Finite Group Databasebeta

← #14685226

Subgroups — #14685226

Order 2816.

2558 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66931C211yesmaximal, characteristic, complemented
2C22×D4×Dic11C211yesmaximal, characteristic
3C2×#10622269C211yesmaximal, characteristic, complemented
4C2×#10622560C211yesmaximal, characteristic, complemented
5C2×#10622563C211yesmaximal, characteristic, complemented
6C2×#10622559C211yesmaximal, characteristic, complemented
7#13066868C211yesmaximal, characteristic, complemented
8#13066861C211yesmaximal, characteristic, complemented
9#13066859C211yesmaximal, characteristic, complemented
10#13066859C211yesmaximal, characteristic, complemented
11#13066857C211yesmaximal, characteristic
12#13066850C211yesmaximal, characteristic, complemented
13#13066847C211yesmaximal, characteristic, complemented
14#13066838C211yesmaximal, characteristic, complemented
15C11×#1438C211yesmaximal, characteristic
16C23×D4×C11C2211yescharacteristic
17C24×Dic11C2211yescharacteristic
18C24×Dic11C2211yescharacteristic
19C23×Dic22C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C2×D4×Dic11—24no—
31C2×D4×Dic11—24no—
32C2×D4×Dic11—24no—
33C22×C4⋊Dic11C2211yescharacteristic
34C22×C4⋊Dic11C2211yescharacteristic
35C22×C4⋊Dic11C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40C2×#66931—24no—
41C2×#66931—24no—
42C2×#66931—24no—
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#10622563—24no—
58#10622560—24no—
59#10622559—24no—
60#10622269—24no—
61C25×C11C2311yescharacteristic
62C25×C11C2311yescharacteristic
63C22×D4×C11—22no—
64C22×D4×C11—22no—
65C22×D4×C11—22no—
66C22×D4×C11—22no—
67C22×D4×C11—22no—
68C22×D4×C11—22no—
69C22×D4×C11Q814yescomplemented
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×Dic11—22no—
76C23×Dic11—22no—
77C23×Dic11—22no—
78C23×Dic11—22no—
79C23×Dic11—22no—
80C23×Dic11—22no—
81C23×Dic11—22no—
82C23×Dic11—22no—
83C23×Dic11—22no—
84C23×Dic11—41no—
85C23×Dic11—41no—
86C23×Dic11—41no—
87C23×Dic11—41no—
88C23×Dic11D414yes—
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C22×Dic22—22no—
98C22×Dic22—22no—
99C22×Dic22—22no—
100C22×Dic22—22no—
101C22×Dic22—22no—
102C22×Dic22—41no—
103C22×Dic22—41no—
104C2×C11×C22⋊C4—22no—
105C2×C11×C22⋊C4—22no—
106C2×C11×C22⋊C4—22no—
107C2×C11×C22⋊C4—22no—
108C2×C11×C22⋊C4—22no—
109C2×C11×C22⋊C4—22no—
110C2×C11×C22⋊C4—22no—
111C2×C11×C22⋊C4—22no—
112C2×C11×C22⋊C4—22no—
113C2×C11×C22⋊C4—22no—
114C2×C11×C22⋊C4—41no—
115C2×C11×C22⋊C4—41no—
116C2×C22⋊Dic11—22no—
117C2×C22⋊Dic11—22no—
118C2×C22⋊Dic11—22no—
119C2×C22⋊Dic11—22no—
120C2×C22⋊Dic11—22no—
121C2×C22⋊Dic11—22no—
122C2×C22⋊Dic11—22no—
123C2×C22⋊Dic11—22no—
124C2×C22⋊Dic11—22no—
125C2×C22⋊Dic11—22no—
126C2×C22⋊Dic11—22no—
127C2×C22⋊Dic11—22no—
128C2×C22⋊Dic11—22no—
129C2×C22⋊Dic11—22no—
130C2×C22⋊Dic11—22no—
131C2×C22⋊Dic11—41no—
132C2×C22⋊Dic11—41no—
133C2×C22⋊Dic11D414yes—
134D4×Dic11—232no—
135C2×C4⋊Dic11—22no—
136C2×C4⋊Dic11—22no—
137C2×C4⋊Dic11—22no—
138C2×C4⋊Dic11—22no—
139C2×C4⋊Dic11—22no—
140C2×C4⋊Dic11—22no—
141C2×C4⋊Dic11—41no—
142C2×C4⋊Dic11D414yes—
143C2×C4⋊Dic11D414yescomplemented
144C2×Dic11⋊C4—22no—
145C2×Dic11⋊C4—22no—
146C2×Dic11⋊C4—22no—
147C2×Dic11⋊C4—22no—
148C2×Dic11⋊C4—22no—
149C2×Dic11⋊C4—22no—
150C2×Dic11⋊C4—22no—
151C2×Dic11⋊C4—41no—
152C2×Dic11⋊C4D414yescomplemented
153C2×C4×Dic11—22no—
154C2×C4×Dic11—22no—
155C2×C4×Dic11—22no—
156#66931—232no—
157C11×#95—22no—
158C11×#95—22no—
159C11⋊#95—22no—
160C11⋊#95—22no—
161C11⋊#95—22no—
162C11⋊#95—22no—
163C11⋊#95—22no—
164C11⋊#95—22no—
165C11⋊#95—22no—
166C11⋊#95—22no—
167C11⋊#95—22no—
168C11⋊#95—22no—
169C11⋊#95—22no—
170C11⋊#95—22no—
171#14723—111nomaximal, Sylow
172C24×C11—21no—
173C24×C11—21no—
174C24×C11—21no—
175C24×C11—21no—
176C24×C11—21no—
177C24×C11—21no—
178C24×C11—21no—
179C24×C11—21no—
180C24×C11—21no—
181C24×C11—21no—
182C24×C11—21no—
183C24×C11—21no—
184C24×C11—21no—
185C24×C11—21no—
186C24×C11—21no—
187C24×C11—21no—
188C24×C11—21no—
189C24×C11—21no—
190C24×C11—21no—
191C24×C11—21no—
192C24×C11—21no—
193C24×C11—21no—
194C24×C11—21no—
195C24×C11—21no—
196C24×C11C2×D412yes—
197C24×C11C2×D412yes—
198C24×C11C2×Q812yes—
199C24×C11C2×Q812yes—
200C24×C11#4112yes—
201C24×C11#4112yes—
202C24×C11C2411yescharacteristic
203C2×D4×C11—28no—
204C2×D4×C11—28no—
205C2×D4×C11—28no—
206C2×D4×C11—28no—
207C2×D4×C11—28no—
208C2×D4×C11—28no—
209C2×D4×C11—28no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—21no—
238C22×C4×C11—21no—
239C22×C4×C11C2×D412yes—
240C22×C4×C11C2×D412yes—
241C22×C4×C11C2×D412yes—
242C22×C4×C11C2×Q812yes—
243C22×C4×C11#4112yes—
244C22×C4×C11#4112yes—
245C22×Dic11—28no—
246C22×Dic11—28no—
247C22×Dic11—28no—
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—21no—
260C22×Dic11—21no—
261C22×Dic11—21no—
262C22×Dic11—21no—
263C22×Dic11—21no—
264C22×Dic11—21no—
265C22×Dic11—21no—
266C22×Dic11—21no—
267C22×Dic11—21no—
268C22×Dic11—21no—
269C22×Dic11—21no—
270C22×Dic11—21no—
271C22×Dic11—21no—
272C22×Dic11—21no—
273C22×Dic11—21no—
274C22×Dic11—21no—
275C22×Dic11—21no—
276C22×Dic11—21no—
277C22×Dic11—21no—
278C22×Dic11—21no—
279C22×Dic11—21no—
280C22×Dic11—21no—
281C22×Dic11—21no—
282C22×Dic11—21no—
283C22×Dic11—21no—
284C22×Dic11—21no—
285C22×Dic11—21no—
286C22×Dic11—21no—
287C22×Dic11—21no—
288C22×Dic11—21no—
289C22×Dic11—21no—
290C22×Dic11—21no—
291C22×Dic11—21no—
292C22×Dic11—21no—
293C22×Dic11—44no—
294C22×Dic11—44no—
295C22×Dic11—44no—
296C22×Dic11—44no—
297C22×Dic11—44no—
298C22×Dic11—44no—
299C22×Dic11—44no—
300C22×Dic11—44no—
301C22×Dic11—44no—
302C22×Dic11—44no—
303C22×Dic11—44no—
304C22×Dic11C2×D412yes—
305C22×Dic11C2×D412yes—
306C22×Dic11C2×D412yes—
307C22×Dic11C2×D412yes—
308C22×Dic11C2×D412yes—
309C22×Dic11C2×D412yes—
310C22×Dic11C2×D412yes—
311C22×Dic11C2×D412yes—
312C22×Dic11C2×D412yes—
313C22×Dic11C2×D412yes—
314C22×Dic11#4112yes—
315C2×Dic22—28no—
316C2×Dic22—44no—
317C2×Dic22—44no—
318C2×Dic22—44no—
319C2×Dic22—44no—
320C2×Dic22—44no—
321C2×Dic22—44no—
322C11×C22⋊C4—28no—
323C11×C22⋊C4—28no—
324C11×C22⋊C4—44no—
325C11×C22⋊C4—44no—
326C22⋊Dic11—28no—
327C22⋊Dic11—28no—
328C22⋊Dic11—28no—
329C22⋊Dic11—28no—
330C22⋊Dic11—44no—
331C22⋊Dic11—44no—
332C4⋊Dic11—28no—
333C4⋊Dic11—28no—
334C4⋊Dic11—44no—
335Dic11⋊C4—28no—
336Dic11⋊C4—28no—
337Dic11⋊C4—44no—
338C4×Dic11—28no—
339C22×C22⋊Q8—111no—
340C22×C4×D4—111no—
341C2×#395—111no—
342C2×#393—111no—
343C2×#385—111no—
344C2×#385—111no—
345#1441—111no—
346#1439—111no—
347#1439—111no—
348#1439—111no—
349#1438—111no—
350#1438D1111yescharacteristic
351#1436—111no—
352#1436—111no—
353C22⋊#95—111no—
354C23×C11—22no—
355C23×C11—22no—
356C23×C11—22no—
357C23×C11—22no—
358C23×C11—22no—
359C23×C11—22no—
360C23×C11—22no—
361C23×C11—22no—
362C23×C11—22no—
363C23×C11—22no—
364C23×C11—22no—
365C23×C11—22no—
366C23×C11—22no—
367C23×C11—22no—
368C23×C11—22no—
369C23×C11—22no—
370C23×C11—22no—
371C23×C11—22no—
372C23×C11—22no—
373C23×C11—22no—
374C23×C11—22no—
375C23×C11—22no—
376C23×C11—22no—
377C23×C11—22no—
378C23×C11—22no—
379C23×C11—22no—
380C23×C11—22no—
381C23×C11—22no—
382C23×C11—22no—
383C23×C11—22no—
384C23×C11—22no—
385C23×C11—22no—
386C23×C11—22no—
387C23×C11—22no—
388C23×C11—22no—
389C23×C11—22no—
390C23×C11—41no—
391C23×C11—41no—
392C23×C11—41no—
393C23×C11—41no—
394C23×C11—41no—
395C23×C11—41no—
396C23×C11—41no—
397C23×C11—41no—
398C23×C11—41no—
399C23×C11—41no—
400C23×C11—41no—
401C23×C11—41no—
402C23×C11—41no—
403C23×C11—41no—
404C23×C11—41no—
405C23×C11—41no—
406C23×C11—41no—
407C23×C11—41no—
408C23×C11—41no—
409C23×C11—41no—
410C23×C11—41no—
411C23×C11—41no—
412C23×C11—41no—
413C23×C11—41no—
414C23×C11—41no—
415C23×C11—41no—
416C23×C11—41no—
417C23×C11—41no—
418C23×C11—41no—
419C23×C11—41no—
420C23×C11—41no—
421C23×C11—41no—
422C23×C11C22⋊Q814yes—
423C23×C11C22⋊Q814yescomplemented
424C23×C11C22×D411yescharacteristic
425C23×C11C22×D411yescharacteristic
426C23×C11C22×D411yescharacteristic
427C23×C11C22×D411yescharacteristic
428C23×C11C22×D411yescharacteristic
429C23×C11C22×Q811yescharacteristic
430C23×C11C2×#4111yescharacteristic
431C23×C11C2×#4111yescharacteristic
432C23×C11C2×#4111yescharacteristic
433C23×C11C2×#4111yescharacteristic
434C23×C11C2×#4111yescharacteristic
435C23×C11H(5,𝔽2)11yescharacteristic
436C23×C11H(5,𝔽2)11yescharacteristic
437C23×C112−1+411yescharacteristic
438C23×C112−1+411yescharacteristic
439D4×C11—232no—
440C2×C4×C11—22no—
441C2×C4×C11—22no—
442C2×C4×C11—22no—
443C2×C4×C11—22no—
444C2×C4×C11—22no—
445C2×C4×C11—22no—
446C2×C4×C11—22no—
447C2×C4×C11—22no—
448C2×C4×C11—22no—
449C2×C4×C11—22no—
450C2×C4×C11—22no—
451C2×C4×C11—22no—
452C2×C4×C11—22no—
453C2×C4×C11—22no—
454C2×C4×C11—22no—
455C2×C4×C11—41no—
456C2×C4×C11—41no—
457C2×C4×C11—41no—
458C2×C4×C11—41no—
459C2×C4×C11—41no—
460C2×C4×C11—41no—
461C2×C4×C11—41no—
462C2×C4×C11—41no—
463C2×C4×C11—41no—
464C2×C4×C11—41no—
465C2×C4×C11—41no—
466C2×C4×C11—41no—
467C2×C4×C11—41no—
468C2×C4×C11—41no—
469C2×C4×C11—41no—
470C2×C4×C11—41no—
471C2×C4×C11—41no—
472C2×C4×C11—41no—
473C2×C4×C11—41no—
474C2×C4×C11C22⋊Q814yescomplemented
475C2×Dic11—22no—
476C2×Dic11—22no—
477C2×Dic11—22no—
478C2×Dic11—22no—
479C2×Dic11—22no—
480C2×Dic11—22no—
481C2×Dic11—22no—
482C2×Dic11—22no—
483C2×Dic11—22no—
484C2×Dic11—22no—
485C2×Dic11—22no—
486C2×Dic11—22no—
487C2×Dic11—22no—
488C2×Dic11—22no—
489C2×Dic11—22no—
490C2×Dic11—22no—
491C2×Dic11—22no—
492C2×Dic11—22no—
493C2×Dic11—22no—
494C2×Dic11—22no—
495C2×Dic11—22no—
496C2×Dic11—22no—
497C2×Dic11—22no—
498C2×Dic11—22no—
499C2×Dic11—22no—
500C2×Dic11—22no—
501C2×Dic11—22no—
502C2×Dic11—416no—
503C2×Dic11—416no—
504C2×Dic11—41no—
505C2×Dic11—41no—
506C2×Dic11—41no—
507C2×Dic11—41no—
508C2×Dic11—41no—
509C2×Dic11—41no—
510C2×Dic11—41no—
511C2×Dic11—41no—
512C2×Dic11—41no—
513C2×Dic11—41no—
514C2×Dic11—41no—
515C2×Dic11—41no—
516C2×Dic11—41no—
517C2×Dic11—41no—
518C2×Dic11—41no—
519C2×Dic11—41no—
520C2×Dic11—41no—
521C2×Dic11—41no—
522C2×Dic11—41no—
523C2×Dic11—41no—
524C2×Dic11—41no—
525C2×Dic11—41no—
526C2×Dic11—41no—
527C2×Dic11—41no—
528C2×Dic11—41no—
529C2×Dic11—41no—
530C2×Dic11—41no—
531C2×Dic11#12014yes—
532C2×Dic11#12014yes—
533Dic22—416no—
534C23×Q8—111no—
535C23×D4C2×D1111yescharacteristic
536C24×C4—111no—
537C24×C4—111no—
538C2×C22⋊Q8—224no—
539C2×C22⋊Q8—224no—
540C2×C22⋊Q8—224no—
541C2×C4×D4—224no—
542C2×C4×D4—224no—
543C2×C4×D4—224no—
544C22×C4⋊C4—111no—
545C22×C4⋊C4—111no—
546C22×C4⋊C4—111no—
547C22×C4⋊C4—111no—
548C22×C4⋊C4—111no—
549C22×C4⋊C4—111no—
550C22×C22⋊C4—111no—
551C22×C22⋊C4—111no—
552C22×C22⋊C4—111no—
553C22×C22⋊C4—111no—
554C22×C22⋊C4—111no—
555C22×C22⋊C4—111no—
556C22×C22⋊C4C2×D1111yescharacteristic
557C22×C22⋊C4C2×D1111yescharacteristic
558C22×C22⋊C4C2×D1111yescharacteristic
559C22×C22⋊C4C2×D1111yescharacteristic
560C22×C42—111no—
561#395—224no—
562#393—224no—
563#385—224no—
564#385—224no—
565C2×#95—111no—
566C2×#95—111no—
567C2×#95—111no—
568C2×#95—111no—
569C2×#95—111no—
570C2×#95—111no—
571C2×#95—111no—
572C2×#95—111no—
573C2×#95—111no—
574C2×#95—111no—
575C2×#95—111no—
576C2×#95—111no—
577C2×#95C2×D1111yescharacteristic
578C2×#95C2×D1111yescharacteristic
579C22×C11—24no—
580C22×C11—24no—
581C22×C11—24no—
582C22×C11—24no—
583C22×C11—24no—
584C22×C11—24no—
585C22×C11—42no—
586C22×C11—42no—
587C22×C11—42no—
588C22×C11—42no—
589C22×C11—42no—
590C22×C11—42no—
591C22×C11—42no—
592C22×C11—42no—
593C22×C11—42no—
594C22×C11—42no—
595C22×C11—42no—
596C22×C11—42no—
597C22×C11—42no—
598C22×C11—42no—
599C22×C11—42no—
600C22×C11—42no—
601C22×C11—42no—
602C22×C11—42no—
603C22×C11—42no—
604C22×C11—42no—
605C22×C11—42no—
606C22×C11—42no—
607C22×C11—42no—
608C22×C11—42no—
609C22×C11C2×#12011yescharacteristic
610C22×C11C2×#12011yescharacteristic
611C22×C11C2×C22⋊Q811yescharacteristic
612C22×C11C2×C22⋊Q811yescharacteristic
613C22×C11C2×C22⋊Q811yescharacteristic
614C22×C11#52511yescharacteristic
615C22×C11#52511yescharacteristic
616C22×C11#52511yescharacteristic
617C22×C11#52511yescharacteristic
618C22×C11#52511yescharacteristic
619C22×C11#53211yescharacteristic
620C22×C11#53211yescharacteristic
621C22×C11#53211yescharacteristic
622C22×C11#53411yescharacteristic
623C22×C11#53611yescharacteristic
624C22×C11#53911yescharacteristic
625C22×C11#53911yescharacteristic
626C22×C11#54211yescharacteristic
627C22×C11#54211yescharacteristic
628C22×C11D4211yescharacteristic
629C22×C11D4211yescharacteristic
630C22×C11D4211yescharacteristic
631C22×C11D4211yescharacteristic
632C22×C11#54711yescharacteristic
633C22×C11#54711yescharacteristic
634C22×C11#54811yescharacteristic
635C22×C11#54811yescharacteristic
636C22×C11#54811yescharacteristic
637C22×C11#54811yescharacteristic
638C22×C11D4×Q811yescharacteristic
639C22×C11D4×Q811yescharacteristic
640C22×C11#55111yescharacteristic
641C22×C11#55111yescharacteristic
642C22×C11#55411yescharacteristic
643C22×C11#55411yescharacteristic
644C4×C11—24no—
645C4×C11—42no—
646C4×C11—42no—
647C4×C11—42no—
648C4×C11—81no—
649Dic11—24no—
650Dic11—24no—
651Dic11—42no—
652Dic11—42no—
653Dic11—42no—
654Dic11—42no—
655Dic11—42no—
656Dic11—81no—
657C25C22×D1111yescharacteristic
658C25C22×D1111yescharacteristic
659C22×Q8—222no—
660C22×Q8—222no—
661C22×Q8—222no—
662C22×Q8—222no—
663C22×Q8—222no—
664C22×Q8—441no—
665C22×Q8—441no—
666C22×D4—22no—
667C22×D4—22no—
668C22×D4—22no—
669C22×D4—22no—
670C22×D4—22no—
671C22×D4—22no—
672C22×D4Dic2214yescomplemented
673C23×C4—111no—
674C23×C4—111no—
675C23×C4—111no—
676C23×C4—111no—
677C23×C4—111no—
678C23×C4—111no—
679C23×C4—111no—
680C23×C4—114no—
681C23×C4—111no—
682C23×C4—222no—
683C23×C4—222no—
684C23×C4—222no—
685C23×C4—222no—
686C23×C4—222no—
687C23×C4—222no—
688C23×C4—222no—
689C23×C4—222no—
690C23×C4—222no—
691C23×C4—441no—
692C23×C4—441no—
693C23×C4—441no—
694C23×C4—441no—
695C23×C4C22×D1111yescharacteristic
696C23×C4C22×D1111yescharacteristic
697C23×C4C22×D1111yescharacteristic
698C23×C4C22×D1111yescharacteristic
699C23×C4C22×D1111yescharacteristic
700C22⋊Q8—2232no—
701C4×D4—2232no—
702C2×C4⋊C4—114no—
703C2×C4⋊C4—114no—
704C2×C4⋊C4—114no—
705C2×C4⋊C4—222no—
706C2×C4⋊C4—222no—
707C2×C4⋊C4—222no—
708C2×C4⋊C4—222no—
709C2×C4⋊C4—222no—
710C2×C4⋊C4—222no—
711C2×C4⋊C4—222no—
712C2×C4⋊C4—222no—
713C2×C4⋊C4—222no—
714C2×C4⋊C4—222no—
715C2×C4⋊C4—222no—
716C2×C4⋊C4—222no—
717C2×C4⋊C4—222no—
718C2×C4⋊C4—441no—
719C2×C4⋊C4—441no—
720C2×C22⋊C4—22no—
721C2×C22⋊C4—22no—
722C2×C22⋊C4—22no—
723C2×C22⋊C4—22no—
724C2×C22⋊C4—22no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4—22no—
728C2×C22⋊C4—22no—
729C2×C22⋊C4—22no—
730C2×C22⋊C4—41no—
731C2×C22⋊C4—41no—
732C2×C22⋊C4—114no—
733C2×C22⋊C4—222no—
734C2×C22⋊C4—222no—
735C2×C22⋊C4—222no—
736C2×C22⋊C4—222no—
737C2×C22⋊C4—222no—
738C2×C22⋊C4—222no—
739C2×C22⋊C4—222no—
740C2×C22⋊C4—222no—
741C2×C22⋊C4—222no—
742C2×C22⋊C4—222no—
743C2×C22⋊C4—222no—
744C2×C22⋊C4—222no—
745C2×C22⋊C4—222no—
746C2×C22⋊C4—222no—
747C2×C22⋊C4—222no—
748C2×C22⋊C4—441no—
749C2×C22⋊C4—441no—
750C2×C42—222no—
751C2×C42—222no—
752C2×C42—222no—
753#95—22no—
754#95—22no—
755#95—222no—
756#95—222no—
757#95—222no—
758#95—222no—
759#95—222no—
760#95—222no—
761#95—222no—
762#95—222no—
763#95—222no—
764#95—222no—
765#95—222no—
766#95—222no—
767C2×C11—44no—
768C2×C11—44no—
769C2×C11#238811yescharacteristic
770C2×C11#240311yescharacteristic
771C2×C11#240911yescharacteristic
772C2×C11#243211yescharacteristic
773C2×C11#244911yescharacteristic
774C2×C11#244911yescharacteristic
775C2×C11#245211yescharacteristic
776C2×C11#245211yescharacteristic
777C2×C11#246111yescharacteristic
778C2×C11#246111yescharacteristic
779C2×C11#246311yescharacteristic
780C2×C11#246311yescharacteristic
781C2×C11#256411yescharacteristic
782C2×C11#263811yescharacteristic
783C2×C11#284811yescharacteristic
784C24—21no—
785C24—21no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—21no—
795C24—21no—
796C24—21no—
797C24—21no—
798C24—21no—
799C24—21no—
800C24—21no—
801C24—21no—
802C24—21no—
803C24—21no—
804C24—21no—
805C24—21no—
806C24—21no—
807C24—21no—
808C24C2×Dic2212yes—
809C24C2×Dic2212yes—
810C24D4×D1112yes—
811C24D4×D1112yes—
812C24#434112yes—
813C24#434112yes—
814C24C23×D1111yescharacteristic
815C2×Q8—228no—
816C2×Q8—444no—
817C2×Q8—444no—
818C2×Q8—444no—
819C2×Q8—444no—
820C2×Q8—444no—
821C2×Q8—444no—
822C2×D4—28no—
823C2×D4—28no—
824C2×D4—28no—
825C2×D4—28no—
826C2×D4—28no—
827C2×D4—28no—
828C2×D4—28no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—112no—
859C22×C4—112no—
860C22×C4—112no—
861C22×C4—112no—
862C22×C4—112no—
863C22×C4—112no—
864C22×C4—112no—
865C22×C4—112no—
866C22×C4—112no—
867C22×C4—112no—
868C22×C4—112no—
869C22×C4—228no—
870C22×C4—228no—
871C22×C4—221no—
872C22×C4—221no—
873C22×C4—221no—
874C22×C4—221no—
875C22×C4—221no—
876C22×C4—221no—
877C22×C4—221no—
878C22×C4—221no—
879C22×C4—228no—
880C22×C4—221no—
881C22×C4—221no—
882C22×C4—221no—
883C22×C4—221no—
884C22×C4—221no—
885C22×C4—221no—
886C22×C4—221no—
887C22×C4—221no—
888C22×C4—221no—
889C22×C4—221no—
890C22×C4—221no—
891C22×C4—221no—
892C22×C4—221no—
893C22×C4—221no—
894C22×C4—221no—
895C22×C4—221no—
896C22×C4—221no—
897C22×C4—221no—
898C22×C4—221no—
899C22×C4—221no—
900C22×C4—221no—
901C22×C4—221no—
902C22×C4—221no—
903C22×C4—221no—
904C22×C4—221no—
905C22×C4—221no—
906C22×C4—221no—
907C22×C4—221no—
908C22×C4—221no—
909C22×C4—221no—
910C22×C4—221no—
911C22×C4—221no—
912C22×C4—221no—
913C22×C4—221no—
914C22×C4—221no—
915C22×C4—221no—
916C22×C4—221no—
917C22×C4—444no—
918C22×C4—444no—
919C22×C4—444no—
920C22×C4—444no—
921C22×C4—444no—
922C22×C4—444no—
923C22×C4—444no—
924C22×C4—444no—
925C22×C4—444no—
926C22×C4—444no—
927C22×C4—444no—
928C22×C4C2×Dic2212yes—
929C22×C4D4×D1112yes—
930C22×C4D4×D1112yes—
931C22×C4D4×D1112yes—
932C22×C4#434112yes—
933C22×C4#434112yes—
934C4⋊C4—228no—
935C4⋊C4—228no—
936C4⋊C4—228no—
937C4⋊C4—228no—
938C4⋊C4—444no—
939C4⋊C4—444no—
940C22⋊C4—28no—
941C22⋊C4—28no—
942C22⋊C4—44no—
943C22⋊C4—44no—
944C22⋊C4—228no—
945C22⋊C4—228no—
946C22⋊C4—228no—
947C22⋊C4—228no—
948C22⋊C4—444no—
949C22⋊C4—444no—
950C42—228no—
951C11#1472311yescharacteristic, complemented, Sylow
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23#6693114yes—
1021C23#6693114yescomplemented
1022C23C22×Dic2211yescharacteristic
1023C23C2×D4×D1111yescharacteristic
1024C23C2×D4×D1111yescharacteristic
1025C23C2×D4×D1111yescharacteristic
1026C23C2×D4×D1111yescharacteristic
1027C23C2×D4×D1111yescharacteristic
1028C23C2×#434111yescharacteristic
1029C23C2×#434111yescharacteristic
1030C23C2×#434111yescharacteristic
1031C23C2×#434111yescharacteristic
1032C23#6703711yescharacteristic
1033C23#41×D1111yescharacteristic
1034C23#6704211yescharacteristic
1035C23#6704311yescharacteristic
1036C23#6704311yescharacteristic
1037Q8—4416no—
1038D4—232no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—114no—
1074C2×C4—114no—
1075C2×C4—222no—
1076C2×C4—222no—
1077C2×C4—222no—
1078C2×C4—222no—
1079C2×C4—222no—
1080C2×C4—222no—
1081C2×C4—222no—
1082C2×C4—222no—
1083C2×C4—222no—
1084C2×C4—222no—
1085C2×C4—222no—
1086C2×C4—222no—
1087C2×C4—222no—
1088C2×C4—222no—
1089C2×C4—222no—
1090C2×C4—222no—
1091C2×C4—222no—
1092C2×C4—222no—
1093C2×C4—222no—
1094C2×C4—222no—
1095C2×C4—222no—
1096C2×C4—222no—
1097C2×C4—222no—
1098C2×C4—222no—
1099C2×C4—222no—
1100C2×C4—222no—
1101C2×C4—222no—
1102C2×C4—4416no—
1103C2×C4—4416no—
1104C2×C4—441no—
1105C2×C4—441no—
1106C2×C4—441no—
1107C2×C4—441no—
1108C2×C4—441no—
1109C2×C4—441no—
1110C2×C4—441no—
1111C2×C4—441no—
1112C2×C4—441no—
1113C2×C4—441no—
1114C2×C4—441no—
1115C2×C4—441no—
1116C2×C4—441no—
1117C2×C4—441no—
1118C2×C4—441no—
1119C2×C4—441no—
1120C2×C4—441no—
1121C2×C4—441no—
1122C2×C4—441no—
1123C2×C4—441no—
1124C2×C4—441no—
1125C2×C4—441no—
1126C2×C4—441no—
1127C2×C4—441no—
1128C2×C4—441no—
1129C2×C4—441no—
1130C2×C4—441no—
1131C2×C4#6693114yescomplemented
1132C22—24no—
1133C22—24no—
1134C22—24no—
1135C22—24no—
1136C22—24no—
1137C22—24no—
1138C22—42no—
1139C22—42no—
1140C22—42no—
1141C22—42no—
1142C22—42no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—42no—
1147C22—42no—
1148C22—42no—
1149C22—42no—
1150C22—42no—
1151C22—42no—
1152C22—42no—
1153C22—42no—
1154C22—42no—
1155C22—42no—
1156C22—42no—
1157C22—42no—
1158C22—42no—
1159C22—42no—
1160C22—42no—
1161C22—42no—
1162C22C2×#6693111yescharacteristic
1163C22C2×#6693111yescharacteristic
1164C22C2×#6693111yescharacteristic
1165C22D4×Dic2211yescharacteristic
1166C22D4×Dic2211yescharacteristic
1167C22#1062307011yescharacteristic
1168C22#1062307411yescharacteristic
1169C22#1062311711yescharacteristic
1170C22#1062311711yescharacteristic
1171C22#1062311711yescharacteristic
1172C22#1062311711yescharacteristic
1173C22#1062311811yescharacteristic
1174C22D11×#12011yescharacteristic
1175C22D11×#12011yescharacteristic
1176C22#1062312111yescharacteristic
1177C22#1062312711yescharacteristic
1178C22#1062312711yescharacteristic
1179C22#1062312911yescharacteristic
1180C22#1062312911yescharacteristic
1181C22#1062312911yescharacteristic
1182C22#1062313311yescharacteristic
1183C22#1062313411yescharacteristic
1184C22#1062313611yescharacteristic
1185C22#1062313711yescharacteristic
1186C22#1062314011yescharacteristic
1187C22#1062314011yescharacteristic
1188C22#1062314211yescharacteristic
1189C22#1062317911yescharacteristic
1190C22#1062318611yescharacteristic
1191C22#1062318911yescharacteristic
1192C22#1062319611yescharacteristic
1193C22#1062320811yescharacteristic
1194C22#1062321311yescharacteristic
1195C22#1062324711yescharacteristic
1196C22#1062324811yescharacteristic
1197C4—24no—
1198C4—42no—
1199C4—42no—
1200C4—42no—
1201C4—81no—
1202C4—224no—
1203C4—224no—
1204C4—442no—
1205C4—442no—
1206C4—442no—
1207C4—442no—
1208C4—442no—
1209C4—881no—
1210C2—44no—
1211C2—44no—
1212C2#1307182811yescharacteristic
1213C2#1307192511yescharacteristic
1214C2#1307197811yescharacteristic
1215C2#1307223911yescharacteristic
1216C2#1307242911yescharacteristic
1217C2#1307243111yescharacteristic
1218C2#1307246811yescharacteristic
1219C2#1307246911yescharacteristic
1220C2#1307257611yescharacteristic
1221C2#1307257811yescharacteristic
1222C2#1307260611yescharacteristic
1223C2#1307260811yescharacteristic
1224C2#1307380011yescharacteristic
1225C2#1307453211yescharacteristic
1226C2#1307690111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC11×#1438C2
prime radicalC23×D4×C11C22
hypercenter#1438D11
hypocenterC11#14723
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
1. C22×#66931C2semidirect
3. C2×#10622269C2semidirect
4. C2×#10622560C2semidirect
5. C2×#10622563C2semidirect
6. C2×#10622559C2semidirect
7. #13066868C2semidirect
8. #13066861C2semidirect
9. #13066859C2semidirect
10. #13066859C2semidirect
12. #13066850C2semidirect
13. #13066847C2semidirect
14. #13066838C2semidirect
69. C22×D4×C11Q8semidirect
143. C2×C4⋊Dic11D4semidirect
152. C2×Dic11⋊C4D4semidirect
423. C23×C11C22⋊Q8semidirect
474. C2×C4×C11C22⋊Q8semidirect
672. C22×D4Dic22semidirect
951. C11#14723semidirect
1021. C23#66931semidirect
1131. C2×C4#66931semidirect

Maximal subgroups

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

subgroupindex
C22×#669312
C22×D4×Dic112
C2×#106222692
C2×#106225602
C2×#106225632
C2×#106225592
#130668682
#130668612
#130668592
#130668572
#130668502
#130668472
#130668382
C11×#14382
#1472311