Finite Group Databasebeta

← #14676551

Subgroups — #14676551

Order 2816.

2742 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66982C211yesmaximal, characteristic
2C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic
3C2×#10622571C211yesmaximal, characteristic
4C22×C11⋊#95C211yesmaximal, characteristic, complemented
5#13066867C212yesmaximal, complemented
6#13066864C212yesmaximal, complemented
7#13066847C212yesmaximal, complemented
8#13066838C211yesmaximal, characteristic, complemented
9#13066838C211yesmaximal, characteristic, complemented
10(C2×D11)⋊#95C212yesmaximal, complemented
11C2×C11×#381C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C23×C22⋊D11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C24×Dic11C2211yescharacteristic
16C23×C4×D11C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C2×#66982—24no—
21C2×#66982—24no—
22C2×#66982C418yescomplemented
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2212yes—
28C22×C4×Dic11C2211yescharacteristic
29C2×(C22⋊D11)⋊C4—24no—
30C2×(C22⋊D11)⋊C4—24no—
31C2×(C22⋊D11)⋊C4—24no—
32C11×#381—24no—
33C2×C11×#95C2212yes—
34C2×C11×#95C2212yes—
35C2×C11⋊#95—24no—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43#10622571—24no—
44C25×C11C2311yescharacteristic
45C24×D11C2311yescharacteristic
46C23×C4×C11—22no—
47C23×C4×C11—22no—
48C23×C4×C11—22no—
49C23×C4×C11—22no—
50C23×C4×C11—22no—
51C23×C4×C11—22no—
52C23×C4×C11C2×C414yescomplemented
53C23×C4×C11C2312yes—
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C22×C22⋊D11—22no—
58C22×C22⋊D11—22no—
59C22×C22⋊D11—22no—
60C22×C22⋊D11—22no—
61C22×C22⋊D11C2×C414yes—
62C22×C22⋊D11D414yes—
63C22×C22⋊D11D414yes—
64C23×Dic11—22no—
65C23×Dic11—22no—
66C23×Dic11—22no—
67C23×Dic11—24no—
68C23×Dic11—24no—
69C23×Dic11—22no—
70C23×Dic11—22no—
71C23×Dic11—42no—
72C23×Dic11—42no—
73C23×Dic11D414yes—
74C23×Dic11C2312yes—
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2312yes—
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C22×C4×D11—22no—
80C22×C4×D11—22no—
81C22×C4×D11—22no—
82C22×C4×D11—24no—
83C22×C4×D11—42no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4D414yes—
90C2×C22⋊Dic11—22no—
91C2×C22⋊Dic11—22no—
92C2×C22⋊Dic11C2×C414yescomplemented
93#66982—232no—
94C2×(C2×D11)⋊C4—22no—
95C2×(C2×D11)⋊C4—24no—
96C2×(C2×D11)⋊C4—24no—
97C2×(C2×D11)⋊C4—22no—
98C2×(C2×D11)⋊C4—22no—
99C2×(C2×D11)⋊C4—24no—
100C2×(C2×D11)⋊C4—24no—
101C2×(C2×D11)⋊C4—42no—
102C2×(C2×D11)⋊C4C2×C418yescomplemented
103C2×Dic11⋊C4—22no—
104C2×Dic11⋊C4—22no—
105C2×Dic11⋊C4—22no—
106C2×Dic11⋊C4—24no—
107C2×Dic11⋊C4—24no—
108C2×Dic11⋊C4C2×C418yescomplemented
109C2×C4×Dic11—22no—
110C2×C4×Dic11—22no—
111C2×C4×Dic11—22no—
112(C22⋊D11)⋊C4—232no—
113C11×#95—24no—
114C11×#95—24no—
115C11⋊#95—24no—
116C11⋊#95—24no—
117C11⋊#95—24no—
118C11⋊#95—24no—
119C11⋊#95—24no—
120C11⋊#95—42no—
121C11⋊#95—42no—
122#13968—111nomaximal, Sylow
123C24×C11—22no—
124C24×C11—22no—
125C24×C11—22no—
126C24×C11—22no—
127C24×C11C22×C412yes—
128C24×C11C2×D412yes—
129C24×C11C2×D412yes—
130C24×C11C2×D412yes—
131C24×C11C2×D412yes—
132C24×C11#4112yes—
133C24×C11#4112yes—
134C24×C11C2411yescharacteristic
135C23×D11—21no—
136C23×D11—21no—
137C23×D11—22no—
138C23×D11—22no—
139C23×D11—21no—
140C23×D11—21no—
141C23×D11—22no—
142C23×D11—22no—
143C23×D11C22×C412yes—
144C23×D11C2×D412yes—
145C23×D11C2×D412yes—
146C22×C4×C11—28no—
147C22×C4×C11—28no—
148C22×C4×C11—28no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—44no—
171C22×C4×C11—44no—
172C22×C4×C11—44no—
173C22×C4×C11—44no—
174C22×C4×C11C22×C414yes—
175C22×C4×C11C2×D412yes—
176C22×C4×C11C2×D412yes—
177C2×C22⋊D11—28no—
178C2×C22⋊D11—28no—
179C2×C22⋊D11—28no—
180C2×C22⋊D11—28no—
181C2×C22⋊D11—28no—
182C2×C22⋊D11—28no—
183C2×C22⋊D11C22⋊C4116yes—
184C22×Dic11—28no—
185C22×Dic11—28no—
186C22×Dic11—28no—
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11—21no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—22no—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—22no—
200C22×Dic11—22no—
201C22×Dic11—22no—
202C22×Dic11—22no—
203C22×Dic11—22no—
204C22×Dic11—22no—
205C22×Dic11—22no—
206C22×Dic11—22no—
207C22×Dic11—22no—
208C22×Dic11—22no—
209C22×Dic11—22no—
210C22×Dic11—44no—
211C22×Dic11—48no—
212C22×Dic11—48no—
213C22×Dic11—48no—
214C22×Dic11—48no—
215C22×Dic11—44no—
216C22×Dic11—44no—
217C22×Dic11C22×C414yes—
218C22×Dic11C22×C412yes—
219C22×Dic11C2×D412yes—
220C22×Dic11C2×D412yes—
221C22×Dic11C2×D412yes—
222C22×Dic11C2×D412yes—
223C22×Dic11#4114yes—
224C22×Dic11#4114yes—
225C2×C4×D11—28no—
226C2×C4×D11—48no—
227C2×C4×D11—48no—
228C2×C4×D11—44no—
229C2×C4×D11—44no—
230C11×C22⋊C4—28no—
231C11×C22⋊C4—44no—
232C22⋊Dic11—28no—
233(C2×D11)⋊C4—28no—
234(C2×D11)⋊C4—216no—
235(C2×D11)⋊C4—48no—
236Dic11⋊C4—28no—
237Dic11⋊C4—216no—
238C4×Dic11—28no—
239C22×#123—111no—
240C22×C4×D4—111no—
241C2×#386—111no—
242C2×#381D1111yescharacteristic, complemented
243C22×#95—111no—
244#1441—112no—
245#1440—112no—
246#1436—112no—
247C22⋊#95—112no—
248C22⋊#95—111no—
249C22⋊#95—111no—
250C23×C11—24no—
251C23×C11—24no—
252C23×C11—22no—
253C23×C11—22no—
254C23×C11—24no—
255C23×C11—22no—
256C23×C11—22no—
257C23×C11—24no—
258C23×C11—24no—
259C23×C11—24no—
260C23×C11—24no—
261C23×C11—24no—
262C23×C11—24no—
263C23×C11—24no—
264C23×C11—24no—
265C23×C11—24no—
266C23×C11C2×C22⋊C414yes—
267C23×C11C4×D414yes—
268C23×C11C4×D414yes—
269C23×C11#12014yes—
270C23×C11#12114yes—
271C23×C11#12114yes—
272C23×C11#12314yes—
273C23×C11C23×C411yescharacteristic
274C23×C11C22×D411yescharacteristic
275C23×C11C22×D411yescharacteristic
276C23×C11C22×D411yescharacteristic
277C23×C11C22×D411yescharacteristic
278C23×C11C2×#4111yescharacteristic
279C23×C11C2×#4111yescharacteristic
280C23×C11C2×#4112yes—
281C23×C11C2×#4112yes—
282C23×C11H(5,𝔽2)12yes—
283C23×C112−1+412yes—
284C22×D11—22no—
285C22×D11—22no—
286C22×D11—24no—
287C22×D11—24no—
288C22×D11—22no—
289C22×D11—22no—
290C22×D11—22no—
291C22×D11—22no—
292C22×D11—24no—
293C22×D11—24no—
294C22×D11—24no—
295C22×D11—24no—
296C22×D11—41no—
297C22×D11—41no—
298C22×D11—42no—
299C22×D11—41no—
300C22×D11—41no—
301C22×D11—42no—
302C22×D11—42no—
303C22×D11—42no—
304C22×D11—42no—
305C22×D11—42no—
306C22×D11C2×C22⋊C414yes—
307C2×C4×C11—24no—
308C2×C4×C11—24no—
309C2×C4×C11—24no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—24no—
313C2×C4×C11—24no—
314C2×C4×C11—42no—
315C2×C4×C11—42no—
316C2×C4×C11—42no—
317C2×C4×C11—41no—
318C2×C4×C11—42no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—42no—
323C2×C4×C11—42no—
324C2×C4×C11—416no—
325C2×C4×C11—42no—
326C2×C4×C11—42no—
327C2×C4×C11—42no—
328C2×C4×C11—42no—
329C2×C4×C11—42no—
330C2×C4×C11—42no—
331C2×C4×C11—42no—
332C22⋊D11—232no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—24no—
342C2×Dic11—24no—
343C2×Dic11—24no—
344C2×Dic11—24no—
345C2×Dic11—24no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—24no—
349C2×Dic11—22no—
350C2×Dic11—24no—
351C2×Dic11—24no—
352C2×Dic11—416no—
353C2×Dic11—416no—
354C2×Dic11—42no—
355C2×Dic11—42no—
356C2×Dic11—42no—
357C2×Dic11—42no—
358C2×Dic11—42no—
359C2×Dic11—42no—
360C2×Dic11—42no—
361C2×Dic11—42no—
362C2×Dic11—42no—
363C2×Dic11—42no—
364C2×Dic11C2×C22⋊C414yes—
365C2×Dic11#12314yescomplemented
366C4×D11—416no—
367C23×D4—111no—
368C24×C4—111no—
369C24×C4—111no—
370C24×C4—111no—
371C24×C4C2×D1111yescharacteristic
372C2×#123—118no—
373C2×#123—224no—
374C2×#123—224no—
375C2×C4×D4—224no—
376C2×C4×D4—224no—
377C2×C4×D4—224no—
378C22×C4⋊C4—112no—
379C22×C4⋊C4—111no—
380C22×C22⋊C4—111no—
381C22×C22⋊C4—112no—
382C22×C22⋊C4—111no—
383C22×C22⋊C4—112no—
384C22×C22⋊C4C2×D1111yescharacteristic
385C22×C22⋊C4C2×D1111yescharacteristic
386C22×C42—111no—
387#386—224no—
388#381—24no—
389C2×#95—112no—
390C2×#95—112no—
391C2×#95—112no—
392C2×#95—112no—
393C2×#95—112no—
394C2×#95—112no—
395C2×#95—112no—
396C2×#95—224no—
397C2×#95C2×D1112yes—
398C2×#95C2×D1112yes—
399C22×C11—24no—
400C22×C11—28no—
401C22×C11—28no—
402C22×C11—24no—
403C22×C11—24no—
404C22×C11—28no—
405C22×C11—28no—
406C22×C11—24no—
407C22×C11—24no—
408C22×C11—24no—
409C22×C11#38618yes—
410C22×C11C22×C22⋊C411yescharacteristic
411C22×C11C2×C4×D411yescharacteristic
412C22×C11C2×C4×D411yescharacteristic
413C22×C11C4×#4112yes—
414C22×C11#52012yes—
415C22×C11C2×#12011yescharacteristic
416C22×C11C2×#12111yescharacteristic
417C22×C11C2×#12111yescharacteristic
418C22×C11C2×#12311yescharacteristic
419C22×C11C2×#12311yescharacteristic
420C22×C11#52511yescharacteristic
421C22×C11#52912yes—
422C22×C11#53411yescharacteristic
423C22×C11#53611yescharacteristic
424C22×C11#53912yes—
425C22×C11#54612yes—
426C22×C11#54612yes—
427C22×C11#54612yes—
428C22×C11#54712yes—
429C22×C11#54712yes—
430C22×C11#54712yes—
431C22×C11#55112yes—
432C22×C11#55212yes—
433C2×D11—28no—
434C2×D11—24no—
435C2×D11—42no—
436C2×D11—44no—
437C2×D11—42no—
438C2×D11—42no—
439C2×D11—44no—
440C2×D11—44no—
441C2×D11—42no—
442C2×D11—42no—
443C2×D11—42no—
444C4×C11—42no—
445C4×C11—42no—
446C4×C11—44no—
447C4×C11—82no—
448Dic11—24no—
449Dic11—24no—
450Dic11—44no—
451Dic11—42no—
452Dic11—44no—
453C25—111no—
454C25C22×D1111yescharacteristic
455C22×D4—114no—
456C22×D4—114no—
457C22×D4—114no—
458C22×D4—222no—
459C22×D4—222no—
460C22×D4—222no—
461C22×D4—222no—
462C23×C4—22no—
463C23×C4—22no—
464C23×C4—22no—
465C23×C4—22no—
466C23×C4—22no—
467C23×C4—22no—
468C23×C4—111no—
469C23×C4—111no—
470C23×C4—112no—
471C23×C4—111no—
472C23×C4—112no—
473C23×C4—114no—
474C23×C4—222no—
475C23×C4—224no—
476C23×C4—222no—
477C23×C4—224no—
478C23×C4—224no—
479C23×C4—222no—
480C23×C4—222no—
481C23×C4—222no—
482C23×C4—222no—
483C23×C4—222no—
484C23×C4—222no—
485C23×C4—442no—
486C23×C4—442no—
487C23×C4—442no—
488C23×C4C4×D1114yescomplemented
489C23×C4C22×D1112yes—
490C23×C4C22×D1112yes—
491C23×C4C22×D1111yescharacteristic
492C23×C4C22×D1111yescharacteristic
493#123—2232no—
494C4×D4—2232no—
495C2×C4⋊C4—118no—
496C2×C4⋊C4—222no—
497C2×C4⋊C4—222no—
498C2×C4⋊C4—224no—
499C2×C4⋊C4—224no—
500C2×C4⋊C4—222no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—114no—
507C2×C22⋊C4—118no—
508C2×C22⋊C4—222no—
509C2×C22⋊C4—222no—
510C2×C22⋊C4—224no—
511C2×C22⋊C4—224no—
512C2×C22⋊C4—222no—
513C2×C22⋊C4—222no—
514C2×C22⋊C4—222no—
515C2×C22⋊C4—224no—
516C2×C22⋊C4—224no—
517C2×C22⋊C4—442no—
518C2×C22⋊C4C22⋊D1114yes—
519C2×C42—222no—
520C2×C42—222no—
521C2×C42—222no—
522#95—24no—
523#95—24no—
524#95—224no—
525#95—224no—
526#95—224no—
527#95—224no—
528#95—224no—
529#95—442no—
530#95—442no—
531C2×C11—28no—
532C2×C11C2×#38611yescharacteristic
533C2×C11C4×#12311yescharacteristic
534C2×C11#232211yescharacteristic
535C2×C11#233912yes—
536C2×C11#235912yes—
537C2×C11#240511yescharacteristic
538C2×C11#240611yescharacteristic
539C2×C11#241912yes—
540C2×C11#242512yes—
541C2×C11#248611yescharacteristic
542C2×C11#253411yescharacteristic
543D11—44no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—112no—
549C24—112no—
550C24—112no—
551C24—221no—
552C24—221no—
553C24—221no—
554C24—222no—
555C24—222no—
556C24—222no—
557C24—222no—
558C24—221no—
559C24C2×C4×D1112yes—
560C24#433912yes—
561C24D4×D1112yes—
562C24D4×D1112yes—
563C24D4×D1112yes—
564C24#434112yes—
565C24C2×C22⋊D1112yes—
566C24C23×D1111yescharacteristic
567C2×D4—1116no—
568C2×D4—228no—
569C2×D4—228no—
570C2×D4—228no—
571C2×D4—228no—
572C2×D4—228no—
573C2×D4—228no—
574C22×C4—28no—
575C22×C4—28no—
576C22×C4—28no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—44no—
602C22×C4—112no—
603C22×C4—112no—
604C22×C4—112no—
605C22×C4—112no—
606C22×C4—114no—
607C22×C4—114no—
608C22×C4—112no—
609C22×C4—114no—
610C22×C4—228no—
611C22×C4—228no—
612C22×C4—221no—
613C22×C4—221no—
614C22×C4—221no—
615C22×C4—221no—
616C22×C4—222no—
617C22×C4—221no—
618C22×C4—221no—
619C22×C4—228no—
620C22×C4—228no—
621C22×C4—222no—
622C22×C4—222no—
623C22×C4—222no—
624C22×C4—222no—
625C22×C4—222no—
626C22×C4—221no—
627C22×C4—222no—
628C22×C4—222no—
629C22×C4—222no—
630C22×C4—222no—
631C22×C4—222no—
632C22×C4—222no—
633C22×C4—222no—
634C22×C4—222no—
635C22×C4—222no—
636C22×C4—221no—
637C22×C4—448no—
638C22×C4—444no—
639C22×C4—448no—
640C22×C4—444no—
641C22×C4—444no—
642C22×C4—448no—
643C22×C4—448no—
644C22×C4—448no—
645C22×C4—448no—
646C22×C4—444no—
647C22×C4—444no—
648C22×C4C2×C4×D1114yes—
649C22×C4C2×C22⋊D1112yes—
650C22×C4C2×C22⋊D1112yes—
651C4⋊C4—2216no—
652C4⋊C4—228no—
653C22⋊C4—28no—
654C22⋊C4—44no—
655C22⋊C4—2216no—
656C22⋊C4—228no—
657C22⋊C4—228no—
658C22⋊C4—448no—
659C42—228no—
660C11#1396811yescharacteristic, complemented, Sylow
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—22no—
668C23—24no—
669C23—22no—
670C23—22no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—22no—
676C23—24no—
677C23—114no—
678C23—222no—
679C23—222no—
680C23—222no—
681C23—224no—
682C23—224no—
683C23—222no—
684C23—222no—
685C23—222no—
686C23—224no—
687C23—224no—
688C23—224no—
689C23—224no—
690C23—442no—
691C23—442no—
692C23—442no—
693C23—442no—
694C23—441no—
695C23—442no—
696C23—441no—
697C23—441no—
698C23—441no—
699C23—442no—
700C23C22⋊C4×D1114yes—
701C23(C22⋊D11)⋊C414yes—
702C23#6693614yes—
703C23#6693714yes—
704C23C4×C22⋊D1114yes—
705C23#6699014yes—
706C23#6699114yes—
707C23C22×C4×D1111yescharacteristic
708C23C2×#433911yescharacteristic
709C23C2×D4×D1111yescharacteristic
710C23C2×D4×D1111yescharacteristic
711C23C2×D4×D1111yescharacteristic
712C23C2×#434111yescharacteristic
713C23#41×D1112yes—
714C23#41×D1112yes—
715C23#6704212yes—
716C23#6704312yes—
717C23C22×C22⋊D1111yescharacteristic
718D4—2232no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—416no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—114no—
745C2×C4—114no—
746C2×C4—222no—
747C2×C4—222no—
748C2×C4—222no—
749C2×C4—222no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—224no—
754C2×C4—222no—
755C2×C4—224no—
756C2×C4—224no—
757C2×C4—224no—
758C2×C4—224no—
759C2×C4—224no—
760C2×C4—222no—
761C2×C4—222no—
762C2×C4—222no—
763C2×C4—224no—
764C2×C4—224no—
765C2×C4—4416no—
766C2×C4—4416no—
767C2×C4—4416no—
768C2×C4—442no—
769C2×C4—442no—
770C2×C4—442no—
771C2×C4—442no—
772C2×C4—442no—
773C2×C4—442no—
774C2×C4—442no—
775C2×C4—442no—
776C2×C4—442no—
777C2×C4—442no—
778C22—24no—
779C22—24no—
780C22—28no—
781C22—24no—
782C22—24no—
783C22—28no—
784C22—24no—
785C22—24no—
786C22—28no—
787C22—28no—
788C22—228no—
789C22—224no—
790C22—442no—
791C22—442no—
792C22—444no—
793C22—442no—
794C22—442no—
795C22—442no—
796C22—442no—
797C22—444no—
798C22—444no—
799C22#1062256918yes—
800C22C2×C22⋊C4×D1111yescharacteristic
801C22C2×(C22⋊D11)⋊C411yescharacteristic
802C22C2×#6693611yescharacteristic
803C22C2×#6693711yescharacteristic
804C22#1062305312yes—
805C22#1062305412yes—
806C22#1062305812yes—
807C22#1062306212yes—
808C22#1062317911yescharacteristic
809C22#1062318012yes—
810C22D11×#12311yescharacteristic
811C22#1062318411yescharacteristic
812C22#1062318512yes—
813C22#1062318512yes—
814C22#1062318612yes—
815C22#1062318612yes—
816C22#1062318711yescharacteristic
817C22#1062319612yes—
818C22C2×C4×C22⋊D1111yescharacteristic
819C22C2×#6699011yescharacteristic
820C22C2×#6699111yescharacteristic
821C22#1062335512yes—
822C22#1062336012yes—
823C4—42no—
824C4—42no—
825C4—44no—
826C4—82no—
827C4—224no—
828C4—224no—
829C4—442no—
830C4—444no—
831C4—444no—
832C2—28no—
833C2—444no—
834C2C2×#1062256911yescharacteristic
835C2#1307113311yescharacteristic
836C2#1307128211yescharacteristic
837C2#1307144012yes—
838C2#1307160812yes—
839C2#1307194011yescharacteristic
840C2#1307194811yescharacteristic
841C2#1307209712yes—
842C2#1307216312yes—
843C2#1307292311yescharacteristic
844C2#1307351111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#381C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#381D11
hypocenterC11#13968
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
4. C22×C11⋊#95C2semidirect
5. #13066867C2semidirect
6. #13066864C2semidirect
7. #13066847C2semidirect
8. #13066838C2semidirect
9. #13066838C2semidirect
10. (C2×D11)⋊#95C2semidirect
11. C2×C11×#381C2semidirect
22. C2×#66982C4semidirect
52. C23×C4×C11C2×C4semidirect
92. C2×C22⋊Dic11C2×C4semidirect
102. C2×(C2×D11)⋊C4C2×C4semidirect
108. C2×Dic11⋊C4C2×C4semidirect
242. C2×#381D11semidirect
365. C2×Dic11#123semidirect
488. C23×C4C4×D11semidirect
660. C11#13968semidirect

Maximal subgroups

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

subgroupindex
C22×#669822
C22×(C22⋊D11)⋊C42
C2×#106225712
C22×C11⋊#952
#130668672
#130668642
#130668472
#130668382
(C2×D11)⋊#952
C2×C11×#3812
#1396811