Finite Group Databasebeta

← C2×#13081411 #15633463

Subgroups — C2×#13081411 #15633463

Order 2816.

2134 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×#10623090C211yesmaximal, characteristic, complemented
2C2×#10623258C211yesmaximal, characteristic, complemented
3#13081411C2116yesmaximal, direct product factor
4C2×#10622702C211yesmaximal, characteristic, complemented
5C2×#10622378C211yesmaximal, characteristic, complemented
6C2×#10622373C211yesmaximal, characteristic, complemented
7C2×#10622467C211yesmaximal, characteristic, complemented
8C2×#10622483C211yesmaximal, characteristic, complemented
9C2×#10622457C211yesmaximal, characteristic, complemented
10C2×#10622400C211yesmaximal, characteristic, complemented
11C2×#10622399C211yesmaximal, characteristic
12C2×#10622441C211yesmaximal, characteristic, complemented
13C2×#10622482C211yesmaximal, characteristic, complemented
14C2×#10622627C211yesmaximal, characteristic, complemented
15C2×#10622465C211yesmaximal, characteristic, complemented
16C2×C11×#476C211yesmaximal, characteristic, complemented
17C22×Q8×D11—21no—
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×#66999—21no—
21C2×#66993C2211yescharacteristic
22C2×#66989C2211yescharacteristic
23C22×#4323C2211yescharacteristic
24C2×#66982—21no—
25C2×C4×C22⋊D11—21no—
26C22×D88C2211yescharacteristic
27C22×#4314C2211yescharacteristic
28#10623258—24no—
29#10623258C2218yescomplemented
30#10623090—24no—
31#10623090C2218yescomplemented
32C2×#66949—21no—
33C2×#66949—21no—
34C2×#66946C2211yescharacteristic
35C2×#66946C2211yescharacteristic
36C2×#66946C2211yescharacteristic
37C2×#66941C2211yescharacteristic
38C2×#66941C2211yescharacteristic
39C2×#66940C2211yescharacteristic
40C2×#66938—21no—
41C2×#66936—21no—
42C2×#66928C2211yescharacteristic
43C2×C4×D44C2211yescharacteristic
44C2×C4×Dic22C2211yescharacteristic
45C11×#476C2218yescomplemented
46C2×C11×#106C2211yescharacteristic
47C2×C11×#106C2211yescharacteristic
48C2×C11×C4⋊C8C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×#66896C2211yescharacteristic
52C2×#66885C2211yescharacteristic
53C2×#66880C2211yescharacteristic
54C2×#66879C2211yescharacteristic
55C2×Dic11⋊C8C2211yescharacteristic
56C2×Dic11⋊C8C2211yescharacteristic
57C2×C8×Dic11C2211yescharacteristic
58#10622702C2218yescomplemented
59#10622627C2218yescomplemented
60C2×#66874C2211yescharacteristic
61C2×#66874C2211yescharacteristic
62C2×#66873C2211yescharacteristic
63C2×#66873C2211yescharacteristic
64C2×#66873C2211yescharacteristic
65C2×#66872C2211yescharacteristic
66C2×#66867C2211yescharacteristic
67#10622483C2218yescomplemented
68#10622482C2218yescomplemented
69#10622467C2218yescomplemented
70#10622465C2218yescomplemented
71#10622457C2218yescomplemented
72#10622441C2218yescomplemented
73#10622400C2218yescomplemented
74#10622399C2218yes—
75#10622378C2218yescomplemented
76#10622373C2218yescomplemented
77C22×Q8×C11—21no—
78C22×D4×C11C2311yescharacteristic
79C23×C4×C11—21no—
80C22×C22⋊D11—21no—
81C22×C22⋊D11—21no—
82C2×Q8×D11—28no—
83C2×Q8×D11—48no—
84C22×D44C2311yescharacteristic
85C22×D44C2311yescharacteristic
86C22×C4×D11—21no—
87C22×C4×D11—21no—
88C22×C4×D11—21no—
89C22×C4×D11—21no—
90C22×Dic22—21no—
91C22×Dic22—21no—
92C22×Dic22D411yescharacteristic
93C22×Dic22C2311yescharacteristic
94C22×C8×C11C2311yescharacteristic
95C22×C8×C11C2311yescharacteristic
96C11×C4⋊Q8—22no—
97C11×C4⋊Q8C2314yes—
98C4×D4×C11—22no—
99C4×D4×C11C2314yes—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C22⋊C4—21no—
105C2×C42×C11C2311yescharacteristic
106C2×C22⋊Dic11—21no—
107C2×C22⋊Dic11—21no—
108#66999—28no—
109#66993—22no—
110#66993C2314yes—
111#66989—22no—
112#66989C2314yes—
113C2×#4323—24no—
114C2×#4323C2314yes—
115#66982—28no—
116C4×C22⋊D11—28no—
117C2×(C2×D11)⋊C4—21no—
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×C4⋊Dic11D411yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×Dic11⋊C4—21no—
126C2×Dic11⋊C4—21no—
127C2×Dic11⋊C4—21no—
128C2×Dic11⋊C4D411yescharacteristic
129C2×Dic11⋊C4D411yescharacteristic
130C2×C4×Dic11—21no—
131C2×C4×Dic11C2311yescharacteristic
132C2×C4×Dic11C2311yescharacteristic
133C22×C11⋊C8C2311yescharacteristic
134C22×C11⋊C8C2311yescharacteristic
135C2×D88—24no—
136C2×D88C2314yes—
137C2×#4314—24no—
138C2×#4314C2314yes—
139#66949—28no—
140#66949—28no—
141#66946—22no—
142#66946—22no—
143#66946—22no—
144#66946C2314yes—
145#66946C2314yes—
146#66946C2314yes—
147#66941—22no—
148#66941—22no—
149#66941C2314yes—
150#66941C2314yes—
151#66940—22no—
152#66940C2314yes—
153#66938—28no—
154#66936—28no—
155#66928—22no—
156#66928C2314yes—
157C4×D44—22no—
158C4×D44C2314yes—
159C4×Dic22D414yes—
160C4×Dic22C2314yes—
161C11×#106C2314yes—
162C11×#106C2314yes—
163C11×C4⋊C8C2314yes—
164C11×#102C2314yes—
165C11×#102C2314yes—
166#66896C2314yes—
167#66885C2314yes—
168#66880C2314yes—
169#66879C2314yes—
170Dic11⋊C8C2314yes—
171Dic11⋊C8C2314yes—
172C8×Dic11C2314yes—
173#66874C2314yes—
174#66874C2314yes—
175#66873C2314yes—
176#66873C2314yes—
177#66873C2314yes—
178#66872C2314yes—
179#66867C2314yes—
180C2×#3373—111nomaximal, Sylow
181C24×C11—21no—
182C23×D11—21no—
183C23×D11—21no—
184C2×Q8×C11—24no—
185C2×Q8×C11—44no—
186C2×D4×C11—21no—
187C2×D4×C11—22no—
188C2×D4×C11—22no—
189C2×D4×C11C2412yes—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—24no—
194C22×C4×C11—82no—
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2411yescharacteristic
198C2×C22⋊D11—24no—
199C2×C22⋊D11—24no—
200C2×C22⋊D11—44no—
201C2×C22⋊D11—82no—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11C2×D411yescharacteristic
205C22×Dic11C2×D411yescharacteristic
206C22×Dic11C2×D411yescharacteristic
207C22×Dic11C2×D411yescharacteristic
208Q8×D11—432no—
209C2×D44—21no—
210C2×D44—21no—
211C2×D44—22no—
212C2×D44—22no—
213C2×D44—22no—
214C2×D44#4114yes—
215C2×D44C2412yes—
216C2×D44C2412yes—
217C2×C4×D11—24no—
218C2×C4×D11—24no—
219C2×C4×D11—24no—
220C2×C4×D11—24no—
221C2×C4×D11—44no—
222C2×C4×D11—44no—
223C2×C4×D11—44no—
224C2×C4×D11—82no—
225C2×Dic22—24no—
226C2×Dic22—24no—
227C2×Dic22—24no—
228C2×Dic22—21no—
229C2×Dic22—22no—
230C2×Dic22—22no—
231C2×Dic22—44no—
232C2×Dic22—44no—
233C2×Dic22C2×D414yes—
234C2×Dic22C2412yes—
235C2×C8×C11—22no—
236C2×C8×C11—22no—
237C2×C8×C11C2412yes—
238C2×C8×C11C2412yes—
239C11×C4⋊C4—21no—
240C11×C4⋊C4—21no—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—24no—
243C11×C4⋊C4C2412yes—
244C11×C4⋊C4C2412yes—
245C11×C4⋊C4C2412yes—
246C11×C22⋊C4—24no—
247C42×C11C2×D412yes—
248C42×C11C2412yes—
249C22⋊Dic11—24no—
250C22⋊Dic11—24no—
251#4323—28no—
252(C2×D11)⋊C4—24no—
253(C2×D11)⋊C4—24no—
254(C2×D11)⋊C4—24no—
255(C2×D11)⋊C4—24no—
256(C2×D11)⋊C4—24no—
257(C2×D11)⋊C4—24no—
258C4⋊Dic11—21no—
259C4⋊Dic11C2×D414yes—
260C4⋊Dic11C2412yes—
261Dic11⋊C4—24no—
262Dic11⋊C4—24no—
263Dic11⋊C4—24no—
264Dic11⋊C4C2×D414yes—
265Dic11⋊C4C2×D414yes—
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—
275D88—28no—
276#4314—28no—
277C2×#559—111no—
278C2×D4×Q8—111no—
279#3373—1116no—
280C2×#489—111no—
281C2×#489—111no—
282C2×#486—111no—
283C2×#475—111no—
284C2×#476—111no—
285C2×#476D1111yescharacteristic, complemented
286C2×#463—111no—
287C2×#463—111no—
288C2×#459—111no—
289C2×#446—111no—
290C2×#442—111no—
291C2×#442—111no—
292C2×C4×SD16—111no—
293C23×C11—22no—
294C23×C11—42no—
295C23×C11—42no—
296C23×C11—42no—
297C23×C11C22×D411yescharacteristic
298C22×D11—24no—
299C22×D11—22no—
300C22×D11—22no—
301C22×D11—42no—
302C22×D11—42no—
303C22×D11—42no—
304C22×D11—42no—
305C22×D11—42no—
306Q8×C11—48no—
307D4×C11—22no—
308D4×C11—22no—
309D4×C11—42no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—42no—
316C2×C4×C11—42no—
317C2×C4×C11—42no—
318C2×C4×C11—84no—
319C2×C4×C11C22×D412yes—
320C2×C4×C11C22×D412yes—
321C2×C4×C11C22×D411yescharacteristic
322C2×C4×C11C2×#4112yes—
323C2×C4×C112−1+412yes—
324C2×C4×C11C2511yescharacteristic
325C22⋊D11—48no—
326C22⋊D11—84no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11AGL(1,ℤ/8)14yes—
335C2×Dic11C22×D412yes—
336C2×Dic11C22×D412yes—
337C2×Dic11C22×D412yes—
338C2×Dic11C22×D412yes—
339D44—24no—
340D44—22no—
341D44—22no—
342D44—22no—
343D44—42no—
344D44C2×#4114yes—
345C4×D11—48no—
346C4×D11—48no—
347C4×D11—48no—
348C4×D11—84no—
349Dic22—28no—
350Dic22—22no—
351Dic22—22no—
352Dic22—48no—
353Dic22—42no—
354Dic22—48no—
355C8×C11—22no—
356C8×C11—22no—
357C11⋊C8—22no—
358C11⋊C8—22no—
359C23×Q8—221no—
360C22×SD16—111no—
361C22×D8—111no—
362C22×D8—111no—
363#559—118no—
364#559—224no—
365D4×Q8—118no—
366D4×Q8—224no—
367C2×C4⋊Q8—111no—
368C2×C4⋊Q8—111no—
369C2×C4⋊Q8C2×D1111yescharacteristic
370C2×#127—111no—
371C2×#124—111no—
372C2×#124—111no—
373C2×#124—221no—
374C2×#123—221no—
375C2×#123—221no—
376C2×C22⋊Q8—221no—
377C2×C22⋊Q8—221no—
378C2×C22⋊Q8—221no—
379C2×C4×Q8—111no—
380C2×C4×Q8—111no—
381C2×C4×D4—111no—
382C2×C4×D4—111no—
383C2×C4×D4—111no—
384C2×C4×D4—111no—
385C2×C4×D4—221no—
386C2×C4×D4C2×D1111yescharacteristic
387#489—118no—
388#489—118no—
389#486—118no—
390#476—118no—
391#476C2×D1118yescomplemented
392#475—118no—
393#463—118no—
394#463—118no—
395#459—118no—
396#446—118no—
397#442—118no—
398#442—118no—
399C4×SD16—118no—
400C2×#106—111no—
401C2×#106C2×D1111yescharacteristic
402C2×#106C2×D1111yescharacteristic
403C2×C4⋊C8—111no—
404C2×C4⋊C8—111no—
405C2×C4⋊C8C2×D1111yescharacteristic
406C2×#103—111no—
407C2×#103—111no—
408C2×#103—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—24no—
428C2×D11—48no—
429C2×D11—42no—
430C2×D11—42no—
431C2×D11—42no—
432C2×D11—42no—
433C2×D11—42no—
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—22no—
444Dic11—22no—
445Dic11—22no—
446Dic11—42no—
447Dic11—42no—
448Dic11C2×AGL(1,ℤ/8)14yes—
449C22×Q8—21no—
450C22×Q8—111no—
451C22×Q8—111no—
452C22×Q8—221no—
453C22×Q8—221no—
454C22×Q8—228no—
455C22×Q8—448no—
456C22×D4—111no—
457C22×D4—111no—
458C22×D4—221no—
459C22×D4—221no—
460C22×D4C22×D1111yescharacteristic
461C23×C4—21no—
462C23×C4—221no—
463C23×C4—221no—
464C23×C4—221no—
465C23×C4—221no—
466C2×SD16—114no—
467C2×SD16—224no—
468C2×D8—114no—
469C2×D8—114no—
470C2×D8—224no—
471C2×D8—224no—
472C22×C8—111no—
473C22×C8—111no—
474C22×C8C22×D1111yescharacteristic
475C22×C8C22×D1111yescharacteristic
476C4⋊Q8—22no—
477C4⋊Q8—114no—
478C4⋊Q8—114no—
479C4⋊Q8—222no—
480C4⋊Q8—222no—
481C4⋊Q8C22×D1114yes—
482#127—114no—
483#127—222no—
484#124—114no—
485#124—114no—
486#124—222no—
487#124—228no—
488#124—222no—
489#123—228no—
490#123—228no—
491C22⋊Q8—228no—
492C22⋊Q8—228no—
493C22⋊Q8—228no—
494C4×Q8—114no—
495C4×Q8—114no—
496C4×Q8—114no—
497C4×Q8—222no—
498C4×D4—22no—
499C4×D4—114no—
500C4×D4—114no—
501C4×D4—114no—
502C4×D4—114no—
503C4×D4—222no—
504C4×D4—222no—
505C4×D4—222no—
506C4×D4—228no—
507C4×D4—222no—
508C4×D4C22×D1114yes—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—111no—
511C2×C4⋊C4—111no—
512C2×C4⋊C4—111no—
513C2×C4⋊C4—111no—
514C2×C4⋊C4—221no—
515C2×C4⋊C4—221no—
516C2×C4⋊C4—221no—
517C2×C4⋊C4C22×D1111yescharacteristic
518C2×C4⋊C4C22×D1111yescharacteristic
519C2×C4⋊C4C22×D1111yescharacteristic
520C2×C22⋊C4—21no—
521C2×C22⋊C4—221no—
522C2×C22⋊C4—221no—
523C2×C22⋊C4—221no—
524C2×C22⋊C4—221no—
525C2×C22⋊C4—221no—
526C2×C22⋊C4—221no—
527C2×C22⋊C4—221no—
528C2×C22⋊C4—221no—
529C2×C42—111no—
530C2×C42—111no—
531C2×C42—221no—
532C2×C42C22×D1111yescharacteristic
533#106—114no—
534#106C22×D1114yes—
535#106C22×D1114yes—
536C4⋊C8—114no—
537C4⋊C8—114no—
538C4⋊C8C22×D1114yes—
539#103—114no—
540#103—114no—
541#103—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#337314yescomplemented
554C2×C11C2×#54811yescharacteristic
555C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
556C2×C11C2×#57711yescharacteristic
557D11—44no—
558D11—82no—
559C24—21no—
560C24—221no—
561C24—221no—
562C2×Q8—24no—
563C2×Q8—44no—
564C2×Q8—114no—
565C2×Q8—112no—
566C2×Q8—224no—
567C2×Q8—224no—
568C2×Q8—224no—
569C2×Q8—221no—
570C2×Q8—222no—
571C2×Q8—222no—
572C2×Q8—444no—
573C2×Q8—444no—
574C2×Q8—4432no—
575C2×D4—21no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—114no—
579C2×D4—112no—
580C2×D4—112no—
581C2×D4—224no—
582C2×D4—224no—
583C2×D4—221no—
584C2×D4—221no—
585C2×D4—222no—
586C2×D4—222no—
587C2×D4—222no—
588C2×D4—444no—
589C2×D4—882no—
590C2×D4C23×D1112yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—24no—
595C22×C4—82no—
596C22×C4—111no—
597C22×C4—111no—
598C22×C4—111no—
599C22×C4—111no—
600C22×C4—224no—
601C22×C4—224no—
602C22×C4—224no—
603C22×C4—221no—
604C22×C4—221no—
605C22×C4—224no—
606C22×C4—444no—
607C22×C4—444no—
608C22×C4—444no—
609C22×C4—882no—
610C22×C4D4×D1111yescharacteristic
611C22×C4D4×D1111yescharacteristic
612C22×C4C23×D1111yescharacteristic
613SD16—228no—
614D8—228no—
615D8—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—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—114no—
629C4⋊C4—114no—
630C4⋊C4—114no—
631C4⋊C4—112no—
632C4⋊C4—224no—
633C4⋊C4—224no—
634C4⋊C4—224no—
635C4⋊C4—221no—
636C4⋊C4C23×D1112yes—
637C4⋊C4C23×D1112yes—
638C4⋊C4C23×D1112yes—
639C22⋊C4—24no—
640C22⋊C4—224no—
641C22⋊C4—224no—
642C22⋊C4—224no—
643C22⋊C4—224no—
644C22⋊C4—224no—
645C22⋊C4—224no—
646C22⋊C4—224no—
647C22⋊C4—224no—
648C42—112no—
649C42—112no—
650C42—112no—
651C42—112no—
652C42—224no—
653C42D4×D1112yes—
654C42C23×D1112yes—
655C11C2×#337311yescharacteristic, complemented, Sylow
656C23—22no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—224no—
661C23—222no—
662C23—222no—
663C23—442no—
664C23—442no—
665C23—442no—
666C23—442no—
667C23—442no—
668C23C2×D4×D1111yescharacteristic
669Q8—48no—
670Q8—228no—
671Q8—222no—
672Q8—222no—
673Q8—448no—
674Q8—448no—
675Q8—442no—
676D4—22no—
677D4—22no—
678D4—42no—
679D4—114no—
680D4—224no—
681D4—222no—
682D4—222no—
683D4—222no—
684D4—448no—
685D4—442no—
686D4—884no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—84no—
696C2×C4—114no—
697C2×C4—112no—
698C2×C4—112no—
699C2×C4—112no—
700C2×C4—112no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—222no—
706C2×C4—448no—
707C2×C4—448no—
708C2×C4—448no—
709C2×C4—442no—
710C2×C4—442no—
711C2×C4—884no—
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—224no—
727C22—448no—
728C22—442no—
729C22—442no—
730C22—442no—
731C22—442no—
732C22—442no—
733C22—884no—
734C22#1062316412yes—
735C22#1062329312yes—
736C22D11×AGL(1,ℤ/8)12yes—
737C22C22×D4×D1111yescharacteristic
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—114no—
744C4—222no—
745C4—222no—
746C4—222no—
747C4—442no—
748C4—442no—
749C4#1062316412yes—
750C4C2×#6704011yescharacteristic
751C4C2×#41×D1111yescharacteristic
752C2—82no—
753C2—444no—
754C2—882no—
755C2#1308141114yesdirect product factor
756C2C2×#1062316411yescharacteristic
757C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
758C2C2×#1062329311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#476C2
socleC23×C11C22×D4
prime radicalC2×#10622399C2
hypercenterC2×#476D11
hypocenterC11C2×#3373
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#10623090C2semidirect
2. C2×#10623258C2semidirect
3. #13081411C2direct (N × H)
4. C2×#10622702C2semidirect
5. C2×#10622378C2semidirect
6. C2×#10622373C2semidirect
7. C2×#10622467C2semidirect
8. C2×#10622483C2semidirect
9. C2×#10622457C2semidirect
10. C2×#10622400C2semidirect
12. C2×#10622441C2semidirect
13. C2×#10622482C2semidirect
14. C2×#10622627C2semidirect
15. C2×#10622465C2semidirect
16. C2×C11×#476C2semidirect
29. #10623258C22semidirect
31. #10623090C22semidirect
45. C11×#476C22semidirect
58. #10622702C22semidirect
59. #10622627C22semidirect
67. #10622483C22semidirect
68. #10622482C22semidirect
69. #10622467C22semidirect
70. #10622465C22semidirect
71. #10622457C22semidirect
72. #10622441C22semidirect
73. #10622400C22semidirect
75. #10622378C22semidirect
76. #10622373C22semidirect
285. C2×#476D11semidirect
391. #476C2×D11semidirect
553. C2×C11#3373semidirect
655. C11C2×#3373semidirect
755. C2#13081411direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230902
C2×#106232582
#130814112
C2×#106227022
C2×#106223782
C2×#106223732
C2×#106224672
C2×#106224832
C2×#106224572
C2×#106224002
C2×#106223992
C2×#106224412
C2×#106224822
C2×#106226272
C2×#106224652
C2×C11×#4762
C2×#337311