Finite Group Databasebeta

← C2×#13080435 #15630107

Subgroups — C2×#13080435 #15630107

Order 2816.

2642 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623166C211yesmaximal, characteristic, complemented
2C2×#10623140C211yesmaximal, characteristic
3#13080435C2116yesmaximal, direct product factor
4C2×#10622373C211yesmaximal, characteristic, complemented
5C2×#10622476C211yesmaximal, characteristic, complemented
6C2×#10622647C211yesmaximal, characteristic, complemented
7C2×#10622483C211yesmaximal, characteristic, complemented
8C2×#10622420C211yesmaximal, characteristic, complemented
9C2×#10622776C211yesmaximal, characteristic, complemented
10C2×#10622659C211yesmaximal, characteristic, complemented
11C2×#10622782C211yesmaximal, characteristic, complemented
12C2×#10622401C211yesmaximal, characteristic, complemented
13C2×C8×C22⋊D11C211yesmaximal, characteristic, complemented
14C22×#66885C211yesmaximal, characteristic, complemented
15C2×D11×#102C211yesmaximal, characteristic, complemented
16C2×C11×#465C211yesmaximal, characteristic, complemented
17C22×D4×D11—21no—
18C22×D4×D11C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C22×C11×SD16C2211yescharacteristic, complemented
21C23×C8×C11C2211yescharacteristic, complemented
22C2×C11×C22⋊Q8C2211yescharacteristic, complemented
23C2×C11×#121C2211yescharacteristic
24C2×#66999C2211yescharacteristic, complemented
25C2×Q8×Dic11C2211yescharacteristic, complemented
26C22×#4325C2211yescharacteristic
27C22×#4325C2211yescharacteristic, complemented
28C2×#66993C2211yescharacteristic
29C2×#66990—21no—
30C2×C4×C22⋊D11C2211yescharacteristic
31C22×C4⋊Dic11C2211yescharacteristic, complemented
32C22×C8×D11C2211yescharacteristic, complemented
33#10623166—24no—
34#10623166C2218yescomplemented
35#10623140—24no—
36#10623140C2218yes—
37C2×#66950—21no—
38C2×#66948C2211yescharacteristic
39C2×#66946C2211yescharacteristic
40C2×C4⋊C4×D11C2211yescharacteristic, complemented
41C2×#66942—21no—
42C2×#66941C2211yescharacteristic, complemented
43C2×#66937—21no—
44C2×#66935—21no—
45C2×(C22⋊D11)⋊C4—21no—
46C2×#66931—21no—
47C11×#465C2218yescomplemented
48C2×C11×#106C2211yescharacteristic, complemented
49C2×C11×#103C2211yescharacteristic, complemented
50C2×C11×#102C2211yescharacteristic, complemented
51C2×#66896C2211yescharacteristic, complemented
52C2×#66896C2211yescharacteristic, complemented
53C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
54#10622782C2218yescomplemented
55#10622776C2218yescomplemented
56C2×#66885C2211yescharacteristic
57C2×#66885C2211yescharacteristic
58C2×#66885C2218yescomplemented
59C2×#66885C2211yescharacteristic, complemented
60C2×#66885C2211yescharacteristic, complemented
61C8×C22⋊D11C2218yescomplemented
62C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
63C2×Dic11⋊C8C2211yescharacteristic, complemented
64C2×C8×Dic11C2211yescharacteristic, complemented
65#10622659C2218yescomplemented
66#10622647C2218yescomplemented
67C2×#66873C2211yescharacteristic
68C2×#66873C2211yescharacteristic, complemented
69C2×#66872C2211yescharacteristic, complemented
70C2×#66872C2211yescharacteristic, complemented
71#10622483C2218yescomplemented
72#10622476C2218yescomplemented
73#10622420C2218yescomplemented
74#10622401C2218yescomplemented
75D11×#102C2218yescomplemented
76#10622373C2218yescomplemented
77C24×D11—21no—
78C24×D11—21no—
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11—21no—
81C22×D4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C22×C22⋊D11D411yescharacteristic
87C23×Dic11—21no—
88C2×D4×D11—28no—
89C2×D4×D11—24no—
90C2×D4×D11—22no—
91C2×D4×D11—42no—
92C2×D4×D11—48no—
93C2×D4×D11C2314yes—
94C22×D44—24no—
95C22×D44—21no—
96C22×D44—21no—
97C22×D44—22no—
98C22×D44—42no—
99C22×D44C2311yescharacteristic
100C22×D44C2314yes—
101C22×D44C2311yescharacteristic
102C22×C4×D11—21no—
103C22×C4×D11—21no—
104C22×C4×D11C2311yescharacteristic
105C22×Dic22—21no—
106C2×C11×SD16—42no—
107C2×C11×SD16C2314yescomplemented
108C22×C8×C11—42no—
109C22×C8×C11C2311yescharacteristic
110C22×C8×C11C2311yescharacteristic
111C22×C8×C11C2314yescomplemented
112C11×C22⋊Q8—22no—
113C11×C22⋊Q8C2314yescomplemented
114C11×#121—22no—
115C11×#121C2314yes—
116C2×C11×C4⋊C4—21no—
117C2×C11×C4⋊C4C2311yescharacteristic
118C2×C11×C4⋊C4C2311yescharacteristic
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4—21no—
121C2×C22⋊Dic11D411yescharacteristic
122#66999—22no—
123#66999C2314yescomplemented
124Q8×Dic11—22no—
125Q8×Dic11C2314yescomplemented
126C2×#4325—24no—
127C2×#4325—42no—
128C2×#4325C2314yes—
129C2×#4325C2314yescomplemented
130#66993—22no—
131#66993C2314yes—
132#66990—28no—
133C4×C22⋊D11D414yes—
134C4×C22⋊D11C2314yes—
135C2×(C2×D11)⋊C4—21no—
136C2×(C2×D11)⋊C4—21no—
137C2×(C2×D11)⋊C4—21no—
138C2×(C2×D11)⋊C4D411yescharacteristic
139C2×C4⋊Dic11—21no—
140C2×C4⋊Dic11—22no—
141C2×C4⋊Dic11—21no—
142C2×C4⋊Dic11C2311yescharacteristic
143C2×C4⋊Dic11C2311yescharacteristic
144C2×C4⋊Dic11C2314yescomplemented
145C2×Dic11⋊C4—21no—
146C2×Dic11⋊C4—21no—
147C2×Dic11⋊C4—21no—
148C2×Dic11⋊C4D411yescharacteristic
149C2×C4×Dic11—21no—
150C2×C4×Dic11C2311yescharacteristic
151C22×C11⋊C8C2311yescharacteristic
152C22×C11⋊C8C2311yescharacteristic
153C2×C8×D11—42no—
154C2×C8×D11C2314yescomplemented
155#66950—28no—
156#66948—22no—
157#66948C2314yes—
158#66946—22no—
159#66946C2314yes—
160C4⋊C4×D11—22no—
161C4⋊C4×D11C2314yescomplemented
162#66942—28no—
163#66941—22no—
164#66941C2314yescomplemented
165#66937—28no—
166#66935—28no—
167(C22⋊D11)⋊C4—28no—
168#66931—28no—
169C11×#106C2314yescomplemented
170C11×#103C2314yescomplemented
171C11×#102C2314yescomplemented
172#66896C2314yescomplemented
173#66896C2314yescomplemented
174C22⋊(C11⋊C8)C2314yescomplemented
175#66885C2314yes—
176#66885C2314yes—
177#66885C2314yescomplemented
178#66885C2314yescomplemented
179(C2×D11)⋊C8C2314yescomplemented
180Dic11⋊C8C2314yescomplemented
181C8×Dic11C2314yescomplemented
182#66873C2314yes—
183#66873C2314yescomplemented
184#66872C2314yescomplemented
185#66872C2314yescomplemented
186C2×#3295—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×Q8×C11—21no—
201C2×Q8×C11—22no—
202C2×Q8×C11—22no—
203C2×Q8×C11C2412yes—
204C2×D4×C11—24no—
205C2×D4×C11—21no—
206C2×D4×C11—22no—
207C2×D4×C11—22no—
208C2×D4×C11—44no—
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—44no—
223C2×C22⋊D11—44no—
224C2×C22⋊D11—82no—
225C2×C22⋊D11SD1618yescomplemented
226C2×C22⋊D11C2×D414yes—
227C22×Dic11—21no—
228C22×Dic11—21no—
229C22×Dic11—24no—
230C22×Dic11—82no—
231C22×Dic11C2×D411yescharacteristic
232C22×Dic11C2×D411yescharacteristic
233C22×Dic11C2×D411yescharacteristic
234D4×D11—28no—
235D4×D11—44no—
236D4×D11—48no—
237D4×D11—432no—
238C2×D44—24no—
239C2×D44—28no—
240C2×D44—21no—
241C2×D44—24no—
242C2×D44—21no—
243C2×D44—22no—
244C2×D44—22no—
245C2×D44—22no—
246C2×D44—44no—
247C2×D44—44no—
248C2×D44—48no—
249C2×D44—44no—
250C2×D44#4114yes—
251C2×D44C2412yes—
252C2×D44C2412yes—
253C2×C4×D11—24no—
254C2×C4×D11—24no—
255C2×C4×D11—22no—
256C2×C4×D11—22no—
257C2×C4×D11—44no—
258C2×C4×D11—82no—
259C2×C4×D11C2×D412yes—
260C2×C4×D11C2412yes—
261C2×Dic22—24no—
262C2×Dic22—82no—
263C11×SD16—44no—
264C2×C8×C11—22no—
265C2×C8×C11—22no—
266C2×C8×C11—44no—
267C2×C8×C11C2412yes—
268C2×C8×C11C2412yes—
269C11×C4⋊C4—21no—
270C11×C4⋊C4—24no—
271C11×C4⋊C4—21no—
272C11×C4⋊C4C2412yes—
273C11×C4⋊C4C2412yes—
274C11×C22⋊C4—24no—
275C11×C22⋊C4—24no—
276C22⋊Dic11C2×D414yes—
277#4325—28no—
278#4325—44no—
279(C2×D11)⋊C4—24no—
280(C2×D11)⋊C4—24no—
281(C2×D11)⋊C4—24no—
282(C2×D11)⋊C4C2×D414yes—
283C4⋊Dic11—24no—
284C4⋊Dic11—21no—
285C4⋊Dic11—24no—
286C4⋊Dic11—21no—
287C4⋊Dic11C2412yes—
288C4⋊Dic11C2412yes—
289Dic11⋊C4—24no—
290Dic11⋊C4—24no—
291Dic11⋊C4—24no—
292Dic11⋊C4C2×D414yes—
293C4×Dic11—24no—
294C4×Dic11C2×D412yes—
295C4×Dic11C2412yes—
296C2×C11⋊C8—22no—
297C2×C11⋊C8—22no—
298C2×C11⋊C8C2412yes—
299C2×C11⋊C8C2412yes—
300C8×D11—44no—
301C2×#554—111no—
302C2×D42—111no—
303#3295—1116no—
304C2×#486—111no—
305C2×#481—111no—
306C2×#481—111no—
307C2×#476—111no—
308C2×#465—111no—
309C2×#465D1111yescharacteristic, complemented
310C2×#460—111no—
311C2×#450—111no—
312C2×#450—111no—
313C2×C4×SD16—111no—
314C2×C8×D4—111no—
315C22×#102—111no—
316C22×#102—111no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—42no—
321C23×C11—42no—
322C23×C11—42no—
323C23×C11C2×SD1614yes—
324C23×C11C22×D412yes—
325C23×C11C22×D411yescharacteristic
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—24no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—48no—
332C22×D11—48no—
333C22×D11—42no—
334C22×D11—42no—
335C22×D11—42no—
336C22×D11—42no—
337C22×D11—48no—
338C22×D11—42no—
339C22×D11—48no—
340C22×D11—84no—
341C22×D11—816no—
342C22×D11—84no—
343C22×D11—816no—
344C22×D11C2×SD1614yes—
345C22×D11C22×D412yes—
346Q8×C11—22no—
347Q8×C11—22no—
348Q8×C11—42no—
349D4×C11—22no—
350D4×C11—22no—
351D4×C11—48no—
352D4×C11—42no—
353C2×C4×C11—22no—
354C2×C4×C11—24no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—42no—
361C2×C4×C11—42no—
362C2×C4×C11—42no—
363C2×C4×C11C22×D412yes—
364C2×C4×C11C22×D411yescharacteristic
365C2×C4×C11C2×#4112yes—
366C2×C4×C11H(5,𝔽2)12yes—
367C2×C4×C11C2511yescharacteristic
368C22⋊D11—48no—
369C22⋊D11—48no—
370C22⋊D11—84no—
371C22⋊D11C2×SD16116yescomplemented
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—42no—
377C2×Dic11—42no—
378C2×Dic11—84no—
379C2×Dic11C2×SD1614yes—
380C2×Dic11C22×D412yes—
381C2×Dic11C22×D412yes—
382C2×Dic11C22×D412yes—
383D44—24no—
384D44—22no—
385D44—22no—
386D44—22no—
387D44—48no—
388D44—48no—
389D44—42no—
390D44C2×#4114yes—
391C4×D11—24no—
392C4×D11—22no—
393C4×D11—22no—
394C4×D11—48no—
395C4×D11—84no—
396Dic22—84no—
397C8×C11—22no—
398C8×C11—22no—
399C11⋊C8—22no—
400C11⋊C8—22no—
401C23×D4—111no—
402C23×D4—111no—
403C23×D4—221no—
404C22×SD16—111no—
405C22×SD16—111no—
406C22×SD16C2×D1111yescharacteristic, complemented
407C23×C8—111no—
408C23×C8C2×D1111yescharacteristic, complemented
409#554—118no—
410#554—224no—
411D42—118no—
412D42—224no—
413C2×C4⋊Q8—111no—
414C2×#127—111no—
415C2×#125—221no—
416C2×C22⋊Q8—111no—
417C2×C22⋊Q8—221no—
418C2×C22⋊Q8—221no—
419C2×C22⋊Q8C2×D1111yescharacteristic, complemented
420C2×#121—111no—
421C2×#121—221no—
422C2×#121C2×D1111yescharacteristic
423C2×#120—221no—
424C2×#120—221no—
425C2×C4×Q8—111no—
426C2×C4×D4—111no—
427C2×C4×D4—111no—
428C2×C4×D4—221no—
429C22×C4⋊C4—111no—
430C22×C4⋊C4—111no—
431#486—118no—
432#481—118no—
433#481—118no—
434#476—118no—
435#465—118no—
436#465C2×D1118yescomplemented
437#460—118no—
438#450—118no—
439#450—118no—
440C4×SD16—118no—
441C8×D4—118no—
442C2×#106—111no—
443C2×#106—111no—
444C2×#106C2×D1111yescharacteristic, complemented
445C2×C4⋊C8—111no—
446C2×#103C2×D1111yescharacteristic, complemented
447C2×#102—111no—
448C2×#102—111no—
449C2×#102—111no—
450C2×#102—111no—
451C2×#102—111no—
452C2×#102—111no—
453C2×#102—118no—
454C2×#102—111no—
455C2×#102—111no—
456C2×#102—118no—
457C2×#102C2×D1111yescharacteristic, complemented
458C2×C22⋊C8—111no—
459C2×C22⋊C8—111no—
460C2×C4×C8—111no—
461C22×C11—22no—
462C22×C11—28no—
463C22×C11—22no—
464C22×C11—42no—
465C22×C11—42no—
466C22×C11—42no—
467C22×C11—84no—
468C22×C11#54612yes—
469C22×C11C22×SD1614yes—
470C22×C11C22×SD1612yes—
471C22×C11#57612yes—
472C22×C11C23×D411yescharacteristic
473C2×D11—22no—
474C2×D11—28no—
475C2×D11—22no—
476C2×D11—24no—
477C2×D11—48no—
478C2×D11—42no—
479C2×D11—42no—
480C2×D11—42no—
481C2×D11—42no—
482C2×D11—42no—
483C2×D11—816no—
484C2×D11—816no—
485C2×D11—84no—
486C2×D11C22×SD1614yes—
487C4×C11—22no—
488C4×C11—42no—
489C4×C11—42no—
490C4×C11—42no—
491C4×C11#54612yes—
492C4×C11C22×#4111yescharacteristic
493C4×C11C2×H(5,𝔽2)11yescharacteristic
494Dic11—22no—
495Dic11—22no—
496Dic11—42no—
497Dic11—42no—
498Dic11C22×SD1614yes—
499C25—221no—
500C25—221no—
501C22×Q8—221no—
502C22×Q8C22×D1111yescharacteristic
503C22×D4—21no—
504C22×D4—111no—
505C22×D4—114no—
506C22×D4—111no—
507C22×D4—111no—
508C22×D4—114no—
509C22×D4—224no—
510C22×D4—221no—
511C22×D4—222no—
512C22×D4—221no—
513C22×D4—221no—
514C22×D4—221no—
515C22×D4—224no—
516C22×D4—228no—
517C22×D4—221no—
518C22×D4—222no—
519C22×D4—442no—
520C22×D4—442no—
521C22×D4—448no—
522C22×D4C22×D1111yescharacteristic
523C23×C4—111no—
524C23×C4—221no—
525C23×C4—221no—
526C23×C4—221no—
527C23×C4C22×D1111yescharacteristic
528C2×SD16—42no—
529C2×SD16—114no—
530C2×SD16—114no—
531C2×SD16—224no—
532C2×SD16—442no—
533C2×SD16C22×D1114yescomplemented
534C22×C8—42no—
535C22×C8—111no—
536C22×C8—111no—
537C22×C8—114no—
538C22×C8—442no—
539C22×C8C22×D1111yescharacteristic
540C22×C8C22×D1111yescharacteristic
541C22×C8C22×D1114yescomplemented
542C4⋊Q8—114no—
543C4⋊Q8—222no—
544#127—114no—
545#127—222no—
546#125—228no—
547C22⋊Q8—22no—
548C22⋊Q8—114no—
549C22⋊Q8—228no—
550C22⋊Q8—228no—
551C22⋊Q8—222no—
552C22⋊Q8C22×D1114yescomplemented
553#121—22no—
554#121—114no—
555#121—228no—
556#121—222no—
557#121C22×D1114yes—
558#120—228no—
559#120—228no—
560C4×Q8—114no—
561C4×Q8—222no—
562C4×D4—114no—
563C4×D4—114no—
564C4×D4—114no—
565C4×D4—222no—
566C4×D4—228no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—111no—
569C2×C4⋊C4—111no—
570C2×C4⋊C4—111no—
571C2×C4⋊C4—114no—
572C2×C4⋊C4—114no—
573C2×C4⋊C4—222no—
574C2×C4⋊C4—221no—
575C2×C4⋊C4—221no—
576C2×C4⋊C4—221no—
577C2×C4⋊C4—221no—
578C2×C4⋊C4—221no—
579C2×C4⋊C4—222no—
580C2×C4⋊C4C22×D1111yescharacteristic
581C2×C4⋊C4C22×D1111yescharacteristic
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—111no—
585C2×C22⋊C4—111no—
586C2×C22⋊C4—221no—
587C2×C22⋊C4—221no—
588C2×C22⋊C4—221no—
589C2×C42—111no—
590C2×C42—221no—
591#106—114no—
592#106—114no—
593#106C22×D1114yescomplemented
594C4⋊C8—114no—
595#103C22×D1114yescomplemented
596#102—114no—
597#102—114no—
598#102—114no—
599#102—114no—
600#102—114no—
601#102—114no—
602#102—114no—
603#102—114no—
604#102C22×D1114yescomplemented
605C22⋊C8—114no—
606C22⋊C8—114no—
607C4×C8—114no—
608C2×C11—24no—
609C2×C11—82no—
610C2×C11#329514yescomplemented
611C2×C11C2×#54611yescharacteristic
612C2×C11C23×SD1611yescharacteristic
613C2×C11C2×#57611yescharacteristic
614D11—24no—
615D11—44no—
616D11—82no—
617C24—21no—
618C24—111no—
619C24—224no—
620C24—221no—
621C24—221no—
622C24—224no—
623C24—444no—
624C24—444no—
625C24—444no—
626C24—444no—
627C24—882no—
628C24—882no—
629C24D4×D1111yescharacteristic
630C2×Q8—21no—
631C2×Q8—22no—
632C2×Q8—22no—
633C2×Q8—224no—
634C2×Q8—882no—
635C2×Q8C23×D1112yes—
636C2×D4—24no—
637C2×D4—21no—
638C2×D4—22no—
639C2×D4—22no—
640C2×D4—44no—
641C2×D4—118no—
642C2×D4—114no—
643C2×D4—114no—
644C2×D4—112no—
645C2×D4—112no—
646C2×D4—228no—
647C2×D4—224no—
648C2×D4—224no—
649C2×D4—224no—
650C2×D4—224no—
651C2×D4—228no—
652C2×D4—221no—
653C2×D4—224no—
654C2×D4—221no—
655C2×D4—222no—
656C2×D4—222no—
657C2×D4—222no—
658C2×D4—444no—
659C2×D4—448no—
660C2×D4—444no—
661C2×D4—444no—
662C2×D4—444no—
663C2×D4—444no—
664C2×D4—448no—
665C2×D4—444no—
666C2×D4—4432no—
667C2×D4—882no—
668C2×D4C23×D1112yes—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—111no—
675C22×C4—111no—
676C22×C4—111no—
677C22×C4—112no—
678C22×C4—112no—
679C22×C4—224no—
680C22×C4—224no—
681C22×C4—222no—
682C22×C4—222no—
683C22×C4—221no—
684C22×C4—221no—
685C22×C4—224no—
686C22×C4—444no—
687C22×C4—882no—
688C22×C4—882no—
689C22×C4D4×D1112yes—
690C22×C4D4×D1111yescharacteristic
691C22×C4C23×D1112yes—
692C22×C4C23×D1111yescharacteristic
693SD16—44no—
694SD16—228no—
695SD16—444no—
696C2×C8—22no—
697C2×C8—22no—
698C2×C8—44no—
699C2×C8—112no—
700C2×C8—112no—
701C2×C8—222no—
702C2×C8—222no—
703C2×C8—444no—
704C2×C8C23×D1112yes—
705C2×C8C23×D1112yes—
706C4⋊C4—24no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—114no—
710C4⋊C4—112no—
711C4⋊C4—112no—
712C4⋊C4—224no—
713C4⋊C4—224no—
714C4⋊C4—224no—
715C4⋊C4—224no—
716C4⋊C4—221no—
717C4⋊C4—224no—
718C4⋊C4—221no—
719C4⋊C4C23×D1112yes—
720C4⋊C4C23×D1112yes—
721C22⋊C4—24no—
722C22⋊C4—24no—
723C22⋊C4—114no—
724C22⋊C4—114no—
725C22⋊C4—224no—
726C22⋊C4—224no—
727C22⋊C4—224no—
728C42—112no—
729C42—112no—
730C42—224no—
731C11C2×#329511yescharacteristic, complemented, Sylow
732C23—22no—
733C23—22no—
734C23—22no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—114no—
739C23—112no—
740C23—222no—
741C23—222no—
742C23—224no—
743C23—222no—
744C23—222no—
745C23—448no—
746C23—448no—
747C23—448no—
748C23—442no—
749C23—442no—
750C23—448no—
751C23—442no—
752C23—442no—
753C23—442no—
754C23—884no—
755C23—8816no—
756C23—884no—
757C23—8816no—
758C23SD16×D1114yes—
759C23C2×D4×D1112yes—
760C23C2×D4×D1111yescharacteristic
761Q8—22no—
762Q8—22no—
763Q8—42no—
764Q8—884no—
765D4—22no—
766D4—22no—
767D4—48no—
768D4—42no—
769D4—1116no—
770D4—114no—
771D4—224no—
772D4—222no—
773D4—222no—
774D4—222no—
775D4—448no—
776D4—448no—
777D4—448no—
778D4—448no—
779D4—442no—
780D4—884no—
781C2×C4—22no—
782C2×C4—24no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—114no—
792C2×C4—112no—
793C2×C4—112no—
794C2×C4—112no—
795C2×C4—222no—
796C2×C4—222no—
797C2×C4—224no—
798C2×C4—222no—
799C2×C4—222no—
800C2×C4—222no—
801C2×C4—222no—
802C2×C4—448no—
803C2×C4—442no—
804C2×C4—442no—
805C2×C4—884no—
806C2×C4—884no—
807C2×C4C2×D4×D1112yes—
808C2×C4C2×D4×D1111yescharacteristic
809C2×C4#6703712yes—
810C2×C4#41×D1112yes—
811C2×C4C24×D1111yescharacteristic
812C8—22no—
813C8—22no—
814C8—222no—
815C8—222no—
816C22—28no—
817C22—22no—
818C22—22no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—84no—
823C22—114no—
824C22—228no—
825C22—222no—
826C22—222no—
827C22—224no—
828C22—448no—
829C22—442no—
830C22—442no—
831C22—442no—
832C22—442no—
833C22—442no—
834C22—8816no—
835C22—8816no—
836C22—884no—
837C22#1062314112yes—
838C22C2×SD16×D1114yes—
839C22C2×SD16×D1112yes—
840C22#1062330012yes—
841C22C22×D4×D1111yescharacteristic
842C4—22no—
843C4—42no—
844C4—42no—
845C4—42no—
846C4—114no—
847C4—222no—
848C4—222no—
849C4—442no—
850C4—442no—
851C4#1062314112yes—
852C4C2×#6703711yescharacteristic
853C4C2×#41×D1111yescharacteristic
854C2—24no—
855C2—82no—
856C2—224no—
857C2—444no—
858C2—882no—
859C2#1308043514yesdirect product factor
860C2C2×#1062314111yescharacteristic
861C2C22×SD16×D1111yescharacteristic
862C2C2×#1062330011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#465C2
socleC23×C11C22×D4
prime radicalC2×#10623140C2
hypercenterC2×#465D11
hypocenterC11C2×#3295
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#10623166C2semidirect
3. #13080435C2direct (N × H)
4. C2×#10622373C2semidirect
5. C2×#10622476C2semidirect
6. C2×#10622647C2semidirect
7. C2×#10622483C2semidirect
8. C2×#10622420C2semidirect
9. C2×#10622776C2semidirect
10. C2×#10622659C2semidirect
11. C2×#10622782C2semidirect
12. C2×#10622401C2semidirect
13. C2×C8×C22⋊D11C2semidirect
14. C22×#66885C2semidirect
15. C2×D11×#102C2semidirect
16. C2×C11×#465C2semidirect
20. C22×C11×SD16C22semidirect
21. C23×C8×C11C22semidirect
22. C2×C11×C22⋊Q8C22semidirect
24. C2×#66999C22semidirect
25. C2×Q8×Dic11C22semidirect
27. C22×#4325C22semidirect
31. C22×C4⋊Dic11C22semidirect
32. C22×C8×D11C22semidirect
34. #10623166C22semidirect
40. C2×C4⋊C4×D11C22semidirect
42. C2×#66941C22semidirect
47. C11×#465C22semidirect
48. C2×C11×#106C22semidirect
49. C2×C11×#103C22semidirect
50. C2×C11×#102C22semidirect
51. C2×#66896C22semidirect
52. C2×#66896C22semidirect
53. C2×C22⋊(C11⋊C8)C22semidirect
54. #10622782C22semidirect
55. #10622776C22semidirect
58. C2×#66885C22semidirect
59. C2×#66885C22semidirect
60. C2×#66885C22semidirect
61. C8×C22⋊D11C22semidirect
62. C2×(C2×D11)⋊C8C22semidirect
63. C2×Dic11⋊C8C22semidirect
64. C2×C8×Dic11C22semidirect
65. #10622659C22semidirect
66. #10622647C22semidirect
68. C2×#66873C22semidirect
69. C2×#66872C22semidirect
70. C2×#66872C22semidirect
71. #10622483C22semidirect
72. #10622476C22semidirect
73. #10622420C22semidirect
74. #10622401C22semidirect
75. D11×#102C22semidirect
76. #10622373C22semidirect
107. C2×C11×SD16C23semidirect
111. C22×C8×C11C23semidirect
113. C11×C22⋊Q8C23semidirect
123. #66999C23semidirect
125. Q8×Dic11C23semidirect
129. C2×#4325C23semidirect
144. C2×C4⋊Dic11C23semidirect
154. C2×C8×D11C23semidirect
161. C4⋊C4×D11C23semidirect
164. #66941C23semidirect
169. C11×#106C23semidirect
170. C11×#103C23semidirect
171. C11×#102C23semidirect
172. #66896C23semidirect
173. #66896C23semidirect
174. C22⋊(C11⋊C8)C23semidirect
177. #66885C23semidirect
178. #66885C23semidirect
179. (C2×D11)⋊C8C23semidirect
180. Dic11⋊C8C23semidirect
181. C8×Dic11C23semidirect
183. #66873C23semidirect
184. #66872C23semidirect
185. #66872C23semidirect
225. C2×C22⋊D11SD16semidirect
309. C2×#465D11semidirect
371. C22⋊D11C2×SD16semidirect
406. C22×SD16C2×D11semidirect
408. C23×C8C2×D11semidirect
419. C2×C22⋊Q8C2×D11semidirect
436. #465C2×D11semidirect
444. C2×#106C2×D11semidirect
446. C2×#103C2×D11semidirect
457. C2×#102C2×D11semidirect
533. C2×SD16C22×D11semidirect
541. C22×C8C22×D11semidirect
552. C22⋊Q8C22×D11semidirect
593. #106C22×D11semidirect
595. #103C22×D11semidirect
604. #102C22×D11semidirect
610. C2×C11#3295semidirect
731. C11C2×#3295semidirect
859. C2#13080435direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231662
C2×#106231402
#130804352
C2×#106223732
C2×#106224762
C2×#106226472
C2×#106224832
C2×#106224202
C2×#106227762
C2×#106226592
C2×#106227822
C2×#106224012
C2×C8×C22⋊D112
C22×#668852
C2×D11×#1022
C2×C11×#4652
C2×#329511