Finite Group Databasebeta

← #14675374

Subgroups — #14675374

Order 2816.

2390 conjugacy classes of subgroups.

The subgroup lattice has 1196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622570C211yesmaximal, characteristic
2C2×#10622571C211yesmaximal, characteristic
3C2×#10622569C211yesmaximal, characteristic
4C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
6C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
7C2×#10622279C211yesmaximal, characteristic, complemented
8#13066853C211yesmaximal, characteristic, complemented
9#13066852C211yesmaximal, characteristic, complemented
10#13066852C211yesmaximal, characteristic, complemented
11#13066851C211yesmaximal, characteristic, complemented
12#13066847C211yesmaximal, characteristic, complemented
13C4×C11⋊#95C211yesmaximal, characteristic, complemented
14#95×Dic11C211yesmaximal, characteristic, complemented
15C11×#1437C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C24×Dic11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C42×C11C2211yescharacteristic
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×Dic11⋊C4C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C22×C4×Dic11C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
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
51#10622571C418yescomplemented
52#10622570C418yescomplemented
53#10622569C418yescomplemented
54C22⋊C4×Dic11—24no—
55C22⋊C4×Dic11—24no—
56C4×(C2×D11)⋊C4—24no—
57#10622279—24no—
58C25×C11C2311yescharacteristic
59C24×D11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11—41no—
67C22×C22⋊D11—41no—
68C22×C22⋊D11—41no—
69C22×C22⋊D11—41no—
70C22×C22⋊D11C2×C414yes—
71C22×C22⋊D11C2×C414yes—
72C22×C22⋊D11C2×C414yes—
73C23×Dic11—22no—
74C23×Dic11—22no—
75C23×Dic11—22no—
76C23×Dic11—22no—
77C23×Dic11—41no—
78C23×Dic11—41no—
79C23×Dic11C2×C414yescomplemented
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
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×D11C2×C414yescomplemented
94C2×C11×C22⋊C4—22no—
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4—22no—
98C2×C11×C22⋊C4—41no—
99C2×C11×C22⋊C4—41no—
100C2×C11×C22⋊C4C2×C414yes—
101C2×C11×C22⋊C4C2×C414yescomplemented
102C2×C11×C22⋊C4C2×C414yescomplemented
103C2×C42×C11—22no—
104C2×C42×C11—22no—
105C2×C42×C11—41no—
106C2×C22⋊Dic11—22no—
107C2×C22⋊Dic11—22no—
108C2×C22⋊Dic11—22no—
109C2×C22⋊Dic11—22no—
110C2×C22⋊Dic11C2×C414yes—
111C2×C22⋊Dic11C2×C414yescomplemented
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—41no—
121C2×(C2×D11)⋊C4—41no—
122C2×(C2×D11)⋊C4C2×C414yes—
123C2×(C2×D11)⋊C4C2×C414yes—
124C2×(C2×D11)⋊C4C2×C414yescomplemented
125C2×(C2×D11)⋊C4C2×C414yescomplemented
126C2×(C2×D11)⋊C4C2×C414yescomplemented
127C2×Dic11⋊C4—41no—
128C2×Dic11⋊C4—41no—
129C2×Dic11⋊C4C2×C414yescomplemented
130C2×C4×Dic11—22no—
131C2×C4×Dic11—22no—
132C2×C4×Dic11—22no—
133C2×C4×Dic11—22no—
134C2×C4×Dic11—22no—
135C2×C4×Dic11—22no—
136C2×C4×Dic11—22no—
137C2×C4×Dic11—22no—
138C2×C4×Dic11—22no—
139C2×C4×Dic11—22no—
140C2×C4×Dic11—41no—
141C2×C4×Dic11—41no—
142C2×C4×Dic11—41no—
143C2×C4×Dic11—41no—
144C2×C4×Dic11—41no—
145C2×C4×Dic11—41no—
146C2×C4×Dic11—41no—
147C2×C4×Dic11C2×C414yescomplemented
148C11×#95—22no—
149C11×#95—22no—
150C11×#95—41no—
151C11⋊#95—22no—
152C11⋊#95—22no—
153C11⋊#95—22no—
154C11⋊#95—22no—
155C11⋊#95—41no—
156C11⋊#95C2×C414yescomplemented
157C11⋊#95C2×C414yescomplemented
158C11⋊#95C2×C414yescomplemented
159C11⋊#95C2×C414yescomplemented
160C11⋊#95D414yescomplemented
161C11⋊#95D414yescomplemented
162#13824—111nomaximal, Sylow
163C24×C11—21no—
164C24×C11—21no—
165C24×C11—21no—
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×C11C22×C412yes—
176C24×C11C22×C412yes—
177C24×C11C22×C412yes—
178C24×C11C2411yescharacteristic
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×D11C22×C412yes—
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×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×C11C22×C412yes—
227C22×C4×C11C22×C412yes—
228C22×C4×C11C22×C412yes—
229C22×C4×C11C22×C412yes—
230C22×C4×C11C22×C412yes—
231C22×C4×C11C22×C412yes—
232C22×C4×C11C2×D412yes—
233C22×C4×C11C2×D412yes—
234C22×C4×C11#4112yes—
235C22×C4×C11#4112yes—
236C2×C22⋊D11—44no—
237C2×C22⋊D11—44no—
238C2×C22⋊D11—44no—
239C2×C22⋊D11—44no—
240C2×C22⋊D11—44no—
241C2×C22⋊D11—44no—
242C2×C22⋊D11C42116yescomplemented
243C22×Dic11—28no—
244C22×Dic11—28no—
245C22×Dic11—21no—
246C22×Dic11—21no—
247C22×Dic11—21no—
248C22×Dic11—21no—
249C22×Dic11—21no—
250C22×Dic11—21no—
251C22×Dic11—21no—
252C22×Dic11—21no—
253C22×Dic11—21no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11—21no—
258C22×Dic11—21no—
259C22×Dic11—21no—
260C22×Dic11—21no—
261C22×Dic11—21no—
262C22×Dic11—21no—
263C22×Dic11—21no—
264C22×Dic11—21no—
265C22×Dic11—21no—
266C22×Dic11—21no—
267C22×Dic11—21no—
268C22×Dic11—21no—
269C22×Dic11—21no—
270C22×Dic11—21no—
271C22×Dic11—21no—
272C22×Dic11—21no—
273C22×Dic11—21no—
274C22×Dic11—21no—
275C22×Dic11—21no—
276C22×Dic11—21no—
277C22×Dic11—44no—
278C22×Dic11—44no—
279C22×Dic11—44no—
280C22×Dic11—44no—
281C22×Dic11—44no—
282C22×Dic11C22×C412yes—
283C22×Dic11C22×C412yes—
284C22×Dic11C22×C412yes—
285C22×Dic11C22×C412yes—
286C22×Dic11C22×C412yes—
287C22×Dic11C22×C412yes—
288C22×Dic11C22×C412yes—
289C22×Dic11C22×C412yes—
290C22×Dic11C22×C412yes—
291C22×Dic11C2×D412yes—
292C22×Dic11C2×D412yes—
293C22×Dic11C2×D412yes—
294C22×Dic11C2×D412yes—
295C22×Dic11#4112yes—
296C22×Dic11#4112yes—
297C22×Dic11#4112yes—
298C22×Dic11#4112yes—
299C2×C4×D11—28no—
300C2×C4×D11—28no—
301C2×C4×D11—44no—
302C2×C4×D11—44no—
303C2×C4×D11—44no—
304C2×C4×D11—44no—
305C2×C4×D11—44no—
306C11×C22⋊C4—28no—
307C11×C22⋊C4—28no—
308C11×C22⋊C4—44no—
309C42×C11—44no—
310C22⋊Dic11—28no—
311C22⋊Dic11—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—44no—
317Dic11⋊C4—44no—
318C4×Dic11—44no—
319C4×Dic11—44no—
320C4×Dic11—44no—
321C4×Dic11—44no—
322C4×Dic11—44no—
323C4×Dic11—44no—
324C2×#390—111no—
325C2×#386—111no—
326C2×#386—111no—
327C2×C4×C22⋊C4—111no—
328C2×C4×C22⋊C4—111no—
329C2×C4×C22⋊C4—111no—
330C2×C4×C22⋊C4—111no—
331#1437—111no—
332#1437—111no—
333#1437—111no—
334#1437D1111yescharacteristic, complemented
335#1436—111no—
336#1436—111no—
337C4×#95—111no—
338C4×#95—111no—
339C23×C11—22no—
340C23×C11—22no—
341C23×C11—22no—
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—41no—
358C23×C11—41no—
359C23×C11—41no—
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×C11C2×C4214yes—
374C23×C11C23×C411yescharacteristic
375C23×C11C23×C411yescharacteristic
376C23×C11C23×C411yescharacteristic
377C23×C11C22×D411yescharacteristic
378C23×C11C22×D411yescharacteristic
379C23×C11C2×#4111yescharacteristic
380C23×C11C2×#4111yescharacteristic
381C23×C11C2×#4111yescharacteristic
382C23×C11C2×#4111yescharacteristic
383C23×C11C2×#4111yescharacteristic
384C23×C11C2×#4111yescharacteristic
385C23×C11H(5,𝔽2)11yescharacteristic
386C23×C11H(5,𝔽2)11yescharacteristic
387C23×C11H(5,𝔽2)11yescharacteristic
388C23×C11H(5,𝔽2)11yescharacteristic
389C22×D11—22no—
390C22×D11—22no—
391C22×D11—22no—
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—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×D11C2×C4214yes—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
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—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×C11C4×D414yes—
465C2×C4×C11C4×D414yes—
466C22⋊D11—416no—
467C2×Dic11—22no—
468C2×Dic11—22no—
469C2×Dic11—22no—
470C2×Dic11—22no—
471C2×Dic11—22no—
472C2×Dic11—22no—
473C2×Dic11—22no—
474C2×Dic11—22no—
475C2×Dic11—22no—
476C2×Dic11—22no—
477C2×Dic11—22no—
478C2×Dic11—22no—
479C2×Dic11—22no—
480C2×Dic11—22no—
481C2×Dic11—22no—
482C2×Dic11—22no—
483C2×Dic11—22no—
484C2×Dic11—22no—
485C2×Dic11—22no—
486C2×Dic11—22no—
487C2×Dic11—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—22no—
501C2×Dic11—22no—
502C2×Dic11—22no—
503C2×Dic11—416no—
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×Dic11C2×C4214yes—
513C2×Dic11C4×D414yes—
514C2×Dic11C4×D414yes—
515C2×Dic11C4×D414yes—
516C2×Dic11C4×D414yes—
517C4×D11—416no—
518C23×D4—111no—
519C24×C4—111no—
520C24×C4—111no—
521C22×C4⋊C4—111no—
522C22×C22⋊C4—111no—
523C22×C22⋊C4—111no—
524C22×C22⋊C4—111no—
525C22×C22⋊C4—111no—
526C22×C22⋊C4—111no—
527C22×C22⋊C4—111no—
528C22×C22⋊C4—111no—
529C22×C22⋊C4C2×D1111yescharacteristic
530C22×C22⋊C4C2×D1111yescharacteristic
531C22×C22⋊C4C2×D1111yescharacteristic
532C22×C42—111no—
533C22×C42—111no—
534C22×C42—111no—
535C22×C42—111no—
536C22×C42—111no—
537C22×C42—111no—
538C22×C42C2×D1111yescharacteristic
539#390—118no—
540#386—118no—
541#386—118no—
542C4×C22⋊C4—224no—
543C4×C22⋊C4—224no—
544C4×C22⋊C4—224no—
545C4×C22⋊C4—224no—
546C2×#95—111no—
547C2×#95—111no—
548C2×#95—111no—
549C2×#95—111no—
550C2×#95—111no—
551C2×#95—111no—
552C2×#95—111no—
553C2×#95—111no—
554C2×#95—111no—
555C2×#95—111no—
556C2×#95—111no—
557C2×#95C2×D1111yescharacteristic
558C2×#95C2×D1111yescharacteristic
559C2×#95C2×D1111yescharacteristic
560C22×C11—24no—
561C22×C11—24no—
562C22×C11—24no—
563C22×C11—42no—
564C22×C11—42no—
565C22×C11—42no—
566C22×C11—42no—
567C22×C11—42no—
568C22×C11—42no—
569C22×C11—42no—
570C22×C11—42no—
571C22×C11—42no—
572C22×C11—42no—
573C22×C11—42no—
574C22×C11—42no—
575C22×C11C22×C4211yescharacteristic
576C22×C11C2×C4×D411yescharacteristic
577C22×C11C2×C4×D411yescharacteristic
578C22×C11C2×C4×D411yescharacteristic
579C22×C11C2×C4×D411yescharacteristic
580C22×C11C2×C4×D411yescharacteristic
581C22×C11C2×C4×D411yescharacteristic
582C22×C11C4×#4111yescharacteristic
583C22×C11C4×#4111yescharacteristic
584C22×C11C4×#4111yescharacteristic
585C22×C11C4×#4111yescharacteristic
586C22×C11C4×#4111yescharacteristic
587C22×C11C4×#4111yescharacteristic
588C22×C11#51811yescharacteristic
589C22×C11#51811yescharacteristic
590C22×C11#51811yescharacteristic
591C22×C11#51811yescharacteristic
592C22×C11#51811yescharacteristic
593C22×C11#51811yescharacteristic
594C22×C11D4211yescharacteristic
595C22×C11#54611yescharacteristic
596C22×C11#54611yescharacteristic
597C22×C11#54611yescharacteristic
598C22×C11#54611yescharacteristic
599C22×C11#55011yescharacteristic
600C22×C11#55011yescharacteristic
601C22×C11#55111yescharacteristic
602C22×C11#55111yescharacteristic
603C22×C11#55311yescharacteristic
604C22×C11#55311yescharacteristic
605C22×C11#55311yescharacteristic
606C22×C11#55311yescharacteristic
607C22×C11#55511yescharacteristic
608C22×C11#55511yescharacteristic
609C22×C11#55911yescharacteristic
610C2×D11—24no—
611C2×D11—24no—
612C2×D11—24no—
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—
625C4×C11—24no—
626C4×C11—24no—
627C4×C11—42no—
628C4×C11—42no—
629C4×C11—42no—
630C4×C11—42no—
631Dic11—24no—
632Dic11—24no—
633Dic11—24no—
634Dic11—24no—
635Dic11—24no—
636Dic11—42no—
637Dic11—42no—
638C25—111no—
639C25C22×D1111yescharacteristic
640C22×D4—114no—
641C22×D4—114no—
642C22×D4—114no—
643C22×D4—441no—
644C22×D4—441no—
645C22×D4—441no—
646C22×D4—441no—
647C23×C4—111no—
648C23×C4—111no—
649C23×C4—111no—
650C23×C4—111no—
651C23×C4—111no—
652C23×C4—111no—
653C23×C4—111no—
654C23×C4—114no—
655C23×C4—114no—
656C23×C4—222no—
657C23×C4—222no—
658C23×C4—222no—
659C23×C4—222no—
660C23×C4—222no—
661C23×C4—222no—
662C23×C4—222no—
663C23×C4—222no—
664C23×C4—441no—
665C23×C4—441no—
666C23×C4—441no—
667C23×C4—441no—
668C23×C4C22×D1111yescharacteristic
669C23×C4C22×D1111yescharacteristic
670C23×C4C22×D1111yescharacteristic
671C23×C4C22×D1111yescharacteristic
672C23×C4C22×D1111yescharacteristic
673C23×C4C22×D1111yescharacteristic
674C2×C4⋊C4—114no—
675C2×C4⋊C4—441no—
676C2×C4⋊C4—441no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—41no—
682C2×C22⋊C4—41no—
683C2×C22⋊C4—114no—
684C2×C22⋊C4—114no—
685C2×C22⋊C4—114no—
686C2×C22⋊C4—114no—
687C2×C22⋊C4—114no—
688C2×C22⋊C4—114no—
689C2×C22⋊C4—114no—
690C2×C22⋊C4—222no—
691C2×C22⋊C4—222no—
692C2×C22⋊C4—222no—
693C2×C22⋊C4—222no—
694C2×C22⋊C4—222no—
695C2×C22⋊C4—222no—
696C2×C22⋊C4—222no—
697C2×C22⋊C4—222no—
698C2×C22⋊C4—222no—
699C2×C22⋊C4—222no—
700C2×C22⋊C4—222no—
701C2×C22⋊C4—222no—
702C2×C22⋊C4—441no—
703C2×C22⋊C4—441no—
704C2×C22⋊C4C4×D1114yes—
705C2×C22⋊C4C4×D1114yescomplemented
706C2×C22⋊C4C4×D1114yescomplemented
707C2×C42—22no—
708C2×C42—22no—
709C2×C42—41no—
710C2×C42—114no—
711C2×C42—222no—
712C2×C42—222no—
713C2×C42—222no—
714C2×C42—222no—
715C2×C42—222no—
716C2×C42—222no—
717C2×C42—222no—
718C2×C42—222no—
719C2×C42—222no—
720C2×C42—222no—
721C2×C42—441no—
722C2×C42—441no—
723C2×C42—441no—
724C2×C42—441no—
725C2×C42—441no—
726C2×C42—441no—
727C2×C42—441no—
728#95—22no—
729#95—22no—
730#95—41no—
731#95—114no—
732#95—114no—
733#95—114no—
734#95—114no—
735#95—114no—
736#95—114no—
737#95—222no—
738#95—222no—
739#95—222no—
740#95—222no—
741#95—441no—
742C2×C11—44no—
743C2×C11C42×D411yescharacteristic
744C2×C11C42×D411yescharacteristic
745C2×C11#227311yescharacteristic
746C2×C11#235811yescharacteristic
747C2×C11#235811yescharacteristic
748C2×C11#236311yescharacteristic
749C2×C11#236311yescharacteristic
750C2×C11#236311yescharacteristic
751C2×C11#236311yescharacteristic
752C2×C11#236411yescharacteristic
753C2×C11#236411yescharacteristic
754C2×C11#236611yescharacteristic
755C2×C11#237211yescharacteristic
756C2×C11#237411yescharacteristic
757C2×C11#237411yescharacteristic
758D11—44no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—112no—
772C24—112no—
773C24—112no—
774C24—221no—
775C24—221no—
776C24—221no—
777C24—221no—
778C24—221no—
779C24—221no—
780C24—221no—
781C24—221no—
782C24—221no—
783C24—221no—
784C24—221no—
785C24—221no—
786C24C2×C4×D1112yes—
787C24C2×C4×D1112yes—
788C24C2×C4×D1112yes—
789C24C23×D1111yescharacteristic
790C2×D4—1116no—
791C2×D4—444no—
792C2×D4—444no—
793C2×D4—444no—
794C2×D4—444no—
795C2×D4—444no—
796C2×D4—444no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—112no—
830C22×C4—112no—
831C22×C4—112no—
832C22×C4—112no—
833C22×C4—112no—
834C22×C4—112no—
835C22×C4—112no—
836C22×C4—112no—
837C22×C4—112no—
838C22×C4—112no—
839C22×C4—112no—
840C22×C4—112no—
841C22×C4—112no—
842C22×C4—112no—
843C22×C4—112no—
844C22×C4—112no—
845C22×C4—112no—
846C22×C4—228no—
847C22×C4—228no—
848C22×C4—228no—
849C22×C4—221no—
850C22×C4—221no—
851C22×C4—221no—
852C22×C4—221no—
853C22×C4—221no—
854C22×C4—221no—
855C22×C4—221no—
856C22×C4—221no—
857C22×C4—221no—
858C22×C4—221no—
859C22×C4—221no—
860C22×C4—221no—
861C22×C4—221no—
862C22×C4—221no—
863C22×C4—221no—
864C22×C4—221no—
865C22×C4—221no—
866C22×C4—221no—
867C22×C4—221no—
868C22×C4—221no—
869C22×C4—221no—
870C22×C4—221no—
871C22×C4—221no—
872C22×C4—221no—
873C22×C4—221no—
874C22×C4—221no—
875C22×C4—221no—
876C22×C4—221no—
877C22×C4—221no—
878C22×C4—221no—
879C22×C4—221no—
880C22×C4—221no—
881C22×C4—228no—
882C22×C4—444no—
883C22×C4—444no—
884C22×C4—444no—
885C22×C4—444no—
886C22×C4—444no—
887C22×C4—444no—
888C22×C4—444no—
889C22×C4—444no—
890C22×C4—444no—
891C22×C4—444no—
892C22×C4C2×C4×D1112yes—
893C22×C4C2×C4×D1112yes—
894C22×C4C2×C4×D1112yes—
895C22×C4C2×C4×D1112yes—
896C22×C4C2×C4×D1112yes—
897C22×C4C2×C4×D1112yes—
898C22×C4D4×D1112yes—
899C22×C4D4×D1112yes—
900C22×C4#434112yes—
901C22×C4#434112yes—
902C4⋊C4—444no—
903C22⋊C4—28no—
904C22⋊C4—28no—
905C22⋊C4—44no—
906C22⋊C4—228no—
907C22⋊C4—228no—
908C22⋊C4—228no—
909C22⋊C4—228no—
910C22⋊C4—228no—
911C22⋊C4—228no—
912C22⋊C4—444no—
913C42—44no—
914C42—444no—
915C42—444no—
916C42—444no—
917C42—444no—
918C42—444no—
919C42—444no—
920C11#1382411yescharacteristic, complemented, Sylow
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
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—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—114no—
956C23—222no—
957C23—222no—
958C23—222no—
959C23—222no—
960C23—222no—
961C23—222no—
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—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—
990C23C42×D1114yes—
991C23C22×C4×D1111yescharacteristic
992C23C22×C4×D1111yescharacteristic
993C23C22×C4×D1111yescharacteristic
994C23C2×D4×D1111yescharacteristic
995C23C2×D4×D1111yescharacteristic
996C23C2×#434111yescharacteristic
997C23C2×#434111yescharacteristic
998C23#6703711yescharacteristic
999C23#6703711yescharacteristic
1000C23#41×D1111yescharacteristic
1001C23#41×D1111yescharacteristic
1002C23#41×D1111yescharacteristic
1003C23#41×D1111yescharacteristic
1004C23#6704211yescharacteristic
1005C23#6704211yescharacteristic
1006D4—4416no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
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—114no—
1048C2×C4—114no—
1049C2×C4—114no—
1050C2×C4—114no—
1051C2×C4—114no—
1052C2×C4—222no—
1053C2×C4—222no—
1054C2×C4—222no—
1055C2×C4—222no—
1056C2×C4—222no—
1057C2×C4—222no—
1058C2×C4—222no—
1059C2×C4—222no—
1060C2×C4—222no—
1061C2×C4—222no—
1062C2×C4—222no—
1063C2×C4—222no—
1064C2×C4—222no—
1065C2×C4—222no—
1066C2×C4—222no—
1067C2×C4—222no—
1068C2×C4—222no—
1069C2×C4—222no—
1070C2×C4—222no—
1071C2×C4—222no—
1072C2×C4—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(C22⋊D11)⋊C414yes—
1099C2×C4(C22⋊D11)⋊C414yes—
1100C22—24no—
1101C22—24no—
1102C22—24no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—224no—
1116C22—224no—
1117C22—224no—
1118C22—442no—
1119C22—442no—
1120C22—442no—
1121C22—442no—
1122C22—442no—
1123C22—442no—
1124C22—442no—
1125C22—442no—
1126C22—442no—
1127C22—442no—
1128C22—442no—
1129C22—442no—
1130C22C2×C42×D1111yescharacteristic
1131C22C2×(C22⋊D11)⋊C411yescharacteristic
1132C22C2×(C22⋊D11)⋊C411yescharacteristic
1133C22#1062301711yescharacteristic
1134C22#1062305211yescharacteristic
1135C22#1062305311yescharacteristic
1136C22#1062305311yescharacteristic
1137C22C4×#434111yescharacteristic
1138C22C4×#434111yescharacteristic
1139C22C4×#434111yescharacteristic
1140C22C4×#434111yescharacteristic
1141C22C4×D4×D1111yescharacteristic
1142C22C4×D4×D1111yescharacteristic
1143C22C4×D4×D1111yescharacteristic
1144C22C4×D4×D1111yescharacteristic
1145C22#1062307611yescharacteristic
1146C22#1062307611yescharacteristic
1147C22#1062307611yescharacteristic
1148C22#1062307611yescharacteristic
1149C22#1062312211yescharacteristic
1150C22#1062313011yescharacteristic
1151C22#1062313211yescharacteristic
1152C22#1062314011yescharacteristic
1153C22#1062314111yescharacteristic
1154C22#1062314711yescharacteristic
1155C22#1062314911yescharacteristic
1156C22#1062318511yescharacteristic
1157C22#1062318911yescharacteristic
1158C22#1062319211yescharacteristic
1159C22#1062320111yescharacteristic
1160C22#1062320711yescharacteristic
1161C22#1062321211yescharacteristic
1162C22#1062323611yescharacteristic
1163C22#1062324011yescharacteristic
1164C22#1062324911yescharacteristic
1165C4—24no—
1166C4—24no—
1167C4—42no—
1168C4—42no—
1169C4—42no—
1170C4—42no—
1171C4—224no—
1172C4—224no—
1173C4—224no—
1174C4—224no—
1175C4—224no—
1176C4—442no—
1177C4—442no—
1178C2—44no—
1179C2—444no—
1180C2C4×(C22⋊D11)⋊C411yescharacteristic
1181C2C4×(C22⋊D11)⋊C411yescharacteristic
1182C2#1307096811yescharacteristic
1183C2#1307159411yescharacteristic
1184C2#1307159611yescharacteristic
1185C2#1307164911yescharacteristic
1186C2#1307165111yescharacteristic
1187C2#1307165711yescharacteristic
1188C2#1307165911yescharacteristic
1189C2#1307166011yescharacteristic
1190C2#1307166411yescharacteristic
1191C2#1307167711yescharacteristic
1192C2#1307172311yescharacteristic
1193C2#1307174411yescharacteristic
1194C2#1307174611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC11×#1437C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenter#1437D11
hypocenterC11#13824
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
4. C2×C22⋊C4×Dic11C2semidirect
5. C2×C22⋊C4×Dic11C2semidirect
6. C2×C4×(C2×D11)⋊C4C2semidirect
7. C2×#10622279C2semidirect
8. #13066853C2semidirect
9. #13066852C2semidirect
10. #13066852C2semidirect
11. #13066851C2semidirect
12. #13066847C2semidirect
13. C4×C11⋊#95C2semidirect
14. #95×Dic11C2semidirect
15. C11×#1437C2semidirect
51. #10622571C4semidirect
52. #10622570C4semidirect
53. #10622569C4semidirect
79. C23×Dic11C2×C4semidirect
93. C22×C4×D11C2×C4semidirect
101. C2×C11×C22⋊C4C2×C4semidirect
102. C2×C11×C22⋊C4C2×C4semidirect
111. C2×C22⋊Dic11C2×C4semidirect
124. C2×(C2×D11)⋊C4C2×C4semidirect
125. C2×(C2×D11)⋊C4C2×C4semidirect
126. C2×(C2×D11)⋊C4C2×C4semidirect
129. C2×Dic11⋊C4C2×C4semidirect
147. C2×C4×Dic11C2×C4semidirect
156. C11⋊#95C2×C4semidirect
157. C11⋊#95C2×C4semidirect
158. C11⋊#95C2×C4semidirect
159. C11⋊#95C2×C4semidirect
160. C11⋊#95D4semidirect
161. C11⋊#95D4semidirect
242. C2×C22⋊D11C42semidirect
334. #1437D11semidirect
705. C2×C22⋊C4C4×D11semidirect
706. C2×C22⋊C4C4×D11semidirect
920. C11#13824semidirect

Maximal subgroups

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

subgroupindex
C2×#106225702
C2×#106225712
C2×#106225692
C2×C22⋊C4×Dic112
C2×C4×(C2×D11)⋊C42
C2×#106222792
#130668532
#130668522
#130668512
#130668472
C4×C11⋊#952
#95×Dic112
C11×#14372
#1382411