Finite Group Databasebeta

← #14676560

Subgroups — #14676560

Order 2816.

2266 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66931C211yesmaximal, characteristic
2C22×#66940C211yesmaximal, characteristic, complemented
3C2×#10622259C211yesmaximal, characteristic, complemented
4C2×#10622555C211yesmaximal, characteristic
5C2×C22⋊C4×Dic11C211yesmaximal, characteristic
6#13066868C211yesmaximal, characteristic, complemented
7#13066866C211yesmaximal, characteristic, complemented
8#13066859C211yesmaximal, characteristic
9#13066853C211yesmaximal, characteristic
10#13066853C211yesmaximal, characteristic
11#13066851C211yesmaximal, characteristic, complemented
12#13066850C211yesmaximal, characteristic, complemented
13Dic11⋊#95C211yesmaximal, characteristic, complemented
14Dic11⋊#95C211yesmaximal, characteristic, complemented
15C11×#1439C211yesmaximal, characteristic
16C24×Dic11C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C2×#66940—24no—
36C2×#66940—24no—
37C2×#66940—24no—
38C2×#66931—24no—
39C2×#66931—24no—
40C2×#66931C418yescomplemented
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
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57#10622555—24no—
58C22⋊C4×Dic11—24no—
59#10622259—24no—
60C25×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×Dic11—22no—
68C23×Dic11—22no—
69C23×Dic11—22no—
70C23×Dic11—22no—
71C23×Dic11—22no—
72C23×Dic11—22no—
73C23×Dic11C2×C414yes—
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C22×Dic22—22no—
83C22×Dic22—22no—
84C22×Dic22—22no—
85C22×Dic22—22no—
86C22×Dic22C2×C414yes—
87C22×Dic22D414yes—
88C22×Dic22D414yes—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4—22no—
91C2×C11×C4⋊C4—22no—
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—22no—
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4—22no—
98C2×C11×C22⋊C4—22no—
99C2×C11×C22⋊C4—41no—
100C2×C11×C22⋊C4C2×C414yes—
101C2×C22⋊Dic11—22no—
102C2×C22⋊Dic11—22no—
103C2×C22⋊Dic11—22no—
104C2×C22⋊Dic11—22no—
105C2×C22⋊Dic11—22no—
106C2×C22⋊Dic11—22no—
107C2×C22⋊Dic11—41no—
108C2×C22⋊Dic11C2×C414yes—
109C2×C22⋊Dic11Q814yescomplemented
110C2×C4⋊Dic11—22no—
111C2×C4⋊Dic11—22no—
112C2×C4⋊Dic11C2×C414yes—
113C2×Dic11⋊C4—22no—
114C2×Dic11⋊C4—22no—
115C2×Dic11⋊C4—22no—
116C2×Dic11⋊C4—22no—
117C2×Dic11⋊C4—22no—
118C2×Dic11⋊C4—22no—
119C2×Dic11⋊C4—22no—
120C2×Dic11⋊C4—22no—
121C2×Dic11⋊C4—22no—
122C2×Dic11⋊C4—22no—
123C2×Dic11⋊C4—22no—
124C2×Dic11⋊C4—22no—
125C2×Dic11⋊C4C2×C414yes—
126C2×Dic11⋊C4C2×C414yes—
127C2×Dic11⋊C4D414yes—
128C2×C4×Dic11—22no—
129C2×C4×Dic11—22no—
130C2×C4×Dic11—22no—
131C2×C4×Dic11—22no—
132C2×C4×Dic11—22no—
133C2×C4×Dic11—22no—
134C2×C4×Dic11—22no—
135C2×C4×Dic11—22no—
136C2×C4×Dic11—22no—
137C2×C4×Dic11—22no—
138C2×C4×Dic11—22no—
139C2×C4×Dic11D414yes—
140#66940—232no—
141#66931—232no—
142C11×#95—22no—
143C11×#95—22no—
144C11×#95—41no—
145C11⋊#95—22no—
146C11⋊#95—22no—
147C11⋊#95—22no—
148C11⋊#95—22no—
149C11⋊#95—22no—
150C11⋊#95—22no—
151C11⋊#95—22no—
152C11⋊#95—22no—
153C11⋊#95—22no—
154C11⋊#95—22no—
155C11⋊#95—41no—
156C11⋊#95—41no—
157C11⋊#95—41no—
158#13969—111nomaximal, Sylow
159C24×C11—21no—
160C24×C11—21no—
161C24×C11—21no—
162C24×C11—21no—
163C24×C11—21no—
164C24×C11—21no—
165C24×C11—21no—
166C24×C11—21no—
167C24×C11—21no—
168C24×C11—21no—
169C24×C11—21no—
170C24×C11—21no—
171C24×C11C22×C412yes—
172C24×C11C2×Q812yes—
173C24×C11#4112yes—
174C24×C11C2411yescharacteristic
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×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11C22×C412yes—
211C22×C4×C11C22×C412yes—
212C22×C4×C11C2×D412yes—
213C22×C4×C11C2×D412yes—
214C22×C4×C11C2×D412yes—
215C22×C4×C11C2×D412yes—
216C22×C4×C11#4112yes—
217C22×Dic11—28no—
218C22×Dic11—28no—
219C22×Dic11—28no—
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×Dic11—21no—
232C22×Dic11—21no—
233C22×Dic11—21no—
234C22×Dic11—21no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—21no—
239C22×Dic11—21no—
240C22×Dic11—21no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11—21no—
247C22×Dic11—21no—
248C22×Dic11—21no—
249C22×Dic11—21no—
250C22×Dic11—21no—
251C22×Dic11—21no—
252C22×Dic11—21no—
253C22×Dic11—21no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11—21no—
258C22×Dic11—21no—
259C22×Dic11—44no—
260C22×Dic11—44no—
261C22×Dic11—44no—
262C22×Dic11—44no—
263C22×Dic11C22×C412yes—
264C22×Dic11C22×C412yes—
265C22×Dic11C22×C412yes—
266C22×Dic11C22×C412yes—
267C22×Dic11C2×D412yes—
268C22×Dic11C2×D412yes—
269C22×Dic11C2×D412yes—
270C22×Dic11C2×D412yes—
271C22×Dic11C2×D412yes—
272C22×Dic11C2×D412yes—
273C22×Dic11C2×D412yes—
274C22×Dic11C2×D412yes—
275C22×Dic11C2×Q812yes—
276C22×Dic11C2×Q812yes—
277C22×Dic11#4112yes—
278C22×Dic11#4112yes—
279C22×Dic11#4112yes—
280C2×Dic22—28no—
281C2×Dic22—28no—
282C2×Dic22—28no—
283C2×Dic22—28no—
284C2×Dic22—28no—
285C2×Dic22—28no—
286C2×Dic22C22⋊C4116yescomplemented
287C11×C4⋊C4—28no—
288C11×C22⋊C4—28no—
289C11×C22⋊C4—28no—
290C11×C22⋊C4—44no—
291C22⋊Dic11—28no—
292C22⋊Dic11—28no—
293C22⋊Dic11—44no—
294C4⋊Dic11—28no—
295Dic11⋊C4—28no—
296Dic11⋊C4—28no—
297Dic11⋊C4—28no—
298Dic11⋊C4—28no—
299Dic11⋊C4—44no—
300C4×Dic11—28no—
301C4×Dic11—28no—
302C4×Dic11—28no—
303C4×Dic11—44no—
304C22×C22⋊Q8—111no—
305C22×C4×Q8—111no—
306C2×#391—111no—
307C2×#380—111no—
308C2×C4×C22⋊C4—111no—
309#1441—111no—
310#1441—111no—
311#1439—111no—
312#1439D1111yescharacteristic
313#1437—111no—
314#1437—111no—
315#1436—111no—
316#1436—111no—
317C4⋊#95—111no—
318C4⋊#95—111no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—22no—
337C23×C11—41no—
338C23×C11—41no—
339C23×C11—41no—
340C23×C11—41no—
341C23×C11—41no—
342C23×C11—41no—
343C23×C11—41no—
344C23×C11—41no—
345C23×C11—41no—
346C23×C11—41no—
347C23×C11—41no—
348C23×C11—41no—
349C23×C11—41no—
350C23×C11—41no—
351C23×C11—41no—
352C23×C11—41no—
353C23×C11C4×Q814yescomplemented
354C23×C11C23×C411yescharacteristic
355C23×C11C22×D411yescharacteristic
356C23×C11C22×D411yescharacteristic
357C23×C11C22×D411yescharacteristic
358C23×C11C22×D411yescharacteristic
359C23×C11C22×Q811yescharacteristic
360C23×C11C2×#4111yescharacteristic
361C23×C11C2×#4111yescharacteristic
362C23×C11C2×#4111yescharacteristic
363C23×C11C2×#4111yescharacteristic
364C23×C11C2×#4111yescharacteristic
365C23×C11H(5,𝔽2)11yescharacteristic
366C23×C112−1+411yescharacteristic
367C23×C112−1+411yescharacteristic
368C23×C112−1+411yescharacteristic
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—41no—
398C2×C4×C11—41no—
399C2×C4×C11—41no—
400C2×C4×C11—41no—
401C2×C4×C11—41no—
402C2×C4×C11—41no—
403C2×C4×C11—41no—
404C2×C4×C11—41no—
405C2×C4×C11—41no—
406C2×C4×C11—41no—
407C2×C4×C11—41no—
408C2×C4×C11—41no—
409C2×C4×C11—41no—
410C2×C4×C11C2×C22⋊C414yes—
411C2×Dic11—22no—
412C2×Dic11—22no—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—22no—
416C2×Dic11—22no—
417C2×Dic11—22no—
418C2×Dic11—22no—
419C2×Dic11—22no—
420C2×Dic11—22no—
421C2×Dic11—22no—
422C2×Dic11—22no—
423C2×Dic11—22no—
424C2×Dic11—22no—
425C2×Dic11—22no—
426C2×Dic11—22no—
427C2×Dic11—22no—
428C2×Dic11—22no—
429C2×Dic11—22no—
430C2×Dic11—22no—
431C2×Dic11—22no—
432C2×Dic11—22no—
433C2×Dic11—22no—
434C2×Dic11—22no—
435C2×Dic11—41no—
436C2×Dic11—41no—
437C2×Dic11—41no—
438C2×Dic11—41no—
439C2×Dic11—41no—
440C2×Dic11—41no—
441C2×Dic11—41no—
442C2×Dic11—41no—
443C2×Dic11—41no—
444C2×Dic11—41no—
445C2×Dic11—41no—
446C2×Dic11—41no—
447C2×Dic11—41no—
448C2×Dic11—41no—
449C2×Dic11—41no—
450C2×Dic11—41no—
451C2×Dic11—416no—
452C2×Dic11—41no—
453C2×Dic11—41no—
454C2×Dic11—41no—
455C2×Dic11—41no—
456C2×Dic11—41no—
457C2×Dic11—41no—
458C2×Dic11—41no—
459C2×Dic11C2×C22⋊C414yes—
460C2×Dic11C2×C22⋊C414yes—
461C2×Dic11C4×D414yes—
462C2×Dic11C4×D414yes—
463C2×Dic11#12014yes—
464C2×Dic11#12114yes—
465C2×Dic11#12114yes—
466C2×Dic11C22⋊Q814yescomplemented
467C2×Dic11#12314yes—
468Dic22—232no—
469C23×Q8—111no—
470C24×C4—111no—
471C2×C22⋊Q8—118no—
472C2×C22⋊Q8—224no—
473C2×C22⋊Q8—224no—
474C2×C4×Q8—224no—
475C2×C4×Q8—224no—
476C2×C4×Q8—224no—
477C22×C4⋊C4—111no—
478C22×C4⋊C4—111no—
479C22×C4⋊C4—111no—
480C22×C4⋊C4—111no—
481C22×C4⋊C4—111no—
482C22×C4⋊C4—111no—
483C22×C4⋊C4C2×D1111yescharacteristic
484C22×C22⋊C4—111no—
485C22×C22⋊C4—111no—
486C22×C22⋊C4—111no—
487C22×C22⋊C4C2×D1111yescharacteristic
488C22×C22⋊C4C2×D1111yescharacteristic
489C22×C22⋊C4C2×D1111yescharacteristic
490C22×C42—111no—
491C22×C42—111no—
492C22×C42—111no—
493C22×C42—111no—
494#391—224no—
495#380—224no—
496C4×C22⋊C4—224no—
497C2×#95—111no—
498C2×#95—111no—
499C2×#95—111no—
500C2×#95—111no—
501C2×#95—111no—
502C2×#95—111no—
503C2×#95—111no—
504C2×#95—111no—
505C2×#95—111no—
506C2×#95—111no—
507C2×#95—111no—
508C2×#95—111no—
509C2×#95—111no—
510C2×#95C2×D1111yescharacteristic
511C2×#95C2×D1111yescharacteristic
512C2×#95C2×D1111yescharacteristic
513C22×C11—24no—
514C22×C11—24no—
515C22×C11—24no—
516C22×C11—42no—
517C22×C11—42no—
518C22×C11—42no—
519C22×C11—42no—
520C22×C11—42no—
521C22×C11—42no—
522C22×C11—42no—
523C22×C11—42no—
524C22×C11—42no—
525C22×C11—42no—
526C22×C11—42no—
527C22×C11—42no—
528C22×C11C22×C22⋊C411yescharacteristic
529C22×C11C2×C4×D411yescharacteristic
530C22×C11C2×C4×D411yescharacteristic
531C22×C11C2×C4×Q811yescharacteristic
532C22×C11C4×#4111yescharacteristic
533C22×C11#51911yescharacteristic
534C22×C11#52011yescharacteristic
535C22×C11C2×#12011yescharacteristic
536C22×C11C2×#12111yescharacteristic
537C22×C11C2×#12111yescharacteristic
538C22×C11C2×C22⋊Q811yescharacteristic
539C22×C11C2×#12311yescharacteristic
540C22×C11#52511yescharacteristic
541C22×C11#52911yescharacteristic
542C22×C11#53311yescharacteristic
543C22×C11#53611yescharacteristic
544C22×C11#53711yescharacteristic
545C22×C11#54111yescharacteristic
546C22×C11#54211yescharacteristic
547C22×C11#54611yescharacteristic
548C22×C11#54711yescharacteristic
549C22×C11#54811yescharacteristic
550C22×C11#54811yescharacteristic
551C22×C11#54811yescharacteristic
552C22×C11#54811yescharacteristic
553C22×C11#54811yescharacteristic
554C22×C11D4×Q811yescharacteristic
555C22×C11D4×Q811yescharacteristic
556C22×C11D4×Q811yescharacteristic
557C22×C11#55011yescharacteristic
558C22×C11#55011yescharacteristic
559C22×C11#55211yescharacteristic
560C22×C11#55211yescharacteristic
561C22×C11#55411yescharacteristic
562C22×C11#55611yescharacteristic
563C4×C11—24no—
564C4×C11—42no—
565C4×C11—42no—
566C4×C11—42no—
567C4×C11—42no—
568C4×C11—81no—
569Dic11—24no—
570Dic11—24no—
571Dic11—42no—
572Dic11—42no—
573Dic11—42no—
574Dic11—42no—
575Dic11—81no—
576Dic11#38618yes—
577C25C22×D1111yescharacteristic
578C22×Q8—114no—
579C22×Q8—114no—
580C22×Q8—114no—
581C22×Q8—222no—
582C22×Q8—222no—
583C22×Q8—222no—
584C22×Q8—222no—
585C23×C4—111no—
586C23×C4—111no—
587C23×C4—111no—
588C23×C4—114no—
589C23×C4—111no—
590C23×C4—111no—
591C23×C4—111no—
592C23×C4—111no—
593C23×C4—111no—
594C23×C4—222no—
595C23×C4—222no—
596C23×C4—222no—
597C23×C4—222no—
598C23×C4—222no—
599C23×C4—222no—
600C23×C4C22×D1111yescharacteristic
601C23×C4C22×D1111yescharacteristic
602C23×C4C22×D1111yescharacteristic
603C23×C4C22×D1111yescharacteristic
604C23×C4C22×D1111yescharacteristic
605C23×C4C22×D1111yescharacteristic
606C22⋊Q8—2232no—
607C4×Q8—2232no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—114no—
612C2×C4⋊C4—114no—
613C2×C4⋊C4—114no—
614C2×C4⋊C4—114no—
615C2×C4⋊C4—222no—
616C2×C4⋊C4—222no—
617C2×C4⋊C4—222no—
618C2×C4⋊C4—222no—
619C2×C4⋊C4—222no—
620C2×C4⋊C4—222no—
621C2×C4⋊C4—222no—
622C2×C4⋊C4—222no—
623C2×C4⋊C4—222no—
624C2×C4⋊C4—222no—
625C2×C4⋊C4—222no—
626C2×C4⋊C4—222no—
627C2×C4⋊C4—222no—
628C2×C4⋊C4—222no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—41no—
637C2×C22⋊C4—114no—
638C2×C22⋊C4—114no—
639C2×C22⋊C4—222no—
640C2×C22⋊C4—222no—
641C2×C22⋊C4—222no—
642C2×C22⋊C4—222no—
643C2×C22⋊C4—222no—
644C2×C22⋊C4—222no—
645C2×C22⋊C4—441no—
646C2×C22⋊C4C4×D1114yes—
647C2×C42—114no—
648C2×C42—222no—
649C2×C42—222no—
650C2×C42—222no—
651C2×C42—222no—
652C2×C42—222no—
653C2×C42—222no—
654C2×C42—222no—
655C2×C42—222no—
656C2×C42—222no—
657C2×C42—222no—
658C2×C42—222no—
659#95—22no—
660#95—22no—
661#95—41no—
662#95—222no—
663#95—222no—
664#95—222no—
665#95—222no—
666#95—222no—
667#95—222no—
668#95—222no—
669#95—222no—
670#95—222no—
671#95—222no—
672#95—441no—
673#95—441no—
674#95—441no—
675C2×C11—44no—
676C2×C11C2×#38611yescharacteristic
677C2×C11C4×C22⋊Q811yescharacteristic
678C2×C11#232311yescharacteristic
679C2×C11Q8×C22⋊C411yescharacteristic
680C2×C11#234111yescharacteristic
681C2×C11#236011yescharacteristic
682C2×C11#236211yescharacteristic
683C2×C11#240711yescharacteristic
684C2×C11#240911yescharacteristic
685C2×C11#242111yescharacteristic
686C2×C11#242311yescharacteristic
687C2×C11#242611yescharacteristic
688C2×C11#242911yescharacteristic
689C2×C11#253611yescharacteristic
690C2×C11#253811yescharacteristic
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24—21no—
698C24—21no—
699C24—21no—
700C24—21no—
701C24—21no—
702C24—21no—
703C24C2×C4×D1112yes—
704C24#434112yes—
705C24Q8×D1112yes—
706C24C23×D1111yescharacteristic
707C2×Q8—1116no—
708C2×Q8—228no—
709C2×Q8—228no—
710C2×Q8—228no—
711C2×Q8—228no—
712C2×Q8—228no—
713C2×Q8—228no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—112no—
750C22×C4—112no—
751C22×C4—112no—
752C22×C4—112no—
753C22×C4—112no—
754C22×C4—112no—
755C22×C4—112no—
756C22×C4—112no—
757C22×C4—112no—
758C22×C4—112no—
759C22×C4—112no—
760C22×C4—112no—
761C22×C4—112no—
762C22×C4—112no—
763C22×C4—112no—
764C22×C4—112no—
765C22×C4—112no—
766C22×C4—228no—
767C22×C4—228no—
768C22×C4—228no—
769C22×C4—221no—
770C22×C4—221no—
771C22×C4—221no—
772C22×C4—221no—
773C22×C4—221no—
774C22×C4—221no—
775C22×C4—221no—
776C22×C4—221no—
777C22×C4—221no—
778C22×C4—221no—
779C22×C4—221no—
780C22×C4—221no—
781C22×C4—221no—
782C22×C4—221no—
783C22×C4—221no—
784C22×C4—221no—
785C22×C4—221no—
786C22×C4—221no—
787C22×C4—221no—
788C22×C4—221no—
789C22×C4—221no—
790C22×C4—221no—
791C22×C4—221no—
792C22×C4—221no—
793C22×C4—221no—
794C22×C4—221no—
795C22×C4—221no—
796C22×C4—221no—
797C22×C4—221no—
798C22×C4—221no—
799C22×C4—221no—
800C22×C4—221no—
801C22×C4—221no—
802C22×C4—221no—
803C22×C4—221no—
804C22×C4—221no—
805C22×C4—221no—
806C22×C4—221no—
807C22×C4—221no—
808C22×C4—444no—
809C22×C4—444no—
810C22×C4—444no—
811C22×C4—444no—
812C22×C4C2×C4×D1112yes—
813C22×C4C2×C4×D1112yes—
814C22×C4D4×D1112yes—
815C22×C4D4×D1112yes—
816C22×C4D4×D1112yes—
817C22×C4D4×D1112yes—
818C22×C4#434112yes—
819C4⋊C4—28no—
820C4⋊C4—228no—
821C4⋊C4—228no—
822C4⋊C4—228no—
823C4⋊C4—228no—
824C4⋊C4—228no—
825C4⋊C4—444no—
826C22⋊C4—28no—
827C22⋊C4—28no—
828C22⋊C4—44no—
829C22⋊C4—228no—
830C22⋊C4—228no—
831C22⋊C4—444no—
832C42—228no—
833C42—228no—
834C42—228no—
835C42—444no—
836C11#1396911yescharacteristic, complemented, Sylow
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23#6694014yescomplemented
872C23C22×C4×D1111yescharacteristic
873C23C2×D4×D1111yescharacteristic
874C23C2×D4×D1111yescharacteristic
875C23C2×D4×D1111yescharacteristic
876C23C2×D4×D1111yescharacteristic
877C23C2×#434111yescharacteristic
878C23C2×#434111yescharacteristic
879C23#6703711yescharacteristic
880C23C2×Q8×D1111yescharacteristic
881C23#41×D1111yescharacteristic
882C23#41×D1111yescharacteristic
883C23#41×D1111yescharacteristic
884C23#6704311yescharacteristic
885C23#6704311yescharacteristic
886C23#6704311yescharacteristic
887Q8—2232no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—114no—
930C2×C4—114no—
931C2×C4—114no—
932C2×C4—114no—
933C2×C4—114no—
934C2×C4—114no—
935C2×C4—114no—
936C2×C4—114no—
937C2×C4—114no—
938C2×C4—222no—
939C2×C4—222no—
940C2×C4—222no—
941C2×C4—222no—
942C2×C4—222no—
943C2×C4—222no—
944C2×C4—222no—
945C2×C4—222no—
946C2×C4—222no—
947C2×C4—222no—
948C2×C4—222no—
949C2×C4—222no—
950C2×C4—222no—
951C2×C4—222no—
952C2×C4—222no—
953C2×C4—222no—
954C2×C4—222no—
955C2×C4—222no—
956C2×C4—222no—
957C2×C4—222no—
958C2×C4—222no—
959C2×C4—222no—
960C2×C4—222no—
961C2×C4—222no—
962C2×C4—4416no—
963C2×C4—441no—
964C2×C4—441no—
965C2×C4—441no—
966C2×C4—441no—
967C2×C4—441no—
968C2×C4—441no—
969C2×C4—441no—
970C2×C4—441no—
971C2×C4—441no—
972C2×C4—441no—
973C2×C4—441no—
974C2×C4—441no—
975C2×C4—441no—
976C2×C4—441no—
977C2×C4—441no—
978C2×C4—441no—
979C2×C4—441no—
980C2×C4—441no—
981C2×C4—441no—
982C2×C4—441no—
983C2×C4—441no—
984C2×C4—441no—
985C2×C4—441no—
986C2×C4C22⋊C4×D1114yes—
987C22—24no—
988C22—24no—
989C22—24no—
990C22—42no—
991C22—42no—
992C22—42no—
993C22—42no—
994C22—42no—
995C22—42no—
996C22—42no—
997C22—42no—
998C22—42no—
999C22—42no—
1000C22—42no—
1001C22—42no—
1002C22C2×C22⋊C4×D1111yescharacteristic
1003C22C2×#6694011yescharacteristic
1004C22#1062304711yescharacteristic
1005C22C4×#434111yescharacteristic
1006C22C4×D4×D1111yescharacteristic
1007C22C4×D4×D1111yescharacteristic
1008C22#1062307711yescharacteristic
1009C22#1062311711yescharacteristic
1010C22D11×#12011yescharacteristic
1011C22#1062312211yescharacteristic
1012C22#1062312811yescharacteristic
1013C22#1062312911yescharacteristic
1014C22#1062312911yescharacteristic
1015C22#1062312911yescharacteristic
1016C22#1062313011yescharacteristic
1017C22D11×#12111yescharacteristic
1018C22D11×#12111yescharacteristic
1019C22#1062314211yescharacteristic
1020C22#1062315311yescharacteristic
1021C22D11×C22⋊Q811yescharacteristic
1022C22#1062316311yescharacteristic
1023C22#1062316311yescharacteristic
1024C22#1062316311yescharacteristic
1025C22#1062316711yescharacteristic
1026C22#1062318011yescharacteristic
1027C22#1062318111yescharacteristic
1028C22#1062318111yescharacteristic
1029C22D11×#12311yescharacteristic
1030C22#1062319311yescharacteristic
1031C22#1062320611yescharacteristic
1032C22#1062320811yescharacteristic
1033C22#1062320811yescharacteristic
1034C22#1062323211yescharacteristic
1035C22#1062323311yescharacteristic
1036C22#1062324911yescharacteristic
1037C4—24no—
1038C4—42no—
1039C4—42no—
1040C4—42no—
1041C4—42no—
1042C4—81no—
1043C4—118no—
1044C4—224no—
1045C4—224no—
1046C4—442no—
1047C4—442no—
1048C4—442no—
1049C4—442no—
1050C4—881no—
1051C2—44no—
1052C2D11×#38611yescharacteristic
1053C2#1307114811yescharacteristic
1054C2#1307129111yescharacteristic
1055C2#1307144811yescharacteristic
1056C2#1307145511yescharacteristic
1057C2#1307161611yescharacteristic
1058C2#1307164011yescharacteristic
1059C2#1307195411yescharacteristic
1060C2#1307197411yescharacteristic
1061C2#1307211211yescharacteristic
1062C2#1307213411yescharacteristic
1063C2#1307217511yescharacteristic
1064C2#1307220811yescharacteristic
1065C2#1307352011yescharacteristic
1066C2#1307353311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenter#1439D11
hypocenterC11#13969
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C22×#66940C2semidirect
3. C2×#10622259C2semidirect
6. #13066868C2semidirect
7. #13066866C2semidirect
11. #13066851C2semidirect
12. #13066850C2semidirect
13. Dic11⋊#95C2semidirect
14. Dic11⋊#95C2semidirect
40. C2×#66931C4semidirect
109. C2×C22⋊Dic11Q8semidirect
286. C2×Dic22C22⋊C4semidirect
353. C23×C11C4×Q8semidirect
466. C2×Dic11C22⋊Q8semidirect
836. C11#13969semidirect
871. C23#66940semidirect

Maximal subgroups

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

subgroupindex
C22×#669312
C22×#669402
C2×#106222592
C2×#106225552
C2×C22⋊C4×Dic112
#130668682
#130668662
#130668592
#130668532
#130668512
#130668502
Dic11⋊#952
C11×#14392
#1396911