Finite Group Databasebeta

← #14677154

Subgroups — #14677154

Order 2816.

1810 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66940C211yesmaximal, characteristic
2C2×#10622259C211yesmaximal, characteristic
3C2×#10622259C211yesmaximal, characteristic
4C2×#10622260C211yesmaximal, characteristic
5C2×#10622262C211yesmaximal, characteristic
6#13066880C211yesmaximal, characteristic
7#13066879C211yesmaximal, characteristic
8#13066874C211yesmaximal, characteristic
9#13066851C211yesmaximal, characteristic
10#13066850C211yesmaximal, characteristic
11#13066847C211yesmaximal, characteristic
12#13066847C211yesmaximal, characteristic
13Dic11⋊#95C211yesmaximal, characteristic
14Dic11⋊#95C211yesmaximal, characteristic
15C11×#1442C211yesmaximal, characteristic
16C23×Dic22C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C22×Dic11⋊C4C2211yescharacteristic
20C22×Dic11⋊C4C2211yescharacteristic
21C22×Dic11⋊C4C2211yescharacteristic
22C22×Dic11⋊C4C2211yescharacteristic
23C22×Dic11⋊C4C2211yescharacteristic
24C22×Dic11⋊C4C2211yescharacteristic
25C22×Dic11⋊C4C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27C22×C4×Dic11C2211yescharacteristic
28C22×C4×Dic11C2211yescharacteristic
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C2×#66940—24no—
32C2×#66940—24no—
33C2×#66940—24no—
34C2×C11×#95C2211yescharacteristic
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
38C2×C11×#95C2211yescharacteristic
39C2×C11×#95C2211yescharacteristic
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2211yescharacteristic
43C2×C11⋊#95C2211yescharacteristic
44C2×C11⋊#95C2211yescharacteristic
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54#10622262—24no—
55#10622260—24no—
56#10622259—24no—
57#10622259C418yescomplemented
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C22×Dic22—22no—
74C22×Dic22—22no—
75C22×Dic22—22no—
76C22×Dic22—22no—
77C22×Dic22C2×C414yes—
78C22×Dic22D414yes—
79C22×Dic22Q814yes—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—22no—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11—41no—
86C2×Dic11⋊C4—22no—
87C2×Dic11⋊C4—22no—
88C2×Dic11⋊C4—22no—
89C2×Dic11⋊C4—22no—
90C2×Dic11⋊C4—22no—
91C2×Dic11⋊C4—22no—
92C2×Dic11⋊C4—22no—
93C2×Dic11⋊C4—22no—
94C2×Dic11⋊C4—22no—
95C2×Dic11⋊C4—22no—
96C2×Dic11⋊C4—22no—
97C2×Dic11⋊C4—22no—
98C2×Dic11⋊C4—22no—
99C2×Dic11⋊C4—22no—
100C2×Dic11⋊C4—22no—
101C2×Dic11⋊C4—22no—
102C2×Dic11⋊C4—22no—
103C2×Dic11⋊C4—41no—
104C2×Dic11⋊C4C2×C414yes—
105C2×Dic11⋊C4D414yes—
106C2×Dic11⋊C4Q814yescomplemented
107C2×C4×Dic11—22no—
108C2×C4×Dic11—22no—
109C2×C4×Dic11—22no—
110C2×C4×Dic11—22no—
111C2×C4×Dic11—22no—
112C2×C4×Dic11—22no—
113C2×C4×Dic11—22no—
114C2×C4×Dic11—22no—
115C2×C4×Dic11—22no—
116C2×C4×Dic11—22no—
117C2×C4×Dic11—22no—
118C2×C4×Dic11—22no—
119C2×C4×Dic11—22no—
120C2×C4×Dic11C2×C414yes—
121C2×C4×Dic11D414yes—
122#66940—232no—
123C11×#95—22no—
124C11×#95—22no—
125C11×#95—22no—
126C11×#95—41no—
127C11×#95—41no—
128C11×#95C2×C414yes—
129C11⋊#95—22no—
130C11⋊#95—22no—
131C11⋊#95—22no—
132C11⋊#95—22no—
133C11⋊#95—22no—
134C11⋊#95—22no—
135C11⋊#95—22no—
136C11⋊#95—22no—
137C11⋊#95—22no—
138C11⋊#95—41no—
139C11⋊#95—41no—
140C11⋊#95C2×C414yes—
141C11⋊#95C2×C414yes—
142C11⋊#95C2×C414yes—
143#14017—111nomaximal, Sylow
144C24×C11C2411yescharacteristic
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11C22×C412yes—
187C22×C4×C11C22×C412yes—
188C22×C4×C11C22×C412yes—
189C22×C4×C11C2×D412yes—
190C22×C4×C11C2×D412yes—
191C22×C4×C11C2×D412yes—
192C22×C4×C11C2×Q812yes—
193C22×C4×C11C2×Q812yes—
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—21no—
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—21no—
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C22×Dic11—21no—
227C22×Dic11—21no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11C22×C412yes—
232C22×Dic11C22×C412yes—
233C22×Dic11C22×C412yes—
234C22×Dic11C22×C412yes—
235C22×Dic11C2×D412yes—
236C22×Dic11C2×D412yes—
237C22×Dic11C2×D412yes—
238C22×Dic11C2×D412yes—
239C22×Dic11C2×D412yes—
240C22×Dic11C2×D412yes—
241C22×Dic11C2×Q812yes—
242C22×Dic11C2×Q812yes—
243C22×Dic11C2×Q812yes—
244C22×Dic11C2×Q812yes—
245C22×Dic11#4112yes—
246C22×Dic11#4112yes—
247C22×Dic11#4112yes—
248C22×Dic11#4112yes—
249C22×Dic11#4112yes—
250C2×Dic22—28no—
251C2×Dic22—28no—
252C2×Dic22—28no—
253C2×Dic22—28no—
254C2×Dic22—28no—
255C2×Dic22—28no—
256C2×Dic22C4⋊C4116yescomplemented
257C11×C4⋊C4—28no—
258C4⋊Dic11—44no—
259Dic11⋊C4—28no—
260Dic11⋊C4—28no—
261Dic11⋊C4—28no—
262Dic11⋊C4—28no—
263Dic11⋊C4—28no—
264Dic11⋊C4—44no—
265Dic11⋊C4—44no—
266C4×Dic11—28no—
267C4×Dic11—28no—
268C4×Dic11—28no—
269C4×Dic11—28no—
270C4×Dic11—44no—
271C22×C4×Q8—111no—
272C2×#391—111no—
273C2×#391—111no—
274C2×#389—111no—
275C2×C4×C4⋊C4—111no—
276#1444—111no—
277#1444—111no—
278#1442—111no—
279#1442D1111yescharacteristic
280#1436—111no—
281#1436—111no—
282#1436—111no—
283#1436—111no—
284C4⋊#95—111no—
285C4⋊#95—111no—
286C23×C11C23×C411yescharacteristic
287C23×C11C22×D411yescharacteristic
288C23×C11C22×D411yescharacteristic
289C23×C11C22×D411yescharacteristic
290C23×C11C22×Q811yescharacteristic
291C23×C11C22×Q811yescharacteristic
292C23×C11C2×#4111yescharacteristic
293C23×C11C2×#4111yescharacteristic
294C23×C11C2×#4111yescharacteristic
295C23×C11C2×#4111yescharacteristic
296C23×C11C2×#4111yescharacteristic
297C23×C11H(5,𝔽2)11yescharacteristic
298C23×C112−1+411yescharacteristic
299C23×C112−1+411yescharacteristic
300C23×C112−1+411yescharacteristic
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—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11C2×C4⋊C414yes—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—41no—
378C2×Dic11—41no—
379C2×Dic11—41no—
380C2×Dic11—41no—
381C2×Dic11—41no—
382C2×Dic11—41no—
383C2×Dic11—41no—
384C2×Dic11—41no—
385C2×Dic11—41no—
386C2×Dic11—41no—
387C2×Dic11—41no—
388C2×Dic11—41no—
389C2×Dic11—41no—
390C2×Dic11—41no—
391C2×Dic11—41no—
392C2×Dic11—41no—
393C2×Dic11—41no—
394C2×Dic11—41no—
395C2×Dic11—41no—
396C2×Dic11C2×C4⋊C414yes—
397C2×Dic11C2×C4⋊C414yes—
398C2×Dic11C4×D414yes—
399C2×Dic11C4×D414yes—
400C2×Dic11C4×Q814yescomplemented
401C2×Dic11#12014yes—
402C2×Dic11C22⋊Q814yes—
403C2×Dic11C22⋊Q814yes—
404C2×Dic11C22⋊Q814yes—
405C2×Dic11#12314yes—
406Dic22—232no—
407C23×Q8—111no—
408C2×C4×Q8—224no—
409C2×C4×Q8—224no—
410C2×C4×Q8—224no—
411C22×C4⋊C4—111no—
412C22×C4⋊C4—111no—
413C22×C4⋊C4—111no—
414C22×C4⋊C4—111no—
415C22×C4⋊C4—111no—
416C22×C4⋊C4—111no—
417C22×C4⋊C4—111no—
418C22×C4⋊C4—111no—
419C22×C4⋊C4C2×D1111yescharacteristic
420C22×C42—111no—
421C22×C42—111no—
422C22×C42—111no—
423C22×C42—111no—
424C22×C42—111no—
425#391—118no—
426#391—224no—
427#389—224no—
428C4×C4⋊C4—224no—
429C2×#95—111no—
430C2×#95—111no—
431C2×#95—111no—
432C2×#95—111no—
433C2×#95—111no—
434C2×#95—111no—
435C2×#95—111no—
436C2×#95—111no—
437C2×#95—111no—
438C2×#95—111no—
439C2×#95—111no—
440C2×#95—111no—
441C2×#95—111no—
442C2×#95—111no—
443C2×#95C2×D1111yescharacteristic
444C2×#95C2×D1111yescharacteristic
445C2×#95C2×D1111yescharacteristic
446C2×#95C2×D1111yescharacteristic
447C2×#95C2×D1111yescharacteristic
448C2×#95C2×D1111yescharacteristic
449C22×C11C22×C4⋊C411yescharacteristic
450C22×C11C2×C4×D411yescharacteristic
451C22×C11C2×C4×D411yescharacteristic
452C22×C11C2×C4×Q811yescharacteristic
453C22×C11C4×#4111yescharacteristic
454C22×C11#51911yescharacteristic
455C22×C11#52011yescharacteristic
456C22×C11C2×#12011yescharacteristic
457C22×C11C2×C22⋊Q811yescharacteristic
458C22×C11C2×C22⋊Q811yescharacteristic
459C22×C11C2×C22⋊Q811yescharacteristic
460C22×C11C2×#12311yescharacteristic
461C22×C11#52511yescharacteristic
462C22×C11#52911yescharacteristic
463C22×C11#53311yescharacteristic
464C22×C11#53611yescharacteristic
465C22×C11#53711yescharacteristic
466C22×C11#54111yescharacteristic
467C22×C11#54211yescharacteristic
468C22×C11#54611yescharacteristic
469C22×C11#54711yescharacteristic
470C22×C11#54811yescharacteristic
471C22×C11#54811yescharacteristic
472C22×C11#54811yescharacteristic
473C22×C11D4×Q811yescharacteristic
474C22×C11D4×Q811yescharacteristic
475C22×C11#55011yescharacteristic
476C22×C11#55611yescharacteristic
477C22×C11#55611yescharacteristic
478C22×C11#55711yescharacteristic
479C22×C11#55711yescharacteristic
480C22×C11#55711yescharacteristic
481C22×C11#55711yescharacteristic
482C22×C11Q8211yescharacteristic
483C22×C11#55911yescharacteristic
484C4×C11—24no—
485C4×C11—42no—
486C4×C11—42no—
487C4×C11—42no—
488C4×C11—42no—
489C4×C11—42no—
490C4×C11—81no—
491Dic11—24no—
492Dic11—24no—
493Dic11—24no—
494Dic11—42no—
495Dic11—42no—
496Dic11—42no—
497Dic11—81no—
498Dic11#38518yes—
499C22×Q8—114no—
500C22×Q8—114no—
501C22×Q8—114no—
502C22×Q8—222no—
503C22×Q8—222no—
504C22×Q8—222no—
505C22×Q8—222no—
506C23×C4—111no—
507C23×C4—111no—
508C23×C4—111no—
509C23×C4—111no—
510C23×C4—111no—
511C23×C4—111no—
512C23×C4—111no—
513C23×C4—111no—
514C23×C4C22×D1111yescharacteristic
515C23×C4C22×D1111yescharacteristic
516C23×C4C22×D1111yescharacteristic
517C23×C4C22×D1111yescharacteristic
518C23×C4C22×D1111yescharacteristic
519C23×C4C22×D1111yescharacteristic
520C23×C4C22×D1111yescharacteristic
521C4×Q8—2232no—
522C2×C4⋊C4—22no—
523C2×C4⋊C4—22no—
524C2×C4⋊C4—22no—
525C2×C4⋊C4—114no—
526C2×C4⋊C4—114no—
527C2×C4⋊C4—114no—
528C2×C4⋊C4—222no—
529C2×C4⋊C4—222no—
530C2×C4⋊C4—222no—
531C2×C4⋊C4—222no—
532C2×C4⋊C4—222no—
533C2×C4⋊C4—222no—
534C2×C4⋊C4—222no—
535C2×C4⋊C4—222no—
536C2×C4⋊C4—222no—
537C2×C4⋊C4—222no—
538C2×C4⋊C4—222no—
539C2×C4⋊C4—222no—
540C2×C4⋊C4—222no—
541C2×C4⋊C4—222no—
542C2×C4⋊C4—222no—
543C2×C4⋊C4—222no—
544C2×C4⋊C4—222no—
545C2×C4⋊C4—222no—
546C2×C4⋊C4—222no—
547C2×C4⋊C4—441no—
548C2×C4⋊C4—441no—
549C2×C42—114no—
550C2×C42—114no—
551C2×C42—222no—
552C2×C42—222no—
553C2×C42—222no—
554C2×C42—222no—
555C2×C42—222no—
556C2×C42—222no—
557C2×C42—222no—
558C2×C42—222no—
559C2×C42—222no—
560C2×C42—222no—
561C2×C42—222no—
562C2×C42—222no—
563C2×C42—222no—
564#95—22no—
565#95—22no—
566#95—22no—
567#95—41no—
568#95—41no—
569#95—114no—
570#95—114no—
571#95—114no—
572#95—222no—
573#95—222no—
574#95—222no—
575#95—222no—
576#95—222no—
577#95—222no—
578#95—222no—
579#95—222no—
580#95—222no—
581#95—441no—
582#95—441no—
583#95C4×D1114yes—
584C2×C11C2×#38511yescharacteristic
585C2×C11C4×C22⋊Q811yescharacteristic
586C2×C11#232311yescharacteristic
587C2×C11Q8×C4⋊C411yescharacteristic
588C2×C11#235111yescharacteristic
589C2×C11#236511yescharacteristic
590C2×C11#236711yescharacteristic
591C2×C11#240711yescharacteristic
592C2×C11#240911yescharacteristic
593C2×C11#244611yescharacteristic
594C2×C11#244811yescharacteristic
595C2×C11#245111yescharacteristic
596C2×C11#245311yescharacteristic
597C2×C11#258111yescharacteristic
598C2×C11#258211yescharacteristic
599C24C23×D1111yescharacteristic
600C2×Q8—1116no—
601C2×Q8—228no—
602C2×Q8—228no—
603C2×Q8—228no—
604C2×Q8—228no—
605C2×Q8—228no—
606C2×Q8—228no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—112no—
649C22×C4—112no—
650C22×C4—112no—
651C22×C4—112no—
652C22×C4—112no—
653C22×C4—112no—
654C22×C4—112no—
655C22×C4—112no—
656C22×C4—112no—
657C22×C4—112no—
658C22×C4—112no—
659C22×C4—112no—
660C22×C4—112no—
661C22×C4—112no—
662C22×C4—112no—
663C22×C4—112no—
664C22×C4—112no—
665C22×C4—112no—
666C22×C4—112no—
667C22×C4—221no—
668C22×C4—221no—
669C22×C4—221no—
670C22×C4—221no—
671C22×C4—221no—
672C22×C4—221no—
673C22×C4—221no—
674C22×C4—221no—
675C22×C4—221no—
676C22×C4—221no—
677C22×C4—221no—
678C22×C4—221no—
679C22×C4—221no—
680C22×C4—221no—
681C22×C4—221no—
682C22×C4—221no—
683C22×C4—221no—
684C22×C4—221no—
685C22×C4—221no—
686C22×C4—221no—
687C22×C4—221no—
688C22×C4—221no—
689C22×C4—221no—
690C22×C4—221no—
691C22×C4—221no—
692C22×C4—221no—
693C22×C4—221no—
694C22×C4—221no—
695C22×C4—221no—
696C22×C4—221no—
697C22×C4—221no—
698C22×C4—221no—
699C22×C4—221no—
700C22×C4—221no—
701C22×C4—221no—
702C22×C4—221no—
703C22×C4—221no—
704C22×C4C2×C4×D1112yes—
705C22×C4C2×C4×D1112yes—
706C22×C4C2×C4×D1112yes—
707C22×C4D4×D1112yes—
708C22×C4D4×D1112yes—
709C22×C4D4×D1112yes—
710C22×C4Q8×D1112yes—
711C22×C4Q8×D1112yes—
712C4⋊C4—28no—
713C4⋊C4—228no—
714C4⋊C4—228no—
715C4⋊C4—228no—
716C4⋊C4—228no—
717C4⋊C4—228no—
718C4⋊C4—444no—
719C4⋊C4—444no—
720C4⋊C4—444no—
721C42—228no—
722C42—228no—
723C42—228no—
724C42—228no—
725C42—444no—
726C11#1401711yescharacteristic, complemented, Sylow
727C23C22×C4×D1111yescharacteristic
728C23C2×D4×D1111yescharacteristic
729C23C2×D4×D1111yescharacteristic
730C23C2×D4×D1111yescharacteristic
731C23#6703711yescharacteristic
732C23C2×Q8×D1111yescharacteristic
733C23C2×Q8×D1111yescharacteristic
734C23#41×D1111yescharacteristic
735C23#41×D1111yescharacteristic
736C23#41×D1111yescharacteristic
737C23#41×D1111yescharacteristic
738C23#41×D1111yescharacteristic
739C23#6704311yescharacteristic
740C23#6704311yescharacteristic
741C23#6704311yescharacteristic
742Q8—2232no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—114no—
792C2×C4—114no—
793C2×C4—114no—
794C2×C4—114no—
795C2×C4—114no—
796C2×C4—114no—
797C2×C4—114no—
798C2×C4—114no—
799C2×C4—114no—
800C2×C4—114no—
801C2×C4—222no—
802C2×C4—222no—
803C2×C4—222no—
804C2×C4—222no—
805C2×C4—222no—
806C2×C4—222no—
807C2×C4—222no—
808C2×C4—222no—
809C2×C4—222no—
810C2×C4—222no—
811C2×C4—222no—
812C2×C4—222no—
813C2×C4—222no—
814C2×C4—222no—
815C2×C4—222no—
816C2×C4—222no—
817C2×C4—222no—
818C2×C4—222no—
819C2×C4—222no—
820C2×C4—222no—
821C2×C4—222no—
822C2×C4—222no—
823C2×C4—222no—
824C2×C4—222no—
825C2×C4—222no—
826C2×C4—222no—
827C2×C4—222no—
828C2×C4—441no—
829C2×C4—441no—
830C2×C4—441no—
831C2×C4—441no—
832C2×C4—441no—
833C2×C4—441no—
834C2×C4—441no—
835C2×C4—441no—
836C2×C4—441no—
837C2×C4—441no—
838C2×C4—441no—
839C2×C4—441no—
840C2×C4—441no—
841C2×C4—441no—
842C2×C4—441no—
843C2×C4—441no—
844C2×C4—441no—
845C2×C4—441no—
846C2×C4—441no—
847C2×C4C4⋊C4×D1114yes—
848C22C2×C4⋊C4×D1111yescharacteristic
849C22#1062304711yescharacteristic
850C22#1062305311yescharacteristic
851C22C4×D4×D1111yescharacteristic
852C22C4×D4×D1111yescharacteristic
853C22#1062307711yescharacteristic
854C22C4×Q8×D1111yescharacteristic
855C22D11×#12011yescharacteristic
856C22#1062312811yescharacteristic
857C22#1062313011yescharacteristic
858C22#1062314111yescharacteristic
859C22D11×C22⋊Q811yescharacteristic
860C22D11×C22⋊Q811yescharacteristic
861C22D11×C22⋊Q811yescharacteristic
862C22#1062316311yescharacteristic
863C22#1062316311yescharacteristic
864C22D11×#12311yescharacteristic
865C22#1062318611yescharacteristic
866C22#1062318711yescharacteristic
867C22#1062319311yescharacteristic
868C22#1062319511yescharacteristic
869C22#1062320611yescharacteristic
870C22#1062320811yescharacteristic
871C22#1062320811yescharacteristic
872C22#1062320811yescharacteristic
873C22#1062321611yescharacteristic
874C22#1062321611yescharacteristic
875C22#1062321611yescharacteristic
876C22#1062321611yescharacteristic
877C22#1062321911yescharacteristic
878C22#1062323211yescharacteristic
879C22#1062323311yescharacteristic
880C22#1062323311yescharacteristic
881C22#1062323711yescharacteristic
882C22#1062325311yescharacteristic
883C4—24no—
884C4—42no—
885C4—42no—
886C4—42no—
887C4—42no—
888C4—42no—
889C4—81no—
890C4—118no—
891C4—224no—
892C4—224no—
893C4—224no—
894C4—442no—
895C4—442no—
896C4—442no—
897C4—881no—
898C2D11×#38511yescharacteristic
899C2#1307115011yescharacteristic
900C2#1307129111yescharacteristic
901C2#1307153011yescharacteristic
902C2#1307153311yescharacteristic
903C2#1307167111yescharacteristic
904C2#1307168211yescharacteristic
905C2#1307195611yescharacteristic
906C2#1307197411yescharacteristic
907C2#1307238711yescharacteristic
908C2#1307240711yescharacteristic
909C2#1307245011yescharacteristic
910C2#1307247011yescharacteristic
911C2#1307397911yescharacteristic
912C2#1307398511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1442C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1442D11
hypocenterC11#14017
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
57. #10622259C4semidirect
106. C2×Dic11⋊C4Q8semidirect
256. C2×Dic22C4⋊C4semidirect
400. C2×Dic11C4×Q8semidirect
726. C11#14017semidirect

Maximal subgroups

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

subgroupindex
C22×#669402
C2×#106222592
C2×#106222602
C2×#106222622
#130668802
#130668792
#130668742
#130668512
#130668502
#130668472
Dic11⋊#952
C11×#14422
#1401711