Finite Group Databasebeta

← C2×#13080537 #15630217

Subgroups — C2×#13080537 #15630217

Order 2816.

2210 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623147C211yesmaximal, characteristic, complemented
2C2×#10623355C211yesmaximal, characteristic, complemented
3#13080537C2116yesmaximal, direct product factor
4C2×#10622405C211yesmaximal, characteristic, complemented
5C2×#10622336C211yesmaximal, characteristic, complemented
6C2×#10622427C211yesmaximal, characteristic, complemented
7C2×#10622374C211yesmaximal, characteristic, complemented
8C2×#10622654C211yesmaximal, characteristic, complemented
9C2×#10622784C211yesmaximal, characteristic, complemented
10C2×#10622775C211yesmaximal, characteristic, complemented
11C2×#10622771C211yesmaximal, characteristic, complemented
12C2×D8×Dic11C211yesmaximal, characteristic, complemented
13C2×(C22⋊D11)⋊C8C211yesmaximal, characteristic, complemented
14C2×#10622846C211yesmaximal, characteristic, complemented
15C2×#10622385C211yesmaximal, characteristic, complemented
16C2×C11×#449C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C22×#4341C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C22×C11×D8C2211yescharacteristic
21C2×C11×#121C2211yescharacteristic
22#10623355—24no—
23#10623355C2218yescomplemented
24C2×#66999C2211yescharacteristic
25C2×#66997C2211yescharacteristic
26C2×#66992—21no—
27C2×#66992—21no—
28C2×#66991C2211yescharacteristic
29C2×#66989—21no—
30C2×#66988—21no—
31C2×D4×Dic11C2211yescharacteristic
32C2×D4×Dic11C2211yescharacteristic
33C22×#4324C2211yescharacteristic
34C2×#66982—21no—
35C2×C4×C22⋊D11C2211yescharacteristic
36C2×#66979C2211yescharacteristic
37C2×#66977C2211yescharacteristic
38C22×Dic11⋊C4—21no—
39C23×C11⋊C8C2211yescharacteristic
40C22×C8×D11C2211yescharacteristic
41#10623147—24no—
42#10623147C2218yescomplemented
43C2×#66945C2211yescharacteristic
44C2×#66941C2211yescharacteristic
45C2×#66938—21no—
46C2×#66930—21no—
47C11×#449C2218yescomplemented
48C2×C11×#103C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×C11×C22⋊C8C2211yescharacteristic
51#10622846C2218yescomplemented
52C2×#66899C2211yescharacteristic
53C2×#66899C2211yescharacteristic
54C2×#66896C2211yescharacteristic
55C2×#66896C2211yescharacteristic
56C2×#66896C2211yescharacteristic
57#10622784C2218yescomplemented
58#10622775C2218yescomplemented
59#10622771C2218yescomplemented
60D8×Dic11C2218yescomplemented
61C2×(C2×D11)⋊C8C2211yescharacteristic
62C2×#66882C2211yescharacteristic
63C2×#66881C2211yescharacteristic
64C2×#66880C2211yescharacteristic
65C2×#66880C2211yescharacteristic
66C2×Dic11⋊C8C2211yescharacteristic
67C2×C8×Dic11C2211yescharacteristic
68#10622654C2218yescomplemented
69C2×#66874C2211yescharacteristic
70C2×#66872C2211yescharacteristic
71#10622427C2218yescomplemented
72#10622405C2218yescomplemented
73#10622385C2218yescomplemented
74#10622374C2218yescomplemented
75(C22⋊D11)⋊C8C2218yescomplemented
76#10622336C2218yescomplemented
77C2×C11×#41—22no—
78C2×C11×#41—24no—
79C2×C11×#41—42no—
80C2×C11×#41C2314yes—
81C22×Q8×C11C2311yescharacteristic
82C22×D4×C11—21no—
83C22×D4×C11—21no—
84C22×D4×C11C2311yescharacteristic
85C22×D4×C11C2311yescharacteristic
86C23×C4×C11—21no—
87C23×C4×C11C2311yescharacteristic
88C22×C22⋊D11—21no—
89C22×C22⋊D11—21no—
90C22×C22⋊D11D411yescharacteristic
91C23×Dic11—21no—
92C23×Dic11—21no—
93C23×Dic11—21no—
94C2×#4341—24no—
95C2×#4341—22no—
96C2×#4341—42no—
97C2×#4341C2314yes—
98C22×C4×D11C2311yescharacteristic
99C22×Dic22—21no—
100C22×Dic22C2311yescharacteristic
101C2×C11×SD16—42no—
102C2×C11×SD16C2314yes—
103C2×C11×D8—24no—
104C2×C11×D8C2314yes—
105C22×C8×C11C2311yescharacteristic
106C22×C8×C11C2311yescharacteristic
107C11×#121—22no—
108C11×#121C2314yes—
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C22⋊C4—21no—
111C2×C22⋊Dic11—21no—
112C2×C22⋊Dic11—21no—
113C2×C22⋊Dic11—21no—
114C2×C22⋊Dic11—21no—
115C2×C22⋊Dic11—21no—
116C2×C22⋊Dic11D411yescharacteristic
117#66999—22no—
118#66999C2314yes—
119#66997—22no—
120#66997C2314yes—
121#66992—28no—
122#66992—28no—
123#66991—22no—
124#66991C2314yes—
125#66989—28no—
126#66988—28no—
127D4×Dic11—22no—
128D4×Dic11—22no—
129D4×Dic11C2314yes—
130D4×Dic11C2314yes—
131C2×#4324—42no—
132C2×#4324C2314yes—
133#66982—28no—
134C4×C22⋊D11D414yes—
135C4×C22⋊D11C2314yes—
136C2×(C2×D11)⋊C4—21no—
137C2×(C2×D11)⋊C4—21no—
138C2×(C2×D11)⋊C4D411yescharacteristic
139#66979—22no—
140#66979C2314yes—
141C2×C4⋊Dic11C2311yescharacteristic
142C2×C4⋊Dic11C2311yescharacteristic
143C2×C4⋊Dic11C2311yescharacteristic
144#66977—22no—
145#66977C2314yes—
146C2×Dic11⋊C4—21no—
147C2×Dic11⋊C4—21no—
148C2×Dic11⋊C4—21no—
149C2×Dic11⋊C4—21no—
150C2×Dic11⋊C4—21no—
151C2×Dic11⋊C4—28no—
152C2×Dic11⋊C4D411yescharacteristic
153C2×C4×Dic11—21no—
154C2×C4×Dic11—21no—
155C2×C4×Dic11C2311yescharacteristic
156C22×C11⋊C8—42no—
157C22×C11⋊C8C2311yescharacteristic
158C22×C11⋊C8C2311yescharacteristic
159C22×C11⋊C8C2314yes—
160C2×C8×D11—42no—
161C2×C8×D11C2314yes—
162#66945—22no—
163#66945C2314yes—
164#66941—22no—
165#66941C2314yes—
166#66938—28no—
167#66930—28no—
168C11×#103C2314yes—
169C11×#102C2314yes—
170C11×C22⋊C8C2314yes—
171#66899C2314yes—
172#66899C2314yes—
173#66896C2314yes—
174#66896C2314yes—
175#66896C2314yes—
176(C2×D11)⋊C8C2314yes—
177#66882C2314yes—
178#66881C2314yes—
179#66880C2314yes—
180#66880C2314yes—
181Dic11⋊C8C2314yes—
182C8×Dic11C2314yes—
183#66874C2314yes—
184#66872C2314yes—
185C2×#3303—111nomaximal, Sylow
186C24×C11—21no—
187C24×C11—21no—
188C24×C11C2×D411yescharacteristic
189C23×D11C2×D411yescharacteristic
190C11×#41—28no—
191C11×#41—44no—
192C11×#41—48no—
193C2×Q8×C11—21no—
194C2×Q8×C11—22no—
195C2×Q8×C11—22no—
196C2×Q8×C11C2412yes—
197C2×D4×C11—24no—
198C2×D4×C11—24no—
199C2×D4×C11—21no—
200C2×D4×C11—21no—
201C2×D4×C11—22no—
202C2×D4×C11—22no—
203C2×D4×C11—22no—
204C2×D4×C11—44no—
205C2×D4×C11—82no—
206C2×D4×C11#4114yes—
207C2×D4×C11C2412yes—
208C2×D4×C11C2412yes—
209C22×C4×C11—22no—
210C22×C4×C11—22no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—24no—
214C22×C4×C11—44no—
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—82no—
224C2×C22⋊D11C2×D414yes—
225C22×Dic11—24no—
226C22×Dic11—24no—
227C22×Dic11—24no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—44no—
233C22×Dic11—44no—
234C22×Dic11—44no—
235C22×Dic11C2×D411yescharacteristic
236C22×Dic11C2×D411yescharacteristic
237C22×Dic11C2×D411yescharacteristic
238#4341—28no—
239#4341—44no—
240#4341—48no—
241C2×C4×D11—22no—
242C2×C4×D11—22no—
243C2×C4×D11C2×D412yes—
244C2×C4×D11C2412yes—
245C2×Dic22—24no—
246C2×Dic22—21no—
247C2×Dic22—22no—
248C2×Dic22—22no—
249C2×Dic22—82no—
250C2×Dic22C2412yes—
251C11×SD16—44no—
252C11×D8—28no—
253C2×C8×C11—22no—
254C2×C8×C11—22no—
255C2×C8×C11C2412yes—
256C2×C8×C11C2412yes—
257C11×C4⋊C4—21no—
258C11×C4⋊C4C2412yes—
259C11×C22⋊C4—24no—
260C22⋊Dic11—24no—
261C22⋊Dic11—24no—
262C22⋊Dic11—24no—
263C22⋊Dic11—24no—
264C22⋊Dic11—24no—
265C22⋊Dic11C2×D414yes—
266#4324—44no—
267(C2×D11)⋊C4—24no—
268(C2×D11)⋊C4—24no—
269(C2×D11)⋊C4C2×D414yes—
270C4⋊Dic11—21no—
271C4⋊Dic11—21no—
272C4⋊Dic11—21no—
273C4⋊Dic11C2412yes—
274C4⋊Dic11C2412yes—
275C4⋊Dic11C2412yes—
276Dic11⋊C4—24no—
277Dic11⋊C4—24no—
278Dic11⋊C4—24no—
279Dic11⋊C4—24no—
280Dic11⋊C4—24no—
281Dic11⋊C4C2×D414yes—
282C4×Dic11—24no—
283C4×Dic11—24no—
284C4×Dic11C2×D412yes—
285C4×Dic11C2412yes—
286C2×C11⋊C8—22no—
287C2×C11⋊C8—22no—
288C2×C11⋊C8—44no—
289C2×C11⋊C8C2412yes—
290C2×C11⋊C8C2412yes—
291C8×D11—44no—
292C2×#555—111no—
293C2×#547—111no—
294#3303—1116no—
295C2×#487—111no—
296C2×#485—111no—
297C2×#485—111no—
298C2×#476—111no—
299C2×#465—111no—
300C2×#465—111no—
301C2×#461—111no—
302C2×#449—111no—
303C2×#449D1111yescharacteristic, complemented
304C2×C4×D8—111no—
305C2×C8×D4—111no—
306C2×#416—111no—
307C2×#416—111no—
308C23×C11—24no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—42no—
315C23×C11—42no—
316C23×C11—42no—
317C23×C11—42no—
318C23×C11—42no—
319C23×C11C22×D412yes—
320C23×C11C22×D411yescharacteristic
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11C22×D412yes—
325Q8×C11—22no—
326Q8×C11—22no—
327Q8×C11—42no—
328D4×C11—24no—
329D4×C11—22no—
330D4×C11—22no—
331D4×C11—22no—
332D4×C11—48no—
333D4×C11—42no—
334D4×C11—84no—
335D4×C11C2×#4114yes—
336C2×C4×C11—22no—
337C2×C4×C11—24no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—48no—
343C2×C4×C11—42no—
344C2×C4×C11—42no—
345C2×C4×C11C22×D412yes—
346C2×C4×C11C22×D411yescharacteristic
347C2×C4×C11C2×#4112yes—
348C2×C4×C11H(5,𝔽2)12yes—
349C2×C4×C11C2511yescharacteristic
350C22⋊D11—28no—
351C22⋊D11—48no—
352C22⋊D11—84no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—48no—
360C2×Dic11—42no—
361C2×Dic11—42no—
362C2×Dic11—42no—
363C2×Dic11—42no—
364C2×Dic11—48no—
365C2×Dic11—48no—
366C2×Dic11#13514yes—
367C2×Dic11C22×D412yes—
368C2×Dic11C22×D412yes—
369C2×Dic11C22×D412yes—
370C4×D11—24no—
371C4×D11—22no—
372C4×D11—22no—
373Dic22—22no—
374Dic22—22no—
375Dic22—42no—
376Dic22—84no—
377C8×C11—22no—
378C8×C11—22no—
379C11⋊C8—22no—
380C11⋊C8—22no—
381C22×#41—111no—
382C22×#41C2×D1111yescharacteristic
383C22×SD16—111no—
384C22×SD16C2×D1111yescharacteristic
385C22×D8C2×D1111yescharacteristic
386C23×C8—111no—
387C23×C8—111no—
388#555—118no—
389#555—224no—
390#547—118no—
391#547—224no—
392C2×C4⋊Q8—111no—
393C2×C4⋊Q8—111no—
394C2×#124—221no—
395C2×#124—221no—
396C2×#123—221no—
397C2×#123—221no—
398C2×C22⋊Q8—111no—
399C2×C22⋊Q8—111no—
400C2×#121—111no—
401C2×#121—221no—
402C2×#121—221no—
403C2×#121C2×D1111yescharacteristic
404C2×C4×D4—111no—
405C2×C4×D4—111no—
406C2×C4×D4—111no—
407C2×#117—111no—
408C2×#117—111no—
409C2×#117—221no—
410C22×C4⋊C4—221no—
411#487—118no—
412#485—118no—
413#485—118no—
414#476—118no—
415#465—118no—
416#465—118no—
417#461—118no—
418#449—118no—
419#449C2×D1118yescomplemented
420C4×D8—118no—
421C8×D4—118no—
422C2×#107—111no—
423C2×#106—111no—
424C2×#106—111no—
425C2×C4⋊C8—111no—
426#416—118no—
427#416—118no—
428C2×#103—111no—
429C2×#103—111no—
430C2×#103—111no—
431C2×#103—111no—
432C2×#103—111no—
433C2×#103C2×D1111yescharacteristic
434C2×#102—111no—
435C2×#102—111no—
436C2×#102—111no—
437C2×#102C2×D1111yescharacteristic
438C2×C22⋊C8—111no—
439C2×C22⋊C8C2×D1111yescharacteristic
440C2×C4×C8—111no—
441C22×C11—22no—
442C22×C11—24no—
443C22×C11—22no—
444C22×C11—22no—
445C22×C11—44no—
446C22×C11—48no—
447C22×C11—42no—
448C22×C11—42no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—84no—
453C22×C11#54612yes—
454C22×C11C2×#13512yes—
455C22×C11#57712yes—
456C22×C11C23×D411yescharacteristic
457C2×D11—22no—
458C2×D11—22no—
459C2×D11—22no—
460C2×D11—44no—
461C4×C11—22no—
462C4×C11—42no—
463C4×C11—42no—
464C4×C11#54612yes—
465C4×C11C22×#4111yescharacteristic
466C4×C11C2×H(5,𝔽2)11yescharacteristic
467Dic11—22no—
468Dic11—22no—
469Dic11—42no—
470Dic11—42no—
471Dic11—42no—
472Dic11—42no—
473Dic11C2×#13514yes—
474C2×#41—22no—
475C2×#41—24no—
476C2×#41—42no—
477C2×#41—114no—
478C2×#41—222no—
479C2×#41—224no—
480C2×#41—442no—
481C2×#41C22×D1114yes—
482C22×Q8—111no—
483C22×Q8—221no—
484C22×Q8C22×D1111yescharacteristic
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—111no—
488C22×D4—221no—
489C22×D4—221no—
490C22×D4C22×D1111yescharacteristic
491C22×D4C22×D1111yescharacteristic
492C23×C4—21no—
493C23×C4—111no—
494C23×C4—221no—
495C23×C4—221no—
496C23×C4—221no—
497C23×C4C22×D1111yescharacteristic
498C2×SD16—42no—
499C2×SD16—114no—
500C2×SD16—442no—
501C2×SD16C22×D1114yes—
502C2×D8—24no—
503C2×D8C22×D1114yes—
504C22×C8—111no—
505C22×C8—111no—
506C22×C8—114no—
507C22×C8—114no—
508C22×C8—442no—
509C22×C8—442no—
510C22×C8C22×D1111yescharacteristic
511C22×C8C22×D1111yescharacteristic
512C4⋊Q8—114no—
513C4⋊Q8—114no—
514C4⋊Q8—222no—
515C4⋊Q8—222no—
516#124—228no—
517#124—228no—
518#123—228no—
519#123—228no—
520C22⋊Q8—114no—
521C22⋊Q8—114no—
522C22⋊Q8—222no—
523C22⋊Q8—222no—
524#121—22no—
525#121—114no—
526#121—222no—
527#121—228no—
528#121—228no—
529#121C22×D1114yes—
530C4×D4—114no—
531C4×D4—114no—
532C4×D4—114no—
533C4×D4—114no—
534C4×D4—222no—
535C4×D4—222no—
536#117—114no—
537#117—114no—
538#117—228no—
539#117—222no—
540#117—222no—
541C2×C4⋊C4—111no—
542C2×C4⋊C4—111no—
543C2×C4⋊C4—111no—
544C2×C4⋊C4—111no—
545C2×C4⋊C4—228no—
546C2×C4⋊C4—221no—
547C2×C4⋊C4—221no—
548C2×C4⋊C4—221no—
549C2×C4⋊C4—221no—
550C2×C4⋊C4—221no—
551C2×C4⋊C4C22×D1111yescharacteristic
552C2×C22⋊C4—21no—
553C2×C22⋊C4—111no—
554C2×C22⋊C4—111no—
555C2×C22⋊C4—221no—
556C2×C22⋊C4—221no—
557C2×C22⋊C4—221no—
558C2×C22⋊C4—221no—
559C2×C22⋊C4—221no—
560C2×C22⋊C4—221no—
561C2×C22⋊C4—221no—
562C2×C42—111no—
563C2×C42—221no—
564C2×C42—221no—
565#107—114no—
566#106—114no—
567#106—114no—
568C4⋊C8—114no—
569#103—114no—
570#103—114no—
571#103—114no—
572#103—114no—
573#103—114no—
574#103C22×D1114yes—
575#102—114no—
576#102—114no—
577#102—114no—
578#102C22×D1114yes—
579C22⋊C8—114no—
580C22⋊C8C22×D1114yes—
581C4×C8—114no—
582C2×C11—42no—
583C2×C11—44no—
584C2×C11—82no—
585C2×C11#330314yescomplemented
586C2×C11C2×#54611yescharacteristic
587C2×C11C22×#13511yescharacteristic
588C2×C11C2×#57711yescharacteristic
589D11—42no—
590C24—21no—
591C24—21no—
592C24—111no—
593C24D4×D1111yescharacteristic
594#41—28no—
595#41—44no—
596#41—48no—
597#41—228no—
598#41—444no—
599#41—448no—
600C2×Q8—21no—
601C2×Q8—22no—
602C2×Q8—22no—
603C2×Q8—112no—
604C2×Q8—224no—
605C2×Q8—221no—
606C2×Q8—222no—
607C2×Q8—222no—
608C2×Q8—882no—
609C2×Q8C23×D1112yes—
610C2×D4—24no—
611C2×D4—24no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—44no—
618C2×D4—82no—
619C2×D4—114no—
620C2×D4—224no—
621C2×D4—224no—
622C2×D4—224no—
623C2×D4—444no—
624C2×D4—882no—
625C2×D4#434114yes—
626C2×D4C23×D1112yes—
627C2×D4C23×D1112yes—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—24no—
633C22×C4—44no—
634C22×C4—111no—
635C22×C4—111no—
636C22×C4—111no—
637C22×C4—112no—
638C22×C4—112no—
639C22×C4—224no—
640C22×C4—224no—
641C22×C4—224no—
642C22×C4—222no—
643C22×C4—222no—
644C22×C4—221no—
645C22×C4—221no—
646C22×C4—221no—
647C22×C4—221no—
648C22×C4—444no—
649C22×C4—444no—
650C22×C4—444no—
651C22×C4D4×D1112yes—
652C22×C4D4×D1111yescharacteristic
653C22×C4C23×D1112yes—
654C22×C4C23×D1111yescharacteristic
655SD16—44no—
656SD16—444no—
657D8—28no—
658C2×C8—22no—
659C2×C8—22no—
660C2×C8—112no—
661C2×C8—112no—
662C2×C8—222no—
663C2×C8—222no—
664C2×C8—444no—
665C2×C8—444no—
666C2×C8C23×D1112yes—
667C2×C8C23×D1112yes—
668C4⋊C4—21no—
669C4⋊C4—114no—
670C4⋊C4—112no—
671C4⋊C4—112no—
672C4⋊C4—112no—
673C4⋊C4—224no—
674C4⋊C4—224no—
675C4⋊C4—224no—
676C4⋊C4—224no—
677C4⋊C4—221no—
678C4⋊C4—221no—
679C4⋊C4—221no—
680C4⋊C4—224no—
681C4⋊C4C23×D1112yes—
682C22⋊C4—24no—
683C22⋊C4—114no—
684C22⋊C4—114no—
685C22⋊C4—224no—
686C22⋊C4—224no—
687C22⋊C4—224no—
688C22⋊C4—224no—
689C22⋊C4—224no—
690C22⋊C4—224no—
691C22⋊C4—224no—
692C42—112no—
693C42—112no—
694C42—224no—
695C42—224no—
696C11C2×#330311yescharacteristic, complemented, Sylow
697C23—22no—
698C23—22no—
699C23—22no—
700C23—24no—
701C23—22no—
702C23—22no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—112no—
709C23—222no—
710C23—222no—
711C23—222no—
712C23C2×D4×D1112yes—
713C23C2×D4×D1111yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—42no—
717Q8—222no—
718Q8—222no—
719Q8—442no—
720Q8—884no—
721D4—24no—
722D4—22no—
723D4—22no—
724D4—22no—
725D4—48no—
726D4—42no—
727D4—84no—
728D4—228no—
729D4—448no—
730D4—884no—
731D4C2×#434114yes—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—48no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—114no—
742C2×C4—112no—
743C2×C4—112no—
744C2×C4—112no—
745C2×C4—222no—
746C2×C4—222no—
747C2×C4—224no—
748C2×C4—222no—
749C2×C4—222no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—448no—
755C2×C4—448no—
756C2×C4—448no—
757C2×C4—442no—
758C2×C4—442no—
759C2×C4—442no—
760C2×C4—442no—
761C2×C4C2×D4×D1112yes—
762C2×C4C2×D4×D1111yescharacteristic
763C2×C4C2×#434112yes—
764C2×C4#6703712yes—
765C2×C4C24×D1111yescharacteristic
766C8—22no—
767C8—22no—
768C8—222no—
769C8—222no—
770C22—22no—
771C22—24no—
772C22—22no—
773C22—22no—
774C22—42no—
775C22—44no—
776C22—48no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—84no—
782C22—222no—
783C22—222no—
784C22—222no—
785C22—444no—
786C22#1062312212yes—
787C22D11×#13512yes—
788C22#1062330612yes—
789C22C22×D4×D1111yescharacteristic
790C4—22no—
791C4—42no—
792C4—42no—
793C4—114no—
794C4—222no—
795C4—222no—
796C4—442no—
797C4—442no—
798C4—442no—
799C4—442no—
800C4#1062312212yes—
801C4C22×#434111yescharacteristic
802C4C2×#6703711yescharacteristic
803C2—42no—
804C2—44no—
805C2—82no—
806C2—442no—
807C2#1308053714yesdirect product factor
808C2C2×#1062312211yescharacteristic
809C2C2×D11×#13511yescharacteristic
810C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#449C2
socleC23×C11C22×D4
hypercenterC2×#449D11
hypocenterC11C2×#3303
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#10623147C2semidirect
2. C2×#10623355C2semidirect
3. #13080537C2direct (N × H)
4. C2×#10622405C2semidirect
5. C2×#10622336C2semidirect
6. C2×#10622427C2semidirect
7. C2×#10622374C2semidirect
8. C2×#10622654C2semidirect
9. C2×#10622784C2semidirect
10. C2×#10622775C2semidirect
11. C2×#10622771C2semidirect
12. C2×D8×Dic11C2semidirect
13. C2×(C22⋊D11)⋊C8C2semidirect
14. C2×#10622846C2semidirect
15. C2×#10622385C2semidirect
16. C2×C11×#449C2semidirect
23. #10623355C22semidirect
42. #10623147C22semidirect
47. C11×#449C22semidirect
51. #10622846C22semidirect
57. #10622784C22semidirect
58. #10622775C22semidirect
59. #10622771C22semidirect
60. D8×Dic11C22semidirect
68. #10622654C22semidirect
71. #10622427C22semidirect
72. #10622405C22semidirect
73. #10622385C22semidirect
74. #10622374C22semidirect
75. (C22⋊D11)⋊C8C22semidirect
76. #10622336C22semidirect
303. C2×#449D11semidirect
419. #449C2×D11semidirect
585. C2×C11#3303semidirect
696. C11C2×#3303semidirect
807. C2#13080537direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231472
C2×#106233552
#130805372
C2×#106224052
C2×#106223362
C2×#106224272
C2×#106223742
C2×#106226542
C2×#106227842
C2×#106227752
C2×#106227712
C2×D8×Dic112
C2×(C22⋊D11)⋊C82
C2×#106228462
C2×#106223852
C2×C11×#4492
C2×#330311