Finite Group Databasebeta

← #14685014

Subgroups — #14685014

Order 2816.

2574 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C42×D11C211yesmaximal, characteristic
2C2×#10622260C211yesmaximal, characteristic, complemented
3C2×#10622585C211yesmaximal, characteristic, complemented
4C2×#10622281C211yesmaximal, characteristic
5C2×#10622602C211yesmaximal, characteristic
6C2×#10622280C211yesmaximal, characteristic
7C2×#10622280C211yesmaximal, characteristic
8#13066850C211yesmaximal, characteristic, complemented
9#13066849C211yesmaximal, characteristic, complemented
10#13066847C211yesmaximal, characteristic, complemented
11Dic11⋊#95C211yesmaximal, characteristic, complemented
12Dic11⋊#95C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic
14(C2×D11)⋊#95C211yesmaximal, characteristic
15C11×#1436C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C2×C42×D11—24no—
36C2×C42×D11—24no—
37C2×C42×D11—24no—
38C2×C11×#95C2211yescharacteristic
39C2×C11×#95C2211yescharacteristic
40C2×C11×#95C2211yescharacteristic
41C2×C11×#95C2211yescharacteristic
42C2×C11×#95C2211yescharacteristic
43C2×C11⋊#95C2211yescharacteristic
44C2×C11⋊#95C2211yescharacteristic
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54#10622602—24no—
55#10622585—24no—
56#10622281—24no—
57#10622280—24no—
58#10622280C418yescomplemented
59#10622260—24no—
60C24×D11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C22×C4×D11—22no—
76C22×C4×D11—22no—
77C22×C4×D11—22no—
78C22×C4×D11—22no—
79C22×C4×D11—22no—
80C22×C4×D11—22no—
81C22×C4×D11—22no—
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×D11C2×C414yes—
92C22×C4×D11D414yes—
93C22×C4×D11D414yes—
94C22×C4×D11Q814yes—
95C22×C4×D11Q814yes—
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)⋊C4C2×C414yes—
113C2×(C2×D11)⋊C4C2×C414yes—
114C2×C4⋊Dic11—22no—
115C2×C4⋊Dic11—22no—
116C2×C4⋊Dic11—22no—
117C2×Dic11⋊C4—22no—
118C2×Dic11⋊C4—22no—
119C2×Dic11⋊C4—22no—
120C2×Dic11⋊C4—22no—
121C2×Dic11⋊C4—22no—
122C2×Dic11⋊C4—22no—
123C2×Dic11⋊C4—22no—
124C2×Dic11⋊C4—22no—
125C2×Dic11⋊C4—22no—
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⋊C4C2×C414yescomplemented
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×Dic11D414yes—
143C2×C4×Dic11D414yes—
144C42×D11—232no—
145C11×#95—22no—
146C11×#95—22no—
147C11×#95—22no—
148C11×#95—22no—
149C11×#95C2×C414yescomplemented
150C11⋊#95—22no—
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⋊#95C2×C414yescomplemented
161#14697—111nomaximal, Sylow
162C24×C11C2411yescharacteristic
163C23×D11—21no—
164C23×D11—21no—
165C23×D11—21no—
166C23×D11—21no—
167C23×D11—21no—
168C23×D11—21no—
169C23×D11—21no—
170C23×D11—21no—
171C23×D11C22×C412yes—
172C23×D11C2×D412yes—
173C23×D11C2×D412yes—
174C23×D11C2×Q812yes—
175C23×D11C2×Q812yes—
176C23×D11#4112yes—
177C23×D11#4112yes—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11C22×C412yes—
217C22×C4×C11C22×C412yes—
218C22×C4×C11C22×C412yes—
219C22×C4×C11C2×D412yes—
220C22×C4×C11C2×D412yes—
221C22×C4×C11C2×D412yes—
222C22×C4×C11C2×D412yes—
223C22×C4×C11C2×Q812yes—
224C22×C4×C11C2×Q812yes—
225C22×C4×C11#4112yes—
226C22×C4×C11#4112yes—
227C22×Dic11—21no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—21no—
233C22×Dic11—21no—
234C22×Dic11—21no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—21no—
239C22×Dic11—21no—
240C22×Dic11—21no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11—21no—
247C22×Dic11—21no—
248C22×Dic11—21no—
249C22×Dic11—21no—
250C22×Dic11—21no—
251C22×Dic11—21no—
252C22×Dic11—21no—
253C22×Dic11—21no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11—21no—
258C22×Dic11—21no—
259C22×Dic11—21no—
260C22×Dic11—21no—
261C22×Dic11C22×C412yes—
262C22×Dic11C22×C412yes—
263C22×Dic11C22×C412yes—
264C22×Dic11C2×D412yes—
265C22×Dic11C2×D412yes—
266C22×Dic11C2×D412yes—
267C22×Dic11C2×D412yes—
268C22×Dic11C2×D412yes—
269C22×Dic11C2×D412yes—
270C22×Dic11C2×Q812yes—
271C22×Dic11C2×Q812yes—
272C22×Dic11#4112yes—
273C22×Dic11#4112yes—
274C22×Dic11#4112yes—
275C22×Dic11#4112yes—
276C2×C4×D11—28no—
277C2×C4×D11—28no—
278C2×C4×D11—28no—
279C2×C4×D11—28no—
280C2×C4×D11—28no—
281C2×C4×D11—28no—
282C2×C4×D11—28no—
283C2×C4×D11—28no—
284C2×C4×D11—28no—
285C2×C4×D11—28no—
286C2×C4×D11—28no—
287C2×C4×D11—28no—
288C2×C4×D11—28no—
289C2×C4×D11—28no—
290C2×C4×D11—28no—
291C2×C4×D11—28no—
292C2×C4×D11—28no—
293C2×C4×D11—28no—
294C2×C4×D11—28no—
295C2×C4×D11—28no—
296C2×C4×D11C4⋊C4116yescomplemented
297C11×C4⋊C4—44no—
298C42×C11—28no—
299(C2×D11)⋊C4—28no—
300(C2×D11)⋊C4—28no—
301(C2×D11)⋊C4—44no—
302(C2×D11)⋊C4—44no—
303C4⋊Dic11—44no—
304Dic11⋊C4—28no—
305Dic11⋊C4—28no—
306Dic11⋊C4—44no—
307Dic11⋊C4—44no—
308Dic11⋊C4—44no—
309Dic11⋊C4—44no—
310C4×Dic11—28no—
311C4×Dic11—28no—
312C4×Dic11—28no—
313C23×C42—111no—
314C2×#389—111no—
315C2×#389—111no—
316C2×#385—111no—
317C2×#385—111no—
318C2×#380—111no—
319C2×#380—111no—
320#1436—111no—
321#1436—111no—
322#1436—111no—
323#1436D1111yescharacteristic, complemented
324C4⋊#95—111no—
325C4⋊#95—111no—
326C22⋊#95—111no—
327C22⋊#95—111no—
328C23×C11C23×C411yescharacteristic
329C23×C11C22×D411yescharacteristic
330C23×C11C22×D411yescharacteristic
331C23×C11C22×D411yescharacteristic
332C23×C11C22×D411yescharacteristic
333C23×C11C22×Q811yescharacteristic
334C23×C11C22×Q811yescharacteristic
335C23×C11C2×#4111yescharacteristic
336C23×C11C2×#4111yescharacteristic
337C23×C11C2×#4111yescharacteristic
338C23×C11C2×#4111yescharacteristic
339C23×C11C2×#4111yescharacteristic
340C23×C11C2×#4111yescharacteristic
341C23×C11C2×#4111yescharacteristic
342C23×C11C2×#4111yescharacteristic
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—22no—
346C22×D11—22no—
347C22×D11—22no—
348C22×D11—22no—
349C22×D11—22no—
350C22×D11—22no—
351C22×D11—22no—
352C22×D11—22no—
353C22×D11—22no—
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—22no—
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×D11C2×C4⋊C414yes—
372C22×D11C4×D414yes—
373C22×D11C4×Q814yes—
374C22×D11#12114yes—
375C22×D11C22⋊Q814yes—
376C22×D11#12514yes—
377C22×D11C4⋊Q814yes—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—22no—
402C2×C4×C11—41no—
403C2×C4×C11—41no—
404C2×C4×C11—41no—
405C2×C4×C11—41no—
406C2×C4×C11—41no—
407C2×C4×C11—41no—
408C2×C4×C11—41no—
409C2×C4×C11—41no—
410C2×C4×C11—41no—
411C2×C4×C11—41no—
412C2×C4×C11—41no—
413C2×C4×C11—41no—
414C2×C4×C11—41no—
415C2×C4×C11—41no—
416C2×C4×C11—41no—
417C2×C4×C11—41no—
418C2×C4×C11—41no—
419C2×C4×C11—41no—
420C2×C4×C11—41no—
421C2×C4×C11—41no—
422C2×C4×C11—41no—
423C2×C4×C11—41no—
424C2×C4×C11C2×C4⋊C414yes—
425C2×C4×C11#12114yes—
426C2×C4×C11C22⋊Q814yes—
427C2×Dic11—22no—
428C2×Dic11—22no—
429C2×Dic11—22no—
430C2×Dic11—22no—
431C2×Dic11—22no—
432C2×Dic11—22no—
433C2×Dic11—22no—
434C2×Dic11—22no—
435C2×Dic11—22no—
436C2×Dic11—22no—
437C2×Dic11—22no—
438C2×Dic11—22no—
439C2×Dic11—22no—
440C2×Dic11—22no—
441C2×Dic11—22no—
442C2×Dic11—22no—
443C2×Dic11—22no—
444C2×Dic11—22no—
445C2×Dic11—41no—
446C2×Dic11—41no—
447C2×Dic11—41no—
448C2×Dic11—41no—
449C2×Dic11—41no—
450C2×Dic11—41no—
451C2×Dic11—41no—
452C2×Dic11—41no—
453C2×Dic11—41no—
454C2×Dic11—41no—
455C2×Dic11—41no—
456C2×Dic11—41no—
457C2×Dic11—41no—
458C2×Dic11—41no—
459C2×Dic11—41no—
460C2×Dic11—41no—
461C2×Dic11—41no—
462C2×Dic11—41no—
463C2×Dic11—41no—
464C2×Dic11—41no—
465C2×Dic11—41no—
466C2×Dic11—41no—
467C2×Dic11C2×C4⋊C414yes—
468C2×Dic11C4×D414yes—
469C2×Dic11C4×D414yes—
470C2×Dic11#12014yes—
471C2×Dic11#12114yes—
472C2×Dic11C22⋊Q814yes—
473C2×Dic11C22⋊Q814yes—
474C2×Dic11C22⋊Q814yes—
475C2×Dic11#12314yes—
476C4×D11—232no—
477C4×D11—232no—
478C4×D11—232no—
479C24×C4—111no—
480C24×C4—111no—
481C24×C4—111no—
482C22×C4⋊C4—111no—
483C22×C4⋊C4—111no—
484C22×C4⋊C4—111no—
485C22×C4⋊C4—111no—
486C22×C4⋊C4—111no—
487C22×C4⋊C4—111no—
488C22×C4⋊C4—111no—
489C22×C4⋊C4C2×D1111yescharacteristic
490C22×C22⋊C4—111no—
491C22×C22⋊C4—111no—
492C22×C22⋊C4—111no—
493C22×C22⋊C4—111no—
494C22×C42—111no—
495C22×C42—111no—
496C22×C42—111no—
497C22×C42—224no—
498C22×C42—224no—
499C22×C42—224no—
500C22×C42C2×D1111yescharacteristic
501#389—224no—
502#389—224no—
503#385—224no—
504#385—224no—
505#380—118no—
506#380—224no—
507C2×#95—111no—
508C2×#95—111no—
509C2×#95—111no—
510C2×#95—111no—
511C2×#95—111no—
512C2×#95—111no—
513C2×#95—111no—
514C2×#95—111no—
515C2×#95—111no—
516C2×#95—111no—
517C2×#95—111no—
518C2×#95C2×D1111yescharacteristic
519C2×#95C2×D1111yescharacteristic
520C2×#95C2×D1111yescharacteristic
521C2×#95C2×D1111yescharacteristic
522C2×#95C2×D1111yescharacteristic
523C22×C11C22×C4⋊C411yescharacteristic
524C22×C11C2×C4×D411yescharacteristic
525C22×C11C2×C4×D411yescharacteristic
526C22×C11C2×C4×D411yescharacteristic
527C22×C11C2×C4×Q811yescharacteristic
528C22×C11C4×#4111yescharacteristic
529C22×C11C4×#4111yescharacteristic
530C22×C11C2×#12011yescharacteristic
531C22×C11C2×#12111yescharacteristic
532C22×C11C2×#12111yescharacteristic
533C22×C11C2×#12111yescharacteristic
534C22×C11C2×C22⋊Q811yescharacteristic
535C22×C11C2×C22⋊Q811yescharacteristic
536C22×C11C2×C22⋊Q811yescharacteristic
537C22×C11C2×C22⋊Q811yescharacteristic
538C22×C11C2×C22⋊Q811yescharacteristic
539C22×C11C2×#12311yescharacteristic
540C22×C11#52511yescharacteristic
541C22×C11#52511yescharacteristic
542C22×C11#52511yescharacteristic
543C22×C11#52511yescharacteristic
544C22×C11#52511yescharacteristic
545C22×C11#52511yescharacteristic
546C22×C11C2×#12511yescharacteristic
547C22×C11#52911yescharacteristic
548C22×C11#52911yescharacteristic
549C22×C11#52911yescharacteristic
550C22×C11#52911yescharacteristic
551C22×C11C2×C4⋊Q811yescharacteristic
552C22×C11#53211yescharacteristic
553C22×C11#53211yescharacteristic
554C22×C11#53311yescharacteristic
555C22×C11#53311yescharacteristic
556C22×C11#53311yescharacteristic
557C22×C11#53311yescharacteristic
558C2×D11—24no—
559C2×D11—24no—
560C2×D11—24no—
561C2×D11—24no—
562C2×D11—24no—
563C2×D11—24no—
564C2×D11—24no—
565C2×D11—24no—
566C2×D11—24no—
567C2×D11—24no—
568C2×D11—24no—
569C2×D11—24no—
570C2×D11—24no—
571C2×D11—24no—
572C2×D11#38918yescomplemented
573C4×C11—24no—
574C4×C11—24no—
575C4×C11—24no—
576C4×C11—42no—
577C4×C11—42no—
578C4×C11—81no—
579C4×C11—81no—
580Dic11—24no—
581Dic11—24no—
582Dic11—42no—
583Dic11—42no—
584Dic11—81no—
585Dic11—81no—
586Dic11#38518yescomplemented
587C25—111no—
588C23×C4—111no—
589C23×C4—111no—
590C23×C4—111no—
591C23×C4—114no—
592C23×C4—114no—
593C23×C4—114no—
594C23×C4—111no—
595C23×C4—111no—
596C23×C4—114no—
597C23×C4—114no—
598C23×C4—111no—
599C23×C4—111no—
600C23×C4—222no—
601C23×C4—222no—
602C23×C4—222no—
603C23×C4—222no—
604C23×C4—222no—
605C23×C4—222no—
606C23×C4—222no—
607C23×C4—222no—
608C23×C4—222no—
609C23×C4—222no—
610C23×C4—222no—
611C23×C4—222no—
612C23×C4—222no—
613C23×C4—222no—
614C23×C4—222no—
615C23×C4—222no—
616C23×C4C22×D1111yescharacteristic
617C23×C4C22×D1111yescharacteristic
618C23×C4C22×D1111yescharacteristic
619C23×C4C22×D1111yescharacteristic
620C23×C4C22×D1111yescharacteristic
621C23×C4C22×D1111yescharacteristic
622C23×C4C22×D1111yescharacteristic
623C2×C4⋊C4—22no—
624C2×C4⋊C4—22no—
625C2×C4⋊C4—22no—
626C2×C4⋊C4—114no—
627C2×C4⋊C4—114no—
628C2×C4⋊C4—222no—
629C2×C4⋊C4—222no—
630C2×C4⋊C4—222no—
631C2×C4⋊C4—222no—
632C2×C4⋊C4—222no—
633C2×C4⋊C4—222no—
634C2×C4⋊C4—222no—
635C2×C4⋊C4—222no—
636C2×C4⋊C4—222no—
637C2×C4⋊C4—222no—
638C2×C4⋊C4—222no—
639C2×C4⋊C4—222no—
640C2×C4⋊C4—222no—
641C2×C4⋊C4—222no—
642C2×C4⋊C4—222no—
643C2×C4⋊C4—222no—
644C2×C4⋊C4—222no—
645C2×C4⋊C4—222no—
646C2×C4⋊C4—222no—
647C2×C22⋊C4—114no—
648C2×C22⋊C4—114no—
649C2×C22⋊C4—222no—
650C2×C22⋊C4—222no—
651C2×C22⋊C4—222no—
652C2×C22⋊C4—222no—
653C2×C22⋊C4—222no—
654C2×C22⋊C4—222no—
655C2×C22⋊C4—222no—
656C2×C22⋊C4—222no—
657C2×C22⋊C4—222no—
658C2×C22⋊C4—222no—
659C2×C42—22no—
660C2×C42—22no—
661C2×C42—22no—
662C2×C42—114no—
663C2×C42—114no—
664C2×C42—2232no—
665C2×C42—222no—
666C2×C42—222no—
667C2×C42—222no—
668C2×C42—222no—
669C2×C42—222no—
670C2×C42—222no—
671C2×C42—222no—
672#95—22no—
673#95—22no—
674#95—22no—
675#95—22no—
676#95—114no—
677#95—222no—
678#95—222no—
679#95—222no—
680#95—222no—
681#95—222no—
682#95—222no—
683#95—222no—
684#95—222no—
685#95—222no—
686#95—222no—
687#95C4×D1114yescomplemented
688C2×C11C2×#38511yescharacteristic
689C2×C11C2×#38911yescharacteristic
690C2×C11#229611yescharacteristic
691C2×C11C4×#12111yescharacteristic
692C2×C11C4×#12111yescharacteristic
693C2×C11C4×C22⋊Q811yescharacteristic
694C2×C11C4×C22⋊Q811yescharacteristic
695C2×C11#284711yescharacteristic
696C2×C11#284811yescharacteristic
697C2×C11#285111yescharacteristic
698C2×C11#285111yescharacteristic
699C2×C11#285411yescharacteristic
700C2×C11#285511yescharacteristic
701C2×C11#285711yescharacteristic
702C2×C11#285711yescharacteristic
703D11—28no—
704C24—112no—
705C24—112no—
706C24—112no—
707C24—112no—
708C24—112no—
709C24—112no—
710C24—112no—
711C24—221no—
712C24—221no—
713C24—221no—
714C24—221no—
715C24—221no—
716C24—221no—
717C24—221no—
718C24—221no—
719C24C23×D1111yescharacteristic
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—112no—
759C22×C4—112no—
760C22×C4—112no—
761C22×C4—112no—
762C22×C4—112no—
763C22×C4—112no—
764C22×C4—112no—
765C22×C4—112no—
766C22×C4—112no—
767C22×C4—112no—
768C22×C4—112no—
769C22×C4—112no—
770C22×C4—112no—
771C22×C4—1116no—
772C22×C4—112no—
773C22×C4—112no—
774C22×C4—228no—
775C22×C4—228no—
776C22×C4—228no—
777C22×C4—228no—
778C22×C4—228no—
779C22×C4—228no—
780C22×C4—228no—
781C22×C4—228no—
782C22×C4—228no—
783C22×C4—228no—
784C22×C4—228no—
785C22×C4—228no—
786C22×C4—228no—
787C22×C4—228no—
788C22×C4—228no—
789C22×C4—228no—
790C22×C4—228no—
791C22×C4—228no—
792C22×C4—221no—
793C22×C4—221no—
794C22×C4—221no—
795C22×C4—221no—
796C22×C4—221no—
797C22×C4—221no—
798C22×C4—221no—
799C22×C4—221no—
800C22×C4—228no—
801C22×C4—228no—
802C22×C4—221no—
803C22×C4—221no—
804C22×C4—221no—
805C22×C4—221no—
806C22×C4—221no—
807C22×C4—221no—
808C22×C4—221no—
809C22×C4—221no—
810C22×C4—221no—
811C22×C4—221no—
812C22×C4—221no—
813C22×C4—221no—
814C22×C4—221no—
815C22×C4—221no—
816C22×C4—221no—
817C22×C4—221no—
818C22×C4—221no—
819C22×C4—221no—
820C22×C4—221no—
821C22×C4—221no—
822C22×C4—221no—
823C22×C4—221no—
824C22×C4—221no—
825C22×C4—221no—
826C22×C4—221no—
827C22×C4—221no—
828C22×C4C2×C4×D1112yes—
829C22×C4C2×C4×D1112yes—
830C22×C4C2×C4×D1112yes—
831C22×C4#433912yes—
832C22×C4#433912yes—
833C22×C4D4×D1112yes—
834C22×C4D4×D1112yes—
835C22×C4D4×D1112yes—
836C22×C4D4×D1112yes—
837C22×C4Q8×D1112yes—
838C22×C4Q8×D1112yes—
839C4⋊C4—44no—
840C4⋊C4—228no—
841C4⋊C4—228no—
842C4⋊C4—444no—
843C4⋊C4—444no—
844C4⋊C4—444no—
845C4⋊C4—444no—
846C4⋊C4—444no—
847C22⋊C4—228no—
848C22⋊C4—228no—
849C22⋊C4—444no—
850C22⋊C4—444no—
851C42—28no—
852C42—228no—
853C42—228no—
854C42—228no—
855C11#1469711yescharacteristic, complemented, Sylow
856C23—114no—
857C23—114no—
858C23—114no—
859C23—114no—
860C23—114no—
861C23—114no—
862C23—114no—
863C23—222no—
864C23—222no—
865C23—222no—
866C23—222no—
867C23—222no—
868C23—222no—
869C23—222no—
870C23—222no—
871C23—222no—
872C23—222no—
873C23—222no—
874C23—222no—
875C23—222no—
876C23—222no—
877C23—222no—
878C23—222no—
879C23—222no—
880C23—222no—
881C23—222no—
882C23—222no—
883C23—222no—
884C23—222no—
885C23—222no—
886C23—222no—
887C23—222no—
888C23—222no—
889C23—222no—
890C23—222no—
891C23C22×C4×D1111yescharacteristic
892C23C2×#433911yescharacteristic
893C23C2×#433911yescharacteristic
894C23C2×D4×D1111yescharacteristic
895C23C2×D4×D1111yescharacteristic
896C23C2×D4×D1111yescharacteristic
897C23C2×D4×D1111yescharacteristic
898C23C2×Q8×D1111yescharacteristic
899C23C2×Q8×D1111yescharacteristic
900C23#41×D1111yescharacteristic
901C23#41×D1111yescharacteristic
902C23#41×D1111yescharacteristic
903C23#41×D1111yescharacteristic
904C23#41×D1111yescharacteristic
905C23#41×D1111yescharacteristic
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—114no—
953C2×C4—114no—
954C2×C4—114no—
955C2×C4—114no—
956C2×C4—114no—
957C2×C4—114no—
958C2×C4—114no—
959C2×C4—114no—
960C2×C4—114no—
961C2×C4—2232no—
962C2×C4—2232no—
963C2×C4—2232no—
964C2×C4—222no—
965C2×C4—222no—
966C2×C4—222no—
967C2×C4—222no—
968C2×C4—222no—
969C2×C4—222no—
970C2×C4—222no—
971C2×C4—222no—
972C2×C4—222no—
973C2×C4—222no—
974C2×C4—222no—
975C2×C4—222no—
976C2×C4—222no—
977C2×C4—222no—
978C2×C4—222no—
979C2×C4—222no—
980C2×C4—222no—
981C2×C4—222no—
982C2×C4—441no—
983C2×C4—441no—
984C2×C4—441no—
985C2×C4—441no—
986C2×C4—441no—
987C2×C4—441no—
988C2×C4—441no—
989C2×C4—441no—
990C2×C4—441no—
991C2×C4—441no—
992C2×C4—441no—
993C2×C4—441no—
994C2×C4—441no—
995C2×C4—441no—
996C2×C4—441no—
997C2×C4—441no—
998C2×C4—441no—
999C2×C4—441no—
1000C2×C4—441no—
1001C2×C4—441no—
1002C2×C4—441no—
1003C2×C4—441no—
1004C2×C4#6693714yes—
1005C2×C4C4⋊C4×D1114yes—
1006C2×C4#6694914yes—
1007C22—118no—
1008C22—224no—
1009C22—224no—
1010C22—224no—
1011C22—224no—
1012C22—224no—
1013C22—224no—
1014C22—224no—
1015C22—224no—
1016C22—224no—
1017C22—224no—
1018C22—224no—
1019C22—224no—
1020C22—224no—
1021C22—224no—
1022C22C4×#433911yescharacteristic
1023C22C2×#6693711yescharacteristic
1024C22C2×C4⋊C4×D1111yescharacteristic
1025C22C2×#6694911yescharacteristic
1026C22#1062305311yescharacteristic
1027C22#1062305911yescharacteristic
1028C22#1062305911yescharacteristic
1029C22C4×D4×D1111yescharacteristic
1030C22C4×D4×D1111yescharacteristic
1031C22C4×D4×D1111yescharacteristic
1032C22#1062307811yescharacteristic
1033C22#1062307811yescharacteristic
1034C22#1062307811yescharacteristic
1035C22#1062307811yescharacteristic
1036C22#1062307911yescharacteristic
1037C22C4×Q8×D1111yescharacteristic
1038C22#1062310911yescharacteristic
1039C22#1062310911yescharacteristic
1040C22#1062310911yescharacteristic
1041C22D11×#12011yescharacteristic
1042C22D11×#12111yescharacteristic
1043C22D11×#12111yescharacteristic
1044C22D11×C22⋊Q811yescharacteristic
1045C22D11×C22⋊Q811yescharacteristic
1046C22D11×C22⋊Q811yescharacteristic
1047C22D11×C22⋊Q811yescharacteristic
1048C22D11×#12311yescharacteristic
1049C22#1062318711yescharacteristic
1050C22#1062318711yescharacteristic
1051C22#1062319911yescharacteristic
1052C22D11×#12511yescharacteristic
1053C22#1062321911yescharacteristic
1054C22#1062323711yescharacteristic
1055C22#1062323711yescharacteristic
1056C22D11×C4⋊Q811yescharacteristic
1057C4—24no—
1058C4—24no—
1059C4—24no—
1060C4—42no—
1061C4—42no—
1062C4—81no—
1063C4—81no—
1064C4—118no—
1065C4—224no—
1066C4—224no—
1067C4—442no—
1068C4—442no—
1069C4—881no—
1070C4—881no—
1071C2—228no—
1072C2D11×#38511yescharacteristic
1073C2D11×#38911yescharacteristic
1074C2#1307109611yescharacteristic
1075C2C4×#6693711yescharacteristic
1076C2#1307112811yescharacteristic
1077C2C4×#6694911yescharacteristic
1078C2#1307115011yescharacteristic
1079C2#1307689711yescharacteristic
1080C2#1307690211yescharacteristic
1081C2#1307692311yescharacteristic
1082C2#1307692311yescharacteristic
1083C2#1307694311yescharacteristic
1084C2#1307695111yescharacteristic
1085C2#1307696511yescharacteristic
1086C2#1307696711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1436D11
hypocenterC11#14697
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C2×#10622260C2semidirect
3. C2×#10622585C2semidirect
8. #13066850C2semidirect
9. #13066849C2semidirect
10. #13066847C2semidirect
11. Dic11⋊#95C2semidirect
12. Dic11⋊#95C2semidirect
15. C11×#1436C2semidirect
58. #10622280C4semidirect
133. C2×Dic11⋊C4C2×C4semidirect
134. C2×Dic11⋊C4C2×C4semidirect
149. C11×#95C2×C4semidirect
160. C11⋊#95C2×C4semidirect
296. C2×C4×D11C4⋊C4semidirect
323. #1436D11semidirect
572. C2×D11#389semidirect
586. Dic11#385semidirect
687. #95C4×D11semidirect
855. C11#14697semidirect

Maximal subgroups

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

subgroupindex
C22×C42×D112
C2×#106222602
C2×#106225852
C2×#106222812
C2×#106226022
C2×#106222802
#130668502
#130668492
#130668472
Dic11⋊#952
(C2×D11)⋊#952
C11×#14362
#1469711