Finite Group Databasebeta

← #14675270

Subgroups — #14675270

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×(C2×D11)⋊C4C212yesmaximal, complemented
4C2×D11×#95C211yesmaximal, characteristic, complemented
5#13066853C212yesmaximal, complemented
6#13066849C212yesmaximal, complemented
7#13066842C211yesmaximal, 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
15C23×C4×D11C2212yes—
16C22×C11×C22⋊C4C2212yes—
17C22×C42×C11C2212yes—
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C22⋊Dic11C2212yes—
20C2×C4×C22⋊D11—28no—
21C2×C4×C22⋊D11C418yescomplemented
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×Dic11⋊C4C2211yescharacteristic
25C22×C4×Dic11C2212yes—
26C22×C4×Dic11C2211yescharacteristic
27C4×C11×C22⋊C4—24no—
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2211yescharacteristic
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38#10622569C4116yescomplemented
39C4×(C2×D11)⋊C4—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×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×Dic11C2311yescharacteristic
59C23×Dic11C2312yes—
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2311yescharacteristic
62C22×C4×D11—24no—
63C22×C4×D11—24no—
64C22×C4×D11—24no—
65C22×C4×D11—22no—
66C22×C4×D11—24no—
67C22×C4×D11—22no—
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—24no—
75C2×C11×C22⋊C4—24no—
76C2×C11×C22⋊C4C2×C418yescomplemented
77C2×C42×C11—24no—
78C2×C42×C11—24no—
79C2×C42×C11—42no—
80C2×C22⋊Dic11—24no—
81C2×C22⋊Dic11—42no—
82C2×C22⋊Dic11—42no—
83C2×C22⋊Dic11C2×C414yescomplemented
84C2×C22⋊Dic11C2×C418yescomplemented
85C4×C22⋊D11—232no—
86C2×(C2×D11)⋊C4—24no—
87C2×(C2×D11)⋊C4—24no—
88C2×(C2×D11)⋊C4C2×C414yes—
89C2×(C2×D11)⋊C4C2×C418yescomplemented
90C2×(C2×D11)⋊C4D418yes—
91C2×Dic11⋊C4—24no—
92C2×Dic11⋊C4C2×C414yescomplemented
93C2×C4×Dic11—24no—
94C2×C4×Dic11—24no—
95C2×C4×Dic11—24no—
96C2×C4×Dic11—42no—
97C2×C4×Dic11C2×C414yescomplemented
98C11×#95—22no—
99C11×#95D414yescomplemented
100C11⋊#95—22no—
101C11⋊#95—24no—
102C11⋊#95—24no—
103C11⋊#95—22no—
104C11⋊#95—24no—
105C11⋊#95—42no—
106C11⋊#95C2×C418yescomplemented
107C11⋊#95C2×C418yescomplemented
108#13813—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×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—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—22no—
167C22×Dic11—22no—
168C22×Dic11—21no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—21no—
174C22×Dic11—21no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—21no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—21no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—21no—
188C22×Dic11C22×C414yes—
189C22×Dic11C22×C414yes—
190C22×Dic11C22×C412yes—
191C22×Dic11C22×C414yes—
192C22×Dic11C22×C412yes—
193C22×Dic11C22×C412yes—
194C22×Dic11C2×D414yes—
195C2×C4×D11—28no—
196C2×C4×D11—216no—
197C2×C4×D11—28no—
198C2×C4×D11—216no—
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—216no—
208C42×C11—48no—
209C22⋊Dic11—28no—
210C22⋊Dic11—48no—
211(C2×D11)⋊C4—216no—
212(C2×D11)⋊C4C22⋊C4116yescomplemented
213Dic11⋊C4—28no—
214C4×Dic11—28no—
215C4×Dic11—48no—
216C22×C4×D4—111no—
217C2×#386—112no—
218C2×C4×C22⋊C4—112no—
219C2×C4×C22⋊C4D1111yescharacteristic, complemented
220C22×#95—111no—
221#1437—112no—
222#1436—112no—
223#1434—111no—
224C22⋊#95—111no—
225C22⋊#95—111no—
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×#4112yes—
256C23×C11C2×#4111yescharacteristic
257C23×C11C2×#4111yescharacteristic
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—24no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—24no—
289C2×C4×C11—22no—
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—24no—
299C2×C4×C11—24no—
300C2×C4×C11—24no—
301C2×C4×C11—416no—
302C2×C4×C11—42no—
303C2×C4×C11—42no—
304C2×C4×C11—42no—
305C2×C4×C11—42no—
306C2×C4×C11C2×C22⋊C414yes—
307C2×C4×C11C4×D414yes—
308C2×C4×C11C4×D418yescomplemented
309C22⋊D11—232no—
310C2×Dic11—22no—
311C2×Dic11—22no—
312C2×Dic11—24no—
313C2×Dic11—24no—
314C2×Dic11—22no—
315C2×Dic11—22no—
316C2×Dic11—24no—
317C2×Dic11—24no—
318C2×Dic11—22no—
319C2×Dic11—24no—
320C2×Dic11—22no—
321C2×Dic11—24no—
322C2×Dic11—24no—
323C2×Dic11—24no—
324C2×Dic11—24no—
325C2×Dic11—24no—
326C2×Dic11—22no—
327C2×Dic11—42no—
328C2×Dic11—42no—
329C2×Dic11—42no—
330C2×Dic11—42no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11—42no—
337C2×Dic11C2×C4214yes—
338C2×Dic11C2×C22⋊C414yes—
339C4×D11—416no—
340C4×D11—432no—
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×C42C2×D1112yes—
356#386—1116no—
357C4×C22⋊C4—24no—
358C4×C22⋊C4—228no—
359C2×#95—112no—
360C2×#95—112no—
361C2×#95—111no—
362C2×#95—111no—
363C2×#95—112no—
364C2×#95—112no—
365C2×#95—112no—
366C2×#95—112no—
367C2×#95—224no—
368C2×#95C2×D1111yescharacteristic
369C2×#95C2×D1111yescharacteristic
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—28no—
418C4×C11—44no—
419Dic11—24no—
420Dic11—24no—
421Dic11—42no—
422Dic11—44no—
423Dic11—44no—
424C25—111no—
425C25C22×D1111yescharacteristic
426C22×D4—114no—
427C22×D4—118no—
428C22×D4—224no—
429C22×D4—222no—
430C22×D4—222no—
431C23×C4—22no—
432C23×C4—24no—
433C23×C4—22no—
434C23×C4—42no—
435C23×C4—111no—
436C23×C4—111no—
437C23×C4—112no—
438C23×C4—111no—
439C23×C4—112no—
440C23×C4—114no—
441C23×C4—118no—
442C23×C4—224no—
443C23×C4—224no—
444C23×C4—224no—
445C23×C4—222no—
446C23×C4—224no—
447C23×C4—222no—
448C23×C4—224no—
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—24no—
461C2×C22⋊C4—24no—
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—442no—
471C2×C22⋊C4—442no—
472C2×C22⋊C4C4×D1118yescomplemented
473C2×C42—24no—
474C2×C42—24no—
475C2×C42—42no—
476C2×C42—114no—
477C2×C42—224no—
478C2×C42—224no—
479C2×C42—224no—
480C2×C42—442no—
481#95—22no—
482#95—118no—
483#95—118no—
484#95—224no—
485#95—222no—
486#95—224no—
487#95—222no—
488#95—224no—
489#95—442no—
490#95C22⋊D1114yescomplemented
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—22no—
505C24—21no—
506C24—22no—
507C24—22no—
508C24—21no—
509C24—21no—
510C24—21no—
511C24—21no—
512C24—21no—
513C24—112no—
514C24—114no—
515C24—114no—
516C24—112no—
517C24—112no—
518C24—221no—
519C24—222no—
520C24—222no—
521C24—221no—
522C24—221no—
523C24—221no—
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—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—28no—
548C22×C4—28no—
549C22×C4—44no—
550C22×C4—48no—
551C22×C4—48no—
552C22×C4—114no—
553C22×C4—112no—
554C22×C4—112no—
555C22×C4—114no—
556C22×C4—114no—
557C22×C4—114no—
558C22×C4—112no—
559C22×C4—228no—
560C22×C4—2216no—
561C22×C4—222no—
562C22×C4—222no—
563C22×C4—221no—
564C22×C4—221no—
565C22×C4—221no—
566C22×C4—221no—
567C22×C4—222no—
568C22×C4—222no—
569C22×C4—221no—
570C22×C4—222no—
571C22×C4—222no—
572C22×C4—222no—
573C22×C4—222no—
574C22×C4—222no—
575C22×C4—222no—
576C22×C4—222no—
577C22×C4—222no—
578C22×C4—222no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4—221no—
582C22×C4—222no—
583C22×C4—228no—
584C22×C4—2216no—
585C22×C4—444no—
586C22×C4—448no—
587C22×C4—448no—
588C22×C4—448no—
589C22×C4—448no—
590C22×C4—448no—
591C22×C4—448no—
592C22×C4—448no—
593C22×C4C2×C4×D1114yes—
594C22×C4C2×C4×D1112yes—
595C22×C4C2×C4×D1112yes—
596C22×C4C2×C4×D1114yes—
597C22×C4#433912yes—
598C22×C4#433914yes—
599C22×C4D4×D1114yes—
600C22×C4C2×C22⋊D1112yes—
601C22×C4C2×C22⋊D1114yes—
602C4⋊C4—228no—
603C22⋊C4—216no—
604C22⋊C4—1116no—
605C22⋊C4—2216no—
606C22⋊C4—228no—
607C22⋊C4—448no—
608C42—48no—
609C42—228no—
610C42—448no—
611C11#1381311yescharacteristic, complemented, Sylow
612C23—24no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—24no—
619C23—22no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—42no—
625C23—41no—
626C23—41no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—41no—
633C23—41no—
634C23—114no—
635C23—114no—
636C23—114no—
637C23—118no—
638C23—118no—
639C23—224no—
640C23—222no—
641C23—222no—
642C23—224no—
643C23—222no—
644C23—222no—
645C23—222no—
646C23—224no—
647C23—222no—
648C23—224no—
649C23—224no—
650C23—224no—
651C23—224no—
652C23—224no—
653C23—224no—
654C23—224no—
655C23—222no—
656C23—222no—
657C23C42×D1114yes—
658C23C22×C4×D1111yescharacteristic
659C23C22×C4×D1112yes—
660C23C2×#433911yescharacteristic
661C23C2×#433912yes—
662C23C2×D4×D1112yes—
663C23#6703712yes—
664C23#41×D1111yescharacteristic
665C23#41×D1111yescharacteristic
666C23#6704211yescharacteristic
667C23#6704311yescharacteristic
668C23C22×C22⋊D1111yescharacteristic
669D4—2232no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—22no—
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—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—416no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—114no—
693C2×C4—114no—
694C2×C4—222no—
695C2×C4—222no—
696C2×C4—222no—
697C2×C4—222no—
698C2×C4—224no—
699C2×C4—224no—
700C2×C4—224no—
701C2×C4—224no—
702C2×C4—224no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—222no—
706C2×C4—224no—
707C2×C4—224no—
708C2×C4—224no—
709C2×C4—224no—
710C2×C4—224no—
711C2×C4—4416no—
712C2×C4—4432no—
713C2×C4—442no—
714C2×C4—442no—
715C2×C4—442no—
716C2×C4—442no—
717C2×C4—442no—
718C2×C4—442no—
719C2×C4—442no—
720C2×C4—442no—
721C2×C4—442no—
722C2×C4—442no—
723C2×C4C22⋊C4×D1114yes—
724C2×C4C4×C22⋊D1114yes—
725C2×C4C4×C22⋊D1118yescomplemented
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
749C22C4×#433912yes—
750C22C4×#433911yescharacteristic
751C22C2×C22⋊C4×D1111yescharacteristic
752C22#1062301711yescharacteristic
753C22#1062302112yes—
754C22D11×#11711yescharacteristic
755C22#1062305411yescharacteristic
756C22#1062306011yescharacteristic
757C22#1062306111yescharacteristic
758C22C4×D4×D1112yes—
759C22C4×D4×D1112yes—
760C22#1062307612yes—
761C22#1062307712yes—
762C22#1062308112yes—
763C22#1062308212yes—
764C22#1062308712yes—
765C22#1062308912yes—
766C22C2×C4×C22⋊D1112yes—
767C22C2×C4×C22⋊D1111yescharacteristic
768C22D4×C22⋊D1112yes—
769C22#1062336011yescharacteristic
770C22#1062336211yescharacteristic
771C4—24no—
772C4—24no—
773C4—28no—
774C4—44no—
775C4—224no—
776C4—224no—
777C4—444no—
778C4—442no—
779C4—444no—
780C2—44no—
781C2—228no—
782C2C4×C22⋊C4×D1111yescharacteristic
783C2C42×C22⋊D1111yescharacteristic
784C2#1307097511yescharacteristic
785C2C22⋊C4×C22⋊D1111yescharacteristic
786C2#1307144711yescharacteristic
787C2#1307154611yescharacteristic
788C2#1307155911yescharacteristic
789C2#1307159312yes—
790C2#1307160912yes—
791C2#1307162812yes—
792C2#1307166712yes—
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#13813
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×(C2×D11)⋊C4C2semidirect
4. C2×D11×#95C2semidirect
5. #13066853C2semidirect
6. #13066849C2semidirect
7. #13066842C2semidirect
8. #13066839C2semidirect
9. (C2×D11)⋊#95C2semidirect
10. #95×Dic11C2semidirect
11. C2×C4×C11×C22⋊C4C2semidirect
21. C2×C4×C22⋊D11C4semidirect
38. #10622569C4semidirect
47. C23×C4×C11C2×C4semidirect
73. C22×C4×D11C2×C4semidirect
76. C2×C11×C22⋊C4C2×C4semidirect
83. C2×C22⋊Dic11C2×C4semidirect
84. C2×C22⋊Dic11C2×C4semidirect
89. C2×(C2×D11)⋊C4C2×C4semidirect
92. C2×Dic11⋊C4C2×C4semidirect
97. C2×C4×Dic11C2×C4semidirect
99. C11×#95D4semidirect
106. C11⋊#95C2×C4semidirect
107. C11⋊#95C2×C4semidirect
165. C2×C22⋊D11C42semidirect
212. (C2×D11)⋊C4C22⋊C4semidirect
219. C2×C4×C22⋊C4D11semidirect
308. C2×C4×C11C4×D4semidirect
414. C2×D11C4×C22⋊C4semidirect
452. C23×C4C4×D11semidirect
472. C2×C22⋊C4C4×D11semidirect
490. #95C22⋊D11semidirect
611. C11#13813semidirect
725. 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×#106225692
C2×C4×(C2×D11)⋊C42
C2×D11×#952
#130668532
#130668492
#130668422
#130668392
(C2×D11)⋊#952
#95×Dic112
C2×C4×C11×C22⋊C42
#1381311