Finite Group Databasebeta

← #14675563

Subgroups — #14675563

Order 2816.

2550 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×(C22⋊D11)⋊C4C211yesmaximal, characteristic
2C2×#10622572C211yesmaximal, characteristic
3C2×#10622262C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
6C2×#10622279C211yesmaximal, characteristic, complemented
7C2×#10622279C211yesmaximal, characteristic, complemented
8#13066871C211yesmaximal, characteristic, complemented
9#13066867C211yesmaximal, characteristic, complemented
10#13066864C211yesmaximal, characteristic, complemented
11#13066860C211yesmaximal, characteristic, complemented
12#13066859C211yesmaximal, characteristic, complemented
13#13066855C211yesmaximal, characteristic
14#95×Dic11C211yesmaximal, characteristic, complemented
15C11×#1440C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C24×Dic11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C22×C4×Dic11C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37C2×(C22⋊D11)⋊C4—24no—
38C2×(C22⋊D11)⋊C4—24no—
39C2×(C22⋊D11)⋊C4—24no—
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
54#10622572C418yescomplemented
55C22⋊C4×Dic11—24no—
56C22⋊C4×Dic11—24no—
57#10622279—24no—
58#10622279—24no—
59#10622262—24no—
60C25×C11C2311yescharacteristic
61C24×D11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C22×C22⋊D11—22no—
69C22×C22⋊D11—22no—
70C22×C22⋊D11—22no—
71C22×C22⋊D11—22no—
72C22×C22⋊D11—22no—
73C22×C22⋊D11—22no—
74C22×C22⋊D11C2×C414yes—
75C23×Dic11—22no—
76C23×Dic11—22no—
77C23×Dic11—22no—
78C23×Dic11—22no—
79C23×Dic11—22no—
80C23×Dic11—22no—
81C23×Dic11D414yes—
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C22×C4×D11—22no—
90C22×C4×D11—22no—
91C22×C4×D11—22no—
92C22×C4×D11—22no—
93C22×C4×D11—22no—
94C22×C4×D11—22no—
95C22×C4×D11D414yes—
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4—22no—
98C2×C11×C22⋊C4—22no—
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⋊C4C2×C414yescomplemented
105C2×C22⋊Dic11—22no—
106C2×C22⋊Dic11—22no—
107C2×C22⋊Dic11—22no—
108C2×C22⋊Dic11—22no—
109C2×C22⋊Dic11—22no—
110C2×C22⋊Dic11C2×C414yescomplemented
111C2×(C2×D11)⋊C4—22no—
112C2×(C2×D11)⋊C4—22no—
113C2×(C2×D11)⋊C4—22no—
114C2×(C2×D11)⋊C4—22no—
115C2×(C2×D11)⋊C4—22no—
116C2×(C2×D11)⋊C4—22no—
117C2×(C2×D11)⋊C4—22no—
118C2×(C2×D11)⋊C4—22no—
119C2×(C2×D11)⋊C4—22no—
120C2×(C2×D11)⋊C4—22no—
121C2×(C2×D11)⋊C4—22no—
122C2×(C2×D11)⋊C4—22no—
123C2×(C2×D11)⋊C4—22no—
124C2×(C2×D11)⋊C4C2×C414yescomplemented
125C2×(C2×D11)⋊C4C2×C414yescomplemented
126C2×Dic11⋊C4—22no—
127C2×Dic11⋊C4—22no—
128C2×Dic11⋊C4—22no—
129C2×Dic11⋊C4—22no—
130C2×Dic11⋊C4—22no—
131C2×Dic11⋊C4—22no—
132C2×Dic11⋊C4—22no—
133C2×Dic11⋊C4—22no—
134C2×Dic11⋊C4C2×C414yescomplemented
135C2×C4×Dic11—22no—
136C2×C4×Dic11—22no—
137C2×C4×Dic11—22no—
138C2×C4×Dic11—22no—
139C2×C4×Dic11—22no—
140C2×C4×Dic11—22no—
141C2×C4×Dic11—22no—
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×Dic11D414yes—
149C2×C4×Dic11D414yescomplemented
150(C22⋊D11)⋊C4—232no—
151C11×#95—22no—
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—22no—
164C11⋊#95C2×C414yescomplemented
165C4×#394—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×C11C22×C412yes—
179C24×C11C2×D412yes—
180C24×C11#4112yes—
181C24×C11C2411yescharacteristic
182C23×D11—21no—
183C23×D11—21no—
184C23×D11—21no—
185C23×D11—21no—
186C23×D11—21no—
187C23×D11—21no—
188C23×D11—21no—
189C23×D11—21no—
190C23×D11—21no—
191C23×D11—21no—
192C23×D11—21no—
193C23×D11—21no—
194C23×D11C22×C412yes—
195C23×D11C2×D412yes—
196C23×D11#4112yes—
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—21no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11C22×C412yes—
234C22×C4×C11C22×C412yes—
235C22×C4×C11C2×D412yes—
236C22×C4×C11C2×D412yes—
237C22×C4×C11C2×D412yes—
238C22×C4×C11#4112yes—
239C2×C22⋊D11—28no—
240C2×C22⋊D11—28no—
241C2×C22⋊D11—28no—
242C2×C22⋊D11—28no—
243C2×C22⋊D11—28no—
244C2×C22⋊D11—28no—
245C2×C22⋊D11—28no—
246C22×Dic11—28no—
247C22×Dic11—28no—
248C22×Dic11—28no—
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×Dic11C22×C412yes—
286C22×Dic11C22×C412yes—
287C22×Dic11C22×C412yes—
288C22×Dic11C2×D412yes—
289C22×Dic11C2×D412yes—
290C22×Dic11C2×D412yes—
291C22×Dic11C2×D412yes—
292C22×Dic11C2×D412yes—
293C22×Dic11C2×D412yes—
294C22×Dic11C2×D412yes—
295C22×Dic11#4112yes—
296C22×Dic11#4112yes—
297C22×Dic11#4112yes—
298C22×Dic11#4112yes—
299C22×Dic11#4112yes—
300C22×Dic11#4112yes—
301C22×Dic11#4112yes—
302C2×C4×D11—28no—
303C2×C4×D11—28no—
304C2×C4×D11—28no—
305C2×C4×D11—44no—
306C2×C4×D11—44no—
307C2×C4×D11—44no—
308C2×C4×D11—44no—
309C11×C22⋊C4—28no—
310C11×C22⋊C4—28no—
311C11×C22⋊C4—28no—
312C22⋊Dic11—28no—
313C22⋊Dic11—28no—
314(C2×D11)⋊C4—28no—
315(C2×D11)⋊C4—28no—
316(C2×D11)⋊C4—28no—
317(C2×D11)⋊C4—28no—
318(C2×D11)⋊C4—28no—
319Dic11⋊C4—28no—
320Dic11⋊C4—28no—
321Dic11⋊C4—28no—
322C4×Dic11—28no—
323C4×Dic11—28no—
324C4×Dic11—44no—
325C4×Dic11—44no—
326C4×Dic11—44no—
327C22×C4×D4—111no—
328C2×#394—111no—
329C2×C4×C4⋊C4—111no—
330C2×C4×C22⋊C4—111no—
331C2×C4×C22⋊C4—111no—
332C2×C4×C22⋊C4—111no—
333C2×C4×C22⋊C4—111no—
334#1442—111no—
335#1441—111no—
336#1440—111no—
337#1440D1111yescharacteristic, complemented
338#1439—111no—
339#1439—111no—
340#1438—111no—
341C4×#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—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×C11C4×D414yes—
377C23×C11C23×C411yescharacteristic
378C23×C11C22×D411yescharacteristic
379C23×C11C22×D411yescharacteristic
380C23×C11C22×D411yescharacteristic
381C23×C11C22×D411yescharacteristic
382C23×C11C2×#4111yescharacteristic
383C23×C11C2×#4111yescharacteristic
384C23×C11C2×#4111yescharacteristic
385C23×C11C2×#4111yescharacteristic
386C23×C11C2×#4111yescharacteristic
387C23×C11C2×#4111yescharacteristic
388C23×C11C2×#4111yescharacteristic
389C23×C11C2×#4111yescharacteristic
390C23×C11C2×#4111yescharacteristic
391C23×C11C2×#4111yescharacteristic
392C22×D11—22no—
393C22×D11—22no—
394C22×D11—22no—
395C22×D11—22no—
396C22×D11—22no—
397C22×D11—22no—
398C22×D11—22no—
399C22×D11—22no—
400C22×D11—22no—
401C22×D11—22no—
402C22×D11—22no—
403C22×D11—22no—
404C22×D11—22no—
405C22×D11—22no—
406C22×D11—22no—
407C22×D11—22no—
408C22×D11—22no—
409C22×D11—22no—
410C22×D11—41no—
411C22×D11—41no—
412C22×D11—41no—
413C22×D11—41no—
414C22×D11—41no—
415C22×D11—41no—
416C22×D11—41no—
417C22×D11—41no—
418C22×D11—41no—
419C22×D11—41no—
420C22×D11—41no—
421C22×D11—41no—
422C22×D11—41no—
423C22×D11—41no—
424C22×D11—41no—
425C22×D11—41no—
426C22×D11C4×D414yes—
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—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—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—41no—
456C2×C4×C11—41no—
457C2×C4×C11—41no—
458C2×C4×C11—41no—
459C2×C4×C11—41no—
460C2×C4×C11—41no—
461C2×C4×C11—41no—
462C2×C4×C11—41no—
463C2×C4×C11—41no—
464C2×C4×C11—41no—
465C2×C4×C11—41no—
466C2×C4×C11—41no—
467C2×C4×C11—41no—
468C2×C4×C11—41no—
469C22⋊D11—232no—
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—22no—
488C2×Dic11—22no—
489C2×Dic11—22no—
490C2×Dic11—22no—
491C2×Dic11—22no—
492C2×Dic11—22no—
493C2×Dic11—22no—
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—416no—
511C2×Dic11C4×D414yes—
512C2×Dic11C4×D414yescomplemented
513C2×Dic11#12014yes—
514C2×Dic11#12114yes—
515C2×Dic11#12114yes—
516C2×Dic11#12114yes—
517C2×Dic11#12314yes—
518C2×Dic11#12314yes—
519C2×Dic11#12414yes—
520C4×D11—416no—
521C23×D4—111no—
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×C22⋊C4—111no—
531C22×C22⋊C4—111no—
532C22×C22⋊C4—111no—
533C22×C22⋊C4—111no—
534C22×C22⋊C4—111no—
535C22×C22⋊C4—111no—
536C22×C22⋊C4—111no—
537C22×C22⋊C4C2×D1111yescharacteristic
538C22×C22⋊C4C2×D1111yescharacteristic
539C22×C22⋊C4C2×D1111yescharacteristic
540C22×C42—111no—
541C22×C42—111no—
542C22×C42—111no—
543C22×C42—111no—
544C22×C42—111no—
545#394—118no—
546C4×C4⋊C4—224no—
547C4×C22⋊C4—224no—
548C4×C22⋊C4—224no—
549C4×C22⋊C4—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×#95C2×D1111yescharacteristic
562C2×#95C2×D1111yescharacteristic
563C2×#95C2×D1111yescharacteristic
564C2×#95C2×D1111yescharacteristic
565C22×C11—24no—
566C22×C11—24no—
567C22×C11—24no—
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×C11C2×C4×D411yescharacteristic
581C22×C11C2×C4×D411yescharacteristic
582C22×C11C2×C4×D411yescharacteristic
583C22×C11C2×C4×D411yescharacteristic
584C22×C11C4×#4111yescharacteristic
585C22×C11C4×#4111yescharacteristic
586C22×C11C4×#4111yescharacteristic
587C22×C11C2×#12011yescharacteristic
588C22×C11C2×#12111yescharacteristic
589C22×C11C2×#12111yescharacteristic
590C22×C11C2×#12111yescharacteristic
591C22×C11C2×#12311yescharacteristic
592C22×C11C2×#12311yescharacteristic
593C22×C11#52511yescharacteristic
594C22×C11#52511yescharacteristic
595C22×C11#52511yescharacteristic
596C22×C11#52511yescharacteristic
597C22×C11#52511yescharacteristic
598C22×C11#52511yescharacteristic
599C22×C11#52511yescharacteristic
600C22×C11#52511yescharacteristic
601C22×C11C2×#12411yescharacteristic
602C22×C11#52911yescharacteristic
603C22×C11#52911yescharacteristic
604C22×C11#52911yescharacteristic
605C22×C11#52911yescharacteristic
606C22×C11#52911yescharacteristic
607C22×C11#52911yescharacteristic
608C22×C11#52911yescharacteristic
609C22×C11#52911yescharacteristic
610C22×C11#52911yescharacteristic
611C22×C11#53211yescharacteristic
612C22×C11#53211yescharacteristic
613C22×C11#53211yescharacteristic
614C22×C11#53211yescharacteristic
615C2×D11—24no—
616C2×D11—24no—
617C2×D11—24no—
618C2×D11—42no—
619C2×D11—42no—
620C2×D11—42no—
621C2×D11—42no—
622C2×D11—42no—
623C2×D11—42no—
624C2×D11—42no—
625C2×D11—42no—
626C2×D11—42no—
627C2×D11—42no—
628C2×D11—42no—
629C2×D11—42no—
630C4×C11—42no—
631C4×C11—42no—
632C4×C11—42no—
633C4×C11—42no—
634C4×C11—42no—
635C4×C11—42no—
636Dic11—24no—
637Dic11—24no—
638Dic11—42no—
639Dic11—42no—
640Dic11—42no—
641Dic11—42no—
642Dic11#39418yescomplemented
643C25—111no—
644C25C22×D1111yescharacteristic
645C22×D4—114no—
646C22×D4—222no—
647C22×D4—222no—
648C22×D4—222no—
649C22×D4—222no—
650C22×D4—222no—
651C22×D4—222no—
652C23×C4—111no—
653C23×C4—111no—
654C23×C4—111no—
655C23×C4—114no—
656C23×C4—111no—
657C23×C4—111no—
658C23×C4—111no—
659C23×C4—111no—
660C23×C4—114no—
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—222no—
671C23×C4—222no—
672C23×C4—222no—
673C23×C4C22×D1111yescharacteristic
674C23×C4C22×D1111yescharacteristic
675C23×C4C22×D1111yescharacteristic
676C23×C4C22×D1111yescharacteristic
677C23×C4C22×D1111yescharacteristic
678C23×C4C22×D1111yescharacteristic
679C4×D4—2232no—
680C2×C4⋊C4—114no—
681C2×C4⋊C4—222no—
682C2×C4⋊C4—222no—
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×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—114no—
698C2×C22⋊C4—114no—
699C2×C22⋊C4—114no—
700C2×C22⋊C4—222no—
701C2×C22⋊C4—222no—
702C2×C22⋊C4—222no—
703C2×C22⋊C4—222no—
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—222no—
718C2×C22⋊C4C4×D1114yescomplemented
719C2×C42—114no—
720C2×C42—114no—
721C2×C42—222no—
722C2×C42—222no—
723C2×C42—222no—
724C2×C42—222no—
725C2×C42—222no—
726C2×C42—222no—
727C2×C42—222no—
728C2×C42—222no—
729C2×C42—222no—
730C2×C42—222no—
731C2×C42—222no—
732C2×C42—222no—
733C2×C42—222no—
734#95—22no—
735#95—22no—
736#95—22no—
737#95—22no—
738#95—114no—
739#95—222no—
740#95—222no—
741#95—222no—
742#95—222no—
743#95—222no—
744#95—222no—
745#95—222no—
746#95—222no—
747#95—222no—
748C2×C11—44no—
749C2×C11C4×#12011yescharacteristic
750C2×C11C4×#12111yescharacteristic
751C2×C11C4×#12111yescharacteristic
752C2×C11C4×#12111yescharacteristic
753C2×C11C4×#12311yescharacteristic
754C2×C11C4×#12311yescharacteristic
755C2×C11C4×#12411yescharacteristic
756C2×C11C2×#39411yescharacteristic
757C2×C11#238811yescharacteristic
758C2×C11#239211yescharacteristic
759C2×C11#239211yescharacteristic
760C2×C11#239211yescharacteristic
761C2×C11#239511yescharacteristic
762C2×C11#239511yescharacteristic
763C2×C11#239811yescharacteristic
764D11—44no—
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—112no—
778C24—112no—
779C24—112no—
780C24—221no—
781C24—221no—
782C24—221no—
783C24—221no—
784C24—221no—
785C24—221no—
786C24—221no—
787C24—221no—
788C24—221no—
789C24—221no—
790C24—221no—
791C24—221no—
792C24C2×C4×D1112yes—
793C24D4×D1112yes—
794C24#434112yes—
795C24C23×D1111yescharacteristic
796C2×D4—228no—
797C2×D4—228no—
798C2×D4—228no—
799C2×D4—228no—
800C2×D4—228no—
801C2×D4—228no—
802C2×D4—228no—
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—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—112no—
840C22×C4—112no—
841C22×C4—112no—
842C22×C4—112no—
843C22×C4—112no—
844C22×C4—112no—
845C22×C4—112no—
846C22×C4—112no—
847C22×C4—112no—
848C22×C4—112no—
849C22×C4—112no—
850C22×C4—112no—
851C22×C4—112no—
852C22×C4—112no—
853C22×C4—112no—
854C22×C4—112no—
855C22×C4—112no—
856C22×C4—228no—
857C22×C4—228no—
858C22×C4—228no—
859C22×C4—228no—
860C22×C4—228no—
861C22×C4—228no—
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—221no—
889C22×C4—221no—
890C22×C4—221no—
891C22×C4—221no—
892C22×C4—221no—
893C22×C4—221no—
894C22×C4—444no—
895C22×C4—444no—
896C22×C4—444no—
897C22×C4—444no—
898C22×C4—444no—
899C22×C4—444no—
900C22×C4—444no—
901C22×C4—444no—
902C22×C4C2×C4×D1112yes—
903C22×C4C2×C4×D1112yes—
904C22×C4D4×D1112yes—
905C22×C4D4×D1112yes—
906C22×C4D4×D1112yes—
907C22×C4#434112yes—
908C4⋊C4—228no—
909C4⋊C4—228no—
910C4⋊C4—228no—
911C22⋊C4—28no—
912C22⋊C4—28no—
913C22⋊C4—28no—
914C22⋊C4—228no—
915C22⋊C4—228no—
916C22⋊C4—228no—
917C22⋊C4—228no—
918C22⋊C4—228no—
919C22⋊C4—228no—
920C22⋊C4—228no—
921C42—228no—
922C42—228no—
923C42—444no—
924C42—444no—
925C42—444no—
926C11C4×#39411yescharacteristic, 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—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—114no—
962C23—222no—
963C23—222no—
964C23—222no—
965C23—222no—
966C23—222no—
967C23—222no—
968C23—222no—
969C23—222no—
970C23—222no—
971C23—222no—
972C23—222no—
973C23—222no—
974C23—222no—
975C23—222no—
976C23—222no—
977C23—222no—
978C23—222no—
979C23—222no—
980C23—441no—
981C23—441no—
982C23—441no—
983C23—441no—
984C23—441no—
985C23—441no—
986C23—441no—
987C23—441no—
988C23—441no—
989C23—441no—
990C23—441no—
991C23—441no—
992C23—441no—
993C23—441no—
994C23—441no—
995C23—441no—
996C23(C22⋊D11)⋊C414yes—
997C23C22×C4×D1111yescharacteristic
998C23C2×D4×D1111yescharacteristic
999C23C2×D4×D1111yescharacteristic
1000C23C2×D4×D1111yescharacteristic
1001C23C2×D4×D1111yescharacteristic
1002C23C2×#434111yescharacteristic
1003C23C2×#434111yescharacteristic
1004C23#41×D1111yescharacteristic
1005C23#41×D1111yescharacteristic
1006C23#41×D1111yescharacteristic
1007C23#41×D1111yescharacteristic
1008C23#41×D1111yescharacteristic
1009C23#41×D1111yescharacteristic
1010C23#41×D1111yescharacteristic
1011C23#41×D1111yescharacteristic
1012D4—2232no—
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—41no—
1032C2×C4—41no—
1033C2×C4—41no—
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—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—114no—
1056C2×C4—114no—
1057C2×C4—114no—
1058C2×C4—114no—
1059C2×C4—114no—
1060C2×C4—114no—
1061C2×C4—114no—
1062C2×C4—114no—
1063C2×C4—114no—
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—222no—
1073C2×C4—222no—
1074C2×C4—222no—
1075C2×C4—222no—
1076C2×C4—222no—
1077C2×C4—222no—
1078C2×C4—222no—
1079C2×C4—222no—
1080C2×C4—222no—
1081C2×C4—222no—
1082C2×C4—222no—
1083C2×C4—222no—
1084C2×C4—222no—
1085C2×C4—222no—
1086C2×C4—222no—
1087C2×C4—222no—
1088C2×C4—4416no—
1089C2×C4—4416no—
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×C4—441no—
1105C2×C4—441no—
1106C22—24no—
1107C22—24no—
1108C22—24no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—224no—
1122C22—224no—
1123C22—224no—
1124C22—442no—
1125C22—442no—
1126C22—442no—
1127C22—442no—
1128C22—442no—
1129C22—442no—
1130C22—442no—
1131C22—442no—
1132C22—442no—
1133C22—442no—
1134C22—442no—
1135C22—442no—
1136C22C2×(C22⋊D11)⋊C411yescharacteristic
1137C22#1062305311yescharacteristic
1138C22#1062305311yescharacteristic
1139C22C4×#434111yescharacteristic
1140C22C4×D4×D1111yescharacteristic
1141C22C4×D4×D1111yescharacteristic
1142C22C4×D4×D1111yescharacteristic
1143C22#1062311711yescharacteristic
1144C22D11×#12011yescharacteristic
1145C22#1062312711yescharacteristic
1146C22#1062312711yescharacteristic
1147C22D11×#12111yescharacteristic
1148C22D11×#12111yescharacteristic
1149C22D11×#12111yescharacteristic
1150C22#1062313711yescharacteristic
1151C22#1062313711yescharacteristic
1152C22#1062313711yescharacteristic
1153C22#1062318011yescharacteristic
1154C22#1062318011yescharacteristic
1155C22#1062318011yescharacteristic
1156C22#1062318011yescharacteristic
1157C22D11×#12311yescharacteristic
1158C22D11×#12311yescharacteristic
1159C22#1062318711yescharacteristic
1160C22#1062318711yescharacteristic
1161C22#1062318711yescharacteristic
1162C22#1062318711yescharacteristic
1163C22#1062319911yescharacteristic
1164C22#1062319911yescharacteristic
1165C22D11×#12411yescharacteristic
1166C22#1062321111yescharacteristic
1167C22#1062323711yescharacteristic
1168C22#1062323711yescharacteristic
1169C22#1062323711yescharacteristic
1170C22#1062323711yescharacteristic
1171C4—42no—
1172C4—42no—
1173C4—42no—
1174C4—42no—
1175C4—42no—
1176C4—42no—
1177C4—118no—
1178C4—224no—
1179C4—224no—
1180C4—442no—
1181C4—442no—
1182C4—442no—
1183C4—442no—
1184C2—44no—
1185C2—444no—
1186C2#1307112111yescharacteristic
1187C2#1307112611yescharacteristic
1188C2#1307112811yescharacteristic
1189C2#1307112811yescharacteristic
1190C2#1307113311yescharacteristic
1191C2#1307114311yescharacteristic
1192C2#1307115711yescharacteristic
1193C2D11×#39411yescharacteristic
1194C2#1307183011yescharacteristic
1195C2#1307185311yescharacteristic
1196C2#1307185511yescharacteristic
1197C2#1307185911yescharacteristic
1198C2#1307187411yescharacteristic
1199C2#1307187811yescharacteristic
1200C2#1307190111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1440C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenter#1440D11
hypocenterC11C4×#394
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
3. C2×#10622262C2semidirect
4. C2×C22⋊C4×Dic11C2semidirect
5. C2×C22⋊C4×Dic11C2semidirect
6. C2×#10622279C2semidirect
7. C2×#10622279C2semidirect
8. #13066871C2semidirect
9. #13066867C2semidirect
10. #13066864C2semidirect
11. #13066860C2semidirect
12. #13066859C2semidirect
14. #95×Dic11C2semidirect
15. C11×#1440C2semidirect
54. #10622572C4semidirect
104. C2×C11×C22⋊C4C2×C4semidirect
110. C2×C22⋊Dic11C2×C4semidirect
124. C2×(C2×D11)⋊C4C2×C4semidirect
125. C2×(C2×D11)⋊C4C2×C4semidirect
134. C2×Dic11⋊C4C2×C4semidirect
149. C2×C4×Dic11D4semidirect
164. C11⋊#95C2×C4semidirect
337. #1440D11semidirect
512. C2×Dic11C4×D4semidirect
642. Dic11#394semidirect
718. C2×C22⋊C4C4×D11semidirect
926. C11C4×#394semidirect

Maximal subgroups

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

subgroupindex
C22×(C22⋊D11)⋊C42
C2×#106225722
C2×#106222622
C2×C22⋊C4×Dic112
C2×#106222792
#130668712
#130668672
#130668642
#130668602
#130668592
#130668552
#95×Dic112
C11×#14402
C4×#39411