Finite Group Databasebeta

← #14680289

Subgroups — #14680289

Order 2816.

2718 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66992C211yesmaximal, characteristic
2C2×#10622833C211yesmaximal, characteristic, complemented
3C2×#10622826C211yesmaximal, characteristic, complemented
4C2×#10622571C211yesmaximal, characteristic, complemented
5C2×#10622555C211yesmaximal, characteristic, complemented
6C22×C11⋊#95C211yesmaximal, characteristic, complemented
7#13066882C212yesmaximal, complemented
8#13066860C212yesmaximal, complemented
9#13066859C212yesmaximal, complemented
10#13066855C212yesmaximal, complemented
11C2×C11×#386C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C23×C22⋊D11C2211yescharacteristic
15C23×C22⋊D11C2211yescharacteristic
16C24×Dic11C2211yescharacteristic
17C24×Dic11C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2212yes—
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2212yes—
23C2×#66992—24no—
24C2×#66992—24no—
25C2×#66992C418yescomplemented
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2212yes—
28C22×(C2×D11)⋊C4C2212yes—
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2212yes—
31C11×#386—24no—
32C2×C11×#95C2212yes—
33#10622833—24no—
34#10622826—24no—
35C2×C11⋊#95—24no—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622571—24no—
43#10622555—24no—
44C25×C11C2311yescharacteristic
45C25×C11C2311yescharacteristic
46C24×D11C2311yescharacteristic
47C22×D4×C11—22no—
48C22×D4×C11—22no—
49C22×D4×C11—22no—
50C22×D4×C11—22no—
51C22×D4×C11—22no—
52C22×D4×C11—22no—
53C22×D4×C11C2×C414yes—
54C23×C4×C11—22no—
55C23×C4×C11—22no—
56C23×C4×C11—42no—
57C23×C4×C11—42no—
58C23×C4×C11D414yescomplemented
59C23×C4×C11C2312yes—
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2312yes—
62C22×C22⋊D11—22no—
63C22×C22⋊D11—22no—
64C22×C22⋊D11—22no—
65C22×C22⋊D11—22no—
66C22×C22⋊D11—22no—
67C22×C22⋊D11—22no—
68C22×C22⋊D11—22no—
69C22×C22⋊D11—22no—
70C22×C22⋊D11—42no—
71C22×C22⋊D11—42no—
72C22×C22⋊D11C2×C414yes—
73C22×C22⋊D11C2×C414yescomplemented
74C23×Dic11—22no—
75C23×Dic11—22no—
76C23×Dic11—42no—
77C23×Dic11—42no—
78C23×Dic11—42no—
79C23×Dic11—42no—
80C23×Dic11C2×C414yes—
81C23×Dic11D414yes—
82C23×Dic11D414yes—
83C23×Dic11D414yescomplemented
84C23×Dic11C2312yes—
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2312yes—
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—24no—
93C2×C11×C22⋊C4—42no—
94C2×C11×C22⋊C4—42no—
95C2×C22⋊Dic11—22no—
96C2×C22⋊Dic11—22no—
97C2×C22⋊Dic11—22no—
98C2×C22⋊Dic11—22no—
99C2×C22⋊Dic11—22no—
100C2×C22⋊Dic11—24no—
101C2×C22⋊Dic11—42no—
102C2×C22⋊Dic11—42no—
103C2×C22⋊Dic11C2×C414yescomplemented
104#66992—232no—
105C2×(C2×D11)⋊C4—22no—
106C2×(C2×D11)⋊C4—22no—
107C2×(C2×D11)⋊C4—24no—
108C2×(C2×D11)⋊C4—24no—
109C2×(C2×D11)⋊C4—42no—
110C2×(C2×D11)⋊C4—42no—
111C2×(C2×D11)⋊C4—42no—
112C2×(C2×D11)⋊C4—42no—
113C2×(C2×D11)⋊C4C2×C414yescomplemented
114C2×Dic11⋊C4—22no—
115C2×Dic11⋊C4—22no—
116C2×Dic11⋊C4—24no—
117C2×Dic11⋊C4—42no—
118C2×Dic11⋊C4—42no—
119C2×Dic11⋊C4C2×C414yescomplemented
120C11×#95—24no—
121C11⋊#95—24no—
122C11⋊#95—24no—
123C11⋊#95—24no—
124C11⋊#95—24no—
125C11⋊#95—24no—
126C11⋊#95—24no—
127#14271—111nomaximal, Sylow
128C24×C11—22no—
129C24×C11—22no—
130C24×C11—22no—
131C24×C11—22no—
132C24×C11—21no—
133C24×C11—21no—
134C24×C11—21no—
135C24×C11—21no—
136C24×C11—21no—
137C24×C11—21no—
138C24×C11—22no—
139C24×C11—22no—
140C24×C11—22no—
141C24×C11—22no—
142C24×C11C22×C412yes—
143C24×C11C22×C412yes—
144C24×C11C2×D412yes—
145C24×C11C2×D412yes—
146C24×C11C2×D412yes—
147C24×C11C2×D412yes—
148C24×C11#4112yes—
149C24×C11#4112yes—
150C24×C11C2411yescharacteristic
151C23×D11—21no—
152C23×D11—21no—
153C23×D11—21no—
154C23×D11—21no—
155C23×D11—21no—
156C23×D11—21no—
157C23×D11—22no—
158C23×D11—22no—
159C23×D11—22no—
160C23×D11—22no—
161C23×D11C22×C412yes—
162C2×D4×C11—28no—
163C2×D4×C11—28no—
164C2×D4×C11—28no—
165C2×D4×C11—44no—
166C2×D4×C11—44no—
167C2×D4×C11—44no—
168C2×D4×C11—44no—
169C22×C4×C11—28no—
170C22×C4×C11—22no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—22no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—22no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11—22no—
189C22×C4×C11—48no—
190C22×C4×C11—44no—
191C22×C4×C11—44no—
192C22×C4×C11—48no—
193C22×C4×C11C22×C412yes—
194C22×C4×C11C2×D414yes—
195C2×C22⋊D11—28no—
196C2×C22⋊D11—28no—
197C2×C22⋊D11—28no—
198C2×C22⋊D11—28no—
199C2×C22⋊D11—48no—
200C2×C22⋊D11—44no—
201C2×C22⋊D11—48no—
202C2×C22⋊D11—44no—
203C2×C22⋊D11—44no—
204C2×C22⋊D11—44no—
205C2×C22⋊D11—44no—
206C2×C22⋊D11—44no—
207C22×Dic11—28no—
208C22×Dic11—22no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—21no—
213C22×Dic11—22no—
214C22×Dic11—22no—
215C22×Dic11—22no—
216C22×Dic11—22no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—22no—
220C22×Dic11—22no—
221C22×Dic11—22no—
222C22×Dic11—22no—
223C22×Dic11—22no—
224C22×Dic11—22no—
225C22×Dic11—22no—
226C22×Dic11—22no—
227C22×Dic11—22no—
228C22×Dic11—22no—
229C22×Dic11—22no—
230C22×Dic11—22no—
231C22×Dic11—48no—
232C22×Dic11—44no—
233C22×Dic11—44no—
234C22×Dic11—48no—
235C22×Dic11—48no—
236C22×Dic11—44no—
237C22×Dic11—44no—
238C22×Dic11—48no—
239C22×Dic11C22⋊C4116yescomplemented
240C22×Dic11C22×C412yes—
241C22×Dic11C22×C412yes—
242C22×Dic11C22×C412yes—
243C22×Dic11C2×D414yes—
244C22×Dic11C2×D412yes—
245C22×Dic11C2×D412yes—
246C22×Dic11C2×D412yes—
247C22×Dic11C2×D412yes—
248C11×C22⋊C4—48no—
249C11×C22⋊C4—44no—
250C22⋊Dic11—28no—
251C22⋊Dic11—48no—
252C22⋊Dic11—44no—
253(C2×D11)⋊C4—28no—
254(C2×D11)⋊C4—48no—
255(C2×D11)⋊C4—48no—
256Dic11⋊C4—28no—
257Dic11⋊C4—48no—
258C22×#121—111no—
259C2×#386—111no—
260C2×#386—111no—
261C2×#386—111no—
262C2×#386D1111yescharacteristic, complemented
263C2×#380—111no—
264C22×#95—111no—
265#1445—112no—
266#1439—112no—
267#1439—112no—
268#1438—112no—
269C23×C11—24no—
270C23×C11—24no—
271C23×C11—22no—
272C23×C11—22no—
273C23×C11—24no—
274C23×C11—24no—
275C23×C11—24no—
276C23×C11—22no—
277C23×C11—22no—
278C23×C11—24no—
279C23×C11—24no—
280C23×C11—24no—
281C23×C11—24no—
282C23×C11—24no—
283C23×C11—24no—
284C23×C11—24no—
285C23×C11—22no—
286C23×C11—22no—
287C23×C11—22no—
288C23×C11—24no—
289C23×C11—24no—
290C23×C11—41no—
291C23×C11—41no—
292C23×C11—41no—
293C23×C11—41no—
294C23×C11—42no—
295C23×C11—42no—
296C23×C11—41no—
297C23×C11—42no—
298C23×C11—41no—
299C23×C11—41no—
300C23×C11—41no—
301C23×C11—42no—
302C23×C11—42no—
303C23×C11—42no—
304C23×C11—42no—
305C23×C11—42no—
306C23×C11—42no—
307C23×C11—42no—
308C23×C11C2×C22⋊C414yes—
309C23×C11C4×D414yes—
310C23×C11C4×D414yes—
311C23×C11#12114yes—
312C23×C11#12114yes—
313C23×C11#12414yes—
314C23×C11#12714yes—
315C23×C11C23×C411yescharacteristic
316C23×C11C22×D411yescharacteristic
317C23×C11C22×D411yescharacteristic
318C23×C11C22×D411yescharacteristic
319C23×C11C22×D411yescharacteristic
320C23×C11C2×#4111yescharacteristic
321C23×C11C2×#4111yescharacteristic
322C23×C11H(5,𝔽2)12yes—
323C23×C11H(5,𝔽2)12yes—
324C23×C11H(5,𝔽2)12yes—
325C23×C112−1+412yes—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—24no—
330C22×D11—24no—
331C22×D11—41no—
332C22×D11—41no—
333C22×D11—41no—
334C22×D11—41no—
335C22×D11—42no—
336C22×D11—42no—
337C22×D11—41no—
338C22×D11—42no—
339C22×D11—41no—
340C22×D11—41no—
341C22×D11—41no—
342C22×D11—42no—
343C22×D11—42no—
344C22×D11—42no—
345C22×D11—42no—
346C22×D11—42no—
347C22×D11—42no—
348C22×D11—42no—
349D4×C11—416no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—24no—
354C2×C4×C11—24no—
355C2×C4×C11—24no—
356C2×C4×C11—416no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
359C2×C4×C11—41no—
360C2×C4×C11—41no—
361C2×C4×C11—42no—
362C2×C4×C11—42no—
363C2×C4×C11—42no—
364C2×C4×C11—42no—
365C2×C4×C11—42no—
366C2×C4×C11—42no—
367C2×C4×C11—42no—
368C2×C4×C11—42no—
369C2×C4×C11—42no—
370C2×C4×C11—42no—
371C2×C4×C11—42no—
372C22⋊D11—416no—
373C22⋊D11—416no—
374C2×Dic11—24no—
375C2×Dic11—24no—
376C2×Dic11—24no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—24no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—24no—
386C2×Dic11—24no—
387C2×Dic11—24no—
388C2×Dic11—416no—
389C2×Dic11—416no—
390C2×Dic11—41no—
391C2×Dic11—41no—
392C2×Dic11—41no—
393C2×Dic11—41no—
394C2×Dic11—42no—
395C2×Dic11—42no—
396C2×Dic11—42no—
397C2×Dic11—42no—
398C2×Dic11—42no—
399C2×Dic11—42no—
400C2×Dic11—42no—
401C2×Dic11—42no—
402C2×Dic11—42no—
403C2×Dic11—42no—
404C2×Dic11—42no—
405C2×Dic11C2×C22⋊C414yes—
406C2×Dic11C2×C22⋊C414yes—
407C23×D4—111no—
408C23×D4—111no—
409C23×D4C2×D1111yescharacteristic
410C24×C4—111no—
411C24×C4—111no—
412C24×C4C2×D1111yescharacteristic
413C2×#121—118no—
414C2×#121—224no—
415C2×#121—224no—
416C22×C4⋊C4—111no—
417C22×C4⋊C4—112no—
418C22×C22⋊C4—111no—
419C22×C22⋊C4—111no—
420C22×C22⋊C4—111no—
421C22×C22⋊C4—112no—
422C22×C22⋊C4—112no—
423C22×C22⋊C4—112no—
424C22×C22⋊C4C2×D1111yescharacteristic
425C22×C22⋊C4C2×D1112yes—
426#386—24no—
427#386—224no—
428#386—224no—
429#386—224no—
430#380—224no—
431C2×#95—112no—
432C2×#95—112no—
433C2×#95—112no—
434C2×#95—112no—
435C2×#95—112no—
436C2×#95—112no—
437C2×#95—224no—
438C2×#95C2×D1112yes—
439C22×C11—24no—
440C22×C11—24no—
441C22×C11—28no—
442C22×C11—28no—
443C22×C11—24no—
444C22×C11—24no—
445C22×C11—24no—
446C22×C11—24no—
447C22×C11—28no—
448C22×C11—28no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—44no—
452C22×C11—44no—
453C22×C11—42no—
454C22×C11—81no—
455C22×C11—81no—
456C22×C11—81no—
457C22×C11—81no—
458C22×C11—82no—
459C22×C11—82no—
460C22×C11#39018yes—
461C22×C11C22×C22⋊C411yescharacteristic
462C22×C11C2×C4×D411yescharacteristic
463C22×C11C2×C4×D411yescharacteristic
464C22×C11#51812yes—
465C22×C11#52012yes—
466C22×C11C2×#12111yescharacteristic
467C22×C11C2×#12111yescharacteristic
468C22×C11C2×#12411yescharacteristic
469C22×C11C2×#12711yescharacteristic
470C22×C11#53412yes—
471C22×C11#53411yescharacteristic
472C22×C11#53412yes—
473C22×C11#53412yes—
474C22×C11#53411yescharacteristic
475C22×C11#53511yescharacteristic
476C22×C11#53611yescharacteristic
477C22×C11#53712yes—
478C22×C11#53712yes—
479C22×C11#53712yes—
480C22×C11#53812yes—
481C22×C11#53812yes—
482C22×C11#53912yes—
483C22×C11#53912yes—
484C2×D11—42no—
485C2×D11—42no—
486C2×D11—44no—
487C2×D11—44no—
488C2×D11—42no—
489C2×D11—81no—
490C2×D11—81no—
491C2×D11—81no—
492C2×D11—81no—
493C2×D11—82no—
494C2×D11—82no—
495C4×C11—44no—
496C4×C11—42no—
497C4×C11—82no—
498Dic11—24no—
499Dic11—24no—
500Dic11—44no—
501Dic11—42no—
502Dic11—82no—
503C25—111no—
504C25C22×D1111yescharacteristic
505C25C22×D1111yescharacteristic
506C22×D4—22no—
507C22×D4—22no—
508C22×D4—22no—
509C22×D4—22no—
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—114no—
513C22×D4—114no—
514C22×D4—222no—
515C22×D4—222no—
516C22×D4—222no—
517C22×D4—222no—
518C22×D4—222no—
519C22×D4—222no—
520C22×D4—222no—
521C22×D4—222no—
522C22×D4—442no—
523C22×D4—442no—
524C22×D4C4×D1114yes—
525C23×C4—22no—
526C23×C4—22no—
527C23×C4—42no—
528C23×C4—42no—
529C23×C4—111no—
530C23×C4—111no—
531C23×C4—114no—
532C23×C4—114no—
533C23×C4—114no—
534C23×C4—112no—
535C23×C4—111no—
536C23×C4—114no—
537C23×C4—112no—
538C23×C4—222no—
539C23×C4—222no—
540C23×C4—442no—
541C23×C4—442no—
542C23×C4—442no—
543C23×C4—442no—
544C23×C4C22⋊D1114yescomplemented
545C23×C4C22×D1112yes—
546C23×C4C22×D1111yescharacteristic
547C23×C4C22×D1112yes—
548#121—2232no—
549C2×C4⋊C4—114no—
550C2×C4⋊C4—222no—
551C2×C4⋊C4—222no—
552C2×C4⋊C4—224no—
553C2×C4⋊C4—442no—
554C2×C4⋊C4—442no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—22no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—42no—
560C2×C22⋊C4—42no—
561C2×C22⋊C4—114no—
562C2×C22⋊C4—114no—
563C2×C22⋊C4—222no—
564C2×C22⋊C4—222no—
565C2×C22⋊C4—222no—
566C2×C22⋊C4—222no—
567C2×C22⋊C4—224no—
568C2×C22⋊C4—224no—
569C2×C22⋊C4—222no—
570C2×C22⋊C4—222no—
571C2×C22⋊C4—222no—
572C2×C22⋊C4—224no—
573C2×C22⋊C4—442no—
574C2×C22⋊C4—442no—
575C2×C22⋊C4—442no—
576C2×C22⋊C4—442no—
577C2×C22⋊C4—442no—
578C2×C22⋊C4—442no—
579#95—24no—
580#95—224no—
581#95—224no—
582#95—224no—
583#95—224no—
584#95—224no—
585#95—224no—
586C2×C11—28no—
587C2×C11—82no—
588C2×C11C2×#39011yescharacteristic
589C2×C11#230811yescharacteristic
590C2×C11#231111yescharacteristic
591C2×C11#232512yes—
592C2×C11#232512yes—
593C2×C11#261711yescharacteristic
594C2×C11#261711yescharacteristic
595C2×C11#261811yescharacteristic
596C2×C11#261811yescharacteristic
597C2×C11#263912yes—
598C2×C11#265612yes—
599D11—82no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—21no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—21no—
614C24—112no—
615C24—221no—
616C24—221no—
617C24—221no—
618C24—221no—
619C24—221no—
620C24—222no—
621C24—222no—
622C24—222no—
623C24—222no—
624C24—221no—
625C24C2×C4×D1112yes—
626C24C2×C4×D1112yes—
627C24#433912yes—
628C24D4×D1112yes—
629C24D4×D1112yes—
630C24D4×D1112yes—
631C24#434112yes—
632C24C2×C22⋊D1112yes—
633C24C23×D1111yescharacteristic
634C2×D4—28no—
635C2×D4—28no—
636C2×D4—28no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—44no—
640C2×D4—44no—
641C2×D4—228no—
642C2×D4—228no—
643C2×D4—228no—
644C2×D4—228no—
645C2×D4—448no—
646C2×D4—444no—
647C2×D4—448no—
648C2×D4—444no—
649C2×D4—444no—
650C2×D4—444no—
651C2×D4—444no—
652C2×D4—444no—
653C22×C4—28no—
654C22×C4—21no—
655C22×C4—22no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—22no—
660C22×C4—21no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—21no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—48no—
674C22×C4—44no—
675C22×C4—44no—
676C22×C4—48no—
677C22×C4—112no—
678C22×C4—112no—
679C22×C4—112no—
680C22×C4—112no—
681C22×C4—112no—
682C22×C4—112no—
683C22×C4—1116no—
684C22×C4—112no—
685C22×C4—114no—
686C22×C4—222no—
687C22×C4—222no—
688C22×C4—222no—
689C22×C4—222no—
690C22×C4—228no—
691C22×C4—222no—
692C22×C4—221no—
693C22×C4—222no—
694C22×C4—221no—
695C22×C4—221no—
696C22×C4—221no—
697C22×C4—221no—
698C22×C4—222no—
699C22×C4—222no—
700C22×C4—222no—
701C22×C4—222no—
702C22×C4—221no—
703C22×C4—222no—
704C22×C4—222no—
705C22×C4—222no—
706C22×C4—222no—
707C22×C4—222no—
708C22×C4—222no—
709C22×C4—222no—
710C22×C4—448no—
711C22×C4—444no—
712C22×C4—448no—
713C22×C4—444no—
714C22×C4—448no—
715C22×C4—448no—
716C22×C4—444no—
717C22×C4—444no—
718C22×C4C2×C4×D1112yes—
719C22×C4C2×C22⋊D1114yes—
720C4⋊C4—228no—
721C4⋊C4—448no—
722C22⋊C4—48no—
723C22⋊C4—44no—
724C22⋊C4—228no—
725C22⋊C4—228no—
726C22⋊C4—448no—
727C22⋊C4—448no—
728C22⋊C4—448no—
729C22⋊C4—444no—
730C11#1427111yescharacteristic, complemented, Sylow
731C23—24no—
732C23—24no—
733C23—24no—
734C23—24no—
735C23—24no—
736C23—24no—
737C23—22no—
738C23—22no—
739C23—24no—
740C23—24no—
741C23—24no—
742C23—24no—
743C23—24no—
744C23—22no—
745C23—22no—
746C23—24no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—24no—
751C23—24no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—41no—
761C23—41no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23—42no—
767C23—41no—
768C23—41no—
769C23—42no—
770C23—222no—
771C23—222no—
772C23—222no—
773C23—224no—
774C23—224no—
775C23—441no—
776C23—441no—
777C23—441no—
778C23—441no—
779C23—442no—
780C23—442no—
781C23—442no—
782C23—442no—
783C23—441no—
784C23—441no—
785C23—442no—
786C23—442no—
787C23—442no—
788C23—442no—
789C23—442no—
790C23—441no—
791C23—441no—
792C23—442no—
793C23C22⋊C4×D1114yes—
794C23(C22⋊D11)⋊C414yes—
795C23#6693714yes—
796C23#6693814yes—
797C23C4×C22⋊D1114yes—
798C23#6699214yes—
799C23#6699314yes—
800C23C22×C4×D1111yescharacteristic
801C23C2×#433911yescharacteristic
802C23C2×D4×D1111yescharacteristic
803C23C2×D4×D1111yescharacteristic
804C23C2×D4×D1111yescharacteristic
805C23C2×#434111yescharacteristic
806C23#6703712yes—
807C23#6703712yes—
808C23#6704212yes—
809C23#6704312yes—
810C23C22×C22⋊D1111yescharacteristic
811D4—416no—
812D4—4416no—
813D4—4416no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—24no—
818C2×C4—24no—
819C2×C4—24no—
820C2×C4—416no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—114no—
837C2×C4—114no—
838C2×C4—224no—
839C2×C4—224no—
840C2×C4—222no—
841C2×C4—222no—
842C2×C4—224no—
843C2×C4—224no—
844C2×C4—222no—
845C2×C4—222no—
846C2×C4—222no—
847C2×C4—222no—
848C2×C4—224no—
849C2×C4—222no—
850C2×C4—224no—
851C2×C4—224no—
852C2×C4—4416no—
853C2×C4—4416no—
854C2×C4—441no—
855C2×C4—441no—
856C2×C4—441no—
857C2×C4—441no—
858C2×C4—442no—
859C2×C4—442no—
860C2×C4—442no—
861C2×C4—442no—
862C2×C4—442no—
863C2×C4—442no—
864C2×C4—442no—
865C2×C4—442no—
866C2×C4—442no—
867C2×C4—442no—
868C2×C4—442no—
869C22—28no—
870C22—24no—
871C22—24no—
872C22—28no—
873C22—24no—
874C22—24no—
875C22—24no—
876C22—24no—
877C22—28no—
878C22—28no—
879C22—42no—
880C22—42no—
881C22—44no—
882C22—44no—
883C22—42no—
884C22—82no—
885C22—82no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22—81no—
890C22—442no—
891C22—442no—
892C22—444no—
893C22—444no—
894C22—442no—
895C22—882no—
896C22—882no—
897C22—881no—
898C22—881no—
899C22—881no—
900C22—881no—
901C22#1062257018yes—
902C22C2×C22⋊C4×D1111yescharacteristic
903C22C2×(C22⋊D11)⋊C411yescharacteristic
904C22C2×#6693711yescharacteristic
905C22C2×#6693811yescharacteristic
906C22#1062307612yes—
907C22#1062307712yes—
908C22#1062309112yes—
909C22#1062309512yes—
910C22#1062312011yescharacteristic
911C22#1062312311yescharacteristic
912C22#1062312412yes—
913C22#1062312812yes—
914C22#1062312812yes—
915C22#1062313612yes—
916C22#1062313612yes—
917C22#1062317911yescharacteristic
918C22#1062318411yescharacteristic
919C22#1062319612yes—
920C22C2×C4×C22⋊D1111yescharacteristic
921C22C2×#6699211yescharacteristic
922C22C2×#6699311yescharacteristic
923C22#1062333512yes—
924C22#1062336412yes—
925C4—44no—
926C4—42no—
927C4—82no—
928C4—224no—
929C4—224no—
930C4—444no—
931C4—442no—
932C4—882no—
933C2—28no—
934C2—82no—
935C2—882no—
936C2C2×#1062257011yescharacteristic
937C2#1307119011yescharacteristic
938C2#1307120311yescharacteristic
939C2#1307131412yes—
940C2#1307131712yes—
941C2#1307435411yescharacteristic
942C2#1307435611yescharacteristic
943C2#1307436211yescharacteristic
944C2#1307436411yescharacteristic
945C2#1307454612yes—
946C2#1307472012yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#386C2
socle, cosocleC24×C11C24
prime radicalC22×#66992C2
hypercenterC2×#386D11
hypocenterC11#14271
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C2×#10622833C2semidirect
3. C2×#10622826C2semidirect
4. C2×#10622571C2semidirect
5. C2×#10622555C2semidirect
6. C22×C11⋊#95C2semidirect
7. #13066882C2semidirect
8. #13066860C2semidirect
9. #13066859C2semidirect
10. #13066855C2semidirect
11. C2×C11×#386C2semidirect
25. C2×#66992C4semidirect
58. C23×C4×C11D4semidirect
73. C22×C22⋊D11C2×C4semidirect
83. C23×Dic11D4semidirect
103. C2×C22⋊Dic11C2×C4semidirect
113. C2×(C2×D11)⋊C4C2×C4semidirect
119. C2×Dic11⋊C4C2×C4semidirect
239. C22×Dic11C22⋊C4semidirect
262. C2×#386D11semidirect
544. C23×C4C22⋊D11semidirect
730. C11#14271semidirect

Maximal subgroups

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

subgroupindex
C22×#669922
C2×#106228332
C2×#106228262
C2×#106225712
C2×#106225552
C22×C11⋊#952
#130668822
#130668602
#130668592
#130668552
C2×C11×#3862
#1427111