Finite Group Databasebeta

← #14679254

Subgroups — #14679254

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×C4×D44C211yesmaximal, characteristic
2C2×#10622285C211yesmaximal, characteristic
3C2×#10622260C211yesmaximal, characteristic, complemented
4C2×#10622282C211yesmaximal, characteristic, complemented
5C2×#10622602C211yesmaximal, characteristic, complemented
6C2×#10622602C211yesmaximal, characteristic, complemented
7C2×#10622279C211yesmaximal, characteristic, complemented
8#13066864C211yesmaximal, characteristic, complemented
9#13066860C211yesmaximal, characteristic, complemented
10#13066856C211yesmaximal, characteristic
11#13066852C211yesmaximal, characteristic, complemented
12#13066850C211yesmaximal, characteristic, complemented
13#13066849C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×#1436C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×C4⋊Dic11C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×C4×Dic11C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37C2×C4×D44—24no—
38C2×C4×D44—24no—
39C2×C4×D44—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#10622602—24no—
56#10622285C418yescomplemented
57#10622282—24no—
58#10622279—24no—
59#10622260—24no—
60C24×D11C2311yescharacteristic
61C24×D11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C22×D44—22no—
76C22×D44—22no—
77C22×D44—22no—
78C22×D44—22no—
79C22×D44—22no—
80C22×D44—22no—
81C22×D44C2×C414yes—
82C22×C4×D11—22no—
83C22×C4×D11—22no—
84C22×C4×D11—22no—
85C22×C4×D11—22no—
86C22×C4×D11—22no—
87C22×C4×D11—22no—
88C22×C4×D11—22no—
89C22×C4×D11—22no—
90C22×C4×D11—22no—
91C22×C4×D11—41no—
92C22×C4×D11—41no—
93C22×C4×D11—41no—
94C22×C4×D11—41no—
95C22×C4×D11D414yes—
96C2×C11×C4⋊C4—22no—
97C2×C11×C4⋊C4—22no—
98C2×C11×C4⋊C4—22no—
99C2×C42×C11—22no—
100C2×C42×C11—22no—
101C2×C42×C11—22no—
102C2×(C2×D11)⋊C4—22no—
103C2×(C2×D11)⋊C4—22no—
104C2×(C2×D11)⋊C4—22no—
105C2×(C2×D11)⋊C4—22no—
106C2×(C2×D11)⋊C4—22no—
107C2×(C2×D11)⋊C4—22no—
108C2×(C2×D11)⋊C4—22no—
109C2×(C2×D11)⋊C4—22no—
110C2×(C2×D11)⋊C4—22no—
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—41no—
124C2×(C2×D11)⋊C4—41no—
125C2×(C2×D11)⋊C4—41no—
126C2×(C2×D11)⋊C4—41no—
127C2×(C2×D11)⋊C4C2×C414yescomplemented
128C2×(C2×D11)⋊C4C2×C414yescomplemented
129C2×(C2×D11)⋊C4C2×C414yescomplemented
130C2×(C2×D11)⋊C4C2×C414yescomplemented
131C2×(C2×D11)⋊C4D414yes—
132C2×C4⋊Dic11—22no—
133C2×C4⋊Dic11—22no—
134C2×C4⋊Dic11D414yes—
135C2×Dic11⋊C4—22no—
136C2×Dic11⋊C4—22no—
137C2×Dic11⋊C4—22no—
138C2×Dic11⋊C4—22no—
139C2×Dic11⋊C4—22no—
140C2×Dic11⋊C4—22no—
141C2×Dic11⋊C4—22no—
142C2×Dic11⋊C4—41no—
143C2×Dic11⋊C4C2×C414yescomplemented
144C2×C4×Dic11—22no—
145C2×C4×Dic11—22no—
146C2×C4×Dic11—22no—
147C2×C4×Dic11—22no—
148C2×C4×Dic11—41no—
149C2×C4×Dic11—41no—
150C4×D44—232no—
151C11×#95—22no—
152C11×#95—22no—
153C11×#95—22no—
154C11×#95—22no—
155C11×#95C2×C414yescomplemented
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×C11C2411yescharacteristic
167C23×D11—21no—
168C23×D11—21no—
169C23×D11—21no—
170C23×D11—21no—
171C23×D11—21no—
172C23×D11—21no—
173C23×D11—21no—
174C23×D11—21no—
175C23×D11—21no—
176C23×D11—21no—
177C23×D11—21no—
178C23×D11—21no—
179C23×D11—21no—
180C23×D11—21no—
181C23×D11—21no—
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×D11C22×C412yes—
192C23×D11C22×C412yes—
193C23×D11C2×D412yes—
194C23×D11C2×D412yes—
195C23×D11#4112yes—
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×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11C22×C412yes—
237C22×C4×C11C22×C412yes—
238C22×C4×C11C22×C412yes—
239C22×C4×C11C2×D412yes—
240C22×C4×C11C2×D412yes—
241C22×C4×C11C2×D412yes—
242C22×C4×C11C2×D412yes—
243C22×C4×C11#4112yes—
244C22×C4×C11#4112yes—
245C22×C4×C11#4112yes—
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×Dic11C22×C412yes—
280C22×Dic11C22×C412yes—
281C22×Dic11C2×D412yes—
282C22×Dic11C2×D412yes—
283C22×Dic11C2×D412yes—
284C22×Dic11C2×D412yes—
285C22×Dic11C2×D412yes—
286C22×Dic11C2×D412yes—
287C22×Dic11#4112yes—
288C2×D44—28no—
289C2×D44—28no—
290C2×D44—28no—
291C2×D44—28no—
292C2×D44—28no—
293C2×D44—28no—
294C2×D44—28no—
295C2×C4×D11—28no—
296C2×C4×D11—28no—
297C2×C4×D11—28no—
298C2×C4×D11—44no—
299C2×C4×D11—44no—
300C2×C4×D11—44no—
301C2×C4×D11—44no—
302C2×C4×D11—44no—
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—
310C42×C11—28no—
311(C2×D11)⋊C4—28no—
312(C2×D11)⋊C4—28no—
313(C2×D11)⋊C4—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—44no—
319(C2×D11)⋊C4—44no—
320(C2×D11)⋊C4—44no—
321C4⋊Dic11—28no—
322Dic11⋊C4—28no—
323Dic11⋊C4—44no—
324Dic11⋊C4—44no—
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#1439—111no—
336#1438—111no—
337#1437—111no—
338#1436—111no—
339#1436—111no—
340#1436D1111yescharacteristic, complemented
341C22⋊#95—111no—
342C23×C11C23×C411yescharacteristic
343C23×C11C22×D411yescharacteristic
344C23×C11C22×D411yescharacteristic
345C23×C11C22×D411yescharacteristic
346C23×C11C22×D411yescharacteristic
347C23×C11C2×#4111yescharacteristic
348C23×C11C2×#4111yescharacteristic
349C23×C11C2×#4111yescharacteristic
350C23×C11C2×#4111yescharacteristic
351C23×C11C2×#4111yescharacteristic
352C23×C11C2×#4111yescharacteristic
353C23×C11H(5,𝔽2)11yescharacteristic
354C23×C11H(5,𝔽2)11yescharacteristic
355C23×C112−1+411yescharacteristic
356C23×C112−1+411yescharacteristic
357C22×D11—22no—
358C22×D11—22no—
359C22×D11—22no—
360C22×D11—22no—
361C22×D11—22no—
362C22×D11—22no—
363C22×D11—22no—
364C22×D11—22no—
365C22×D11—22no—
366C22×D11—22no—
367C22×D11—22no—
368C22×D11—22no—
369C22×D11—22no—
370C22×D11—22no—
371C22×D11—22no—
372C22×D11—22no—
373C22×D11—22no—
374C22×D11—22no—
375C22×D11—22no—
376C22×D11—22no—
377C22×D11—22no—
378C22×D11—22no—
379C22×D11—22no—
380C22×D11—22no—
381C22×D11—22no—
382C22×D11—22no—
383C22×D11—22no—
384C22×D11—22no—
385C22×D11—22no—
386C22×D11—22no—
387C22×D11—22no—
388C22×D11—22no—
389C22×D11—22no—
390C22×D11—22no—
391C22×D11—22no—
392C22×D11—22no—
393C22×D11—41no—
394C22×D11—41no—
395C22×D11—41no—
396C22×D11—41no—
397C22×D11—41no—
398C22×D11—41no—
399C22×D11—41no—
400C22×D11—41no—
401C22×D11—41no—
402C22×D11—41no—
403C22×D11—41no—
404C22×D11—41no—
405C22×D11—41no—
406C22×D11—41no—
407C22×D11—41no—
408C22×D11—41no—
409C22×D11—41no—
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×D11C4×D414yes—
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—22no—
446C2×C4×C11—22no—
447C2×C4×C11—22no—
448C2×C4×C11—22no—
449C2×C4×C11—22no—
450C2×C4×C11—22no—
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—
469C2×C4×C11—41no—
470C2×C4×C11—41no—
471C2×C4×C11—41no—
472C2×C4×C11—41no—
473C2×C4×C11—41no—
474C2×C4×C11C4×D414yes—
475C2×C4×C11#12114yes—
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—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×Dic11C4×D414yescomplemented
517C2×Dic11#12014yes—
518D44—232no—
519C4×D11—416no—
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⋊C4—111no—
540C22×C22⋊C4—111no—
541C22×C22⋊C4—111no—
542C22×C42—111no—
543C22×C42—111no—
544C22×C42C2×D1111yescharacteristic
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×#95C2×D1111yescharacteristic
561C2×#95C2×D1111yescharacteristic
562C2×#95C2×D1111yescharacteristic
563C2×#95C2×D1111yescharacteristic
564C2×#95C2×D1111yescharacteristic
565C22×C11C2×C4×D411yescharacteristic
566C22×C11C2×C4×D411yescharacteristic
567C22×C11C2×C4×D411yescharacteristic
568C22×C11C2×C4×D411yescharacteristic
569C22×C11C4×#4111yescharacteristic
570C22×C11#52011yescharacteristic
571C22×C11#52011yescharacteristic
572C22×C11C2×#12011yescharacteristic
573C22×C11C2×#12111yescharacteristic
574C22×C11#52511yescharacteristic
575C22×C11#52511yescharacteristic
576C22×C11#52511yescharacteristic
577C22×C11#52511yescharacteristic
578C22×C11#52911yescharacteristic
579C22×C11#53211yescharacteristic
580C22×C11#53411yescharacteristic
581C22×C11#53611yescharacteristic
582C22×C11#53911yescharacteristic
583C22×C11#53911yescharacteristic
584C22×C11D4211yescharacteristic
585C22×C11D4211yescharacteristic
586C22×C11#54611yescharacteristic
587C22×C11#54611yescharacteristic
588C22×C11#54711yescharacteristic
589C22×C11#54711yescharacteristic
590C22×C11#54711yescharacteristic
591C22×C11#54811yescharacteristic
592C22×C11#54811yescharacteristic
593C22×C11#54811yescharacteristic
594C22×C11#55111yescharacteristic
595C22×C11#55211yescharacteristic
596C22×C11#55311yescharacteristic
597C22×C11#55311yescharacteristic
598C22×C11#55611yescharacteristic
599C22×C11#55911yescharacteristic
600C2×D11—24no—
601C2×D11—24no—
602C2×D11—24no—
603C2×D11—24no—
604C2×D11—24no—
605C2×D11—24no—
606C2×D11—42no—
607C2×D11—42no—
608C2×D11—42no—
609C2×D11—42no—
610C2×D11—42no—
611C2×D11—42no—
612C2×D11—42no—
613C2×D11—42no—
614C2×D11—42no—
615C2×D11—42no—
616C2×D11—42no—
617C2×D11—42no—
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—24no—
632C4×C11—42no—
633C4×C11—42no—
634C4×C11—42no—
635C4×C11—42no—
636C4×C11—81no—
637Dic11—24no—
638Dic11—24no—
639Dic11—42no—
640Dic11—42no—
641Dic11—42no—
642Dic11—81no—
643C25—111no—
644C25—111no—
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—114no—
658C23×C4—111no—
659C23×C4—222no—
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—441no—
669C23×C4—441no—
670C23×C4—441no—
671C23×C4—441no—
672C23×C4C22×D1111yescharacteristic
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—22no—
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—441no—
695C2×C22⋊C4—114no—
696C2×C22⋊C4—114no—
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⋊C4—222no—
719C2×C22⋊C4—222no—
720C2×C22⋊C4—222no—
721C2×C22⋊C4—441no—
722C2×C22⋊C4—441no—
723C2×C22⋊C4—441no—
724C2×C22⋊C4—441no—
725C2×C42—22no—
726C2×C42—22no—
727C2×C42—22no—
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—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—441no—
747#95C4×D1114yescomplemented
748C2×C11C4×#12011yescharacteristic
749C2×C11C4×#12111yescharacteristic
750C2×C11#232211yescharacteristic
751C2×C11#235911yescharacteristic
752C2×C11#236111yescharacteristic
753C2×C11#236111yescharacteristic
754C2×C11#236711yescharacteristic
755C2×C11#241011yescharacteristic
756C2×C11#241511yescharacteristic
757C2×C11#243211yescharacteristic
758C2×C11#245511yescharacteristic
759C2×C11#246011yescharacteristic
760C2×C11#246311yescharacteristic
761C2×C11#246611yescharacteristic
762C2×C11#260211yescharacteristic
763D11—44no—
764D11—44no—
765C24—112no—
766C24—112no—
767C24—112no—
768C24—112no—
769C24—112no—
770C24—112no—
771C24—221no—
772C24—221no—
773C24—221no—
774C24—221no—
775C24—221no—
776C24—221no—
777C24—221no—
778C24—221no—
779C24—221no—
780C24—221no—
781C24—221no—
782C24—221no—
783C24—221no—
784C24—221no—
785C24—221no—
786C24—221no—
787C24—221no—
788C24—221no—
789C24—221no—
790C24—221no—
791C24—221no—
792C24—221no—
793C24—221no—
794C24—221no—
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—21no—
840C22×C4—21no—
841C22×C4—21no—
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—228no—
852C22×C4—228no—
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—228no—
880C22×C4—221no—
881C22×C4—221no—
882C22×C4—221no—
883C22×C4—221no—
884C22×C4—221no—
885C22×C4—221no—
886C22×C4—221no—
887C22×C4—444no—
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×C4C2×C4×D1112yes—
899C22×C4C2×C4×D1112yes—
900C22×C4C2×C4×D1112yes—
901C22×C4#433912yes—
902C22×C4#433912yes—
903C22×C4D4×D1112yes—
904C22×C4D4×D1112yes—
905C22×C4D4×D1112yes—
906C22×C4D4×D1112yes—
907C22×C4#434312yes—
908C4⋊C4—44no—
909C4⋊C4—228no—
910C4⋊C4—228no—
911C4⋊C4—444no—
912C4⋊C4—444no—
913C22⋊C4—228no—
914C22⋊C4—228no—
915C22⋊C4—228no—
916C22⋊C4—228no—
917C22⋊C4—228no—
918C22⋊C4—228no—
919C22⋊C4—228no—
920C22⋊C4—444no—
921C22⋊C4—444no—
922C22⋊C4—444no—
923C42—28no—
924C42—444no—
925C42—444no—
926C11#1418511yescharacteristic, complemented, Sylow
927C23—114no—
928C23—114no—
929C23—222no—
930C23—222no—
931C23—222no—
932C23—222no—
933C23—222no—
934C23—222no—
935C23—222no—
936C23—222no—
937C23—222no—
938C23—222no—
939C23—222no—
940C23—222no—
941C23—222no—
942C23—222no—
943C23—222no—
944C23—222no—
945C23—222no—
946C23—222no—
947C23—222no—
948C23—222no—
949C23—222no—
950C23—222no—
951C23—222no—
952C23—222no—
953C23—222no—
954C23—222no—
955C23—222no—
956C23—222no—
957C23—222no—
958C23—222no—
959C23—222no—
960C23—222no—
961C23—222no—
962C23—222no—
963C23—222no—
964C23—222no—
965C23—441no—
966C23—441no—
967C23—441no—
968C23—441no—
969C23—441no—
970C23—441no—
971C23—441no—
972C23—441no—
973C23—441no—
974C23—441no—
975C23—441no—
976C23—441no—
977C23—441no—
978C23—441no—
979C23—441no—
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—441no—
997C23C22×C4×D1111yescharacteristic
998C23C2×#433911yescharacteristic
999C23C2×#433911yescharacteristic
1000C23C2×D4×D1111yescharacteristic
1001C23C2×D4×D1111yescharacteristic
1002C23C2×D4×D1111yescharacteristic
1003C23C2×D4×D1111yescharacteristic
1004C23C2×#434311yescharacteristic
1005C23#6704011yescharacteristic
1006C23#41×D1111yescharacteristic
1007C23#41×D1111yescharacteristic
1008C23#41×D1111yescharacteristic
1009C23#6704211yescharacteristic
1010C23#6704211yescharacteristic
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—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
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—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—114no—
1061C2×C4—114no—
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—4416no—
1084C2×C4—4416no—
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×C4#6693714yes—
1105C2×C4#6694614yes—
1106C22—224no—
1107C22—224no—
1108C22—224no—
1109C22—224no—
1110C22—224no—
1111C22—224no—
1112C22—442no—
1113C22—442no—
1114C22—442no—
1115C22—442no—
1116C22—442no—
1117C22—442no—
1118C22—442no—
1119C22—442no—
1120C22—442no—
1121C22—442no—
1122C22—442no—
1123C22—442no—
1124C22—442no—
1125C22—442no—
1126C22—442no—
1127C22—442no—
1128C22—442no—
1129C22—442no—
1130C22—442no—
1131C22—442no—
1132C22—442no—
1133C22—442no—
1134C22—442no—
1135C22—442no—
1136C22C4×#433911yescharacteristic
1137C22C2×#6693711yescharacteristic
1138C22C2×#6694611yescharacteristic
1139C22#1062303811yescharacteristic
1140C22#1062305411yescharacteristic
1141C22#1062305811yescharacteristic
1142C22#1062305911yescharacteristic
1143C22C4×D4×D1111yescharacteristic
1144C22C4×D4×D1111yescharacteristic
1145C22C4×D4×D1111yescharacteristic
1146C22#1062307811yescharacteristic
1147C22#1062307911yescharacteristic
1148C22#1062308111yescharacteristic
1149C22#1062308111yescharacteristic
1150C22#1062308311yescharacteristic
1151C22#1062310511yescharacteristic
1152C22#1062311211yescharacteristic
1153C22#1062311511yescharacteristic
1154C22#1062311611yescharacteristic
1155C22D11×#12011yescharacteristic
1156C22#1062314011yescharacteristic
1157C22#1062314011yescharacteristic
1158C22#1062315811yescharacteristic
1159C22#1062315811yescharacteristic
1160C22#1062315911yescharacteristic
1161C22#1062316411yescharacteristic
1162C22#1062318411yescharacteristic
1163C22#1062318611yescharacteristic
1164C22#1062318711yescharacteristic
1165C22#1062320811yescharacteristic
1166C22#1062322311yescharacteristic
1167C22#1062322611yescharacteristic
1168C22#1062323811yescharacteristic
1169C22#1062324011yescharacteristic
1170C22#1062325711yescharacteristic
1171C4—24no—
1172C4—24no—
1173C4—42no—
1174C4—42no—
1175C4—42no—
1176C4—42no—
1177C4—81no—
1178C4—224no—
1179C4—224no—
1180C4—442no—
1181C4—442no—
1182C4—442no—
1183C4—881no—
1184C2—444no—
1185C2—444no—
1186C2#1307111711yescharacteristic
1187C2C4×#6693711yescharacteristic
1188C2#1307128911yescharacteristic
1189C2#1307161311yescharacteristic
1190C2#1307162911yescharacteristic
1191C2#1307163111yescharacteristic
1192C2#1307168511yescharacteristic
1193C2#1307199311yescharacteristic
1194C2#1307204811yescharacteristic
1195C2#1307224211yescharacteristic
1196C2#1307250011yescharacteristic
1197C2#1307256511yescharacteristic
1198C2#1307261011yescharacteristic
1199C2#1307265911yescharacteristic
1200C2#1307422611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1436D11
hypocenterC11#14185
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
3. C2×#10622260C2semidirect
4. C2×#10622282C2semidirect
5. C2×#10622602C2semidirect
6. C2×#10622602C2semidirect
7. C2×#10622279C2semidirect
8. #13066864C2semidirect
9. #13066860C2semidirect
11. #13066852C2semidirect
12. #13066850C2semidirect
13. #13066849C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1436C2semidirect
56. #10622285C4semidirect
127. C2×(C2×D11)⋊C4C2×C4semidirect
128. C2×(C2×D11)⋊C4C2×C4semidirect
129. C2×(C2×D11)⋊C4C2×C4semidirect
130. C2×(C2×D11)⋊C4C2×C4semidirect
143. C2×Dic11⋊C4C2×C4semidirect
155. C11×#95C2×C4semidirect
164. C11⋊#95D4semidirect
340. #1436D11semidirect
516. C2×Dic11C4×D4semidirect
747. #95C4×D11semidirect
926. C11#14185semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D442
C2×#106222852
C2×#106222602
C2×#106222822
C2×#106226022
C2×#106222792
#130668642
#130668602
#130668562
#130668522
#130668502
#130668492
(C2×D11)⋊#952
C11×#14362
#1418511