Finite Group Databasebeta

← C2×#13071955 #14922082

Subgroups — C2×#13071955 #14922082

Order 2816.

5998 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
1C22×#66999C211yesmaximal, characteristic, complemented
2C22×#66991C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
4#13071955C2116yesmaximal, direct product factor
5C2×#10622835C212yesmaximal, complemented
6C2×#10622836C212yesmaximal, complemented
7C2×#10622843C211yesmaximal, characteristic, complemented
8C2×#10622834C211yesmaximal, characteristic, complemented
9C2×#10622826C212yesmaximal, complemented
10C2×#10622823C212yesmaximal, complemented
11C2×#10622825C211yesmaximal, characteristic, complemented
12C23×C11×#41C211yesmaximal, characteristic, complemented
13C22×C11×#41—28no—
14C22×C11×#41—28no—
15C22×C11×#41—28no—
16C22×C11×#41C2218yescomplemented
17C23×Q8×C11C2211yescharacteristic
18C23×D4×C11C2212yes—
19C23×D4×C11C2211yescharacteristic
20C24×C4×C11C2212yes—
21C24×C4×C11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic
23C23×C22⋊D11C2212yes—
24C23×C4×D11C2211yescharacteristic
25C22×C22⋊Dic11C2212yes—
26C22×C22⋊Dic11C2212yes—
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2212yes—
29C22×C22⋊Dic11C2212yes—
30C2×#66999—28no—
31C2×#66999C2218yescomplemented
32C2×#66991—28no—
33C2×#66991C2218yescomplemented
34C2×C4×C22⋊D11—28no—
35C2×C4×C22⋊D11C2218yescomplemented
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2212yes—
38C22×C4⋊Dic11C2211yescharacteristic
39C22×C4⋊Dic11C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2212yes—
42C22×C4×Dic11C2211yescharacteristic
43#10622843C2218yescomplemented
44#10622836C22116yescomplemented
45#10622835C22116yescomplemented
46#10622834C2218yescomplemented
47#10622826C22116yescomplemented
48#10622825C2218yescomplemented
49#10622823C22116yescomplemented
50C2×C11⋊#95C2212yes—
51C2×C11⋊#95C2212yes—
52C2×C11⋊#95C2212yes—
53C25×C11C2312yes—
54C25×C11C2311yescharacteristic
55C24×D11C2311yescharacteristic
56C2×C11×#41—2128no—
57C2×C11×#41—232no—
58C2×C11×#41—232no—
59C2×C11×#41—232no—
60C22×Q8×C11—24no—
61C22×Q8×C11—24no—
62C22×Q8×C11D418yescomplemented
63C22×Q8×C11C2314yes—
64C22×D4×C11—28no—
65C22×D4×C11—28no—
66C22×D4×C11—28no—
67C22×D4×C11—24no—
68C22×D4×C11—24no—
69C22×D4×C11D418yescomplemented
70C22×D4×C11C2318yes—
71C22×D4×C11C2314yes—
72C23×C4×C11—28no—
73C23×C4×C11—28no—
74C23×C4×C11—28no—
75C23×C4×C11—24no—
76C23×C4×C11—24no—
77C23×C4×C11D418yescomplemented
78C23×C4×C11C2318yes—
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2312yes—
81C23×C4×C11C2314yes—
82C23×C4×C11C2311yescharacteristic
83C22×C22⋊D11—24no—
84C22×C22⋊D11—24no—
85C22×C22⋊D11—28no—
86C22×C22⋊D11—28no—
87C22×C22⋊D11—24no—
88C22×C22⋊D11—44no—
89C22×C22⋊D11C2314yes—
90C22×C22⋊D11C2318yes—
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2312yes—
94C23×Dic11C2312yes—
95C23×Dic11C2311yescharacteristic
96C22×C4×D11—24no—
97C22×C4×D11—24no—
98C22×C4×D11—24no—
99C22×C4×D11C2314yes—
100C2×C22⋊Dic11—24no—
101C2×C22⋊Dic11—28no—
102C2×C22⋊Dic11—28no—
103C2×C22⋊Dic11—44no—
104C2×C22⋊Dic11—44no—
105C2×C22⋊Dic11C2314yes—
106C2×C22⋊Dic11C2318yes—
107C2×C22⋊Dic11C2318yes—
108C2×C22⋊Dic11C2318yes—
109C2×C22⋊Dic11C2318yes—
110#66999—232no—
111#66991—232no—
112C4×C22⋊D11—232no—
113C2×(C2×D11)⋊C4—24no—
114C2×(C2×D11)⋊C4—28no—
115C2×(C2×D11)⋊C4C2314yes—
116C2×(C2×D11)⋊C4C2318yes—
117C2×C4⋊Dic11—24no—
118C2×C4⋊Dic11—24no—
119C2×C4⋊Dic11C2314yes—
120C2×C4⋊Dic11C2314yes—
121C2×Dic11⋊C4—24no—
122C2×Dic11⋊C4—28no—
123C2×Dic11⋊C4C2314yes—
124C2×Dic11⋊C4C2318yes—
125C2×C4×Dic11—24no—
126C2×C4×Dic11C2314yes—
127C11⋊#95C2318yes—
128C11⋊#95C2318yes—
129C11⋊#95C2318yes—
130C2×#2407—111nomaximal, Sylow
131C24×C11—24no—
132C24×C11—22no—
133C24×C11—24no—
134C24×C11—22no—
135C24×C11—24no—
136C24×C11—22no—
137C24×C11—22no—
138C24×C11—24no—
139C24×C11—22no—
140C24×C11—24no—
141C24×C11—22no—
142C24×C11—24no—
143C24×C11C2×D418yes—
144C24×C11C2×D414yes—
145C24×C11C2414yes—
146C24×C11C2412yes—
147C24×C11C2411yescharacteristic
148C23×D11—22no—
149C23×D11—22no—
150C23×D11—22no—
151C23×D11—22no—
152C23×D11—22no—
153C23×D11—22no—
154C23×D11#4114yescomplemented
155C23×D11C2412yes—
156C11×#41—2256no—
157C2×Q8×C11—232no—
158C2×Q8×C11—28no—
159C2×Q8×C11—28no—
160C2×Q8×C11C2×D4116yescomplemented
161C2×D4×C11—264no—
162C2×D4×C11—216no—
163C2×D4×C11—216no—
164C2×D4×C11—232no—
165C2×D4×C11—216no—
166C2×D4×C11—28no—
167C2×D4×C11—28no—
168C2×D4×C11C2×D4116yescomplemented
169C22×C4×C11—264no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—24no—
173C22×C4×C11—24no—
174C22×C4×C11—216no—
175C22×C4×C11—232no—
176C22×C4×C11—216no—
177C22×C4×C11—216no—
178C22×C4×C11—28no—
179C22×C4×C11—28no—
180C22×C4×C11C2×D414yes—
181C22×C4×C11C2×D418yes—
182C22×C4×C11C2×D414yes—
183C22×C4×C11C2×D414yes—
184C22×C4×C11C2×D414yes—
185C22×C4×C11C2×D4116yescomplemented
186C22×C4×C11C2412yes—
187C22×C4×C11C2414yes—
188C22×C4×C11C2412yes—
189C2×C22⋊D11—232no—
190C2×C22⋊D11—28no—
191C2×C22⋊D11—28no—
192C2×C22⋊D11—216no—
193C2×C22⋊D11—28no—
194C2×C22⋊D11—216no—
195C2×C22⋊D11—48no—
196C2×C22⋊D11—432no—
197C22×Dic11—22no—
198C22×Dic11—22no—
199C22×Dic11—22no—
200C22×Dic11—24no—
201C22×Dic11—22no—
202C22×Dic11—24no—
203C22×Dic11—22no—
204C22×Dic11—22no—
205C22×Dic11—24no—
206C22×Dic11—24no—
207C22×Dic11—22no—
208C22×Dic11—24no—
209C22×Dic11—24no—
210C22×Dic11—22no—
211C22×Dic11#4114yescomplemented
212C22×Dic11C2414yes—
213C22×Dic11C2412yes—
214C22×Dic11C2414yes—
215C22×Dic11C2412yes—
216C22×Dic11C2412yes—
217C2×C4×D11—28no—
218C2×C4×D11—28no—
219C2×C4×D11—28no—
220C2×C4×D11—416no—
221C22⋊Dic11—216no—
222C22⋊Dic11—28no—
223C22⋊Dic11—216no—
224C22⋊Dic11—48no—
225C22⋊Dic11—48no—
226(C2×D11)⋊C4—28no—
227(C2×D11)⋊C4—216no—
228C4⋊Dic11—28no—
229C4⋊Dic11—28no—
230Dic11⋊C4—28no—
231Dic11⋊C4—216no—
232C4×Dic11—28no—
233C23×#41D1111yescharacteristic, complemented
234C22×C22⋊Q8—111no—
235C22×#121—111no—
236C22×C4×D4—111no—
237#2407—1116no—
238C2×#394—112no—
239C2×#392—112no—
240C2×#391—111no—
241C2×#390—111no—
242C2×#386—112no—
243C2×#385—112no—
244C2×#380—111no—
245C23×C11—216no—
246C23×C11—28no—
247C23×C11—28no—
248C23×C11—28no—
249C23×C11—216no—
250C23×C11—216no—
251C23×C11—24no—
252C23×C11—22no—
253C23×C11—24no—
254C23×C11—22no—
255C23×C11—24no—
256C23×C11—22no—
257C23×C11—22no—
258C23×C11—24no—
259C23×C11—22no—
260C23×C11—24no—
261C23×C11—22no—
262C23×C11—24no—
263C23×C11—48no—
264C23×C11—48no—
265C23×C11—44no—
266C23×C11—44no—
267C23×C11—44no—
268C23×C11—48no—
269C23×C11—48no—
270C23×C11—44no—
271C23×C11C22×D418yes—
272C23×C11C22×D414yes—
273C23×C11C22×D412yes—
274C23×C11C22×D412yes—
275C23×C11C22×D412yes—
276C23×C11C2×#4112yes—
277C23×C11C2×#4112yes—
278C23×C11H(5,𝔽2)12yes—
279C23×C112−1+412yes—
280C23×C11C2511yescharacteristic
281C22×D11—28no—
282C22×D11—28no—
283C22×D11—28no—
284C22×D11—22no—
285C22×D11—22no—
286C22×D11—22no—
287C22×D11—22no—
288C22×D11—22no—
289C22×D11—22no—
290C22×D11—44no—
291C22×D11—44no—
292C22×D11—44no—
293C22×D11—44no—
294C22×D11C2×#4114yescomplemented
295Q8×C11—232no—
296D4×C11—264no—
297D4×C11—232no—
298C2×C4×C11—264no—
299C2×C4×C11—28no—
300C2×C4×C11—216no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—24no—
304C2×C4×C11—24no—
305C2×C4×C11—232no—
306C2×C4×C11#120116yes—
307C2×C4×C11C22×D414yes—
308C2×C4×C11C22×D418yes—
309C2×C4×C11C22×D414yes—
310C2×C4×C11C22×D414yes—
311C2×C4×C11C22×D414yes—
312C22⋊D11—232no—
313C22⋊D11—432no—
314C2×Dic11—28no—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—24no—
320C2×Dic11—22no—
321C2×Dic11—24no—
322C2×Dic11—22no—
323C2×Dic11—24no—
324C2×Dic11—24no—
325C2×Dic11—22no—
326C2×Dic11—24no—
327C2×Dic11—24no—
328C2×Dic11—22no—
329C2×Dic11—44no—
330C2×Dic11—44no—
331C2×Dic11—48no—
332C2×Dic11—48no—
333C2×Dic11C2×#4114yescomplemented
334C4×D11—416no—
335C22×#41—28no—
336C22×#41—28no—
337C22×#41—28no—
338C22×#41C2×D1118yescomplemented
339C23×Q8C2×D1111yescharacteristic
340C23×D4—111no—
341C23×D4—112no—
342C23×D4C2×D1112yes—
343C23×D4C2×D1111yescharacteristic
344C24×C4—111no—
345C24×C4C2×D1112yes—
346C24×C4C2×D1111yescharacteristic
347C2×C22⋊Q8—118no—
348C2×C22⋊Q8—228no—
349C2×#121—118no—
350C2×#121—228no—
351C2×C4×D4—118no—
352C2×C4×D4—228no—
353C22×C4⋊C4—112no—
354C22×C4⋊C4—111no—
355C22×C4⋊C4—111no—
356C22×C4⋊C4—111no—
357C22×C22⋊C4—112no—
358C22×C22⋊C4—111no—
359C22×C22⋊C4—112no—
360C22×C22⋊C4—112no—
361C22×C22⋊C4—111no—
362C22×C22⋊C4—112no—
363C22×C22⋊C4—112no—
364C22×C42—111no—
365#394—1116no—
366#392—1116no—
367#391—118no—
368#390—118no—
369#386—1116no—
370#385—1116no—
371#380—118no—
372C2×#95—112no—
373C2×#95—112no—
374C2×#95—112no—
375C22×C11—28no—
376C22×C11—24no—
377C22×C11—24no—
378C22×C11—24no—
379C22×C11—28no—
380C22×C11—28no—
381C22×C11—416no—
382C22×C11—432no—
383C22×C11—44no—
384C22×C11—44no—
385C22×C11—42no—
386C22×C11—42no—
387C22×C11—42no—
388C22×C11—44no—
389C22×C11—44no—
390C22×C11—42no—
391C22×C11C2×#12014yes—
392C22×C11#52514yes—
393C22×C11#53714yes—
394C22×C11#54614yes—
395C22×C11#54714yes—
396C22×C11#54814yes—
397C22×C11#55014yes—
398C22×C11C23×D411yescharacteristic
399C22×C11C23×D411yescharacteristic
400C22×C11C23×D411yescharacteristic
401C22×C11C22×#4111yescharacteristic
402C22×C11C22×#4111yescharacteristic
403C22×C11C2×H(5,𝔽2)11yescharacteristic
404C22×C11C2×2−1+411yescharacteristic
405C2×D11—24no—
406C2×D11—24no—
407C2×D11—24no—
408C2×D11—416no—
409C2×D11—42no—
410C2×D11—42no—
411C2×D11—42no—
412C2×D11—42no—
413C4×C11—24no—
414C4×C11—28no—
415C4×C11C2×#12018yes—
416Dic11—24no—
417Dic11—42no—
418Dic11—42no—
419Dic11—44no—
420Dic11—44no—
421C25—111no—
422C25C22×D1112yes—
423C25C22×D1111yescharacteristic
424C2×#41—2128no—
425C2×#41—232no—
426C2×#41—232no—
427C2×#41—232no—
428C22×Q8—24no—
429C22×Q8—24no—
430C22×Q8C22⋊D1118yescomplemented
431C22×Q8C22×D1114yes—
432C22×D4—28no—
433C22×D4—28no—
434C22×D4—28no—
435C22×D4—24no—
436C22×D4—24no—
437C22×D4—114no—
438C22×D4—118no—
439C22×D4—224no—
440C22×D4—224no—
441C22×D4—224no—
442C22×D4—228no—
443C22×D4—228no—
444C22×D4—444no—
445C22×D4C22⋊D1118yescomplemented
446C22×D4C22×D1118yes—
447C22×D4C22×D1114yes—
448C23×C4—28no—
449C23×C4—28no—
450C23×C4—28no—
451C23×C4—24no—
452C23×C4—24no—
453C23×C4—111no—
454C23×C4—112no—
455C23×C4—111no—
456C23×C4—111no—
457C23×C4—112no—
458C23×C4—114no—
459C23×C4—224no—
460C23×C4—224no—
461C23×C4—224no—
462C23×C4C22⋊D1118yescomplemented
463C23×C4C22×D1118yes—
464C23×C4C22×D1111yescharacteristic
465C23×C4C22×D1112yes—
466C23×C4C22×D1114yes—
467C23×C4C22×D1111yescharacteristic
468C22⋊Q8—2232no—
469#121—2232no—
470C4×D4—2232no—
471C2×C4⋊C4—114no—
472C2×C4⋊C4—114no—
473C2×C4⋊C4—114no—
474C2×C4⋊C4—118no—
475C2×C4⋊C4—224no—
476C2×C4⋊C4—224no—
477C2×C4⋊C4—228no—
478C2×C4⋊C4—224no—
479C2×C22⋊C4—114no—
480C2×C22⋊C4—118no—
481C2×C22⋊C4—118no—
482C2×C22⋊C4—114no—
483C2×C22⋊C4—118no—
484C2×C22⋊C4—118no—
485C2×C22⋊C4—118no—
486C2×C22⋊C4—228no—
487C2×C22⋊C4—224no—
488C2×C22⋊C4—228no—
489C2×C22⋊C4—224no—
490C2×C22⋊C4—228no—
491C2×C22⋊C4—444no—
492C2×C22⋊C4—444no—
493C2×C42—114no—
494C2×C42—224no—
495#95—118no—
496#95—118no—
497#95—118no—
498C2×C11—44no—
499C2×C11—48no—
500C2×C11#240718yescomplemented
501C2×C11C22×#12011yescharacteristic
502C2×C11C2×#52511yescharacteristic
503C2×C11C2×#53711yescharacteristic
504C2×C11C2×#54611yescharacteristic
505C2×C11C2×#54711yescharacteristic
506C2×C11C2×#54811yescharacteristic
507C2×C11C2×#55011yescharacteristic
508D11—44no—
509C24—24no—
510C24—22no—
511C24—22no—
512C24—24no—
513C24—22no—
514C24—24no—
515C24—24no—
516C24—22no—
517C24—22no—
518C24—24no—
519C24—24no—
520C24—22no—
521C24—114no—
522C24—112no—
523C24—222no—
524C24—222no—
525C24—222no—
526C24—222no—
527C24—222no—
528C24—222no—
529C24C2×C22⋊D1118yes—
530C24C2×C22⋊D1114yes—
531C24C23×D1114yes—
532C24C23×D1112yes—
533C24C23×D1111yescharacteristic
534#41—2256no—
535C2×Q8—232no—
536C2×Q8—28no—
537C2×Q8—28no—
538C2×Q8C2×C22⋊D11116yescomplemented
539C2×D4—264no—
540C2×D4—216no—
541C2×D4—216no—
542C2×D4—232no—
543C2×D4—216no—
544C2×D4—28no—
545C2×D4—28no—
546C2×D4—228no—
547C2×D4—228no—
548C2×D4—2232no—
549C2×D4—228no—
550C2×D4—2216no—
551C2×D4—2216no—
552C2×D4—448no—
553C2×D4—4432no—
554C2×D4C2×C22⋊D11116yescomplemented
555C22×C4—264no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—216no—
561C22×C4—232no—
562C22×C4—216no—
563C22×C4—216no—
564C22×C4—28no—
565C22×C4—28no—
566C22×C4—114no—
567C22×C4—112no—
568C22×C4—114no—
569C22×C4—112no—
570C22×C4—114no—
571C22×C4—112no—
572C22×C4—222no—
573C22×C4—222no—
574C22×C4—224no—
575C22×C4—224no—
576C22×C4—222no—
577C22×C4—224no—
578C22×C4—224no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4—222no—
582C22×C4—224no—
583C22×C4—222no—
584C22×C4—224no—
585C22×C4—222no—
586C22×C4—228no—
587C22×C4—228no—
588C22×C4—228no—
589C22×C4—4416no—
590C22×C4C2×C22⋊D1114yes—
591C22×C4C2×C22⋊D1118yes—
592C22×C4C2×C22⋊D1114yes—
593C22×C4C2×C22⋊D1114yes—
594C22×C4C2×C22⋊D1114yes—
595C22×C4C2×C22⋊D11116yescomplemented
596C22×C4C23×D1112yes—
597C22×C4C23×D1114yes—
598C22×C4C23×D1112yes—
599C4⋊C4—228no—
600C4⋊C4—228no—
601C4⋊C4—2216no—
602C4⋊C4—228no—
603C22⋊C4—2216no—
604C22⋊C4—228no—
605C22⋊C4—2216no—
606C22⋊C4—228no—
607C22⋊C4—2216no—
608C22⋊C4—448no—
609C22⋊C4—448no—
610C42—228no—
611C11C2×#240711yescharacteristic, complemented, Sylow
612C23—216no—
613C23—28no—
614C23—216no—
615C23—28no—
616C23—216no—
617C23—28no—
618C23—24no—
619C23—24no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—24no—
624C23—22no—
625C23—24no—
626C23—24no—
627C23—22no—
628C23—24no—
629C23—22no—
630C23—44no—
631C23—48no—
632C23—44no—
633C23—48no—
634C23—44no—
635C23—48no—
636C23—48no—
637C23—44no—
638C23—114no—
639C23—228no—
640C23—228no—
641C23—228no—
642C23—222no—
643C23—222no—
644C23—222no—
645C23—222no—
646C23—222no—
647C23—222no—
648C23—444no—
649C23—444no—
650C23—444no—
651C23—444no—
652C23#41×D1112yes—
653C23#41×D1112yes—
654C23#6704212yes—
655C23#6704312yes—
656C23C22×C22⋊D1118yes—
657C23C22×C22⋊D1114yes—
658C23C22×C22⋊D1112yes—
659C23C22×C22⋊D1112yes—
660C23C22×C22⋊D1112yes—
661C23C24×D1111yescharacteristic
662Q8—232no—
663D4—264no—
664D4—232no—
665D4—2232no—
666D4—4432no—
667C2×C4—264no—
668C2×C4—28no—
669C2×C4—216no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—232no—
675C2×C4—114no—
676C2×C4—228no—
677C2×C4—222no—
678C2×C4—222no—
679C2×C4—224no—
680C2×C4—224no—
681C2×C4—222no—
682C2×C4—224no—
683C2×C4—224no—
684C2×C4—222no—
685C2×C4—222no—
686C2×C4—222no—
687C2×C4—224no—
688C2×C4—222no—
689C2×C4—224no—
690C2×C4—222no—
691C2×C4—448no—
692C2×C4—444no—
693C2×C4—448no—
694C2×C4—444no—
695C2×C4—4416no—
696C2×C4#67006116yes—
697C2×C4C22×C22⋊D1114yes—
698C2×C4C22×C22⋊D1118yes—
699C2×C4C22×C22⋊D1114yes—
700C2×C4C22×C22⋊D1114yes—
701C2×C4C22×C22⋊D1114yes—
702C22—24no—
703C22—28no—
704C22—28no—
705C22—28no—
706C22—24no—
707C22—24no—
708C22—44no—
709C22—432no—
710C22—416no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—44no—
715C22—44no—
716C22—42no—
717C22—44no—
718C22—224no—
719C22—224no—
720C22—224no—
721C22—442no—
722C22—4416no—
723C22—442no—
724C22—442no—
725C22—442no—
726C22#1062335514yes—
727C22#1062335914yes—
728C22#1062336014yes—
729C22#1062336214yes—
730C22#1062336414yes—
731C22#1062336514yes—
732C22C2×#6700614yes—
733C22C2×#41×D1111yescharacteristic
734C22C2×#41×D1111yescharacteristic
735C22C2×#6704211yescharacteristic
736C22C2×#6704311yescharacteristic
737C22C23×C22⋊D1111yescharacteristic
738C22C23×C22⋊D1111yescharacteristic
739C22C23×C22⋊D1111yescharacteristic
740C4—24no—
741C4—28no—
742C4—224no—
743C4—442no—
744C4—444no—
745C4—442no—
746C4—444no—
747C4C2×#6700618yes—
748C2—44no—
749C2—48no—
750C2—444no—
751C2#1307195518yesdirect product factor
752C2C22×#6700611yescharacteristic
753C2C2×#1062335911yescharacteristic
754C2C2×#1062336411yescharacteristic
755C2C2×#1062336011yescharacteristic
756C2C2×#1062335511yescharacteristic
757C2C2×#1062336211yescharacteristic
758C2C2×#1062336511yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC23×C11×#41C2
socleC24×C11C24
hypercenterC23×#41D11
hypocenterC11C2×#2407
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×#41

Complements

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

NH ≅ G/Ntype
1. C22×#66999C2semidirect
2. C22×#66991C2semidirect
3. C22×C4×C22⋊D11C2semidirect
4. #13071955C2direct (N × H)
5. C2×#10622835C2semidirect
6. C2×#10622836C2semidirect
7. C2×#10622843C2semidirect
8. C2×#10622834C2semidirect
9. C2×#10622826C2semidirect
10. C2×#10622823C2semidirect
11. C2×#10622825C2semidirect
12. C23×C11×#41C2semidirect
16. C22×C11×#41C22semidirect
31. C2×#66999C22semidirect
33. C2×#66991C22semidirect
35. C2×C4×C22⋊D11C22semidirect
43. #10622843C22semidirect
44. #10622836C22semidirect
45. #10622835C22semidirect
46. #10622834C22semidirect
47. #10622826C22semidirect
48. #10622825C22semidirect
49. #10622823C22semidirect
62. C22×Q8×C11D4semidirect
69. C22×D4×C11D4semidirect
77. C23×C4×C11D4semidirect
154. C23×D11#41semidirect
160. C2×Q8×C11C2×D4semidirect
168. C2×D4×C11C2×D4semidirect
185. C22×C4×C11C2×D4semidirect
211. C22×Dic11#41semidirect
233. C23×#41D11semidirect
294. C22×D11C2×#41semidirect
333. C2×Dic11C2×#41semidirect
338. C22×#41C2×D11semidirect
430. C22×Q8C22⋊D11semidirect
445. C22×D4C22⋊D11semidirect
462. C23×C4C22⋊D11semidirect
500. C2×C11#2407semidirect
538. C2×Q8C2×C22⋊D11semidirect
554. C2×D4C2×C22⋊D11semidirect
595. C22×C4C2×C22⋊D11semidirect
611. C11C2×#2407semidirect
751. C2#13071955direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669992
C22×#669912
C22×C4×C22⋊D112
#130719552
C2×#106228352
C2×#106228362
C2×#106228432
C2×#106228342
C2×#106228262
C2×#106228232
C2×#106228252
C23×C11×#412
C2×#240711