Finite Group Databasebeta

← #14681337

Subgroups — #14681337

Order 2816.

1866 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622564C211yesmaximal, characteristic, complemented
2C2×#10622833C211yesmaximal, characteristic
3C2×#10622563C211yesmaximal, characteristic, complemented
4C2×#10622549C211yesmaximal, characteristic, complemented
5#13066869C211yesmaximal, characteristic, complemented
6#13066865C211yesmaximal, characteristic, complemented
7#13066861C211yesmaximal, characteristic, complemented
8#13066861C211yesmaximal, characteristic, complemented
9#13066861C211yesmaximal, characteristic, complemented
10#13066857C211yesmaximal, characteristic
11#13066853C211yesmaximal, characteristic, complemented
12#13066848C211yesmaximal, characteristic, complemented
13#13066843C211yesmaximal, characteristic, complemented
14#13066838C211yesmaximal, characteristic, complemented
15C2×C11×#390C211yesmaximal, characteristic
16C23×D4×C11C2211yescharacteristic
17C24×Dic11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C42×C11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C4⋊Dic11C2211yescharacteristic
32C22×C4⋊Dic11C2211yescharacteristic
33C22×C4⋊Dic11C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C11×#390C418yescomplemented
36#10622833—24no—
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2211yescharacteristic
43C2×C11⋊#95C2211yescharacteristic
44C2×C11⋊#95C2211yescharacteristic
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53#10622564—24no—
54#10622563—24no—
55#10622549—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×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×Dic11—22no—
71C23×Dic11—22no—
72C23×Dic11—22no—
73C23×Dic11—41no—
74C23×Dic11—41no—
75C23×Dic11—41no—
76C23×Dic11—41no—
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C2×C11×C4⋊C4—41no—
86C2×C11×C4⋊C4—41no—
87C2×C11×C4⋊C4C2×C414yescomplemented
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—41no—
93C2×C11×C22⋊C4—41no—
94C2×C11×C22⋊C4—41no—
95C2×C11×C22⋊C4—41no—
96C2×C11×C22⋊C4C2×C414yes—
97C2×C11×C22⋊C4C2×C414yes—
98C2×C11×C22⋊C4C2×C414yescomplemented
99C2×C11×C22⋊C4C2×C414yescomplemented
100C2×C42×C11—22no—
101C2×C42×C11—22no—
102C2×C42×C11C2×C414yescomplemented
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—41no—
113C2×C22⋊Dic11—41no—
114C2×C22⋊Dic11—41no—
115C2×C22⋊Dic11—41no—
116C2×C22⋊Dic11—41no—
117C2×C22⋊Dic11—41no—
118C2×C22⋊Dic11—41no—
119C2×C22⋊Dic11—41no—
120C2×C22⋊Dic11—41no—
121C2×C22⋊Dic11—41no—
122C2×C22⋊Dic11—41no—
123C2×C22⋊Dic11—41no—
124C2×C4⋊Dic11—22no—
125C2×C4⋊Dic11—22no—
126C2×C4⋊Dic11—22no—
127C2×C4⋊Dic11—22no—
128C2×C4⋊Dic11—22no—
129C2×C4⋊Dic11—41no—
130C2×C4⋊Dic11—41no—
131C2×C4⋊Dic11—41no—
132C2×C4⋊Dic11—41no—
133C2×C4×Dic11—22no—
134C2×C4×Dic11—41no—
135C2×C4×Dic11—41no—
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—41no—
145C11⋊#95—41no—
146C11⋊#95—41no—
147C11⋊#95—41no—
148C11⋊#95—41no—
149C11⋊#95—41no—
150C11⋊#95D414yes—
151C11⋊#95D414yescomplemented
152#14377—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×C11—21no—
178C24×C11—21no—
179C24×C11C22×C412yes—
180C24×C11C22×C412yes—
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—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×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×C11C22×C412yes—
218C22×C4×C11C22×C412yes—
219C22×C4×C11C22×C412yes—
220C22×C4×C11C22×C412yes—
221C22×C4×C11C22×C412yes—
222C22×C4×C11C2×D412yes—
223C22×C4×C11C2×D412yes—
224C22×C4×C11#4112yes—
225C22×C4×C11#4112yes—
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—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—44no—
279C22×Dic11—44no—
280C22×Dic11—44no—
281C22×Dic11—44no—
282C22×Dic11—44no—
283C22×Dic11—44no—
284C22×Dic11—44no—
285C22×Dic11C2×D412yes—
286C22×Dic11C2×D412yes—
287C22×Dic11C2×D412yes—
288C22×Dic11C2×D412yes—
289C11×C4⋊C4—44no—
290C11×C22⋊C4—28no—
291C11×C22⋊C4—28no—
292C11×C22⋊C4—44no—
293C11×C22⋊C4—44no—
294C42×C11—28no—
295C22⋊Dic11—44no—
296C22⋊Dic11—44no—
297C22⋊Dic11—44no—
298C22⋊Dic11—44no—
299C22⋊Dic11—44no—
300C22⋊Dic11—44no—
301C22⋊Dic11—44no—
302C4⋊Dic11—44no—
303C4⋊Dic11—44no—
304C4⋊Dic11—44no—
305C4×Dic11—44no—
306C2×#390D1111yescharacteristic
307C2×#388—111no—
308C2×#386—111no—
309C2×#385—111no—
310C2×#382—111no—
311#1441—111no—
312#1440—111no—
313#1439—111no—
314#1439—111no—
315#1439—111no—
316#1438—111no—
317#1437—111no—
318#1436—111no—
319#1434—111no—
320C22⋊#95—111no—
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—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—41no—
347C23×C11—41no—
348C23×C11—41no—
349C23×C11—41no—
350C23×C11—41no—
351C23×C11—41no—
352C23×C11—41no—
353C23×C11—41no—
354C23×C11—41no—
355C23×C11—41no—
356C23×C11—41no—
357C23×C11—41no—
358C23×C11—41no—
359C23×C11—41no—
360C23×C11—41no—
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#11714yes—
391C23×C11C23×C411yescharacteristic
392C23×C11C22×D411yescharacteristic
393C23×C11C22×D411yescharacteristic
394C23×C11C2×#4111yescharacteristic
395C23×C11C2×#4111yescharacteristic
396C23×C11C2×#4111yescharacteristic
397C23×C11C2×#4111yescharacteristic
398C23×C11H(5,𝔽2)11yescharacteristic
399C23×C11H(5,𝔽2)11yescharacteristic
400C23×C11H(5,𝔽2)11yescharacteristic
401C23×C11H(5,𝔽2)11yescharacteristic
402C23×C11H(5,𝔽2)11yescharacteristic
403C23×C11H(5,𝔽2)11yescharacteristic
404C23×C112−1+411yescharacteristic
405C23×C112−1+411yescharacteristic
406D4×C11—416no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
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—22no—
427C2×C4×C11—22no—
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×C11C4×D414yes—
441C2×C4×C11C4×D414yes—
442C2×Dic11—22no—
443C2×Dic11—22no—
444C2×Dic11—22no—
445C2×Dic11—22no—
446C2×Dic11—22no—
447C2×Dic11—22no—
448C2×Dic11—22no—
449C2×Dic11—22no—
450C2×Dic11—22no—
451C2×Dic11—22no—
452C2×Dic11—22no—
453C2×Dic11—22no—
454C2×Dic11—416no—
455C2×Dic11—41no—
456C2×Dic11—41no—
457C2×Dic11—41no—
458C2×Dic11—41no—
459C2×Dic11—41no—
460C2×Dic11—41no—
461C2×Dic11—41no—
462C2×Dic11—41no—
463C2×Dic11—41no—
464C2×Dic11—41no—
465C2×Dic11—41no—
466C2×Dic11—41no—
467C2×Dic11—41no—
468C2×Dic11—41no—
469C2×Dic11—41no—
470C2×Dic11—41no—
471C2×Dic11—41no—
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—
499C23×D4C2×D1111yescharacteristic
500C24×C4—111no—
501C22×C4⋊C4—111no—
502C22×C4⋊C4—111no—
503C22×C4⋊C4—111no—
504C22×C4⋊C4C2×D1111yescharacteristic
505C22×C22⋊C4—111no—
506C22×C22⋊C4—111no—
507C22×C22⋊C4—111no—
508C22×C22⋊C4—111no—
509C22×C22⋊C4—111no—
510C22×C22⋊C4—111no—
511C22×C22⋊C4—111no—
512C22×C22⋊C4C2×D1111yescharacteristic
513C22×C22⋊C4C2×D1111yescharacteristic
514C22×C22⋊C4C2×D1111yescharacteristic
515C22×C22⋊C4C2×D1111yescharacteristic
516C22×C42—111no—
517C22×C42C2×D1111yescharacteristic
518#390Dic1118yescomplemented
519#388—224no—
520#386—224no—
521#385—224no—
522#382—224no—
523C2×#95—111no—
524C2×#95—111no—
525C2×#95—111no—
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—
539C22×C11—24no—
540C22×C11—24no—
541C22×C11—24no—
542C22×C11—42no—
543C22×C11—42no—
544C22×C11—42no—
545C22×C11—42no—
546C22×C11—42no—
547C22×C11—42no—
548C22×C11—42no—
549C22×C11—42no—
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—81no—
562C22×C11—81no—
563C22×C11—81no—
564C22×C11—81no—
565C22×C11—81no—
566C22×C11—81no—
567C22×C11—81no—
568C22×C11—81no—
569C22×C11C2×#11711yescharacteristic
570C22×C11C2×C4×D411yescharacteristic
571C22×C11C2×C4×D411yescharacteristic
572C22×C11#51811yescharacteristic
573C22×C11#51811yescharacteristic
574C22×C11#52011yescharacteristic
575C22×C11#52011yescharacteristic
576C22×C11#53511yescharacteristic
577C22×C11#53511yescharacteristic
578C22×C11#53511yescharacteristic
579C22×C11#53711yescharacteristic
580C22×C11#53811yescharacteristic
581C22×C11#53811yescharacteristic
582C22×C11#53911yescharacteristic
583C22×C11#53911yescharacteristic
584C22×C11#54011yescharacteristic
585C22×C11#54011yescharacteristic
586C22×C11#54011yescharacteristic
587C22×C11#54211yescharacteristic
588C22×C11D4211yescharacteristic
589C22×C11#54611yescharacteristic
590C22×C11#54611yescharacteristic
591C22×C11#54611yescharacteristic
592C22×C11#54711yescharacteristic
593C22×C11#54811yescharacteristic
594C22×C11#54811yescharacteristic
595C22×C11#55111yescharacteristic
596C22×C11#55111yescharacteristic
597C22×C11#55211yescharacteristic
598C22×C11#55311yescharacteristic
599C22×C11#55311yescharacteristic
600C22×C11H(3,𝔽4)11yescharacteristic
601C22×C11#56211yescharacteristic
602C22×C11#56211yescharacteristic
603C22×C11#56311yescharacteristic
604C4×C11—24no—
605C4×C11—24no—
606C4×C11—42no—
607C4×C11—42no—
608C4×C11—42no—
609Dic11—42no—
610Dic11—42no—
611Dic11—42no—
612Dic11—42no—
613Dic11—81no—
614Dic11—81no—
615Dic11—81no—
616Dic11—81no—
617C25C22×D1111yescharacteristic
618C25C22×D1111yescharacteristic
619C22×D4—22no—
620C22×D4—22no—
621C22×D4—22no—
622C22×D4—22no—
623C22×D4—41no—
624C22×D4—41no—
625C22×D4C2×Dic1114yes—
626C23×C4—111no—
627C23×C4—111no—
628C23×C4—111no—
629C23×C4—111no—
630C23×C4—111no—
631C23×C4—111no—
632C23×C4—111no—
633C23×C4—111no—
634C23×C4—222no—
635C23×C4—222no—
636C23×C4—222no—
637C23×C4—441no—
638C23×C4—441no—
639C23×C4—441no—
640C23×C4—441no—
641C23×C4C22×D1111yescharacteristic
642C23×C4C22×D1111yescharacteristic
643C23×C4C22×D1111yescharacteristic
644C23×C4C22×D1111yescharacteristic
645C23×C4C22×D1111yescharacteristic
646C2×C4⋊C4—41no—
647C2×C4⋊C4—41no—
648C2×C4⋊C4—222no—
649C2×C4⋊C4—222no—
650C2×C4⋊C4—222no—
651C2×C4⋊C4—222no—
652C2×C4⋊C4—222no—
653C2×C4⋊C4—441no—
654C2×C4⋊C4—441no—
655C2×C4⋊C4—441no—
656C2×C4⋊C4—441no—
657C2×C4⋊C4C2×Dic1114yescomplemented
658C2×C22⋊C4—22no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—22no—
662C2×C22⋊C4—41no—
663C2×C22⋊C4—41no—
664C2×C22⋊C4—41no—
665C2×C22⋊C4—41no—
666C2×C22⋊C4—222no—
667C2×C22⋊C4—222no—
668C2×C22⋊C4—222no—
669C2×C22⋊C4—222no—
670C2×C22⋊C4—222no—
671C2×C22⋊C4—222no—
672C2×C22⋊C4—222no—
673C2×C22⋊C4—222no—
674C2×C22⋊C4—222no—
675C2×C22⋊C4—441no—
676C2×C22⋊C4—441no—
677C2×C22⋊C4—441no—
678C2×C22⋊C4—441no—
679C2×C22⋊C4—441no—
680C2×C22⋊C4—441no—
681C2×C22⋊C4—441no—
682C2×C22⋊C4—441no—
683C2×C22⋊C4—441no—
684C2×C22⋊C4—441no—
685C2×C22⋊C4—441no—
686C2×C22⋊C4—441no—
687C2×C22⋊C4C2×Dic1114yes—
688C2×C22⋊C4C2×Dic1114yes—
689C2×C22⋊C4C2×Dic1114yescomplemented
690C2×C22⋊C4C2×Dic1114yescomplemented
691C2×C42—22no—
692C2×C42—22no—
693C2×C42—222no—
694C2×C42—441no—
695C2×C42—441no—
696C2×C42C2×Dic1114yescomplemented
697#95—114no—
698#95—114no—
699#95—222no—
700#95—222no—
701#95—222no—
702#95—222no—
703#95—222no—
704#95—222no—
705#95—222no—
706#95—222no—
707#95—441no—
708#95—441no—
709#95—441no—
710#95—441no—
711#95—441no—
712#95—441no—
713C2×C11—44no—
714C2×C11—82no—
715C2×C11#231811yescharacteristic
716C2×C11#232411yescharacteristic
717C2×C11#232811yescharacteristic
718C2×C11#234211yescharacteristic
719C2×C11#235211yescharacteristic
720C2×C11#236111yescharacteristic
721C2×C11#237911yescharacteristic
722C2×C11#267011yescharacteristic
723C2×C11#267611yescharacteristic
724C2×C11#270611yescharacteristic
725C2×C11#270711yescharacteristic
726C2×C11#271111yescharacteristic
727C2×C11#272311yescharacteristic
728C2×C11#275311yescharacteristic
729C2×C11#276111yescharacteristic
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
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#433912yes—
757C24#433912yes—
758C24C22×Dic1112yes—
759C24C22×Dic1112yes—
760C24C23×D1111yescharacteristic
761C2×D4—28no—
762C2×D4—28no—
763C2×D4—44no—
764C2×D4—44no—
765C2×D4—44no—
766C2×D4—44no—
767C2×D4—44no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
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—112no—
795C22×C4—112no—
796C22×C4—112no—
797C22×C4—112no—
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—221no—
809C22×C4—221no—
810C22×C4—221no—
811C22×C4—221no—
812C22×C4—221no—
813C22×C4—221no—
814C22×C4—221no—
815C22×C4—221no—
816C22×C4—221no—
817C22×C4—221no—
818C22×C4—221no—
819C22×C4—221no—
820C22×C4—221no—
821C22×C4—221no—
822C22×C4—221no—
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—444no—
851C22×C4—444no—
852C22×C4—444no—
853C22×C4—444no—
854C22×C4—444no—
855C22×C4—444no—
856C22×C4—444no—
857C22×C4D4×D1112yes—
858C22×C4D4×D1112yes—
859C22×C4#434112yes—
860C22×C4#434112yes—
861C22×C4C22×Dic1112yes—
862C22×C4C22×Dic1112yes—
863C22×C4C22×Dic1112yes—
864C22×C4C22×Dic1112yes—
865C22×C4C22×Dic1112yes—
866C4⋊C4—44no—
867C4⋊C4—444no—
868C4⋊C4—444no—
869C4⋊C4—444no—
870C22⋊C4—28no—
871C22⋊C4—28no—
872C22⋊C4—44no—
873C22⋊C4—44no—
874C22⋊C4—444no—
875C22⋊C4—444no—
876C22⋊C4—444no—
877C22⋊C4—444no—
878C22⋊C4—444no—
879C22⋊C4—444no—
880C22⋊C4—444no—
881C42—28no—
882C42—444no—
883C11#1437711yescharacteristic, complemented, Sylow
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
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—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
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#6697914yes—
954C23C2×#433911yescharacteristic
955C23C2×#433911yescharacteristic
956C23C2×D4×D1111yescharacteristic
957C23C2×D4×D1111yescharacteristic
958C23C2×#434111yescharacteristic
959C23C2×#434111yescharacteristic
960C23#6703711yescharacteristic
961C23#6703711yescharacteristic
962C23#6703711yescharacteristic
963C23#6703711yescharacteristic
964C23#6704211yescharacteristic
965C23#6704211yescharacteristic
966C23#6704311yescharacteristic
967C23#6704311yescharacteristic
968C23C23×Dic1111yescharacteristic
969D4—416no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
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—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
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—222no—
1004C2×C4—222no—
1005C2×C4—222no—
1006C2×C4—222no—
1007C2×C4—222no—
1008C2×C4—222no—
1009C2×C4—222no—
1010C2×C4—222no—
1011C2×C4—222no—
1012C2×C4—222no—
1013C2×C4—222no—
1014C2×C4—222no—
1015C2×C4—4416no—
1016C2×C4—441no—
1017C2×C4—441no—
1018C2×C4—441no—
1019C2×C4—441no—
1020C2×C4—441no—
1021C2×C4—441no—
1022C2×C4—441no—
1023C2×C4—441no—
1024C2×C4—441no—
1025C2×C4—441no—
1026C2×C4—441no—
1027C2×C4—441no—
1028C2×C4—441no—
1029C2×C4—441no—
1030C2×C4—441no—
1031C2×C4—441no—
1032C2×C4—441no—
1033C2×C4—441no—
1034C2×C4—441no—
1035C2×C4—441no—
1036C2×C4—441no—
1037C2×C4—441no—
1038C2×C4—441no—
1039C2×C4—441no—
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×C4D4×Dic1114yes—
1061C2×C4D4×Dic1114yes—
1062C22—24no—
1063C22—24no—
1064C22—24no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—81no—
1085C22—81no—
1086C22—81no—
1087C22—81no—
1088C22—81no—
1089C22—81no—
1090C22—81no—
1091C22—81no—
1092C22#1062302111yescharacteristic
1093C22#1062302111yescharacteristic
1094C22#1062302611yescharacteristic
1095C22#1062302611yescharacteristic
1096C22#1062307211yescharacteristic
1097C22#1062308111yescharacteristic
1098C22#1062308311yescharacteristic
1099C22#1062309111yescharacteristic
1100C22#1062309111yescharacteristic
1101C22#1062309511yescharacteristic
1102C22#1062309511yescharacteristic
1103C22#1062309611yescharacteristic
1104C22#1062312911yescharacteristic
1105C22#1062313411yescharacteristic
1106C22#1062313811yescharacteristic
1107C22#1062313911yescharacteristic
1108C22#1062314011yescharacteristic
1109C22#1062314211yescharacteristic
1110C22#1062314911yescharacteristic
1111C22#1062315011yescharacteristic
1112C22#1062320311yescharacteristic
1113C22#1062321411yescharacteristic
1114C22#1062321511yescharacteristic
1115C22#1062321511yescharacteristic
1116C22#1062324611yescharacteristic
1117C22#1062324611yescharacteristic
1118C22#1062325011yescharacteristic
1119C22#1062325011yescharacteristic
1120C22C2×#6697911yescharacteristic
1121C22C2×D4×Dic1111yescharacteristic
1122C22C2×D4×Dic1111yescharacteristic
1123C22#1062332911yescharacteristic
1124C22#1062332911yescharacteristic
1125C22#1062335811yescharacteristic
1126C22#1062335811yescharacteristic
1127C4—24no—
1128C4—24no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—442no—
1133C4—442no—
1134C4—442no—
1135C4—442no—
1136C4—881no—
1137C4—881no—
1138C4—881no—
1139C4—881no—
1140C2—44no—
1141C2—82no—
1142C2#1307124911yescharacteristic
1143C2#1307131111yescharacteristic
1144C2#1307134211yescharacteristic
1145C2#1307146511yescharacteristic
1146C2#1307154511yescharacteristic
1147C2#1307163611yescharacteristic
1148C2#1307179011yescharacteristic
1149C2#1307483911yescharacteristic
1150C2#1307491411yescharacteristic
1151C2#1307529911yescharacteristic
1152C2#1307532211yescharacteristic
1153C2#1307537311yescharacteristic
1154C2#1307553211yescharacteristic
1155C2#1307589311yescharacteristic
1156C2#1307599711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#390C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#390D11
hypocenterC11#14377
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C2×#10622564C2semidirect
3. C2×#10622563C2semidirect
4. C2×#10622549C2semidirect
5. #13066869C2semidirect
6. #13066865C2semidirect
7. #13066861C2semidirect
8. #13066861C2semidirect
9. #13066861C2semidirect
11. #13066853C2semidirect
12. #13066848C2semidirect
13. #13066843C2semidirect
14. #13066838C2semidirect
35. C11×#390C4semidirect
87. C2×C11×C4⋊C4C2×C4semidirect
98. C2×C11×C22⋊C4C2×C4semidirect
99. C2×C11×C22⋊C4C2×C4semidirect
102. C2×C42×C11C2×C4semidirect
151. C11⋊#95D4semidirect
518. #390Dic11semidirect
657. C2×C4⋊C4C2×Dic11semidirect
689. C2×C22⋊C4C2×Dic11semidirect
690. C2×C22⋊C4C2×Dic11semidirect
696. C2×C42C2×Dic11semidirect
883. C11#14377semidirect

Maximal subgroups

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

subgroupindex
C2×#106225642
C2×#106228332
C2×#106225632
C2×#106225492
#130668692
#130668652
#130668612
#130668572
#130668532
#130668482
#130668432
#130668382
C2×C11×#3902
#1437711