Finite Group Databasebeta

← #14680941

Subgroups — #14680941

Order 2816.

3390 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊C4×D11C211yesmaximal, characteristic
2C2×#10622280C211yesmaximal, characteristic, complemented
3C2×#10622600C211yesmaximal, characteristic, complemented
4C2×#10622568C212yesmaximal
5#13066862C211yesmaximal, characteristic, complemented
6#13066861C211yesmaximal, characteristic, complemented
7#13066860C212yesmaximal, complemented
8#13066859C212yesmaximal, complemented
9#13066858C211yesmaximal, characteristic, complemented
10(C2×D11)⋊#95C212yesmaximal, complemented
11C11×#1439C211yesmaximal, characteristic, complemented
12C25×D11C2211yescharacteristic
13C23×C4×D11C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic, complemented
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2212yes—
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C22⋊Dic11C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×C4⋊Dic11C2211yescharacteristic, complemented
27C22×Dic11⋊C4C2212yescomplemented
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#10622280—24no—
41C25×C11C2311yescharacteristic
42C24×D11—22no—
43C24×D11—22no—
44C24×D11—22no—
45C24×D11—22no—
46C24×D11—42no—
47C24×D11—42no—
48C24×D11—42no—
49C24×D11—42no—
50C24×D11C2×C414yes—
51C24×D11D414yes—
52C24×D11Q814yes—
53C24×D11C2311yescharacteristic
54C24×D11C2311yescharacteristic
55C23×C4×C11C2312yes—
56C23×C4×C11C2312yes—
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×Dic11C2312yes—
60C23×Dic11C2312yes—
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2311yescharacteristic
63C22×C4×D11—22no—
64C22×C4×D11—22no—
65C22×C4×D11—42no—
66C22×C4×D11—42no—
67C22×C4×D11—42no—
68C22×C4×D11—42no—
69C22×C4×D11C2×C414yes—
70C22×C4×D11C2×C414yes—
71C22×C4×D11D414yes—
72C22×C4×D11D414yes—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—42no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—24no—
78C2×C11×C22⋊C4—42no—
79C2×C11×C22⋊C4—42no—
80C2×C11×C22⋊C4C2×C414yes—
81C2×C22⋊Dic11—22no—
82C2×C22⋊Dic11—22no—
83C2×C22⋊Dic11—24no—
84C2×C22⋊Dic11—42no—
85C2×C22⋊Dic11—42no—
86C2×C22⋊Dic11C2×C414yes—
87C2×(C2×D11)⋊C4—22no—
88C2×(C2×D11)⋊C4—22no—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4—22no—
91C2×(C2×D11)⋊C4—24no—
92C2×(C2×D11)⋊C4—24no—
93C2×(C2×D11)⋊C4—24no—
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—42no—
100C2×(C2×D11)⋊C4—42no—
101C2×(C2×D11)⋊C4—42no—
102C2×(C2×D11)⋊C4—42no—
103C2×(C2×D11)⋊C4C2×C414yes—
104C2×(C2×D11)⋊C4C2×C414yes—
105C2×C4⋊Dic11—22no—
106C2×C4⋊Dic11—42no—
107C2×Dic11⋊C4—24no—
108C2×Dic11⋊C4—42no—
109C2×Dic11⋊C4—42no—
110C22⋊C4×D11—232no—
111C11×#95—22no—
112C11×#95—42no—
113C11⋊#95—22no—
114C11⋊#95—24no—
115C11⋊#95—42no—
116C11⋊#95—42no—
117C11⋊#95—42no—
118#14338—111nomaximal, Sylow
119C24×C11—21no—
120C24×C11—21no—
121C24×C11—21no—
122C24×C11—21no—
123C24×C11—22no—
124C24×C11—22no—
125C24×C11—22no—
126C24×C11—22no—
127C24×C11C22×C412yes—
128C24×C11C2×D412yes—
129C24×C11C2×Q812yes—
130C24×C11C2411yescharacteristic
131C23×D11—22no—
132C23×D11—22no—
133C23×D11—22no—
134C23×D11—22no—
135C23×D11—21no—
136C23×D11—21no—
137C23×D11—21no—
138C23×D11—21no—
139C23×D11—22no—
140C23×D11—22no—
141C23×D11—22no—
142C23×D11—22no—
143C23×D11—28no—
144C23×D11—28no—
145C23×D11—28no—
146C23×D11—28no—
147C23×D11—28no—
148C23×D11—28no—
149C23×D11—48no—
150C23×D11—48no—
151C23×D11—48no—
152C23×D11—48no—
153C23×D11—48no—
154C23×D11—48no—
155C23×D11—44no—
156C23×D11—48no—
157C23×D11—44no—
158C23×D11—44no—
159C23×D11—48no—
160C23×D11—44no—
161C23×D11—48no—
162C23×D11—48no—
163C23×D11—48no—
164C23×D11—48no—
165C23×D11C4⋊C4116yescomplemented
166C23×D11C22×C412yes—
167C23×D11C22×C412yes—
168C23×D11C2×D412yes—
169C23×D11C2×D412yes—
170C23×D11C2×D412yes—
171C23×D11C2×D412yes—
172C23×D11C2×Q812yes—
173C23×D11C2×Q812yes—
174C23×D11#4112yes—
175C23×D11#4112yes—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
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—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×D412yes—
199C22×C4×C11C2×D412yes—
200C22×Dic11—21no—
201C22×Dic11—21no—
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—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×D412yes—
223C22×Dic11C2×D412yes—
224C2×C4×D11—28no—
225C2×C4×D11—48no—
226C2×C4×D11—48no—
227C2×C4×D11—44no—
228C2×C4×D11—44no—
229C2×C4×D11—48no—
230C2×C4×D11—44no—
231C2×C4×D11—48no—
232C2×C4×D11—44no—
233C2×C4×D11C22⋊C4116yescomplemented
234C11×C4⋊C4—44no—
235C11×C22⋊C4—28no—
236C11×C22⋊C4—48no—
237C22⋊Dic11—28no—
238C22⋊Dic11—48no—
239(C2×D11)⋊C4—28no—
240(C2×D11)⋊C4—28no—
241(C2×D11)⋊C4—48no—
242(C2×D11)⋊C4—48no—
243(C2×D11)⋊C4—48no—
244(C2×D11)⋊C4—48no—
245C4⋊Dic11—44no—
246Dic11⋊C4—48no—
247C23×C22⋊C4—111no—
248C2×#380—111no—
249C2×#380—111no—
250C2×#379—112no—
251#1439—112no—
252#1439—111no—
253#1439—111no—
254#1439—112no—
255#1439—111no—
256#1439D1111yescharacteristic, complemented
257C22⋊#95—112no—
258C23×C11—22no—
259C23×C11—22no—
260C23×C11—24no—
261C23×C11—24no—
262C23×C11—22no—
263C23×C11—22no—
264C23×C11—22no—
265C23×C11—22no—
266C23×C11—24no—
267C23×C11—24no—
268C23×C11—24no—
269C23×C11—24no—
270C23×C11—41no—
271C23×C11—42no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—42no—
275C23×C11—41no—
276C23×C11—42no—
277C23×C11—42no—
278C23×C11—42no—
279C23×C11—42no—
280C23×C11C2×C4⋊C414yes—
281C23×C11C23×C411yescharacteristic
282C23×C11C22×D411yescharacteristic
283C23×C11C22×D411yescharacteristic
284C23×C11C22×D411yescharacteristic
285C23×C11C22×Q811yescharacteristic
286C23×C11C2×#4111yescharacteristic
287C23×C11C2×#4111yescharacteristic
288C23×C11H(5,𝔽2)12yes—
289C23×C11H(5,𝔽2)12yes—
290C23×C11H(5,𝔽2)12yes—
291C23×C11H(5,𝔽2)12yes—
292C22×D11—24no—
293C22×D11—24no—
294C22×D11—22no—
295C22×D11—24no—
296C22×D11—22no—
297C22×D11—24no—
298C22×D11—24no—
299C22×D11—22no—
300C22×D11—24no—
301C22×D11—22no—
302C22×D11—24no—
303C22×D11—24no—
304C22×D11—24no—
305C22×D11—24no—
306C22×D11—24no—
307C22×D11—24no—
308C22×D11—22no—
309C22×D11—22no—
310C22×D11—24no—
311C22×D11—24no—
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—24no—
317C22×D11—24no—
318C22×D11—24no—
319C22×D11—24no—
320C22×D11—232no—
321C22×D11—432no—
322C22×D11—416no—
323C22×D11—416no—
324C22×D11—432no—
325C22×D11—416no—
326C22×D11—416no—
327C22×D11—432no—
328C22×D11—416no—
329C22×D11—416no—
330C22×D11—432no—
331C22×D11—41no—
332C22×D11—42no—
333C22×D11—41no—
334C22×D11—41no—
335C22×D11—42no—
336C22×D11—41no—
337C22×D11—42no—
338C22×D11—42no—
339C22×D11—42no—
340C22×D11—42no—
341C22×D11C2×C22⋊C414yes—
342C22×D11C2×C4⋊C414yes—
343C22×D11C2×C4⋊C414yes—
344C22×D11#11714yes—
345C22×D11#12114yes—
346C22×D11#12114yes—
347C22×D11C22⋊Q814yes—
348C22×D11C22⋊Q814yes—
349C2×C4×C11—24no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—24no—
353C2×C4×C11—22no—
354C2×C4×C11—24no—
355C2×C4×C11—41no—
356C2×C4×C11—42no—
357C2×C4×C11—41no—
358C2×C4×C11—42no—
359C2×C4×C11—42no—
360C2×C4×C11—42no—
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—
372C2×C4×C11C2×C22⋊C414yes—
373C2×Dic11—24no—
374C2×Dic11—24no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—24no—
379C2×Dic11—41no—
380C2×Dic11—42no—
381C2×Dic11—41no—
382C2×Dic11—42no—
383C2×Dic11—42no—
384C2×Dic11—42no—
385C2×Dic11—42no—
386C2×Dic11—42no—
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×Dic11C2×C22⋊C414yes—
397C4×D11—416no—
398C4×D11—416no—
399C26—111no—
400C24×C4—111no—
401C24×C4—111no—
402C22×C4⋊C4—112no—
403C22×C4⋊C4—111no—
404C22×C4⋊C4C2×D1111yescharacteristic, complemented
405C22×C22⋊C4—111no—
406C22×C22⋊C4—111no—
407C22×C22⋊C4—111no—
408C22×C22⋊C4—118no—
409C22×C22⋊C4—112no—
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×D1111yescharacteristic
417C22×C22⋊C4C2×D1112yes—
418#380—224no—
419#380—224no—
420#379—228no—
421C2×#95—112no—
422C2×#95—111no—
423C2×#95—112no—
424C2×#95—112no—
425C2×#95—112no—
426C2×#95C2×D1111yescharacteristic, complemented
427C2×#95C2×D1112yescomplemented
428C22×C11—28no—
429C22×C11—24no—
430C22×C11—42no—
431C22×C11—42no—
432C22×C11—44no—
433C22×C11—42no—
434C22×C11—42no—
435C22×C11—44no—
436C22×C11—42no—
437C22×C11—42no—
438C22×C11—44no—
439C22×C11C22×C22⋊C411yescharacteristic
440C22×C11C22×C4⋊C411yescharacteristic
441C22×C11C2×#11711yescharacteristic
442C22×C11#51812yes—
443C22×C11#51812yes—
444C22×C11C2×#12111yescharacteristic
445C22×C11C2×#12111yescharacteristic
446C22×C11C2×C22⋊Q811yescharacteristic
447C22×C11C2×C22⋊Q811yescharacteristic
448C22×C11#53411yescharacteristic
449C22×C11#53412yes—
450C22×C11#53412yes—
451C22×C11#53411yescharacteristic
452C22×C11#53412yes—
453C22×C11#53511yescharacteristic
454C22×C11#53512yes—
455C22×C11#53511yescharacteristic
456C22×C11#53812yes—
457C22×C11#53812yes—
458C22×C11#53812yes—
459C22×C11#53812yes—
460C22×C11#54312yes—
461C22×C11#54312yes—
462C2×D11—24no—
463C2×D11—24no—
464C2×D11—28no—
465C2×D11—28no—
466C2×D11—24no—
467C2×D11—24no—
468C2×D11—28no—
469C2×D11—24no—
470C2×D11—24no—
471C2×D11—28no—
472C2×D11—28no—
473C2×D11—24no—
474C2×D11—464no—
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—44no—
478C2×D11—42no—
479C2×D11—42no—
480C2×D11—44no—
481C2×D11—42no—
482C2×D11—42no—
483C2×D11—44no—
484C2×D11#38018yes—
485C4×C11—24no—
486C4×C11—42no—
487C4×C11—82no—
488C4×C11—82no—
489Dic11—24no—
490Dic11—42no—
491Dic11—82no—
492Dic11—82no—
493C25—111no—
494C25—111no—
495C25—114no—
496C25—114no—
497C25—114no—
498C25—222no—
499C25—222no—
500C25—222no—
501C25—222no—
502C25—442no—
503C25—442no—
504C25—442no—
505C25—442no—
506C25C22×D1111yescharacteristic
507C23×C4—111no—
508C23×C4—114no—
509C23×C4—114no—
510C23×C4—114no—
511C23×C4—111no—
512C23×C4—114no—
513C23×C4—112no—
514C23×C4—112no—
515C23×C4—222no—
516C23×C4—222no—
517C23×C4—442no—
518C23×C4—442no—
519C23×C4—442no—
520C23×C4—442no—
521C23×C4C22×D1112yes—
522C23×C4C22×D1112yes—
523C23×C4C22×D1111yescharacteristic
524C23×C4C22×D1111yescharacteristic
525C2×C4⋊C4—22no—
526C2×C4⋊C4—42no—
527C2×C4⋊C4—224no—
528C2×C4⋊C4—222no—
529C2×C4⋊C4—442no—
530C2×C4⋊C4—442no—
531C2×C4⋊C4—442no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—42no—
536C2×C22⋊C4—42no—
537C2×C22⋊C4—114no—
538C2×C22⋊C4—114no—
539C2×C22⋊C4—114no—
540C2×C22⋊C4—2232no—
541C2×C22⋊C4—222no—
542C2×C22⋊C4—222no—
543C2×C22⋊C4—222no—
544C2×C22⋊C4—222no—
545C2×C22⋊C4—222no—
546C2×C22⋊C4—222no—
547C2×C22⋊C4—224no—
548C2×C22⋊C4—224no—
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—442no—
557C2×C22⋊C4—442no—
558C2×C22⋊C4—442no—
559C2×C22⋊C4—442no—
560C2×C22⋊C4—442no—
561C2×C22⋊C4—442no—
562C2×C22⋊C4C4×D1114yes—
563#95—22no—
564#95—42no—
565#95—224no—
566#95—222no—
567#95—442no—
568#95—442no—
569#95—442no—
570C2×C11—44no—
571C2×C11C2×#38011yescharacteristic
572C2×C11#230811yescharacteristic
573C2×C11#230911yescharacteristic
574C2×C11#231212yes—
575C2×C11#231512yes—
576C2×C11#261711yescharacteristic
577C2×C11#261711yescharacteristic
578C2×C11#261712yes—
579C2×C11#262611yescharacteristic
580C2×C11#262611yescharacteristic
581C2×C11#262612yes—
582D11—28no—
583D11—44no—
584C24—21no—
585C24—21no—
586C24—22no—
587C24—22no—
588C24—21no—
589C24—21no—
590C24—22no—
591C24—22no—
592C24—112no—
593C24—112no—
594C24—112no—
595C24—112no—
596C24—112no—
597C24—112no—
598C24—112no—
599C24—112no—
600C24—112no—
601C24—112no—
602C24—1116no—
603C24—228no—
604C24—228no—
605C24—228no—
606C24—228no—
607C24—228no—
608C24—228no—
609C24—222no—
610C24—222no—
611C24—222no—
612C24—222no—
613C24—221no—
614C24—221no—
615C24—222no—
616C24—222no—
617C24—221no—
618C24—221no—
619C24—222no—
620C24—222no—
621C24—448no—
622C24—448no—
623C24—448no—
624C24—448no—
625C24—448no—
626C24—448no—
627C24—448no—
628C24—444no—
629C24—444no—
630C24—448no—
631C24—448no—
632C24—448no—
633C24—444no—
634C24—448no—
635C24—444no—
636C24—448no—
637C24C2×C4×D1112yes—
638C24D4×D1112yes—
639C24Q8×D1112yes—
640C24C23×D1111yescharacteristic
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
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—112no—
662C22×C4—112no—
663C22×C4—112no—
664C22×C4—1116no—
665C22×C4—112no—
666C22×C4—228no—
667C22×C4—222no—
668C22×C4—222no—
669C22×C4—221no—
670C22×C4—221no—
671C22×C4—222no—
672C22×C4—222no—
673C22×C4—222no—
674C22×C4—222no—
675C22×C4—222no—
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—448no—
688C22×C4—444no—
689C22×C4—448no—
690C22×C4—444no—
691C22×C4—448no—
692C22×C4—444no—
693C22×C4—448no—
694C22×C4—444no—
695C22×C4C2×C4×D1112yes—
696C22×C4C2×C4×D1112yes—
697C22×C4D4×D1112yes—
698C22×C4D4×D1112yes—
699C4⋊C4—44no—
700C4⋊C4—444no—
701C4⋊C4—448no—
702C22⋊C4—28no—
703C22⋊C4—48no—
704C22⋊C4—228no—
705C22⋊C4—228no—
706C22⋊C4—228no—
707C22⋊C4—448no—
708C22⋊C4—448no—
709C22⋊C4—448no—
710C22⋊C4—448no—
711C22⋊C4—448no—
712C11#1433811yescharacteristic, complemented, Sylow
713C23—22no—
714C23—22no—
715C23—24no—
716C23—24no—
717C23—24no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—42no—
726C23—41no—
727C23—41no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—41no—
732C23—42no—
733C23—41no—
734C23—42no—
735C23—114no—
736C23—114no—
737C23—114no—
738C23—114no—
739C23—114no—
740C23—114no—
741C23—114no—
742C23—114no—
743C23—2232no—
744C23—224no—
745C23—222no—
746C23—224no—
747C23—224no—
748C23—222no—
749C23—224no—
750C23—224no—
751C23—224no—
752C23—224no—
753C23—224no—
754C23—224no—
755C23—222no—
756C23—224no—
757C23—224no—
758C23—222no—
759C23—224no—
760C23—222no—
761C23—222no—
762C23—224no—
763C23—224no—
764C23—224no—
765C23—222no—
766C23—222no—
767C23—222no—
768C23—222no—
769C23—224no—
770C23—224no—
771C23—224no—
772C23—4432no—
773C23—4416no—
774C23—4416no—
775C23—4432no—
776C23—4416no—
777C23—4416no—
778C23—4432no—
779C23—4416no—
780C23—4416no—
781C23—4432no—
782C23—442no—
783C23—441no—
784C23—441no—
785C23—442no—
786C23—442no—
787C23—442no—
788C23—441no—
789C23—442no—
790C23—441no—
791C23—442no—
792C23C4⋊C4×D1114yes—
793C23C22×C4×D1111yescharacteristic
794C23C2×D4×D1111yescharacteristic
795C23C2×D4×D1111yescharacteristic
796C23C2×D4×D1111yescharacteristic
797C23#6703712yes—
798C23#6703712yes—
799C23C2×Q8×D1111yescharacteristic
800C23#41×D1111yescharacteristic
801C23#41×D1111yescharacteristic
802C23#6704212yes—
803C23#6704212yes—
804C2×C4—24no—
805C2×C4—22no—
806C2×C4—24no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—41no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—114no—
828C2×C4—224no—
829C2×C4—222no—
830C2×C4—224no—
831C2×C4—222no—
832C2×C4—222no—
833C2×C4—224no—
834C2×C4—4416no—
835C2×C4—4416no—
836C2×C4—441no—
837C2×C4—442no—
838C2×C4—441no—
839C2×C4—442no—
840C2×C4—442no—
841C2×C4—442no—
842C2×C4—442no—
843C2×C4—442no—
844C2×C4—442no—
845C2×C4—442no—
846C2×C4—442no—
847C2×C4—442no—
848C2×C4—442no—
849C2×C4—442no—
850C2×C4—442no—
851C2×C4—442no—
852C2×C4—442no—
853C2×C4C22⋊C4×D1114yes—
854C22—28no—
855C22—24no—
856C22—42no—
857C22—42no—
858C22—44no—
859C22—42no—
860C22—42no—
861C22—44no—
862C22—42no—
863C22—42no—
864C22—44no—
865C22—118no—
866C22—224no—
867C22—224no—
868C22—228no—
869C22—228no—
870C22—224no—
871C22—224no—
872C22—228no—
873C22—224no—
874C22—224no—
875C22—228no—
876C22—228no—
877C22—224no—
878C22—4464no—
879C22—442no—
880C22—442no—
881C22—444no—
882C22—442no—
883C22—442no—
884C22—444no—
885C22—442no—
886C22—442no—
887C22—444no—
888C22C2×C22⋊C4×D1111yescharacteristic
889C22C2×C4⋊C4×D1111yescharacteristic
890C22D11×#11711yescharacteristic
891C22#1062307612yes—
892C22#1062307612yes—
893C22#1062312011yescharacteristic
894C22#1062312012yes—
895C22D11×#12111yescharacteristic
896C22D11×#12111yescharacteristic
897C22#1062313612yes—
898C22#1062313812yes—
899C22#1062314412yes—
900C22D11×C22⋊Q811yescharacteristic
901C22D11×C22⋊Q811yescharacteristic
902C22#1062316512yes—
903C22#1062316512yes—
904C22#1062318411yescharacteristic
905C22#1062318412yes—
906C22#1062318812yes—
907C22#1062320511yescharacteristic
908C22#1062320912yes—
909C22#1062323512yes—
910C22#1062324611yescharacteristic
911C4—24no—
912C4—42no—
913C4—82no—
914C4—82no—
915C4—224no—
916C4—442no—
917C4—882no—
918C4—882no—
919C2—44no—
920C2—228no—
921C2—444no—
922C2D11×#38011yescharacteristic
923C2#1307119011yescharacteristic
924C2#1307119511yescharacteristic
925C2#1307121012yes—
926C2#1307122712yes—
927C2#1307434911yescharacteristic
928C2#1307435111yescharacteristic
929C2#1307435512yes—
930C2#1307442011yescharacteristic
931C2#1307442211yescharacteristic
932C2#1307442612yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC25×D11C22
hypercenter#1439D11
hypocenterC11#14338
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#10622280C2semidirect
3. C2×#10622600C2semidirect
5. #13066862C2semidirect
6. #13066861C2semidirect
7. #13066860C2semidirect
8. #13066859C2semidirect
9. #13066858C2semidirect
10. (C2×D11)⋊#95C2semidirect
11. C11×#1439C2semidirect
15. C22×C11×C4⋊C4C22semidirect
26. C22×C4⋊Dic11C22semidirect
27. C22×Dic11⋊C4C22semidirect
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
165. C23×D11C4⋊C4semidirect
233. C2×C4×D11C22⋊C4semidirect
256. #1439D11semidirect
404. C22×C4⋊C4C2×D11semidirect
426. C2×#95C2×D11semidirect
427. C2×#95C2×D11semidirect
712. C11#14338semidirect

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×#106222802
C2×#106226002
C2×#106225682
#130668622
#130668612
#130668602
#130668592
#130668582
(C2×D11)⋊#952
C11×#14392
#1433811