Finite Group Databasebeta

← C2×#13079716 #15625134

Subgroups — C2×#13079716 #15625134

Order 2816.

2278 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623174C211yesmaximal, characteristic, complemented
2C2×#10623361C211yesmaximal, characteristic, complemented
3#13079716C2116yesmaximal, direct product factor
4C2×#10622789C211yesmaximal, characteristic, complemented
5C2×#10622804C211yesmaximal, characteristic, complemented
6C2×#10622408C211yesmaximal, characteristic, complemented
7C2×#10622373C211yesmaximal, characteristic, complemented
8C2×#10622798C211yesmaximal, characteristic, complemented
9C2×#10622776C211yesmaximal, characteristic, complemented
10C2×#10622432C211yesmaximal, characteristic, complemented
11C2×#10622399C211yesmaximal, characteristic, complemented
12C2×#10622851C211yesmaximal, characteristic, complemented
13C2×#10622659C211yesmaximal, characteristic, complemented
14C2×#10622345C211yesmaximal, characteristic, complemented
15C2×#10622333C211yesmaximal, characteristic, complemented
16C2×C11×#452C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C22×C11×Q16C2211yescharacteristic, complemented
20C22×C11×SD16C2211yescharacteristic, complemented
21C2×C11×C22⋊Q8C2211yescharacteristic
22#10623361—24no—
23#10623361C2218yescomplemented
24C2×#67000C2211yescharacteristic
25C2×#67000C2211yescharacteristic
26C2×#67000C2211yescharacteristic, complemented
27C2×Q8×Dic11C2211yescharacteristic, complemented
28C22×#4325C2211yescharacteristic
29C22×#4325C2211yescharacteristic
30C22×#4325C2211yescharacteristic, complemented
31C2×#66993C2211yescharacteristic
32C2×#66993C2211yescharacteristic
33C2×#66990—21no—
34C2×#66990—21no—
35C22×#4323C2211yescharacteristic, complemented
36C2×#66983—21no—
37C2×#66983—21no—
38C2×#66983C2211yescharacteristic
39C2×#66979C2211yescharacteristic
40C22×D88C2211yescharacteristic
41C22×D88C2211yescharacteristic
42#10623174—24no—
43#10623174C2218yescomplemented
44C2×#66951—21no—
45C2×#66950—21no—
46C2×#66946C2211yescharacteristic, complemented
47C2×#66941C2211yescharacteristic, complemented
48C2×#66938—21no—
49C2×#66936—21no—
50C11×#452C2218yescomplemented
51C2×C11×#103C2211yescharacteristic, complemented
52C2×C11×#102C2211yescharacteristic, complemented
53C2×C11×C22⋊C8C2211yescharacteristic
54#10622851C2218yescomplemented
55C2×#66899C2211yescharacteristic, complemented
56C2×#66896C2211yescharacteristic, complemented
57C2×C22⋊(C11⋊C8)C2211yescharacteristic
58#10622804C2218yescomplemented
59#10622798C2218yescomplemented
60#10622789C2218yescomplemented
61#10622776C2218yescomplemented
62C2×#66885C2211yescharacteristic
63C2×#66885C2211yescharacteristic
64C2×#66879C2211yescharacteristic, complemented
65C2×Dic11⋊C8C2211yescharacteristic, complemented
66C2×Dic11⋊C8C2211yescharacteristic, complemented
67C2×C8×Dic11C2211yescharacteristic, complemented
68#10622659C2218yescomplemented
69C2×#66873C2211yescharacteristic
70C2×#66873C2211yescharacteristic
71#10622432C2218yescomplemented
72#10622408C2218yescomplemented
73#10622399C2218yescomplemented
74#10622373C2218yescomplemented
75#10622345C2218yescomplemented
76#10622333C2218yescomplemented
77C24×D11—21no—
78C2×C11×#41—22no—
79C2×C11×#41—42no—
80C2×C11×#41—42no—
81C2×C11×#41C2314yes—
82C22×Q8×C11C2311yescharacteristic
83C22×Q8×C11C2311yescharacteristic
84C22×D4×C11—21no—
85C22×D4×C11C2311yescharacteristic
86C23×C4×C11—21no—
87C23×C4×C11C2311yescharacteristic
88C22×C22⋊D11—21no—
89C22×C22⋊D11—21no—
90C22×C22⋊D11—21no—
91C22×C22⋊D11—21no—
92C22×C22⋊D11—21no—
93C22×D44—21no—
94C22×D44—22no—
95C22×D44—42no—
96C22×D44—42no—
97C22×D44C2311yescharacteristic
98C22×D44C2311yescharacteristic
99C22×D44C2311yescharacteristic
100C22×D44C2314yes—
101C22×C4×D11—21no—
102C22×Dic22—21no—
103C2×C11×Q16—42no—
104C2×C11×Q16C2314yescomplemented
105C2×C11×SD16—42no—
106C2×C11×SD16C2314yescomplemented
107C22×C8×C11C2311yescharacteristic
108C22×C8×C11C2311yescharacteristic
109C11×C22⋊Q8—22no—
110C11×C22⋊Q8C2314yes—
111C2×C11×C4⋊C4—21no—
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C22⋊C4—21no—
114C2×C22⋊Dic11D411yescharacteristic
115C2×C22⋊Dic11D411yescharacteristic
116#67000—22no—
117#67000—22no—
118#67000—22no—
119#67000C2314yes—
120#67000C2314yes—
121#67000C2314yescomplemented
122Q8×Dic11—22no—
123Q8×Dic11C2314yescomplemented
124C2×#4325—42no—
125C2×#4325—42no—
126C2×#4325—42no—
127C2×#4325C2314yes—
128C2×#4325C2314yes—
129C2×#4325C2314yescomplemented
130#66993—22no—
131#66993—22no—
132#66993C2314yes—
133#66993C2314yes—
134#66990—28no—
135#66990—28no—
136C2×#4323—42no—
137C2×#4323C2314yescomplemented
138#66983—22no—
139#66983—28no—
140#66983—28no—
141#66983C2314yes—
142C2×(C2×D11)⋊C4—21no—
143C2×(C2×D11)⋊C4—21no—
144C2×(C2×D11)⋊C4—21no—
145C2×(C2×D11)⋊C4—21no—
146C2×(C2×D11)⋊C4—21no—
147C2×(C2×D11)⋊C4—21no—
148C2×(C2×D11)⋊C4—21no—
149C2×(C2×D11)⋊C4—21no—
150#66979D414yes—
151#66979C2314yes—
152C2×C4⋊Dic11—21no—
153C2×C4⋊Dic11D411yescharacteristic
154C2×C4⋊Dic11D411yescharacteristic
155C2×C4⋊Dic11C2311yescharacteristic
156C2×Dic11⋊C4—21no—
157C2×C4×Dic11—21no—
158C2×C4×Dic11C2311yescharacteristic
159C2×C4×Dic11C2311yescharacteristic
160C22×C11⋊C8C2311yescharacteristic
161C22×C11⋊C8C2311yescharacteristic
162C2×D88—42no—
163C2×D88—42no—
164C2×D88C2314yes—
165C2×D88C2314yes—
166#66951—28no—
167#66950—28no—
168#66946—22no—
169#66946C2314yescomplemented
170#66941—22no—
171#66941C2314yescomplemented
172#66938—28no—
173#66936—28no—
174C11×#103C2314yescomplemented
175C11×#102C2314yescomplemented
176C11×C22⋊C8C2314yes—
177#66899C2314yescomplemented
178#66896C2314yescomplemented
179C22⋊(C11⋊C8)C2314yes—
180#66885C2314yes—
181#66885C2314yes—
182#66879C2314yescomplemented
183Dic11⋊C8C2314yescomplemented
184Dic11⋊C8C2314yescomplemented
185C8×Dic11C2314yescomplemented
186#66873C2314yes—
187#66873C2314yes—
188C2×#3224—111nomaximal, Sylow
189C24×C11—21no—
190C24×C11C2×D411yescharacteristic
191C23×D11—21no—
192C23×D11—21no—
193C23×D11—21no—
194C23×D11—24no—
195C23×D11—44no—
196C23×D11—82no—
197C23×D11—82no—
198C11×#41—44no—
199C11×#41—44no—
200C11×#41—48no—
201C2×Q8×C11—21no—
202C2×Q8×C11—21no—
203C2×Q8×C11—22no—
204C2×Q8×C11—22no—
205C2×Q8×C11—22no—
206C2×Q8×C11—22no—
207C2×Q8×C11C2412yes—
208C2×Q8×C11C2412yes—
209C2×D4×C11—24no—
210C2×D4×C11—21no—
211C2×D4×C11—22no—
212C2×D4×C11—22no—
213C2×D4×C11—44no—
214C2×D4×C11C2412yes—
215C22×C4×C11—22no—
216C22×C4×C11—22no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—24no—
221C22×C4×C11—44no—
222C22×C4×C11C2×D411yescharacteristic
223C22×C4×C11C2×D412yes—
224C22×C4×C11C2412yes—
225C22×C4×C11C2411yescharacteristic
226C2×C22⋊D11—24no—
227C2×C22⋊D11—24no—
228C2×C22⋊D11—24no—
229C2×C22⋊D11—24no—
230C2×C22⋊D11—24no—
231C2×C22⋊D11—82no—
232C2×C22⋊D11—82no—
233C2×C22⋊D11—82no—
234C2×C22⋊D11—82no—
235C2×C22⋊D11—82no—
236C22×Dic11—21no—
237C22×Dic11C2×D411yescharacteristic
238C22×Dic11C2×D411yescharacteristic
239C22×Dic11C2×D411yescharacteristic
240C22×Dic11C2×D411yescharacteristic
241C2×D44—21no—
242C2×D44—24no—
243C2×D44—21no—
244C2×D44—21no—
245C2×D44—22no—
246C2×D44—22no—
247C2×D44—22no—
248C2×D44—22no—
249C2×D44—22no—
250C2×D44—22no—
251C2×D44—44no—
252C2×D44—44no—
253C2×D44—44no—
254C2×D44—48no—
255C2×D44C2412yes—
256C2×D44C2412yes—
257C2×D44C2412yes—
258C2×C4×D11—24no—
259C2×C4×D11—82no—
260C2×Dic22—24no—
261C2×Dic22—82no—
262C11×Q16—44no—
263C11×SD16—44no—
264C2×C8×C11—22no—
265C2×C8×C11—22no—
266C2×C8×C11C2412yes—
267C2×C8×C11C2412yes—
268C11×C4⋊C4—21no—
269C11×C4⋊C4—24no—
270C11×C4⋊C4C2412yes—
271C11×C22⋊C4—24no—
272C22⋊Dic11C2×D414yes—
273C22⋊Dic11C2×D414yes—
274#4325—44no—
275#4325—44no—
276#4325—44no—
277#4323—44no—
278(C2×D11)⋊C4—24no—
279(C2×D11)⋊C4—24no—
280(C2×D11)⋊C4—24no—
281(C2×D11)⋊C4—24no—
282(C2×D11)⋊C4—24no—
283(C2×D11)⋊C4—24no—
284(C2×D11)⋊C4—24no—
285(C2×D11)⋊C4—24no—
286C4⋊Dic11—24no—
287C4⋊Dic11—21no—
288C4⋊Dic11C2×D414yes—
289C4⋊Dic11C2×D414yes—
290C4⋊Dic11C2412yes—
291Dic11⋊C4—24no—
292C4×Dic11—24no—
293C4×Dic11C2×D412yes—
294C4×Dic11C2×D412yes—
295C4×Dic11C2412yes—
296C4×Dic11C2412yes—
297C2×C11⋊C8—22no—
298C2×C11⋊C8—22no—
299C2×C11⋊C8C2412yes—
300C2×C11⋊C8C2412yes—
301D88—44no—
302D88—44no—
303C2×#542—111no—
304C2×#535—111no—
305#3224—1116no—
306C2×#496—111no—
307C2×#495—111no—
308C2×#489—111no—
309C2×#486—111no—
310C2×#464—111no—
311C2×#460—111no—
312C2×#463—111no—
313C2×#459—111no—
314C2×#452D1111yescharacteristic, complemented
315C2×#449—111no—
316C2×#450—111no—
317C2×#447—111no—
318C2×#433—111no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—42no—
324C23×C11—42no—
325C23×C11—42no—
326C23×C11C22×D412yes—
327C23×C11C22×D411yescharacteristic
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—48no—
332C22×D11—42no—
333C22×D11—42no—
334C22×D11—42no—
335C22×D11—42no—
336C22×D11—42no—
337C22×D11—42no—
338C22×D11—42no—
339C22×D11—42no—
340C22×D11—42no—
341C22×D11—84no—
342C22×D11—84no—
343C22×D11—816no—
344Q8×C11—22no—
345Q8×C11—22no—
346Q8×C11—22no—
347Q8×C11—22no—
348Q8×C11—42no—
349Q8×C11—42no—
350D4×C11—22no—
351D4×C11—22no—
352D4×C11—48no—
353D4×C11—42no—
354C2×C4×C11—22no—
355C2×C4×C11—24no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—48no—
362C2×C4×C11—42no—
363C2×C4×C11—42no—
364C2×C4×C11—42no—
365C2×C4×C11C22×D412yes—
366C2×C4×C11C22×D411yescharacteristic
367C2×C4×C11H(5,𝔽2)12yes—
368C2×C4×C11H(5,𝔽2)12yes—
369C2×C4×C11C2511yescharacteristic
370C22⋊D11—84no—
371C22⋊D11—84no—
372C22⋊D11—84no—
373C22⋊D11—84no—
374C22⋊D11—84no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—42no—
381C2×Dic11C22×D412yes—
382C2×Dic11C22×D412yes—
383C2×Dic11C22×D412yes—
384C2×Dic11C22×D412yes—
385D44—22no—
386D44—22no—
387D44—22no—
388D44—22no—
389D44—22no—
390D44—22no—
391D44—48no—
392D44—42no—
393D44—42no—
394D44—42no—
395C4×D11—84no—
396Dic22—84no—
397C8×C11—22no—
398C8×C11—22no—
399C11⋊C8—22no—
400C11⋊C8—22no—
401C22×#41C2×D1111yescharacteristic
402C23×D4—111no—
403C22×Q16C2×D1111yescharacteristic, complemented
404C22×SD16—111no—
405C22×SD16—111no—
406C22×SD16—111no—
407C22×SD16C2×D1111yescharacteristic, complemented
408C22×D8—111no—
409C22×D8—111no—
410C22×D8—111no—
411#542—118no—
412#542—224no—
413#535—118no—
414#535—224no—
415C2×C4⋊Q8—111no—
416C2×#127—111no—
417C2×#127—111no—
418C2×#126—221no—
419C2×#124—111no—
420C2×#124—111no—
421C2×#124—111no—
422C2×#124—221no—
423C2×#123—221no—
424C2×C22⋊Q8—221no—
425C2×C22⋊Q8C2×D1111yescharacteristic
426C2×#121—111no—
427C2×#121—221no—
428C2×#121—221no—
429C2×#120—221no—
430C2×#120—221no—
431C2×C4×Q8—111no—
432C2×C4×D4—111no—
433C2×#117—111no—
434#496—118no—
435#495—118no—
436#489—118no—
437#486—118no—
438#464—118no—
439#463—118no—
440#460—118no—
441#459—118no—
442#452C2×D1118yescomplemented
443#450—118no—
444#449—118no—
445#447—118no—
446#433—118no—
447C2×C4⋊C8—111no—
448C2×C4⋊C8—111no—
449C2×#103—111no—
450C2×#103C2×D1111yescharacteristic, complemented
451C2×#102—111no—
452C2×#102—111no—
453C2×#102—111no—
454C2×#102—111no—
455C2×#102—111no—
456C2×#102C2×D1111yescharacteristic, complemented
457C2×C22⋊C8—111no—
458C2×C22⋊C8C2×D1111yescharacteristic
459C2×#97—111no—
460C2×C4×C8—111no—
461C22×C11—22no—
462C22×C11—22no—
463C22×C11—22no—
464C22×C11—44no—
465C22×C11—42no—
466C22×C11—42no—
467C22×C11—42no—
468C22×C11—84no—
469C22×C11#53512yes—
470C22×C11#57612yes—
471C22×C11#57712yes—
472C22×C11C23×D411yescharacteristic
473C2×D11—42no—
474C2×D11—42no—
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—42no—
479C2×D11—42no—
480C2×D11—42no—
481C2×D11—42no—
482C2×D11—816no—
483C2×D11—84no—
484C2×D11—84no—
485C2×D11—84no—
486C4×C11—22no—
487C4×C11—42no—
488C4×C11—42no—
489C4×C11—42no—
490C4×C11#53512yes—
491C4×C11C2×H(5,𝔽2)11yescharacteristic
492C4×C11C2×H(5,𝔽2)11yescharacteristic
493Dic11—22no—
494Dic11—22no—
495Dic11—22no—
496Dic11—22no—
497Dic11—42no—
498C25—221no—
499C2×#41—22no—
500C2×#41—42no—
501C2×#41—42no—
502C2×#41C22×D1114yes—
503C22×Q8—221no—
504C22×Q8C22×D1111yescharacteristic
505C22×Q8C22×D1111yescharacteristic
506C22×D4—21no—
507C22×D4—111no—
508C22×D4—111no—
509C22×D4—111no—
510C22×D4—114no—
511C22×D4—221no—
512C22×D4—221no—
513C22×D4—221no—
514C22×D4—221no—
515C22×D4—221no—
516C22×D4—221no—
517C22×D4—222no—
518C22×D4—442no—
519C22×D4—442no—
520C22×D4C22×D1111yescharacteristic
521C23×C4—21no—
522C23×C4—221no—
523C23×C4C22×D1111yescharacteristic
524C2×Q16—42no—
525C2×Q16C22×D1114yescomplemented
526C2×SD16—42no—
527C2×SD16—114no—
528C2×SD16—114no—
529C2×SD16—114no—
530C2×SD16—442no—
531C2×SD16—442no—
532C2×SD16—442no—
533C2×SD16C22×D1114yescomplemented
534C2×D8—114no—
535C2×D8—114no—
536C2×D8—114no—
537C2×D8—442no—
538C2×D8—442no—
539C2×D8—442no—
540C22×C8—111no—
541C22×C8—111no—
542C22×C8C22×D1111yescharacteristic
543C22×C8C22×D1111yescharacteristic
544C4⋊Q8—114no—
545C4⋊Q8—222no—
546#127—114no—
547#127—114no—
548#127—222no—
549#127—222no—
550#126—228no—
551#124—114no—
552#124—114no—
553#124—114no—
554#124—222no—
555#124—222no—
556#124—222no—
557#124—228no—
558#123—228no—
559C22⋊Q8—22no—
560C22⋊Q8—228no—
561C22⋊Q8C22×D1114yes—
562#121—114no—
563#121—228no—
564#121—228no—
565#121—222no—
566#120—228no—
567#120—228no—
568C4×Q8—114no—
569C4×Q8—222no—
570C4×D4—114no—
571C4×D4—222no—
572#117—114no—
573#117—114no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—111no—
576C2×C4⋊C4—111no—
577C2×C4⋊C4—111no—
578C2×C4⋊C4—221no—
579C2×C4⋊C4—221no—
580C2×C4⋊C4C22×D1111yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—111no—
583C2×C22⋊C4—111no—
584C2×C22⋊C4—221no—
585C2×C22⋊C4—221no—
586C2×C22⋊C4—221no—
587C2×C22⋊C4—221no—
588C2×C22⋊C4—221no—
589C2×C22⋊C4—221no—
590C2×C22⋊C4—221no—
591C2×C22⋊C4—221no—
592C2×C42—111no—
593C2×C42—111no—
594C2×C42—221no—
595C4⋊C8—114no—
596C4⋊C8—114no—
597#103—114no—
598#103C22×D1114yescomplemented
599#102—114no—
600#102—114no—
601#102—114no—
602#102—114no—
603#102—114no—
604#102C22×D1114yescomplemented
605C22⋊C8—114no—
606C22⋊C8C22×D1114yes—
607#97—114no—
608C4×C8—114no—
609C2×C11—42no—
610C2×C11—82no—
611C2×C11#322414yescomplemented
612C2×C11C2×#53511yescharacteristic
613C2×C11C2×#57611yescharacteristic
614C2×C11C2×#57711yescharacteristic
615D11—82no—
616D11—82no—
617D11—82no—
618C24—21no—
619C24—221no—
620C24—221no—
621C24—221no—
622C24—224no—
623C24—444no—
624C24—882no—
625C24—882no—
626C24D4×D1111yescharacteristic
627#41—44no—
628#41—44no—
629#41—48no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8—22no—
633C2×Q8—22no—
634C2×Q8—22no—
635C2×Q8—22no—
636C2×Q8—224no—
637C2×Q8—882no—
638C2×Q8C23×D1112yes—
639C2×Q8C23×D1112yes—
640C2×D4—24no—
641C2×D4—21no—
642C2×D4—22no—
643C2×D4—22no—
644C2×D4—44no—
645C2×D4—112no—
646C2×D4—112no—
647C2×D4—112no—
648C2×D4—224no—
649C2×D4—224no—
650C2×D4—224no—
651C2×D4—224no—
652C2×D4—224no—
653C2×D4—221no—
654C2×D4—224no—
655C2×D4—221no—
656C2×D4—221no—
657C2×D4—222no—
658C2×D4—222no—
659C2×D4—222no—
660C2×D4—222no—
661C2×D4—222no—
662C2×D4—222no—
663C2×D4—444no—
664C2×D4—444no—
665C2×D4—444no—
666C2×D4—448no—
667C2×D4—882no—
668C2×D4—882no—
669C2×D4—882no—
670C2×D4—882no—
671C2×D4—882no—
672C2×D4C23×D1112yes—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—24no—
679C22×C4—44no—
680C22×C4—111no—
681C22×C4—111no—
682C22×C4—111no—
683C22×C4—111no—
684C22×C4—224no—
685C22×C4—221no—
686C22×C4—882no—
687C22×C4D4×D1112yes—
688C22×C4D4×D1111yescharacteristic
689C22×C4C23×D1112yes—
690C22×C4C23×D1111yescharacteristic
691Q16—44no—
692SD16—44no—
693SD16—444no—
694SD16—444no—
695SD16—444no—
696D8—444no—
697D8—444no—
698D8—444no—
699C2×C8—22no—
700C2×C8—22no—
701C2×C8—112no—
702C2×C8—112no—
703C2×C8—222no—
704C2×C8—222no—
705C2×C8C23×D1112yes—
706C2×C8C23×D1112yes—
707C4⋊C4—24no—
708C4⋊C4—21no—
709C4⋊C4—114no—
710C4⋊C4—114no—
711C4⋊C4—112no—
712C4⋊C4—224no—
713C4⋊C4—224no—
714C4⋊C4—221no—
715C4⋊C4C23×D1112yes—
716C22⋊C4—24no—
717C22⋊C4—114no—
718C22⋊C4—114no—
719C22⋊C4—224no—
720C22⋊C4—224no—
721C22⋊C4—224no—
722C22⋊C4—224no—
723C22⋊C4—224no—
724C22⋊C4—224no—
725C22⋊C4—224no—
726C22⋊C4—224no—
727C42—112no—
728C42—112no—
729C42—112no—
730C42—112no—
731C42—224no—
732C11C2×#322411yescharacteristic, complemented, Sylow
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—222no—
741C23—222no—
742C23—222no—
743C23—448no—
744C23—442no—
745C23—442no—
746C23—442no—
747C23—442no—
748C23—442no—
749C23—442no—
750C23—442no—
751C23—442no—
752C23—442no—
753C23—884no—
754C23—884no—
755C23—8816no—
756C23C2×D4×D1112yes—
757C23C2×D4×D1111yescharacteristic
758Q8—22no—
759Q8—22no—
760Q8—22no—
761Q8—22no—
762Q8—42no—
763Q8—42no—
764Q8—884no—
765D4—22no—
766D4—22no—
767D4—48no—
768D4—42no—
769D4—222no—
770D4—222no—
771D4—222no—
772D4—222no—
773D4—222no—
774D4—222no—
775D4—448no—
776D4—442no—
777D4—442no—
778D4—442no—
779D4—884no—
780D4—884no—
781D4—884no—
782D4—884no—
783D4—884no—
784C2×C4—22no—
785C2×C4—24no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—48no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—112no—
796C2×C4—112no—
797C2×C4—112no—
798C2×C4—112no—
799C2×C4—222no—
800C2×C4—222no—
801C2×C4—222no—
802C2×C4—222no—
803C2×C4—222no—
804C2×C4—442no—
805C2×C4—884no—
806C2×C4C2×D4×D1112yes—
807C2×C4C2×D4×D1111yescharacteristic
808C2×C4#6703712yes—
809C2×C4#6703712yes—
810C2×C4C24×D1111yescharacteristic
811C8—22no—
812C8—22no—
813C8—222no—
814C8—222no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—44no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—84no—
823C22—442no—
824C22—442no—
825C22—442no—
826C22—442no—
827C22—442no—
828C22—442no—
829C22—442no—
830C22—442no—
831C22—442no—
832C22—8816no—
833C22—884no—
834C22—884no—
835C22—884no—
836C22#1062312312yes—
837C22#1062330012yes—
838C22#1062330912yes—
839C22C22×D4×D1111yescharacteristic
840C4—22no—
841C4—42no—
842C4—42no—
843C4—42no—
844C4—222no—
845C4—222no—
846C4—222no—
847C4—222no—
848C4—442no—
849C4#1062312312yes—
850C4C2×#6703711yescharacteristic
851C4C2×#6703711yescharacteristic
852C2—42no—
853C2—82no—
854C2—882no—
855C2—882no—
856C2—882no—
857C2#1307971614yesdirect product factor
858C2C2×#1062312311yescharacteristic
859C2C2×#1062330011yescharacteristic
860C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#452C2
socleC23×C11C22×D4
hypercenterC2×#452D11
hypocenterC11C2×#3224
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#10623174C2semidirect
2. C2×#10623361C2semidirect
3. #13079716C2direct (N × H)
4. C2×#10622789C2semidirect
5. C2×#10622804C2semidirect
6. C2×#10622408C2semidirect
7. C2×#10622373C2semidirect
8. C2×#10622798C2semidirect
9. C2×#10622776C2semidirect
10. C2×#10622432C2semidirect
11. C2×#10622399C2semidirect
12. C2×#10622851C2semidirect
13. C2×#10622659C2semidirect
14. C2×#10622345C2semidirect
15. C2×#10622333C2semidirect
16. C2×C11×#452C2semidirect
19. C22×C11×Q16C22semidirect
20. C22×C11×SD16C22semidirect
23. #10623361C22semidirect
26. C2×#67000C22semidirect
27. C2×Q8×Dic11C22semidirect
30. C22×#4325C22semidirect
35. C22×#4323C22semidirect
43. #10623174C22semidirect
46. C2×#66946C22semidirect
47. C2×#66941C22semidirect
50. C11×#452C22semidirect
51. C2×C11×#103C22semidirect
52. C2×C11×#102C22semidirect
54. #10622851C22semidirect
55. C2×#66899C22semidirect
56. C2×#66896C22semidirect
58. #10622804C22semidirect
59. #10622798C22semidirect
60. #10622789C22semidirect
61. #10622776C22semidirect
64. C2×#66879C22semidirect
65. C2×Dic11⋊C8C22semidirect
66. C2×Dic11⋊C8C22semidirect
67. C2×C8×Dic11C22semidirect
68. #10622659C22semidirect
71. #10622432C22semidirect
72. #10622408C22semidirect
73. #10622399C22semidirect
74. #10622373C22semidirect
75. #10622345C22semidirect
76. #10622333C22semidirect
104. C2×C11×Q16C23semidirect
106. C2×C11×SD16C23semidirect
121. #67000C23semidirect
123. Q8×Dic11C23semidirect
129. C2×#4325C23semidirect
137. C2×#4323C23semidirect
169. #66946C23semidirect
171. #66941C23semidirect
174. C11×#103C23semidirect
175. C11×#102C23semidirect
177. #66899C23semidirect
178. #66896C23semidirect
182. #66879C23semidirect
183. Dic11⋊C8C23semidirect
184. Dic11⋊C8C23semidirect
185. C8×Dic11C23semidirect
314. C2×#452D11semidirect
403. C22×Q16C2×D11semidirect
407. C22×SD16C2×D11semidirect
442. #452C2×D11semidirect
450. C2×#103C2×D11semidirect
456. C2×#102C2×D11semidirect
525. C2×Q16C22×D11semidirect
533. C2×SD16C22×D11semidirect
598. #103C22×D11semidirect
604. #102C22×D11semidirect
611. C2×C11#3224semidirect
732. C11C2×#3224semidirect
857. C2#13079716direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231742
C2×#106233612
#130797162
C2×#106227892
C2×#106228042
C2×#106224082
C2×#106223732
C2×#106227982
C2×#106227762
C2×#106224322
C2×#106223992
C2×#106228512
C2×#106226592
C2×#106223452
C2×#106223332
C2×C11×#4522
C2×#322411