Finite Group Databasebeta

← C2×#13080054 #15626712

Subgroups — C2×#13080054 #15626712

Order 2816.

2010 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623229C211yesmaximal, characteristic, complemented
2C2×#10623093C211yesmaximal, characteristic, complemented
3#13080054C2116yesmaximal, direct product factor
4C2×#10622504C211yesmaximal, characteristic, complemented
5C2×#10622484C211yesmaximal, characteristic, complemented
6C2×#10622679C211yesmaximal, characteristic, complemented
7C2×#10622478C211yesmaximal, characteristic, complemented
8C2×#10622395C211yesmaximal, characteristic, complemented
9C2×#10622496C211yesmaximal, characteristic, complemented
10C2×#10622388C211yesmaximal, characteristic, complemented
11C2×#10622456C211yesmaximal, characteristic, complemented
12C2×#10622628C211yesmaximal, characteristic, complemented
13C2×#10622399C211yesmaximal, characteristic, complemented
14C2×#10622399C211yesmaximal, characteristic, complemented
15C2×#10622452C211yesmaximal, characteristic, complemented
16C2×C11×#478C211yesmaximal, characteristic, complemented
17C2×C11×#125C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×#66993C2211yescharacteristic
20C2×#66991C2211yescharacteristic
21C22×#4323C2211yescharacteristic
22C22×#4323C2211yescharacteristic
23C2×#66983—21no—
24C2×#66982—21no—
25C22×D88C2211yescharacteristic
26C22×D88C2211yescharacteristic
27C22×#4313C2211yescharacteristic
28C22×C8×D11C2211yescharacteristic
29#10623229—24no—
30#10623229C2218yescomplemented
31#10623093—24no—
32#10623093C2218yescomplemented
33C2×#66948—21no—
34C2×#66948—21no—
35C2×#66948C2211yescharacteristic
36C2×#66948C2211yescharacteristic
37C2×#66948C2211yescharacteristic
38C2×#66947—21no—
39C2×#66947—21no—
40C2×#66946C2211yescharacteristic
41C2×#66946C2211yescharacteristic
42C2×#66943C2211yescharacteristic
43C2×#66937—21no—
44C2×#66936—21no—
45C2×#66927C2211yescharacteristic
46C2×C4×D44C2211yescharacteristic
47C2×#66925C2211yescharacteristic
48C11×#478C2218yescomplemented
49C2×C11×#107C2211yescharacteristic
50C2×C11×#106C2211yescharacteristic
51C2×C11×C4⋊C8C2211yescharacteristic
52C2×C11×#102C2211yescharacteristic
53C2×C11×#102C2211yescharacteristic
54C2×#66885C2211yescharacteristic
55C2×#66885C2211yescharacteristic
56C2×Dic11⋊C8C2211yescharacteristic
57C2×Dic11⋊C8C2211yescharacteristic
58#10622679C2218yescomplemented
59#10622628C2218yescomplemented
60C2×#66873C2211yescharacteristic
61C2×#66873C2211yescharacteristic
62C2×#66873C2211yescharacteristic
63C2×#66873C2211yescharacteristic
64C2×#66872C2211yescharacteristic
65C2×#66871C2211yescharacteristic
66C2×C4⋊(C11⋊C8)C2211yescharacteristic
67#10622504C2218yescomplemented
68#10622496C2218yescomplemented
69#10622484C2218yescomplemented
70#10622478C2218yescomplemented
71#10622456C2218yescomplemented
72#10622452C2218yescomplemented
73#10622399C2218yescomplemented
74#10622399C2218yescomplemented
75#10622395C2218yescomplemented
76#10622388C2218yescomplemented
77C22×D4×C11C2311yescharacteristic
78C23×C4×C11—21no—
79C22×C22⋊D11—21no—
80C22×C22⋊D11—21no—
81C22×C22⋊D11—21no—
82C22×D44—21no—
83C22×D44—21no—
84C22×D44—21no—
85C22×D44—21no—
86C22×D44—21no—
87C22×D44C2311yescharacteristic
88C22×D44C2311yescharacteristic
89C22×D44C2311yescharacteristic
90C22×C4×D11—21no—
91C22×C4×D11—21no—
92C22×C4×D11—21no—
93C22×C4×D11C2311yescharacteristic
94C22×C8×C11C2311yescharacteristic
95C22×C8×C11C2311yescharacteristic
96C11×#125—22no—
97C11×#125C2314yes—
98C4×D4×C11—22no—
99C4×D4×C11C2314yes—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C22⋊C4—21no—
106C2×C42×C11C2311yescharacteristic
107C2×C22⋊Dic11—21no—
108#66993—22no—
109#66993C2314yes—
110#66991—22no—
111#66991C2314yes—
112C2×#4323—42no—
113C2×#4323—42no—
114C2×#4323C2314yes—
115C2×#4323C2314yes—
116#66983—28no—
117#66982—28no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×(C2×D11)⋊C4—21no—
121C2×(C2×D11)⋊C4—21no—
122C2×(C2×D11)⋊C4—21no—
123C2×(C2×D11)⋊C4—21no—
124C2×(C2×D11)⋊C4D411yescharacteristic
125C2×(C2×D11)⋊C4D411yescharacteristic
126C2×C4⋊Dic11—21no—
127C2×C4⋊Dic11C2311yescharacteristic
128C2×Dic11⋊C4—21no—
129C2×Dic11⋊C4D411yescharacteristic
130C2×Dic11⋊C4D411yescharacteristic
131C2×C4×Dic11C2311yescharacteristic
132C22×C11⋊C8C2311yescharacteristic
133C22×C11⋊C8C2311yescharacteristic
134C2×D88—42no—
135C2×D88—42no—
136C2×D88C2314yes—
137C2×D88C2314yes—
138C2×#4313—42no—
139C2×#4313C2314yes—
140C2×C8×D11—42no—
141C2×C8×D11C2314yes—
142#66948—22no—
143#66948—22no—
144#66948—22no—
145#66948—28no—
146#66948—28no—
147#66948C2314yes—
148#66948C2314yes—
149#66948C2314yes—
150#66947—28no—
151#66947—28no—
152#66946—22no—
153#66946—22no—
154#66946C2314yes—
155#66946C2314yes—
156#66943—22no—
157#66943C2314yes—
158#66937—28no—
159#66936—28no—
160#66927—22no—
161#66927C2314yes—
162C4×D44—22no—
163C4×D44C2314yes—
164#66925D414yes—
165#66925C2314yes—
166C11×#107C2314yes—
167C11×#106C2314yes—
168C11×C4⋊C8C2314yes—
169C11×#102C2314yes—
170C11×#102C2314yes—
171#66885C2314yes—
172#66885C2314yes—
173Dic11⋊C8C2314yes—
174Dic11⋊C8C2314yes—
175#66873C2314yes—
176#66873C2314yes—
177#66873C2314yes—
178#66873C2314yes—
179#66872C2314yes—
180#66871C2314yes—
181C4⋊(C11⋊C8)C2314yes—
182C2×#3259—111nomaximal, Sylow
183C24×C11—21no—
184C23×D11—21no—
185C23×D11—21no—
186C23×D11—21no—
187C23×D11C2×D411yescharacteristic
188C2×D4×C11—21no—
189C2×D4×C11—22no—
190C2×D4×C11—22no—
191C2×D4×C11C2412yes—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—24no—
196C22×C4×C11—82no—
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2411yescharacteristic
200C2×C22⋊D11—24no—
201C2×C22⋊D11—24no—
202C2×C22⋊D11—24no—
203C2×C22⋊D11—82no—
204C2×C22⋊D11—82no—
205C2×C22⋊D11—82no—
206C22×Dic11—21no—
207C22×Dic11C2×D411yescharacteristic
208C22×Dic11C2×D411yescharacteristic
209C22×Dic11C2×D411yescharacteristic
210C2×D44—24no—
211C2×D44—24no—
212C2×D44—24no—
213C2×D44—21no—
214C2×D44—21no—
215C2×D44—21no—
216C2×D44—24no—
217C2×D44—24no—
218C2×D44—22no—
219C2×D44—22no—
220C2×D44—22no—
221C2×D44—22no—
222C2×D44—22no—
223C2×D44—22no—
224C2×D44—82no—
225C2×D44—82no—
226C2×D44—82no—
227C2×D44—82no—
228C2×D44—82no—
229C2×D44C2412yes—
230C2×D44C2412yes—
231C2×D44C2412yes—
232C2×C4×D11—24no—
233C2×C4×D11—24no—
234C2×C4×D11—24no—
235C2×C4×D11—22no—
236C2×C4×D11—22no—
237C2×C4×D11—82no—
238C2×C4×D11—82no—
239C2×C4×D11—82no—
240C2×C4×D11C2×D412yes—
241C2×C4×D11C2412yes—
242C2×C8×C11—22no—
243C2×C8×C11—22no—
244C2×C8×C11C2412yes—
245C2×C8×C11C2412yes—
246C11×C4⋊C4—21no—
247C11×C4⋊C4—21no—
248C11×C4⋊C4—21no—
249C11×C4⋊C4—24no—
250C11×C4⋊C4—24no—
251C11×C4⋊C4C2412yes—
252C11×C4⋊C4C2412yes—
253C11×C4⋊C4C2412yes—
254C11×C22⋊C4—24no—
255C42×C11C2×D412yes—
256C42×C11C2412yes—
257C22⋊Dic11—24no—
258#4323—44no—
259#4323—44no—
260(C2×D11)⋊C4—24no—
261(C2×D11)⋊C4—24no—
262(C2×D11)⋊C4—24no—
263(C2×D11)⋊C4—24no—
264(C2×D11)⋊C4—24no—
265(C2×D11)⋊C4—24no—
266(C2×D11)⋊C4C2×D414yes—
267(C2×D11)⋊C4C2×D414yes—
268C4⋊Dic11—24no—
269C4⋊Dic11—21no—
270C4⋊Dic11C2412yes—
271Dic11⋊C4—24no—
272Dic11⋊C4C2×D414yes—
273Dic11⋊C4C2×D414yes—
274C4×Dic11C2×D412yes—
275C4×Dic11C2412yes—
276C2×C11⋊C8—22no—
277C2×C11⋊C8—22no—
278C2×C11⋊C8C2412yes—
279C2×C11⋊C8C2412yes—
280D88—44no—
281D88—44no—
282#4313—44no—
283C8×D11—44no—
284C2×#540—111no—
285C2×#540—111no—
286#3259—1116no—
287C2×#478—111no—
288C2×#478—111no—
289C2×#478—111no—
290C2×#478D1111yescharacteristic, complemented
291C2×#469—111no—
292C2×#469—111no—
293C2×#466—111no—
294C2×#466—111no—
295C2×#459—111no—
296C2×#459—111no—
297C2×#459—111no—
298C2×#459—111no—
299C2×#424—111no—
300C23×C11—22no—
301C23×C11—42no—
302C23×C11—42no—
303C23×C11—42no—
304C23×C11C22×D411yescharacteristic
305C22×D11—22no—
306C22×D11—22no—
307C22×D11—22no—
308C22×D11—22no—
309C22×D11—22no—
310C22×D11—22no—
311C22×D11—42no—
312C22×D11—42no—
313C22×D11—42no—
314C22×D11—42no—
315C22×D11—42no—
316C22×D11—42no—
317C22×D11—42no—
318C22×D11—42no—
319C22×D11—42no—
320C22×D11C22×D412yes—
321D4×C11—22no—
322D4×C11—22no—
323D4×C11—42no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—42no—
330C2×C4×C11—42no—
331C2×C4×C11—42no—
332C2×C4×C11—84no—
333C2×C4×C11C22×D412yes—
334C2×C4×C11C22×D412yes—
335C2×C4×C11C22×D411yescharacteristic
336C2×C4×C11H(5,𝔽2)12yes—
337C2×C4×C112−1+412yes—
338C2×C4×C11C2511yescharacteristic
339C22⋊D11—84no—
340C22⋊D11—84no—
341C22⋊D11—84no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—22no—
346C2×Dic11—42no—
347C2×Dic11C22×D412yes—
348C2×Dic11C22×D412yes—
349C2×Dic11C22×D412yes—
350D44—22no—
351D44—22no—
352D44—22no—
353D44—22no—
354D44—22no—
355D44—22no—
356D44—42no—
357D44—42no—
358D44—42no—
359D44—84no—
360D44—84no—
361D44—84no—
362D44—84no—
363D44—84no—
364C4×D11—24no—
365C4×D11—22no—
366C4×D11—22no—
367C4×D11—84no—
368C4×D11—84no—
369C4×D11—84no—
370C8×C11—22no—
371C8×C11—22no—
372C11⋊C8—22no—
373C11⋊C8—22no—
374C22×D8—111no—
375C22×D8—111no—
376C22×D8—111no—
377C22×D8—111no—
378C22×M16—111no—
379C23×C8—111no—
380#540—118no—
381#540—118no—
382#540—224no—
383#540—224no—
384C2×#127—111no—
385C2×#127—111no—
386C2×#125—111no—
387C2×#125C2×D1111yescharacteristic
388C2×#123—221no—
389C2×#123—221no—
390C2×#123—221no—
391C2×#123—221no—
392C2×#121—111no—
393C2×#121—111no—
394C2×#121—111no—
395C2×#121—111no—
396C2×#121—221no—
397C2×#121—221no—
398C2×#121—221no—
399C2×#121—221no—
400C2×C4×D4—111no—
401C2×C4×D4—111no—
402C2×C4×D4—111no—
403C2×C4×D4C2×D1111yescharacteristic
404C2×#117—111no—
405#478—118no—
406#478—118no—
407#478—118no—
408#478C2×D1118yescomplemented
409#469—118no—
410#469—118no—
411#466—118no—
412#466—118no—
413#459—118no—
414#459—118no—
415#459—118no—
416#459—118no—
417C2×#107—111no—
418C2×#107C2×D1111yescharacteristic
419C2×#106—111no—
420C2×#106C2×D1111yescharacteristic
421#424—118no—
422C2×C4⋊C8—111no—
423C2×C4⋊C8—111no—
424C2×C4⋊C8—111no—
425C2×C4⋊C8C2×D1111yescharacteristic
426C2×#102—111no—
427C2×#102—111no—
428C2×#102—111no—
429C2×#102—111no—
430C2×#102—111no—
431C2×#102—111no—
432C2×#102C2×D1111yescharacteristic
433C2×#102C2×D1111yescharacteristic
434C22×C11—42no—
435C22×C11—42no—
436C22×C11—42no—
437C22×C11—84no—
438C22×C11#53712yes—
439C22×C11#57612yes—
440C22×C11#57612yes—
441C22×C11C23×D411yescharacteristic
442C2×D11—22no—
443C2×D11—22no—
444C2×D11—22no—
445C2×D11—44no—
446C2×D11—42no—
447C2×D11—42no—
448C2×D11—42no—
449C2×D11—42no—
450C2×D11—42no—
451C2×D11—42no—
452C2×D11—42no—
453C2×D11—42no—
454C2×D11—42no—
455C2×D11—84no—
456C2×D11—84no—
457C2×D11—84no—
458C4×C11—22no—
459C4×C11—22no—
460C4×C11—42no—
461C4×C11—42no—
462C4×C11—42no—
463C4×C11#53712yes—
464C4×C11C2×H(5,𝔽2)11yescharacteristic
465C4×C11C2×2−1+411yescharacteristic
466Dic11—22no—
467Dic11—22no—
468Dic11—22no—
469Dic11—42no—
470C22×D4—111no—
471C22×D4—111no—
472C22×D4—111no—
473C22×D4—221no—
474C22×D4—221no—
475C22×D4—221no—
476C22×D4—221no—
477C22×D4—221no—
478C22×D4—221no—
479C22×D4—221no—
480C22×D4—221no—
481C22×D4C22×D1111yescharacteristic
482C23×C4—21no—
483C23×C4—111no—
484C23×C4—221no—
485C23×C4—221no—
486C23×C4—221no—
487C2×D8—114no—
488C2×D8—114no—
489C2×D8—114no—
490C2×D8—114no—
491C2×D8—442no—
492C2×D8—442no—
493C2×D8—442no—
494C2×D8—442no—
495C2×M16—114no—
496C2×M16—442no—
497C22×C8—111no—
498C22×C8—111no—
499C22×C8—114no—
500C22×C8—442no—
501C22×C8C22×D1111yescharacteristic
502C22×C8C22×D1111yescharacteristic
503#127—114no—
504#127—114no—
505#127—222no—
506#127—222no—
507#125—22no—
508#125—114no—
509#125—222no—
510#125C22×D1114yes—
511#123—228no—
512#123—228no—
513#123—228no—
514#123—228no—
515#121—114no—
516#121—114no—
517#121—114no—
518#121—114no—
519#121—228no—
520#121—228no—
521#121—228no—
522#121—228no—
523#121—222no—
524#121—222no—
525#121—222no—
526#121—222no—
527C4×D4—22no—
528C4×D4—114no—
529C4×D4—114no—
530C4×D4—114no—
531C4×D4—222no—
532C4×D4—222no—
533C4×D4—222no—
534C4×D4C22×D1114yes—
535#117—114no—
536#117—114no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—111no—
540C2×C4⋊C4—111no—
541C2×C4⋊C4—111no—
542C2×C4⋊C4—221no—
543C2×C4⋊C4—221no—
544C2×C4⋊C4C22×D1111yescharacteristic
545C2×C4⋊C4C22×D1111yescharacteristic
546C2×C4⋊C4C22×D1111yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—111no—
549C2×C22⋊C4—111no—
550C2×C22⋊C4—221no—
551C2×C22⋊C4—221no—
552C2×C22⋊C4—221no—
553C2×C22⋊C4—221no—
554C2×C22⋊C4—221no—
555C2×C22⋊C4—221no—
556C2×C22⋊C4—221no—
557C2×C42—111no—
558C2×C42C22×D1111yescharacteristic
559#107—114no—
560#107C22×D1114yes—
561#106—114no—
562#106C22×D1114yes—
563C4⋊C8—114no—
564C4⋊C8—114no—
565C4⋊C8—114no—
566C4⋊C8C22×D1114yes—
567#102—114no—
568#102—114no—
569#102—114no—
570#102—114no—
571#102—114no—
572#102—114no—
573#102C22×D1114yes—
574#102C22×D1114yes—
575C2×C11—82no—
576C2×C11#325914yescomplemented
577C2×C11C2×#53711yescharacteristic
578C2×C11C2×#57611yescharacteristic
579C2×C11C2×#57611yescharacteristic
580D11—42no—
581D11—82no—
582D11—82no—
583D11—82no—
584C24—21no—
585C24—111no—
586C24—221no—
587C24—221no—
588C24—221no—
589C2×D4—21no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—112no—
593C2×D4—112no—
594C2×D4—112no—
595C2×D4—224no—
596C2×D4—224no—
597C2×D4—224no—
598C2×D4—224no—
599C2×D4—224no—
600C2×D4—224no—
601C2×D4—221no—
602C2×D4—221no—
603C2×D4—221no—
604C2×D4—224no—
605C2×D4—224no—
606C2×D4—222no—
607C2×D4—222no—
608C2×D4—222no—
609C2×D4—222no—
610C2×D4—222no—
611C2×D4—222no—
612C2×D4—882no—
613C2×D4—882no—
614C2×D4—882no—
615C2×D4—882no—
616C2×D4—882no—
617C2×D4—882no—
618C2×D4—882no—
619C2×D4—882no—
620C2×D4C23×D1112yes—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—24no—
625C22×C4—82no—
626C22×C4—111no—
627C22×C4—111no—
628C22×C4—111no—
629C22×C4—112no—
630C22×C4—112no—
631C22×C4—224no—
632C22×C4—224no—
633C22×C4—222no—
634C22×C4—222no—
635C22×C4—221no—
636C22×C4—224no—
637C22×C4—882no—
638C22×C4—882no—
639C22×C4—882no—
640C22×C4D4×D1111yescharacteristic
641C22×C4D4×D1111yescharacteristic
642C22×C4C23×D1111yescharacteristic
643D8—444no—
644D8—444no—
645D8—444no—
646D8—444no—
647M16—444no—
648C2×C8—22no—
649C2×C8—22no—
650C2×C8—112no—
651C2×C8—112no—
652C2×C8—222no—
653C2×C8—222no—
654C2×C8—444no—
655C2×C8C23×D1112yes—
656C2×C8C23×D1112yes—
657C4⋊C4—24no—
658C4⋊C4—24no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—114no—
663C4⋊C4—114no—
664C4⋊C4—112no—
665C4⋊C4—224no—
666C4⋊C4—224no—
667C4⋊C4—221no—
668C4⋊C4C23×D1112yes—
669C4⋊C4C23×D1112yes—
670C4⋊C4C23×D1112yes—
671C22⋊C4—24no—
672C22⋊C4—114no—
673C22⋊C4—114no—
674C22⋊C4—224no—
675C22⋊C4—224no—
676C22⋊C4—224no—
677C22⋊C4—224no—
678C22⋊C4—224no—
679C22⋊C4—224no—
680C22⋊C4—224no—
681C42—112no—
682C42—112no—
683C42D4×D1112yes—
684C42C23×D1112yes—
685C11C2×#325911yescharacteristic, complemented, Sylow
686C23—22no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—112no—
691C23—222no—
692C23—222no—
693C23—222no—
694C23—222no—
695C23—222no—
696C23—222no—
697C23—442no—
698C23—442no—
699C23—442no—
700C23—442no—
701C23—442no—
702C23—442no—
703C23—442no—
704C23—442no—
705C23—442no—
706C23C2×D4×D1111yescharacteristic
707D4—22no—
708D4—22no—
709D4—42no—
710D4—222no—
711D4—222no—
712D4—222no—
713D4—222no—
714D4—222no—
715D4—222no—
716D4—442no—
717D4—442no—
718D4—442no—
719D4—884no—
720D4—884no—
721D4—884no—
722D4—884no—
723D4—884no—
724D4—884no—
725D4—884no—
726D4—884no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—84no—
736C2×C4—112no—
737C2×C4—112no—
738C2×C4—112no—
739C2×C4—222no—
740C2×C4—222no—
741C2×C4—222no—
742C2×C4—224no—
743C2×C4—222no—
744C2×C4—222no—
745C2×C4—222no—
746C2×C4—442no—
747C2×C4—884no—
748C2×C4—884no—
749C2×C4—884no—
750C2×C4C2×D4×D1112yes—
751C2×C4C2×D4×D1112yes—
752C2×C4C2×D4×D1111yescharacteristic
753C2×C4#6704012yes—
754C2×C4#6704212yes—
755C2×C4C24×D1111yescharacteristic
756C8—22no—
757C8—22no—
758C8—222no—
759C8—222no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—84no—
764C22—222no—
765C22—222no—
766C22—222no—
767C22—444no—
768C22—442no—
769C22—442no—
770C22—442no—
771C22—442no—
772C22—442no—
773C22—442no—
774C22—442no—
775C22—442no—
776C22—442no—
777C22—884no—
778C22—884no—
779C22—884no—
780C22#1062316012yes—
781C22#1062330012yes—
782C22#1062330512yes—
783C22C22×D4×D1111yescharacteristic
784C4—22no—
785C4—22no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—222no—
790C4—222no—
791C4—222no—
792C4—442no—
793C4#1062316012yes—
794C4C2×#6704011yescharacteristic
795C4C2×#6704211yescharacteristic
796C2—82no—
797C2—442no—
798C2—882no—
799C2—882no—
800C2—882no—
801C2#1308005414yesdirect product factor
802C2C2×#1062316011yescharacteristic
803C2C2×#1062330011yescharacteristic
804C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#478C2
socleC23×C11C22×D4
hypercenterC2×#478D11
hypocenterC11C2×#3259
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#10623229C2semidirect
2. C2×#10623093C2semidirect
3. #13080054C2direct (N × H)
4. C2×#10622504C2semidirect
5. C2×#10622484C2semidirect
6. C2×#10622679C2semidirect
7. C2×#10622478C2semidirect
8. C2×#10622395C2semidirect
9. C2×#10622496C2semidirect
10. C2×#10622388C2semidirect
11. C2×#10622456C2semidirect
12. C2×#10622628C2semidirect
13. C2×#10622399C2semidirect
14. C2×#10622399C2semidirect
15. C2×#10622452C2semidirect
16. C2×C11×#478C2semidirect
30. #10623229C22semidirect
32. #10623093C22semidirect
48. C11×#478C22semidirect
58. #10622679C22semidirect
59. #10622628C22semidirect
67. #10622504C22semidirect
68. #10622496C22semidirect
69. #10622484C22semidirect
70. #10622478C22semidirect
71. #10622456C22semidirect
72. #10622452C22semidirect
73. #10622399C22semidirect
74. #10622399C22semidirect
75. #10622395C22semidirect
76. #10622388C22semidirect
290. C2×#478D11semidirect
408. #478C2×D11semidirect
576. C2×C11#3259semidirect
685. C11C2×#3259semidirect
801. C2#13080054direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232292
C2×#106230932
#130800542
C2×#106225042
C2×#106224842
C2×#106226792
C2×#106224782
C2×#106223952
C2×#106224962
C2×#106223882
C2×#106224562
C2×#106226282
C2×#106223992
C2×#106224522
C2×C11×#4782
C2×#325911