Finite Group Databasebeta

← #14675340

Subgroups — #14675340

Order 2816.

2666 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D11C211yesmaximal, characteristic
2C2×#10622570C212yesmaximal
3C2×C4×Dic11⋊C4C212yesmaximal, complemented
4C2×#10622279C211yesmaximal, characteristic, complemented
5#13066854C212yesmaximal, complemented
6#13066853C212yesmaximal, complemented
7Dic11⋊#95C211yesmaximal, characteristic, complemented
8#13066839C211yesmaximal, characteristic, complemented
9(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
10#95×Dic11C211yesmaximal, characteristic, complemented
11C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C23×C22⋊D11C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C22×C11×C22⋊C4C2212yes—
16C22×C42×C11C2212yes—
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C22⋊Dic11C2212yes—
19C2×C4×C22⋊D11—28no—
20C2×C4×C22⋊D11C418yescomplemented
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×Dic11⋊C4C2212yes—
25C22×Dic11⋊C4C2211yescharacteristic
26C22×C4×Dic11C2212yes—
27C22×C4×Dic11C2211yescharacteristic
28C22×C4×Dic11C2212yes—
29C4×C11×C22⋊C4—24no—
30C2×C11×#95C2211yescharacteristic
31C2×C11×#95C2211yescharacteristic
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38#10622570C4116yescomplemented
39C4×Dic11⋊C4—28no—
40#10622279—24no—
41C25×C11C2311yescharacteristic
42C24×D11C2311yescharacteristic
43C23×C4×C11—24no—
44C23×C4×C11—22no—
45C23×C4×C11—22no—
46C23×C4×C11—42no—
47C23×C4×C11C2×C414yes—
48C23×C4×C11C2312yes—
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2312yes—
51C23×C4×C11C2311yescharacteristic
52C22×C22⋊D11—24no—
53C22×C22⋊D11—22no—
54C22×C22⋊D11—22no—
55C22×C22⋊D11C2×C414yes—
56C22×C22⋊D11C2×C418yes—
57C23×Dic11C2312yes—
58C23×Dic11C2312yes—
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2311yescharacteristic
62C22×C4×D11—22no—
63C22×C4×D11—22no—
64C22×C4×D11—24no—
65C22×C4×D11—42no—
66C22×C4×D11C2×C414yes—
67C2×C11×C22⋊C4—24no—
68C2×C11×C22⋊C4—24no—
69C2×C11×C22⋊C4C2×C418yescomplemented
70C2×C42×C11—24no—
71C2×C42×C11—24no—
72C2×C42×C11—42no—
73C2×C22⋊Dic11—24no—
74C2×C22⋊Dic11—42no—
75C2×C22⋊Dic11—42no—
76C2×C22⋊Dic11C2×C414yes—
77C2×C22⋊Dic11C2×C418yescomplemented
78C4×C22⋊D11—232no—
79C2×(C2×D11)⋊C4—24no—
80C2×(C2×D11)⋊C4—24no—
81C2×(C2×D11)⋊C4—24no—
82C2×(C2×D11)⋊C4—42no—
83C2×(C2×D11)⋊C4—42no—
84C2×(C2×D11)⋊C4C2×C414yes—
85C2×(C2×D11)⋊C4C2×C418yescomplemented
86C2×(C2×D11)⋊C4C2×C418yescomplemented
87C2×Dic11⋊C4—24no—
88C2×Dic11⋊C4—24no—
89C2×Dic11⋊C4C2×C414yes—
90C2×Dic11⋊C4C2×C418yescomplemented
91C2×Dic11⋊C4D418yes—
92C2×C4×Dic11—24no—
93C2×C4×Dic11—24no—
94C2×C4×Dic11—24no—
95C2×C4×Dic11—24no—
96C2×C4×Dic11—24no—
97C2×C4×Dic11—42no—
98C2×C4×Dic11C2×C414yes—
99C2×C4×Dic11C2×C418yescomplemented
100C11×#95—22no—
101C11×#95D414yescomplemented
102C11⋊#95—22no—
103C11⋊#95—24no—
104C11⋊#95—22no—
105C11⋊#95—24no—
106C11⋊#95—24no—
107C11⋊#95—42no—
108#13820—111nomaximal, Sylow
109C24×C11—22no—
110C24×C11—21no—
111C24×C11—22no—
112C24×C11—21no—
113C24×C11—21no—
114C24×C11—21no—
115C24×C11—21no—
116C24×C11—22no—
117C24×C11—21no—
118C24×C11C22×C412yes—
119C24×C11C22×C414yes—
120C24×C11C2411yescharacteristic
121C23×D11—21no—
122C23×D11—22no—
123C23×D11—22no—
124C23×D11—21no—
125C23×D11—21no—
126C23×D11—21no—
127C23×D11—21no—
128C23×D11—22no—
129C23×D11—21no—
130C23×D11C22×C412yes—
131C23×D11C22×C414yes—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—21no—
135C22×C4×C11—22no—
136C22×C4×C11—21no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—28no—
148C22×C4×C11—28no—
149C22×C4×C11—44no—
150C22×C4×C11—48no—
151C22×C4×C11—48no—
152C22×C4×C11C22×C414yes—
153C22×C4×C11C22×C412yes—
154C22×C4×C11C22×C412yes—
155C22×C4×C11C22×C414yes—
156C22×C4×C11C2×D414yes—
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×D414yes—
159C22×C4×C11#4112yes—
160C22×C4×C11#4114yes—
161C2×C22⋊D11—28no—
162C2×C22⋊D11—28no—
163C2×C22⋊D11—216no—
164C2×C22⋊D11—216no—
165C2×C22⋊D11C42116yescomplemented
166C22×Dic11—21no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—21no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—21no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—21no—
185C22×Dic11C22×C412yes—
186C22×Dic11C22×C414yes—
187C22×Dic11C22×C414yes—
188C22×Dic11C22×C412yes—
189C22×Dic11C22×C412yes—
190C22×Dic11C22×C414yes—
191C22×Dic11C2×D414yes—
192C22×Dic11C2×D414yes—
193C22×Dic11#4112yes—
194C22×Dic11#4112yes—
195C2×C4×D11—28no—
196C2×C4×D11—28no—
197C2×C4×D11—44no—
198C2×C4×D11—48no—
199C2×C4×D11—48no—
200C11×C22⋊C4—216no—
201C42×C11—48no—
202C22⋊Dic11—28no—
203C22⋊Dic11—48no—
204(C2×D11)⋊C4—28no—
205(C2×D11)⋊C4—216no—
206(C2×D11)⋊C4—48no—
207Dic11⋊C4—216no—
208Dic11⋊C4C22⋊C4116yescomplemented
209C4×Dic11—28no—
210C4×Dic11—216no—
211C4×Dic11—48no—
212C22×C4×D4—111no—
213C2×#390—112no—
214C2×C4×C4⋊C4—112no—
215C2×C4×C22⋊C4—111no—
216C2×C4×C22⋊C4D1111yescharacteristic, complemented
217#1437—112no—
218#1437—112no—
219C4⋊#95—111no—
220C22⋊#95—111no—
221C22⋊#95—111no—
222C4×#95—111no—
223C23×C11—22no—
224C23×C11—22no—
225C23×C11—24no—
226C23×C11—24no—
227C23×C11—24no—
228C23×C11—22no—
229C23×C11—22no—
230C23×C11—24no—
231C23×C11—24no—
232C23×C11—22no—
233C23×C11—22no—
234C23×C11—24no—
235C23×C11—42no—
236C23×C11—42no—
237C23×C11—41no—
238C23×C11—42no—
239C23×C11—42no—
240C23×C11—41no—
241C23×C11—42no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—42no—
245C23×C11C2×C4214yes—
246C23×C11C23×C411yescharacteristic
247C23×C11C23×C412yes—
248C23×C11C22×D412yes—
249C23×C11C22×D411yescharacteristic
250C23×C11C2×#4111yescharacteristic
251C23×C11C2×#4112yes—
252C23×C11C2×#4111yescharacteristic
253C23×C11C2×#4111yescharacteristic
254C23×C11H(5,𝔽2)12yes—
255C23×C11H(5,𝔽2)11yescharacteristic
256C23×C112−1+411yescharacteristic
257C22×D11—22no—
258C22×D11—22no—
259C22×D11—24no—
260C22×D11—22no—
261C22×D11—24no—
262C22×D11—24no—
263C22×D11—22no—
264C22×D11—24no—
265C22×D11—24no—
266C22×D11—22no—
267C22×D11—22no—
268C22×D11—24no—
269C22×D11—42no—
270C22×D11—42no—
271C22×D11—41no—
272C22×D11—42no—
273C22×D11—42no—
274C22×D11—41no—
275C22×D11—42no—
276C22×D11—41no—
277C22×D11—41no—
278C22×D11—42no—
279C22×D11C2×C4214yes—
280C2×C4×C11—22no—
281C2×C4×C11—24no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—24no—
286C2×C4×C11—24no—
287C2×C4×C11—24no—
288C2×C4×C11—24no—
289C2×C4×C11—24no—
290C2×C4×C11—24no—
291C2×C4×C11—24no—
292C2×C4×C11—24no—
293C2×C4×C11—24no—
294C2×C4×C11—24no—
295C2×C4×C11—24no—
296C2×C4×C11—24no—
297C2×C4×C11—416no—
298C2×C4×C11—42no—
299C2×C4×C11—42no—
300C2×C4×C11—42no—
301C2×C4×C11—42no—
302C2×C4×C11C2×C22⋊C414yes—
303C2×C4×C11C4×D414yes—
304C2×C4×C11C4×D418yescomplemented
305C22⋊D11—232no—
306C2×Dic11—22no—
307C2×Dic11—22no—
308C2×Dic11—24no—
309C2×Dic11—24no—
310C2×Dic11—22no—
311C2×Dic11—24no—
312C2×Dic11—24no—
313C2×Dic11—24no—
314C2×Dic11—22no—
315C2×Dic11—24no—
316C2×Dic11—24no—
317C2×Dic11—24no—
318C2×Dic11—22no—
319C2×Dic11—42no—
320C2×Dic11—42no—
321C2×Dic11—42no—
322C2×Dic11—42no—
323C2×Dic11—42no—
324C2×Dic11—42no—
325C2×Dic11—42no—
326C2×Dic11—42no—
327C2×Dic11—42no—
328C2×Dic11—42no—
329C2×Dic11C2×C4214yes—
330C2×Dic11C2×C22⋊C414yes—
331C2×Dic11C2×C22⋊C414yes—
332C2×Dic11#11714yes—
333C2×Dic11C4×D418yes—
334C2×Dic11C4×D418yes—
335C4×D11—416no—
336C23×D4—111no—
337C24×C4—111no—
338C24×C4C2×D1111yescharacteristic
339C2×C4×D4—118no—
340C2×C4×D4—228no—
341C22×C4⋊C4—111no—
342C22×C4⋊C4—112no—
343C22×C22⋊C4—111no—
344C22×C22⋊C4—111no—
345C22×C22⋊C4—112no—
346C22×C22⋊C4—112no—
347C22×C22⋊C4—112no—
348C22×C22⋊C4C2×D1112yes—
349C22×C42—111no—
350C22×C42—112no—
351C22×C42—112no—
352C22×C42C2×D1112yes—
353#390—1116no—
354C4×C4⋊C4—228no—
355C4×C22⋊C4—24no—
356C4×C22⋊C4—224no—
357C2×#95—111no—
358C2×#95—112no—
359C2×#95—111no—
360C2×#95—112no—
361C2×#95—112no—
362C2×#95—112no—
363C2×#95C2×D1111yescharacteristic
364C2×#95C2×D1111yescharacteristic
365C22×C11—24no—
366C22×C11—24no—
367C22×C11—24no—
368C22×C11—42no—
369C22×C11—42no—
370C22×C11—42no—
371C22×C11—42no—
372C22×C11—44no—
373C22×C11—44no—
374C22×C11—44no—
375C22×C11—44no—
376C22×C11C22×C4211yescharacteristic
377C22×C11C22×C22⋊C411yescharacteristic
378C22×C11C2×#11711yescharacteristic
379C22×C11C2×C4×D411yescharacteristic
380C22×C11C2×C4×D412yes—
381C22×C11C2×C4×D412yes—
382C22×C11C2×C4×D412yes—
383C22×C11C4×#4111yescharacteristic
384C22×C11C4×#4112yes—
385C22×C11#51811yescharacteristic
386C22×C11#51812yes—
387C22×C11#52011yescharacteristic
388C22×C11#52012yes—
389C22×C11D4212yes—
390C22×C11#54612yes—
391C22×C11#54711yescharacteristic
392C22×C11#54812yes—
393C22×C11#55012yes—
394C22×C11#55011yescharacteristic
395C22×C11#55312yes—
396C22×C11#55511yescharacteristic
397C22×C11#55611yescharacteristic
398C22×C11#55912yes—
399C2×D11—24no—
400C2×D11—24no—
401C2×D11—24no—
402C2×D11—42no—
403C2×D11—42no—
404C2×D11—42no—
405C2×D11—42no—
406C2×D11—44no—
407C2×D11—44no—
408C2×D11—44no—
409C2×D11—44no—
410C4×C11—24no—
411C4×C11—24no—
412C4×C11—28no—
413C4×C11—44no—
414Dic11—24no—
415Dic11—42no—
416Dic11—44no—
417Dic11—44no—
418Dic11C4×C22⋊C418yescomplemented
419C25—111no—
420C25C22×D1111yescharacteristic
421C22×D4—114no—
422C22×D4—118no—
423C22×D4—224no—
424C22×D4—222no—
425C22×D4—222no—
426C23×C4—22no—
427C23×C4—24no—
428C23×C4—22no—
429C23×C4—42no—
430C23×C4—111no—
431C23×C4—111no—
432C23×C4—112no—
433C23×C4—112no—
434C23×C4—111no—
435C23×C4—114no—
436C23×C4—224no—
437C23×C4—222no—
438C23×C4—222no—
439C23×C4—442no—
440C23×C4C4×D1114yes—
441C23×C4C22×D1112yes—
442C23×C4C22×D1112yes—
443C23×C4C22×D1111yescharacteristic
444C23×C4C22×D1111yescharacteristic
445C4×D4—2232no—
446C2×C4⋊C4—114no—
447C2×C4⋊C4—118no—
448C2×C4⋊C4—118no—
449C2×C4⋊C4—224no—
450C2×C4⋊C4—224no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—114no—
454C2×C22⋊C4—114no—
455C2×C22⋊C4—118no—
456C2×C22⋊C4—118no—
457C2×C22⋊C4—118no—
458C2×C22⋊C4—224no—
459C2×C22⋊C4—224no—
460C2×C22⋊C4—224no—
461C2×C22⋊C4—224no—
462C2×C22⋊C4—442no—
463C2×C22⋊C4—442no—
464C2×C22⋊C4—442no—
465C2×C22⋊C4—442no—
466C2×C22⋊C4C4×D1118yescomplemented
467C2×C42—24no—
468C2×C42—24no—
469C2×C42—42no—
470C2×C42—114no—
471C2×C42—118no—
472C2×C42—224no—
473C2×C42—224no—
474C2×C42—224no—
475C2×C42—224no—
476C2×C42—224no—
477C2×C42—442no—
478#95—22no—
479#95—224no—
480#95—222no—
481#95—224no—
482#95—224no—
483#95—222no—
484#95—442no—
485#95C22⋊D1114yescomplemented
486C2×C11—44no—
487C2×C11C2×C4×C22⋊C411yescharacteristic
488C2×C11C42×D411yescharacteristic
489C2×C11#227511yescharacteristic
490C2×C11D4×C22⋊C411yescharacteristic
491C2×C11#234111yescharacteristic
492C2×C11#235411yescharacteristic
493C2×C11#235711yescharacteristic
494C2×C11#236112yes—
495C2×C11#236312yes—
496C2×C11#236612yes—
497C2×C11#236712yes—
498D11—44no—
499C24—22no—
500C24—21no—
501C24—22no—
502C24—22no—
503C24—21no—
504C24—21no—
505C24—21no—
506C24—21no—
507C24—21no—
508C24—114no—
509C24—112no—
510C24—222no—
511C24—221no—
512C24—222no—
513C24—222no—
514C24—221no—
515C24—221no—
516C24—221no—
517C24—221no—
518C24—221no—
519C24C2×C4×D1114yes—
520C24C2×C4×D1112yes—
521C24C23×D1111yescharacteristic
522C2×D4—1116no—
523C2×D4—228no—
524C2×D4—228no—
525C2×D4—2216no—
526C2×D4—2216no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—28no—
543C22×C4—28no—
544C22×C4—44no—
545C22×C4—48no—
546C22×C4—48no—
547C22×C4—112no—
548C22×C4—114no—
549C22×C4—114no—
550C22×C4—112no—
551C22×C4—112no—
552C22×C4—112no—
553C22×C4—114no—
554C22×C4—112no—
555C22×C4—114no—
556C22×C4—114no—
557C22×C4—228no—
558C22×C4—221no—
559C22×C4—222no—
560C22×C4—221no—
561C22×C4—222no—
562C22×C4—222no—
563C22×C4—222no—
564C22×C4—222no—
565C22×C4—222no—
566C22×C4—222no—
567C22×C4—222no—
568C22×C4—222no—
569C22×C4—222no—
570C22×C4—222no—
571C22×C4—222no—
572C22×C4—221no—
573C22×C4—222no—
574C22×C4—222no—
575C22×C4—221no—
576C22×C4—222no—
577C22×C4—228no—
578C22×C4—444no—
579C22×C4—448no—
580C22×C4—448no—
581C22×C4C2×C4×D1114yes—
582C22×C4C2×C4×D1112yes—
583C22×C4C2×C4×D1112yes—
584C22×C4C2×C4×D1114yes—
585C22×C4#433912yes—
586C22×C4#433914yes—
587C22×C4D4×D1114yes—
588C22×C4C2×C22⋊D1112yes—
589C22×C4C2×C22⋊D1114yes—
590C4⋊C4—1116no—
591C4⋊C4—2216no—
592C22⋊C4—216no—
593C22⋊C4—228no—
594C22⋊C4—228no—
595C22⋊C4—2216no—
596C22⋊C4—448no—
597C22⋊C4—448no—
598C42—48no—
599C42—228no—
600C42—2216no—
601C42—448no—
602C11#1382011yescharacteristic, complemented, Sylow
603C23—24no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—24no—
610C23—22no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—42no—
616C23—41no—
617C23—41no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—41no—
624C23—41no—
625C23—114no—
626C23—224no—
627C23—222no—
628C23—222no—
629C23—222no—
630C23—222no—
631C23—222no—
632C23—224no—
633C23—222no—
634C23—224no—
635C23—224no—
636C23—224no—
637C23—224no—
638C23—442no—
639C23—441no—
640C23—441no—
641C23—442no—
642C23—442no—
643C23—442no—
644C23—442no—
645C23—442no—
646C23—441no—
647C23—441no—
648C23C42×D1114yes—
649C23C22×C4×D1111yescharacteristic
650C23C22×C4×D1112yes—
651C23C2×#433911yescharacteristic
652C23C2×#433912yes—
653C23C2×D4×D1112yes—
654C23#6703712yes—
655C23#41×D1111yescharacteristic
656C23#41×D1111yescharacteristic
657C23#6704211yescharacteristic
658C23#6704311yescharacteristic
659C23C22×C22⋊D1111yescharacteristic
660D4—2232no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—416no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—114no—
684C2×C4—114no—
685C2×C4—114no—
686C2×C4—118no—
687C2×C4—118no—
688C2×C4—114no—
689C2×C4—222no—
690C2×C4—224no—
691C2×C4—222no—
692C2×C4—224no—
693C2×C4—224no—
694C2×C4—222no—
695C2×C4—222no—
696C2×C4—222no—
697C2×C4—224no—
698C2×C4—224no—
699C2×C4—224no—
700C2×C4—224no—
701C2×C4—224no—
702C2×C4—4416no—
703C2×C4—442no—
704C2×C4—442no—
705C2×C4—442no—
706C2×C4—442no—
707C2×C4—442no—
708C2×C4—442no—
709C2×C4—442no—
710C2×C4—442no—
711C2×C4—442no—
712C2×C4—442no—
713C2×C4C22⋊C4×D1114yes—
714C2×C4C4×C22⋊D1114yes—
715C2×C4C4×C22⋊D1118yescomplemented
716C22—24no—
717C22—24no—
718C22—24no—
719C22—44no—
720C22—44no—
721C22—44no—
722C22—44no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—224no—
728C22—224no—
729C22—224no—
730C22—444no—
731C22—444no—
732C22—444no—
733C22—444no—
734C22—442no—
735C22—442no—
736C22—442no—
737C22—442no—
738C22C2×C42×D1111yescharacteristic
739C22C4×#433912yes—
740C22C4×#433911yescharacteristic
741C22C2×C22⋊C4×D1111yescharacteristic
742C22#1062301711yescharacteristic
743C22#1062302112yes—
744C22D11×#11711yescharacteristic
745C22#1062305411yescharacteristic
746C22#1062306311yescharacteristic
747C22#1062306411yescharacteristic
748C22#1062307112yes—
749C22C4×D4×D1112yes—
750C22C4×D4×D1112yes—
751C22#1062307612yes—
752C22#1062307712yes—
753C22#1062308312yes—
754C22#1062308412yes—
755C22#1062309012yes—
756C22C2×C4×C22⋊D1112yes—
757C22C2×C4×C22⋊D1111yescharacteristic
758C22D4×C22⋊D1112yes—
759C22#1062335511yescharacteristic
760C22#1062336511yescharacteristic
761C4—28no—
762C4—24no—
763C4—24no—
764C4—44no—
765C4—118no—
766C4—224no—
767C4—444no—
768C4—444no—
769C4—442no—
770C2—44no—
771C2—444no—
772C2C4×C22⋊C4×D1111yescharacteristic
773C2C42×C22⋊D1111yescharacteristic
774C2#1307097511yescharacteristic
775C2C22⋊C4×C22⋊D1111yescharacteristic
776C2#1307145611yescharacteristic
777C2#1307156611yescharacteristic
778C2#1307159011yescharacteristic
779C2#1307163312yes—
780C2#1307165512yes—
781C2#1307167812yes—
782C2#1307168812yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC2×C4×C11×C22⋊C4C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#13820
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×Dic11⋊C4C2semidirect
4. C2×#10622279C2semidirect
5. #13066854C2semidirect
6. #13066853C2semidirect
7. Dic11⋊#95C2semidirect
8. #13066839C2semidirect
9. (C2×D11)⋊#95C2semidirect
10. #95×Dic11C2semidirect
11. C2×C4×C11×C22⋊C4C2semidirect
20. C2×C4×C22⋊D11C4semidirect
38. #10622570C4semidirect
69. C2×C11×C22⋊C4C2×C4semidirect
77. C2×C22⋊Dic11C2×C4semidirect
85. C2×(C2×D11)⋊C4C2×C4semidirect
86. C2×(C2×D11)⋊C4C2×C4semidirect
90. C2×Dic11⋊C4C2×C4semidirect
99. C2×C4×Dic11C2×C4semidirect
101. C11×#95D4semidirect
165. C2×C22⋊D11C42semidirect
208. Dic11⋊C4C22⋊C4semidirect
216. C2×C4×C22⋊C4D11semidirect
304. C2×C4×C11C4×D4semidirect
418. Dic11C4×C22⋊C4semidirect
466. C2×C22⋊C4C4×D11semidirect
485. #95C22⋊D11semidirect
602. C11#13820semidirect
715. C2×C4C4×C22⋊D11semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D112
C2×#106225702
C2×C4×Dic11⋊C42
C2×#106222792
#130668542
#130668532
Dic11⋊#952
#130668392
(C2×D11)⋊#952
#95×Dic112
C2×C4×C11×C22⋊C42
#1382011