Finite Group Databasebeta

← C2×#13079464 #15624422

Subgroups — C2×#13079464 #15624422

Order 2816.

2378 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623139C211yesmaximal, characteristic, complemented
2C2×#10623336C211yesmaximal, characteristic, complemented
3#13079464C2116yesmaximal, direct product factor
4C2×#10622390C211yesmaximal, characteristic, complemented
5C2×#10622336C211yesmaximal, characteristic, complemented
6C2×#10622648C211yesmaximal, characteristic, complemented
7C2×#10622387C211yesmaximal, characteristic, complemented
8C2×#10622772C211yesmaximal, characteristic, complemented
9C2×#10622393C211yesmaximal, characteristic, complemented
10C2×#10622770C211yesmaximal, characteristic, complemented
11C2×#10622391C211yesmaximal, characteristic, complemented
12C2×#10622771C211yesmaximal, characteristic, complemented
13C2×#10622771C211yesmaximal, characteristic, complemented
14C2×#10622831C211yesmaximal, characteristic, complemented
15C2×#10622340C211yesmaximal, characteristic, complemented
16C2×C11×#447C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C22×#4341C2211yescharacteristic, complemented
19C22×#4339C2211yescharacteristic
20C22×C11×D8C2211yescharacteristic
21C22×C11×D8C2211yescharacteristic
22C2×C11×#121C2211yescharacteristic
23C2×#67006—21no—
24C2×#67006—21no—
25#10623336—24no—
26#10623336C2218yescomplemented
27C2×#66993—21no—
28C2×#66992—21no—
29C2×#66991—21no—
30C2×#66991C2211yescharacteristic
31C2×#66991C2211yescharacteristic
32C2×#66991C2211yescharacteristic
33C2×#66991C2211yescharacteristic
34C2×#66991C2211yescharacteristic, complemented
35C2×#66989—21no—
36C22×#4324C2211yescharacteristic
37C22×#4324C2211yescharacteristic
38C2×#66979C2211yescharacteristic
39C2×#66977C2211yescharacteristic
40C22×#4313C2211yescharacteristic, complemented
41C22×C8×D11C2211yescharacteristic, complemented
42#10623139—24no—
43#10623139C2218yescomplemented
44C2×#66950C2211yescharacteristic, complemented
45C2×C4⋊C4×D11C2211yescharacteristic, complemented
46C2×#66937—21no—
47C2×#66931—21no—
48C11×#447C2218yescomplemented
49C2×C11×#102C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×C11×C22⋊C8C2211yescharacteristic
52#10622831C2218yescomplemented
53C2×#66896C2211yescharacteristic
54C2×#66896C2211yescharacteristic
55C2×#66896C2211yescharacteristic, complemented
56C2×#66896C2211yescharacteristic, complemented
57C2×C22⋊(C11⋊C8)C2211yescharacteristic
58#10622772C2218yescomplemented
59#10622771C2218yescomplemented
60#10622771C2218yescomplemented
61#10622770C2218yescomplemented
62C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
63C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
64C2×#66882C2211yescharacteristic, complemented
65C2×#66881C2211yescharacteristic, complemented
66C2×#66880C2211yescharacteristic, complemented
67C2×#66880C2211yescharacteristic, complemented
68#10622648C2218yescomplemented
69C2×#66872C2211yescharacteristic, complemented
70C2×#66871C2211yescharacteristic, complemented
71#10622393C2218yescomplemented
72#10622391C2218yescomplemented
73#10622390C2218yescomplemented
74#10622387C2218yescomplemented
75#10622340C2218yescomplemented
76#10622336C2218yescomplemented
77C25×C11—21no—
78C22×D4×C11—21no—
79C22×D4×C11—21no—
80C22×D4×C11—22no—
81C22×D4×C11—42no—
82C22×D4×C11—42no—
83C22×D4×C11C2311yescharacteristic
84C22×D4×C11C2311yescharacteristic
85C22×D4×C11C2311yescharacteristic
86C22×D4×C11C2314yes—
87C23×C4×C11C2311yescharacteristic
88C22×C22⋊D11—21no—
89C22×C22⋊D11—21no—
90C22×C22⋊D11—21no—
91C22×C22⋊D11—21no—
92C22×C22⋊D11—21no—
93C22×C22⋊D11—21no—
94C22×C22⋊D11D411yescharacteristic
95C22×C22⋊D11D411yescharacteristic
96C23×Dic11—21no—
97C2×#4341—22no—
98C2×#4341—42no—
99C2×#4341—42no—
100C2×#4341C2314yescomplemented
101C2×#4339—42no—
102C2×#4339—42no—
103C2×#4339D414yes—
104C2×#4339C2314yes—
105C22×D44D411yescharacteristic
106C22×C4×D11—21no—
107C22×C4×D11C2311yescharacteristic
108C22×C4×D11C2311yescharacteristic
109C22×Dic22D411yescharacteristic
110C22×Dic22C2311yescharacteristic
111C2×C11×D8—42no—
112C2×C11×D8—42no—
113C2×C11×D8C2314yes—
114C2×C11×D8C2314yes—
115C22×C8×C11C2311yescharacteristic
116C22×C8×C11C2311yescharacteristic
117C11×#121—22no—
118C11×#121C2314yes—
119C2×C11×C4⋊C4C2311yescharacteristic
120C2×C11×C22⋊C4—21no—
121#67006—28no—
122#67006—28no—
123C2×C22⋊Dic11—21no—
124C2×C22⋊Dic11—21no—
125C2×C22⋊Dic11—21no—
126C2×C22⋊Dic11—21no—
127C2×C22⋊Dic11—21no—
128C2×C22⋊Dic11—21no—
129C2×C22⋊Dic11—21no—
130#66993—28no—
131#66992—28no—
132#66991—28no—
133#66991—22no—
134#66991—22no—
135#66991—22no—
136#66991—22no—
137#66991—22no—
138#66991C2314yes—
139#66991C2314yes—
140#66991C2314yes—
141#66991C2314yes—
142#66991C2314yescomplemented
143#66989—28no—
144C2×#4324—42no—
145C2×#4324—42no—
146C2×#4324C2314yes—
147C2×#4324C2314yes—
148C2×(C2×D11)⋊C4—21no—
149#66979—22no—
150#66979C2314yes—
151C2×C4⋊Dic11—21no—
152C2×C4⋊Dic11C2311yescharacteristic
153C2×C4⋊Dic11C2311yescharacteristic
154C2×C4⋊Dic11C2311yescharacteristic
155#66977—22no—
156#66977C2314yes—
157C2×Dic11⋊C4—21no—
158C2×Dic11⋊C4—21no—
159C2×C4×Dic11—21no—
160C22×C11⋊C8C2311yescharacteristic
161C22×C11⋊C8C2311yescharacteristic
162C2×#4313—42no—
163C2×#4313C2314yescomplemented
164C2×C8×D11—42no—
165C2×C8×D11C2314yescomplemented
166#66950—22no—
167#66950C2314yescomplemented
168C4⋊C4×D11—22no—
169C4⋊C4×D11C2314yescomplemented
170#66937—28no—
171#66931—28no—
172C11×#102C2314yes—
173C11×#102C2314yes—
174C11×C22⋊C8C2314yes—
175#66896C2314yes—
176#66896C2314yes—
177#66896C2314yescomplemented
178#66896C2314yescomplemented
179C22⋊(C11⋊C8)C2314yes—
180(C2×D11)⋊C8C2314yescomplemented
181(C2×D11)⋊C8C2314yescomplemented
182#66882C2314yescomplemented
183#66881C2314yescomplemented
184#66880C2314yescomplemented
185#66880C2314yescomplemented
186#66872C2314yescomplemented
187#66871C2314yescomplemented
188C2×#3198—111nomaximal, Sylow
189C24×C11—21no—
190C24×C11—21no—
191C24×C11—21no—
192C24×C11—24no—
193C24×C11—44no—
194C24×C11—82no—
195C24×C11—82no—
196C24×C11C2×D411yescharacteristic
197C23×D11C2×D411yescharacteristic
198C23×D11C2×D411yescharacteristic
199C2×D4×C11—24no—
200C2×D4×C11—24no—
201C2×D4×C11—21no—
202C2×D4×C11—21no—
203C2×D4×C11—21no—
204C2×D4×C11—22no—
205C2×D4×C11—22no—
206C2×D4×C11—22no—
207C2×D4×C11—22no—
208C2×D4×C11—22no—
209C2×D4×C11—22no—
210C2×D4×C11—44no—
211C2×D4×C11—44no—
212C2×D4×C11—44no—
213C2×D4×C11—48no—
214C2×D4×C11—82no—
215C2×D4×C11C2412yes—
216C2×D4×C11C2412yes—
217C2×D4×C11C2412yes—
218C22×C4×C11—22no—
219C22×C4×C11—22no—
220C22×C4×C11—21no—
221C22×C4×C11C2×D411yescharacteristic
222C22×C4×C11C2×D412yes—
223C22×C4×C11C2412yes—
224C22×C4×C11C2411yescharacteristic
225C2×C22⋊D11—24no—
226C2×C22⋊D11—24no—
227C2×C22⋊D11—24no—
228C2×C22⋊D11—24no—
229C2×C22⋊D11—24no—
230C2×C22⋊D11—24no—
231C2×C22⋊D11—42no—
232C2×C22⋊D11—42no—
233C2×C22⋊D11—44no—
234C2×C22⋊D11—82no—
235C2×C22⋊D11—82no—
236C2×C22⋊D11—82no—
237C2×C22⋊D11—82no—
238C2×C22⋊D11—82no—
239C2×C22⋊D11C2×D414yes—
240C2×C22⋊D11C2×D414yes—
241C22×Dic11—24no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11—44no—
247C22×Dic11C2×D411yescharacteristic
248C22×Dic11C2×D411yescharacteristic
249#4341—44no—
250#4341—44no—
251#4341—48no—
252#4339—48no—
253#4339—44no—
254#4339—44no—
255C2×D44—42no—
256C2×D44C2×D414yes—
257C2×C4×D11—24no—
258C2×C4×D11—22no—
259C2×C4×D11—22no—
260C2×C4×D11—22no—
261C2×C4×D11—22no—
262C2×C4×D11—82no—
263C2×C4×D11C2×D412yes—
264C2×C4×D11C2×D412yes—
265C2×C4×D11C2412yes—
266C2×C4×D11C2412yes—
267C2×Dic22—21no—
268C2×Dic22—22no—
269C2×Dic22—22no—
270C2×Dic22—42no—
271C2×Dic22C2×D414yes—
272C2×Dic22C2412yes—
273C11×D8—44no—
274C11×D8—44no—
275C2×C8×C11—22no—
276C2×C8×C11—22no—
277C2×C8×C11C2412yes—
278C2×C8×C11C2412yes—
279C11×C4⋊C4—21no—
280C11×C4⋊C4C2412yes—
281C11×C22⋊C4—24no—
282C22⋊Dic11—24no—
283C22⋊Dic11—24no—
284C22⋊Dic11—24no—
285C22⋊Dic11—24no—
286C22⋊Dic11—24no—
287C22⋊Dic11—24no—
288C22⋊Dic11—24no—
289#4324—44no—
290#4324—44no—
291(C2×D11)⋊C4—24no—
292C4⋊Dic11—24no—
293C4⋊Dic11—21no—
294C4⋊Dic11—21no—
295C4⋊Dic11—21no—
296C4⋊Dic11C2412yes—
297C4⋊Dic11C2412yes—
298C4⋊Dic11C2412yes—
299Dic11⋊C4—24no—
300Dic11⋊C4—24no—
301C4×Dic11—24no—
302C2×C11⋊C8—22no—
303C2×C11⋊C8—22no—
304C2×C11⋊C8C2412yes—
305C2×C11⋊C8C2412yes—
306#4313—44no—
307C8×D11—44no—
308C2×#537—111no—
309C2×#535—111no—
310#3198—1116no—
311C2×#481—111no—
312C2×#485—111no—
313C2×#482—111no—
314C2×#480—111no—
315C2×#469—111no—
316C2×#468—111no—
317C2×#466—111no—
318C2×#465—111no—
319C2×#449—111no—
320C2×#449—111no—
321C2×#450—111no—
322C2×#447D1111yescharacteristic, complemented
323C2×#408—111no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—48no—
331C23×C11—42no—
332C23×C11—42no—
333C23×C11—42no—
334C23×C11—42no—
335C23×C11—42no—
336C23×C11—42no—
337C23×C11—42no—
338C23×C11—42no—
339C23×C11—42no—
340C23×C11—84no—
341C23×C11—84no—
342C23×C11—816no—
343C23×C11C22×D412yes—
344C23×C11C22×D411yescharacteristic
345C22×D11—22no—
346C22×D11—22no—
347C22×D11—22no—
348C22×D11—22no—
349C22×D11—22no—
350C22×D11—22no—
351C22×D11C22×D412yes—
352C22×D11C22×D412yes—
353D4×C11—22no—
354D4×C11—22no—
355D4×C11—22no—
356D4×C11—22no—
357D4×C11—22no—
358D4×C11—22no—
359D4×C11—48no—
360D4×C11—42no—
361D4×C11—42no—
362D4×C11—42no—
363D4×C11—84no—
364C2×C4×C11—22no—
365C2×C4×C11—24no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—42no—
370C2×C4×C11C22×D412yes—
371C2×C4×C11C22×D411yescharacteristic
372C2×C4×C11H(5,𝔽2)12yes—
373C2×C4×C11H(5,𝔽2)12yes—
374C2×C4×C11C2511yescharacteristic
375C22⋊D11—44no—
376C22⋊D11—44no—
377C22⋊D11—48no—
378C22⋊D11—84no—
379C22⋊D11—84no—
380C22⋊D11—84no—
381C22⋊D11—84no—
382C22⋊D11—84no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—22no—
387C2×Dic11—22no—
388C2×Dic11—22no—
389C2×Dic11—48no—
390C2×Dic11—42no—
391C2×Dic11—42no—
392C2×Dic11—42no—
393C2×Dic11—42no—
394C2×Dic11C22×D412yes—
395C2×Dic11C22×D412yes—
396D44—44no—
397C4×D11—24no—
398C4×D11—24no—
399C4×D11—22no—
400C4×D11—22no—
401C4×D11—22no—
402C4×D11—22no—
403C4×D11—84no—
404Dic22—22no—
405Dic22—22no—
406Dic22—44no—
407Dic22—42no—
408C8×C11—22no—
409C8×C11—22no—
410C11⋊C8—22no—
411C11⋊C8—22no—
412C22×#41—111no—
413C22×#41—111no—
414C23×D4C2×D1111yescharacteristic
415C22×SD16—111no—
416C22×SD16—111no—
417C22×D8C2×D1111yescharacteristic
418C22×D8C2×D1111yescharacteristic
419C22×M16—111no—
420C23×C8—111no—
421#537—118no—
422#537—224no—
423#535—118no—
424#535—224no—
425C2×#127—221no—
426C2×#124—221no—
427C2×C22⋊Q8—111no—
428C2×C22⋊Q8—111no—
429C2×C22⋊Q8—221no—
430C2×#121—111no—
431C2×#121—111no—
432C2×#121—111no—
433C2×#121—111no—
434C2×#121—111no—
435C2×#121—221no—
436C2×#121—221no—
437C2×#121—221no—
438C2×#121C2×D1111yescharacteristic
439C2×#120—221no—
440C2×#120—221no—
441C2×#117—111no—
442C22×C4⋊C4—111no—
443#485—118no—
444#482—118no—
445#481—118no—
446#480—118no—
447#469—118no—
448#468—118no—
449#466—118no—
450#465—118no—
451#450—118no—
452#449—118no—
453#449—118no—
454#447C2×D1118yescomplemented
455C2×#107—111no—
456C2×#107—111no—
457C2×#106—111no—
458C2×#106—111no—
459C2×#103—111no—
460C2×#103—111no—
461C2×#102—111no—
462C2×#102—111no—
463C2×#102—111no—
464C2×#102—111no—
465C2×#102C2×D1111yescharacteristic
466C2×#102C2×D1111yescharacteristic
467#408—118no—
468C2×C22⋊C8—111no—
469C2×C22⋊C8—111no—
470C2×C22⋊C8—111no—
471C2×C22⋊C8C2×D1111yescharacteristic
472C22×C11—22no—
473C22×C11—22no—
474C22×C11—22no—
475C22×C11—44no—
476C22×C11—42no—
477C22×C11—42no—
478C22×C11—42no—
479C22×C11—42no—
480C22×C11—42no—
481C22×C11—42no—
482C22×C11—42no—
483C22×C11—42no—
484C22×C11—42no—
485C22×C11—816no—
486C22×C11—84no—
487C22×C11—84no—
488C22×C11—84no—
489C22×C11#53412yes—
490C22×C11#57612yes—
491C22×C11#57712yes—
492C22×C11C23×D411yescharacteristic
493C2×D11—22no—
494C2×D11—22no—
495C2×D11—22no—
496C2×D11—22no—
497C2×D11—22no—
498C2×D11—22no—
499C2×D11—44no—
500C2×D11—44no—
501C4×C11—22no—
502C4×C11—42no—
503C4×C11#53412yes—
504C4×C11C2×H(5,𝔽2)11yescharacteristic
505C4×C11C2×H(5,𝔽2)11yescharacteristic
506Dic11—22no—
507Dic11—22no—
508Dic11—42no—
509Dic11—42no—
510Dic11—42no—
511Dic11—42no—
512C25—21no—
513C2×#41—114no—
514C2×#41—114no—
515C2×#41—114no—
516C2×#41—222no—
517C2×#41—442no—
518C2×#41—442no—
519C2×#41—442no—
520C2×#41—442no—
521C22×Q8—111no—
522C22×Q8—111no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—22no—
526C22×D4—42no—
527C22×D4—42no—
528C22×D4—111no—
529C22×D4—111no—
530C22×D4—111no—
531C22×D4—221no—
532C22×D4—221no—
533C22×D4—221no—
534C22×D4—221no—
535C22×D4—221no—
536C22×D4—221no—
537C22×D4C22×D1111yescharacteristic
538C22×D4C22×D1111yescharacteristic
539C22×D4C22×D1111yescharacteristic
540C22×D4C22×D1114yes—
541C23×C4—111no—
542C23×C4—111no—
543C23×C4—221no—
544C23×C4—221no—
545C23×C4C22×D1111yescharacteristic
546C2×SD16—114no—
547C2×SD16—114no—
548C2×SD16—442no—
549C2×SD16—442no—
550C2×D8—42no—
551C2×D8—42no—
552C2×D8C22×D1114yes—
553C2×D8C22×D1114yes—
554C2×M16—114no—
555C2×M16—442no—
556C22×C8—111no—
557C22×C8—111no—
558C22×C8—114no—
559C22×C8—442no—
560C22×C8C22×D1111yescharacteristic
561C22×C8C22×D1111yescharacteristic
562#127—228no—
563#124—228no—
564C22⋊Q8—114no—
565C22⋊Q8—114no—
566C22⋊Q8—228no—
567C22⋊Q8—222no—
568C22⋊Q8—222no—
569#121—22no—
570#121—114no—
571#121—114no—
572#121—114no—
573#121—114no—
574#121—114no—
575#121—228no—
576#121—222no—
577#121—222no—
578#121—222no—
579#121—222no—
580#121—222no—
581#121—228no—
582#121—228no—
583#121C22×D1114yes—
584#120—228no—
585#120—228no—
586#117—114no—
587#117—222no—
588C2×C4⋊C4—111no—
589C2×C4⋊C4—111no—
590C2×C4⋊C4—111no—
591C2×C4⋊C4—114no—
592C2×C4⋊C4—222no—
593C2×C4⋊C4—221no—
594C2×C4⋊C4—221no—
595C2×C4⋊C4—221no—
596C2×C4⋊C4C22×D1111yescharacteristic
597C2×C22⋊C4—21no—
598C2×C22⋊C4—221no—
599C2×C22⋊C4—221no—
600C2×C22⋊C4—221no—
601C2×C22⋊C4—221no—
602C2×C22⋊C4—221no—
603C2×C22⋊C4—221no—
604C2×C22⋊C4—221no—
605C2×C22⋊C4—221no—
606C2×C42—221no—
607#107—114no—
608#107—114no—
609#106—114no—
610#106—114no—
611#103—114no—
612#103—114no—
613#102—114no—
614#102—114no—
615#102—114no—
616#102—114no—
617#102C22×D1114yes—
618#102C22×D1114yes—
619C22⋊C8—114no—
620C22⋊C8—114no—
621C22⋊C8—114no—
622C22⋊C8C22×D1114yes—
623C2×C11—42no—
624C2×C11—82no—
625C2×C11—82no—
626C2×C11—82no—
627C2×C11#319814yescomplemented
628C2×C11C2×#53411yescharacteristic
629C2×C11C2×#57611yescharacteristic
630C2×C11C2×#57711yescharacteristic
631D11—42no—
632D11—42no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—24no—
637C24—44no—
638C24—82no—
639C24—82no—
640C24—111no—
641C24—111no—
642C24D4×D1111yescharacteristic
643#41—448no—
644#41—444no—
645#41—444no—
646#41—444no—
647#41—444no—
648#41—448no—
649C2×Q8—114no—
650C2×Q8—112no—
651C2×Q8—221no—
652C2×Q8—222no—
653C2×Q8—222no—
654C2×Q8—442no—
655C2×D4—24no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—24no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—22no—
663C2×D4—22no—
664C2×D4—22no—
665C2×D4—22no—
666C2×D4—44no—
667C2×D4—44no—
668C2×D4—44no—
669C2×D4—48no—
670C2×D4—82no—
671C2×D4—114no—
672C2×D4—114no—
673C2×D4—114no—
674C2×D4—224no—
675C2×D4—224no—
676C2×D4—224no—
677C2×D4—224no—
678C2×D4—224no—
679C2×D4—224no—
680C2×D4—442no—
681C2×D4—442no—
682C2×D4—442no—
683C2×D4—444no—
684C2×D4—882no—
685C2×D4—882no—
686C2×D4—882no—
687C2×D4—882no—
688C2×D4—882no—
689C2×D4C23×D1112yes—
690C2×D4C23×D1112yes—
691C2×D4C23×D1112yes—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—21no—
695C22×C4—111no—
696C22×C4—111no—
697C22×C4—112no—
698C22×C4—112no—
699C22×C4—112no—
700C22×C4—112no—
701C22×C4—224no—
702C22×C4—224no—
703C22×C4—222no—
704C22×C4—222no—
705C22×C4—222no—
706C22×C4—222no—
707C22×C4—221no—
708C22×C4—221no—
709C22×C4—221no—
710C22×C4—221no—
711C22×C4—444no—
712C22×C4—882no—
713C22×C4D4×D1112yes—
714C22×C4D4×D1111yescharacteristic
715C22×C4C23×D1112yes—
716C22×C4C23×D1111yescharacteristic
717SD16—444no—
718SD16—444no—
719D8—44no—
720D8—44no—
721M16—444no—
722C2×C8—22no—
723C2×C8—22no—
724C2×C8—112no—
725C2×C8—112no—
726C2×C8—222no—
727C2×C8—222no—
728C2×C8—444no—
729C2×C8C23×D1112yes—
730C2×C8C23×D1112yes—
731C4⋊C4—21no—
732C4⋊C4—112no—
733C4⋊C4—112no—
734C4⋊C4—112no—
735C4⋊C4—224no—
736C4⋊C4—224no—
737C4⋊C4—221no—
738C4⋊C4—221no—
739C4⋊C4—221no—
740C4⋊C4—224no—
741C4⋊C4C23×D1112yes—
742C22⋊C4—24no—
743C22⋊C4—224no—
744C22⋊C4—224no—
745C22⋊C4—224no—
746C22⋊C4—224no—
747C22⋊C4—224no—
748C22⋊C4—224no—
749C22⋊C4—224no—
750C22⋊C4—224no—
751C42—224no—
752C11C2×#319811yescharacteristic, complemented, Sylow
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—48no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23—42no—
767C23—42no—
768C23—42no—
769C23—84no—
770C23—84no—
771C23—816no—
772C23—112no—
773C23—112no—
774C23—222no—
775C23—222no—
776C23—222no—
777C23—222no—
778C23—222no—
779C23—222no—
780C23C2×D4×D1112yes—
781C23C2×D4×D1111yescharacteristic
782Q8—222no—
783Q8—222no—
784Q8—444no—
785Q8—442no—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—22no—
790D4—22no—
791D4—22no—
792D4—48no—
793D4—42no—
794D4—42no—
795D4—42no—
796D4—84no—
797D4—444no—
798D4—444no—
799D4—444no—
800D4—448no—
801D4—884no—
802D4—884no—
803D4—884no—
804D4—884no—
805D4—884no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—42no—
812C2×C4—112no—
813C2×C4—112no—
814C2×C4—222no—
815C2×C4—222no—
816C2×C4—224no—
817C2×C4—224no—
818C2×C4—222no—
819C2×C4—222no—
820C2×C4—222no—
821C2×C4—222no—
822C2×C4—222no—
823C2×C4—222no—
824C2×C4—222no—
825C2×C4—222no—
826C2×C4—448no—
827C2×C4—442no—
828C2×C4—442no—
829C2×C4—442no—
830C2×C4—442no—
831C2×C4—884no—
832C2×C4C2×D4×D1112yes—
833C2×C4C2×D4×D1111yescharacteristic
834C2×C4#6703712yes—
835C2×C4#6703712yes—
836C2×C4C24×D1111yescharacteristic
837C8—22no—
838C8—22no—
839C8—222no—
840C8—222no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—44no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—816no—
855C22—84no—
856C22—84no—
857C22—84no—
858C22—222no—
859C22—222no—
860C22—222no—
861C22—222no—
862C22—222no—
863C22—222no—
864C22—444no—
865C22—444no—
866C22#1062312012yes—
867C22#1062328812yes—
868C22#1062330612yes—
869C22C22×D4×D1111yescharacteristic
870C4—22no—
871C4—42no—
872C4—222no—
873C4—222no—
874C4—442no—
875C4—442no—
876C4—442no—
877C4—442no—
878C4#1062312012yes—
879C4C2×#6703711yescharacteristic
880C4C2×#6703711yescharacteristic
881C2—42no—
882C2—82no—
883C2—82no—
884C2—82no—
885C2—442no—
886C2—442no—
887C2#1307946414yesdirect product factor
888C2C2×#1062312011yescharacteristic
889C2C2×#1062328811yescharacteristic
890C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#447C2
socleC23×C11C22×D4
hypercenterC2×#447D11
hypocenterC11C2×#3198
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#447

Complements

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

NH ≅ G/Ntype
1. C2×#10623139C2semidirect
2. C2×#10623336C2semidirect
3. #13079464C2direct (N × H)
4. C2×#10622390C2semidirect
5. C2×#10622336C2semidirect
6. C2×#10622648C2semidirect
7. C2×#10622387C2semidirect
8. C2×#10622772C2semidirect
9. C2×#10622393C2semidirect
10. C2×#10622770C2semidirect
11. C2×#10622391C2semidirect
12. C2×#10622771C2semidirect
13. C2×#10622771C2semidirect
14. C2×#10622831C2semidirect
15. C2×#10622340C2semidirect
16. C2×C11×#447C2semidirect
18. C22×#4341C22semidirect
26. #10623336C22semidirect
34. C2×#66991C22semidirect
40. C22×#4313C22semidirect
41. C22×C8×D11C22semidirect
43. #10623139C22semidirect
44. C2×#66950C22semidirect
45. C2×C4⋊C4×D11C22semidirect
48. C11×#447C22semidirect
52. #10622831C22semidirect
55. C2×#66896C22semidirect
56. C2×#66896C22semidirect
58. #10622772C22semidirect
59. #10622771C22semidirect
60. #10622771C22semidirect
61. #10622770C22semidirect
62. C2×(C2×D11)⋊C8C22semidirect
63. C2×(C2×D11)⋊C8C22semidirect
64. C2×#66882C22semidirect
65. C2×#66881C22semidirect
66. C2×#66880C22semidirect
67. C2×#66880C22semidirect
68. #10622648C22semidirect
69. C2×#66872C22semidirect
70. C2×#66871C22semidirect
71. #10622393C22semidirect
72. #10622391C22semidirect
73. #10622390C22semidirect
74. #10622387C22semidirect
75. #10622340C22semidirect
76. #10622336C22semidirect
100. C2×#4341C23semidirect
142. #66991C23semidirect
163. C2×#4313C23semidirect
165. C2×C8×D11C23semidirect
167. #66950C23semidirect
169. C4⋊C4×D11C23semidirect
177. #66896C23semidirect
178. #66896C23semidirect
180. (C2×D11)⋊C8C23semidirect
181. (C2×D11)⋊C8C23semidirect
182. #66882C23semidirect
183. #66881C23semidirect
184. #66880C23semidirect
185. #66880C23semidirect
186. #66872C23semidirect
187. #66871C23semidirect
322. C2×#447D11semidirect
454. #447C2×D11semidirect
627. C2×C11#3198semidirect
752. C11C2×#3198semidirect
887. C2#13079464direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231392
C2×#106233362
#130794642
C2×#106223902
C2×#106223362
C2×#106226482
C2×#106223872
C2×#106227722
C2×#106223932
C2×#106227702
C2×#106223912
C2×#106227712
C2×#106228312
C2×#106223402
C2×C11×#4472
C2×#319811