Finite Group Databasebeta

← #14685012

Subgroups — #14685012

Order 2816.

2574 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C42×D11C211yesmaximal, characteristic
2C2×#10622586C211yesmaximal, characteristic, complemented
3C2×#10622602C212yesmaximal
4C2×#10622600C211yesmaximal, characteristic
5C2×#10622600C211yesmaximal, characteristic
6#13066848C212yesmaximal, complemented
7#13066847C212yesmaximal, complemented
8#13066846C211yesmaximal, characteristic, complemented
9#13066845C211yesmaximal, characteristic, complemented
10(C2×D11)⋊#95C212yesmaximal
11C2×C11×#389C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C23×C4×D11C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C22×C11×C4⋊C4C2212yes—
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×C4⋊Dic11C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C22×Dic11⋊C4C2212yes—
24C22×C4×Dic11C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27C2×C42×D11—24no—
28C2×C42×D11—24no—
29C2×C42×D11—24no—
30C11×#389—24no—
31C2×C11×#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39#10622602—28no—
40#10622600—24no—
41#10622600C418yescomplemented
42#10622586—24no—
43C24×D11C2311yescharacteristic
44C23×C4×C11C2312yes—
45C23×C4×C11C2312yes—
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C23×Dic11C2312yes—
50C23×Dic11C2312yes—
51C23×Dic11C2311yescharacteristic
52C23×Dic11C2311yescharacteristic
53C23×Dic11C2311yescharacteristic
54C22×C4×D11—22no—
55C22×C4×D11—22no—
56C22×C4×D11—22no—
57C22×C4×D11—22no—
58C22×C4×D11—22no—
59C22×C4×D11—22no—
60C22×C4×D11—22no—
61C22×C4×D11—22no—
62C22×C4×D11—22no—
63C22×C4×D11—22no—
64C22×C4×D11—22no—
65C22×C4×D11—22no—
66C22×C4×D11—22no—
67C22×C4×D11—22no—
68C22×C4×D11—22no—
69C22×C4×D11—22no—
70C22×C4×D11C2×C414yes—
71C22×C4×D11D414yes—
72C22×C4×D11D414yes—
73C22×C4×D11Q814yes—
74C22×C4×D11Q814yes—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—24no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—24no—
82C2×C11×C4⋊C4—24no—
83C2×C11×C4⋊C4C2×C414yescomplemented
84C2×C42×C11—22no—
85C2×C42×C11—22no—
86C2×C42×C11D414yes—
87C2×(C2×D11)⋊C4—24no—
88C2×(C2×D11)⋊C4—24no—
89C2×(C2×D11)⋊C4—24no—
90C2×(C2×D11)⋊C4—24no—
91C2×(C2×D11)⋊C4—24no—
92C2×(C2×D11)⋊C4C2×C418yes—
93C2×C4⋊Dic11—22no—
94C2×C4⋊Dic11—22no—
95C2×C4⋊Dic11—22no—
96C2×C4⋊Dic11—22no—
97C2×C4⋊Dic11—22no—
98C2×C4⋊Dic11C2×C414yescomplemented
99C2×Dic11⋊C4—24no—
100C2×Dic11⋊C4—24no—
101C2×Dic11⋊C4—24no—
102C2×C4×Dic11—22no—
103C2×C4×Dic11—22no—
104C2×C4×Dic11—22no—
105C2×C4×Dic11—22no—
106C2×C4×Dic11—22no—
107C2×C4×Dic11—22no—
108C2×C4×Dic11—22no—
109C2×C4×Dic11—22no—
110C2×C4×Dic11D414yes—
111C42×D11—232no—
112C11×#95—24no—
113C11⋊#95—24no—
114C11⋊#95—24no—
115C11⋊#95—24no—
116C11⋊#95—24no—
117C11⋊#95—24no—
118C11⋊#95—24no—
119C11⋊#95C2×C418yescomplemented
120#14697—111nomaximal, Sylow
121C24×C11C2411yescharacteristic
122C23×D11—21no—
123C23×D11—21no—
124C23×D11—21no—
125C23×D11—21no—
126C23×D11—21no—
127C23×D11—21no—
128C23×D11—21no—
129C23×D11—21no—
130C23×D11C22×C412yes—
131C23×D11C2×D412yes—
132C23×D11C2×D412yes—
133C23×D11C2×Q812yes—
134C23×D11C2×Q812yes—
135C23×D11#4112yes—
136C23×D11#4112yes—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
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×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11C22×C414yes—
159C22×C4×C11C22×C412yes—
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D412yes—
164C22×C4×C11C2×D412yes—
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×Q812yes—
167C22×C4×C11C2×Q812yes—
168C22×C4×C11#4112yes—
169C22×C4×C11#4112yes—
170C22×C4×C11#4112yes—
171C22×C4×C11#4112yes—
172C22×Dic11—21no—
173C22×Dic11—21no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—21no—
183C22×Dic11—21no—
184C22×Dic11—21no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—22no—
195C22×Dic11—22no—
196C22×Dic11—22no—
197C22×Dic11C22×C414yes—
198C22×Dic11C22×C412yes—
199C22×Dic11C2×D412yes—
200C22×Dic11C2×D412yes—
201C22×Dic11C2×D412yes—
202C22×Dic11C2×D412yes—
203C22×Dic11C2×Q812yes—
204C22×Dic11C2×Q812yes—
205C22×Dic11#4112yes—
206C22×Dic11#4112yes—
207C2×C4×D11—28no—
208C2×C4×D11—28no—
209C2×C4×D11—28no—
210C2×C4×D11—28no—
211C2×C4×D11—28no—
212C2×C4×D11—28no—
213C2×C4×D11—28no—
214C2×C4×D11—28no—
215C2×C4×D11—28no—
216C2×C4×D11—28no—
217C2×C4×D11—28no—
218C2×C4×D11—28no—
219C2×C4×D11—28no—
220C2×C4×D11—28no—
221C2×C4×D11—28no—
222C2×C4×D11—28no—
223C2×C4×D11—28no—
224C2×C4×D11—28no—
225C2×C4×D11—28no—
226C2×C4×D11—28no—
227C2×C4×D11C4⋊C4116yescomplemented
228C11×C4⋊C4—28no—
229C11×C4⋊C4—44no—
230C11×C4⋊C4—48no—
231C42×C11—28no—
232(C2×D11)⋊C4—216no—
233(C2×D11)⋊C4—48no—
234C4⋊Dic11—28no—
235C4⋊Dic11—44no—
236Dic11⋊C4—48no—
237C4×Dic11—28no—
238C4×Dic11—28no—
239C4×Dic11—28no—
240C23×C42—111no—
241C2×#389—111no—
242C2×#389D1111yescharacteristic, complemented
243C2×#385—112no—
244C2×#380—111no—
245C2×#380—111no—
246#1436—112no—
247#1436—112no—
248C4⋊#95—111no—
249C4⋊#95—111no—
250C22⋊#95—112no—
251C23×C11C23×C411yescharacteristic
252C23×C11C22×D411yescharacteristic
253C23×C11C22×D411yescharacteristic
254C23×C11C22×D411yescharacteristic
255C23×C11C22×D411yescharacteristic
256C23×C11C22×Q811yescharacteristic
257C23×C11C22×Q811yescharacteristic
258C23×C11C2×#4111yescharacteristic
259C23×C11C2×#4111yescharacteristic
260C23×C11C2×#4111yescharacteristic
261C23×C11C2×#4111yescharacteristic
262C23×C11C2×#4111yescharacteristic
263C23×C11C2×#4111yescharacteristic
264C23×C11C2×#4111yescharacteristic
265C23×C11C2×#4111yescharacteristic
266C22×D11—22no—
267C22×D11—22no—
268C22×D11—22no—
269C22×D11—22no—
270C22×D11—22no—
271C22×D11—22no—
272C22×D11—22no—
273C22×D11—22no—
274C22×D11—22no—
275C22×D11—22no—
276C22×D11—22no—
277C22×D11—22no—
278C22×D11—22no—
279C22×D11—22no—
280C22×D11—22no—
281C22×D11—22no—
282C22×D11—22no—
283C22×D11—22no—
284C22×D11—22no—
285C22×D11—22no—
286C22×D11—22no—
287C22×D11—22no—
288C22×D11—22no—
289C22×D11—22no—
290C22×D11—22no—
291C22×D11—22no—
292C22×D11—22no—
293C22×D11—22no—
294C22×D11C2×C4⋊C414yes—
295C22×D11C4×D414yes—
296C22×D11C4×Q814yes—
297C22×D11#12114yes—
298C22×D11C22⋊Q814yes—
299C22×D11#12514yes—
300C22×D11C4⋊Q814yes—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—24no—
314C2×C4×C11—24no—
315C2×C4×C11—24no—
316C2×C4×C11—42no—
317C2×C4×C11—42no—
318C2×C4×C11—42no—
319C2×C4×C11—42no—
320C2×C4×C11—42no—
321C2×C4×C11—42no—
322C2×C4×C11—42no—
323C2×C4×C11—42no—
324C2×C4×C11—42no—
325C2×C4×C11—42no—
326C2×C4×C11—42no—
327C2×C4×C11C2×C4⋊C414yes—
328C2×C4×C11C4×D414yes—
329C2×C4×C11C4×D414yes—
330C2×C4×C11#12014yes—
331C2×C4×C11#12114yes—
332C2×C4×C11C22⋊Q814yes—
333C2×C4×C11C22⋊Q814yes—
334C2×C4×C11C22⋊Q814yes—
335C2×C4×C11#12314yes—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—24no—
355C2×Dic11—24no—
356C2×Dic11—24no—
357C2×Dic11—42no—
358C2×Dic11—42no—
359C2×Dic11—42no—
360C2×Dic11—42no—
361C2×Dic11—42no—
362C2×Dic11—42no—
363C2×Dic11—42no—
364C2×Dic11—42no—
365C2×Dic11—42no—
366C2×Dic11—42no—
367C2×Dic11—42no—
368C2×Dic11C2×C4⋊C414yes—
369C2×Dic11#12114yes—
370C2×Dic11C22⋊Q814yes—
371C4×D11—232no—
372C4×D11—232no—
373C4×D11—232no—
374C24×C4—111no—
375C24×C4—111no—
376C24×C4—111no—
377C22×C4⋊C4—111no—
378C22×C4⋊C4—112no—
379C22×C4⋊C4—111no—
380C22×C4⋊C4C2×D1112yes—
381C22×C4⋊C4C2×D1111yescharacteristic
382C22×C4⋊C4C2×D1111yescharacteristic
383C22×C22⋊C4—112no—
384C22×C22⋊C4—112no—
385C22×C42—111no—
386C22×C42—111no—
387C22×C42—111no—
388C22×C42—224no—
389C22×C42—224no—
390C22×C42—224no—
391C22×C42C2×D1111yescharacteristic
392#389—24no—
393#389—224no—
394#385—228no—
395#380—118no—
396#380—224no—
397C2×#95—112no—
398C2×#95—112no—
399C2×#95—112no—
400C2×#95—112no—
401C2×#95—112no—
402C2×#95—112no—
403C2×#95—112no—
404C2×#95C2×D1112yes—
405C22×C11C22×C4⋊C411yescharacteristic
406C22×C11C2×C4×D411yescharacteristic
407C22×C11C2×C4×D411yescharacteristic
408C22×C11C2×C4×D411yescharacteristic
409C22×C11C2×C4×Q811yescharacteristic
410C22×C11C4×#4111yescharacteristic
411C22×C11C4×#4111yescharacteristic
412C22×C11C2×#12011yescharacteristic
413C22×C11C2×#12111yescharacteristic
414C22×C11C2×#12111yescharacteristic
415C22×C11C2×#12111yescharacteristic
416C22×C11C2×C22⋊Q811yescharacteristic
417C22×C11C2×C22⋊Q811yescharacteristic
418C22×C11C2×C22⋊Q811yescharacteristic
419C22×C11C2×C22⋊Q811yescharacteristic
420C22×C11C2×C22⋊Q811yescharacteristic
421C22×C11C2×#12311yescharacteristic
422C22×C11#52511yescharacteristic
423C22×C11#52511yescharacteristic
424C22×C11#52511yescharacteristic
425C22×C11#52511yescharacteristic
426C22×C11#52511yescharacteristic
427C22×C11#52511yescharacteristic
428C22×C11C2×#12511yescharacteristic
429C22×C11#52911yescharacteristic
430C22×C11#52911yescharacteristic
431C22×C11#52911yescharacteristic
432C22×C11#52911yescharacteristic
433C22×C11C2×C4⋊Q811yescharacteristic
434C22×C11#53211yescharacteristic
435C22×C11#53211yescharacteristic
436C22×C11#53311yescharacteristic
437C22×C11#53311yescharacteristic
438C22×C11#53311yescharacteristic
439C22×C11#53311yescharacteristic
440C2×D11—24no—
441C2×D11—24no—
442C2×D11—24no—
443C2×D11—24no—
444C2×D11—24no—
445C2×D11—24no—
446C2×D11—24no—
447C2×D11—24no—
448C2×D11—24no—
449C2×D11—24no—
450C2×D11—24no—
451C2×D11—24no—
452C2×D11—24no—
453C2×D11—24no—
454C2×D11#38918yescomplemented
455C4×C11—24no—
456C4×C11—24no—
457C4×C11—44no—
458C4×C11—82no—
459C4×C11#38518yescomplemented
460Dic11—24no—
461Dic11—24no—
462Dic11—24no—
463Dic11—44no—
464Dic11—82no—
465C25—111no—
466C23×C4—111no—
467C23×C4—111no—
468C23×C4—111no—
469C23×C4—114no—
470C23×C4—114no—
471C23×C4—114no—
472C23×C4—112no—
473C23×C4—114no—
474C23×C4—114no—
475C23×C4—112no—
476C23×C4—222no—
477C23×C4—222no—
478C23×C4—222no—
479C23×C4—222no—
480C23×C4—222no—
481C23×C4—222no—
482C23×C4—222no—
483C23×C4—222no—
484C23×C4—222no—
485C23×C4—222no—
486C23×C4—222no—
487C23×C4—222no—
488C23×C4—222no—
489C23×C4—222no—
490C23×C4—222no—
491C23×C4—222no—
492C23×C4C22×D1112yes—
493C23×C4C22×D1112yes—
494C23×C4C22×D1111yescharacteristic
495C23×C4C22×D1111yescharacteristic
496C23×C4C22×D1111yescharacteristic
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—24no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—24no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—24no—
505C2×C4⋊C4—114no—
506C2×C4⋊C4—222no—
507C2×C4⋊C4—222no—
508C2×C4⋊C4—224no—
509C2×C4⋊C4—224no—
510C2×C4⋊C4—224no—
511C2×C4⋊C4—222no—
512C2×C4⋊C4—222no—
513C2×C4⋊C4—222no—
514C2×C4⋊C4C4×D1114yescomplemented
515C2×C22⋊C4—118no—
516C2×C22⋊C4—224no—
517C2×C22⋊C4—224no—
518C2×C22⋊C4—224no—
519C2×C22⋊C4—224no—
520C2×C22⋊C4—224no—
521C2×C42—22no—
522C2×C42—22no—
523C2×C42—114no—
524C2×C42—2232no—
525C2×C42—222no—
526C2×C42—222no—
527C2×C42—222no—
528C2×C42—222no—
529C2×C42—222no—
530C2×C42—222no—
531C2×C42—222no—
532C2×C42—222no—
533C2×C42C22⋊D1114yes—
534#95—24no—
535#95—118no—
536#95—224no—
537#95—224no—
538#95—224no—
539#95—224no—
540#95—224no—
541#95—224no—
542C2×C11C2×#38511yescharacteristic
543C2×C11C2×#38911yescharacteristic
544C2×C11#229611yescharacteristic
545C2×C11C4×#12111yescharacteristic
546C2×C11C4×#12111yescharacteristic
547C2×C11C4×C22⋊Q811yescharacteristic
548C2×C11C4×C22⋊Q811yescharacteristic
549C2×C11#284711yescharacteristic
550C2×C11#284811yescharacteristic
551C2×C11#285111yescharacteristic
552C2×C11#285111yescharacteristic
553C2×C11#285411yescharacteristic
554C2×C11#285511yescharacteristic
555C2×C11#285711yescharacteristic
556C2×C11#285711yescharacteristic
557D11—28no—
558C24—112no—
559C24—112no—
560C24—112no—
561C24—112no—
562C24—112no—
563C24—112no—
564C24—112no—
565C24—221no—
566C24—221no—
567C24—221no—
568C24—221no—
569C24—221no—
570C24—221no—
571C24—221no—
572C24—221no—
573C24C23×D1111yescharacteristic
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—112no—
596C22×C4—112no—
597C22×C4—112no—
598C22×C4—112no—
599C22×C4—112no—
600C22×C4—112no—
601C22×C4—112no—
602C22×C4—112no—
603C22×C4—112no—
604C22×C4—1116no—
605C22×C4—114no—
606C22×C4—228no—
607C22×C4—228no—
608C22×C4—228no—
609C22×C4—228no—
610C22×C4—228no—
611C22×C4—228no—
612C22×C4—228no—
613C22×C4—228no—
614C22×C4—228no—
615C22×C4—228no—
616C22×C4—228no—
617C22×C4—228no—
618C22×C4—221no—
619C22×C4—221no—
620C22×C4—221no—
621C22×C4—221no—
622C22×C4—221no—
623C22×C4—221no—
624C22×C4—221no—
625C22×C4—221no—
626C22×C4—221no—
627C22×C4—221no—
628C22×C4—221no—
629C22×C4—221no—
630C22×C4—228no—
631C22×C4—228no—
632C22×C4—228no—
633C22×C4—228no—
634C22×C4—228no—
635C22×C4—228no—
636C22×C4—228no—
637C22×C4—228no—
638C22×C4—222no—
639C22×C4—222no—
640C22×C4—222no—
641C22×C4—222no—
642C22×C4—222no—
643C22×C4—222no—
644C22×C4—222no—
645C22×C4—222no—
646C22×C4—222no—
647C22×C4—222no—
648C22×C4—222no—
649C22×C4—222no—
650C22×C4—222no—
651C22×C4C2×C4×D1114yes—
652C22×C4C2×C4×D1112yes—
653C22×C4#433912yes—
654C22×C4D4×D1112yes—
655C22×C4D4×D1112yes—
656C22×C4D4×D1112yes—
657C22×C4#434112yes—
658C22×C4Q8×D1112yes—
659C22×C4Q8×D1112yes—
660C22×C4#434312yes—
661C22×C4#434312yes—
662C22×C4C2×C22⋊D1112yes—
663C22×C4C2×C22⋊D1112yes—
664C22×C4C2×C22⋊D1112yes—
665C4⋊C4—28no—
666C4⋊C4—44no—
667C4⋊C4—48no—
668C4⋊C4—228no—
669C4⋊C4—448no—
670C4⋊C4—444no—
671C22⋊C4—2216no—
672C22⋊C4—448no—
673C42—28no—
674C42—228no—
675C42—228no—
676C42—228no—
677C11#1469711yescharacteristic, complemented, Sylow
678C23—114no—
679C23—114no—
680C23—114no—
681C23—114no—
682C23—114no—
683C23—114no—
684C23—114no—
685C23—222no—
686C23—222no—
687C23—222no—
688C23—222no—
689C23—222no—
690C23—222no—
691C23—222no—
692C23—222no—
693C23—222no—
694C23—222no—
695C23—222no—
696C23—222no—
697C23—222no—
698C23—222no—
699C23—222no—
700C23—222no—
701C23—222no—
702C23—222no—
703C23—222no—
704C23—222no—
705C23—222no—
706C23—222no—
707C23—222no—
708C23—222no—
709C23—222no—
710C23—222no—
711C23—222no—
712C23—222no—
713C23C22×C4×D1111yescharacteristic
714C23C2×#433911yescharacteristic
715C23C2×D4×D1111yescharacteristic
716C23C2×D4×D1111yescharacteristic
717C23C2×D4×D1111yescharacteristic
718C23C2×#434111yescharacteristic
719C23C2×Q8×D1111yescharacteristic
720C23C2×Q8×D1111yescharacteristic
721C23C2×#434311yescharacteristic
722C23C2×#434311yescharacteristic
723C23#41×D1111yescharacteristic
724C23#41×D1111yescharacteristic
725C23#41×D1111yescharacteristic
726C23#41×D1111yescharacteristic
727C23C22×C22⋊D1111yescharacteristic
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—114no—
755C2×C4—114no—
756C2×C4—114no—
757C2×C4—2232no—
758C2×C4—2232no—
759C2×C4—222no—
760C2×C4—222no—
761C2×C4—222no—
762C2×C4—222no—
763C2×C4—222no—
764C2×C4—222no—
765C2×C4—222no—
766C2×C4—222no—
767C2×C4—222no—
768C2×C4—222no—
769C2×C4—222no—
770C2×C4—222no—
771C2×C4—222no—
772C2×C4—222no—
773C2×C4—222no—
774C2×C4—222no—
775C2×C4—222no—
776C2×C4—222no—
777C2×C4—2232no—
778C2×C4—224no—
779C2×C4—224no—
780C2×C4—224no—
781C2×C4—442no—
782C2×C4—442no—
783C2×C4—442no—
784C2×C4—442no—
785C2×C4—442no—
786C2×C4—442no—
787C2×C4—442no—
788C2×C4—442no—
789C2×C4—442no—
790C2×C4—442no—
791C2×C4—442no—
792C2×C4C4⋊C4×D1114yes—
793C2×C4#6694614yes—
794C2×C4#6694714yes—
795C2×C4#6694914yes—
796C2×C4C4×C22⋊D1114yes—
797C2×C4#6699014yes—
798C2×C4#6699114yes—
799C2×C4#6699914yes—
800C2×C4#6699914yes—
801C22—118no—
802C22—224no—
803C22—224no—
804C22—224no—
805C22—224no—
806C22—224no—
807C22—224no—
808C22—224no—
809C22—224no—
810C22—224no—
811C22—224no—
812C22—224no—
813C22—224no—
814C22—224no—
815C22—224no—
816C22C2×C4⋊C4×D1111yescharacteristic
817C22C2×#6694611yescharacteristic
818C22C2×#6694711yescharacteristic
819C22C2×#6694911yescharacteristic
820C22C4×#434111yescharacteristic
821C22C4×D4×D1111yescharacteristic
822C22#1062307911yescharacteristic
823C22#1062308811yescharacteristic
824C22C4×Q8×D1111yescharacteristic
825C22C4×#434311yescharacteristic
826C22#1062310911yescharacteristic
827C22#1062311111yescharacteristic
828C22D11×#12111yescharacteristic
829C22D11×#12111yescharacteristic
830C22#1062313711yescharacteristic
831C22#1062313711yescharacteristic
832C22D11×C22⋊Q811yescharacteristic
833C22D11×C22⋊Q811yescharacteristic
834C22#1062315811yescharacteristic
835C22#1062315811yescharacteristic
836C22D11×#12511yescharacteristic
837C22#1062321911yescharacteristic
838C22#1062322211yescharacteristic
839C22#1062322211yescharacteristic
840C22D11×C4⋊Q811yescharacteristic
841C22#1062325611yescharacteristic
842C22#1062325911yescharacteristic
843C22#1062325911yescharacteristic
844C22C2×C4×C22⋊D1111yescharacteristic
845C22C2×#6699011yescharacteristic
846C22C2×#6699111yescharacteristic
847C22C2×#6699911yescharacteristic
848C22C2×#6699911yescharacteristic
849C22#1062335911yescharacteristic
850C22#1062335911yescharacteristic
851C4—24no—
852C4—24no—
853C4—44no—
854C4—82no—
855C4—224no—
856C4—224no—
857C4—224no—
858C4—444no—
859C4—882no—
860C4#1062260218yescomplemented
861C2—228no—
862C2C2×#1062260211yescharacteristic
863C2D11×#38911yescharacteristic
864C2#1307109711yescharacteristic
865C2C4×#6699111yescharacteristic
866C2#1307112411yescharacteristic
867C2C4×#6699911yescharacteristic
868C2#1307114611yescharacteristic
869C2#1307689511yescharacteristic
870C2#1307690011yescharacteristic
871C2#1307692111yescharacteristic
872C2#1307692511yescharacteristic
873C2#1307694911yescharacteristic
874C2#1307695411yescharacteristic
875C2#1307696311yescharacteristic
876C2#1307696711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#389C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×#389D11
hypocenterC11#14697
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C2×#10622586C2semidirect
6. #13066848C2semidirect
7. #13066847C2semidirect
8. #13066846C2semidirect
9. #13066845C2semidirect
11. C2×C11×#389C2semidirect
41. #10622600C4semidirect
83. C2×C11×C4⋊C4C2×C4semidirect
98. C2×C4⋊Dic11C2×C4semidirect
119. C11⋊#95C2×C4semidirect
227. C2×C4×D11C4⋊C4semidirect
242. C2×#389D11semidirect
454. C2×D11#389semidirect
459. C4×C11#385semidirect
514. C2×C4⋊C4C4×D11semidirect
677. C11#14697semidirect
860. C4#10622602semidirect

Maximal subgroups

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

subgroupindex
C22×C42×D112
C2×#106225862
C2×#106226022
C2×#106226002
#130668482
#130668472
#130668462
#130668452
(C2×D11)⋊#952
C2×C11×#3892
#1469711