Finite Group Databasebeta

← C2×#13080812 #15630565

Subgroups — C2×#13080812 #15630565

Order 2816.

2318 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623149C211yesmaximal, characteristic, complemented
2C2×#10623143C211yesmaximal, characteristic, complemented
3#13080812C2116yesmaximal, direct product factor
4C2×#10622381C211yesmaximal, characteristic, complemented
5C2×#10622480C211yesmaximal, characteristic, complemented
6C2×#10622646C211yesmaximal, characteristic, complemented
7C2×#10622484C211yesmaximal, characteristic, complemented
8C2×#10622393C211yesmaximal, characteristic, complemented
9C2×#10622766C211yesmaximal, characteristic, complemented
10C2×#10622650C211yesmaximal, characteristic, complemented
11C2×#10622769C211yesmaximal, characteristic, complemented
12C2×#10622369C211yesmaximal, characteristic, complemented
13C2×#10622741C211yesmaximal, characteristic, complemented
14C2×#10622746C211yesmaximal, characteristic, complemented
15C2×#10622383C211yesmaximal, characteristic, complemented
16C2×C11×#469C211yesmaximal, characteristic, complemented
17C22×D4×D11C2211yescharacteristic
18C22×#4339C2211yescharacteristic
19C22×C11×D8C2211yescharacteristic
20C22×C11×M16C2211yescharacteristic, complemented
21C2×C11×#121C2211yescharacteristic
22C2×C11×#121C2211yescharacteristic, complemented
23C2×#66992—21no—
24C2×#66991—21no—
25C2×#66991C2211yescharacteristic
26C2×#66990—21no—
27C2×#66989C2211yescharacteristic
28C2×D4×Dic11—21no—
29C2×D4×Dic11C2211yescharacteristic, complemented
30C22×#4324C2211yescharacteristic, complemented
31C22×#4323C2211yescharacteristic
32C2×C4×C22⋊D11C2211yescharacteristic
33C22×C4⋊Dic11C2211yescharacteristic, complemented
34C22×#4313C2211yescharacteristic
35#10623149—24no—
36#10623149C2218yescomplemented
37#10623143—24no—
38#10623143C2218yescomplemented
39C2×#66950C2211yescharacteristic
40C2×#66946C2211yescharacteristic
41C2×#66945C2211yescharacteristic
42C2×#66943C2211yescharacteristic, complemented
43C2×#66939—21no—
44C2×#66936—21no—
45C2×C22⋊C4×D11—21no—
46C2×#66932—21no—
47C11×#469C2218yescomplemented
48C2×C11×#106C2211yescharacteristic, complemented
49C2×C11×#102C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic, complemented
51C2×#66896C2211yescharacteristic
52C2×#66896C2211yescharacteristic
53C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
54#10622769C2218yescomplemented
55#10622766C2218yescomplemented
56#10622746C2218yescomplemented
57#10622741C2218yescomplemented
58C2×#66885C2211yescharacteristic
59C2×#66885C2211yescharacteristic
60C2×(C2×D11)⋊C8C2211yescharacteristic
61C2×#66880C2211yescharacteristic, complemented
62C2×#66880C2211yescharacteristic, complemented
63C2×Dic11⋊C8C2211yescharacteristic, complemented
64C2×C8×Dic11C2211yescharacteristic, complemented
65#10622650C2218yescomplemented
66#10622646C2218yescomplemented
67C2×#66874C2211yescharacteristic, complemented
68C2×#66873C2211yescharacteristic
69C2×#66871C2211yescharacteristic, complemented
70C2×#66871C2211yescharacteristic, complemented
71#10622484C2218yescomplemented
72#10622480C2218yescomplemented
73#10622393C2218yescomplemented
74#10622383C2218yescomplemented
75#10622381C2218yescomplemented
76#10622369C2218yescomplemented
77C24×D11—21no—
78C22×D4×C11—21no—
79C22×D4×C11—21no—
80C22×D4×C11C2311yescharacteristic
81C22×D4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C22×C22⋊D11D411yescharacteristic
87C23×Dic11—21no—
88C23×Dic11—21no—
89C2×D4×D11—24no—
90C2×D4×D11—22no—
91C2×D4×D11—42no—
92C2×D4×D11C2314yes—
93C2×#4339—22no—
94C2×#4339—24no—
95C2×#4339—42no—
96C2×#4339C2314yes—
97C22×D44C2311yescharacteristic
98C22×C4×D11—21no—
99C22×C4×D11—21no—
100C22×C4×D11C2311yescharacteristic
101C22×Dic22C2311yescharacteristic
102C2×C11×D8—42no—
103C2×C11×D8C2314yes—
104C2×C11×M16—42no—
105C2×C11×M16C2314yescomplemented
106C22×C8×C11C2311yescharacteristic
107C22×C8×C11C2311yescharacteristic
108C11×#121—22no—
109C11×#121—22no—
110C11×#121C2314yes—
111C11×#121C2314yescomplemented
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—21no—
116C2×C22⋊Dic11—21no—
117C2×C22⋊Dic11—21no—
118C2×C22⋊Dic11—21no—
119C2×C22⋊Dic11—21no—
120C2×C22⋊Dic11D411yescharacteristic
121#66992—28no—
122#66991—22no—
123#66991—28no—
124#66991C2314yes—
125#66990—28no—
126#66989—22no—
127#66989C2314yes—
128D4×Dic11—28no—
129D4×Dic11—22no—
130D4×Dic11C2314yescomplemented
131C2×#4324—42no—
132C2×#4324C2314yescomplemented
133C2×#4323—24no—
134C2×#4323C2314yes—
135C4×C22⋊D11D414yes—
136C4×C22⋊D11C2314yes—
137C2×(C2×D11)⋊C4—21no—
138C2×(C2×D11)⋊C4—21no—
139C2×(C2×D11)⋊C4—21no—
140C2×(C2×D11)⋊C4D411yescharacteristic
141C2×C4⋊Dic11—21no—
142C2×C4⋊Dic11—22no—
143C2×C4⋊Dic11—21no—
144C2×C4⋊Dic11—21no—
145C2×C4⋊Dic11C2311yescharacteristic
146C2×C4⋊Dic11C2311yescharacteristic
147C2×C4⋊Dic11C2314yescomplemented
148C2×Dic11⋊C4—21no—
149C2×Dic11⋊C4D411yescharacteristic
150C2×C4×Dic11—21no—
151C2×C4×Dic11C2311yescharacteristic
152C22×C11⋊C8C2311yescharacteristic
153C22×C11⋊C8C2311yescharacteristic
154C2×#4313—42no—
155C2×#4313C2314yes—
156#66950—22no—
157#66950C2314yes—
158#66946—22no—
159#66946C2314yes—
160#66945—22no—
161#66945C2314yes—
162#66943—22no—
163#66943C2314yescomplemented
164#66939—28no—
165#66936—28no—
166C22⋊C4×D11—28no—
167#66932—28no—
168C11×#106C2314yescomplemented
169C11×#102C2314yes—
170C11×#102C2314yescomplemented
171#66896C2314yes—
172#66896C2314yes—
173C22⋊(C11⋊C8)C2314yescomplemented
174#66885C2314yes—
175#66885C2314yes—
176(C2×D11)⋊C8C2314yes—
177#66880C2314yescomplemented
178#66880C2314yescomplemented
179Dic11⋊C8C2314yescomplemented
180C8×Dic11C2314yescomplemented
181#66874C2314yescomplemented
182#66873C2314yes—
183#66871C2314yescomplemented
184#66871C2314yescomplemented
185C2×#3322—111nomaximal, Sylow
186C24×C11—21no—
187C24×C11—21no—
188C24×C11C2×D411yescharacteristic
189C23×D11—21no—
190C23×D11—24no—
191C23×D11—44no—
192C23×D11—44no—
193C23×D11—82no—
194C23×D11C2×D411yescharacteristic
195C2×D4×C11—24no—
196C2×D4×C11—24no—
197C2×D4×C11—21no—
198C2×D4×C11—21no—
199C2×D4×C11—22no—
200C2×D4×C11—22no—
201C2×D4×C11—22no—
202C2×D4×C11—22no—
203C2×D4×C11—44no—
204C2×D4×C11—82no—
205C2×D4×C11C2412yes—
206C2×D4×C11C2412yes—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
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—42no—
219C2×C22⋊D11—44no—
220C2×C22⋊D11—44no—
221C2×C22⋊D11—82no—
222C2×C22⋊D11C2×D414yes—
223C22×Dic11—24no—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C22×Dic11—21no—
227C22×Dic11—24no—
228C22×Dic11—82no—
229C22×Dic11—82no—
230C22×Dic11C2×D411yescharacteristic
231C22×Dic11C2×D411yescharacteristic
232C22×Dic11C2×D411yescharacteristic
233D4×D11—28no—
234D4×D11—44no—
235D4×D11—48no—
236#4339—28no—
237#4339—44no—
238#4339—48no—
239C2×D44—21no—
240C2×D44—22no—
241C2×D44#4114yes—
242C2×D44C2412yes—
243C2×C4×D11—24no—
244C2×C4×D11—24no—
245C2×C4×D11—22no—
246C2×C4×D11—22no—
247C2×C4×D11—44no—
248C2×C4×D11—82no—
249C2×C4×D11C2×D412yes—
250C2×C4×D11C2412yes—
251C2×Dic22—21no—
252C2×Dic22—22no—
253C2×Dic22—22no—
254C2×Dic22C2412yes—
255C11×D8—44no—
256C11×M16—44no—
257C2×C8×C11—22no—
258C2×C8×C11—22no—
259C2×C8×C11C2412yes—
260C2×C8×C11C2412yes—
261C11×C4⋊C4—21no—
262C11×C4⋊C4—21no—
263C11×C4⋊C4C2412yes—
264C11×C4⋊C4C2412yes—
265C11×C22⋊C4—24no—
266C11×C22⋊C4—24no—
267C22⋊Dic11—24no—
268C22⋊Dic11—24no—
269C22⋊Dic11—24no—
270C22⋊Dic11—24no—
271C22⋊Dic11C2×D414yes—
272#4324—44no—
273#4323—28no—
274(C2×D11)⋊C4—24no—
275(C2×D11)⋊C4—24no—
276(C2×D11)⋊C4—24no—
277(C2×D11)⋊C4C2×D414yes—
278C4⋊Dic11—24no—
279C4⋊Dic11—24no—
280C4⋊Dic11—24no—
281C4⋊Dic11—21no—
282C4⋊Dic11—21no—
283C4⋊Dic11C2412yes—
284C4⋊Dic11C2412yes—
285Dic11⋊C4—24no—
286Dic11⋊C4C2×D414yes—
287C4×Dic11—24no—
288C4×Dic11C2×D412yes—
289C4×Dic11C2412yes—
290C2×C11⋊C8—22no—
291C2×C11⋊C8—22no—
292C2×C11⋊C8C2412yes—
293C2×C11⋊C8C2412yes—
294#4313—44no—
295C2×#553—111no—
296C2×#546—111no—
297#3322—1116no—
298C2×#488—111no—
299C2×#485—111no—
300C2×#480—111no—
301C2×#478—111no—
302C2×#469D1111yescharacteristic, complemented
303C2×#468—111no—
304C2×#463—111no—
305C2×#449—111no—
306C2×#447—111no—
307C2×C4×D8—111no—
308C2×#436—111no—
309C2×#417—111no—
310C2×#418—111no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—42no—
317C23×C11—42no—
318C23×C11—42no—
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—48no—
330C22×D11—48no—
331C22×D11—42no—
332C22×D11—42no—
333C22×D11—84no—
334C22×D11—816no—
335C22×D11C22×D412yes—
336D4×C11—22no—
337D4×C11—22no—
338D4×C11—22no—
339D4×C11—22no—
340D4×C11—48no—
341D4×C11—42no—
342D4×C11—42no—
343D4×C11—84no—
344C2×C4×C11—22no—
345C2×C4×C11—24no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—42no—
351C2×C4×C11—42no—
352C2×C4×C11C22×D412yes—
353C2×C4×C11C22×D411yescharacteristic
354C2×C4×C11C2×#4112yes—
355C2×C4×C11H(5,𝔽2)12yes—
356C2×C4×C11C2511yescharacteristic
357C22⋊D11—44no—
358C22⋊D11—48no—
359C22⋊D11—48no—
360C22⋊D11—84no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—42no—
368C2×Dic11—42no—
369C2×Dic11—42no—
370C2×Dic11—84no—
371C2×Dic11—84no—
372C2×Dic11C22×D412yes—
373C2×Dic11C22×D412yes—
374C2×Dic11C22×D412yes—
375D44—24no—
376D44—22no—
377D44C2×#4114yes—
378C4×D11—24no—
379C4×D11—22no—
380C4×D11—22no—
381C4×D11—48no—
382C4×D11—84no—
383Dic22—22no—
384Dic22—22no—
385Dic22—42no—
386C8×C11—22no—
387C8×C11—22no—
388C11⋊C8—22no—
389C11⋊C8—22no—
390C22×#41—111no—
391C23×D4—111no—
392C22×SD16—111no—
393C22×D8—111no—
394C22×D8C2×D1111yescharacteristic
395C22×M16—111no—
396C22×M16C2×D1111yescharacteristic, complemented
397#553—118no—
398#553—224no—
399#546—118no—
400#546—224no—
401C2×#126—221no—
402C2×#125—111no—
403C2×#124—111no—
404C2×#123—221no—
405C2×#123—221no—
406C2×C22⋊Q8—111no—
407C2×#121—111no—
408C2×#121—221no—
409C2×#121—221no—
410C2×#121C2×D1111yescharacteristic
411C2×#121C2×D1111yescharacteristic, complemented
412C2×#120—221no—
413C2×C4×D4—111no—
414C2×C4×D4—111no—
415C2×C4×D4—111no—
416C2×C4×D4—221no—
417C2×#117—111no—
418C22×C4⋊C4—111no—
419C22×C22⋊C4—221no—
420#488—118no—
421#485—118no—
422#480—118no—
423#478—118no—
424#469C2×D1118yescomplemented
425#468—118no—
426#463—118no—
427#449—118no—
428#447—118no—
429C4×D8—118no—
430#436—118no—
431C2×#107—111no—
432C2×#107—111no—
433C2×#106C2×D1111yescharacteristic, complemented
434C2×C4⋊C8—111no—
435#418—118no—
436#417—118no—
437C2×#103—111no—
438C2×#103—111no—
439C2×#103—111no—
440C2×#102—111no—
441C2×#102—111no—
442C2×#102—111no—
443C2×#102—111no—
444C2×#102—111no—
445C2×#102C2×D1111yescharacteristic
446C2×#102C2×D1111yescharacteristic, complemented
447C2×C22⋊C8—111no—
448C2×C22⋊C8—111no—
449C2×C4×C8—111no—
450C22×C11—22no—
451C22×C11—22no—
452C22×C11—22no—
453C22×C11—44no—
454C22×C11—42no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—84no—
461C22×C11—84no—
462C22×C11#54612yes—
463C22×C11#57512yes—
464C22×C11#57612yes—
465C22×C11C23×D411yescharacteristic
466C2×D11—24no—
467C2×D11—22no—
468C2×D11—22no—
469C2×D11—22no—
470C2×D11—44no—
471C2×D11—48no—
472C2×D11—42no—
473C2×D11—42no—
474C2×D11—816no—
475C4×C11—22no—
476C4×C11—42no—
477C4×C11—42no—
478C4×C11#54612yes—
479C4×C11C22×#4111yescharacteristic
480C4×C11C2×H(5,𝔽2)11yescharacteristic
481Dic11—22no—
482Dic11—22no—
483Dic11—22no—
484Dic11—42no—
485Dic11—42no—
486Dic11—42no—
487C25—221no—
488C2×#41—114no—
489C2×#41—224no—
490C2×#41—222no—
491C2×#41—442no—
492C22×Q8—111no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—111no—
496C22×D4—114no—
497C22×D4—111no—
498C22×D4—222no—
499C22×D4—221no—
500C22×D4—224no—
501C22×D4—221no—
502C22×D4—221no—
503C22×D4—442no—
504C22×D4C22×D1111yescharacteristic
505C22×D4C22×D1111yescharacteristic
506C23×C4—111no—
507C23×C4—221no—
508C23×C4—221no—
509C23×C4—221no—
510C23×C4—221no—
511C23×C4C22×D1111yescharacteristic
512C2×SD16—114no—
513C2×SD16—442no—
514C2×D8—42no—
515C2×D8—114no—
516C2×D8—224no—
517C2×D8C22×D1114yes—
518C2×M16—42no—
519C2×M16—114no—
520C2×M16—442no—
521C2×M16C22×D1114yescomplemented
522C22×C8—111no—
523C22×C8—111no—
524C22×C8C22×D1111yescharacteristic
525C22×C8C22×D1111yescharacteristic
526#126—228no—
527#125—114no—
528#125—222no—
529#124—114no—
530#124—222no—
531#123—228no—
532#123—228no—
533C22⋊Q8—114no—
534C22⋊Q8—222no—
535#121—22no—
536#121—22no—
537#121—114no—
538#121—228no—
539#121—222no—
540#121—228no—
541#121C22×D1114yes—
542#121C22×D1114yescomplemented
543#120—228no—
544C4×D4—114no—
545C4×D4—114no—
546C4×D4—114no—
547C4×D4—114no—
548C4×D4—222no—
549C4×D4—222no—
550C4×D4—228no—
551#117—114no—
552#117—222no—
553C2×C4⋊C4—111no—
554C2×C4⋊C4—111no—
555C2×C4⋊C4—111no—
556C2×C4⋊C4—114no—
557C2×C4⋊C4—221no—
558C2×C4⋊C4—221no—
559C2×C4⋊C4—221no—
560C2×C4⋊C4—221no—
561C2×C4⋊C4—222no—
562C2×C4⋊C4C22×D1111yescharacteristic
563C2×C4⋊C4C22×D1111yescharacteristic
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—111no—
567C2×C22⋊C4—111no—
568C2×C22⋊C4—228no—
569C2×C22⋊C4—221no—
570C2×C22⋊C4—221no—
571C2×C22⋊C4—221no—
572C2×C22⋊C4—221no—
573C2×C22⋊C4—221no—
574C2×C22⋊C4—221no—
575C2×C22⋊C4—221no—
576C2×C42—111no—
577C2×C42—221no—
578#107—114no—
579#107—114no—
580#106C22×D1114yescomplemented
581C4⋊C8—114no—
582#103—114no—
583#103—114no—
584#103—114no—
585#102—114no—
586#102—114no—
587#102—114no—
588#102—114no—
589#102—114no—
590#102C22×D1114yes—
591#102C22×D1114yescomplemented
592C22⋊C8—114no—
593C22⋊C8—114no—
594C4×C8—114no—
595C2×C11—42no—
596C2×C11—82no—
597C2×C11—82no—
598C2×C11#332214yescomplemented
599C2×C11C2×#54611yescharacteristic
600C2×C11C2×#57511yescharacteristic
601C2×C11C2×#57611yescharacteristic
602D11—42no—
603D11—44no—
604C24—21no—
605C24—21no—
606C24—111no—
607C24—224no—
608C24—221no—
609C24—444no—
610C24—444no—
611C24—882no—
612C24D4×D1111yescharacteristic
613#41—228no—
614#41—444no—
615#41—448no—
616C2×Q8—112no—
617C2×Q8—221no—
618C2×Q8—222no—
619C2×Q8—222no—
620C2×D4—24no—
621C2×D4—24no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—44no—
629C2×D4—82no—
630C2×D4—114no—
631C2×D4—114no—
632C2×D4—112no—
633C2×D4—224no—
634C2×D4—228no—
635C2×D4—224no—
636C2×D4—224no—
637C2×D4—221no—
638C2×D4—222no—
639C2×D4—444no—
640C2×D4—448no—
641C2×D4—442no—
642C2×D4—444no—
643C2×D4—444no—
644C2×D4—882no—
645C2×D4C23×D1112yes—
646C2×D4C23×D1112yes—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—111no—
652C22×C4—111no—
653C22×C4—111no—
654C22×C4—112no—
655C22×C4—112no—
656C22×C4—224no—
657C22×C4—224no—
658C22×C4—222no—
659C22×C4—222no—
660C22×C4—221no—
661C22×C4—221no—
662C22×C4—221no—
663C22×C4—224no—
664C22×C4—224no—
665C22×C4—444no—
666C22×C4—882no—
667C22×C4—882no—
668C22×C4—882no—
669C22×C4D4×D1112yes—
670C22×C4D4×D1111yescharacteristic
671C22×C4C23×D1112yes—
672C22×C4C23×D1111yescharacteristic
673SD16—444no—
674D8—44no—
675D8—228no—
676M16—44no—
677M16—444no—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—112no—
681C2×C8—112no—
682C2×C8—222no—
683C2×C8—222no—
684C2×C8C23×D1112yes—
685C2×C8C23×D1112yes—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—114no—
689C4⋊C4—112no—
690C4⋊C4—112no—
691C4⋊C4—224no—
692C4⋊C4—224no—
693C4⋊C4—224no—
694C4⋊C4—221no—
695C4⋊C4—221no—
696C4⋊C4—224no—
697C4⋊C4C23×D1112yes—
698C4⋊C4C23×D1112yes—
699C22⋊C4—24no—
700C22⋊C4—24no—
701C22⋊C4—114no—
702C22⋊C4—114no—
703C22⋊C4—224no—
704C22⋊C4—224no—
705C22⋊C4—224no—
706C22⋊C4—224no—
707C22⋊C4—224no—
708C22⋊C4—224no—
709C22⋊C4—224no—
710C42—112no—
711C42—112no—
712C42—224no—
713C11C2×#332211yescharacteristic, complemented, Sylow
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—112no—
726C23—222no—
727C23—222no—
728C23—222no—
729C23—224no—
730C23—222no—
731C23—448no—
732C23—448no—
733C23—442no—
734C23—442no—
735C23—884no—
736C23—8816no—
737C23C2×D4×D1112yes—
738C23C2×D4×D1111yescharacteristic
739Q8—222no—
740Q8—222no—
741Q8—442no—
742D4—22no—
743D4—22no—
744D4—22no—
745D4—22no—
746D4—48no—
747D4—42no—
748D4—42no—
749D4—84no—
750D4—114no—
751D4—224no—
752D4—222no—
753D4—444no—
754D4—448no—
755D4—448no—
756D4—884no—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—112no—
766C2×C4—112no—
767C2×C4—112no—
768C2×C4—222no—
769C2×C4—222no—
770C2×C4—222no—
771C2×C4—224no—
772C2×C4—222no—
773C2×C4—222no—
774C2×C4—222no—
775C2×C4—222no—
776C2×C4—222no—
777C2×C4—448no—
778C2×C4—442no—
779C2×C4—442no—
780C2×C4—442no—
781C2×C4—884no—
782C2×C4—884no—
783C2×C4—884no—
784C2×C4C2×D4×D1112yes—
785C2×C4C2×D4×D1111yescharacteristic
786C2×C4#6703712yes—
787C2×C4#41×D1112yes—
788C2×C4C24×D1111yescharacteristic
789C8—22no—
790C8—22no—
791C8—222no—
792C8—222no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—44no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—84no—
804C22—84no—
805C22—222no—
806C22—224no—
807C22—222no—
808C22—222no—
809C22—442no—
810C22—442no—
811C22—444no—
812C22—448no—
813C22—8816no—
814C22#1062314112yes—
815C22#1062330412yes—
816C22#1062330512yes—
817C22C22×D4×D1111yescharacteristic
818C4—22no—
819C4—42no—
820C4—42no—
821C4—222no—
822C4—222no—
823C4—222no—
824C4—442no—
825C4—442no—
826C4—442no—
827C4#1062314112yes—
828C4C2×#6703711yescharacteristic
829C4C2×#41×D1111yescharacteristic
830C2—42no—
831C2—82no—
832C2—82no—
833C2—442no—
834C2—444no—
835C2#1308081214yesdirect product factor
836C2C2×#1062314111yescharacteristic
837C2C2×#1062330411yescharacteristic
838C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#469C2
socleC23×C11C22×D4
hypercenterC2×#469D11
hypocenterC11C2×#3322
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#469

Complements

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

NH ≅ G/Ntype
1. C2×#10623149C2semidirect
2. C2×#10623143C2semidirect
3. #13080812C2direct (N × H)
4. C2×#10622381C2semidirect
5. C2×#10622480C2semidirect
6. C2×#10622646C2semidirect
7. C2×#10622484C2semidirect
8. C2×#10622393C2semidirect
9. C2×#10622766C2semidirect
10. C2×#10622650C2semidirect
11. C2×#10622769C2semidirect
12. C2×#10622369C2semidirect
13. C2×#10622741C2semidirect
14. C2×#10622746C2semidirect
15. C2×#10622383C2semidirect
16. C2×C11×#469C2semidirect
20. C22×C11×M16C22semidirect
22. C2×C11×#121C22semidirect
29. C2×D4×Dic11C22semidirect
30. C22×#4324C22semidirect
33. C22×C4⋊Dic11C22semidirect
36. #10623149C22semidirect
38. #10623143C22semidirect
42. C2×#66943C22semidirect
47. C11×#469C22semidirect
48. C2×C11×#106C22semidirect
50. C2×C11×#102C22semidirect
53. C2×C22⋊(C11⋊C8)C22semidirect
54. #10622769C22semidirect
55. #10622766C22semidirect
56. #10622746C22semidirect
57. #10622741C22semidirect
61. C2×#66880C22semidirect
62. C2×#66880C22semidirect
63. C2×Dic11⋊C8C22semidirect
64. C2×C8×Dic11C22semidirect
65. #10622650C22semidirect
66. #10622646C22semidirect
67. C2×#66874C22semidirect
69. C2×#66871C22semidirect
70. C2×#66871C22semidirect
71. #10622484C22semidirect
72. #10622480C22semidirect
73. #10622393C22semidirect
74. #10622383C22semidirect
75. #10622381C22semidirect
76. #10622369C22semidirect
105. C2×C11×M16C23semidirect
111. C11×#121C23semidirect
130. D4×Dic11C23semidirect
132. C2×#4324C23semidirect
147. C2×C4⋊Dic11C23semidirect
163. #66943C23semidirect
168. C11×#106C23semidirect
170. C11×#102C23semidirect
173. C22⋊(C11⋊C8)C23semidirect
177. #66880C23semidirect
178. #66880C23semidirect
179. Dic11⋊C8C23semidirect
180. C8×Dic11C23semidirect
181. #66874C23semidirect
183. #66871C23semidirect
184. #66871C23semidirect
302. C2×#469D11semidirect
396. C22×M16C2×D11semidirect
411. C2×#121C2×D11semidirect
424. #469C2×D11semidirect
433. C2×#106C2×D11semidirect
446. C2×#102C2×D11semidirect
521. C2×M16C22×D11semidirect
542. #121C22×D11semidirect
580. #106C22×D11semidirect
591. #102C22×D11semidirect
598. C2×C11#3322semidirect
713. C11C2×#3322semidirect
835. C2#13080812direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231492
C2×#106231432
#130808122
C2×#106223812
C2×#106224802
C2×#106226462
C2×#106224842
C2×#106223932
C2×#106227662
C2×#106226502
C2×#106227692
C2×#106223692
C2×#106227412
C2×#106227462
C2×#106223832
C2×C11×#4692
C2×#332211