Finite Group Databasebeta

← #14810865

Subgroups — #14810865

Order 2816.

1162 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
1C2×#10622460C211yesmaximal, characteristic, complemented
2C22×#66885C211yesmaximal, characteristic
3#13072340C211yesmaximal, characteristic, complemented
4C22⋊C4×D44C211yesmaximal, characteristic
5#13070136C211yesmaximal, characteristic, complemented
6#13070003C211yesmaximal, characteristic, complemented
7#13069989C211yesmaximal, characteristic, complemented
8#13069763C211yesmaximal, characteristic, complemented
9#13068880C211yesmaximal, characteristic, complemented
10#13068866C211yesmaximal, characteristic, complemented
11#13068811C211yesmaximal, characteristic, complemented
12#13068645C211yesmaximal, characteristic, complemented
13#13068627C211yesmaximal, characteristic, complemented
14#13068548C211yesmaximal, characteristic
15C11×#1850C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C2×C22⋊C4×D11—21no—
20C2×C4×D44C2211yescharacteristic
21C2×C4×D44C2211yescharacteristic
22C2×#66923C2211yescharacteristic, complemented
23C2×C11×C4⋊C8C2211yescharacteristic, complemented
24C2×C11×C4⋊C8C2211yescharacteristic, complemented
25C2×C11×C22⋊C8C2211yescharacteristic
26C4×C11×C22⋊C4C2211yescharacteristic
27#10622825C2211yescharacteristic
28#10622825C2211yescharacteristic
29C2×#66885—24no—
30C2×#66885C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66885C2211yescharacteristic
33C2×#66885C2211yescharacteristic
34C2×#66885C2211yescharacteristic
35C2×#66885C2211yescharacteristic
36C2×#66885C2211yescharacteristic
37C2×#66885C2211yescharacteristic
38C2×#66882C2211yescharacteristic, complemented
39C2×#66882C2211yescharacteristic, complemented
40C2×#66881C2211yescharacteristic, complemented
41C2×#66881C2211yescharacteristic, complemented
42#10622568—21no—
43#10622559—21no—
44#10622555—21no—
45#10622552C2211yescharacteristic
46#10622552C2211yescharacteristic
47#10622549C2211yescharacteristic, complemented
48#10622541C2211yescharacteristic, complemented
49#10622541C2211yescharacteristic, complemented
50#10622460—24no—
51#10622278—21no—
52#10622278—21no—
53#10622273—21no—
54#10622270—21no—
55C11×#336C2211yescharacteristic, complemented
56C11×#336C2211yescharacteristic, complemented
57#10622189C2211yescharacteristic, complemented
58#10622189C2211yescharacteristic, complemented
59#10622189C2211yescharacteristic, complemented
60#10622189C2211yescharacteristic, complemented
61C24×D11—21no—
62C23×C4×C11C2311yescharacteristic
63C23×Dic11—21no—
64C22×D44—22no—
65C22×D44—22no—
66C22×D44—21no—
67C22×D44—22no—
68C22×D44—41no—
69C22×D44—41no—
70C22×D44Q814yes—
71C22×D44C2311yescharacteristic
72C22×D44C2311yescharacteristic
73C22×C4×D11—21no—
74C22×C4×D11—21no—
75C22×C8×C11—22no—
76C22×C8×C11—22no—
77C22×C8×C11—41no—
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C2×C11×C22⋊C4D411yescharacteristic
83C2×C11×C22⋊C4D411yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×C4⋊Dic11—22no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11—41no—
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—21no—
105C2×Dic11⋊C4—21no—
106C2×Dic11⋊C4—21no—
107C22⋊C4×D11—44no—
108C4×D44—22no—
109C4×D44—22no—
110C4×D44—41no—
111C4×D44—41no—
112#66923—22no—
113#66923—41no—
114C11×C4⋊C8—22no—
115C11×C4⋊C8—41no—
116C11×C22⋊C8—22no—
117C11×#95D411yescharacteristic
118C11×#95D411yescharacteristic
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125#66885—22no—
126#66885—22no—
127#66885—22no—
128#66885—22no—
129#66885—22no—
130#66885—41no—
131#66885—41no—
132#66885D414yes—
133#66882—22no—
134#66882—41no—
135#66881—22no—
136#66881—41no—
137#25952—111nomaximal, Sylow
138C24×C11C2×D411yescharacteristic
139C23×D11—21no—
140C23×D11—21no—
141C23×D11—24no—
142C23×D11—42no—
143C23×D11—42no—
144C23×D11—42no—
145C23×D11—42no—
146C23×D11—81no—
147C23×D11—81no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×Q812yes—
158C22×C4×C11#4112yes—
159C22×C4×C11C2411yescharacteristic
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—42no—
167C22×Dic11—42no—
168C22×Dic11—81no—
169C2×D44—28no—
170C2×D44—24no—
171C2×D44—21no—
172C2×D44—21no—
173C2×D44—21no—
174C2×D44—21no—
175C2×D44—21no—
176C2×D44—21no—
177C2×D44—21no—
178C2×D44—21no—
179C2×D44—42no—
180C2×D44—42no—
181C2×D44—44no—
182C2×D44—44no—
183C2×D44—44no—
184C2×D44C2×D412yes—
185C2×D44C2×Q812yes—
186C2×D44C2×Q812yes—
187C2×D44#4112yes—
188C2×C4×D11—42no—
189C2×C4×D11—42no—
190C2×C4×D11—42no—
191C2×C4×D11—42no—
192C2×C4×D11—81no—
193C2×C4×D11—81no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—44no—
206C2×C8×C11C2×D412yes—
207C11×C22⋊C4—22no—
208C11×C22⋊C4—22no—
209C42×C11—21no—
210C42×C11—21no—
211C42×C11—21no—
212C42×C11—21no—
213C22⋊Dic11—42no—
214C22⋊Dic11—42no—
215(C2×D11)⋊C4—42no—
216(C2×D11)⋊C4—42no—
217(C2×D11)⋊C4—42no—
218(C2×D11)⋊C4—42no—
219(C2×D11)⋊C4—81no—
220(C2×D11)⋊C4—81no—
221C4⋊Dic11—21no—
222C4⋊Dic11—21no—
223C4⋊Dic11—21no—
224C4⋊Dic11—21no—
225C4⋊Dic11—21no—
226C4⋊Dic11—21no—
227C4⋊Dic11—21no—
228C4⋊Dic11—21no—
229C4⋊Dic11—21no—
230C4⋊Dic11—21no—
231C4⋊Dic11—21no—
232C4⋊Dic11—42no—
233C4⋊Dic11C2×D412yes—
234Dic11⋊C4—42no—
235Dic11⋊C4—42no—
236Dic11⋊C4—81no—
237Dic11⋊C4—81no—
238C2×#478—111no—
239C22×#102—111no—
240#2442—111no—
241D4×C22⋊C4—111no—
242#2092—111no—
243#2067—111no—
244#2065—111no—
245#2025—111no—
246#1864—111no—
247#1862—111no—
248#1853—111no—
249#1850D1111yescharacteristic, complemented
250#1808—111no—
251#1804—111no—
252#1786—111no—
253C23×C11—21no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11C22⋊Q812yes—
258C23×C11#13512yes—
259C23×C11AGL(1,ℤ/8)12yes—
260C23×C11C22×D411yescharacteristic
261C22×D11—22no—
262C22×D11—22no—
263C22×D11—22no—
264C22×D11—22no—
265C22×D11—48no—
266C22×D11—41no—
267C22×D11—41no—
268C22×D11—41no—
269C22×D11—41no—
270C22×D11—41no—
271C22×D11—41no—
272C22×D11—41no—
273C22×D11—41no—
274C22×D11—41no—
275C22×D11—41no—
276C22×D11—48no—
277C22×D11—84no—
278C22×D11—84no—
279C22×D11—84no—
280C22×D11—84no—
281C22×D11—84no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11C22⋊Q812yes—
301C2×C4×C11C22×D411yescharacteristic
302C2×C4×C11C22×Q811yescharacteristic
303C2×C4×C11C2×#4111yescharacteristic
304C2×C4×C11C2×#4111yescharacteristic
305C2×C4×C11H(5,𝔽2)11yescharacteristic
306C2×C4×C11H(5,𝔽2)11yescharacteristic
307C2×Dic11—22no—
308C2×Dic11—41no—
309C2×Dic11—41no—
310C2×Dic11—41no—
311C2×Dic11—41no—
312C2×Dic11—41no—
313C2×Dic11—41no—
314C2×Dic11—41no—
315C2×Dic11—41no—
316C2×Dic11—41no—
317C2×Dic11—41no—
318C2×Dic11—41no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—84no—
326D44—22no—
327D44—22no—
328D44—22no—
329D44—22no—
330D44—22no—
331D44—48no—
332D44—41no—
333D44—41no—
334D44C22⋊Q814yes—
335C4×D11—84no—
336C4×D11—84no—
337C8×C11—22no—
338C8×C11—41no—
339C8×C11—41no—
340C8×C11—41no—
341C23×D4—111no—
342C23×C8C2×D1111yescharacteristic
343C2×#125—111no—
344C2×C4×D4—111no—
345C2×C4×D4—111no—
346C22×C4⋊C4—111no—
347C22×C22⋊C4—221no—
348#478—224no—
349C2×#107—111no—
350C2×#107—111no—
351C2×#106—111no—
352C2×#106—111no—
353C2×C4⋊C8C2×D1111yescharacteristic, complemented
354C2×C4⋊C8C2×D1111yescharacteristic, complemented
355C2×#102—111no—
356C2×#102—111no—
357C2×#102—111no—
358C2×#102—111no—
359C2×#102—111no—
360C2×#102—111no—
361C2×#102—111no—
362C2×#102—111no—
363C2×#102—224no—
364C2×C22⋊C8C2×D1111yescharacteristic
365#400—221no—
366#398—221no—
367#390—111no—
368#390—111no—
369#389—111no—
370#389—111no—
371#386—221no—
372#386—221no—
373#385—221no—
374#382—111no—
375#380—111no—
376#380—111no—
377#380—221no—
378#379—221no—
379C4×C22⋊C4C2×D1111yescharacteristic
380#340—111no—
381#340—111no—
382#340—111no—
383#340—111no—
384#336C2×D1111yescharacteristic, complemented
385#336C2×D1111yescharacteristic, complemented
386C22×C11—22no—
387C22×C11—22no—
388C22×C11—22no—
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—22no—
392C22×C11#47814yescomplemented
393C22×C11C2×C22⋊Q811yescharacteristic
394C22×C11D4211yescharacteristic
395C22×C11#54611yescharacteristic
396C22×C11C2×#13511yescharacteristic
397C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
398C22×C11#57611yescharacteristic
399C22×C11#57711yescharacteristic
400C2×D11—24no—
401C2×D11—42no—
402C2×D11—42no—
403C2×D11—42no—
404C2×D11—42no—
405C2×D11—42no—
406C2×D11—42no—
407C2×D11—42no—
408C2×D11—42no—
409C2×D11—42no—
410C2×D11—816no—
411C2×D11—81no—
412C2×D11—81no—
413C2×D11—81no—
414C2×D11—81no—
415C4×C11—22no—
416C4×C11—41no—
417C4×C11—41no—
418C4×C11—41no—
419C4×C11—41no—
420C4×C11C2×C22⋊Q811yescharacteristic
421C4×C11#54311yescharacteristic
422C4×C11#54611yescharacteristic
423C4×C11#55111yescharacteristic
424Dic11—42no—
425Dic11—81no—
426Dic11—81no—
427Dic11—81no—
428Dic11—81no—
429Dic11—81no—
430C25—221no—
431C22×D4—114no—
432C22×D4—111no—
433C22×D4—111no—
434C22×D4—222no—
435C22×D4—222no—
436C22×D4—221no—
437C22×D4—222no—
438C22×D4—441no—
439C22×D4—441no—
440C23×C4—221no—
441C23×C4—221no—
442C23×C4—221no—
443C23×C4C22×D1111yescharacteristic
444C22×C8—22no—
445C22×C8—22no—
446C22×C8—41no—
447C22×C8C22×D1111yescharacteristic
448C22×C8C22×D1111yescharacteristic
449C22×C8C22×D1111yescharacteristic
450C22×C8C22×D1111yescharacteristic
451#125—222no—
452#125—441no—
453C4×D4—222no—
454C4×D4—222no—
455C4×D4—441no—
456C4×D4—441no—
457C2×C4⋊C4—111no—
458C2×C4⋊C4—111no—
459C2×C4⋊C4—111no—
460C2×C4⋊C4—111no—
461C2×C4⋊C4—111no—
462C2×C4⋊C4—111no—
463C2×C4⋊C4—222no—
464C2×C4⋊C4—221no—
465C2×C4⋊C4—221no—
466C2×C4⋊C4—221no—
467C2×C4⋊C4—221no—
468C2×C4⋊C4—221no—
469C2×C4⋊C4—441no—
470C2×C22⋊C4—221no—
471C2×C22⋊C4—221no—
472C2×C22⋊C4—221no—
473C2×C22⋊C4—221no—
474C2×C22⋊C4—221no—
475C2×C22⋊C4—221no—
476C2×C22⋊C4—221no—
477C2×C22⋊C4—221no—
478C2×C22⋊C4—444no—
479C2×C22⋊C4D4411yescharacteristic
480C2×C22⋊C4D4411yescharacteristic
481C2×C42C22×D1111yescharacteristic
482C2×C42C22×D1111yescharacteristic
483#107—222no—
484#107—441no—
485#106—222no—
486#106—441no—
487C4⋊C8—22no—
488C4⋊C8—41no—
489#102—114no—
490#102—222no—
491#102—222no—
492#102—222no—
493#102—222no—
494#102—222no—
495#102—441no—
496#102—441no—
497C22⋊C8—22no—
498#95—221no—
499#95—221no—
500#95—221no—
501#95—221no—
502#95—221no—
503#95—221no—
504#95D4411yescharacteristic
505#95D4411yescharacteristic
506C2×C11—24no—
507C2×C11#243711yescharacteristic
508C2×C11C2×#47811yescharacteristic
509C2×C11#308111yescharacteristic
510C2×C11#326511yescharacteristic
511C2×C11#328011yescharacteristic
512C2×C11#329611yescharacteristic
513C2×C11#331811yescharacteristic
514D11—44no—
515D11—82no—
516C24—221no—
517C24—221no—
518C24—224no—
519C24—442no—
520C24—442no—
521C24—442no—
522C24—442no—
523C24—881no—
524C24—881no—
525C24C2×D4411yescharacteristic
526C2×D4—112no—
527C2×D4—112no—
528C2×D4—112no—
529C2×D4—112no—
530C2×D4—228no—
531C2×D4—224no—
532C2×D4—221no—
533C2×D4—221no—
534C2×D4—221no—
535C2×D4—221no—
536C2×D4—221no—
537C2×D4—221no—
538C2×D4—221no—
539C2×D4—221no—
540C2×D4—444no—
541C2×D4—444no—
542C2×D4—444no—
543C2×D4—442no—
544C2×D4—442no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—221no—
550C22×C4—221no—
551C22×C4—221no—
552C22×C4—221no—
553C22×C4—221no—
554C22×C4—221no—
555C22×C4—442no—
556C22×C4—442no—
557C22×C4—442no—
558C22×C4—442no—
559C22×C4—442no—
560C22×C4—442no—
561C22×C4—881no—
562C22×C4—881no—
563C22×C4—881no—
564C22×C4C2×D4411yescharacteristic
565C22×C4C2×D4411yescharacteristic
566C22×C4C2×D4411yescharacteristic
567C22×C4C2×D4411yescharacteristic
568C22×C4C2×D4411yescharacteristic
569C22×C4#434112yes—
570C22×C4Q8×D1112yes—
571C22×C4C23×D1111yescharacteristic
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—44no—
584C2×C8D4×D1112yes—
585C4⋊C4—112no—
586C4⋊C4—221no—
587C4⋊C4—221no—
588C4⋊C4—221no—
589C4⋊C4—221no—
590C4⋊C4—221no—
591C4⋊C4—221no—
592C4⋊C4—221no—
593C4⋊C4—221no—
594C4⋊C4—221no—
595C4⋊C4—221no—
596C4⋊C4—221no—
597C4⋊C4—442no—
598C4⋊C4—442no—
599C4⋊C4—442no—
600C4⋊C4—881no—
601C4⋊C4—881no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—442no—
605C22⋊C4—442no—
606C22⋊C4—442no—
607C22⋊C4—442no—
608C22⋊C4—442no—
609C22⋊C4—442no—
610C22⋊C4—881no—
611C22⋊C4—881no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C11#2595211yescharacteristic, complemented, Sylow
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—222no—
622C23—222no—
623C23—222no—
624C23—222no—
625C23—448no—
626C23—441no—
627C23—441no—
628C23—441no—
629C23—441no—
630C23—441no—
631C23—441no—
632C23—441no—
633C23—441no—
634C23—441no—
635C23—441no—
636C23—448no—
637C23—884no—
638C23—884no—
639C23—884no—
640C23—884no—
641C23—884no—
642C23#6695012yes—
643C23#6695712yes—
644C23#6696112yes—
645C23C22×D4411yescharacteristic
646D4—114no—
647D4—222no—
648D4—222no—
649D4—222no—
650D4—222no—
651D4—222no—
652D4—448no—
653D4—441no—
654D4—441no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—222no—
674C2×C4—441no—
675C2×C4—441no—
676C2×C4—441no—
677C2×C4—441no—
678C2×C4—441no—
679C2×C4—441no—
680C2×C4—441no—
681C2×C4—441no—
682C2×C4—441no—
683C2×C4—441no—
684C2×C4—441no—
685C2×C4—441no—
686C2×C4—441no—
687C2×C4—441no—
688C2×C4—441no—
689C2×C4—441no—
690C2×C4—441no—
691C2×C4—884no—
692C2×C4—884no—
693C2×C4—884no—
694C2×C4#6695012yes—
695C2×C4C2×D4×D1111yescharacteristic
696C2×C4C2×#434111yescharacteristic
697C2×C4#6703711yescharacteristic
698C2×C4C2×Q8×D1111yescharacteristic
699C2×C4#41×D1111yescharacteristic
700C2×C4#6704211yescharacteristic
701C8—22no—
702C8—41no—
703C8—41no—
704C8—41no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—224no—
712C22—442no—
713C22—442no—
714C22—442no—
715C22—442no—
716C22—442no—
717C22—442no—
718C22—442no—
719C22—442no—
720C22—442no—
721C22—8816no—
722C22—881no—
723C22—881no—
724C22—881no—
725C22—881no—
726C22#1062246014yescomplemented
727C22C2×#6695011yescharacteristic
728C22D4×D4411yescharacteristic
729C22#1062308511yescharacteristic
730C22C2×#6695711yescharacteristic
731C22C2×#6696111yescharacteristic
732C22#1062328211yescharacteristic
733C22#1062328311yescharacteristic
734C4—22no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—41no—
739C4—442no—
740C4—881no—
741C4—881no—
742C4—881no—
743C4—881no—
744C4—881no—
745C4#1062312211yescharacteristic
746C4D11×C22⋊Q811yescharacteristic
747C4#1062316511yescharacteristic
748C4#1062318911yescharacteristic
749C2—24no—
750C2—444no—
751C2—882no—
752C2#1307228011yescharacteristic
753C2C2×#1062246011yescharacteristic
754C2#1307844811yescharacteristic
755C2#1308011611yescharacteristic
756C2#1308030311yescharacteristic
757C2#1308045311yescharacteristic
758C2#1308075911yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1850C2
socleC23×C11C22×D4
prime radicalC23×D44C22
hypercenter#1850D11
hypocenterC11#25952
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
1. C2×#10622460C2semidirect
3. #13072340C2semidirect
5. #13070136C2semidirect
6. #13070003C2semidirect
7. #13069989C2semidirect
8. #13069763C2semidirect
9. #13068880C2semidirect
10. #13068866C2semidirect
11. #13068811C2semidirect
12. #13068645C2semidirect
13. #13068627C2semidirect
15. C11×#1850C2semidirect
22. C2×#66923C22semidirect
23. C2×C11×C4⋊C8C22semidirect
24. C2×C11×C4⋊C8C22semidirect
38. C2×#66882C22semidirect
39. C2×#66882C22semidirect
40. C2×#66881C22semidirect
41. C2×#66881C22semidirect
47. #10622549C22semidirect
48. #10622541C22semidirect
49. #10622541C22semidirect
55. C11×#336C22semidirect
56. C11×#336C22semidirect
57. #10622189C22semidirect
58. #10622189C22semidirect
59. #10622189C22semidirect
60. #10622189C22semidirect
249. #1850D11semidirect
353. C2×C4⋊C8C2×D11semidirect
354. C2×C4⋊C8C2×D11semidirect
384. #336C2×D11semidirect
385. #336C2×D11semidirect
392. C22×C11#478semidirect
616. C11#25952semidirect
726. C22#10622460semidirect

Maximal subgroups

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

subgroupindex
C2×#106224602
C22×#668852
#130723402
C22⋊C4×D442
#130701362
#130700032
#130699892
#130697632
#130688802
#130688662
#130688112
#130686452
#130686272
#130685482
C11×#18502
#2595211