Finite Group Databasebeta

← #14679240

Subgroups — #14679240

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×(C22⋊D11)⋊C4C211yesmaximal, characteristic
2C2×#10622574C211yesmaximal, characteristic
3C2×#10622586C211yesmaximal, characteristic, complemented
4C2×#10622282C211yesmaximal, characteristic, complemented
5C2×#10622559C211yesmaximal, characteristic, complemented
6C2×#10622602C211yesmaximal, characteristic, complemented
7C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
8#13066863C211yesmaximal, characteristic, complemented
9#13066855C211yesmaximal, characteristic
10#13066852C211yesmaximal, characteristic, complemented
11#13066850C211yesmaximal, characteristic, complemented
12#13066847C211yesmaximal, characteristic, complemented
13#13066847C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×#1439C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C24×Dic11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
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#10622602—24no—
55#10622586—24no—
56#10622574C418yescomplemented
57#10622559—24no—
58C22⋊C4×Dic11—24no—
59#10622282—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—41no—
80C23×Dic11—41no—
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—41no—
95C22×C4×D11—41no—
96C2×C11×C4⋊C4—22no—
97C2×C11×C4⋊C4—22no—
98C2×C11×C4⋊C4—41no—
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—41no—
106C2×C11×C22⋊C4—41no—
107C2×C11×C22⋊C4C2×C414yescomplemented
108C2×C22⋊Dic11—22no—
109C2×C22⋊Dic11—22no—
110C2×C22⋊Dic11—22no—
111C2×C22⋊Dic11—22no—
112C2×C22⋊Dic11—22no—
113C2×C22⋊Dic11C2×C414yescomplemented
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)⋊C4—41no—
125C2×(C2×D11)⋊C4—41no—
126C2×(C2×D11)⋊C4C2×C414yescomplemented
127C2×(C2×D11)⋊C4C2×C414yescomplemented
128C2×(C2×D11)⋊C4D414yes—
129C2×C4⋊Dic11—22no—
130C2×C4⋊Dic11—22no—
131C2×C4⋊Dic11C2×C414yescomplemented
132C2×Dic11⋊C4—22no—
133C2×Dic11⋊C4—22no—
134C2×Dic11⋊C4—22no—
135C2×Dic11⋊C4—22no—
136C2×Dic11⋊C4—22no—
137C2×Dic11⋊C4—22no—
138C2×Dic11⋊C4—22no—
139C2×Dic11⋊C4—22no—
140C2×Dic11⋊C4D414yes—
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×Dic11—41no—
149C2×C4×Dic11—41no—
150(C22⋊D11)⋊C4—232no—
151C11×#95—22no—
152C11×#95—22no—
153C11×#95—41no—
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⋊#95C2×C414yescomplemented
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×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—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—44no—
285C22×Dic11—44no—
286C22×Dic11—44no—
287C22×Dic11—44no—
288C22×Dic11—44no—
289C22×Dic11C22×C412yes—
290C22×Dic11C22×C412yes—
291C22×Dic11C22×C412yes—
292C22×Dic11C2×D412yes—
293C22×Dic11C2×D412yes—
294C22×Dic11C2×D412yes—
295C22×Dic11C2×D412yes—
296C22×Dic11C2×D412yes—
297C22×Dic11C2×D412yes—
298C22×Dic11C2×D412yes—
299C22×Dic11#4112yes—
300C22×Dic11#4112yes—
301C22×Dic11#4112yes—
302C2×C4×D11—28no—
303C2×C4×D11—44no—
304C2×C4×D11—44no—
305C2×C4×D11—44no—
306C2×C4×D11—44no—
307C2×C4×D11—44no—
308C2×C4×D11—44no—
309C11×C4⋊C4—44no—
310C11×C22⋊C4—28no—
311C11×C22⋊C4—28no—
312C11×C22⋊C4—44no—
313C22⋊Dic11—28no—
314C22⋊Dic11—28no—
315(C2×D11)⋊C4—28no—
316(C2×D11)⋊C4—28no—
317(C2×D11)⋊C4—28no—
318(C2×D11)⋊C4—44no—
319(C2×D11)⋊C4—44no—
320C4⋊Dic11—28no—
321Dic11⋊C4—28no—
322Dic11⋊C4—44no—
323Dic11⋊C4—44no—
324C4×Dic11—28no—
325C4×Dic11—44no—
326C4×Dic11—44no—
327C22×C4×D4—111no—
328C2×#394—111no—
329C2×#389—111no—
330C2×#388—111no—
331C2×#385—111no—
332C2×#385—111no—
333C2×C4×C22⋊C4—111no—
334#1440—111no—
335#1439D1111yescharacteristic, complemented
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—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×C11H(5,𝔽2)11yescharacteristic
389C23×C11H(5,𝔽2)11yescharacteristic
390C23×C112−1+411yescharacteristic
391C23×C112−1+411yescharacteristic
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—41no—
443C2×C4×C11—41no—
444C2×C4×C11—41no—
445C2×C4×C11—41no—
446C2×C4×C11—41no—
447C2×C4×C11—41no—
448C2×C4×C11—41no—
449C2×C4×C11—41no—
450C2×C4×C11—41no—
451C2×C4×C11—41no—
452C2×C4×C11—41no—
453C2×C4×C11—41no—
454C2×C4×C11—41no—
455C2×C4×C11—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×C11C4×D414yescomplemented
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—22no—
495C2×Dic11—22no—
496C2×Dic11—22no—
497C2×Dic11—22no—
498C2×Dic11—22no—
499C2×Dic11—22no—
500C2×Dic11—416no—
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×Dic11C4×D414yes—
518C2×Dic11#12014yes—
519C2×Dic11#12114yes—
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×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⋊C4—111no—
539C22×C22⋊C4C2×D1111yescharacteristic
540C22×C22⋊C4C2×D1111yescharacteristic
541C22×C22⋊C4C2×D1111yescharacteristic
542C22×C42—111no—
543C22×C42—111no—
544C22×C42—111no—
545#394—118no—
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×#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×C11#52011yescharacteristic
586C22×C11#52011yescharacteristic
587C22×C11C2×#12011yescharacteristic
588C22×C11C2×#12111yescharacteristic
589C22×C11#52511yescharacteristic
590C22×C11#52511yescharacteristic
591C22×C11#52511yescharacteristic
592C22×C11#52511yescharacteristic
593C22×C11#52911yescharacteristic
594C22×C11#53211yescharacteristic
595C22×C11#53411yescharacteristic
596C22×C11#53611yescharacteristic
597C22×C11#53911yescharacteristic
598C22×C11#53911yescharacteristic
599C22×C11D4211yescharacteristic
600C22×C11D4211yescharacteristic
601C22×C11#54611yescharacteristic
602C22×C11#54611yescharacteristic
603C22×C11#54711yescharacteristic
604C22×C11#54711yescharacteristic
605C22×C11#54711yescharacteristic
606C22×C11#54811yescharacteristic
607C22×C11#54811yescharacteristic
608C22×C11#54811yescharacteristic
609C22×C11#55111yescharacteristic
610C22×C11#55211yescharacteristic
611C22×C11#55311yescharacteristic
612C22×C11#55311yescharacteristic
613C22×C11#55611yescharacteristic
614C22×C11#55911yescharacteristic
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—24no—
631C4×C11—42no—
632C4×C11—42no—
633C4×C11—42no—
634C4×C11—81no—
635C4×C11—81no—
636Dic11—24no—
637Dic11—24no—
638Dic11—24no—
639Dic11—42no—
640Dic11—42no—
641Dic11—42no—
642Dic11—42no—
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—111no—
656C23×C4—111no—
657C23×C4—111no—
658C23×C4—111no—
659C23×C4—114no—
660C23×C4—222no—
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—441no—
670C23×C4—441no—
671C23×C4—441no—
672C23×C4—441no—
673C23×C4C22×D1111yescharacteristic
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—41no—
683C2×C4⋊C4—114no—
684C2×C4⋊C4—114no—
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—222no—
694C2×C4⋊C4—222no—
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—41no—
702C2×C22⋊C4—41no—
703C2×C22⋊C4—114no—
704C2×C22⋊C4—114no—
705C2×C22⋊C4—114no—
706C2×C22⋊C4—114no—
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⋊C4—222no—
719C2×C22⋊C4—222no—
720C2×C22⋊C4—222no—
721C2×C22⋊C4—222no—
722C2×C22⋊C4—441no—
723C2×C22⋊C4—441no—
724C2×C22⋊C4C4×D1114yescomplemented
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—22no—
735#95—22no—
736#95—41no—
737#95—114no—
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×C11#232211yescharacteristic
752C2×C11#235911yescharacteristic
753C2×C11#236111yescharacteristic
754C2×C11#236111yescharacteristic
755C2×C11#236711yescharacteristic
756C2×C11#241011yescharacteristic
757C2×C11#241511yescharacteristic
758C2×C11#243211yescharacteristic
759C2×C11#245511yescharacteristic
760C2×C11#246011yescharacteristic
761C2×C11#246311yescharacteristic
762C2×C11#246611yescharacteristic
763C2×C11#260211yescharacteristic
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#434312yes—
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—228no—
853C22×C4—228no—
854C22×C4—228no—
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—221no—
889C22×C4—221no—
890C22×C4—221no—
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×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—44no—
909C4⋊C4—228no—
910C4⋊C4—228no—
911C4⋊C4—444no—
912C4⋊C4—444no—
913C22⋊C4—28no—
914C22⋊C4—28no—
915C22⋊C4—44no—
916C22⋊C4—228no—
917C22⋊C4—228no—
918C22⋊C4—228no—
919C22⋊C4—228no—
920C22⋊C4—228no—
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—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#6694614yes—
997C23C22×C4×D1111yescharacteristic
998C23C2×D4×D1111yescharacteristic
999C23C2×D4×D1111yescharacteristic
1000C23C2×D4×D1111yescharacteristic
1001C23C2×D4×D1111yescharacteristic
1002C23C2×#434111yescharacteristic
1003C23#6703711yescharacteristic
1004C23#6703711yescharacteristic
1005C23C2×#434311yescharacteristic
1006C23#41×D1111yescharacteristic
1007C23#41×D1111yescharacteristic
1008C23#41×D1111yescharacteristic
1009C23#41×D1111yescharacteristic
1010C23#6704311yescharacteristic
1011C23#6704311yescharacteristic
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—41no—
1029C2×C4—41no—
1030C2×C4—41no—
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—114no—
1055C2×C4—114no—
1056C2×C4—114no—
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—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—4416no—
1088C2×C4—4416no—
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×C4—441no—
1105C2×C4(C22⋊D11)⋊C414yescomplemented
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
1137C22C2×#6694611yescharacteristic
1138C22#1062305311yescharacteristic
1139C22C4×D4×D1111yescharacteristic
1140C22C4×D4×D1111yescharacteristic
1141C22#1062307711yescharacteristic
1142C22#1062307711yescharacteristic
1143C22D11×#12011yescharacteristic
1144C22#1062312011yescharacteristic
1145C22#1062312111yescharacteristic
1146C22#1062312711yescharacteristic
1147C22#1062312911yescharacteristic
1148C22#1062313211yescharacteristic
1149C22D11×#12111yescharacteristic
1150C22#1062314111yescharacteristic
1151C22#1062314211yescharacteristic
1152C22#1062314311yescharacteristic
1153C22#1062314511yescharacteristic
1154C22#1062315511yescharacteristic
1155C22#1062315811yescharacteristic
1156C22#1062315811yescharacteristic
1157C22#1062315811yescharacteristic
1158C22#1062317611yescharacteristic
1159C22#1062317611yescharacteristic
1160C22#1062317911yescharacteristic
1161C22#1062318611yescharacteristic
1162C22#1062318611yescharacteristic
1163C22#1062318711yescharacteristic
1164C22#1062319511yescharacteristic
1165C22#1062320811yescharacteristic
1166C22#1062320811yescharacteristic
1167C22#1062321011yescharacteristic
1168C22#1062323311yescharacteristic
1169C22#1062323911yescharacteristic
1170C22#1062324811yescharacteristic
1171C4—24no—
1172C4—42no—
1173C4—42no—
1174C4—42no—
1175C4—81no—
1176C4—81no—
1177C4—224no—
1178C4—224no—
1179C4—224no—
1180C4—442no—
1181C4—442no—
1182C4—442no—
1183C4—442no—
1184C2—44no—
1185C2—444no—
1186C2#1307111711yescharacteristic
1187C2#1307112211yescharacteristic
1188C2#1307128411yescharacteristic
1189C2#1307160511yescharacteristic
1190C2#1307162711yescharacteristic
1191C2#1307163711yescharacteristic
1192C2#1307168211yescharacteristic
1193C2#1307198311yescharacteristic
1194C2#1307204011yescharacteristic
1195C2#1307223911yescharacteristic
1196C2#1307249911yescharacteristic
1197C2#1307257111yescharacteristic
1198C2#1307261311yescharacteristic
1199C2#1307265511yescharacteristic
1200C2#1307423111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenter#1439D11
hypocenterC11#14185
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
3. C2×#10622586C2semidirect
4. C2×#10622282C2semidirect
5. C2×#10622559C2semidirect
6. C2×#10622602C2semidirect
7. C2×C22⋊C4×Dic11C2semidirect
8. #13066863C2semidirect
10. #13066852C2semidirect
11. #13066850C2semidirect
12. #13066847C2semidirect
13. #13066847C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1439C2semidirect
56. #10622574C4semidirect
107. C2×C11×C22⋊C4C2×C4semidirect
113. C2×C22⋊Dic11C2×C4semidirect
126. C2×(C2×D11)⋊C4C2×C4semidirect
127. C2×(C2×D11)⋊C4C2×C4semidirect
131. C2×C4⋊Dic11C2×C4semidirect
163. C11⋊#95C2×C4semidirect
164. C11⋊#95D4semidirect
335. #1439D11semidirect
468. C2×C4×C11C4×D4semidirect
724. C2×C22⋊C4C4×D11semidirect
926. C11#14185semidirect
1105. C2×C4(C22⋊D11)⋊C4semidirect

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×#106225742
C2×#106225862
C2×#106222822
C2×#106225592
C2×#106226022
C2×C22⋊C4×Dic112
#130668632
#130668552
#130668522
#130668502
#130668472
(C2×D11)⋊#952
C11×#14392
#1418511