Finite Group Databasebeta

← #14675274

Subgroups — #14675274

Order 2816.

2882 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D11C211yesmaximal, characteristic
2C2×#10622569C212yesmaximal
3C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
4C2×#10622279C212yesmaximal, complemented
5C2×D11×#95C211yesmaximal, characteristic, complemented
6#13066853C212yesmaximal, complemented
7#13066851C212yesmaximal, complemented
8#13066842C211yesmaximal, characteristic, complemented
9(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
10#95×Dic11C211yesmaximal, characteristic, complemented
11C11×C22⋊#95C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C23×C22⋊D11C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C23×C4×D11C2212yes—
16C22×C11×C22⋊C4C2212yes—
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2211yescharacteristic
19C2×C4×C22⋊D11—28no—
20C2×C4×C22⋊D11C418yescomplemented
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×Dic11⋊C4C2211yescharacteristic
24C22×C4×Dic11C2212yes—
25C22×C4×Dic11C2212yes—
26C22×C4×Dic11C2211yescharacteristic
27C2×C11×#95C2211yescharacteristic
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2212yes—
30C4×C22⋊Dic11—24no—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2211yescharacteristic
38#10622569C4116yescomplemented
39#10622279—28no—
40D11×#95—24no—
41C25×C11C2311yescharacteristic
42C24×D11C2311yescharacteristic
43C23×C4×C11—24no—
44C23×C4×C11—22no—
45C23×C4×C11—22no—
46C23×C4×C11—42no—
47C23×C4×C11C2×C414yescomplemented
48C23×C4×C11C2312yes—
49C23×C4×C11C2312yes—
50C23×C4×C11C2311yescharacteristic
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×Dic11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2312yes—
62C22×C4×D11—24no—
63C22×C4×D11—24no—
64C22×C4×D11—24no—
65C22×C4×D11—22no—
66C22×C4×D11—22no—
67C22×C4×D11—24no—
68C22×C4×D11—24no—
69C22×C4×D11—42no—
70C22×C4×D11—42no—
71C22×C4×D11—42no—
72C22×C4×D11C2×C414yes—
73C22×C4×D11C2×C418yescomplemented
74C2×C11×C22⋊C4—42no—
75C2×C11×C22⋊C4—42no—
76C2×C11×C22⋊C4C2×C418yescomplemented
77C2×C22⋊Dic11—24no—
78C2×C22⋊Dic11—24no—
79C2×C22⋊Dic11—24no—
80C2×C22⋊Dic11C2×C414yescomplemented
81C2×C22⋊Dic11C2×C418yescomplemented
82C4×C22⋊D11—232no—
83C2×(C2×D11)⋊C4—24no—
84C2×(C2×D11)⋊C4—24no—
85C2×(C2×D11)⋊C4C2×C414yes—
86C2×(C2×D11)⋊C4C2×C418yescomplemented
87C2×(C2×D11)⋊C4D418yes—
88C2×Dic11⋊C4—24no—
89C2×Dic11⋊C4C2×C414yescomplemented
90C2×C4×Dic11—24no—
91C2×C4×Dic11—24no—
92C2×C4×Dic11—24no—
93C2×C4×Dic11—24no—
94C2×C4×Dic11—24no—
95C2×C4×Dic11—42no—
96C2×C4×Dic11—42no—
97C2×C4×Dic11C2×C414yescomplemented
98C11×#95—22no—
99C11×#95—24no—
100C11×#95—22no—
101C11⋊#95—22no—
102C11⋊#95—24no—
103C11⋊#95—24no—
104C11⋊#95—42no—
105C11⋊#95C2×C418yescomplemented
106C11⋊#95C2×C418yescomplemented
107C11⋊#95D414yescomplemented
108#13813—111nomaximal, Sylow
109C24×C11—21no—
110C24×C11—22no—
111C24×C11—22no—
112C24×C11—21no—
113C24×C11—21no—
114C24×C11—21no—
115C24×C11—21no—
116C24×C11—22no—
117C24×C11—21no—
118C24×C11C22×C414yes—
119C24×C11C22×C412yes—
120C24×C11C2411yescharacteristic
121C23×D11—21no—
122C23×D11—21no—
123C23×D11—22no—
124C23×D11—22no—
125C23×D11—21no—
126C23×D11—21no—
127C23×D11C22×C412yes—
128C23×D11C22×C414yes—
129C23×D11C2×D414yes—
130C23×D11#4112yes—
131C23×D11#4112yes—
132C22×C4×C11—21no—
133C22×C4×C11—22no—
134C22×C4×C11—21no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
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—22no—
148C22×C4×C11—22no—
149C22×C4×C11—28no—
150C22×C4×C11—28no—
151C22×C4×C11—44no—
152C22×C4×C11—48no—
153C22×C4×C11—48no—
154C22×C4×C11C22×C414yes—
155C22×C4×C11C22×C414yes—
156C22×C4×C11C22×C412yes—
157C22×C4×C11C22×C412yes—
158C22×C4×C11C2×D414yes—
159C22×C4×C11C2×D412yes—
160C22×C4×C11#4112yes—
161C2×C22⋊D11—28no—
162C2×C22⋊D11—28no—
163C2×C22⋊D11—216no—
164C2×C22⋊D11—216no—
165C2×C22⋊D11C42116yescomplemented
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—21no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—21no—
185C22×Dic11—22no—
186C22×Dic11C22×C414yes—
187C22×Dic11C22×C412yes—
188C22×Dic11C22×C414yes—
189C22×Dic11C22×C412yes—
190C22×Dic11C22×C412yes—
191C22×Dic11C22×C414yes—
192C22×Dic11C2×D414yes—
193C22×Dic11C2×D414yes—
194C22×Dic11#4114yes—
195C2×C4×D11—216no—
196C2×C4×D11—28no—
197C2×C4×D11—216no—
198C2×C4×D11—28no—
199C2×C4×D11—44no—
200C2×C4×D11—48no—
201C2×C4×D11—48no—
202C2×C4×D11—48no—
203C2×C4×D11—48no—
204C2×C4×D11—48no—
205C2×C4×D11—48no—
206C2×C4×D11—48no—
207C11×C22⋊C4—48no—
208C22⋊Dic11—28no—
209C22⋊Dic11—216no—
210(C2×D11)⋊C4—216no—
211(C2×D11)⋊C4C22⋊C4116yescomplemented
212Dic11⋊C4—28no—
213C4×Dic11—28no—
214C4×Dic11—48no—
215C4×Dic11—48no—
216C22×C4×D4—111no—
217C2×#386—112no—
218C2×C4×C22⋊C4—112no—
219C2×C4×C22⋊C4—111no—
220C22×#95—111no—
221#1437—112no—
222#1436—112no—
223#1434—111no—
224C22⋊#95—111no—
225C22⋊#95D1111yescharacteristic, complemented
226C4×#95—111no—
227C23×C11—22no—
228C23×C11—22no—
229C23×C11—24no—
230C23×C11—24no—
231C23×C11—24no—
232C23×C11—22no—
233C23×C11—22no—
234C23×C11—24no—
235C23×C11—24no—
236C23×C11—22no—
237C23×C11—22no—
238C23×C11—24no—
239C23×C11—42no—
240C23×C11—42no—
241C23×C11—42no—
242C23×C11—41no—
243C23×C11—42no—
244C23×C11—41no—
245C23×C11—42no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11—42no—
249C23×C11C2×C4214yes—
250C23×C11C23×C411yescharacteristic
251C23×C11C23×C412yes—
252C23×C11C22×D412yes—
253C23×C11C22×D411yescharacteristic
254C23×C11C2×#4111yescharacteristic
255C23×C11C2×#4111yescharacteristic
256C23×C11C2×#4111yescharacteristic
257C23×C11C2×#4112yes—
258C23×C11H(5,𝔽2)12yes—
259C23×C11H(5,𝔽2)11yescharacteristic
260C23×C112−1+411yescharacteristic
261C22×D11—22no—
262C22×D11—24no—
263C22×D11—22no—
264C22×D11—24no—
265C22×D11—22no—
266C22×D11—24no—
267C22×D11—22no—
268C22×D11—24no—
269C22×D11—24no—
270C22×D11—22no—
271C22×D11—24no—
272C22×D11—24no—
273C22×D11—24no—
274C22×D11—22no—
275C22×D11—24no—
276C22×D11—22no—
277C22×D11—22no—
278C22×D11—24no—
279C22×D11C2×C4214yes—
280C22×D11C2×C22⋊C414yes—
281C22×D11#11714yes—
282C22×D11C4×D418yes—
283C22×D11C4×D418yes—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
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—24no—
298C2×C4×C11—416no—
299C2×C4×C11—42no—
300C2×C4×C11—42no—
301C2×C4×C11—42no—
302C2×C4×C11—42no—
303C2×C4×C11—42no—
304C2×C4×C11—42no—
305C2×C4×C11—42no—
306C2×C4×C11—42no—
307C2×C4×C11C2×C22⋊C414yes—
308C2×C4×C11C4×D414yes—
309C22⋊D11—232no—
310C2×Dic11—22no—
311C2×Dic11—22no—
312C2×Dic11—24no—
313C2×Dic11—24no—
314C2×Dic11—24no—
315C2×Dic11—22no—
316C2×Dic11—24no—
317C2×Dic11—22no—
318C2×Dic11—24no—
319C2×Dic11—24no—
320C2×Dic11—24no—
321C2×Dic11—24no—
322C2×Dic11—24no—
323C2×Dic11—24no—
324C2×Dic11—22no—
325C2×Dic11—24no—
326C2×Dic11—24no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—24no—
330C2×Dic11—42no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11C2×C4214yes—
337C2×Dic11C2×C22⋊C414yes—
338C2×Dic11C4×D418yescomplemented
339C4×D11—432no—
340C4×D11—416no—
341C23×D4—111no—
342C24×C4—111no—
343C24×C4—112no—
344C24×C4C2×D1111yescharacteristic
345C2×C4×D4—118no—
346C2×C4×D4—228no—
347C22×C4⋊C4—111no—
348C22×C22⋊C4—111no—
349C22×C22⋊C4—111no—
350C22×C22⋊C4—112no—
351C22×C22⋊C4—112no—
352C22×C22⋊C4C2×D1112yes—
353C22×C42—111no—
354C22×C42—112no—
355C22×C42—112no—
356#386—1116no—
357C4×C22⋊C4—228no—
358C4×C22⋊C4—224no—
359C2×#95—112no—
360C2×#95—111no—
361C2×#95—112no—
362C2×#95—111no—
363C2×#95—112no—
364C2×#95—112no—
365C2×#95—112no—
366C2×#95—224no—
367C2×#95C2×D1111yescharacteristic
368C2×#95C2×D1111yescharacteristic
369C2×#95C2×D1112yes—
370C22×C11—24no—
371C22×C11—24no—
372C22×C11—24no—
373C22×C11—42no—
374C22×C11—42no—
375C22×C11—42no—
376C22×C11—42no—
377C22×C11—44no—
378C22×C11—44no—
379C22×C11—44no—
380C22×C11—44no—
381C22×C11C22×C4211yescharacteristic
382C22×C11C22×C22⋊C411yescharacteristic
383C22×C11C2×#11711yescharacteristic
384C22×C11C2×C4×D411yescharacteristic
385C22×C11C2×C4×D412yes—
386C22×C11C2×C4×D412yes—
387C22×C11C2×C4×D412yes—
388C22×C11C4×#4111yescharacteristic
389C22×C11C4×#4112yes—
390C22×C11#51811yescharacteristic
391C22×C11#51812yes—
392C22×C11#52011yescharacteristic
393C22×C11#52012yes—
394C22×C11D4212yes—
395C22×C11#54612yes—
396C22×C11#54612yes—
397C22×C11#54611yescharacteristic
398C22×C11#54712yes—
399C22×C11#54811yescharacteristic
400C22×C11#55112yes—
401C22×C11#55211yescharacteristic
402C22×C11#55311yescharacteristic
403C22×C11#55312yes—
404C2×D11—24no—
405C2×D11—24no—
406C2×D11—24no—
407C2×D11—24no—
408C2×D11—28no—
409C2×D11—28no—
410C2×D11—28no—
411C2×D11—28no—
412C2×D11—24no—
413C2×D11—24no—
414C2×D11C4×C22⋊C418yescomplemented
415C4×C11—24no—
416C4×C11—24no—
417C4×C11—44no—
418C4×C11—44no—
419Dic11—24no—
420Dic11—28no—
421Dic11—24no—
422Dic11—42no—
423Dic11—44no—
424C25—111no—
425C25C22×D1111yescharacteristic
426C22×D4—114no—
427C22×D4—118no—
428C22×D4—224no—
429C22×D4—222no—
430C22×D4—222no—
431C23×C4—24no—
432C23×C4—22no—
433C23×C4—22no—
434C23×C4—42no—
435C23×C4—111no—
436C23×C4—112no—
437C23×C4—111no—
438C23×C4—112no—
439C23×C4—111no—
440C23×C4—114no—
441C23×C4—118no—
442C23×C4—224no—
443C23×C4—224no—
444C23×C4—224no—
445C23×C4—224no—
446C23×C4—224no—
447C23×C4—222no—
448C23×C4—222no—
449C23×C4—442no—
450C23×C4—442no—
451C23×C4—442no—
452C23×C4C4×D1114yescomplemented
453C23×C4C22×D1112yes—
454C23×C4C22×D1112yes—
455C23×C4C22×D1111yescharacteristic
456C23×C4C22×D1111yescharacteristic
457C4×D4—2232no—
458C2×C4⋊C4—114no—
459C2×C4⋊C4—224no—
460C2×C22⋊C4—42no—
461C2×C22⋊C4—42no—
462C2×C22⋊C4—114no—
463C2×C22⋊C4—118no—
464C2×C22⋊C4—114no—
465C2×C22⋊C4—118no—
466C2×C22⋊C4—118no—
467C2×C22⋊C4—224no—
468C2×C22⋊C4—224no—
469C2×C22⋊C4—224no—
470C2×C22⋊C4—224no—
471C2×C22⋊C4—224no—
472C2×C22⋊C4C4×D1118yescomplemented
473C2×C42—114no—
474C2×C42—224no—
475C2×C42—224no—
476C2×C42—224no—
477C2×C42—224no—
478C2×C42—224no—
479C2×C42—442no—
480C2×C42—442no—
481#95—22no—
482#95—24no—
483#95—22no—
484#95—118no—
485#95—118no—
486#95—114no—
487#95—224no—
488#95—224no—
489#95—222no—
490#95—442no—
491C2×C11—44no—
492C2×C11C2×C4×C22⋊C411yescharacteristic
493C2×C11C42×D411yescharacteristic
494C2×C11#227511yescharacteristic
495C2×C11D4×C22⋊C411yescharacteristic
496C2×C11#233911yescharacteristic
497C2×C11#235211yescharacteristic
498C2×C11#235311yescharacteristic
499C2×C11#235812yes—
500C2×C11#235912yes—
501C2×C11#236112yes—
502C2×C11#236412yes—
503D11—28no—
504C24—21no—
505C24—22no—
506C24—21no—
507C24—21no—
508C24—22no—
509C24—21no—
510C24—22no—
511C24—21no—
512C24—21no—
513C24—112no—
514C24—114no—
515C24—114no—
516C24—112no—
517C24—112no—
518C24—221no—
519C24—221no—
520C24—222no—
521C24—221no—
522C24—221no—
523C24—222no—
524C24C2×C4×D1114yes—
525C24C2×C4×D1112yes—
526C24C23×D1111yescharacteristic
527C2×D4—1116no—
528C2×D4—228no—
529C2×D4—228no—
530C2×D4—2216no—
531C2×D4—2216no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—28no—
550C22×C4—28no—
551C22×C4—44no—
552C22×C4—48no—
553C22×C4—48no—
554C22×C4—114no—
555C22×C4—114no—
556C22×C4—112no—
557C22×C4—112no—
558C22×C4—114no—
559C22×C4—114no—
560C22×C4—114no—
561C22×C4—114no—
562C22×C4—112no—
563C22×C4—2216no—
564C22×C4—228no—
565C22×C4—2216no—
566C22×C4—222no—
567C22×C4—222no—
568C22×C4—221no—
569C22×C4—222no—
570C22×C4—222no—
571C22×C4—221no—
572C22×C4—222no—
573C22×C4—222no—
574C22×C4—221no—
575C22×C4—221no—
576C22×C4—221no—
577C22×C4—222no—
578C22×C4—222no—
579C22×C4—222no—
580C22×C4—221no—
581C22×C4—222no—
582C22×C4—222no—
583C22×C4—222no—
584C22×C4—222no—
585C22×C4—222no—
586C22×C4—228no—
587C22×C4—444no—
588C22×C4—448no—
589C22×C4—448no—
590C22×C4—448no—
591C22×C4—448no—
592C22×C4—448no—
593C22×C4—448no—
594C22×C4—448no—
595C22×C4C2×C4×D1114yes—
596C22×C4C2×C4×D1114yes—
597C22×C4C2×C4×D1112yes—
598C22×C4C2×C4×D1112yes—
599C22×C4D4×D1114yes—
600C22×C4D4×D1112yes—
601C22×C4#434112yes—
602C4⋊C4—228no—
603C22⋊C4—48no—
604C22⋊C4—1116no—
605C22⋊C4—2216no—
606C22⋊C4—228no—
607C22⋊C4—2216no—
608C42—228no—
609C42—448no—
610C42—448no—
611C11#1381311yescharacteristic, complemented, Sylow
612C23—22no—
613C23—22no—
614C23—24no—
615C23—22no—
616C23—24no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—41no—
628C23—41no—
629C23—42no—
630C23—41no—
631C23—41no—
632C23—42no—
633C23—42no—
634C23—114no—
635C23—114no—
636C23—114no—
637C23—118no—
638C23—118no—
639C23—222no—
640C23—224no—
641C23—222no—
642C23—224no—
643C23—222no—
644C23—222no—
645C23—224no—
646C23—224no—
647C23—224no—
648C23—224no—
649C23—222no—
650C23—224no—
651C23—222no—
652C23—224no—
653C23—222no—
654C23—222no—
655C23—224no—
656C23—224no—
657C23C42×D1114yes—
658C23C22×C4×D1111yescharacteristic
659C23C22×C4×D1112yes—
660C23C2×D4×D1112yes—
661C23C2×D4×D1111yescharacteristic
662C23C2×#434111yescharacteristic
663C23#6703712yes—
664C23#6703711yescharacteristic
665C23#6704011yescharacteristic
666C23#41×D1111yescharacteristic
667C23#41×D1111yescharacteristic
668C23#41×D1112yes—
669D4—2232no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—416no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—114no—
694C2×C4—114no—
695C2×C4—118no—
696C2×C4—222no—
697C2×C4—224no—
698C2×C4—222no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—224no—
702C2×C4—224no—
703C2×C4—224no—
704C2×C4—224no—
705C2×C4—224no—
706C2×C4—224no—
707C2×C4—224no—
708C2×C4—224no—
709C2×C4—224no—
710C2×C4—222no—
711C2×C4—222no—
712C2×C4—222no—
713C2×C4—224no—
714C2×C4—224no—
715C2×C4—224no—
716C2×C4—4416no—
717C2×C4—4432no—
718C2×C4—442no—
719C2×C4—442no—
720C2×C4—442no—
721C2×C4—442no—
722C2×C4—442no—
723C2×C4—442no—
724C2×C4C22⋊C4×D1114yes—
725C2×C4(C22⋊D11)⋊C414yes—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—44no—
730C22—44no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—44no—
736C22—44no—
737C22—118no—
738C22—228no—
739C22—228no—
740C22—224no—
741C22—224no—
742C22—224no—
743C22—224no—
744C22—224no—
745C22—224no—
746C22—228no—
747C22—228no—
748C22C2×C42×D1111yescharacteristic
749C22C2×C22⋊C4×D1111yescharacteristic
750C22C2×(C22⋊D11)⋊C411yescharacteristic
751C22#1062301712yes—
752C22#1062301711yescharacteristic
753C22#1062303512yes—
754C22#1062303511yescharacteristic
755C22D11×#11711yescharacteristic
756C22#1062305311yescharacteristic
757C22C4×#434112yes—
758C22C4×D4×D1112yes—
759C22C4×D4×D1112yes—
760C22C4×D4×D1112yes—
761C22#1062312112yes—
762C22#1062312212yes—
763C22#1062314312yes—
764C22#1062314311yescharacteristic
765C22#1062314511yescharacteristic
766C22#1062316212yes—
767C22#1062316411yescharacteristic
768C22#1062317011yescharacteristic
769C22#1062319012yes—
770C22#1062319212yes—
771C4—24no—
772C4—24no—
773C4—44no—
774C4—44no—
775C4—224no—
776C4—224no—
777C4—228no—
778C4—444no—
779C4—442no—
780C2—44no—
781C2—228no—
782C2C4×C22⋊C4×D1111yescharacteristic
783C2C4×(C22⋊D11)⋊C411yescharacteristic
784C2#1307097411yescharacteristic
785C2#1307143211yescharacteristic
786C2#1307144411yescharacteristic
787C2#1307153811yescharacteristic
788C2#1307155311yescharacteristic
789C2#1307159912yes—
790C2#1307161112yes—
791C2#1307163512yes—
792C2#1307166512yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC22⋊#95D11
hypocenterC11#13813
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×C4×C22⋊Dic11C2semidirect
4. C2×#10622279C2semidirect
5. C2×D11×#95C2semidirect
6. #13066853C2semidirect
7. #13066851C2semidirect
8. #13066842C2semidirect
9. (C2×D11)⋊#95C2semidirect
10. #95×Dic11C2semidirect
11. C11×C22⋊#95C2semidirect
20. C2×C4×C22⋊D11C4semidirect
38. #10622569C4semidirect
47. C23×C4×C11C2×C4semidirect
73. C22×C4×D11C2×C4semidirect
76. C2×C11×C22⋊C4C2×C4semidirect
80. C2×C22⋊Dic11C2×C4semidirect
81. C2×C22⋊Dic11C2×C4semidirect
86. C2×(C2×D11)⋊C4C2×C4semidirect
89. C2×Dic11⋊C4C2×C4semidirect
97. C2×C4×Dic11C2×C4semidirect
105. C11⋊#95C2×C4semidirect
106. C11⋊#95C2×C4semidirect
107. C11⋊#95D4semidirect
165. C2×C22⋊D11C42semidirect
211. (C2×D11)⋊C4C22⋊C4semidirect
225. C22⋊#95D11semidirect
338. C2×Dic11C4×D4semidirect
414. C2×D11C4×C22⋊C4semidirect
452. C23×C4C4×D11semidirect
472. C2×C22⋊C4C4×D11semidirect
611. C11#13813semidirect

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×#106225692
C2×C4×C22⋊Dic112
C2×#106222792
C2×D11×#952
#130668532
#130668512
#130668422
(C2×D11)⋊#952
#95×Dic112
C11×C22⋊#952
#1381311