Finite Group Databasebeta

← #14675993

Subgroups — #14675993

Order 2816.

3526 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊C4×D11C211yesmaximal, characteristic
2C2×#10622277C212yesmaximal, complemented
3C2×#10622600C211yesmaximal, characteristic, complemented
4C2×#10622568C212yesmaximal
5C2×#10622279C211yesmaximal, characteristic, complemented
6#13066862C211yesmaximal, characteristic, complemented
7#13066861C211yesmaximal, characteristic, complemented
8#13066858C211yesmaximal, characteristic, complemented
9#13066853C212yesmaximal, complemented
10#13066852C212yesmaximal, complemented
11C11×#1439C211yesmaximal, characteristic, complemented
12C25×D11C2211yescharacteristic
13C23×C4×D11C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic, complemented
16C22×C11×C22⋊C4C2212yes—
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C22⋊Dic11C2212yes—
19C22×C22⋊Dic11C2211yescharacteristic
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2212yes—
26C22×C4⋊Dic11C2211yescharacteristic, complemented
27C22×C4×Dic11C2212yescomplemented
28C2×C22⋊C4×D11—24no—
29C2×C22⋊C4×D11—24no—
30C2×C22⋊C4×D11C418yescomplemented
31C2×C11×#95C2211yescharacteristic, complemented
32C2×C11×#95C2212yescomplemented
33C2×C11⋊#95C2211yescharacteristic, complemented
34C2×C11⋊#95C2212yescomplemented
35C2×C11⋊#95C2212yescomplemented
36C2×C11⋊#95C2212yescomplemented
37C2×C11⋊#95C2212yescomplemented
38#10622600—24no—
39#10622568—28no—
40#10622279—24no—
41#10622277—28no—
42C25×C11C2311yescharacteristic
43C24×D11—22no—
44C24×D11—22no—
45C24×D11—22no—
46C24×D11—22no—
47C24×D11—22no—
48C24×D11—22no—
49C24×D11—24no—
50C24×D11—24no—
51C24×D11—42no—
52C24×D11—42no—
53C24×D11C2×C414yes—
54C24×D11C2311yescharacteristic
55C24×D11C2311yescharacteristic
56C23×C4×C11C2312yes—
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2312yes—
59C23×C4×C11C2311yescharacteristic
60C23×Dic11C2312yes—
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2312yes—
63C23×Dic11C2311yescharacteristic
64C22×C4×D11—22no—
65C22×C4×D11—22no—
66C22×C4×D11—24no—
67C22×C4×D11—24no—
68C22×C4×D11—42no—
69C22×C4×D11—42no—
70C22×C4×D11C2×C414yes—
71C22×C4×D11C2×C414yes—
72C22×C4×D11D414yes—
73C22×C4×D11D414yes—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—42no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—24no—
79C2×C11×C22⋊C4—24no—
80C2×C11×C22⋊C4—42no—
81C2×C11×C22⋊C4C2×C414yes—
82C2×C22⋊Dic11—22no—
83C2×C22⋊Dic11—22no—
84C2×C22⋊Dic11—24no—
85C2×C22⋊Dic11—24no—
86C2×C22⋊Dic11—42no—
87C2×C22⋊Dic11C2×C414yes—
88C2×(C2×D11)⋊C4—24no—
89C2×(C2×D11)⋊C4—24no—
90C2×(C2×D11)⋊C4—22no—
91C2×(C2×D11)⋊C4—22no—
92C2×(C2×D11)⋊C4—22no—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—24no—
95C2×(C2×D11)⋊C4—24no—
96C2×(C2×D11)⋊C4—24no—
97C2×(C2×D11)⋊C4—24no—
98C2×(C2×D11)⋊C4—24no—
99C2×(C2×D11)⋊C4—24no—
100C2×(C2×D11)⋊C4—24no—
101C2×(C2×D11)⋊C4—42no—
102C2×(C2×D11)⋊C4—42no—
103C2×(C2×D11)⋊C4C2×C414yes—
104C2×(C2×D11)⋊C4C2×C414yes—
105C2×(C2×D11)⋊C4D418yes—
106C2×C4⋊Dic11—22no—
107C2×C4⋊Dic11—42no—
108C2×C4×Dic11—24no—
109C2×C4×Dic11—42no—
110C2×C4×Dic11—42no—
111C22⋊C4×D11—232no—
112C11×#95—24no—
113C11×#95—22no—
114C11⋊#95—24no—
115C11⋊#95—22no—
116C11⋊#95—24no—
117C11⋊#95—24no—
118C11⋊#95—24no—
119#13903—111nomaximal, Sylow
120C24×C11—21no—
121C24×C11—21no—
122C24×C11—22no—
123C24×C11—21no—
124C24×C11—21no—
125C24×C11—22no—
126C24×C11—22no—
127C24×C11—22no—
128C24×C11C22×C412yes—
129C24×C11#4112yes—
130C24×C11#4112yes—
131C24×C11C2411yescharacteristic
132C23×D11—21no—
133C23×D11—21no—
134C23×D11—21no—
135C23×D11—21no—
136C23×D11—22no—
137C23×D11—22no—
138C23×D11—28no—
139C23×D11—28no—
140C23×D11—28no—
141C23×D11—28no—
142C23×D11—28no—
143C23×D11—21no—
144C23×D11—21no—
145C23×D11—22no—
146C23×D11—21no—
147C23×D11—21no—
148C23×D11—22no—
149C23×D11—22no—
150C23×D11—22no—
151C23×D11—28no—
152C23×D11—28no—
153C23×D11—216no—
154C23×D11—48no—
155C23×D11—48no—
156C23×D11—48no—
157C23×D11—48no—
158C23×D11—48no—
159C23×D11—48no—
160C23×D11—48no—
161C23×D11—48no—
162C23×D11—48no—
163C23×D11—44no—
164C23×D11—48no—
165C23×D11—44no—
166C23×D11—48no—
167C23×D11—44no—
168C23×D11—44no—
169C23×D11C22×C412yes—
170C23×D11C22×C412yes—
171C23×D11C2×D412yes—
172C23×D11C2×D412yes—
173C23×D11C2×D414yes—
174C23×D11#4112yes—
175C23×D11#4112yes—
176C23×D11#4114yes—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
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—22no—
190C22×C4×C11—22no—
191C22×C4×C11—22no—
192C22×C4×C11—22no—
193C22×C4×C11—22no—
194C22×C4×C11—22no—
195C22×C4×C11—22no—
196C22×C4×C11C22×C412yes—
197C22×C4×C11C22×C412yes—
198C22×C4×C11C2×D414yes—
199C22×C4×C11C2×D412yes—
200C22×C4×C11C2×D412yes—
201C22×Dic11—22no—
202C22×Dic11—22no—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11—22no—
206C22×Dic11—22no—
207C22×Dic11—22no—
208C22×Dic11—22no—
209C22×Dic11—22no—
210C22×Dic11—22no—
211C22×Dic11—22no—
212C22×Dic11—22no—
213C22×Dic11—22no—
214C22×Dic11—22no—
215C22×Dic11—22no—
216C22×Dic11—22no—
217C22×Dic11—22no—
218C22×Dic11—22no—
219C22×Dic11—22no—
220C22×Dic11C22×C412yes—
221C22×Dic11C22×C412yes—
222C22×Dic11C2×D414yes—
223C22×Dic11C2×D412yes—
224C22×Dic11C2×D412yes—
225C2×C4×D11—28no—
226C2×C4×D11—216no—
227C2×C4×D11—48no—
228C2×C4×D11—44no—
229C2×C4×D11—44no—
230C2×C4×D11—48no—
231C2×C4×D11—48no—
232C2×C4×D11—44no—
233C2×C4×D11—44no—
234C2×C4×D11C22⋊C4116yescomplemented
235C11×C4⋊C4—44no—
236C11×C22⋊C4—28no—
237C11×C22⋊C4—48no—
238C22⋊Dic11—28no—
239C22⋊Dic11—48no—
240(C2×D11)⋊C4—28no—
241(C2×D11)⋊C4—216no—
242(C2×D11)⋊C4—28no—
243(C2×D11)⋊C4—48no—
244(C2×D11)⋊C4—48no—
245(C2×D11)⋊C4—48no—
246C4⋊Dic11—44no—
247C4×Dic11—48no—
248C23×C22⋊C4—111no—
249C2×#381—112no—
250C2×#380—111no—
251C2×#379—112no—
252C2×C4×C22⋊C4—111no—
253#1439—111no—
254#1439—111no—
255#1439—111no—
256#1439D1111yescharacteristic, complemented
257#1437—112no—
258#1437—112no—
259C23×C11—22no—
260C23×C11—22no—
261C23×C11—24no—
262C23×C11—24no—
263C23×C11—22no—
264C23×C11—22no—
265C23×C11—22no—
266C23×C11—22no—
267C23×C11—24no—
268C23×C11—24no—
269C23×C11—24no—
270C23×C11—24no—
271C23×C11—42no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—42no—
276C23×C11—41no—
277C23×C11—42no—
278C23×C11—42no—
279C23×C11—42no—
280C23×C11—42no—
281C23×C11#11714yes—
282C23×C11C23×C411yescharacteristic
283C23×C11C22×D411yescharacteristic
284C23×C11C22×D411yescharacteristic
285C23×C11C22×D412yes—
286C23×C11C2×#4111yescharacteristic
287C23×C11C2×#4111yescharacteristic
288C23×C11C2×#4111yescharacteristic
289C23×C11C2×#4111yescharacteristic
290C23×C11C2×#4112yes—
291C23×C11H(5,𝔽2)12yes—
292C23×C11H(5,𝔽2)12yes—
293C22×D11—22no—
294C22×D11—22no—
295C22×D11—24no—
296C22×D11—22no—
297C22×D11—22no—
298C22×D11—22no—
299C22×D11—22no—
300C22×D11—22no—
301C22×D11—24no—
302C22×D11—22no—
303C22×D11—24no—
304C22×D11—24no—
305C22×D11—24no—
306C22×D11—24no—
307C22×D11—24no—
308C22×D11—24no—
309C22×D11—24no—
310C22×D11—24no—
311C22×D11—232no—
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—24no—
315C22×D11—24no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—24no—
321C22×D11—24no—
322C22×D11—24no—
323C22×D11—24no—
324C22×D11—432no—
325C22×D11—432no—
326C22×D11—416no—
327C22×D11—416no—
328C22×D11—416no—
329C22×D11—432no—
330C22×D11—432no—
331C22×D11—416no—
332C22×D11—416no—
333C22×D11—42no—
334C22×D11—41no—
335C22×D11—41no—
336C22×D11—41no—
337C22×D11—42no—
338C22×D11—41no—
339C22×D11—42no—
340C22×D11—42no—
341C22×D11—42no—
342C22×D11—42no—
343C22×D11—416no—
344C22×D11C2×C22⋊C414yes—
345C22×D11#11714yes—
346C22×D11C4×D418yes—
347C22×D11#12118yes—
348C22×D11#12414yes—
349C22×D11#12714yes—
350C2×C4×C11—24no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—24no—
354C2×C4×C11—22no—
355C2×C4×C11—24no—
356C2×C4×C11—24no—
357C2×C4×C11—24no—
358C2×C4×C11—24no—
359C2×C4×C11—42no—
360C2×C4×C11—42no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
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—
372C2×C4×C11—42no—
373C2×C4×C11C2×C22⋊C414yes—
374C2×Dic11—24no—
375C2×Dic11—24no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—24no—
380C2×Dic11—24no—
381C2×Dic11—24no—
382C2×Dic11—24no—
383C2×Dic11—42no—
384C2×Dic11—42no—
385C2×Dic11—41no—
386C2×Dic11—41no—
387C2×Dic11—42no—
388C2×Dic11—42no—
389C2×Dic11—42no—
390C2×Dic11—42no—
391C2×Dic11—42no—
392C2×Dic11—42no—
393C2×Dic11—42no—
394C2×Dic11—42no—
395C2×Dic11—42no—
396C2×Dic11—42no—
397C2×Dic11C2×C22⋊C414yes—
398C4×D11—416no—
399C4×D11—416no—
400C26—111no—
401C24×C4—111no—
402C24×C4—111no—
403C22×C4⋊C4—111no—
404C22×C4⋊C4C2×D1111yescharacteristic, complemented
405C22×C22⋊C4—111no—
406C22×C22⋊C4—111no—
407C22×C22⋊C4—111no—
408C22×C22⋊C4—112no—
409C22×C22⋊C4—118no—
410C22×C22⋊C4—112no—
411C22×C22⋊C4—112no—
412C22×C22⋊C4—112no—
413C22×C22⋊C4—112no—
414C22×C22⋊C4—224no—
415C22×C22⋊C4—224no—
416C22×C22⋊C4C2×D1112yes—
417C22×C22⋊C4C2×D1111yescharacteristic
418C22×C42—112no—
419#381—228no—
420#380—224no—
421#379—228no—
422C4×C22⋊C4—224no—
423C2×#95—112no—
424C2×#95—112no—
425C2×#95—112no—
426C2×#95—112no—
427C2×#95—111no—
428C2×#95C2×D1112yescomplemented
429C2×#95C2×D1111yescharacteristic, complemented
430C22×C11—28no—
431C22×C11—24no—
432C22×C11—42no—
433C22×C11—42no—
434C22×C11—42no—
435C22×C11—44no—
436C22×C11—44no—
437C22×C11—44no—
438C22×C11—42no—
439C22×C11—42no—
440C22×C11—42no—
441C22×C11C22×C22⋊C411yescharacteristic
442C22×C11C2×#11711yescharacteristic
443C22×C11C2×#11711yescharacteristic
444C22×C11C2×C4×D412yes—
445C22×C11#51812yes—
446C22×C11C2×#12112yes—
447C22×C11#52511yescharacteristic
448C22×C11#52511yescharacteristic
449C22×C11#52511yescharacteristic
450C22×C11#52511yescharacteristic
451C22×C11C2×#12411yescharacteristic
452C22×C11C2×#12711yescharacteristic
453C22×C11#53411yescharacteristic
454C22×C11#53412yes—
455C22×C11#53411yescharacteristic
456C22×C11#54612yes—
457C22×C11#54612yes—
458C22×C11#54612yes—
459C22×C11#54612yes—
460C22×C11#55112yes—
461C22×C11#55112yes—
462C22×C11#55112yes—
463C22×C11#55112yes—
464C2×D11—24no—
465C2×D11—24no—
466C2×D11—24no—
467C2×D11—28no—
468C2×D11—28no—
469C2×D11—28no—
470C2×D11—28no—
471C2×D11—24no—
472C2×D11—24no—
473C2×D11—24no—
474C2×D11—28no—
475C2×D11—24no—
476C2×D11—464no—
477C2×D11—42no—
478C2×D11—42no—
479C2×D11—42no—
480C2×D11—44no—
481C2×D11—44no—
482C2×D11—44no—
483C2×D11—42no—
484C2×D11—42no—
485C2×D11—42no—
486C2×D11#39018yes—
487C4×C11—24no—
488C4×C11—44no—
489C4×C11—42no—
490C4×C11—82no—
491Dic11—24no—
492Dic11—44no—
493Dic11—42no—
494Dic11—82no—
495C25—111no—
496C25—111no—
497C25—114no—
498C25—222no—
499C25—222no—
500C25—222no—
501C25—222no—
502C25—224no—
503C25—224no—
504C25—222no—
505C25—222no—
506C25—442no—
507C25—442no—
508C25C22×D1111yescharacteristic
509C23×C4—111no—
510C23×C4—114no—
511C23×C4—114no—
512C23×C4—114no—
513C23×C4—112no—
514C23×C4—111no—
515C23×C4—114no—
516C23×C4—112no—
517C23×C4—222no—
518C23×C4—222no—
519C23×C4—224no—
520C23×C4—224no—
521C23×C4—442no—
522C23×C4—442no—
523C23×C4C22×D1112yes—
524C23×C4C22×D1111yescharacteristic
525C23×C4C22×D1112yes—
526C23×C4C22×D1111yescharacteristic
527C2×C4⋊C4—22no—
528C2×C4⋊C4—42no—
529C2×C4⋊C4—222no—
530C2×C4⋊C4—442no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—42no—
536C2×C22⋊C4—114no—
537C2×C22⋊C4—114no—
538C2×C22⋊C4—114no—
539C2×C22⋊C4—118no—
540C2×C22⋊C4—2232no—
541C2×C22⋊C4—222no—
542C2×C22⋊C4—222no—
543C2×C22⋊C4—224no—
544C2×C22⋊C4—224no—
545C2×C22⋊C4—222no—
546C2×C22⋊C4—222no—
547C2×C22⋊C4—222no—
548C2×C22⋊C4—222no—
549C2×C22⋊C4—224no—
550C2×C22⋊C4—224no—
551C2×C22⋊C4—224no—
552C2×C22⋊C4—224no—
553C2×C22⋊C4—224no—
554C2×C22⋊C4—224no—
555C2×C22⋊C4—224no—
556C2×C22⋊C4—224no—
557C2×C22⋊C4—224no—
558C2×C22⋊C4—442no—
559C2×C22⋊C4—442no—
560C2×C22⋊C4—442no—
561C2×C22⋊C4C4×D1114yes—
562C2×C42—224no—
563C2×C42—442no—
564C2×C42—442no—
565#95—22no—
566#95—24no—
567#95—224no—
568#95—224no—
569#95—224no—
570#95—222no—
571#95—224no—
572C2×C11—44no—
573C2×C11#228011yescharacteristic
574C2×C11C2×#39011yescharacteristic
575C2×C11#230811yescharacteristic
576C2×C11#234212yes—
577C2×C11#234212yes—
578C2×C11#253412yes—
579C2×C11#253412yes—
580C2×C11#253911yescharacteristic
581C2×C11#253911yescharacteristic
582C2×C11#256111yescharacteristic
583C2×C11#256111yescharacteristic
584D11—28no—
585D11—44no—
586C24—21no—
587C24—21no—
588C24—22no—
589C24—22no—
590C24—21no—
591C24—21no—
592C24—22no—
593C24—22no—
594C24—112no—
595C24—114no—
596C24—112no—
597C24—112no—
598C24—114no—
599C24—112no—
600C24—112no—
601C24—112no—
602C24—228no—
603C24—228no—
604C24—2216no—
605C24—228no—
606C24—228no—
607C24—228no—
608C24—228no—
609C24—221no—
610C24—222no—
611C24—221no—
612C24—221no—
613C24—221no—
614C24—222no—
615C24—228no—
616C24—221no—
617C24—221no—
618C24—222no—
619C24—221no—
620C24—222no—
621C24—221no—
622C24—222no—
623C24—222no—
624C24—448no—
625C24—448no—
626C24—448no—
627C24—448no—
628C24—448no—
629C24—444no—
630C24—448no—
631C24—444no—
632C24—448no—
633C24—448no—
634C24—448no—
635C24—448no—
636C24—444no—
637C24—448no—
638C24—444no—
639C24C2×C4×D1112yes—
640C24#434112yes—
641C24#434312yes—
642C24C23×D1111yescharacteristic
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—112no—
663C22×C4—112no—
664C22×C4—112no—
665C22×C4—1116no—
666C22×C4—112no—
667C22×C4—114no—
668C22×C4—228no—
669C22×C4—2216no—
670C22×C4—222no—
671C22×C4—222no—
672C22×C4—222no—
673C22×C4—222no—
674C22×C4—221no—
675C22×C4—221no—
676C22×C4—222no—
677C22×C4—222no—
678C22×C4—222no—
679C22×C4—222no—
680C22×C4—222no—
681C22×C4—222no—
682C22×C4—222no—
683C22×C4—222no—
684C22×C4—222no—
685C22×C4—222no—
686C22×C4—222no—
687C22×C4—222no—
688C22×C4—222no—
689C22×C4—448no—
690C22×C4—444no—
691C22×C4—448no—
692C22×C4—444no—
693C22×C4—444no—
694C22×C4—448no—
695C22×C4—444no—
696C22×C4C2×C4×D1112yes—
697C22×C4C2×C4×D1112yes—
698C22×C4D4×D1114yes—
699C22×C4D4×D1112yes—
700C22×C4D4×D1112yes—
701C4⋊C4—44no—
702C4⋊C4—444no—
703C22⋊C4—28no—
704C22⋊C4—48no—
705C22⋊C4—228no—
706C22⋊C4—2216no—
707C22⋊C4—228no—
708C22⋊C4—228no—
709C22⋊C4—448no—
710C22⋊C4—448no—
711C22⋊C4—448no—
712C22⋊C4—448no—
713C42—448no—
714C11#1390311yescharacteristic, complemented, Sylow
715C23—22no—
716C23—22no—
717C23—24no—
718C23—24no—
719C23—24no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—42no—
728C23—41no—
729C23—41no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—41no—
734C23—42no—
735C23—41no—
736C23—42no—
737C23—114no—
738C23—114no—
739C23—118no—
740C23—118no—
741C23—114no—
742C23—114no—
743C23—2232no—
744C23—224no—
745C23—222no—
746C23—222no—
747C23—224no—
748C23—222no—
749C23—224no—
750C23—224no—
751C23—222no—
752C23—222no—
753C23—224no—
754C23—222no—
755C23—222no—
756C23—224no—
757C23—224no—
758C23—222no—
759C23—224no—
760C23—224no—
761C23—224no—
762C23—224no—
763C23—222no—
764C23—222no—
765C23—224no—
766C23—224no—
767C23—222no—
768C23—222no—
769C23—224no—
770C23—222no—
771C23—222no—
772C23—224no—
773C23—224no—
774C23—4432no—
775C23—4416no—
776C23—4432no—
777C23—4416no—
778C23—4432no—
779C23—4432no—
780C23—4416no—
781C23—4416no—
782C23—4416no—
783C23—4416no—
784C23—441no—
785C23—441no—
786C23—442no—
787C23—442no—
788C23—442no—
789C23—442no—
790C23—442no—
791C23—441no—
792C23—442no—
793C23—441no—
794C23#6694514yes—
795C23C22×C4×D1111yescharacteristic
796C23C2×D4×D1111yescharacteristic
797C23C2×D4×D1112yes—
798C23C2×D4×D1111yescharacteristic
799C23C2×#434111yescharacteristic
800C23#6703712yes—
801C23C2×#434311yescharacteristic
802C23#41×D1111yescharacteristic
803C23#41×D1112yes—
804C23#41×D1111yescharacteristic
805C23#6704212yes—
806C2×C4—24no—
807C2×C4—22no—
808C2×C4—24no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—41no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—41no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—114no—
830C2×C4—224no—
831C2×C4—222no—
832C2×C4—224no—
833C2×C4—222no—
834C2×C4—222no—
835C2×C4—224no—
836C2×C4—224no—
837C2×C4—224no—
838C2×C4—224no—
839C2×C4—4416no—
840C2×C4—4416no—
841C2×C4—442no—
842C2×C4—441no—
843C2×C4—442no—
844C2×C4—442no—
845C2×C4—442no—
846C2×C4—442no—
847C2×C4—441no—
848C2×C4—442no—
849C2×C4—442no—
850C2×C4—442no—
851C2×C4—442no—
852C2×C4—442no—
853C2×C4—442no—
854C2×C4—442no—
855C2×C4C22⋊C4×D1114yes—
856C22—28no—
857C22—24no—
858C22—42no—
859C22—44no—
860C22—44no—
861C22—44no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—42no—
866C22—42no—
867C22—118no—
868C22—224no—
869C22—228no—
870C22—228no—
871C22—228no—
872C22—228no—
873C22—224no—
874C22—224no—
875C22—224no—
876C22—224no—
877C22—224no—
878C22—228no—
879C22—224no—
880C22—4464no—
881C22—442no—
882C22—444no—
883C22—444no—
884C22—444no—
885C22—442no—
886C22—442no—
887C22—442no—
888C22—442no—
889C22—442no—
890C22C2×C22⋊C4×D1111yescharacteristic
891C22C2×#6694511yescharacteristic
892C22D11×#11711yescharacteristic
893C22C4×D4×D1112yes—
894C22#1062307612yes—
895C22#1062312011yescharacteristic
896C22#1062312212yes—
897C22D11×#12112yes—
898C22#1062313612yes—
899C22#1062313711yescharacteristic
900C22#1062313711yescharacteristic
901C22#1062314312yes—
902C22#1062315811yescharacteristic
903C22#1062315811yescharacteristic
904C22#1062316112yes—
905C22#1062316812yes—
906C22#1062318411yescharacteristic
907C22#1062318512yes—
908C22#1062318912yes—
909C22D11×#12411yescharacteristic
910C22#1062321012yes—
911C22#1062323612yes—
912C22D11×#12711yescharacteristic
913C4—24no—
914C4—44no—
915C4—42no—
916C4—82no—
917C4—224no—
918C4—444no—
919C4—442no—
920C4—882no—
921C2—44no—
922C2—228no—
923C2—444no—
924C2#1307099811yescharacteristic
925C2D11×#39011yescharacteristic
926C2#1307119011yescharacteristic
927C2#1307146012yes—
928C2#1307146312yes—
929C2#1307350112yes—
930C2#1307350712yes—
931C2#1307354111yescharacteristic
932C2#1307354311yescharacteristic
933C2#1307376811yescharacteristic
934C2#1307377011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC25×D11C22
hypercenter#1439D11
hypocenterC11#13903
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#10622277C2semidirect
3. C2×#10622600C2semidirect
5. C2×#10622279C2semidirect
6. #13066862C2semidirect
7. #13066861C2semidirect
8. #13066858C2semidirect
9. #13066853C2semidirect
10. #13066852C2semidirect
11. C11×#1439C2semidirect
15. C22×C11×C4⋊C4C22semidirect
26. C22×C4⋊Dic11C22semidirect
27. C22×C4×Dic11C22semidirect
30. C2×C22⋊C4×D11C4semidirect
31. C2×C11×#95C22semidirect
32. C2×C11×#95C22semidirect
33. C2×C11⋊#95C22semidirect
34. C2×C11⋊#95C22semidirect
35. C2×C11⋊#95C22semidirect
36. C2×C11⋊#95C22semidirect
37. C2×C11⋊#95C22semidirect
234. C2×C4×D11C22⋊C4semidirect
256. #1439D11semidirect
404. C22×C4⋊C4C2×D11semidirect
428. C2×#95C2×D11semidirect
429. C2×#95C2×D11semidirect
714. C11#13903semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊C4×D112
C2×#106222772
C2×#106226002
C2×#106225682
C2×#106222792
#130668622
#130668612
#130668582
#130668532
#130668522
C11×#14392
#1390311