Finite Group Databasebeta

← #14679189

Subgroups — #14679189

Order 2816.

2062 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622835C211yesmaximal, characteristic
2C2×#10622833C211yesmaximal, characteristic
3C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
5#13066882C211yesmaximal, characteristic, complemented
6#13066863C211yesmaximal, characteristic, complemented
7#13066863C211yesmaximal, characteristic, complemented
8#13066853C211yesmaximal, characteristic, complemented
9#13066853C211yesmaximal, characteristic, complemented
10#13066847C211yesmaximal, characteristic, complemented
11#13066842C211yesmaximal, characteristic, complemented
12#13066840C211yesmaximal, characteristic, complemented
13#13066839C211yesmaximal, 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×C4×Dic11C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C11×#386—24no—
34C2×C11×#95C2211yescharacteristic
35C2×C11×#95C2211yescharacteristic
36#10622835C418yescomplemented
37#10622833—24no—
38C4×C22⋊Dic11—24no—
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
54C2×C11⋊#95C2211yescharacteristic
55C22⋊C4×Dic11—24no—
56C25×C11C2311yescharacteristic
57C25×C11C2311yescharacteristic
58C22×D4×C11—22no—
59C22×D4×C11—22no—
60C22×D4×C11—22no—
61C22×D4×C11—22no—
62C22×D4×C11—41no—
63C22×D4×C11—41no—
64C22×D4×C11C2×C414yes—
65C23×C4×C11—22no—
66C23×C4×C11—22no—
67C23×C4×C11—22no—
68C23×C4×C11—22no—
69C23×C4×C11—22no—
70C23×C4×C11—41no—
71C23×C4×C11—41no—
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×Dic11—22no—
78C23×Dic11—22no—
79C23×Dic11—22no—
80C23×Dic11—22no—
81C23×Dic11—22no—
82C23×Dic11—41no—
83C23×Dic11—41no—
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
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—41no—
99C2×C11×C22⋊C4—41no—
100C2×C11×C22⋊C4D414yes—
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—22no—
108C2×C22⋊Dic11—22no—
109C2×C22⋊Dic11—22no—
110C2×C22⋊Dic11—22no—
111C2×C22⋊Dic11—41no—
112C2×C22⋊Dic11—41no—
113C2×C22⋊Dic11—41no—
114C2×C22⋊Dic11—41no—
115C2×C22⋊Dic11—41no—
116C2×C22⋊Dic11—41no—
117C2×C22⋊Dic11C2×C414yescomplemented
118C2×C22⋊Dic11C2×C414yescomplemented
119C2×C22⋊Dic11C2×C414yescomplemented
120C2×C22⋊Dic11C2×C414yescomplemented
121C2×C22⋊Dic11D414yes—
122C2×Dic11⋊C4—41no—
123C2×Dic11⋊C4—41no—
124C2×Dic11⋊C4C2×C414yescomplemented
125C2×C4×Dic11—22no—
126C2×C4×Dic11—22no—
127C2×C4×Dic11—22no—
128C2×C4×Dic11—22no—
129C2×C4×Dic11—22no—
130C2×C4×Dic11—22no—
131C2×C4×Dic11—41no—
132C2×C4×Dic11—41no—
133C2×C4×Dic11—41no—
134C11×#95—22no—
135C11×#95—22no—
136C11⋊#95—22no—
137C11⋊#95—22no—
138C11⋊#95—22no—
139C11⋊#95—22no—
140C11⋊#95—22no—
141C11⋊#95—22no—
142C11⋊#95—22no—
143C11⋊#95—22no—
144C11⋊#95—22no—
145C11⋊#95—22no—
146C11⋊#95—41no—
147C11⋊#95—41no—
148C11⋊#95—41no—
149C11⋊#95—41no—
150C11⋊#95—41no—
151C11⋊#95C2×C414yescomplemented
152#14181—111nomaximal, Sylow
153C24×C11—21no—
154C24×C11—21no—
155C24×C11—21no—
156C24×C11—21no—
157C24×C11—21no—
158C24×C11—21no—
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×C11—21no—
172C24×C11—21no—
173C24×C11—21no—
174C24×C11—21no—
175C24×C11—21no—
176C24×C11—21no—
177C24×C11C22×C412yes—
178C24×C11C22×C412yes—
179C24×C11C2×D412yes—
180C24×C11C2×D412yes—
181C24×C11#4112yes—
182C24×C11#4112yes—
183C24×C11C2411yescharacteristic
184C2×D4×C11—28no—
185C2×D4×C11—28no—
186C2×D4×C11—44no—
187C2×D4×C11—44no—
188C2×D4×C11—44no—
189C2×D4×C11—44no—
190C2×D4×C11—44no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—28no—
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×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—44no—
222C22×C4×C11—44no—
223C22×C4×C11—44no—
224C22×C4×C11—44no—
225C22×C4×C11—44no—
226C22×C4×C11—44no—
227C22×C4×C11C22×C412yes—
228C22×C4×C11C2×D412yes—
229C22×C4×C11C2×D412yes—
230C22×C4×C11#4112yes—
231C22×C4×C11#4112yes—
232C22×C4×C11#4112yes—
233C22×Dic11—28no—
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—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—44no—
282C22×Dic11—44no—
283C22×Dic11—44no—
284C22×Dic11—44no—
285C22×Dic11—44no—
286C22×Dic11—44no—
287C22×Dic11C22×C412yes—
288C22×Dic11C22×C412yes—
289C22×Dic11C22×C412yes—
290C22×Dic11C22×C412yes—
291C22×Dic11C2×D412yes—
292C22×Dic11C2×D412yes—
293C22×Dic11#4112yes—
294C22×Dic11#4112yes—
295C22×Dic11#4112yes—
296C11×C22⋊C4—28no—
297C11×C22⋊C4—44no—
298C11×C22⋊C4—44no—
299C22⋊Dic11—28no—
300C22⋊Dic11—28no—
301C22⋊Dic11—28no—
302C22⋊Dic11—44no—
303C22⋊Dic11—44no—
304C22⋊Dic11—44no—
305C22⋊Dic11—44no—
306Dic11⋊C4—44no—
307C4×Dic11—44no—
308C4×Dic11—44no—
309C4×Dic11—44no—
310C2×#394—111no—
311C2×#386—111no—
312C2×#386D1111yescharacteristic
313C2×C4×C22⋊C4—111no—
314C2×C4×C22⋊C4—111no—
315#1445—111no—
316#1440—111no—
317#1440—111no—
318#1437—111no—
319#1437—111no—
320#1436—111no—
321#1434—111no—
322#1434—111no—
323C22⋊#95—111no—
324C22⋊#95—111no—
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—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—41no—
362C23×C11—41no—
363C23×C11—41no—
364C23×C11—41no—
365C23×C11—41no—
366C23×C11—41no—
367C23×C11—41no—
368C23×C11—41no—
369C23×C11—41no—
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×C11C4×D414yes—
394C23×C11C4×D414yes—
395C23×C11C23×C411yescharacteristic
396C23×C11C22×D411yescharacteristic
397C23×C11C22×D411yescharacteristic
398C23×C11C2×#4111yescharacteristic
399C23×C11C2×#4111yescharacteristic
400C23×C11C2×#4111yescharacteristic
401C23×C11C2×#4111yescharacteristic
402C23×C11C2×#4111yescharacteristic
403C23×C11C2×#4111yescharacteristic
404C23×C11C2×#4111yescharacteristic
405C23×C11C2×#4111yescharacteristic
406C23×C11H(5,𝔽2)11yescharacteristic
407C23×C11H(5,𝔽2)11yescharacteristic
408C23×C11H(5,𝔽2)11yescharacteristic
409C23×C11H(5,𝔽2)11yescharacteristic
410D4×C11—416no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—22no—
419C2×C4×C11—22no—
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—416no—
427C2×C4×C11—41no—
428C2×C4×C11—41no—
429C2×C4×C11—41no—
430C2×C4×C11—41no—
431C2×C4×C11—41no—
432C2×C4×C11—41no—
433C2×C4×C11—41no—
434C2×C4×C11—41no—
435C2×C4×C11—41no—
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#12314yes—
447C2×Dic11—22no—
448C2×Dic11—22no—
449C2×Dic11—22no—
450C2×Dic11—22no—
451C2×Dic11—22no—
452C2×Dic11—22no—
453C2×Dic11—22no—
454C2×Dic11—22no—
455C2×Dic11—22no—
456C2×Dic11—22no—
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—416no—
472C2×Dic11—41no—
473C2×Dic11—41no—
474C2×Dic11—41no—
475C2×Dic11—41no—
476C2×Dic11—41no—
477C2×Dic11—41no—
478C2×Dic11—41no—
479C2×Dic11—41no—
480C2×Dic11—41no—
481C2×Dic11—41no—
482C2×Dic11—41no—
483C2×Dic11—41no—
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#12314yes—
504C23×D4C2×D1111yescharacteristic
505C24×C4—111no—
506C24×C4C2×D1111yescharacteristic
507C22×C4⋊C4—111no—
508C22×C22⋊C4—111no—
509C22×C22⋊C4—111no—
510C22×C22⋊C4—111no—
511C22×C22⋊C4—111no—
512C22×C22⋊C4—111no—
513C22×C22⋊C4—111no—
514C22×C22⋊C4—111no—
515C22×C22⋊C4C2×D1111yescharacteristic
516C22×C22⋊C4C2×D1111yescharacteristic
517C22×C22⋊C4C2×D1111yescharacteristic
518C22×C42—111no—
519C22×C42—111no—
520C22×C42—111no—
521#394—118no—
522#386—24no—
523#386—224no—
524C4×C22⋊C4—224no—
525C4×C22⋊C4—224no—
526C2×#95—111no—
527C2×#95—111no—
528C2×#95—111no—
529C2×#95—111no—
530C2×#95—111no—
531C2×#95—111no—
532C2×#95—111no—
533C2×#95—111no—
534C2×#95—111no—
535C2×#95—111no—
536C2×#95—111no—
537C2×#95—111no—
538C2×#95—111no—
539C2×#95—111no—
540C2×#95—111no—
541C2×#95—111no—
542C2×#95C2×D1111yescharacteristic
543C2×#95C2×D1111yescharacteristic
544C22×C11—24no—
545C22×C11—24no—
546C22×C11—24no—
547C22×C11—24no—
548C22×C11—24no—
549C22×C11—24no—
550C22×C11—42no—
551C22×C11—42no—
552C22×C11—42no—
553C22×C11—42no—
554C22×C11—42no—
555C22×C11—42no—
556C22×C11—42no—
557C22×C11—42no—
558C22×C11—42no—
559C22×C11—42no—
560C22×C11—42no—
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×C11C2×C4×D411yescharacteristic
575C22×C11C2×C4×D411yescharacteristic
576C22×C11C4×#4111yescharacteristic
577C22×C11C4×#4111yescharacteristic
578C22×C11C4×#4111yescharacteristic
579C22×C11#51811yescharacteristic
580C22×C11#51811yescharacteristic
581C22×C11C2×#12311yescharacteristic
582C22×C11C2×#12311yescharacteristic
583C22×C11#52511yescharacteristic
584C22×C11#52511yescharacteristic
585C22×C11#52911yescharacteristic
586C22×C11#52911yescharacteristic
587C22×C11#52911yescharacteristic
588C22×C11#52911yescharacteristic
589C22×C11#53811yescharacteristic
590C22×C11#53811yescharacteristic
591C22×C11#54011yescharacteristic
592C22×C11#54011yescharacteristic
593C22×C11D4211yescharacteristic
594C22×C11#54611yescharacteristic
595C22×C11#54611yescharacteristic
596C22×C11#54611yescharacteristic
597C22×C11#54611yescharacteristic
598C22×C11#54611yescharacteristic
599C22×C11#54611yescharacteristic
600C22×C11#55111yescharacteristic
601C22×C11#55111yescharacteristic
602C22×C11#55111yescharacteristic
603C22×C11#55311yescharacteristic
604C22×C11#55311yescharacteristic
605C22×C11#55311yescharacteristic
606C22×C11#55311yescharacteristic
607C22×C11#55511yescharacteristic
608C22×C11#55511yescharacteristic
609C4×C11—24no—
610C4×C11—42no—
611C4×C11—42no—
612C4×C11—42no—
613C4×C11—81no—
614Dic11—24no—
615Dic11—42no—
616Dic11—42no—
617Dic11—42no—
618Dic11—42no—
619Dic11—42no—
620Dic11—42no—
621Dic11—81no—
622C25C22×D1111yescharacteristic
623C25C22×D1111yescharacteristic
624C22×D4—22no—
625C22×D4—22no—
626C22×D4—22no—
627C22×D4—22no—
628C22×D4—41no—
629C22×D4—41no—
630C22×D4C4×D1114yes—
631C23×C4—22no—
632C23×C4—22no—
633C23×C4—22no—
634C23×C4—22no—
635C23×C4—22no—
636C23×C4—41no—
637C23×C4—41no—
638C23×C4—111no—
639C23×C4—111no—
640C23×C4—111no—
641C23×C4—111no—
642C23×C4—111no—
643C23×C4—111no—
644C23×C4—111no—
645C23×C4—111no—
646C23×C4—222no—
647C23×C4—222no—
648C23×C4—222no—
649C23×C4—222no—
650C23×C4—222no—
651C23×C4—441no—
652C23×C4—441no—
653C23×C4C22×D1111yescharacteristic
654C23×C4C22×D1111yescharacteristic
655C23×C4C22×D1111yescharacteristic
656C23×C4C22×D1111yescharacteristic
657C23×C4C22×D1111yescharacteristic
658C2×C4⋊C4—114no—
659C2×C4⋊C4—441no—
660C2×C4⋊C4—441no—
661C2×C22⋊C4—22no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—22no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—22no—
666C2×C22⋊C4—22no—
667C2×C22⋊C4—41no—
668C2×C22⋊C4—41no—
669C2×C22⋊C4—114no—
670C2×C22⋊C4—114no—
671C2×C22⋊C4—114no—
672C2×C22⋊C4—114no—
673C2×C22⋊C4—114no—
674C2×C22⋊C4—222no—
675C2×C22⋊C4—222no—
676C2×C22⋊C4—222no—
677C2×C22⋊C4—222no—
678C2×C22⋊C4—222no—
679C2×C22⋊C4—222no—
680C2×C22⋊C4—222no—
681C2×C22⋊C4—222no—
682C2×C22⋊C4—222no—
683C2×C22⋊C4—222no—
684C2×C22⋊C4—441no—
685C2×C22⋊C4—441no—
686C2×C22⋊C4—441no—
687C2×C22⋊C4—441no—
688C2×C22⋊C4—441no—
689C2×C22⋊C4—441no—
690C2×C22⋊C4C22⋊D1114yes—
691C2×C42—222no—
692C2×C42—222no—
693C2×C42—222no—
694C2×C42—222no—
695C2×C42—222no—
696C2×C42—222no—
697C2×C42—441no—
698C2×C42—441no—
699C2×C42—441no—
700#95—22no—
701#95—22no—
702#95—114no—
703#95—222no—
704#95—222no—
705#95—222no—
706#95—222no—
707#95—222no—
708#95—222no—
709#95—222no—
710#95—222no—
711#95—222no—
712#95—222no—
713#95—441no—
714#95—441no—
715#95—441no—
716#95—441no—
717#95—441no—
718C2×C11—44no—
719C2×C11—44no—
720C2×C11C4×#12311yescharacteristic
721C2×C11C4×#12311yescharacteristic
722C2×C11#233311yescharacteristic
723C2×C11#235811yescharacteristic
724C2×C11#236411yescharacteristic
725C2×C11#236411yescharacteristic
726C2×C11#237211yescharacteristic
727C2×C11#241811yescharacteristic
728C2×C11#241811yescharacteristic
729C2×C11#242011yescharacteristic
730C2×C11#242011yescharacteristic
731C2×C11#247611yescharacteristic
732C2×C11#247611yescharacteristic
733C2×C11#257811yescharacteristic
734C2×C11#257811yescharacteristic
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24C2×C4×D1112yes—
760C24C2×C4×D1112yes—
761C24#433912yes—
762C24D4×D1112yes—
763C24#434112yes—
764C24C2×C22⋊D1112yes—
765C24C23×D1111yescharacteristic
766C2×D4—28no—
767C2×D4—28no—
768C2×D4—44no—
769C2×D4—44no—
770C2×D4—44no—
771C2×D4—44no—
772C2×D4—44no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—28no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
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—44no—
804C22×C4—44no—
805C22×C4—44no—
806C22×C4—44no—
807C22×C4—44no—
808C22×C4—44no—
809C22×C4—112no—
810C22×C4—112no—
811C22×C4—112no—
812C22×C4—112no—
813C22×C4—112no—
814C22×C4—112no—
815C22×C4—112no—
816C22×C4—112no—
817C22×C4—112no—
818C22×C4—221no—
819C22×C4—221no—
820C22×C4—221no—
821C22×C4—221no—
822C22×C4—228no—
823C22×C4—221no—
824C22×C4—221no—
825C22×C4—221no—
826C22×C4—221no—
827C22×C4—221no—
828C22×C4—221no—
829C22×C4—221no—
830C22×C4—221no—
831C22×C4—221no—
832C22×C4—221no—
833C22×C4—221no—
834C22×C4—221no—
835C22×C4—221no—
836C22×C4—221no—
837C22×C4—221no—
838C22×C4—221no—
839C22×C4—221no—
840C22×C4—221no—
841C22×C4—221no—
842C22×C4—221no—
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—444no—
867C22×C4—444no—
868C22×C4—444no—
869C22×C4—444no—
870C22×C4—444no—
871C22×C4—444no—
872C22×C4C2×C4×D1112yes—
873C22×C4#434112yes—
874C22×C4#434112yes—
875C22×C4#434112yes—
876C22×C4C2×C22⋊D1112yes—
877C22×C4C2×C22⋊D1112yes—
878C4⋊C4—444no—
879C22⋊C4—28no—
880C22⋊C4—44no—
881C22⋊C4—44no—
882C22⋊C4—228no—
883C22⋊C4—228no—
884C22⋊C4—228no—
885C22⋊C4—444no—
886C22⋊C4—444no—
887C22⋊C4—444no—
888C22⋊C4—444no—
889C42—444no—
890C42—444no—
891C42—444no—
892C11#1418111yescharacteristic, complemented, Sylow
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
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—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
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(C22⋊D11)⋊C414yes—
962C23C4×C22⋊D1114yes—
963C23C22×C4×D1111yescharacteristic
964C23C2×#433911yescharacteristic
965C23C2×D4×D1111yescharacteristic
966C23C2×#434111yescharacteristic
967C23C2×#434111yescharacteristic
968C23C2×#434111yescharacteristic
969C23C2×#434111yescharacteristic
970C23#6703711yescharacteristic
971C23#6703711yescharacteristic
972C23#6703711yescharacteristic
973C23#41×D1111yescharacteristic
974C23#41×D1111yescharacteristic
975C23#41×D1111yescharacteristic
976C23#6704211yescharacteristic
977C23C22×C22⋊D1111yescharacteristic
978D4—416no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—416no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—114no—
1015C2×C4—222no—
1016C2×C4—222no—
1017C2×C4—222no—
1018C2×C4—222no—
1019C2×C4—222no—
1020C2×C4—222no—
1021C2×C4—222no—
1022C2×C4—222no—
1023C2×C4—222no—
1024C2×C4—222no—
1025C2×C4—222no—
1026C2×C4—222no—
1027C2×C4—222no—
1028C2×C4—222no—
1029C2×C4—222no—
1030C2×C4—222no—
1031C2×C4—222no—
1032C2×C4—222no—
1033C2×C4—222no—
1034C2×C4—222no—
1035C2×C4—222no—
1036C2×C4—222no—
1037C2×C4—222no—
1038C2×C4—222no—
1039C2×C4—4416no—
1040C2×C4—441no—
1041C2×C4—441no—
1042C2×C4—441no—
1043C2×C4—441no—
1044C2×C4—441no—
1045C2×C4—441no—
1046C2×C4—441no—
1047C2×C4—441no—
1048C2×C4—441no—
1049C2×C4—441no—
1050C2×C4—441no—
1051C2×C4—441no—
1052C2×C4—441no—
1053C2×C4—441no—
1054C2×C4—441no—
1055C2×C4—441no—
1056C2×C4—441no—
1057C2×C4—441no—
1058C2×C4—441no—
1059C2×C4—441no—
1060C2×C4—441no—
1061C2×C4—441no—
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#6698814yes—
1072C22—24no—
1073C22—24no—
1074C22—24no—
1075C22—24no—
1076C22—24no—
1077C22—24no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22C2×(C22⋊D11)⋊C411yescharacteristic
1103C22#1062301711yescharacteristic
1104C22#1062302111yescharacteristic
1105C22#1062302611yescharacteristic
1106C22C4×#434111yescharacteristic
1107C22C4×#434111yescharacteristic
1108C22C4×#434111yescharacteristic
1109C22#1062306911yescharacteristic
1110C22#1062306911yescharacteristic
1111C22#1062307111yescharacteristic
1112C22#1062307611yescharacteristic
1113C22#1062309611yescharacteristic
1114C22#1062311711yescharacteristic
1115C22#1062311811yescharacteristic
1116C22#1062312211yescharacteristic
1117C22#1062312411yescharacteristic
1118C22#1062313111yescharacteristic
1119C22#1062313111yescharacteristic
1120C22#1062313211yescharacteristic
1121C22#1062314611yescharacteristic
1122C22#1062314711yescharacteristic
1123C22#1062314711yescharacteristic
1124C22#1062314911yescharacteristic
1125C22#1062315011yescharacteristic
1126C22D11×#12311yescharacteristic
1127C22#1062318511yescharacteristic
1128C22#1062318811yescharacteristic
1129C22#1062319011yescharacteristic
1130C22C2×C4×C22⋊D1111yescharacteristic
1131C22C2×#6698811yescharacteristic
1132C22D4×C22⋊D1111yescharacteristic
1133C22#1062333711yescharacteristic
1134C22#1062333711yescharacteristic
1135C22#1062335911yescharacteristic
1136C22#1062336011yescharacteristic
1137C4—24no—
1138C4—42no—
1139C4—42no—
1140C4—42no—
1141C4—81no—
1142C4—224no—
1143C4—442no—
1144C4—442no—
1145C4—442no—
1146C4—442no—
1147C4—442no—
1148C4—442no—
1149C4—881no—
1150C2—44no—
1151C2—44no—
1152C2C4×#6698811yescharacteristic
1153C2#1307114111yescharacteristic
1154C2#1307137711yescharacteristic
1155C2#1307159511yescharacteristic
1156C2#1307166111yescharacteristic
1157C2#1307166411yescharacteristic
1158C2#1307172511yescharacteristic
1159C2#1307207411yescharacteristic
1160C2#1307207511yescharacteristic
1161C2#1307210411yescharacteristic
1162C2#1307210511yescharacteristic
1163C2#1307279811yescharacteristic
1164C2#1307279911yescharacteristic
1165C2#1307394711yescharacteristic
1166C2#1307395411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#386C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#386D11
hypocenterC11#14181
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
3. C2×C22⋊C4×Dic11C2semidirect
4. C2×C4×C22⋊Dic11C2semidirect
5. #13066882C2semidirect
6. #13066863C2semidirect
7. #13066863C2semidirect
8. #13066853C2semidirect
9. #13066853C2semidirect
10. #13066847C2semidirect
11. #13066842C2semidirect
12. #13066840C2semidirect
13. #13066839C2semidirect
14. #13066838C2semidirect
36. #10622835C4semidirect
117. C2×C22⋊Dic11C2×C4semidirect
118. C2×C22⋊Dic11C2×C4semidirect
119. C2×C22⋊Dic11C2×C4semidirect
120. C2×C22⋊Dic11C2×C4semidirect
124. C2×Dic11⋊C4C2×C4semidirect
151. C11⋊#95C2×C4semidirect
892. C11#14181semidirect

Maximal subgroups

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

subgroupindex
C2×#106228352
C2×#106228332
C2×C22⋊C4×Dic112
C2×C4×C22⋊Dic112
#130668822
#130668632
#130668532
#130668472
#130668422
#130668402
#130668392
#130668382
C2×C11×#3862
#1418111