Finite Group Databasebeta

← C2×#13081198 #15632475

Subgroups — C2×#13081198 #15632475

Order 2816.

2082 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623064C211yesmaximal, characteristic, complemented
2C2×#10623142C211yesmaximal, characteristic
3#13081198C2116yesmaximal, direct product factor
4C2×#10622487C211yesmaximal, characteristic, complemented
5C2×#10622497C211yesmaximal, characteristic, complemented
6C2×#10622335C211yesmaximal, characteristic, complemented
7C2×#10622397C211yesmaximal, characteristic, complemented
8C2×#10622467C211yesmaximal, characteristic, complemented
9C2×#10622372C211yesmaximal, characteristic, complemented
10C2×#10622393C211yesmaximal, characteristic, complemented
11C2×#10622655C211yesmaximal, characteristic, complemented
12C2×#10622371C211yesmaximal, characteristic, complemented
13C2×#10622342C211yesmaximal, characteristic, complemented
14C2×#10622608C211yesmaximal, characteristic, complemented
15C2×#10622474C211yesmaximal, characteristic, complemented
16C2×C11×#482C211yesmaximal, characteristic, complemented
17C22×#4341—21no—
18C2×C11×#121C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C2×#66991C2211yescharacteristic
21C2×#66988—21no—
22C2×D4×Dic11C2211yescharacteristic
23C22×#4324C2211yescharacteristic
24C2×C4×C22⋊D11C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C2×#66977C2211yescharacteristic
27C22×#4318C2211yescharacteristic
28C22×#4313C2211yescharacteristic
29#10623142—24no—
30#10623142C2218yes—
31#10623064—24no—
32#10623064C2218yescomplemented
33C2×#66950C2211yescharacteristic
34C2×#66945C2211yescharacteristic
35C2×C4⋊C4×D11C2211yescharacteristic
36C2×#66941C2211yescharacteristic
37C2×#66941C2211yescharacteristic
38C2×#66940C2211yescharacteristic
39C2×#66938—21no—
40C2×#66936—21no—
41C2×#66932—21no—
42C2×#66931—21no—
43C2×#66929—21no—
44C2×C4×Dic22—21no—
45C11×#482C2218yescomplemented
46C2×C11×#107C2211yescharacteristic
47C2×C11×#106C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×C11×C22⋊C8C2211yescharacteristic
51C2×#66896C2211yescharacteristic
52C2×(C2×D11)⋊C8C2211yescharacteristic
53C2×#66882C2211yescharacteristic
54C2×#66882C2211yescharacteristic
55C2×#66880C2211yescharacteristic
56C2×#66880C2211yescharacteristic
57C2×Dic11⋊C8C2211yescharacteristic
58C2×C8×Dic11C2211yescharacteristic
59#10622655C2218yescomplemented
60#10622608C2218yescomplemented
61C2×#66874C2211yescharacteristic
62C2×#66872C2211yescharacteristic
63C2×#66872C2211yescharacteristic
64C2×#66871C2211yescharacteristic
65C2×#66871C2211yescharacteristic
66C2×#66871C2211yescharacteristic
67#10622497C2218yescomplemented
68#10622487C2218yescomplemented
69#10622474C2218yescomplemented
70#10622467C2218yescomplemented
71#10622397C2218yescomplemented
72#10622393C2218yescomplemented
73#10622372C2218yescomplemented
74#10622371C2218yescomplemented
75#10622342C2218yescomplemented
76#10622335C2218yescomplemented
77C22×D4×C11—21no—
78C22×D4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C22×C22⋊D11—21no—
81C22×C22⋊D11D411yescharacteristic
82C23×Dic11—21no—
83C23×Dic11—21no—
84C2×#4341—28no—
85C2×#4341—48no—
86C22×C4×D11—21no—
87C22×C4×D11C2311yescharacteristic
88C22×Dic22—21no—
89C22×Dic22—21no—
90C22×Dic22C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C22×C8×C11C2311yescharacteristic
93C11×#121—22no—
94C11×#121C2314yes—
95C11×#117—22no—
96C11×#117C2314yes—
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C42×C11—21no—
103C2×C22⋊Dic11—21no—
104C2×C22⋊Dic11—21no—
105C2×C22⋊Dic11—21no—
106C2×C22⋊Dic11D411yescharacteristic
107#66991—22no—
108#66991C2314yes—
109#66988—28no—
110D4×Dic11—22no—
111D4×Dic11C2314yes—
112C2×#4324—24no—
113C2×#4324C2314yes—
114C4×C22⋊D11D414yes—
115C4×C22⋊D11C2314yes—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4D411yescharacteristic
119C2×C4⋊Dic11—21no—
120C2×C4⋊Dic11—22no—
121C2×C4⋊Dic11—21no—
122C2×C4⋊Dic11C2311yescharacteristic
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2314yes—
126#66977—22no—
127#66977C2314yes—
128C2×Dic11⋊C4—21no—
129C2×Dic11⋊C4—21no—
130C2×Dic11⋊C4—21no—
131C2×Dic11⋊C4—21no—
132C2×Dic11⋊C4—21no—
133C2×Dic11⋊C4D411yescharacteristic
134C2×C4×Dic11—21no—
135C2×C4×Dic11—21no—
136C2×C4×Dic11C2311yescharacteristic
137C2×#4318—24no—
138C2×#4318C2314yes—
139C22×C11⋊C8C2311yescharacteristic
140C22×C11⋊C8C2311yescharacteristic
141C2×#4313—24no—
142C2×#4313C2314yes—
143#66950—22no—
144#66950C2314yes—
145#66945—22no—
146#66945C2314yes—
147C4⋊C4×D11—22no—
148C4⋊C4×D11C2314yes—
149#66941—22no—
150#66941—22no—
151#66941C2314yes—
152#66941C2314yes—
153#66940—22no—
154#66940C2314yes—
155#66938—28no—
156#66936—28no—
157#66932—28no—
158#66931—28no—
159#66929—28no—
160C4×Dic22—28no—
161C11×#107C2314yes—
162C11×#106C2314yes—
163C11×#102C2314yes—
164C11×#102C2314yes—
165C11×C22⋊C8C2314yes—
166#66896C2314yes—
167(C2×D11)⋊C8C2314yes—
168#66882C2314yes—
169#66882C2314yes—
170#66880C2314yes—
171#66880C2314yes—
172Dic11⋊C8C2314yes—
173C8×Dic11C2314yes—
174#66874C2314yes—
175#66872C2314yes—
176#66872C2314yes—
177#66871C2314yes—
178#66871C2314yes—
179#66871C2314yes—
180C2×#3353—111nomaximal, Sylow
181C24×C11—21no—
182C24×C11C2×D411yescharacteristic
183C23×D11C2×D411yescharacteristic
184C2×D4×C11—24no—
185C2×D4×C11—21no—
186C2×D4×C11—22no—
187C2×D4×C11—22no—
188C2×D4×C11—44no—
189C2×D4×C11C2412yes—
190C22×C4×C11—22no—
191C22×C4×C11—22no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D412yes—
197C22×C4×C11C2412yes—
198C22×C4×C11C2411yescharacteristic
199C2×C22⋊D11—24no—
200C2×C22⋊D11—24no—
201C2×C22⋊D11—44no—
202C2×C22⋊D11C2×D414yes—
203C22×Dic11—24no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—24no—
209C22×Dic11—44no—
210C22×Dic11—44no—
211C22×Dic11C2×D411yescharacteristic
212C22×Dic11C2×D411yescharacteristic
213C22×Dic11C2×D411yescharacteristic
214#4341—432no—
215C2×C4×D11—24no—
216C2×C4×D11—22no—
217C2×C4×D11—22no—
218C2×C4×D11—44no—
219C2×C4×D11C2×D412yes—
220C2×C4×D11C2412yes—
221C2×Dic22—24no—
222C2×Dic22—24no—
223C2×Dic22—21no—
224C2×Dic22—22no—
225C2×Dic22—22no—
226C2×Dic22—44no—
227C2×Dic22—44no—
228C2×Dic22C2412yes—
229C2×C8×C11—22no—
230C2×C8×C11—22no—
231C2×C8×C11C2412yes—
232C2×C8×C11C2412yes—
233C11×C4⋊C4—21no—
234C11×C4⋊C4—21no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4C2412yes—
237C11×C4⋊C4C2412yes—
238C11×C4⋊C4C2412yes—
239C11×C22⋊C4—24no—
240C11×C22⋊C4—24no—
241C42×C11—24no—
242C22⋊Dic11—24no—
243C22⋊Dic11—24no—
244C22⋊Dic11—24no—
245C22⋊Dic11C2×D414yes—
246#4324—28no—
247(C2×D11)⋊C4—24no—
248(C2×D11)⋊C4—24no—
249(C2×D11)⋊C4C2×D414yes—
250C4⋊Dic11—24no—
251C4⋊Dic11—24no—
252C4⋊Dic11—21no—
253C4⋊Dic11—21no—
254C4⋊Dic11—21no—
255C4⋊Dic11C2412yes—
256C4⋊Dic11C2412yes—
257C4⋊Dic11C2412yes—
258Dic11⋊C4—24no—
259Dic11⋊C4—24no—
260Dic11⋊C4—24no—
261Dic11⋊C4—24no—
262Dic11⋊C4—24no—
263Dic11⋊C4C2×D414yes—
264C4×Dic11—24no—
265C4×Dic11—24no—
266C4×Dic11C2×D412yes—
267C4×Dic11C2412yes—
268#4318—28no—
269C2×C11⋊C8—22no—
270C2×C11⋊C8#4114yescomplemented
271C2×C11⋊C8C2412yes—
272C2×C11⋊C8C2412yes—
273#4313—28no—
274C2×#556—111no—
275C2×#547—111no—
276#3353—1116no—
277C2×#500—111no—
278C2×#484—111no—
279C2×#484—111no—
280C2×#482—111no—
281C2×#482D1111yescharacteristic, complemented
282C2×#475—111no—
283C2×#474—111no—
284C2×#468—111no—
285C2×#468—111no—
286C2×C4×SD16—111no—
287C2×#436—111no—
288C2×#428—111no—
289C2×#428—111no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—42no—
295C23×C11—42no—
296C23×C11—42no—
297C23×C11C22×D412yes—
298C23×C11C22×D411yescharacteristic
299C22×D11—22no—
300C22×D11—22no—
301C22×D11—22no—
302C22×D11C22×D412yes—
303D4×C11—22no—
304D4×C11—22no—
305D4×C11—48no—
306D4×C11—42no—
307C2×C4×C11—22no—
308C2×C4×C11—24no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—42no—
315C2×C4×C11—42no—
316C2×C4×C11—42no—
317C2×C4×C11C22×D412yes—
318C2×C4×C11C22×D411yescharacteristic
319C2×C4×C11C2×#4112yes—
320C2×C4×C112−1+412yes—
321C2×C4×C11C2511yescharacteristic
322C22⋊D11—28no—
323C22⋊D11—48no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—48no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11—42no—
335C2×Dic11—48no—
336C2×Dic11AGL(1,ℤ/8)14yes—
337C2×Dic11C22×D412yes—
338C2×Dic11C22×D412yes—
339C2×Dic11C22×D412yes—
340C4×D11—24no—
341C4×D11—22no—
342C4×D11—22no—
343C4×D11—48no—
344Dic22—22no—
345Dic22—22no—
346Dic22—42no—
347Dic22—48no—
348Dic22—48no—
349C8×C11—22no—
350C8×C11—22no—
351C11⋊C8—22no—
352C11⋊C8C2×#4114yescomplemented
353C22×#41—221no—
354C22×SD16—111no—
355C22×M16—111no—
356C22×M16—111no—
357#556—118no—
358#556—224no—
359#547—118no—
360#547—224no—
361C2×C4⋊Q8—111no—
362C2×C4⋊Q8—111no—
363C2×#126—221no—
364C2×#126—221no—
365C2×#124—221no—
366C2×#123—221no—
367C2×#123—221no—
368C2×C22⋊Q8—111no—
369C2×C22⋊Q8—111no—
370C2×C22⋊Q8—221no—
371C2×#121—111no—
372C2×#121C2×D1111yescharacteristic
373C2×C4×Q8—111no—
374C2×C4×Q8—221no—
375C2×C4×D4—111no—
376C2×C4×D4—111no—
377C2×#117—111no—
378C2×#117C2×D1111yescharacteristic
379C22×C4⋊C4—111no—
380C22×C4⋊C4—111no—
381#500—118no—
382#484—118no—
383#484—118no—
384#482—118no—
385#482C2×D1118yescomplemented
386#475—118no—
387#474—118no—
388#468—118no—
389#468—118no—
390C4×SD16—118no—
391#436—118no—
392#428—118no—
393#428—118no—
394C2×#107—111no—
395C2×#107—111no—
396C2×#107—111no—
397C2×#107—111no—
398C2×#107—111no—
399C2×#107C2×D1111yescharacteristic
400C2×#106—111no—
401C2×#106—111no—
402C2×#106C2×D1111yescharacteristic
403C2×C4⋊C8—111no—
404C2×#103—111no—
405C2×#103—111no—
406C2×#103—111no—
407C2×#102—111no—
408C2×#102C2×D1111yescharacteristic
409C2×#102C2×D1111yescharacteristic
410C2×C22⋊C8—111no—
411C2×C22⋊C8C2×D1111yescharacteristic
412C2×C4×C8—111no—
413C22×C11—22no—
414C22×C11—22no—
415C22×C11—22no—
416C22×C11—44no—
417C22×C11—42no—
418C22×C11—42no—
419C22×C11—42no—
420C22×C11—84no—
421C22×C11#54712yes—
422C22×C11C2×AGL(1,ℤ/8)12yes—
423C22×C11#57812yes—
424C22×C11C23×D411yescharacteristic
425C2×D11—22no—
426C2×D11—22no—
427C2×D11—22no—
428C2×D11—44no—
429C4×C11—22no—
430C4×C11—42no—
431C4×C11—42no—
432C4×C11—42no—
433C4×C11#54712yes—
434C4×C11C22×#4111yescharacteristic
435C4×C11C2×2−1+411yescharacteristic
436Dic11—22no—
437Dic11—22no—
438Dic11—42no—
439Dic11—42no—
440Dic11—42no—
441Dic11—42no—
442Dic11C2×AGL(1,ℤ/8)14yes—
443C2×#41—228no—
444C2×#41—448no—
445C22×Q8—111no—
446C22×Q8—221no—
447C22×Q8—221no—
448C22×D4—21no—
449C22×D4—111no—
450C22×D4—221no—
451C22×D4C22×D1111yescharacteristic
452C23×C4—111no—
453C23×C4—221no—
454C23×C4—221no—
455C23×C4—221no—
456C23×C4C22×D1111yescharacteristic
457C2×SD16—114no—
458C2×SD16—224no—
459C2×M16—114no—
460C2×M16—114no—
461C2×M16—224no—
462C2×M16—224no—
463C22×C8—111no—
464C22×C8—111no—
465C22×C8C22×D1111yescharacteristic
466C22×C8C22×D1111yescharacteristic
467C4⋊Q8—114no—
468C4⋊Q8—114no—
469C4⋊Q8—222no—
470C4⋊Q8—222no—
471#126—228no—
472#126—228no—
473#124—228no—
474#123—228no—
475#123—228no—
476C22⋊Q8—114no—
477C22⋊Q8—114no—
478C22⋊Q8—228no—
479C22⋊Q8—222no—
480C22⋊Q8—222no—
481#121—22no—
482#121—114no—
483#121—222no—
484#121C22×D1114yes—
485C4×Q8—114no—
486C4×Q8—228no—
487C4×Q8—222no—
488C4×D4—114no—
489C4×D4—114no—
490C4×D4—114no—
491C4×D4—222no—
492#117—22no—
493#117—114no—
494#117—222no—
495#117C22×D1114yes—
496C2×C4⋊C4—111no—
497C2×C4⋊C4—111no—
498C2×C4⋊C4—111no—
499C2×C4⋊C4—114no—
500C2×C4⋊C4—111no—
501C2×C4⋊C4—114no—
502C2×C4⋊C4—222no—
503C2×C4⋊C4—221no—
504C2×C4⋊C4—221no—
505C2×C4⋊C4—221no—
506C2×C4⋊C4—221no—
507C2×C4⋊C4—221no—
508C2×C4⋊C4—221no—
509C2×C4⋊C4—222no—
510C2×C4⋊C4—221no—
511C2×C4⋊C4C22×D1111yescharacteristic
512C2×C4⋊C4C22×D1111yescharacteristic
513C2×C4⋊C4C22×D1111yescharacteristic
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—111no—
517C2×C22⋊C4—111no—
518C2×C22⋊C4—221no—
519C2×C22⋊C4—221no—
520C2×C22⋊C4—221no—
521C2×C22⋊C4—221no—
522C2×C22⋊C4—221no—
523C2×C42—21no—
524C2×C42—111no—
525C2×C42—221no—
526C2×C42—221no—
527#107—114no—
528#107—114no—
529#107—114no—
530#107—114no—
531#107—114no—
532#107C22×D1114yes—
533#106—114no—
534#106—114no—
535#106C22×D1114yes—
536C4⋊C8—114no—
537#103—114no—
538#103—114no—
539#103—114no—
540#102—114no—
541#102C22×D1114yes—
542#102C22×D1114yes—
543C22⋊C8—114no—
544C22⋊C8C22×D1114yes—
545C4×C8—114no—
546C2×C11—42no—
547C2×C11—82no—
548C2×C11#335314yescomplemented
549C2×C11C2×#54711yescharacteristic
550C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
551C2×C11C2×#57811yescharacteristic
552D11—42no—
553C24—21no—
554C24—111no—
555C24D4×D1111yescharacteristic
556#41—4432no—
557C2×Q8—112no—
558C2×Q8—224no—
559C2×Q8—224no—
560C2×Q8—221no—
561C2×Q8—222no—
562C2×Q8—222no—
563C2×Q8—444no—
564C2×Q8—444no—
565C2×D4—24no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—44no—
570C2×D4—114no—
571C2×D4—224no—
572C2×D4—224no—
573C2×D4—444no—
574C2×D4C23×D1112yes—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—111no—
581C22×C4—111no—
582C22×C4—111no—
583C22×C4—112no—
584C22×C4—112no—
585C22×C4—224no—
586C22×C4—224no—
587C22×C4—222no—
588C22×C4—222no—
589C22×C4—224no—
590C22×C4—221no—
591C22×C4—221no—
592C22×C4—221no—
593C22×C4—221no—
594C22×C4—444no—
595C22×C4—444no—
596C22×C4—444no—
597C22×C4D4×D1112yes—
598C22×C4D4×D1111yescharacteristic
599C22×C4C23×D1112yes—
600C22×C4C23×D1111yescharacteristic
601SD16—228no—
602M16—228no—
603M16—228no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—114no—
607C2×C8—112no—
608C2×C8—112no—
609C2×C8—222no—
610C2×C8C23×D1112yes—
611C2×C8C23×D1112yes—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—114no—
616C4⋊C4—112no—
617C4⋊C4—112no—
618C4⋊C4—112no—
619C4⋊C4—224no—
620C4⋊C4—224no—
621C4⋊C4—224no—
622C4⋊C4—224no—
623C4⋊C4—224no—
624C4⋊C4—221no—
625C4⋊C4—221no—
626C4⋊C4—224no—
627C4⋊C4—221no—
628C4⋊C4—224no—
629C4⋊C4C23×D1112yes—
630C4⋊C4C23×D1112yes—
631C4⋊C4C23×D1112yes—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—114no—
635C22⋊C4—114no—
636C22⋊C4—224no—
637C22⋊C4—224no—
638C22⋊C4—224no—
639C22⋊C4—224no—
640C22⋊C4—224no—
641C42—24no—
642C42—112no—
643C42—112no—
644C42—224no—
645C42—224no—
646C11C2×#335311yescharacteristic, complemented, Sylow
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—112no—
655C23—222no—
656C23—222no—
657C23—222no—
658C23C2×D4×D1112yes—
659C23C2×D4×D1111yescharacteristic
660Q8—222no—
661Q8—222no—
662Q8—448no—
663Q8—448no—
664Q8—442no—
665D4—22no—
666D4—22no—
667D4—48no—
668D4—42no—
669D4—228no—
670D4—448no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—114no—
682C2×C4—112no—
683C2×C4—112no—
684C2×C4—112no—
685C2×C4—222no—
686C2×C4—222no—
687C2×C4—224no—
688C2×C4—222no—
689C2×C4—222no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—222no—
693C2×C4—222no—
694C2×C4—448no—
695C2×C4—448no—
696C2×C4—448no—
697C2×C4—442no—
698C2×C4—442no—
699C2×C4—442no—
700C2×C4—442no—
701C2×C4C2×D4×D1112yes—
702C2×C4C2×D4×D1111yescharacteristic
703C2×C4#41×D1112yes—
704C2×C4#6704312yes—
705C2×C4C24×D1111yescharacteristic
706C8—22no—
707C8—22no—
708C8—114no—
709C8—222no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—84no—
718C22—222no—
719C22—222no—
720C22—222no—
721C22—444no—
722C22#1062318612yes—
723C22#1062330212yes—
724C22D11×AGL(1,ℤ/8)12yes—
725C22C22×D4×D1111yescharacteristic
726C4—22no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—114no—
731C4—222no—
732C4—222no—
733C4—442no—
734C4—442no—
735C4—442no—
736C4—442no—
737C4#1062318612yes—
738C4C2×#41×D1111yescharacteristic
739C4C2×#6704311yescharacteristic
740C2—42no—
741C2—82no—
742C2—442no—
743C2#1308119814yesdirect product factor
744C2C2×#1062318611yescharacteristic
745C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
746C2C2×#1062330211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#482C2
socleC23×C11C22×D4
prime radicalC2×#10623142C2
hypercenterC2×#482D11
hypocenterC11C2×#3353
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#10623064C2semidirect
3. #13081198C2direct (N × H)
4. C2×#10622487C2semidirect
5. C2×#10622497C2semidirect
6. C2×#10622335C2semidirect
7. C2×#10622397C2semidirect
8. C2×#10622467C2semidirect
9. C2×#10622372C2semidirect
10. C2×#10622393C2semidirect
11. C2×#10622655C2semidirect
12. C2×#10622371C2semidirect
13. C2×#10622342C2semidirect
14. C2×#10622608C2semidirect
15. C2×#10622474C2semidirect
16. C2×C11×#482C2semidirect
32. #10623064C22semidirect
45. C11×#482C22semidirect
59. #10622655C22semidirect
60. #10622608C22semidirect
67. #10622497C22semidirect
68. #10622487C22semidirect
69. #10622474C22semidirect
70. #10622467C22semidirect
71. #10622397C22semidirect
72. #10622393C22semidirect
73. #10622372C22semidirect
74. #10622371C22semidirect
75. #10622342C22semidirect
76. #10622335C22semidirect
270. C2×C11⋊C8#41semidirect
281. C2×#482D11semidirect
352. C11⋊C8C2×#41semidirect
385. #482C2×D11semidirect
548. C2×C11#3353semidirect
646. C11C2×#3353semidirect
743. C2#13081198direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230642
C2×#106231422
#130811982
C2×#106224872
C2×#106224972
C2×#106223352
C2×#106223972
C2×#106224672
C2×#106223722
C2×#106223932
C2×#106226552
C2×#106223712
C2×#106223422
C2×#106226082
C2×#106224742
C2×C11×#4822
C2×#335311