Finite Group Databasebeta

← C2×#13079711 #15625129

Subgroups — C2×#13079711 #15625129

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×#10623264C211yesmaximal, characteristic, complemented
2C2×#10623205C211yesmaximal, characteristic, complemented
3#13079711C2116yesmaximal, direct product factor
4C2×#10622325C211yesmaximal, characteristic, complemented
5C2×#10622672C211yesmaximal, characteristic, complemented
6C2×#10622701C211yesmaximal, characteristic, complemented
7C2×#10622411C211yesmaximal, characteristic, complemented
8C2×#10622375C211yesmaximal, characteristic, complemented
9C2×#10622432C211yesmaximal, characteristic, complemented
10C2×#10622399C211yesmaximal, characteristic, complemented
11C2×#10622423C211yesmaximal, characteristic, complemented
12C2×#10622424C211yesmaximal, characteristic, complemented
13C2×#10622389C211yesmaximal, characteristic, complemented
14C2×#10622386C211yesmaximal, characteristic, complemented
15C2×#10622322C211yesmaximal, characteristic, complemented
16C2×C11×#489C211yesmaximal, characteristic, complemented
17C22×#4343C2211yescharacteristic
18C22×D4×D11C2211yescharacteristic
19C2×C11×C4⋊Q8C2211yescharacteristic, complemented
20C2×C11×#124C2211yescharacteristic
21C2×#67000—21no—
22C2×#67000C2211yescharacteristic
23C2×#66999—21no—
24C22×#4326C2211yescharacteristic, complemented
25C22×#4325C2211yescharacteristic, complemented
26C2×#66993C2211yescharacteristic
27C22×#4324C2211yescharacteristic
28C22×#4323C2211yescharacteristic
29C22×D88C2211yescharacteristic
30C22×D88C2211yescharacteristic, complemented
31C22×#4314C2211yescharacteristic
32C22×#4314C2211yescharacteristic, complemented
33#10623264—24no—
34#10623264C2218yescomplemented
35#10623205—24no—
36#10623205C2218yescomplemented
37C2×#66951—21no—
38C2×#66950C2211yescharacteristic
39C2×#66948C2211yescharacteristic
40C2×#66947—21no—
41C2×#66946C2211yescharacteristic, complemented
42C2×#66940C2211yescharacteristic, complemented
43C2×#66937—21no—
44C2×#66937—21no—
45C2×#66935—21no—
46C2×#66935—21no—
47C2×#66928C2211yescharacteristic, complemented
48C2×#66927C2211yescharacteristic
49C2×#66925C2211yescharacteristic
50C11×#489C2218yescomplemented
51C2×C11×#103C2211yescharacteristic, complemented
52C2×C11×#103C2211yescharacteristic, complemented
53C2×C11×#102C2211yescharacteristic
54C2×C11×#102C2211yescharacteristic
55C2×C11×#97C2211yescharacteristic, complemented
56C2×(C2×D11)⋊C8C2211yescharacteristic
57C2×(C2×D11)⋊C8C2211yescharacteristic
58C2×Dic11⋊C8C2211yescharacteristic, complemented
59C2×Dic11⋊C8C2211yescharacteristic, complemented
60#10622701C2218yescomplemented
61#10622672C2218yescomplemented
62C2×#66873C2211yescharacteristic
63C2×#66873C2211yescharacteristic
64C2×#66873C2211yescharacteristic, complemented
65C2×#66873C2211yescharacteristic, complemented
66C2×C4×C11⋊C8C2211yescharacteristic, complemented
67#10622432C2218yescomplemented
68#10622424C2218yescomplemented
69#10622423C2218yescomplemented
70#10622411C2218yescomplemented
71#10622399C2218yescomplemented
72#10622389C2218yescomplemented
73#10622386C2218yescomplemented
74#10622375C2218yescomplemented
75#10622325C2218yescomplemented
76#10622322C2218yescomplemented
77C24×D11—21no—
78C22×Q8×C11—21no—
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11C2311yescharacteristic
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C2×#4343—22no—
85C2×#4343—42no—
86C2×#4343—42no—
87C2×#4343C2314yes—
88C2×D4×D11—22no—
89C2×D4×D11—42no—
90C2×D4×D11—42no—
91C2×D4×D11C2314yes—
92C22×D44—21no—
93C22×D44—21no—
94C22×D44—21no—
95C22×D44—21no—
96C22×D44C2311yescharacteristic
97C22×D44C2311yescharacteristic
98C22×D44C2311yescharacteristic
99C22×C4×D11—21no—
100C22×C4×D11—21no—
101C22×C4×D11C2311yescharacteristic
102C22×Dic22C2311yescharacteristic
103C22×C8×C11C2311yescharacteristic
104C22×C8×C11C2311yescharacteristic
105C11×C4⋊Q8—22no—
106C11×C4⋊Q8C2314yescomplemented
107C11×#124—22no—
108C11×#124C2314yes—
109C2×C11×C4⋊C4—21no—
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—21no—
114C2×C42×C11C2311yescharacteristic
115#67000—28no—
116#67000—22no—
117#67000C2314yes—
118#66999—28no—
119C2×#4326—42no—
120C2×#4326C2314yescomplemented
121C2×#4325—42no—
122C2×#4325C2314yescomplemented
123#66993—22no—
124#66993C2314yes—
125C2×#4324—42no—
126C2×#4324C2314yes—
127C2×#4323—42no—
128C2×#4323C2314yes—
129C2×(C2×D11)⋊C4—21no—
130C2×(C2×D11)⋊C4—21no—
131C2×(C2×D11)⋊C4—21no—
132C2×(C2×D11)⋊C4—21no—
133C2×(C2×D11)⋊C4—21no—
134C2×(C2×D11)⋊C4—21no—
135C2×(C2×D11)⋊C4—21no—
136C2×(C2×D11)⋊C4D411yescharacteristic
137C2×(C2×D11)⋊C4D411yescharacteristic
138C2×C4⋊Dic11—21no—
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4D411yescharacteristic
141C2×Dic11⋊C4D411yescharacteristic
142C2×C4×Dic11—21no—
143C2×C4×Dic11C2311yescharacteristic
144C22×C11⋊C8C2311yescharacteristic
145C22×C11⋊C8C2311yescharacteristic
146C2×D88—42no—
147C2×D88—42no—
148C2×D88C2314yes—
149C2×D88C2314yescomplemented
150C2×#4314—42no—
151C2×#4314—42no—
152C2×#4314C2314yes—
153C2×#4314C2314yescomplemented
154#66951—28no—
155#66950—22no—
156#66950C2314yes—
157#66948—22no—
158#66948C2314yes—
159#66947—28no—
160#66946—22no—
161#66946C2314yescomplemented
162#66940—22no—
163#66940C2314yescomplemented
164#66937—28no—
165#66937—28no—
166#66935—28no—
167#66935—28no—
168#66928—22no—
169#66928C2314yescomplemented
170#66927—22no—
171#66927C2314yes—
172#66925D414yes—
173#66925C2314yes—
174C11×#103C2314yescomplemented
175C11×#103C2314yescomplemented
176C11×#102C2314yes—
177C11×#102C2314yes—
178C11×#97C2314yescomplemented
179(C2×D11)⋊C8C2314yes—
180(C2×D11)⋊C8C2314yes—
181Dic11⋊C8C2314yescomplemented
182Dic11⋊C8C2314yescomplemented
183#66873C2314yes—
184#66873C2314yes—
185#66873C2314yescomplemented
186#66873C2314yescomplemented
187C4×C11⋊C8C2314yescomplemented
188C2×#3224—111nomaximal, Sylow
189C24×C11—21no—
190C23×D11—21no—
191C23×D11—21no—
192C23×D11—21no—
193C23×D11—24no—
194C23×D11—44no—
195C23×D11—82no—
196C23×D11—82no—
197C23×D11C2×D411yescharacteristic
198C2×Q8×C11—21no—
199C2×Q8×C11—24no—
200C2×Q8×C11—22no—
201C2×Q8×C11—22no—
202C2×Q8×C11—82no—
203C2×Q8×C11C2412yes—
204C2×D4×C11—21no—
205C2×D4×C11—22no—
206C2×D4×C11—22no—
207C2×D4×C11C2412yes—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2411yescharacteristic
214C2×C22⋊D11—24no—
215C2×C22⋊D11—24no—
216C2×C22⋊D11—24no—
217C2×C22⋊D11—44no—
218C2×C22⋊D11—82no—
219C2×C22⋊D11—82no—
220C22×Dic11—21no—
221C22×Dic11C2×D411yescharacteristic
222C22×Dic11C2×D411yescharacteristic
223C22×Dic11C2×D411yescharacteristic
224#4343—44no—
225#4343—44no—
226#4343—48no—
227D4×D11—44no—
228D4×D11—44no—
229D4×D11—48no—
230C2×D44—24no—
231C2×D44—24no—
232C2×D44—21no—
233C2×D44—21no—
234C2×D44—21no—
235C2×D44—24no—
236C2×D44—24no—
237C2×D44—22no—
238C2×D44—22no—
239C2×D44—22no—
240C2×D44—22no—
241C2×D44—22no—
242C2×D44—22no—
243C2×D44—44no—
244C2×D44—82no—
245C2×D44—82no—
246C2×D44—82no—
247C2×D44C2412yes—
248C2×D44C2412yes—
249C2×D44C2412yes—
250C2×C4×D11—24no—
251C2×C4×D11—24no—
252C2×C4×D11—22no—
253C2×C4×D11—22no—
254C2×C4×D11—44no—
255C2×C4×D11—82no—
256C2×C4×D11C2×D412yes—
257C2×C4×D11C2412yes—
258C2×Dic22—21no—
259C2×Dic22—22no—
260C2×Dic22—22no—
261C2×Dic22C2412yes—
262C2×C8×C11—22no—
263C2×C8×C11—22no—
264C2×C8×C11C2412yes—
265C2×C8×C11C2412yes—
266C11×C4⋊C4—21no—
267C11×C4⋊C4—21no—
268C11×C4⋊C4—24no—
269C11×C4⋊C4C2412yes—
270C11×C4⋊C4C2412yes—
271C11×C22⋊C4—24no—
272C11×C22⋊C4—24no—
273C42×C11C2×D412yes—
274C42×C11C2412yes—
275#4326—44no—
276#4325—44no—
277#4324—44no—
278#4323—44no—
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—
286(C2×D11)⋊C4C2×D414yes—
287(C2×D11)⋊C4C2×D414yes—
288C4⋊Dic11—24no—
289Dic11⋊C4—24no—
290Dic11⋊C4C2×D414yes—
291Dic11⋊C4C2×D414yes—
292C4×Dic11—24no—
293C4×Dic11C2×D412yes—
294C4×Dic11C2412yes—
295C2×C11⋊C8—22no—
296C2×C11⋊C8—22no—
297C2×C11⋊C8C2412yes—
298C2×C11⋊C8C2412yes—
299D88—44no—
300D88—44no—
301#4314—44no—
302#4314—44no—
303C2×#542—111no—
304C2×#535—111no—
305#3224—1116no—
306C2×#496—111no—
307C2×#495—111no—
308C2×#489D1111yescharacteristic, complemented
309C2×#486—111no—
310C2×#464—111no—
311C2×#460—111no—
312C2×#463—111no—
313C2×#459—111no—
314C2×#452—111no—
315C2×#449—111no—
316C2×#450—111no—
317C2×#447—111no—
318C2×#433—111no—
319C23×C11—22no—
320C23×C11—42no—
321C23×C11—42no—
322C23×C11—42no—
323C23×C11C22×D411yescharacteristic
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—48no—
331C22×D11—42no—
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—84no—
341C22×D11—84no—
342C22×D11—816no—
343C22×D11C22×D412yes—
344Q8×C11—22no—
345Q8×C11—22no—
346Q8×C11—42no—
347Q8×C11—84no—
348D4×C11—22no—
349D4×C11—22no—
350D4×C11—42no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—42no—
357C2×C4×C11—42no—
358C2×C4×C11—42no—
359C2×C4×C11C22×D412yes—
360C2×C4×C11C22×D412yes—
361C2×C4×C11C22×D411yescharacteristic
362C2×C4×C11H(5,𝔽2)12yes—
363C2×C4×C11H(5,𝔽2)12yes—
364C2×C4×C11C2511yescharacteristic
365C22⋊D11—48no—
366C22⋊D11—84no—
367C22⋊D11—84no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—42no—
373C2×Dic11C22×D412yes—
374C2×Dic11C22×D412yes—
375C2×Dic11C22×D412yes—
376D44—22no—
377D44—22no—
378D44—22no—
379D44—22no—
380D44—22no—
381D44—22no—
382D44—48no—
383D44—42no—
384D44—42no—
385D44—42no—
386D44—84no—
387D44—84no—
388D44—84no—
389C4×D11—24no—
390C4×D11—22no—
391C4×D11—22no—
392C4×D11—48no—
393C4×D11—84no—
394Dic22—22no—
395Dic22—22no—
396Dic22—42no—
397C8×C11—22no—
398C8×C11—22no—
399C11⋊C8—22no—
400C11⋊C8—22no—
401C22×#41—111no—
402C23×D4—111no—
403C22×Q16—111no—
404C22×SD16—111no—
405C22×SD16—111no—
406C22×SD16—111no—
407C22×SD16—111no—
408C22×D8—111no—
409C22×D8—111no—
410C22×D8—111no—
411#542—118no—
412#542—224no—
413#535—118no—
414#535—224no—
415C2×C4⋊Q8C2×D1111yescharacteristic, complemented
416C2×#127—111no—
417C2×#127—111no—
418C2×#126—221no—
419C2×#124—111no—
420C2×#124—111no—
421C2×#124—221no—
422C2×#124C2×D1111yescharacteristic
423C2×#123—221no—
424C2×C22⋊Q8—111no—
425C2×C22⋊Q8—221no—
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#489C2×D1118yescomplemented
437#486—118no—
438#464—118no—
439#463—118no—
440#460—118no—
441#459—118no—
442#452—118no—
443#450—118no—
444#449—118no—
445#447—118no—
446#433—118no—
447C2×C4⋊C8—111no—
448C2×C4⋊C8—111no—
449C2×#103C2×D1111yescharacteristic, complemented
450C2×#103C2×D1111yescharacteristic, complemented
451C2×#102—111no—
452C2×#102—111no—
453C2×#102—111no—
454C2×#102—111no—
455C2×#102C2×D1111yescharacteristic
456C2×#102C2×D1111yescharacteristic
457C2×C22⋊C8—111no—
458C2×C22⋊C8—111no—
459C2×#97C2×D1111yescharacteristic, complemented
460C2×C4×C8—111no—
461C22×C11—42no—
462C22×C11—42no—
463C22×C11—42no—
464C22×C11—84no—
465C22×C11#53512yes—
466C22×C11#57612yes—
467C22×C11#57712yes—
468C22×C11C23×D411yescharacteristic
469C2×D11—22no—
470C2×D11—22no—
471C2×D11—22no—
472C2×D11—44no—
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—22no—
488C4×C11—42no—
489C4×C11—42no—
490C4×C11—42no—
491C4×C11#53512yes—
492C4×C11C2×H(5,𝔽2)11yescharacteristic
493C4×C11C2×H(5,𝔽2)11yescharacteristic
494Dic11—22no—
495Dic11—22no—
496Dic11—22no—
497Dic11—42no—
498C25—221no—
499C2×#41—114no—
500C2×#41—222no—
501C2×#41—442no—
502C2×#41—442no—
503C22×Q8—21no—
504C22×Q8—111no—
505C22×Q8C22×D1111yescharacteristic
506C22×D4—114no—
507C22×D4—111no—
508C22×D4—111no—
509C22×D4—111no—
510C22×D4—221no—
511C22×D4—221no—
512C22×D4—222no—
513C22×D4—221no—
514C22×D4—221no—
515C22×D4—221no—
516C22×D4—221no—
517C22×D4—221no—
518C22×D4—442no—
519C22×D4—442no—
520C22×D4C22×D1111yescharacteristic
521C23×C4—111no—
522C23×C4—221no—
523C23×C4—221no—
524C2×Q16—114no—
525C2×Q16—442no—
526C2×SD16—114no—
527C2×SD16—114no—
528C2×SD16—114no—
529C2×SD16—114no—
530C2×SD16—442no—
531C2×SD16—442no—
532C2×SD16—442no—
533C2×SD16—442no—
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—22no—
545C4⋊Q8C22×D1114yescomplemented
546#127—114no—
547#127—114no—
548#127—222no—
549#127—222no—
550#126—228no—
551#124—22no—
552#124—114no—
553#124—114no—
554#124—222no—
555#124—228no—
556#124—222no—
557#124C22×D1114yes—
558#123—228no—
559C22⋊Q8—114no—
560C22⋊Q8—222no—
561C22⋊Q8—228no—
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—221no—
578C2×C4⋊C4—221no—
579C2×C4⋊C4C22×D1111yescharacteristic
580C2×C4⋊C4C22×D1111yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—111no—
584C2×C22⋊C4—111no—
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—221no—
594C2×C42C22×D1111yescharacteristic
595C4⋊C8—114no—
596C4⋊C8—114no—
597#103C22×D1114yescomplemented
598#103C22×D1114yescomplemented
599#102—114no—
600#102—114no—
601#102—114no—
602#102—114no—
603#102C22×D1114yes—
604#102C22×D1114yes—
605C22⋊C8—114no—
606C22⋊C8—114no—
607#97C22×D1114yescomplemented
608C4×C8—114no—
609C2×C11—82no—
610C2×C11#322414yescomplemented
611C2×C11C2×#53511yescharacteristic
612C2×C11C2×#57611yescharacteristic
613C2×C11C2×#57711yescharacteristic
614D11—42no—
615D11—82no—
616D11—82no—
617D11—82no—
618C24—21no—
619C24—111no—
620C24—224no—
621C24—221no—
622C24—221no—
623C24—221no—
624C24—444no—
625C24—882no—
626C24—882no—
627#41—444no—
628#41—444no—
629#41—448no—
630C2×Q8—21no—
631C2×Q8—24no—
632C2×Q8—22no—
633C2×Q8—22no—
634C2×Q8—82no—
635C2×Q8—112no—
636C2×Q8—221no—
637C2×Q8—222no—
638C2×Q8—222no—
639C2×Q8C23×D1112yes—
640C2×D4—21no—
641C2×D4—22no—
642C2×D4—22no—
643C2×D4—112no—
644C2×D4—112no—
645C2×D4—112no—
646C2×D4—224no—
647C2×D4—224no—
648C2×D4—224no—
649C2×D4—224no—
650C2×D4—224no—
651C2×D4—221no—
652C2×D4—221no—
653C2×D4—221no—
654C2×D4—224no—
655C2×D4—224no—
656C2×D4—222no—
657C2×D4—222no—
658C2×D4—222no—
659C2×D4—222no—
660C2×D4—222no—
661C2×D4—222no—
662C2×D4—444no—
663C2×D4—444no—
664C2×D4—444no—
665C2×D4—448no—
666C2×D4—444no—
667C2×D4—882no—
668C2×D4—882no—
669C2×D4—882no—
670C2×D4—882no—
671C2×D4—882no—
672C2×D4C23×D1112yes—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—111no—
677C22×C4—111no—
678C22×C4—111no—
679C22×C4—112no—
680C22×C4—112no—
681C22×C4—224no—
682C22×C4—224no—
683C22×C4—222no—
684C22×C4—222no—
685C22×C4—221no—
686C22×C4—444no—
687C22×C4—882no—
688C22×C4D4×D1111yescharacteristic
689C22×C4D4×D1111yescharacteristic
690C22×C4C23×D1111yescharacteristic
691Q16—444no—
692SD16—444no—
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—21no—
710C4⋊C4—114no—
711C4⋊C4—114no—
712C4⋊C4—224no—
713C4⋊C4—224no—
714C4⋊C4C23×D1112yes—
715C4⋊C4C23×D1112yes—
716C22⋊C4—24no—
717C22⋊C4—24no—
718C22⋊C4—114no—
719C22⋊C4—114no—
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—224no—
730C42D4×D1112yes—
731C42C23×D1112yes—
732C11C2×#322411yescharacteristic, complemented, Sylow
733C23—22no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—112no—
738C23—222no—
739C23—222no—
740C23—222no—
741C23—222no—
742C23—222no—
743C23—222no—
744C23—448no—
745C23—442no—
746C23—442no—
747C23—442no—
748C23—442no—
749C23—442no—
750C23—442no—
751C23—442no—
752C23—442no—
753C23—442no—
754C23—884no—
755C23—884no—
756C23—8816no—
757C23C2×D4×D1111yescharacteristic
758Q8—22no—
759Q8—22no—
760Q8—42no—
761Q8—84no—
762Q8—222no—
763Q8—222no—
764Q8—442no—
765D4—22no—
766D4—22no—
767D4—42no—
768D4—222no—
769D4—222no—
770D4—222no—
771D4—222no—
772D4—222no—
773D4—222no—
774D4—448no—
775D4—448no—
776D4—442no—
777D4—442no—
778D4—442no—
779D4—884no—
780D4—884no—
781D4—884no—
782D4—884no—
783D4—884no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—112no—
793C2×C4—112no—
794C2×C4—112no—
795C2×C4—222no—
796C2×C4—222no—
797C2×C4—222no—
798C2×C4—222no—
799C2×C4—222no—
800C2×C4—224no—
801C2×C4—222no—
802C2×C4—448no—
803C2×C4—442no—
804C2×C4—884no—
805C2×C4C2×D4×D1112yes—
806C2×C4C2×D4×D1112yes—
807C2×C4C2×D4×D1111yescharacteristic
808C2×C4#6704212yes—
809C2×C4#6704212yes—
810C2×C4C24×D1111yescharacteristic
811C8—22no—
812C8—22no—
813C8—222no—
814C8—222no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—84no—
819C22—222no—
820C22—222no—
821C22—222no—
822C22—444no—
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#1062320512yes—
837C22#1062330512yes—
838C22#1062330912yes—
839C22C22×D4×D1111yescharacteristic
840C4—22no—
841C4—22no—
842C4—42no—
843C4—42no—
844C4—42no—
845C4—222no—
846C4—222no—
847C4—222no—
848C4—442no—
849C4#1062320512yes—
850C4C2×#6704211yescharacteristic
851C4C2×#6704211yescharacteristic
852C2—82no—
853C2—442no—
854C2—882no—
855C2—882no—
856C2—882no—
857C2#1307971114yesdirect product factor
858C2C2×#1062320511yescharacteristic
859C2C2×#1062330511yescharacteristic
860C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#489C2
socleC23×C11C22×D4
hypercenterC2×#489D11
hypocenterC11C2×#3224
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×#10623264C2semidirect
2. C2×#10623205C2semidirect
3. #13079711C2direct (N × H)
4. C2×#10622325C2semidirect
5. C2×#10622672C2semidirect
6. C2×#10622701C2semidirect
7. C2×#10622411C2semidirect
8. C2×#10622375C2semidirect
9. C2×#10622432C2semidirect
10. C2×#10622399C2semidirect
11. C2×#10622423C2semidirect
12. C2×#10622424C2semidirect
13. C2×#10622389C2semidirect
14. C2×#10622386C2semidirect
15. C2×#10622322C2semidirect
16. C2×C11×#489C2semidirect
19. C2×C11×C4⋊Q8C22semidirect
24. C22×#4326C22semidirect
25. C22×#4325C22semidirect
30. C22×D88C22semidirect
32. C22×#4314C22semidirect
34. #10623264C22semidirect
36. #10623205C22semidirect
41. C2×#66946C22semidirect
42. C2×#66940C22semidirect
47. C2×#66928C22semidirect
50. C11×#489C22semidirect
51. C2×C11×#103C22semidirect
52. C2×C11×#103C22semidirect
55. C2×C11×#97C22semidirect
58. C2×Dic11⋊C8C22semidirect
59. C2×Dic11⋊C8C22semidirect
60. #10622701C22semidirect
61. #10622672C22semidirect
64. C2×#66873C22semidirect
65. C2×#66873C22semidirect
66. C2×C4×C11⋊C8C22semidirect
67. #10622432C22semidirect
68. #10622424C22semidirect
69. #10622423C22semidirect
70. #10622411C22semidirect
71. #10622399C22semidirect
72. #10622389C22semidirect
73. #10622386C22semidirect
74. #10622375C22semidirect
75. #10622325C22semidirect
76. #10622322C22semidirect
106. C11×C4⋊Q8C23semidirect
120. C2×#4326C23semidirect
122. C2×#4325C23semidirect
149. C2×D88C23semidirect
153. C2×#4314C23semidirect
161. #66946C23semidirect
163. #66940C23semidirect
169. #66928C23semidirect
174. C11×#103C23semidirect
175. C11×#103C23semidirect
178. C11×#97C23semidirect
181. Dic11⋊C8C23semidirect
182. Dic11⋊C8C23semidirect
185. #66873C23semidirect
186. #66873C23semidirect
187. C4×C11⋊C8C23semidirect
308. C2×#489D11semidirect
415. C2×C4⋊Q8C2×D11semidirect
436. #489C2×D11semidirect
449. C2×#103C2×D11semidirect
450. C2×#103C2×D11semidirect
459. C2×#97C2×D11semidirect
545. C4⋊Q8C22×D11semidirect
597. #103C22×D11semidirect
598. #103C22×D11semidirect
607. #97C22×D11semidirect
610. C2×C11#3224semidirect
732. C11C2×#3224semidirect
857. C2#13079711direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232642
C2×#106232052
#130797112
C2×#106223252
C2×#106226722
C2×#106227012
C2×#106224112
C2×#106223752
C2×#106224322
C2×#106223992
C2×#106224232
C2×#106224242
C2×#106223892
C2×#106223862
C2×#106223222
C2×C11×#4892
C2×#322411