Finite Group Databasebeta

← #14677749

Subgroups — #14677749

Order 2816.

2330 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66930C211yesmaximal, characteristic, complemented
2C2×#10622833C211yesmaximal, characteristic
3C2×#10622823C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
5#13066874C211yesmaximal, characteristic, complemented
6#13066859C211yesmaximal, characteristic, complemented
7#13066859C211yesmaximal, characteristic, complemented
8#13066857C211yesmaximal, characteristic
9#13066853C211yesmaximal, characteristic, complemented
10#13066853C211yesmaximal, characteristic, complemented
11#13066851C211yesmaximal, characteristic, complemented
12#13066847C211yesmaximal, characteristic, complemented
13#13066840C211yesmaximal, characteristic, complemented
14#13066838C211yesmaximal, characteristic, complemented
15C2×C11×#386C211yesmaximal, characteristic
16C23×D4×C11C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C24×Dic11C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C2×#66930—24no—
36C2×#66930—24no—
37C2×#66930—24no—
38C11×#386—24no—
39C2×C11×#95C2211yescharacteristic
40C2×C11×#95C2211yescharacteristic
41#10622833C418yescomplemented
42#10622823—24no—
43C4×C22⋊Dic11—24no—
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
57C2×C11⋊#95C2211yescharacteristic
58C25×C11C2311yescharacteristic
59C25×C11C2311yescharacteristic
60C22×D4×C11—22no—
61C22×D4×C11—22no—
62C22×D4×C11—22no—
63C22×D4×C11—22no—
64C22×D4×C11—41no—
65C22×D4×C11—41no—
66C22×D4×C11C2×C414yes—
67C23×C4×C11—22no—
68C23×C4×C11—22no—
69C23×C4×C11—22no—
70C23×C4×C11—22no—
71C23×C4×C11—22no—
72C23×C4×C11—41no—
73C23×C4×C11—41no—
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×Dic11—22no—
80C23×Dic11—22no—
81C23×Dic11—22no—
82C23×Dic11—22no—
83C23×Dic11—22no—
84C23×Dic11—22no—
85C23×Dic11C2×C414yescomplemented
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
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—22no—
100C2×C11×C22⋊C4—41no—
101C2×C11×C22⋊C4—41no—
102C2×C11×C22⋊C4D414yes—
103C2×C22⋊Dic11—22no—
104C2×C22⋊Dic11—22no—
105C2×C22⋊Dic11—22no—
106C2×C22⋊Dic11—22no—
107C2×C22⋊Dic11—22no—
108C2×C22⋊Dic11—22no—
109C2×C22⋊Dic11—22no—
110C2×C22⋊Dic11—22no—
111C2×C22⋊Dic11—22no—
112C2×C22⋊Dic11—22no—
113C2×C22⋊Dic11—22no—
114C2×C22⋊Dic11—22no—
115C2×C22⋊Dic11—22no—
116C2×C22⋊Dic11—22no—
117C2×C22⋊Dic11—41no—
118C2×C22⋊Dic11—41no—
119C2×C22⋊Dic11—41no—
120C2×C22⋊Dic11—41no—
121C2×C22⋊Dic11C2×C414yes—
122C2×C22⋊Dic11C2×C414yes—
123C2×C22⋊Dic11C2×C414yescomplemented
124C2×Dic11⋊C4—22no—
125C2×Dic11⋊C4—22no—
126C2×Dic11⋊C4—22no—
127C2×Dic11⋊C4—22no—
128C2×Dic11⋊C4—22no—
129C2×Dic11⋊C4—22no—
130C2×Dic11⋊C4—22no—
131C2×Dic11⋊C4—41no—
132C2×Dic11⋊C4D414yescomplemented
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×Dic11—41no—
140C2×C4×Dic11—41no—
141C2×C4×Dic11D414yescomplemented
142#66930—232no—
143C11×#95—22no—
144C11×#95—22no—
145C11⋊#95—22no—
146C11⋊#95—22no—
147C11⋊#95—22no—
148C11⋊#95—22no—
149C11⋊#95—22no—
150C11⋊#95—22no—
151C11⋊#95—22no—
152C11⋊#95—41no—
153C11⋊#95—41no—
154C11⋊#95—41no—
155C11⋊#95—41no—
156C11⋊#95—41no—
157C11⋊#95C2×C414yescomplemented
158C11⋊#95C2×C414yescomplemented
159#14064—111nomaximal, Sylow
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×C11—21no—
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×C11C22×C412yes—
185C24×C11C22×C412yes—
186C24×C11C2×D412yes—
187C24×C11#4112yes—
188C24×C11#4112yes—
189C24×C11#4112yes—
190C24×C11C2411yescharacteristic
191C2×D4×C11—28no—
192C2×D4×C11—28no—
193C2×D4×C11—44no—
194C2×D4×C11—44no—
195C2×D4×C11—44no—
196C2×D4×C11—44no—
197C2×D4×C11—44no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—28no—
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×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—44no—
229C22×C4×C11—44no—
230C22×C4×C11—44no—
231C22×C4×C11—44no—
232C22×C4×C11—44no—
233C22×C4×C11—44no—
234C22×C4×C11C22×C412yes—
235C22×C4×C11C2×D412yes—
236C22×C4×C11C2×D412yes—
237C22×C4×C11C2×D412yes—
238C22×C4×C11C2×D412yes—
239C22×C4×C11#4112yes—
240C22×Dic11—28no—
241C22×Dic11—28no—
242C22×Dic11—28no—
243C22×Dic11—28no—
244C22×Dic11—28no—
245C22×Dic11—28no—
246C22×Dic11—28no—
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—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×Dic11C22×C412yes—
293C22×Dic11C22×C412yes—
294C22×Dic11C22×C412yes—
295C22×Dic11C22×C412yes—
296C22×Dic11C2×D412yes—
297C22×Dic11C2×D412yes—
298C22×Dic11C2×D412yes—
299C22×Dic11C2×D412yes—
300C22×Dic11#4112yes—
301C22×Dic11#4112yes—
302C22×Dic11#4112yes—
303C11×C22⋊C4—28no—
304C11×C22⋊C4—44no—
305C11×C22⋊C4—44no—
306C22⋊Dic11—28no—
307C22⋊Dic11—28no—
308C22⋊Dic11—28no—
309C22⋊Dic11—28no—
310C22⋊Dic11—44no—
311C22⋊Dic11—44no—
312C22⋊Dic11—44no—
313Dic11⋊C4—28no—
314Dic11⋊C4—28no—
315Dic11⋊C4—44no—
316C4×Dic11—28no—
317C4×Dic11—28no—
318C4×Dic11—44no—
319C22×#117—111no—
320C2×#386—111no—
321C2×#386D1111yescharacteristic
322C2×#385—111no—
323C2×C4×C22⋊C4—111no—
324#1442—111no—
325#1439—111no—
326#1439—111no—
327#1438—111no—
328#1437—111no—
329#1437—111no—
330#1436—111no—
331#1436—111no—
332#1434—111no—
333C22⋊#95—111no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—22no—
337C23×C11—22no—
338C23×C11—22no—
339C23×C11—22no—
340C23×C11—22no—
341C23×C11—22no—
342C23×C11—22no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—22no—
352C23×C11—22no—
353C23×C11—22no—
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—41no—
371C23×C11—41no—
372C23×C11—41no—
373C23×C11—41no—
374C23×C11—41no—
375C23×C11—41no—
376C23×C11—41no—
377C23×C11—41no—
378C23×C11—41no—
379C23×C11—41no—
380C23×C11—41no—
381C23×C11—41no—
382C23×C11—41no—
383C23×C11—41no—
384C23×C11—41no—
385C23×C11—41no—
386C23×C11—41no—
387C23×C11—41no—
388C23×C11—41no—
389C23×C11—41no—
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#11714yescomplemented
403C23×C11C4×D414yes—
404C23×C11C23×C411yescharacteristic
405C23×C11C22×D411yescharacteristic
406C23×C11C22×D411yescharacteristic
407C23×C11C22×D411yescharacteristic
408C23×C11C2×#4111yescharacteristic
409C23×C11C2×#4111yescharacteristic
410C23×C11C2×#4111yescharacteristic
411C23×C11C2×#4111yescharacteristic
412C23×C11C2×#4111yescharacteristic
413C23×C11C2×#4111yescharacteristic
414C23×C11C2×#4111yescharacteristic
415C23×C11H(5,𝔽2)11yescharacteristic
416C23×C11H(5,𝔽2)11yescharacteristic
417C23×C11H(5,𝔽2)11yescharacteristic
418C23×C112−1+411yescharacteristic
419D4×C11—416no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
427C2×C4×C11—22no—
428C2×C4×C11—22no—
429C2×C4×C11—22no—
430C2×C4×C11—22no—
431C2×C4×C11—22no—
432C2×C4×C11—22no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—416no—
436C2×C4×C11—41no—
437C2×C4×C11—41no—
438C2×C4×C11—41no—
439C2×C4×C11—41no—
440C2×C4×C11—41no—
441C2×C4×C11—41no—
442C2×C4×C11—41no—
443C2×C4×C11—41no—
444C2×C4×C11—41no—
445C2×C4×C11—41no—
446C2×C4×C11—41no—
447C2×C4×C11—41no—
448C2×C4×C11—41no—
449C2×C4×C11—41no—
450C2×C4×C11—41no—
451C2×C4×C11—41no—
452C2×C4×C11—41no—
453C2×C4×C11—41no—
454C2×C4×C11—41no—
455C2×C4×C11#12014yes—
456C2×Dic11—232no—
457C2×Dic11—22no—
458C2×Dic11—22no—
459C2×Dic11—22no—
460C2×Dic11—22no—
461C2×Dic11—22no—
462C2×Dic11—22no—
463C2×Dic11—22no—
464C2×Dic11—22no—
465C2×Dic11—22no—
466C2×Dic11—22no—
467C2×Dic11—22no—
468C2×Dic11—22no—
469C2×Dic11—22no—
470C2×Dic11—22no—
471C2×Dic11—22no—
472C2×Dic11—22no—
473C2×Dic11—22no—
474C2×Dic11—22no—
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—41no—
485C2×Dic11—41no—
486C2×Dic11—41no—
487C2×Dic11—41no—
488C2×Dic11—41no—
489C2×Dic11—41no—
490C2×Dic11—41no—
491C2×Dic11—41no—
492C2×Dic11—41no—
493C2×Dic11—41no—
494C2×Dic11—41no—
495C2×Dic11—41no—
496C2×Dic11—41no—
497C2×Dic11—41no—
498C2×Dic11—41no—
499C2×Dic11—41no—
500C2×Dic11—41no—
501C2×Dic11—41no—
502C2×Dic11—41no—
503C2×Dic11—41no—
504C2×Dic11—41no—
505C2×Dic11—41no—
506C2×Dic11—41no—
507C2×Dic11—41no—
508C2×Dic11—41no—
509C2×Dic11—41no—
510C2×Dic11—41no—
511C2×Dic11C4×D414yes—
512C2×Dic11C4×D414yes—
513C23×D4C2×D1111yescharacteristic
514C24×C4—111no—
515C24×C4C2×D1111yescharacteristic
516C2×#117—224no—
517C2×#117—224no—
518C2×#117—224no—
519C22×C4⋊C4—111no—
520C22×C4⋊C4—111no—
521C22×C4⋊C4—111no—
522C22×C22⋊C4—111no—
523C22×C22⋊C4—111no—
524C22×C22⋊C4—111no—
525C22×C22⋊C4—111no—
526C22×C22⋊C4—111no—
527C22×C22⋊C4—111no—
528C22×C22⋊C4—111no—
529C22×C22⋊C4C2×D1111yescharacteristic
530C22×C22⋊C4C2×D1111yescharacteristic
531C22×C22⋊C4C2×D1111yescharacteristic
532C22×C42—111no—
533C22×C42—111no—
534C22×C42—111no—
535#386—24no—
536#386—118no—
537#385—224no—
538C4×C22⋊C4—224no—
539C2×#95—111no—
540C2×#95—111no—
541C2×#95—111no—
542C2×#95—111no—
543C2×#95—111no—
544C2×#95—111no—
545C2×#95—111no—
546C2×#95—111no—
547C2×#95—111no—
548C2×#95—111no—
549C2×#95—111no—
550C2×#95—111no—
551C2×#95—111no—
552C2×#95—111no—
553C2×#95C2×D1111yescharacteristic
554C2×#95C2×D1111yescharacteristic
555C22×C11—24no—
556C22×C11—24no—
557C22×C11—24no—
558C22×C11—24no—
559C22×C11—24no—
560C22×C11—24no—
561C22×C11—42no—
562C22×C11—42no—
563C22×C11—42no—
564C22×C11—42no—
565C22×C11—42no—
566C22×C11—42no—
567C22×C11—42no—
568C22×C11—42no—
569C22×C11—42no—
570C22×C11—42no—
571C22×C11—42no—
572C22×C11—42no—
573C22×C11—42no—
574C22×C11—42no—
575C22×C11—42no—
576C22×C11—42no—
577C22×C11—42no—
578C22×C11—42no—
579C22×C11—42no—
580C22×C11—42no—
581C22×C11—42no—
582C22×C11—42no—
583C22×C11—42no—
584C22×C11—42no—
585C22×C11C2×#11711yescharacteristic
586C22×C11C2×C4×D411yescharacteristic
587C22×C11C2×C4×D411yescharacteristic
588C22×C11C2×C4×D411yescharacteristic
589C22×C11C4×#4111yescharacteristic
590C22×C11#51811yescharacteristic
591C22×C11#52011yescharacteristic
592C22×C11C2×#12011yescharacteristic
593C22×C11#52511yescharacteristic
594C22×C11#52511yescharacteristic
595C22×C11#52511yescharacteristic
596C22×C11#52511yescharacteristic
597C22×C11#52511yescharacteristic
598C22×C11#52911yescharacteristic
599C22×C11#52911yescharacteristic
600C22×C11#53511yescharacteristic
601C22×C11#53711yescharacteristic
602C22×C11#54011yescharacteristic
603C22×C11#54211yescharacteristic
604C22×C11#54611yescharacteristic
605C22×C11#54611yescharacteristic
606C22×C11#54611yescharacteristic
607C22×C11#54611yescharacteristic
608C22×C11#54611yescharacteristic
609C22×C11#54711yescharacteristic
610C22×C11#54811yescharacteristic
611C22×C11#55011yescharacteristic
612C22×C11#55111yescharacteristic
613C22×C11#55111yescharacteristic
614C22×C11#55111yescharacteristic
615C22×C11#55211yescharacteristic
616C22×C11#55211yescharacteristic
617C22×C11#55311yescharacteristic
618C22×C11#55311yescharacteristic
619C22×C11#55511yescharacteristic
620C4×C11—24no—
621C4×C11—42no—
622C4×C11—42no—
623C4×C11—42no—
624C4×C11—81no—
625Dic11—24no—
626Dic11—24no—
627Dic11—42no—
628Dic11—42no—
629Dic11—42no—
630Dic11—42no—
631Dic11—42no—
632Dic11—81no—
633C25C22×D1111yescharacteristic
634C25C22×D1111yescharacteristic
635C22×D4—22no—
636C22×D4—22no—
637C22×D4—22no—
638C22×D4—22no—
639C22×D4—41no—
640C22×D4—41no—
641C22×D4C4×D1114yes—
642C23×C4—22no—
643C23×C4—22no—
644C23×C4—22no—
645C23×C4—22no—
646C23×C4—22no—
647C23×C4—41no—
648C23×C4—41no—
649C23×C4—111no—
650C23×C4—111no—
651C23×C4—114no—
652C23×C4—111no—
653C23×C4—111no—
654C23×C4—111no—
655C23×C4—111no—
656C23×C4—111no—
657C23×C4—111no—
658C23×C4—222no—
659C23×C4—222no—
660C23×C4—222no—
661C23×C4—222no—
662C23×C4—222no—
663C23×C4—222no—
664C23×C4C22×D1111yescharacteristic
665C23×C4C22×D1111yescharacteristic
666C23×C4C22×D1111yescharacteristic
667C23×C4C22×D1111yescharacteristic
668C23×C4C22×D1111yescharacteristic
669#117—2232no—
670C2×C4⋊C4—114no—
671C2×C4⋊C4—222no—
672C2×C4⋊C4—222no—
673C2×C4⋊C4—222no—
674C2×C4⋊C4—222no—
675C2×C4⋊C4—222no—
676C2×C4⋊C4—222no—
677C2×C4⋊C4—222no—
678C2×C4⋊C4—441no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—41no—
686C2×C22⋊C4—41no—
687C2×C22⋊C4—114no—
688C2×C22⋊C4—114no—
689C2×C22⋊C4—114no—
690C2×C22⋊C4—222no—
691C2×C22⋊C4—222no—
692C2×C22⋊C4—222no—
693C2×C22⋊C4—222no—
694C2×C22⋊C4—222no—
695C2×C22⋊C4—222no—
696C2×C22⋊C4—222no—
697C2×C22⋊C4—222no—
698C2×C22⋊C4—222no—
699C2×C22⋊C4—222no—
700C2×C22⋊C4—222no—
701C2×C22⋊C4—222no—
702C2×C22⋊C4—222no—
703C2×C22⋊C4—222no—
704C2×C22⋊C4—441no—
705C2×C22⋊C4—441no—
706C2×C22⋊C4—441no—
707C2×C22⋊C4—441no—
708C2×C22⋊C4C22⋊D1114yes—
709C2×C42—114no—
710C2×C42—222no—
711C2×C42—222no—
712C2×C42—222no—
713C2×C42—222no—
714C2×C42—222no—
715C2×C42—222no—
716C2×C42—441no—
717C2×C42—441no—
718#95—22no—
719#95—22no—
720#95—114no—
721#95—114no—
722#95—222no—
723#95—222no—
724#95—222no—
725#95—222no—
726#95—222no—
727#95—222no—
728#95—222no—
729#95—441no—
730#95—441no—
731#95—441no—
732#95—441no—
733#95—441no—
734C2×C11—44no—
735C2×C11—44no—
736C2×C11#229011yescharacteristic
737C2×C11C4×#12011yescharacteristic
738C2×C11#232411yescharacteristic
739C2×C11#234211yescharacteristic
740C2×C11#235211yescharacteristic
741C2×C11#235911yescharacteristic
742C2×C11#236311yescharacteristic
743C2×C11#240411yescharacteristic
744C2×C11#240711yescharacteristic
745C2×C11#247011yescharacteristic
746C2×C11#247111yescharacteristic
747C2×C11#247611yescharacteristic
748C2×C11#247711yescharacteristic
749C2×C11#259811yescharacteristic
750C2×C11#260911yescharacteristic
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24C2×C4×D1112yes—
776C24C2×C4×D1112yes—
777C24#433912yes—
778C24#434112yes—
779C24#434112yes—
780C24C2×C22⋊D1112yes—
781C24C23×D1111yescharacteristic
782C2×D4—28no—
783C2×D4—28no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—44no—
788C2×D4—44no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—28no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—44no—
820C22×C4—44no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—112no—
826C22×C4—112no—
827C22×C4—112no—
828C22×C4—112no—
829C22×C4—112no—
830C22×C4—112no—
831C22×C4—112no—
832C22×C4—112no—
833C22×C4—112no—
834C22×C4—112no—
835C22×C4—112no—
836C22×C4—228no—
837C22×C4—228no—
838C22×C4—228no—
839C22×C4—228no—
840C22×C4—228no—
841C22×C4—228no—
842C22×C4—228no—
843C22×C4—221no—
844C22×C4—221no—
845C22×C4—221no—
846C22×C4—221no—
847C22×C4—221no—
848C22×C4—221no—
849C22×C4—221no—
850C22×C4—221no—
851C22×C4—221no—
852C22×C4—221no—
853C22×C4—221no—
854C22×C4—221no—
855C22×C4—221no—
856C22×C4—221no—
857C22×C4—221no—
858C22×C4—221no—
859C22×C4—221no—
860C22×C4—221no—
861C22×C4—221no—
862C22×C4—221no—
863C22×C4—221no—
864C22×C4—221no—
865C22×C4—221no—
866C22×C4—221no—
867C22×C4—221no—
868C22×C4—221no—
869C22×C4—221no—
870C22×C4—221no—
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—221no—
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×C4C2×C4×D1112yes—
889C22×C4D4×D1112yes—
890C22×C4D4×D1112yes—
891C22×C4#434112yes—
892C22×C4C2×C22⋊D1112yes—
893C22×C4C2×C22⋊D1112yes—
894C4⋊C4—228no—
895C4⋊C4—228no—
896C4⋊C4—444no—
897C22⋊C4—28no—
898C22⋊C4—44no—
899C22⋊C4—44no—
900C22⋊C4—228no—
901C22⋊C4—228no—
902C22⋊C4—228no—
903C22⋊C4—228no—
904C22⋊C4—444no—
905C22⋊C4—444no—
906C22⋊C4—444no—
907C42—228no—
908C42—228no—
909C42—444no—
910C11#1406411yescharacteristic, complemented, Sylow
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23#6693014yescomplemented
980C23C4×C22⋊D1114yes—
981C23C22×C4×D1111yescharacteristic
982C23C2×#433911yescharacteristic
983C23C2×D4×D1111yescharacteristic
984C23C2×D4×D1111yescharacteristic
985C23C2×#434111yescharacteristic
986C23C2×#434111yescharacteristic
987C23C2×#434111yescharacteristic
988C23#6703711yescharacteristic
989C23#6703711yescharacteristic
990C23#6703711yescharacteristic
991C23#41×D1111yescharacteristic
992C23#41×D1111yescharacteristic
993C23#41×D1111yescharacteristic
994C23#6704311yescharacteristic
995C23C22×C22⋊D1111yescharacteristic
996D4—416no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—416no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—114no—
1033C2×C4—114no—
1034C2×C4—2232no—
1035C2×C4—222no—
1036C2×C4—222no—
1037C2×C4—222no—
1038C2×C4—222no—
1039C2×C4—222no—
1040C2×C4—222no—
1041C2×C4—222no—
1042C2×C4—222no—
1043C2×C4—222no—
1044C2×C4—222no—
1045C2×C4—222no—
1046C2×C4—222no—
1047C2×C4—222no—
1048C2×C4—222no—
1049C2×C4—222no—
1050C2×C4—222no—
1051C2×C4—222no—
1052C2×C4—222no—
1053C2×C4—222no—
1054C2×C4—222no—
1055C2×C4—222no—
1056C2×C4—222no—
1057C2×C4—222no—
1058C2×C4—222no—
1059C2×C4—222no—
1060C2×C4—222no—
1061C2×C4—222no—
1062C2×C4—441no—
1063C2×C4—441no—
1064C2×C4—441no—
1065C2×C4—441no—
1066C2×C4—441no—
1067C2×C4—441no—
1068C2×C4—441no—
1069C2×C4—441no—
1070C2×C4—441no—
1071C2×C4—441no—
1072C2×C4—441no—
1073C2×C4—441no—
1074C2×C4—441no—
1075C2×C4—441no—
1076C2×C4—441no—
1077C2×C4—441no—
1078C2×C4—441no—
1079C2×C4—441no—
1080C2×C4—441no—
1081C2×C4—441no—
1082C2×C4—441no—
1083C2×C4—441no—
1084C2×C4—441no—
1085C2×C4—441no—
1086C2×C4—441no—
1087C2×C4—441no—
1088C2×C4—441no—
1089C2×C4#6699014yes—
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—24no—
1094C22—24no—
1095C22—24no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22C2×#6693011yescharacteristic
1121C22#1062301711yescharacteristic
1122C22#1062302611yescharacteristic
1123C22#1062302611yescharacteristic
1124C22C4×#434111yescharacteristic
1125C22#1062307211yescharacteristic
1126C22C4×D4×D1111yescharacteristic
1127C22C4×D4×D1111yescharacteristic
1128C22#1062307711yescharacteristic
1129C22#1062307811yescharacteristic
1130C22#1062307811yescharacteristic
1131C22#1062308711yescharacteristic
1132C22#1062311711yescharacteristic
1133C22#1062312211yescharacteristic
1134C22#1062312211yescharacteristic
1135C22#1062312311yescharacteristic
1136C22#1062312911yescharacteristic
1137C22#1062313011yescharacteristic
1138C22#1062313111yescharacteristic
1139C22#1062313211yescharacteristic
1140C22#1062313711yescharacteristic
1141C22#1062313911yescharacteristic
1142C22#1062314611yescharacteristic
1143C22#1062314711yescharacteristic
1144C22#1062318011yescharacteristic
1145C22#1062318111yescharacteristic
1146C22#1062319211yescharacteristic
1147C22#1062319311yescharacteristic
1148C22C2×C4×C22⋊D1111yescharacteristic
1149C22C2×#6699011yescharacteristic
1150C22#1062333711yescharacteristic
1151C22#1062333711yescharacteristic
1152C22#1062333711yescharacteristic
1153C22#1062335511yescharacteristic
1154C22#1062335911yescharacteristic
1155C4—24no—
1156C4—42no—
1157C4—42no—
1158C4—42no—
1159C4—81no—
1160C4—224no—
1161C4—224no—
1162C4—442no—
1163C4—442no—
1164C4—442no—
1165C4—442no—
1166C4—442no—
1167C4—881no—
1168C2—44no—
1169C2—44no—
1170C2#1307105611yescharacteristic
1171C2C4×#6699011yescharacteristic
1172C2#1307130611yescharacteristic
1173C2#1307146111yescharacteristic
1174C2#1307154311yescharacteristic
1175C2#1307160211yescharacteristic
1176C2#1307165711yescharacteristic
1177C2#1307193211yescharacteristic
1178C2#1307195711yescharacteristic
1179C2#1307270811yescharacteristic
1180C2#1307273111yescharacteristic
1181C2#1307279811yescharacteristic
1182C2#1307282111yescharacteristic
1183C2#1307417911yescharacteristic
1184C2#1307429011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#386C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#386D11
hypocenterC11#14064
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#66930C2semidirect
3. C2×#10622823C2semidirect
4. C2×C4×C22⋊Dic11C2semidirect
5. #13066874C2semidirect
6. #13066859C2semidirect
7. #13066859C2semidirect
9. #13066853C2semidirect
10. #13066853C2semidirect
11. #13066851C2semidirect
12. #13066847C2semidirect
13. #13066840C2semidirect
14. #13066838C2semidirect
41. #10622833C4semidirect
85. C23×Dic11C2×C4semidirect
123. C2×C22⋊Dic11C2×C4semidirect
132. C2×Dic11⋊C4D4semidirect
141. C2×C4×Dic11D4semidirect
157. C11⋊#95C2×C4semidirect
158. C11⋊#95C2×C4semidirect
402. C23×C11#117semidirect
910. C11#14064semidirect
979. C23#66930semidirect

Maximal subgroups

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

subgroupindex
C22×#669302
C2×#106228332
C2×#106228232
C2×C4×C22⋊Dic112
#130668742
#130668592
#130668572
#130668532
#130668512
#130668472
#130668402
#130668382
C2×C11×#3862
#1406411