Finite Group Databasebeta

← #14680665

Subgroups — #14680665

Order 2816.

2198 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622573C211yesmaximal, characteristic
2C2×#10622601C211yesmaximal, characteristic, complemented
3C2×#10622571C212yesmaximal, complemented
4C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
5#13066875C211yesmaximal, characteristic, complemented
6#13066864C212yesmaximal, complemented
7#13066856C211yesmaximal, characteristic, complemented
8#13066855C212yesmaximal, complemented
9#13066852C212yesmaximal, complemented
10#13066841C211yesmaximal, characteristic, complemented
11C11×#1439C211yesmaximal, characteristic, complemented
12C23×C22⋊D11C2212yes—
13C24×Dic11C2211yescharacteristic
14C23×D44C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2212yes—
18C22×C22⋊Dic11C2211yescharacteristic
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×C4×Dic11C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C2×C11×#95C2211yescharacteristic
27C2×C11×#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2211yescharacteristic
35#10622601—24no—
36#10622573C418yescomplemented
37#10622571—28no—
38C22⋊C4×Dic11—24no—
39C25×C11C2311yescharacteristic
40C24×D11C2312yes—
41C23×C4×C11C2312yes—
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C22×C22⋊D11—24no—
46C22×C22⋊D11—24no—
47C22×C22⋊D11—42no—
48C22×C22⋊D11—42no—
49C22×C22⋊D11—42no—
50C22×C22⋊D11—42no—
51C22×C22⋊D11C2×C418yes—
52C23×Dic11—22no—
53C23×Dic11—22no—
54C23×Dic11—42no—
55C23×Dic11—42no—
56C23×Dic11D414yescomplemented
57C23×Dic11C2312yes—
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2311yescharacteristic
62C22×D44—22no—
63C22×D44—22no—
64C22×D44—42no—
65C22×D44—42no—
66C22×D44C2×C414yescomplemented
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—42no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—24no—
72C2×C11×C22⋊C4—42no—
73C2×C11×C22⋊C4—42no—
74C2×C11×C22⋊C4C2×C414yes—
75C2×C22⋊Dic11—22no—
76C2×C22⋊Dic11—22no—
77C2×C22⋊Dic11—22no—
78C2×(C2×D11)⋊C4—24no—
79C2×(C2×D11)⋊C4—24no—
80C2×(C2×D11)⋊C4—24no—
81C2×(C2×D11)⋊C4—24no—
82C2×(C2×D11)⋊C4—24no—
83C2×(C2×D11)⋊C4—24no—
84C2×(C2×D11)⋊C4—42no—
85C2×(C2×D11)⋊C4—42no—
86C2×(C2×D11)⋊C4—42no—
87C2×(C2×D11)⋊C4—42no—
88C2×(C2×D11)⋊C4—42no—
89C2×(C2×D11)⋊C4—42no—
90C2×(C2×D11)⋊C4—42no—
91C2×(C2×D11)⋊C4—42no—
92C2×(C2×D11)⋊C4C2×C418yescomplemented
93C2×C4×Dic11—22no—
94C2×C4×Dic11—42no—
95C2×C4×Dic11—42no—
96C2×C4×Dic11D414yescomplemented
97C11×#95—22no—
98C11×#95—42no—
99C11⋊#95—22no—
100C11⋊#95—22no—
101C11⋊#95—24no—
102C11⋊#95—24no—
103C11⋊#95—42no—
104C11⋊#95—42no—
105C11⋊#95C2×C414yescomplemented
106#14311—111nomaximal, Sylow
107C24×C11—21no—
108C24×C11—21no—
109C24×C11—21no—
110C24×C11—21no—
111C24×C11—22no—
112C24×C11—22no—
113C24×C11—22no—
114C24×C11—22no—
115C24×C11C22×C412yes—
116C24×C11C2×D412yes—
117C24×C11#4112yes—
118C24×C11C2411yescharacteristic
119C23×D11—22no—
120C23×D11—22no—
121C23×D11—22no—
122C23×D11—22no—
123C23×D11—22no—
124C23×D11—22no—
125C23×D11—22no—
126C23×D11—22no—
127C23×D11—22no—
128C23×D11—22no—
129C23×D11—22no—
130C23×D11—22no—
131C23×D11—22no—
132C23×D11—22no—
133C23×D11C22×C414yes—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
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—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11C22×C412yes—
155C22×C4×C11C22×C412yes—
156C22×C4×C11C2×D412yes—
157C22×C4×C11#4112yes—
158C2×C22⋊D11—216no—
159C2×C22⋊D11—48no—
160C2×C22⋊D11—48no—
161C2×C22⋊D11—48no—
162C2×C22⋊D11—48no—
163C2×C22⋊D11—48no—
164C2×C22⋊D11—48no—
165C22×Dic11—28no—
166C22×Dic11—21no—
167C22×Dic11—22no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—21no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—48no—
187C22×Dic11—44no—
188C22×Dic11—44no—
189C22×Dic11—48no—
190C22×Dic11C22×C414yes—
191C22×Dic11C2×D412yes—
192C22×Dic11C2×D412yes—
193C22×Dic11C2×D412yes—
194C22×Dic11C2×D412yes—
195C22×Dic11#4112yes—
196C22×Dic11#4112yes—
197C2×D44—28no—
198C2×D44—48no—
199C2×D44—44no—
200C2×D44—44no—
201C2×D44—48no—
202C11×C4⋊C4—44no—
203C11×C22⋊C4—28no—
204C11×C22⋊C4—48no—
205C22⋊Dic11—28no—
206(C2×D11)⋊C4—48no—
207(C2×D11)⋊C4—48no—
208(C2×D11)⋊C4—48no—
209(C2×D11)⋊C4—48no—
210(C2×D11)⋊C4—48no—
211C4×Dic11—44no—
212C4×Dic11—44no—
213C2×#392—111no—
214C2×#390—111no—
215C2×#386—112no—
216C2×C4×C22⋊C4—111no—
217#1442—111no—
218#1440—112no—
219#1439D1111yescharacteristic, complemented
220#1438—111no—
221#1438—112no—
222#1437—112no—
223#1434—111no—
224C23×C11—22no—
225C23×C11—22no—
226C23×C11—24no—
227C23×C11—24no—
228C23×C11—22no—
229C23×C11—22no—
230C23×C11—22no—
231C23×C11—22no—
232C23×C11—24no—
233C23×C11—24no—
234C23×C11—24no—
235C23×C11—24no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—42no—
241C23×C11—42no—
242C23×C11—42no—
243C23×C11—42no—
244C23×C11—42no—
245C23×C11—42no—
246C23×C11C4×D414yes—
247C23×C11C23×C411yescharacteristic
248C23×C11C22×D411yescharacteristic
249C23×C11C22×D411yescharacteristic
250C23×C11C2×#4111yescharacteristic
251C23×C11C2×#4111yescharacteristic
252C23×C11C2×#4111yescharacteristic
253C23×C11C2×#4111yescharacteristic
254C23×C11H(5,𝔽2)12yes—
255C23×C11H(5,𝔽2)12yes—
256C23×C11H(5,𝔽2)12yes—
257C23×C11H(5,𝔽2)12yes—
258C22×D11—24no—
259C22×D11—24no—
260C22×D11—24no—
261C22×D11—24no—
262C22×D11—24no—
263C22×D11—24no—
264C22×D11—24no—
265C22×D11—42no—
266C22×D11—42no—
267C22×D11—42no—
268C22×D11—42no—
269C22×D11—42no—
270C22×D11—42no—
271C22×D11—42no—
272C22×D11—42no—
273C22×D11—42no—
274C22×D11—42no—
275C22×D11—42no—
276C22×D11—42no—
277C22×D11—42no—
278C22×D11—42no—
279C22×D11—42no—
280C22×D11—42no—
281C22×D11—42no—
282C22×D11—42no—
283C22×D11—42no—
284C22×D11—42no—
285C22×D11—42no—
286C22×D11—42no—
287C22×D11—42no—
288C22×D11—42no—
289C22×D11—42no—
290C22×D11—42no—
291C22×D11—42no—
292C22×D11—42no—
293C2×C4×C11—24no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—24no—
297C2×C4×C11—22no—
298C2×C4×C11—24no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
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×C11—42no—
308C2×C4×C11—42no—
309C2×C4×C11—42no—
310C2×C4×C11—42no—
311C2×C4×C11—42no—
312C2×C4×C11—42no—
313C2×C4×C11—42no—
314C2×C4×C11—42no—
315C2×C4×C11—42no—
316C2×C4×C11C4×D414yes—
317C22⋊D11—432no—
318C2×Dic11—22no—
319C2×Dic11—24no—
320C2×Dic11—22no—
321C2×Dic11—24no—
322C2×Dic11—24no—
323C2×Dic11—24no—
324C2×Dic11—24no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—24no—
330C2×Dic11—22no—
331C2×Dic11—24no—
332C2×Dic11—416no—
333C2×Dic11—41no—
334C2×Dic11—42no—
335C2×Dic11—41no—
336C2×Dic11—41no—
337C2×Dic11—41no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C2×Dic11—42no—
342C2×Dic11—42no—
343C2×Dic11—42no—
344C2×Dic11—42no—
345C2×Dic11#12114yes—
346D44—416no—
347C23×D4—112no—
348C23×D4—111no—
349C24×C4—111no—
350C22×C4⋊C4C2×D1111yescharacteristic
351C22×C22⋊C4—112no—
352C22×C22⋊C4—111no—
353C22×C22⋊C4—112no—
354C22×C22⋊C4—112no—
355C22×C22⋊C4—112no—
356C22×C22⋊C4—112no—
357C22×C22⋊C4C2×D1111yescharacteristic
358C22×C22⋊C4C2×D1112yes—
359C22×C42—111no—
360C22×C42—111no—
361#392—118no—
362#390—224no—
363#386—228no—
364C4×C22⋊C4—224no—
365C2×#95—111no—
366C2×#95—112no—
367C2×#95—111no—
368C2×#95—111no—
369C2×#95—112no—
370C2×#95—112no—
371C2×#95—112no—
372C2×#95C2×D1111yescharacteristic
373C2×#95C2×D1112yes—
374C22×C11—28no—
375C22×C11—24no—
376C22×C11—42no—
377C22×C11—42no—
378C22×C11—44no—
379C22×C11—42no—
380C22×C11—42no—
381C22×C11—42no—
382C22×C11—42no—
383C22×C11—44no—
384C22×C11—44no—
385C22×C11C2×C4×D411yescharacteristic
386C22×C11C2×C4×D411yescharacteristic
387C22×C11C4×#4111yescharacteristic
388C22×C11#51812yes—
389C22×C11#51812yes—
390C22×C11C2×#12111yescharacteristic
391C22×C11#52511yescharacteristic
392C22×C11#52911yescharacteristic
393C22×C11#53211yescharacteristic
394C22×C11#53411yescharacteristic
395C22×C11#53412yes—
396C22×C11#53511yescharacteristic
397C22×C11#53511yescharacteristic
398C22×C11#53512yes—
399C22×C11#53511yescharacteristic
400C22×C11#53812yes—
401C22×C11#53812yes—
402C22×C11#53812yes—
403C22×C11#53812yes—
404C22×C11#53812yes—
405C22×C11#54012yes—
406C22×C11#54012yes—
407C22×C11#54012yes—
408C2×D11—44no—
409C2×D11—44no—
410C2×D11—44no—
411C2×D11—44no—
412C2×D11—44no—
413C2×D11—44no—
414C2×D11—44no—
415C2×D11—82no—
416C2×D11—82no—
417C2×D11—82no—
418C2×D11—82no—
419C2×D11—82no—
420C2×D11—82no—
421C2×D11—82no—
422C2×D11—82no—
423C4×C11—24no—
424C4×C11—42no—
425C4×C11—82no—
426C4×C11—82no—
427Dic11—24no—
428Dic11—44no—
429Dic11—42no—
430Dic11—42no—
431Dic11—42no—
432C25—112no—
433C25C22×D1111yescharacteristic
434C22×D4—118no—
435C22×D4—114no—
436C22×D4—224no—
437C22×D4—224no—
438C22×D4—222no—
439C22×D4—222no—
440C22×D4—442no—
441C22×D4—442no—
442C22×D4—442no—
443C22×D4—442no—
444C22×D4—442no—
445C22×D4—442no—
446C23×C4—111no—
447C23×C4—111no—
448C23×C4—111no—
449C23×C4—111no—
450C23×C4—112no—
451C23×C4—114no—
452C23×C4—222no—
453C23×C4—222no—
454C23×C4—442no—
455C23×C4—442no—
456C23×C4C22×D1112yes—
457C23×C4C22×D1112yes—
458C23×C4C22×D1111yescharacteristic
459C23×C4C22×D1111yescharacteristic
460C2×C4⋊C4—22no—
461C2×C4⋊C4—42no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—42no—
466C2×C22⋊C4—42no—
467C2×C22⋊C4—118no—
468C2×C22⋊C4—222no—
469C2×C22⋊C4—222no—
470C2×C22⋊C4—222no—
471C2×C22⋊C4—224no—
472C2×C22⋊C4—224no—
473C2×C22⋊C4—224no—
474C2×C22⋊C4—224no—
475C2×C22⋊C4—224no—
476C2×C22⋊C4—224no—
477C2×C22⋊C4—442no—
478C2×C22⋊C4—442no—
479C2×C22⋊C4—442no—
480C2×C22⋊C4—442no—
481C2×C22⋊C4—442no—
482C2×C22⋊C4—442no—
483C2×C22⋊C4—442no—
484C2×C22⋊C4—442no—
485C2×C22⋊C4C4×D1114yes—
486C2×C42—114no—
487C2×C42—222no—
488C2×C42—442no—
489C2×C42—442no—
490#95—22no—
491#95—42no—
492#95—114no—
493#95—222no—
494#95—224no—
495#95—224no—
496#95—222no—
497#95—442no—
498#95—442no—
499C2×C11—44no—
500C2×C11C4×#12111yescharacteristic
501C2×C11#232112yes—
502C2×C11#232111yescharacteristic
503C2×C11#232811yescharacteristic
504C2×C11#233312yes—
505C2×C11#261711yescharacteristic
506C2×C11#261911yescharacteristic
507C2×C11#263111yescharacteristic
508C2×C11#263511yescharacteristic
509C2×C11#264812yes—
510C2×C11#266112yes—
511D11—84no—
512C24—21no—
513C24—21no—
514C24—22no—
515C24—22no—
516C24—21no—
517C24—21no—
518C24—22no—
519C24—22no—
520C24—114no—
521C24—222no—
522C24—222no—
523C24—222no—
524C24—222no—
525C24—222no—
526C24—222no—
527C24—222no—
528C24—222no—
529C24—222no—
530C24—222no—
531C24—222no—
532C24—222no—
533C24—222no—
534C24—222no—
535C24C2×C4×D1112yes—
536C24D4×D1112yes—
537C24#434312yes—
538C24C23×D1111yescharacteristic
539C2×D4—2216no—
540C2×D4—228no—
541C2×D4—448no—
542C2×D4—444no—
543C2×D4—448no—
544C2×D4—444no—
545C2×D4—448no—
546C2×D4—448no—
547C2×D4—448no—
548C2×D4—448no—
549C2×D4—448no—
550C2×D4—448no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—112no—
572C22×C4—112no—
573C22×C4—112no—
574C22×C4—114no—
575C22×C4—112no—
576C22×C4—112no—
577C22×C4—112no—
578C22×C4—228no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4—221no—
582C22×C4—222no—
583C22×C4—221no—
584C22×C4—222no—
585C22×C4—222no—
586C22×C4—222no—
587C22×C4—222no—
588C22×C4—221no—
589C22×C4—221no—
590C22×C4—222no—
591C22×C4—221no—
592C22×C4—221no—
593C22×C4—222no—
594C22×C4—222no—
595C22×C4—222no—
596C22×C4—222no—
597C22×C4—222no—
598C22×C4—222no—
599C22×C4—448no—
600C22×C4—448no—
601C22×C4—444no—
602C22×C4—444no—
603C22×C4C2×C4×D1112yes—
604C22×C4C2×C4×D1112yes—
605C22×C4D4×D1112yes—
606C22×C4#434112yes—
607C4⋊C4—44no—
608C22⋊C4—28no—
609C22⋊C4—48no—
610C22⋊C4—228no—
611C22⋊C4—448no—
612C22⋊C4—448no—
613C22⋊C4—448no—
614C22⋊C4—448no—
615C22⋊C4—448no—
616C42—444no—
617C42—444no—
618C11#1431111yescharacteristic, complemented, Sylow
619C23—22no—
620C23—22no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—42no—
632C23—41no—
633C23—41no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—41no—
638C23—42no—
639C23—41no—
640C23—42no—
641C23—224no—
642C23—224no—
643C23—224no—
644C23—224no—
645C23—224no—
646C23—224no—
647C23—224no—
648C23—442no—
649C23—442no—
650C23—442no—
651C23—442no—
652C23—442no—
653C23—442no—
654C23—442no—
655C23—442no—
656C23—442no—
657C23—442no—
658C23—442no—
659C23—442no—
660C23—442no—
661C23—442no—
662C23—442no—
663C23—442no—
664C23—442no—
665C23—442no—
666C23—442no—
667C23—442no—
668C23—442no—
669C23—442no—
670C23—442no—
671C23—442no—
672C23—442no—
673C23—442no—
674C23—442no—
675C23—442no—
676C23#6694614yes—
677C23C22×C4×D1111yescharacteristic
678C23C2×D4×D1111yescharacteristic
679C23C2×D4×D1111yescharacteristic
680C23C2×#434111yescharacteristic
681C23#6703712yes—
682C23#6703712yes—
683C23C2×#434311yescharacteristic
684C23#41×D1111yescharacteristic
685C23#41×D1111yescharacteristic
686C23#6704212yes—
687C23#6704212yes—
688D4—4416no—
689D4—4432no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—41no—
697C2×C4—42no—
698C2×C4—41no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—114no—
714C2×C4—224no—
715C2×C4—222no—
716C2×C4—224no—
717C2×C4—222no—
718C2×C4—222no—
719C2×C4—224no—
720C2×C4—224no—
721C2×C4—224no—
722C2×C4—222no—
723C2×C4—222no—
724C2×C4—222no—
725C2×C4—222no—
726C2×C4—224no—
727C2×C4—224no—
728C2×C4—4416no—
729C2×C4—442no—
730C2×C4—442no—
731C2×C4—441no—
732C2×C4—442no—
733C2×C4—442no—
734C2×C4—442no—
735C2×C4—442no—
736C2×C4—441no—
737C2×C4—442no—
738C2×C4—442no—
739C2×C4—441no—
740C2×C4—441no—
741C2×C4(C22⋊D11)⋊C414yes—
742C22—24no—
743C22—28no—
744C22—44no—
745C22—42no—
746C22—44no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—44no—
751C22—42no—
752C22—42no—
753C22—444no—
754C22—444no—
755C22—444no—
756C22—444no—
757C22—444no—
758C22—444no—
759C22—444no—
760C22—882no—
761C22—882no—
762C22—882no—
763C22—882no—
764C22—882no—
765C22—882no—
766C22—882no—
767C22—882no—
768C22C2×(C22⋊D11)⋊C411yescharacteristic
769C22C2×#6694611yescharacteristic
770C22#1062305311yescharacteristic
771C22#1062307612yes—
772C22#1062307612yes—
773C22#1062312311yescharacteristic
774C22#1062312312yes—
775C22#1062312711yescharacteristic
776C22D11×#12111yescharacteristic
777C22#1062314612yes—
778C22#1062314812yes—
779C22#1062315012yes—
780C22#1062315511yescharacteristic
781C22#1062315811yescharacteristic
782C22#1062317512yes—
783C22#1062317512yes—
784C22#1062318412yes—
785C22#1062318411yescharacteristic
786C22#1062319412yes—
787C22#1062320511yescharacteristic
788C22#1062320912yes—
789C22#1062323512yes—
790C22#1062324611yescharacteristic
791C4—24no—
792C4—42no—
793C4—82no—
794C4—82no—
795C4—224no—
796C4—442no—
797C4—442no—
798C4—444no—
799C4—442no—
800C2—44no—
801C2—884no—
802C2#1307112211yescharacteristic
803C2#1307127312yes—
804C2#1307127911yescharacteristic
805C2#1307134011yescharacteristic
806C2#1307137912yes—
807C2#1307435111yescharacteristic
808C2#1307436511yescharacteristic
809C2#1307447411yescharacteristic
810C2#1307450611yescharacteristic
811C2#1307460712yes—
812C2#1307474312yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC2×#10622573C2
hypercenter#1439D11
hypocenterC11#14311
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#10622601C2semidirect
3. C2×#10622571C2semidirect
4. C2×C22⋊C4×Dic11C2semidirect
5. #13066875C2semidirect
6. #13066864C2semidirect
7. #13066856C2semidirect
8. #13066855C2semidirect
9. #13066852C2semidirect
10. #13066841C2semidirect
11. C11×#1439C2semidirect
36. #10622573C4semidirect
56. C23×Dic11D4semidirect
66. C22×D44C2×C4semidirect
92. C2×(C2×D11)⋊C4C2×C4semidirect
96. C2×C4×Dic11D4semidirect
105. C11⋊#95C2×C4semidirect
219. #1439D11semidirect
618. C11#14311semidirect

Maximal subgroups

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

subgroupindex
C2×#106225732
C2×#106226012
C2×#106225712
C2×C22⋊C4×Dic112
#130668752
#130668642
#130668562
#130668552
#130668522
#130668412
C11×#14392
#1431111