Finite Group Databasebeta

← #14679248

Subgroups — #14679248

Order 2816.

2422 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic11C211yesmaximal, characteristic
2C2×#10622598C211yesmaximal, characteristic, complemented
3C2×#10622564C211yesmaximal, characteristic, complemented
4C2×#10622563C211yesmaximal, characteristic, complemented
5C2×#10622563C211yesmaximal, characteristic, complemented
6C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
7#13066865C211yesmaximal, characteristic, complemented
8#13066861C211yesmaximal, characteristic, complemented
9#13066857C211yesmaximal, characteristic
10#13066853C211yesmaximal, characteristic, complemented
11#13066850C211yesmaximal, characteristic, complemented
12#13066850C211yesmaximal, characteristic, complemented
13#13066848C211yesmaximal, characteristic, complemented
14#13066838C211yesmaximal, characteristic, complemented
15C2×C11×#394C211yesmaximal, characteristic
16C23×D4×C11C2211yescharacteristic
17C24×Dic11C2211yescharacteristic
18C24×Dic11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
37C22×C4×Dic11C2211yescharacteristic
38C22×C4×Dic11C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40C11×#394C418yescomplemented
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
55#10622598—24no—
56#10622564—24no—
57#10622563—24no—
58#10622563—24no—
59C22⋊C4×Dic11—24no—
60C25×C11C2311yescharacteristic
61C25×C11C2311yescharacteristic
62C22×D4×C11—22no—
63C22×D4×C11—22no—
64C22×D4×C11—22no—
65C22×D4×C11—22no—
66C22×D4×C11—22no—
67C22×D4×C11—22no—
68C22×D4×C11C2×C414yes—
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×Dic11—22no—
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—41no—
84C23×Dic11—41no—
85C23×Dic11—41no—
86C23×Dic11—41no—
87C23×Dic11D414yes—
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C2×C11×C4⋊C4—22no—
97C2×C11×C4⋊C4—22no—
98C2×C11×C4⋊C4C2×C414yescomplemented
99C2×C11×C22⋊C4—22no—
100C2×C11×C22⋊C4—22no—
101C2×C11×C22⋊C4—22no—
102C2×C11×C22⋊C4—22no—
103C2×C11×C22⋊C4—22no—
104C2×C11×C22⋊C4—22no—
105C2×C11×C22⋊C4—22no—
106C2×C11×C22⋊C4—22no—
107C2×C11×C22⋊C4C2×C414yescomplemented
108C2×C11×C22⋊C4C2×C414yescomplemented
109C2×C11×C22⋊C4C2×C414yescomplemented
110C2×C11×C22⋊C4C2×C414yescomplemented
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—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—41no—
125C2×C22⋊Dic11—41no—
126C2×C22⋊Dic11—41no—
127C2×C22⋊Dic11—41no—
128C2×C22⋊Dic11D414yes—
129D4×Dic11—232no—
130C2×C4⋊Dic11—22no—
131C2×C4⋊Dic11—22no—
132C2×C4⋊Dic11—22no—
133C2×C4⋊Dic11—22no—
134C2×C4⋊Dic11—22no—
135C2×C4⋊Dic11—22no—
136C2×C4⋊Dic11—22no—
137C2×C4⋊Dic11—22no—
138C2×C4⋊Dic11—22no—
139C2×C4⋊Dic11—22no—
140C2×C4⋊Dic11—41no—
141C2×C4⋊Dic11D414yes—
142C2×C4×Dic11—22no—
143C2×C4×Dic11—22no—
144C2×C4×Dic11—22no—
145C2×C4×Dic11—22no—
146C2×C4×Dic11—22no—
147C2×C4×Dic11—22no—
148C2×C4×Dic11—22no—
149C2×C4×Dic11—41no—
150C2×C4×Dic11—41no—
151C11×#95C2×C414yescomplemented
152C11⋊#95—22no—
153C11⋊#95—22no—
154C11⋊#95—22no—
155C11⋊#95—22no—
156C11⋊#95—22no—
157C11⋊#95—22no—
158C11⋊#95—22no—
159C11⋊#95—22no—
160C11⋊#95—22no—
161C11⋊#95—22no—
162C11⋊#95—22no—
163C11⋊#95—41no—
164C11⋊#95D414yescomplemented
165#14185—111nomaximal, Sylow
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×C11—21no—
185C24×C11—21no—
186C24×C11—21no—
187C24×C11—21no—
188C24×C11—21no—
189C24×C11—21no—
190C24×C11C22×C412yes—
191C24×C11C22×C412yes—
192C24×C11C2×D412yes—
193C24×C11C2×D412yes—
194C24×C11#4112yes—
195C24×C11#4112yes—
196C24×C11C2411yescharacteristic
197C2×D4×C11—28no—
198C2×D4×C11—28no—
199C2×D4×C11—28no—
200C2×D4×C11—28no—
201C2×D4×C11—28no—
202C2×D4×C11—28no—
203C2×D4×C11—28no—
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—21no—
229C22×C4×C11—21no—
230C22×C4×C11C22×C412yes—
231C22×C4×C11C22×C412yes—
232C22×C4×C11C22×C412yes—
233C22×C4×C11C22×C412yes—
234C22×C4×C11C22×C412yes—
235C22×C4×C11C2×D412yes—
236C22×C4×C11C2×D412yes—
237C22×C4×C11#4112yes—
238C22×C4×C11#4112yes—
239C22×Dic11—28no—
240C22×Dic11—28no—
241C22×Dic11—28no—
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—21no—
282C22×Dic11—21no—
283C22×Dic11—21no—
284C22×Dic11—21no—
285C22×Dic11—21no—
286C22×Dic11—21no—
287C22×Dic11—21no—
288C22×Dic11—44no—
289C22×Dic11—44no—
290C22×Dic11—44no—
291C22×Dic11—44no—
292C22×Dic11—44no—
293C22×Dic11—44no—
294C22×Dic11—44no—
295C22×Dic11—44no—
296C22×Dic11—44no—
297C22×Dic11—44no—
298C22×Dic11—44no—
299C22×Dic11C2×D412yes—
300C22×Dic11C2×D412yes—
301C22×Dic11C2×D412yes—
302C22×Dic11C2×D412yes—
303C22×Dic11C2×D412yes—
304C22×Dic11C2×D412yes—
305C22×Dic11C2×D412yes—
306C22×Dic11C2×D412yes—
307C22×Dic11#4112yes—
308C22×Dic11#4112yes—
309C11×C4⋊C4—28no—
310C11×C22⋊C4—28no—
311C11×C22⋊C4—28no—
312C11×C22⋊C4—28no—
313C11×C22⋊C4—28no—
314C22⋊Dic11—28no—
315C22⋊Dic11—28no—
316C22⋊Dic11—28no—
317C22⋊Dic11—44no—
318C22⋊Dic11—44no—
319C22⋊Dic11—44no—
320C4⋊Dic11—28no—
321C4⋊Dic11—44no—
322C4⋊Dic11—44no—
323C4⋊Dic11—44no—
324C4×Dic11—28no—
325C4×Dic11—44no—
326C4×Dic11—44no—
327C22×C4×D4—111no—
328C2×#394D1111yescharacteristic
329C2×#389—111no—
330C2×#388—111no—
331C2×#385—111no—
332C2×#385—111no—
333C2×C4×C22⋊C4—111no—
334#1440—111no—
335#1439—111no—
336#1438—111no—
337#1437—111no—
338#1436—111no—
339#1436—111no—
340#1436—111no—
341C22⋊#95—111no—
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—22no—
371C23×C11—22no—
372C23×C11—22no—
373C23×C11—22no—
374C23×C11—22no—
375C23×C11—22no—
376C23×C11—22no—
377C23×C11—22no—
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—41no—
403C23×C11—41no—
404C23×C11—41no—
405C23×C11—41no—
406C23×C11—41no—
407C23×C11—41no—
408C23×C11—41no—
409C23×C11—41no—
410C23×C11C4×D414yes—
411C23×C11C4×D414yes—
412C23×C11C23×C411yescharacteristic
413C23×C11C22×D411yescharacteristic
414C23×C11C22×D411yescharacteristic
415C23×C11C22×D411yescharacteristic
416C23×C11C22×D411yescharacteristic
417C23×C11C2×#4111yescharacteristic
418C23×C11C2×#4111yescharacteristic
419C23×C11C2×#4111yescharacteristic
420C23×C11C2×#4111yescharacteristic
421C23×C11C2×#4111yescharacteristic
422C23×C11C2×#4111yescharacteristic
423C23×C11H(5,𝔽2)11yescharacteristic
424C23×C11H(5,𝔽2)11yescharacteristic
425C23×C112−1+411yescharacteristic
426C23×C112−1+411yescharacteristic
427D4×C11—232no—
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—22no—
436C2×C4×C11—22no—
437C2×C4×C11—22no—
438C2×C4×C11—22no—
439C2×C4×C11—22no—
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—41no—
450C2×C4×C11—41no—
451C2×C4×C11—41no—
452C2×C4×C11—41no—
453C2×C4×C11—41no—
454C2×C4×C11—41no—
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×C11C4×D414yes—
462C2×C4×C11C4×D414yescomplemented
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—22no—
485C2×Dic11—22no—
486C2×Dic11—22no—
487C2×Dic11—416no—
488C2×Dic11—416no—
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×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#12014yes—
520C2×Dic11#12114yes—
521C23×D4C2×D1111yescharacteristic
522C24×C4—111no—
523C24×C4—111no—
524C2×C4×D4—224no—
525C2×C4×D4—224no—
526C2×C4×D4—224no—
527C22×C4⋊C4—111no—
528C22×C4⋊C4—111no—
529C22×C4⋊C4—111no—
530C22×C4⋊C4—111no—
531C22×C4⋊C4C2×D1111yescharacteristic
532C22×C22⋊C4—111no—
533C22×C22⋊C4—111no—
534C22×C22⋊C4—111no—
535C22×C22⋊C4—111no—
536C22×C22⋊C4—111no—
537C22×C22⋊C4—111no—
538C22×C22⋊C4C2×D1111yescharacteristic
539C22×C22⋊C4C2×D1111yescharacteristic
540C22×C22⋊C4C2×D1111yescharacteristic
541C22×C22⋊C4C2×D1111yescharacteristic
542C22×C42—111no—
543C22×C42—111no—
544C22×C42—111no—
545#394Dic1118yescomplemented
546#389—224no—
547#388—224no—
548#385—224no—
549#385—224no—
550C4×C22⋊C4—224no—
551C2×#95—111no—
552C2×#95—111no—
553C2×#95—111no—
554C2×#95—111no—
555C2×#95—111no—
556C2×#95—111no—
557C2×#95—111no—
558C2×#95—111no—
559C2×#95—111no—
560C2×#95—111no—
561C2×#95—111no—
562C2×#95—111no—
563C2×#95—111no—
564C2×#95C2×D1111yescharacteristic
565C22×C11—24no—
566C22×C11—24no—
567C22×C11—24no—
568C22×C11—24no—
569C22×C11—24no—
570C22×C11—24no—
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×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×C11C2×C4×D411yescharacteristic
596C22×C11C2×C4×D411yescharacteristic
597C22×C11C2×C4×D411yescharacteristic
598C22×C11C2×C4×D411yescharacteristic
599C22×C11C4×#4111yescharacteristic
600C22×C11#52011yescharacteristic
601C22×C11#52011yescharacteristic
602C22×C11C2×#12011yescharacteristic
603C22×C11C2×#12111yescharacteristic
604C22×C11#52511yescharacteristic
605C22×C11#52511yescharacteristic
606C22×C11#52511yescharacteristic
607C22×C11#52511yescharacteristic
608C22×C11#52911yescharacteristic
609C22×C11#53211yescharacteristic
610C22×C11#53411yescharacteristic
611C22×C11#53611yescharacteristic
612C22×C11#53911yescharacteristic
613C22×C11#53911yescharacteristic
614C22×C11D4211yescharacteristic
615C22×C11D4211yescharacteristic
616C22×C11#54611yescharacteristic
617C22×C11#54611yescharacteristic
618C22×C11#54711yescharacteristic
619C22×C11#54711yescharacteristic
620C22×C11#54711yescharacteristic
621C22×C11#54811yescharacteristic
622C22×C11#54811yescharacteristic
623C22×C11#54811yescharacteristic
624C22×C11#55111yescharacteristic
625C22×C11#55211yescharacteristic
626C22×C11#55311yescharacteristic
627C22×C11#55311yescharacteristic
628C22×C11#55611yescharacteristic
629C22×C11#55911yescharacteristic
630C4×C11—24no—
631C4×C11—24no—
632C4×C11—42no—
633C4×C11—42no—
634C4×C11—42no—
635Dic11—24no—
636Dic11—24no—
637Dic11—42no—
638Dic11—42no—
639Dic11—42no—
640Dic11—42no—
641Dic11—81no—
642Dic11—81no—
643C25C22×D1111yescharacteristic
644C25C22×D1111yescharacteristic
645C22×D4—22no—
646C22×D4—22no—
647C22×D4—22no—
648C22×D4—22no—
649C22×D4—22no—
650C22×D4—22no—
651C22×D4C2×Dic1114yes—
652C23×C4—111no—
653C23×C4—111no—
654C23×C4—111no—
655C23×C4—111no—
656C23×C4—111no—
657C23×C4—111no—
658C23×C4—114no—
659C23×C4—111no—
660C23×C4—111no—
661C23×C4—222no—
662C23×C4—222no—
663C23×C4—222no—
664C23×C4—222no—
665C23×C4—222no—
666C23×C4—222no—
667C23×C4—222no—
668C23×C4—222no—
669C23×C4—222no—
670C23×C4—441no—
671C23×C4—441no—
672C23×C4—441no—
673C23×C4—441no—
674C23×C4C22×D1111yescharacteristic
675C23×C4C22×D1111yescharacteristic
676C23×C4C22×D1111yescharacteristic
677C23×C4C22×D1111yescharacteristic
678C23×C4C22×D1111yescharacteristic
679C4×D4—2232no—
680C2×C4⋊C4—22no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—114no—
683C2×C4⋊C4—222no—
684C2×C4⋊C4—222no—
685C2×C4⋊C4—222no—
686C2×C4⋊C4—222no—
687C2×C4⋊C4—222no—
688C2×C4⋊C4—222no—
689C2×C4⋊C4—222no—
690C2×C4⋊C4—222no—
691C2×C4⋊C4—222no—
692C2×C4⋊C4—222no—
693C2×C4⋊C4—441no—
694C2×C4⋊C4C2×Dic1114yescomplemented
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—114no—
704C2×C22⋊C4—222no—
705C2×C22⋊C4—222no—
706C2×C22⋊C4—222no—
707C2×C22⋊C4—222no—
708C2×C22⋊C4—222no—
709C2×C22⋊C4—222no—
710C2×C22⋊C4—222no—
711C2×C22⋊C4—222no—
712C2×C22⋊C4—222no—
713C2×C22⋊C4—222no—
714C2×C22⋊C4—222no—
715C2×C22⋊C4—222no—
716C2×C22⋊C4—222no—
717C2×C22⋊C4—441no—
718C2×C22⋊C4—441no—
719C2×C22⋊C4—441no—
720C2×C22⋊C4—441no—
721C2×C22⋊C4C2×Dic1114yescomplemented
722C2×C22⋊C4C2×Dic1114yescomplemented
723C2×C22⋊C4C2×Dic1114yescomplemented
724C2×C22⋊C4C2×Dic1114yescomplemented
725C2×C42—222no—
726C2×C42—222no—
727C2×C42—222no—
728C2×C42—222no—
729C2×C42—222no—
730C2×C42—222no—
731C2×C42—222no—
732C2×C42—441no—
733C2×C42—441no—
734#95—114no—
735#95—222no—
736#95—222no—
737#95—222no—
738#95—222no—
739#95—222no—
740#95—222no—
741#95—222no—
742#95—222no—
743#95—222no—
744#95—222no—
745#95—222no—
746#95—441no—
747#95C2×Dic1114yescomplemented
748C2×C11—44no—
749C2×C11—44no—
750C2×C11C4×#12011yescharacteristic
751C2×C11C4×#12111yescharacteristic
752C2×C11#232211yescharacteristic
753C2×C11#235911yescharacteristic
754C2×C11#236111yescharacteristic
755C2×C11#236111yescharacteristic
756C2×C11#236711yescharacteristic
757C2×C11#241011yescharacteristic
758C2×C11#241511yescharacteristic
759C2×C11#243211yescharacteristic
760C2×C11#245511yescharacteristic
761C2×C11#246011yescharacteristic
762C2×C11#246311yescharacteristic
763C2×C11#246611yescharacteristic
764C2×C11#260211yescharacteristic
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—21no—
785C24—21no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24D4×D1112yes—
790C24D4×D1112yes—
791C24#434112yes—
792C24#434112yes—
793C24C22×Dic1112yes—
794C24C22×Dic1112yes—
795C24C23×D1111yescharacteristic
796C2×D4—28no—
797C2×D4—28no—
798C2×D4—28no—
799C2×D4—28no—
800C2×D4—28no—
801C2×D4—28no—
802C2×D4—28no—
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—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—112no—
830C22×C4—112no—
831C22×C4—112no—
832C22×C4—112no—
833C22×C4—112no—
834C22×C4—112no—
835C22×C4—112no—
836C22×C4—112no—
837C22×C4—112no—
838C22×C4—112no—
839C22×C4—228no—
840C22×C4—228no—
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—228no—
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×C4—444no—
889C22×C4—444no—
890C22×C4—444no—
891C22×C4—444no—
892C22×C4—444no—
893C22×C4—444no—
894C22×C4—444no—
895C22×C4—444no—
896C22×C4—444no—
897C22×C4—444no—
898C22×C4—444no—
899C22×C4D4×D1112yes—
900C22×C4D4×D1112yes—
901C22×C4#434112yes—
902C22×C4#434112yes—
903C22×C4C22×Dic1112yes—
904C22×C4C22×Dic1112yes—
905C22×C4C22×Dic1112yes—
906C22×C4C22×Dic1112yes—
907C22×C4C22×Dic1112yes—
908C4⋊C4—28no—
909C4⋊C4—228no—
910C4⋊C4—444no—
911C4⋊C4—444no—
912C4⋊C4—444no—
913C22⋊C4—28no—
914C22⋊C4—28no—
915C22⋊C4—28no—
916C22⋊C4—28no—
917C22⋊C4—228no—
918C22⋊C4—228no—
919C22⋊C4—228no—
920C22⋊C4—444no—
921C22⋊C4—444no—
922C22⋊C4—444no—
923C42—228no—
924C42—444no—
925C42—444no—
926C11#1418511yescharacteristic, complemented, Sylow
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—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
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—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23D4×Dic1114yes—
996C23D4×Dic1114yes—
997C23C2×D4×D1111yescharacteristic
998C23C2×D4×D1111yescharacteristic
999C23C2×D4×D1111yescharacteristic
1000C23C2×D4×D1111yescharacteristic
1001C23C2×#434111yescharacteristic
1002C23C2×#434111yescharacteristic
1003C23C2×#434111yescharacteristic
1004C23C2×#434111yescharacteristic
1005C23#41×D1111yescharacteristic
1006C23#41×D1111yescharacteristic
1007C23#6704211yescharacteristic
1008C23#6704211yescharacteristic
1009C23#6704311yescharacteristic
1010C23#6704311yescharacteristic
1011C23C23×Dic1111yescharacteristic
1012D4—232no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—114no—
1047C2×C4—114no—
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—222no—
1063C2×C4—222no—
1064C2×C4—222no—
1065C2×C4—222no—
1066C2×C4—222no—
1067C2×C4—222no—
1068C2×C4—222no—
1069C2×C4—222no—
1070C2×C4—222no—
1071C2×C4—222no—
1072C2×C4—4416no—
1073C2×C4—4416no—
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—441no—
1090C2×C4—441no—
1091C2×C4—441no—
1092C2×C4—441no—
1093C2×C4—441no—
1094C2×C4—441no—
1095C2×C4—441no—
1096C2×C4—441no—
1097C2×C4—441no—
1098C2×C4—441no—
1099C2×C4—441no—
1100C2×C4—441no—
1101C2×C4—441no—
1102C2×C4—441no—
1103C2×C4—441no—
1104C2×C4D4×Dic1114yes—
1105C2×C4D4×Dic1114yescomplemented
1106C22—24no—
1107C22—24no—
1108C22—24no—
1109C22—24no—
1110C22—24no—
1111C22—24no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—42no—
1135C22—42no—
1136C22#1062311711yescharacteristic
1137C22#1062311711yescharacteristic
1138C22#1062311711yescharacteristic
1139C22D11×#12011yescharacteristic
1140C22#1062312711yescharacteristic
1141C22#1062312911yescharacteristic
1142C22#1062312911yescharacteristic
1143C22#1062313111yescharacteristic
1144C22D11×#12111yescharacteristic
1145C22#1062313711yescharacteristic
1146C22#1062314011yescharacteristic
1147C22#1062314011yescharacteristic
1148C22#1062314211yescharacteristic
1149C22#1062314211yescharacteristic
1150C22#1062314911yescharacteristic
1151C22#1062314911yescharacteristic
1152C22#1062317911yescharacteristic
1153C22#1062318111yescharacteristic
1154C22#1062318411yescharacteristic
1155C22#1062318511yescharacteristic
1156C22#1062318611yescharacteristic
1157C22#1062318911yescharacteristic
1158C22#1062319611yescharacteristic
1159C22#1062319611yescharacteristic
1160C22#1062320211yescharacteristic
1161C22#1062320711yescharacteristic
1162C22#1062320811yescharacteristic
1163C22#1062321211yescharacteristic
1164C22C2×D4×Dic1111yescharacteristic
1165C22C2×D4×Dic1111yescharacteristic
1166C22C2×D4×Dic1111yescharacteristic
1167C22C2×D4×Dic1111yescharacteristic
1168C22#41×Dic1111yescharacteristic
1169C22#1062335811yescharacteristic
1170C22#1062335811yescharacteristic
1171C4—24no—
1172C4—24no—
1173C4—42no—
1174C4—42no—
1175C4—42no—
1176C4—224no—
1177C4—224no—
1178C4—442no—
1179C4—442no—
1180C4—442no—
1181C4—442no—
1182C4—881no—
1183C4—881no—
1184C2—44no—
1185C2—44no—
1186C2#120×Dic1111yescharacteristic
1187C2#121×Dic1111yescharacteristic
1188C2#1307128811yescharacteristic
1189C2#1307161211yescharacteristic
1190C2#1307163611yescharacteristic
1191C2#1307163611yescharacteristic
1192C2#1307169111yescharacteristic
1193C2#1307198511yescharacteristic
1194C2#1307203811yescharacteristic
1195C2#1307223911yescharacteristic
1196C2#1307249411yescharacteristic
1197C2#1307256311yescharacteristic
1198C2#1307260811yescharacteristic
1199C2#1307264711yescharacteristic
1200C2#1307422911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#394C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#394D11
hypocenterC11#14185
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
2. C2×#10622598C2semidirect
3. C2×#10622564C2semidirect
4. C2×#10622563C2semidirect
5. C2×#10622563C2semidirect
6. C2×C22⋊C4×Dic11C2semidirect
7. #13066865C2semidirect
8. #13066861C2semidirect
10. #13066853C2semidirect
11. #13066850C2semidirect
12. #13066850C2semidirect
13. #13066848C2semidirect
14. #13066838C2semidirect
40. C11×#394C4semidirect
98. C2×C11×C4⋊C4C2×C4semidirect
107. C2×C11×C22⋊C4C2×C4semidirect
108. C2×C11×C22⋊C4C2×C4semidirect
109. C2×C11×C22⋊C4C2×C4semidirect
110. C2×C11×C22⋊C4C2×C4semidirect
151. C11×#95C2×C4semidirect
164. C11⋊#95D4semidirect
462. C2×C4×C11C4×D4semidirect
545. #394Dic11semidirect
694. C2×C4⋊C4C2×Dic11semidirect
721. C2×C22⋊C4C2×Dic11semidirect
722. C2×C22⋊C4C2×Dic11semidirect
723. C2×C22⋊C4C2×Dic11semidirect
724. C2×C22⋊C4C2×Dic11semidirect
747. #95C2×Dic11semidirect
926. C11#14185semidirect
1105. C2×C4D4×Dic11semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic112
C2×#106225982
C2×#106225642
C2×#106225632
C2×C22⋊C4×Dic112
#130668652
#130668612
#130668572
#130668532
#130668502
#130668482
#130668382
C2×C11×#3942
#1418511