Finite Group Databasebeta

← C2×#13081096 #15632347

Subgroups — C2×#13081096 #15632347

Order 2816.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623166C211yesmaximal, characteristic, complemented
2C2×#10623145C211yesmaximal, characteristic
3#13081096C2116yesmaximal, direct product factor
4C2×#10622489C211yesmaximal, characteristic, complemented
5C2×#10622422C211yesmaximal, characteristic, complemented
6C2×#10622390C211yesmaximal, characteristic, complemented
7C2×#10622658C211yesmaximal, characteristic, complemented
8C2×#10622646C211yesmaximal, characteristic, complemented
9C2×#10622412C211yesmaximal, characteristic, complemented
10C2×#10622372C211yesmaximal, characteristic, complemented
11C2×#10622784C211yesmaximal, characteristic, complemented
12C2×#10622777C211yesmaximal, characteristic, complemented
13C2×#10622740C211yesmaximal, characteristic, complemented
14C2×#10622734C211yesmaximal, characteristic, complemented
15C2×D11×#107C211yesmaximal, characteristic, complemented
16C2×C11×#468C211yesmaximal, characteristic, complemented
17C22×C11×SD16C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic
21C2×#66999C2211yescharacteristic
22C2×Q8×Dic11C2211yescharacteristic
23C2×#66991—21no—
24C2×#66991C2211yescharacteristic
25C2×#66988—21no—
26C2×D4×Dic11C2211yescharacteristic
27C2×C4×C22⋊D11C2211yescharacteristic
28C2×#66979C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
30C22×C8×D11C2211yescharacteristic
31#10623166—24no—
32#10623166C2218yescomplemented
33#10623145—24no—
34#10623145C2218yes—
35C2×#66950—21no—
36C2×C4⋊C4×D11C2211yescharacteristic
37C2×C4⋊C4×D11C2211yescharacteristic
38C2×#66943C2211yescharacteristic
39C2×#66942—21no—
40C2×#66941C2211yescharacteristic
41C2×(C22⋊D11)⋊C4—21no—
42C2×(C22⋊D11)⋊C4—21no—
43C2×#66932—21no—
44C2×#66931—21no—
45C11×#468C2218yescomplemented
46C2×C11×#107C2211yescharacteristic
47C2×C11×#103C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×#66899C2211yescharacteristic
50C2×#66899C2211yescharacteristic
51C2×#66896C2211yescharacteristic
52C2×#66896C2211yescharacteristic
53C2×C22⋊(C11⋊C8)C2211yescharacteristic
54#10622784C2218yescomplemented
55#10622777C2218yescomplemented
56#10622740C2218yescomplemented
57#10622734C2218yescomplemented
58C2×(C2×D11)⋊C8C2211yescharacteristic
59C2×#66882C2211yescharacteristic
60C2×#66882C2211yescharacteristic
61C2×#66881C2211yescharacteristic
62C2×#66881C2211yescharacteristic
63C2×#66879C2211yescharacteristic
64C2×Dic11⋊C8C2211yescharacteristic
65#10622658C2218yescomplemented
66#10622646C2218yescomplemented
67C2×#66872C2211yescharacteristic
68C2×#66871C2211yescharacteristic
69C2×#66871C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71D11×#107C2218yescomplemented
72#10622489C2218yescomplemented
73#10622422C2218yescomplemented
74#10622412C2218yescomplemented
75#10622390C2218yescomplemented
76#10622372C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11—21no—
79C22×D4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C22×C22⋊D11—21no—
82C22×C22⋊D11D411yescharacteristic
83C23×Dic11—21no—
84C23×Dic11—21no—
85C22×C4×D11—21no—
86C22×C4×D11—21no—
87C22×C4×D11C2311yescharacteristic
88C22×Dic22—21no—
89C2×C11×SD16—24no—
90C2×C11×SD16C2314yes—
91C2×C11×M16—24no—
92C2×C11×M16C2314yes—
93C22×C8×C11C2311yescharacteristic
94C22×C8×C11C2311yescharacteristic
95C11×C22⋊Q8—22no—
96C11×C22⋊Q8C2314yes—
97C11×#121—22no—
98C11×#121C2314yes—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C22⋊Dic11—21no—
105C2×C22⋊Dic11—21no—
106C2×C22⋊Dic11—21no—
107C2×C22⋊Dic11D411yescharacteristic
108#66999—22no—
109#66999C2314yes—
110Q8×Dic11—22no—
111Q8×Dic11C2314yes—
112#66991—28no—
113#66991—22no—
114#66991C2314yes—
115#66988—28no—
116D4×Dic11—22no—
117D4×Dic11C2314yes—
118C4×C22⋊D11D414yes—
119C4×C22⋊D11C2314yes—
120C2×(C2×D11)⋊C4—21no—
121C2×(C2×D11)⋊C4D411yescharacteristic
122#66979—22no—
123#66979C2314yes—
124C2×C4⋊Dic11—21no—
125C2×C4⋊Dic11—22no—
126C2×C4⋊Dic11—21no—
127C2×C4⋊Dic11—21no—
128C2×C4⋊Dic11C2314yes—
129C2×C4⋊Dic11C2311yescharacteristic
130C2×C4⋊Dic11C2311yescharacteristic
131C2×C4⋊Dic11C2311yescharacteristic
132C2×C4⋊Dic11C2311yescharacteristic
133C2×Dic11⋊C4—21no—
134C2×Dic11⋊C4—21no—
135C2×Dic11⋊C4—21no—
136C2×Dic11⋊C4—21no—
137C2×Dic11⋊C4—21no—
138C2×Dic11⋊C4D411yescharacteristic
139C2×C4×Dic11—21no—
140C2×C4×Dic11—21no—
141C2×C4×Dic11C2311yescharacteristic
142C22×C11⋊C8C2311yescharacteristic
143C22×C11⋊C8C2311yescharacteristic
144C2×C8×D11—24no—
145C2×C8×D11C2314yes—
146#66950—28no—
147C4⋊C4×D11—22no—
148C4⋊C4×D11—22no—
149C4⋊C4×D11C2314yes—
150C4⋊C4×D11C2314yes—
151#66943—22no—
152#66943C2314yes—
153#66942—28no—
154#66941—22no—
155#66941C2314yes—
156(C22⋊D11)⋊C4—28no—
157(C22⋊D11)⋊C4—28no—
158#66932—28no—
159#66931—28no—
160C11×#107C2314yes—
161C11×#103C2314yes—
162C11×#102C2314yes—
163#66899C2314yes—
164#66899C2314yes—
165#66896C2314yes—
166#66896C2314yes—
167C22⋊(C11⋊C8)C2314yes—
168(C2×D11)⋊C8C2314yes—
169#66882C2314yes—
170#66882C2314yes—
171#66881C2314yes—
172#66881C2314yes—
173#66879C2314yes—
174Dic11⋊C8C2314yes—
175#66872C2314yes—
176#66871C2314yes—
177#66871C2314yes—
178#66871C2314yes—
179C2×#3346—111nomaximal, Sylow
180C24×C11—21no—
181C24×C11C2×D411yescharacteristic
182C23×D11C2×D411yescharacteristic
183C2×Q8×C11—21no—
184C2×Q8×C11—22no—
185C2×Q8×C11—22no—
186C2×Q8×C11C2412yes—
187C2×D4×C11—24no—
188C2×D4×C11—21no—
189C2×D4×C11—22no—
190C2×D4×C11—22no—
191C2×D4×C11—82no—
192C2×D4×C11C2412yes—
193C22×C4×C11—22no—
194C22×C4×C11—22no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2×D412yes—
200C22×C4×C11C2412yes—
201C22×C4×C11C2411yescharacteristic
202C2×C22⋊D11—24no—
203C2×C22⋊D11—24no—
204C2×C22⋊D11—44no—
205C2×C22⋊D11C2×D414yes—
206C22×Dic11—24no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—24no—
212C22×Dic11—82no—
213C22×Dic11—82no—
214C22×Dic11C2×D411yescharacteristic
215C22×Dic11C2×D411yescharacteristic
216C22×Dic11C2×D411yescharacteristic
217C2×C4×D11—24no—
218C2×C4×D11—24no—
219C2×C4×D11—22no—
220C2×C4×D11—22no—
221C2×C4×D11—82no—
222C2×C4×D11—82no—
223C2×C4×D11C2×D412yes—
224C2×C4×D11C2412yes—
225C2×Dic22—24no—
226C2×Dic22—82no—
227C11×SD16—28no—
228C11×M16—28no—
229C2×C8×C11—22no—
230C2×C8×C11#4114yes—
231C2×C8×C11C2412yes—
232C2×C8×C11C2412yes—
233C11×C4⋊C4—21no—
234C11×C4⋊C4—24no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4C2412yes—
237C11×C4⋊C4C2412yes—
238C11×C22⋊C4—24no—
239C11×C22⋊C4—24no—
240C22⋊Dic11—24no—
241C22⋊Dic11—24no—
242C22⋊Dic11—24no—
243C22⋊Dic11C2×D414yes—
244(C2×D11)⋊C4—24no—
245(C2×D11)⋊C4C2×D414yes—
246C4⋊Dic11—24no—
247C4⋊Dic11—24no—
248C4⋊Dic11—21no—
249C4⋊Dic11—24no—
250C4⋊Dic11—21no—
251C4⋊Dic11—21no—
252C4⋊Dic11—21no—
253C4⋊Dic11C2412yes—
254C4⋊Dic11C2412yes—
255C4⋊Dic11C2412yes—
256C4⋊Dic11C2412yes—
257Dic11⋊C4—24no—
258Dic11⋊C4—24no—
259Dic11⋊C4—24no—
260Dic11⋊C4—24no—
261Dic11⋊C4—24no—
262Dic11⋊C4C2×D414yes—
263C4×Dic11—24no—
264C4×Dic11—24no—
265C4×Dic11C2×D412yes—
266C4×Dic11C2412yes—
267C2×C11⋊C8—22no—
268C2×C11⋊C8—22no—
269C2×C11⋊C8C2412yes—
270C2×C11⋊C8C2412yes—
271C8×D11—28no—
272C2×#554—111no—
273C2×#553—111no—
274#3346—1116no—
275C2×#501—111no—
276C2×#484—111no—
277C2×#481—111no—
278C2×#485—111no—
279C2×#480—111no—
280C2×#479—111no—
281C2×#474—111no—
282C2×#468D1111yescharacteristic, complemented
283C2×#465—111no—
284C2×#440—111no—
285C2×#435—111no—
286C2×#428—111no—
287C22×#107—111no—
288C23×C11—22no—
289C23×C11—22no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—42no—
293C23×C11—42no—
294C23×C11—42no—
295C23×C11C22×D412yes—
296C23×C11C22×D411yescharacteristic
297C22×D11—22no—
298C22×D11—22no—
299C22×D11#13714yes—
300C22×D11C22×D412yes—
301Q8×C11—22no—
302Q8×C11—22no—
303Q8×C11—42no—
304D4×C11—22no—
305D4×C11—22no—
306D4×C11—42no—
307D4×C11—84no—
308C2×C4×C11—22no—
309C2×C4×C11—24no—
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×C11C22×D412yes—
319C2×C4×C11C22×D411yescharacteristic
320C2×C4×C11C2×#4112yes—
321C2×C4×C112−1+412yes—
322C2×C4×C11C2511yescharacteristic
323C22⋊D11—28no—
324C22⋊D11—48no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11—84no—
337C2×Dic11—84no—
338C2×Dic11C22×D412yes—
339C2×Dic11C22×D412yes—
340C2×Dic11C22×D412yes—
341C4×D11—24no—
342C4×D11—22no—
343C4×D11—22no—
344C4×D11—84no—
345C4×D11—84no—
346Dic22—84no—
347C8×C11—22no—
348C8×C11C2×#4114yes—
349C11⋊C8—22no—
350C11⋊C8—22no—
351C22×SD16C2×D1111yescharacteristic
352C22×M16C2×D1111yescharacteristic
353C23×C8—111no—
354#554—118no—
355#554—224no—
356#553—118no—
357#553—224no—
358C2×C4⋊Q8—111no—
359C2×#126—221no—
360C2×#125—111no—
361C2×#125—221no—
362C2×#123—221no—
363C2×C22⋊Q8—111no—
364C2×C22⋊Q8—221no—
365C2×C22⋊Q8—221no—
366C2×C22⋊Q8C2×D1111yescharacteristic
367C2×#121—111no—
368C2×#121—221no—
369C2×#121C2×D1111yescharacteristic
370C2×C4×Q8—111no—
371C2×C4×D4—111no—
372C2×C4×D4—111no—
373C2×C4×D4—221no—
374C2×C4×D4—221no—
375C2×#117—111no—
376C22×C4⋊C4—111no—
377C22×C4⋊C4—111no—
378C22×C4⋊C4—111no—
379#501—118no—
380#485—118no—
381#484—118no—
382#481—118no—
383#480—118no—
384#479—118no—
385#474—118no—
386#468C2×D1118yescomplemented
387#465—118no—
388#440—118no—
389#435—118no—
390#428—118no—
391C2×#107—111no—
392C2×#107—111no—
393C2×#107—111no—
394C2×#107—111no—
395C2×#107—111no—
396C2×#107—118no—
397C2×#107C2×D1111yescharacteristic
398C2×#106—111no—
399C2×#106—111no—
400C2×#106—111no—
401C2×C4⋊C8—111no—
402C2×#103—111no—
403C2×#103—111no—
404C2×#103C2×D1111yescharacteristic
405C2×#102—111no—
406C2×#102—111no—
407C2×#102C2×D1111yescharacteristic
408C2×C22⋊C8—111no—
409C2×C22⋊C8—111no—
410C2×#97—111no—
411C22×C11—22no—
412C22×C11—22no—
413C22×C11—22no—
414C22×C11—44no—
415C22×C11—42no—
416C22×C11—42no—
417C22×C11—42no—
418C22×C11—84no—
419C22×C11#54712yes—
420C22×C11C2×#13712yes—
421C22×C11#57612yes—
422C22×C11C23×D411yescharacteristic
423C2×D11—28no—
424C2×D11—22no—
425C2×D11—22no—
426C2×D11C2×#13714yes—
427C4×C11—22no—
428C4×C11—42no—
429C4×C11—42no—
430C4×C11—42no—
431C4×C11#54712yes—
432C4×C11C22×#4111yescharacteristic
433C4×C11C2×2−1+411yescharacteristic
434Dic11—22no—
435Dic11—22no—
436Dic11—22no—
437Dic11—42no—
438Dic11—42no—
439Dic11—42no—
440Dic11—42no—
441C22×Q8—221no—
442C22×Q8C22×D1111yescharacteristic
443C22×D4—21no—
444C22×D4—111no—
445C22×D4—221no—
446C22×D4C22×D1111yescharacteristic
447C23×C4—111no—
448C23×C4—221no—
449C23×C4—221no—
450C23×C4—221no—
451C23×C4—221no—
452C23×C4C22×D1111yescharacteristic
453C2×SD16—24no—
454C2×SD16C22×D1114yes—
455C2×M16—24no—
456C2×M16C22×D1114yes—
457C22×C8—111no—
458C22×C8—111no—
459C22×C8—114no—
460C22×C8—224no—
461C22×C8C22×D1111yescharacteristic
462C22×C8C22×D1111yescharacteristic
463C4⋊Q8—114no—
464C4⋊Q8—222no—
465#126—228no—
466#125—114no—
467#125—222no—
468#125—228no—
469#123—228no—
470C22⋊Q8—22no—
471C22⋊Q8—114no—
472C22⋊Q8—228no—
473C22⋊Q8—228no—
474C22⋊Q8—222no—
475C22⋊Q8C22×D1114yes—
476#121—22no—
477#121—114no—
478#121—222no—
479#121—228no—
480#121C22×D1114yes—
481C4×Q8—114no—
482C4×Q8—222no—
483C4×D4—114no—
484C4×D4—114no—
485C4×D4—114no—
486C4×D4—222no—
487C4×D4—228no—
488C4×D4—228no—
489#117—114no—
490#117—222no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—111no—
493C2×C4⋊C4—111no—
494C2×C4⋊C4—111no—
495C2×C4⋊C4—111no—
496C2×C4⋊C4—114no—
497C2×C4⋊C4—111no—
498C2×C4⋊C4—114no—
499C2×C4⋊C4—114no—
500C2×C4⋊C4—222no—
501C2×C4⋊C4—222no—
502C2×C4⋊C4—221no—
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—221no—
510C2×C4⋊C4—222no—
511C2×C4⋊C4C22×D1111yescharacteristic
512C2×C4⋊C4C22×D1111yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—111no—
516C2×C22⋊C4—111no—
517C2×C22⋊C4—221no—
518C2×C22⋊C4—221no—
519C2×C22⋊C4—221no—
520C2×C22⋊C4—221no—
521C2×C42—111no—
522C2×C42—221no—
523C2×C42—221no—
524#107—114no—
525#107—114no—
526#107—114no—
527#107—114no—
528#107—114no—
529#107C22×D1114yes—
530#106—114no—
531#106—114no—
532#106—114no—
533C4⋊C8—114no—
534#103—114no—
535#103—114no—
536#103C22×D1114yes—
537#102—114no—
538#102—114no—
539#102C22×D1114yes—
540C22⋊C8—114no—
541C22⋊C8—114no—
542#97—114no—
543C2×C11—42no—
544C2×C11—82no—
545C2×C11#334614yescomplemented
546C2×C11C2×#54711yescharacteristic
547C2×C11C22×#13711yescharacteristic
548C2×C11C2×#57611yescharacteristic
549D11—24no—
550C24—21no—
551C24—111no—
552C24D4×D1111yescharacteristic
553C2×Q8—21no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—224no—
557C2×Q8—882no—
558C2×Q8C23×D1112yes—
559C2×D4—24no—
560C2×D4—21no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—82no—
564C2×D4—114no—
565C2×D4—224no—
566C2×D4—224no—
567C2×D4—444no—
568C2×D4C23×D1112yes—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—111no—
575C22×C4—111no—
576C22×C4—111no—
577C22×C4—112no—
578C22×C4—112no—
579C22×C4—224no—
580C22×C4—224no—
581C22×C4—224no—
582C22×C4—222no—
583C22×C4—222no—
584C22×C4—221no—
585C22×C4—221no—
586C22×C4—221no—
587C22×C4—221no—
588C22×C4—224no—
589C22×C4—882no—
590C22×C4—882no—
591C22×C4—882no—
592C22×C4—882no—
593C22×C4D4×D1112yes—
594C22×C4D4×D1111yescharacteristic
595C22×C4C23×D1112yes—
596C22×C4C23×D1111yescharacteristic
597SD16—28no—
598M16—28no—
599C2×C8—22no—
600C2×C8—112no—
601C2×C8—112no—
602C2×C8—222no—
603C2×C8—222no—
604C2×C8—228no—
605C2×C8#434114yes—
606C2×C8C23×D1112yes—
607C2×C8C23×D1112yes—
608C4⋊C4—24no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—114no—
612C4⋊C4—112no—
613C4⋊C4—112no—
614C4⋊C4—112no—
615C4⋊C4—112no—
616C4⋊C4—224no—
617C4⋊C4—224no—
618C4⋊C4—224no—
619C4⋊C4—224no—
620C4⋊C4—224no—
621C4⋊C4—224no—
622C4⋊C4—224no—
623C4⋊C4—221no—
624C4⋊C4—221no—
625C4⋊C4—224no—
626C4⋊C4—221no—
627C4⋊C4—221no—
628C4⋊C4C23×D1112yes—
629C4⋊C4C23×D1112yes—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—114no—
633C22⋊C4—114no—
634C22⋊C4—224no—
635C22⋊C4—224no—
636C22⋊C4—224no—
637C22⋊C4—224no—
638C42—112no—
639C42—112no—
640C42—224no—
641C42—224no—
642C11C2×#334611yescharacteristic, complemented, Sylow
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—114no—
651C23—112no—
652C23—222no—
653C23—222no—
654C23C2×D4×D1112yes—
655C23C2×D4×D1111yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—884no—
660D4—22no—
661D4—22no—
662D4—42no—
663D4—84no—
664D4—228no—
665D4—448no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—112no—
677C2×C4—112no—
678C2×C4—112no—
679C2×C4—222no—
680C2×C4—222no—
681C2×C4—222no—
682C2×C4—224no—
683C2×C4—222no—
684C2×C4—222no—
685C2×C4—222no—
686C2×C4—222no—
687C2×C4—222no—
688C2×C4—222no—
689C2×C4—442no—
690C2×C4—442no—
691C2×C4—442no—
692C2×C4—442no—
693C2×C4—884no—
694C2×C4—884no—
695C2×C4—884no—
696C2×C4—884no—
697C2×C4C2×D4×D1112yes—
698C2×C4C2×D4×D1111yescharacteristic
699C2×C4C2×#434112yes—
700C2×C4#6704312yes—
701C2×C4C24×D1111yescharacteristic
702C8—22no—
703C8—222no—
704C8—222no—
705C8C2×#434114yes—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—44no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—84no—
714C22—114no—
715C22—228no—
716C22—222no—
717C22—222no—
718C22#1062314212yes—
719C22#1062330512yes—
720C22D11×#13712yes—
721C22C22×D4×D1111yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—222no—
727C4—222no—
728C4—222no—
729C4—442no—
730C4—442no—
731C4—442no—
732C4—442no—
733C4#1062314212yes—
734C4C22×#434111yescharacteristic
735C4C2×#6704311yescharacteristic
736C2—42no—
737C2—82no—
738C2—224no—
739C2#1308109614yesdirect product factor
740C2C2×#1062314211yescharacteristic
741C2C2×D11×#13711yescharacteristic
742C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#468C2
socleC23×C11C22×D4
prime radicalC2×#10623145C2
hypercenterC2×#468D11
hypocenterC11C2×#3346
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#10623166C2semidirect
3. #13081096C2direct (N × H)
4. C2×#10622489C2semidirect
5. C2×#10622422C2semidirect
6. C2×#10622390C2semidirect
7. C2×#10622658C2semidirect
8. C2×#10622646C2semidirect
9. C2×#10622412C2semidirect
10. C2×#10622372C2semidirect
11. C2×#10622784C2semidirect
12. C2×#10622777C2semidirect
13. C2×#10622740C2semidirect
14. C2×#10622734C2semidirect
15. C2×D11×#107C2semidirect
16. C2×C11×#468C2semidirect
32. #10623166C22semidirect
45. C11×#468C22semidirect
54. #10622784C22semidirect
55. #10622777C22semidirect
56. #10622740C22semidirect
57. #10622734C22semidirect
65. #10622658C22semidirect
66. #10622646C22semidirect
71. D11×#107C22semidirect
72. #10622489C22semidirect
73. #10622422C22semidirect
74. #10622412C22semidirect
75. #10622390C22semidirect
76. #10622372C22semidirect
282. C2×#468D11semidirect
386. #468C2×D11semidirect
545. C2×C11#3346semidirect
642. C11C2×#3346semidirect
739. C2#13081096direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231662
C2×#106231452
#130810962
C2×#106224892
C2×#106224222
C2×#106223902
C2×#106226582
C2×#106226462
C2×#106224122
C2×#106223722
C2×#106227842
C2×#106227772
C2×#106227402
C2×#106227342
C2×D11×#1072
C2×C11×#4682
C2×#334611