Finite Group Databasebeta

← C2×#13081348 #15633475

Subgroups — C2×#13081348 #15633475

Order 2816.

2122 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623216C211yesmaximal, characteristic, complemented
2C2×#10623084C211yesmaximal, characteristic
3#13081348C2116yesmaximal, direct product factor
4C2×#10622680C211yesmaximal, characteristic, complemented
5C2×#10622377C211yesmaximal, characteristic, complemented
6C2×#10622373C211yesmaximal, characteristic, complemented
7C2×#10622484C211yesmaximal, characteristic, complemented
8C2×#10622503C211yesmaximal, characteristic, complemented
9C2×#10622461C211yesmaximal, characteristic, complemented
10C2×#10622375C211yesmaximal, characteristic, complemented
11C2×#10622375C211yesmaximal, characteristic, complemented
12C2×#10622441C211yesmaximal, characteristic, complemented
13C2×#10622631C211yesmaximal, characteristic, complemented
14C2×#10622502C211yesmaximal, characteristic, complemented
15C2×#10622465C211yesmaximal, characteristic, complemented
16C2×C11×#478C211yesmaximal, characteristic, complemented
17C22×#4339—21no—
18C2×C11×#125C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×#66993C2211yescharacteristic
21C2×#66993C2211yescharacteristic
22C22×#4324C2211yescharacteristic
23C2×#66983—21no—
24C22×#4314C2211yescharacteristic
25C22×#4314C2211yescharacteristic
26#10623216—24no—
27#10623216C2218yescomplemented
28#10623084—24no—
29#10623084C2218yes—
30C2×#66946C2211yescharacteristic
31C2×#66946C2211yescharacteristic
32C2×#66943C2211yescharacteristic
33C2×#66942—21no—
34C2×#66942—21no—
35C2×#66941—21no—
36C2×#66941C2211yescharacteristic
37C2×#66940—21no—
38C2×#66940C2211yescharacteristic
39C2×#66940C2211yescharacteristic
40C2×#66937—21no—
41C2×#66937—21no—
42C2×#66927C2211yescharacteristic
43C2×C4×Dic22C2211yescharacteristic
44C2×C4×Dic22C2211yescharacteristic
45C11×#478C2218yescomplemented
46C2×C11×#107C2211yescharacteristic
47C2×C11×#106C2211yescharacteristic
48C2×C11×C4⋊C8C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×#66896C2211yescharacteristic
52C2×#66885C2211yescharacteristic
53C2×#66885C2211yescharacteristic
54C2×#66879C2211yescharacteristic
55C2×Dic11⋊C8C2211yescharacteristic
56C2×Dic11⋊C8C2211yescharacteristic
57C2×C8×Dic11C2211yescharacteristic
58#10622680C2218yescomplemented
59#10622631C2218yescomplemented
60C2×#66874C2211yescharacteristic
61C2×#66873C2211yescharacteristic
62C2×#66873C2211yescharacteristic
63C2×#66873C2211yescharacteristic
64C2×#66873C2211yescharacteristic
65C2×#66871C2211yescharacteristic
66C2×#66867C2211yescharacteristic
67#10622503C2218yescomplemented
68#10622502C2218yescomplemented
69#10622484C2218yescomplemented
70#10622465C2218yescomplemented
71#10622461C2218yescomplemented
72#10622441C2218yescomplemented
73#10622377C2218yescomplemented
74#10622375C2218yescomplemented
75#10622375C2218yescomplemented
76#10622373C2218yescomplemented
77C22×D4×C11C2311yescharacteristic
78C23×C4×C11—21no—
79C22×C22⋊D11—21no—
80C22×C22⋊D11—21no—
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C2×#4339—28no—
84C2×#4339—48no—
85C22×D44—21no—
86C22×D44—21no—
87C22×D44C2311yescharacteristic
88C22×D44C2311yescharacteristic
89C22×C4×D11—21no—
90C22×C4×D11—21no—
91C22×Dic22—21no—
92C22×Dic22D411yescharacteristic
93C22×Dic22C2311yescharacteristic
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
107#66993—22no—
108#66993—22no—
109#66993C2314yes—
110#66993C2314yes—
111C2×#4324—24no—
112C2×#4324C2314yes—
113#66983—28no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×C4⋊Dic11—21no—
117C2×C4⋊Dic11D411yescharacteristic
118C2×C4⋊Dic11C2311yescharacteristic
119C2×Dic11⋊C4—21no—
120C2×Dic11⋊C4—21no—
121C2×Dic11⋊C4—21no—
122C2×Dic11⋊C4—21no—
123C2×Dic11⋊C4—21no—
124C2×Dic11⋊C4D411yescharacteristic
125C2×Dic11⋊C4D411yescharacteristic
126C2×C4×Dic11—21no—
127C2×C4×Dic11—21no—
128C2×C4×Dic11—21no—
129C2×C4×Dic11C2311yescharacteristic
130C2×C4×Dic11C2311yescharacteristic
131C22×C11⋊C8C2311yescharacteristic
132C22×C11⋊C8C2311yescharacteristic
133C2×#4314—24no—
134C2×#4314—24no—
135C2×#4314C2314yes—
136C2×#4314C2314yes—
137#66946—22no—
138#66946—22no—
139#66946C2314yes—
140#66946C2314yes—
141#66943—22no—
142#66943C2314yes—
143#66942—28no—
144#66942—28no—
145#66941—28no—
146#66941—22no—
147#66941C2314yes—
148#66940—28no—
149#66940—22no—
150#66940—22no—
151#66940C2314yes—
152#66940C2314yes—
153#66937—28no—
154#66937—28no—
155#66927—22no—
156#66927C2314yes—
157C4×Dic22—22no—
158C4×Dic22D414yes—
159C4×Dic22C2314yes—
160C4×Dic22C2314yes—
161C11×#107C2314yes—
162C11×#106C2314yes—
163C11×C4⋊C8C2314yes—
164C11×#102C2314yes—
165C11×#102C2314yes—
166#66896C2314yes—
167#66885C2314yes—
168#66885C2314yes—
169#66879C2314yes—
170Dic11⋊C8C2314yes—
171Dic11⋊C8C2314yes—
172C8×Dic11C2314yes—
173#66874C2314yes—
174#66873C2314yes—
175#66873C2314yes—
176#66873C2314yes—
177#66873C2314yes—
178#66871C2314yes—
179#66867C2314yes—
180C2×#3368—111nomaximal, Sylow
181C24×C11—21no—
182C23×D11—21no—
183C23×D11—21no—
184C2×D4×C11—21no—
185C2×D4×C11—22no—
186C2×D4×C11—22no—
187C2×D4×C11C2412yes—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—24no—
192C22×C4×C11—44no—
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2411yescharacteristic
196C2×C22⋊D11—24no—
197C2×C22⋊D11—24no—
198C2×C22⋊D11—24no—
199C2×C22⋊D11—24no—
200C2×C22⋊D11—44no—
201C2×C22⋊D11—44no—
202C2×C22⋊D11—82no—
203C2×C22⋊D11—82no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11C2×D411yescharacteristic
207C22×Dic11C2×D411yescharacteristic
208C22×Dic11C2×D411yescharacteristic
209C22×Dic11C2×D411yescharacteristic
210#4339—432no—
211C2×D44—21no—
212C2×D44—21no—
213C2×D44—24no—
214C2×D44—24no—
215C2×D44—22no—
216C2×D44—22no—
217C2×D44—22no—
218C2×D44—22no—
219C2×D44—44no—
220C2×D44—82no—
221C2×D44C2412yes—
222C2×D44C2412yes—
223C2×C4×D11—24no—
224C2×C4×D11—24no—
225C2×C4×D11—44no—
226C2×C4×D11—44no—
227C2×Dic22—24no—
228C2×Dic22—24no—
229C2×Dic22—21no—
230C2×Dic22—22no—
231C2×Dic22—44no—
232C2×Dic22C2×D414yes—
233C2×Dic22#4114yescomplemented
234C2×Dic22C2412yes—
235C2×C8×C11—22no—
236C2×C8×C11—22no—
237C2×C8×C11C2412yes—
238C2×C8×C11C2412yes—
239C11×C4⋊C4—21no—
240C11×C4⋊C4—24no—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—24no—
243C11×C4⋊C4—21no—
244C11×C4⋊C4C2412yes—
245C11×C4⋊C4C2412yes—
246C11×C4⋊C4C2412yes—
247C11×C22⋊C4—24no—
248C42×C11C2×D412yes—
249C42×C11C2412yes—
250#4324—28no—
251(C2×D11)⋊C4—24no—
252(C2×D11)⋊C4—24no—
253C4⋊Dic11—24no—
254C4⋊Dic11—21no—
255C4⋊Dic11C2×D414yes—
256C4⋊Dic11C2412yes—
257Dic11⋊C4—24no—
258Dic11⋊C4—24no—
259Dic11⋊C4—24no—
260Dic11⋊C4—24no—
261Dic11⋊C4—24no—
262Dic11⋊C4C2×D414yes—
263Dic11⋊C4C2×D414yes—
264C4×Dic11—24no—
265C4×Dic11—24no—
266C4×Dic11—24no—
267C4×Dic11C2×D412yes—
268C4×Dic11C2×D412yes—
269C4×Dic11C2412yes—
270C4×Dic11C2412yes—
271C2×C11⋊C8—22no—
272C2×C11⋊C8—22no—
273C2×C11⋊C8C2412yes—
274C2×C11⋊C8C2412yes—
275#4314—28no—
276#4314—28no—
277C2×#557—111no—
278C2×#550—111no—
279#3368—1116no—
280C2×#490—111no—
281C2×#490—111no—
282C2×#486—111no—
283C2×#478—111no—
284C2×#478D1111yescharacteristic, complemented
285C2×#474—111no—
286C2×#460—111no—
287C2×#460—111no—
288C2×#460—111no—
289C2×#446—111no—
290C2×#440—111no—
291C2×#440—111no—
292C2×C4×SD16—111no—
293C23×C11—22no—
294C23×C11—42no—
295C23×C11—42no—
296C23×C11—42no—
297C23×C11C22×D411yescharacteristic
298C22×D11—22no—
299C22×D11—22no—
300C22×D11—42no—
301C22×D11—42no—
302C22×D11—42no—
303C22×D11—42no—
304C22×D11—42no—
305C22×D11—42no—
306D4×C11—22no—
307D4×C11—22no—
308D4×C11—42no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—48no—
315C2×C4×C11—42no—
316C2×C4×C11—42no—
317C2×C4×C11—42no—
318C2×C4×C11C22×D412yes—
319C2×C4×C11C22×D412yes—
320C2×C4×C11C22×D411yescharacteristic
321C2×C4×C11C2×#4112yes—
322C2×C4×C112−1+412yes—
323C2×C4×C11C2511yescharacteristic
324C22⋊D11—48no—
325C22⋊D11—48no—
326C22⋊D11—84no—
327C22⋊D11—84no—
328C2×Dic11—24no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—42no—
335C2×Dic11AGL(1,ℤ/8)14yes—
336C2×Dic11C22×D412yes—
337C2×Dic11C22×D412yes—
338C2×Dic11C22×D412yes—
339C2×Dic11C22×D412yes—
340D44—22no—
341D44—22no—
342D44—22no—
343D44—22no—
344D44—48no—
345D44—42no—
346D44—42no—
347D44—84no—
348C4×D11—48no—
349C4×D11—48no—
350Dic22—24no—
351Dic22—22no—
352Dic22—28no—
353Dic22—48no—
354Dic22C2×#4114yescomplemented
355C8×C11—22no—
356C8×C11—22no—
357C11⋊C8—22no—
358C11⋊C8—22no—
359C22×#41—221no—
360C22×SD16—111no—
361C22×SD16—111no—
362C22×SD16—111no—
363#557—118no—
364#557—224no—
365#550—118no—
366#550—224no—
367C2×C4⋊Q8—111no—
368C2×C4⋊Q8—221no—
369C2×#127—111no—
370C2×#127—111no—
371C2×#127—111no—
372C2×#125—111no—
373C2×#125—221no—
374C2×#125—221no—
375C2×#125C2×D1111yescharacteristic
376C2×#121—221no—
377C2×#121—221no—
378C2×#121—221no—
379C2×C4×Q8—111no—
380C2×C4×Q8—111no—
381C2×C4×Q8—111no—
382C2×C4×Q8—111no—
383C2×C4×Q8—221no—
384C2×C4×D4—111no—
385C2×C4×D4—111no—
386C2×C4×D4C2×D1111yescharacteristic
387#490—118no—
388#490—118no—
389#486—118no—
390#478—118no—
391#478C2×D1118yescomplemented
392#474—118no—
393#460—118no—
394#460—118no—
395#460—118no—
396#446—118no—
397#440—118no—
398#440—118no—
399C4×SD16—118no—
400C2×#107—111no—
401C2×#107C2×D1111yescharacteristic
402C2×#106C2×D1111yescharacteristic
403C2×C4⋊C8—111no—
404C2×C4⋊C8—111no—
405C2×C4⋊C8C2×D1111yescharacteristic
406C2×#103—111no—
407C2×#102—111no—
408C2×#102—111no—
409C2×#102—111no—
410C2×#102—111no—
411C2×#102—111no—
412C2×#102—111no—
413C2×#102—111no—
414C2×#102C2×D1111yescharacteristic
415C2×#102C2×D1111yescharacteristic
416C2×#97—111no—
417C2×#97—111no—
418C2×C4×C8—111no—
419C22×C11—42no—
420C22×C11—42no—
421C22×C11—42no—
422C22×C11—84no—
423C22×C11#54812yes—
424C22×C11C2×AGL(1,ℤ/8)12yes—
425C22×C11#57712yes—
426C22×C11C23×D411yescharacteristic
427C2×D11—42no—
428C2×D11—42no—
429C2×D11—42no—
430C2×D11—42no—
431C2×D11—42no—
432C2×D11—42no—
433C2×D11—84no—
434C2×D11—84no—
435C4×C11—22no—
436C4×C11—22no—
437C4×C11—42no—
438C4×C11—42no—
439C4×C11—42no—
440C4×C11#54812yes—
441C4×C11C22×#4111yescharacteristic
442C4×C11C2×2−1+411yescharacteristic
443Dic11—24no—
444Dic11—22no—
445Dic11—22no—
446Dic11—22no—
447Dic11—42no—
448Dic11C2×AGL(1,ℤ/8)14yes—
449C2×#41—228no—
450C2×#41—448no—
451C22×Q8—111no—
452C22×Q8—111no—
453C22×Q8—221no—
454C22×D4—111no—
455C22×D4—111no—
456C22×D4—221no—
457C22×D4—221no—
458C22×D4—221no—
459C22×D4—221no—
460C22×D4—221no—
461C22×D4—221no—
462C22×D4C22×D1111yescharacteristic
463C23×C4—21no—
464C23×C4—221no—
465C23×C4—221no—
466C2×SD16—114no—
467C2×SD16—114no—
468C2×SD16—114no—
469C2×SD16—224no—
470C2×SD16—224no—
471C2×SD16—224no—
472C22×C8—111no—
473C22×C8—111no—
474C22×C8C22×D1111yescharacteristic
475C22×C8C22×D1111yescharacteristic
476C4⋊Q8—114no—
477C4⋊Q8—222no—
478C4⋊Q8—228no—
479#127—114no—
480#127—114no—
481#127—114no—
482#127—222no—
483#127—222no—
484#127—222no—
485#125—22no—
486#125—114no—
487#125—222no—
488#125—228no—
489#125—228no—
490#125C22×D1114yes—
491#121—228no—
492#121—228no—
493#121—228no—
494C4×Q8—114no—
495C4×Q8—114no—
496C4×Q8—114no—
497C4×Q8—114no—
498C4×Q8—114no—
499C4×Q8—222no—
500C4×Q8—222no—
501C4×Q8—228no—
502C4×Q8—222no—
503C4×D4—22no—
504C4×D4—114no—
505C4×D4—114no—
506C4×D4—222no—
507C4×D4—222no—
508C4×D4C22×D1114yes—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—111no—
512C2×C4⋊C4—111no—
513C2×C4⋊C4—111no—
514C2×C4⋊C4—111no—
515C2×C4⋊C4—221no—
516C2×C4⋊C4—221no—
517C2×C4⋊C4—221no—
518C2×C4⋊C4—221no—
519C2×C4⋊C4—221no—
520C2×C4⋊C4—221no—
521C2×C4⋊C4C22×D1111yescharacteristic
522C2×C4⋊C4C22×D1111yescharacteristic
523C2×C4⋊C4C22×D1111yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—221no—
526C2×C22⋊C4—221no—
527C2×C42—111no—
528C2×C42—111no—
529C2×C42—221no—
530C2×C42—221no—
531C2×C42—221no—
532C2×C42C22×D1111yescharacteristic
533#107—114no—
534#107C22×D1114yes—
535#106C22×D1114yes—
536C4⋊C8—114no—
537C4⋊C8—114no—
538C4⋊C8C22×D1114yes—
539#103—114no—
540#102—114no—
541#102—114no—
542#102—114no—
543#102—114no—
544#102—114no—
545#102—114no—
546#102—114no—
547#102C22×D1114yes—
548#102C22×D1114yes—
549#97—114no—
550#97—114no—
551C4×C8—114no—
552C2×C11—82no—
553C2×C11#336814yescomplemented
554C2×C11C2×#54811yescharacteristic
555C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
556C2×C11C2×#57711yescharacteristic
557D11—82no—
558D11—82no—
559C24—21no—
560C24—221no—
561C24—221no—
562#41—4432no—
563C2×Q8—114no—
564C2×Q8—114no—
565C2×Q8—112no—
566C2×Q8—224no—
567C2×Q8—224no—
568C2×Q8—221no—
569C2×Q8—222no—
570C2×Q8—444no—
571C2×D4—21no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—112no—
575C2×D4—112no—
576C2×D4—224no—
577C2×D4—224no—
578C2×D4—224no—
579C2×D4—224no—
580C2×D4—221no—
581C2×D4—221no—
582C2×D4—224no—
583C2×D4—224no—
584C2×D4—222no—
585C2×D4—222no—
586C2×D4—222no—
587C2×D4—222no—
588C2×D4—444no—
589C2×D4—444no—
590C2×D4—444no—
591C2×D4—882no—
592C2×D4—882no—
593C2×D4—882no—
594C2×D4C23×D1112yes—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—24no—
599C22×C4—44no—
600C22×C4—111no—
601C22×C4—111no—
602C22×C4—111no—
603C22×C4—111no—
604C22×C4—224no—
605C22×C4—224no—
606C22×C4—221no—
607C22×C4—221no—
608C22×C4—444no—
609C22×C4—444no—
610C22×C4D4×D1111yescharacteristic
611C22×C4D4×D1111yescharacteristic
612C22×C4C23×D1111yescharacteristic
613SD16—228no—
614SD16—228no—
615SD16—228no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—112no—
619C2×C8—112no—
620C2×C8—222no—
621C2×C8—222no—
622C2×C8C23×D1112yes—
623C2×C8C23×D1112yes—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—114no—
630C4⋊C4—114no—
631C4⋊C4—114no—
632C4⋊C4—112no—
633C4⋊C4—224no—
634C4⋊C4—224no—
635C4⋊C4—224no—
636C4⋊C4—224no—
637C4⋊C4—224no—
638C4⋊C4—221no—
639C4⋊C4—224no—
640C4⋊C4C23×D1112yes—
641C4⋊C4C23×D1112yes—
642C4⋊C4C23×D1112yes—
643C22⋊C4—24no—
644C22⋊C4—224no—
645C22⋊C4—224no—
646C42—112no—
647C42—112no—
648C42—112no—
649C42—112no—
650C42—224no—
651C42—224no—
652C42—224no—
653C42D4×D1112yes—
654C42C23×D1112yes—
655C11C2×#336811yescharacteristic, complemented, Sylow
656C23—22no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—222no—
661C23—222no—
662C23—442no—
663C23—442no—
664C23—442no—
665C23—442no—
666C23—442no—
667C23—442no—
668C23C2×D4×D1111yescharacteristic
669Q8—114no—
670Q8—228no—
671Q8—224no—
672Q8—222no—
673Q8—448no—
674D4—22no—
675D4—22no—
676D4—42no—
677D4—222no—
678D4—222no—
679D4—222no—
680D4—222no—
681D4—448no—
682D4—448no—
683D4—448no—
684D4—442no—
685D4—442no—
686D4—884no—
687D4—884no—
688D4—884no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—48no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—114no—
699C2×C4—112no—
700C2×C4—112no—
701C2×C4—112no—
702C2×C4—112no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—222no—
706C2×C4—224no—
707C2×C4—222no—
708C2×C4—222no—
709C2×C4—448no—
710C2×C4—448no—
711C2×C4—442no—
712C2×C4C2×D4×D1112yes—
713C2×C4C2×D4×D1112yes—
714C2×C4C2×D4×D1111yescharacteristic
715C2×C4#6704012yes—
716C2×C4#41×D1112yes—
717C2×C4C24×D1111yescharacteristic
718C8—22no—
719C8—22no—
720C8—222no—
721C8—222no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—442no—
727C22—442no—
728C22—442no—
729C22—442no—
730C22—442no—
731C22—442no—
732C22—884no—
733C22—884no—
734C22#1062316412yes—
735C22#1062330112yes—
736C22D11×AGL(1,ℤ/8)12yes—
737C22C22×D4×D1111yescharacteristic
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—114no—
744C4—222no—
745C4—224no—
746C4—222no—
747C4—222no—
748C4—442no—
749C4#1062316412yes—
750C4C2×#6704011yescharacteristic
751C4C2×#41×D1111yescharacteristic
752C2—82no—
753C2—882no—
754C2—882no—
755C2#1308134814yesdirect product factor
756C2C2×#1062316411yescharacteristic
757C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
758C2C2×#1062330111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#478C2
socleC23×C11C22×D4
prime radicalC2×#10623084C2
hypercenterC2×#478D11
hypocenterC11C2×#3368
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×#10623216C2semidirect
3. #13081348C2direct (N × H)
4. C2×#10622680C2semidirect
5. C2×#10622377C2semidirect
6. C2×#10622373C2semidirect
7. C2×#10622484C2semidirect
8. C2×#10622503C2semidirect
9. C2×#10622461C2semidirect
10. C2×#10622375C2semidirect
11. C2×#10622375C2semidirect
12. C2×#10622441C2semidirect
13. C2×#10622631C2semidirect
14. C2×#10622502C2semidirect
15. C2×#10622465C2semidirect
16. C2×C11×#478C2semidirect
27. #10623216C22semidirect
45. C11×#478C22semidirect
58. #10622680C22semidirect
59. #10622631C22semidirect
67. #10622503C22semidirect
68. #10622502C22semidirect
69. #10622484C22semidirect
70. #10622465C22semidirect
71. #10622461C22semidirect
72. #10622441C22semidirect
73. #10622377C22semidirect
74. #10622375C22semidirect
75. #10622375C22semidirect
76. #10622373C22semidirect
233. C2×Dic22#41semidirect
284. C2×#478D11semidirect
354. Dic22C2×#41semidirect
391. #478C2×D11semidirect
553. C2×C11#3368semidirect
655. C11C2×#3368semidirect
755. C2#13081348direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232162
C2×#106230842
#130813482
C2×#106226802
C2×#106223772
C2×#106223732
C2×#106224842
C2×#106225032
C2×#106224612
C2×#106223752
C2×#106224412
C2×#106226312
C2×#106225022
C2×#106224652
C2×C11×#4782
C2×#336811