no—
841C4—442no—
842C4—442no—
843C4#1062318512yes—
844C4C2×#41×D1111yescharacteristic
845C4C2×#6704211yescharacteristic
846C2—42no—
847C2—82no—
848C2—442no—
849C2—444no—
850C2—882no—
851C2#1308084514yesdirect product factor
852C2C2×#1062318511yescharacteristic
853C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
854C2C2×#1062330111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#482C2
socleC23×C11C22×D4
prime radicalC2×#10623140C2
hypercenterC2×#482D11
hypocenterC11C2×#3324
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×#10623064C2semidirect
3. #13080845C2direct (N × H)
4. C2×#10622373C2semidirect
5. C2×#10622479C2semidirect
6. C2×#10622503C2semidirect
7. C2×#10622499C2semidirect
8. C2×#10622655C2semidirect
9. C2×#10622375C2semidirect
10. C2×#10622344C2semidirect
11. C2×#10622389C2semidirect
12. C2×#10622465C2semidirect
13. C2×#10622342C2semidirect
14. C2×#10622614C2semidirect
15. C2×#10622383C2semidirect
16. C2×C11×#482C2semidirect
21. C2×C11×#117C22semidirect
24. C22×#4324C22semidirect
26. C2×#66977C22semidirect
27. C22×#4318C22semidirect
29. C22×#4314C22semidirect
30. C22×#4313C22semidirect
34. #10623064C22semidirect
35. C2×#66950C22semidirect
38. C2×#66945C22semidirect
39. C2×#66941C22semidirect
40. C2×#66940C22semidirect
47. C11×#482C22semidirect
48. C2×C11×#107C22semidirect
49. C2×C11×#106C22semidirect
50. C2×C11×#102C22semidirect
51. C2×C11×#102C22semidirect
52. C2×C11×C22⋊C8C22semidirect
53. C2×#66896C22semidirect
55. C2×#66885C22semidirect
56. C2×(C2×D11)⋊C8C22semidirect
57. C2×Dic11⋊C8C22semidirect
58. C2×C8×Dic11C22semidirect
59. #10622655C22semidirect
60. #10622614C22semidirect
61. C2×#66874C22semidirect
64. C2×#66873C22semidirect
65. C2×#66873C22semidirect
66. C2×#66871C22semidirect
67. #10622503C22semidirect
68. #10622499C22semidirect
69. #10622479C22semidirect
70. #10622465C22semidirect
71. #10622389C22semidirect
72. #10622383C22semidirect
73. #10622375C22semidirect
74. #10622373C22semidirect
75. #10622344C22semidirect
76. #10622342C22semidirect
109. C11×#117C23semidirect
122. C2×#4324C23semidirect
133. #66977C23semidirect
142. C2×#4318C23semidirect
148. C2×#4314C23semidirect
150. C2×#4313C23semidirect
152. #66950C23semidirect
158. #66945C23semidirect
160. #66941C23semidirect
162. #66940C23semidirect
169. C11×#107C23semidirect
170. C11×#106C23semidirect
171. C11×#102C23semidirect
172. C11×#102C23semidirect
173. C11×C22⋊C8C23semidirect
174. #66896C23semidirect
176. #66885C23semidirect
177. (C2×D11)⋊C8C23semidirect
178. Dic11⋊C8C23semidirect
179. C8×Dic11C23semidirect
180. #66874C23semidirect
183. #66873C23semidirect
184. #66873C23semidirect
185. #66871C23semidirect
304. C2×#482D11semidirect
426. C2×#117C2×D11semidirect
429. #482C2×D11semidirect
439. C2×#107C2×D11semidirect
440. C2×#106C2×D11semidirect
452. C2×#102C2×D11semidirect
453. C2×#102C2×D11semidirect
455. C2×C22⋊C8C2×D11semidirect
564. #117C22×D11semidirect
588. #107C22×D11semidirect
589. #106C22×D11semidirect
599. #102C22×D11semidirect
600. #102C22×D11semidirect
602. C22⋊C8C22×D11semidirect
606. C2×C11#3324semidirect
725. C11C2×#3324semidirect
851. C2#13080845direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230642
C2×#106231402
#130808452
C2×#106223732
C2×#106224792
C2×#106225032
C2×#106224992
C2×#106226552
C2×#106223752
C2×#106223442
C2×#106223892
C2×#106224652
C2×#106223422
C2×#106226142
C2×#106223832
C2×C11×#4822
C2×#332411