Finite Group Databasebeta

← #14676983

Subgroups — #14676983

Order 2816.

2106 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622586C211yesmaximal, characteristic, complemented
2C2×#10622281C211yesmaximal, characteristic
3C2×#10622281C211yesmaximal, characteristic
4C2×#10622602C211yesmaximal, characteristic
5C2×#10622280C211yesmaximal, characteristic
6C2×#10622279C211yesmaximal, characteristic
7C2×D11×#95C211yesmaximal, characteristic
8#13066880C211yesmaximal, characteristic, complemented
9#13066868C211yesmaximal, characteristic, complemented
10#13066867C211yesmaximal, characteristic, complemented
11#13066851C211yesmaximal, characteristic, complemented
12#13066850C211yesmaximal, characteristic, complemented
13Dic11⋊#95C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic
15C11×#1442C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C2×C11×#95C2211yescharacteristic
34C2×C11×#95C2211yescharacteristic
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2211yescharacteristic
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#10622602—24no—
52#10622586—24no—
53#10622281—24no—
54#10622281C418yescomplemented
55#10622280—24no—
56#10622279—24no—
57D11×#95—24no—
58C24×D11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C22×C4×D11—22no—
74C22×C4×D11—22no—
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—41no—
87C22×C4×D11—41no—
88C22×C4×D11—41no—
89C22×C4×D11—41no—
90C22×C4×D11—41no—
91C22×C4×D11—41no—
92C22×C4×D11C2×C414yes—
93C22×C4×D11Q814yes—
94C2×C11×C4⋊C4—22no—
95C2×C11×C4⋊C4—22no—
96C2×C11×C4⋊C4—41no—
97C2×(C2×D11)⋊C4—22no—
98C2×(C2×D11)⋊C4—22no—
99C2×(C2×D11)⋊C4—22no—
100C2×(C2×D11)⋊C4—22no—
101C2×(C2×D11)⋊C4—22no—
102C2×(C2×D11)⋊C4—22no—
103C2×(C2×D11)⋊C4—22no—
104C2×(C2×D11)⋊C4C2×C414yes—
105C2×(C2×D11)⋊C4C2×C414yes—
106C2×(C2×D11)⋊C4D414yes—
107C2×(C2×D11)⋊C4D414yes—
108C2×(C2×D11)⋊C4Q814yes—
109C2×C4⋊Dic11—22no—
110C2×C4⋊Dic11—22no—
111C2×C4⋊Dic11—22no—
112C2×C4⋊Dic11—22no—
113C2×C4⋊Dic11—41no—
114C2×C4⋊Dic11C2×C414yescomplemented
115C2×Dic11⋊C4—22no—
116C2×Dic11⋊C4—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—41no—
124C2×Dic11⋊C4—41no—
125C2×Dic11⋊C4—41no—
126C2×Dic11⋊C4—41no—
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—41no—
135C2×C4×Dic11—41no—
136C11×#95—22no—
137C11×#95—22no—
138C11×#95—22no—
139C11×#95—22no—
140C11×#95—41no—
141C11×#95C2×C414yescomplemented
142C11⋊#95—22no—
143C11⋊#95—22no—
144C11⋊#95—22no—
145C11⋊#95—22no—
146C11⋊#95—22no—
147C11⋊#95—22no—
148C11⋊#95—22no—
149C11⋊#95—22no—
150C11⋊#95—22no—
151C11⋊#95—41no—
152C11⋊#95C2×C414yescomplemented
153C11⋊#95D414yes—
154#14004—111nomaximal, Sylow
155C24×C11C2411yescharacteristic
156C23×D11—21no—
157C23×D11—21no—
158C23×D11—21no—
159C23×D11—21no—
160C23×D11—21no—
161C23×D11—21no—
162C23×D11—21no—
163C23×D11—21no—
164C23×D11C22×C412yes—
165C23×D11C2×D412yes—
166C23×D11C2×D412yes—
167C23×D11C2×Q812yes—
168C23×D11C2×Q812yes—
169C23×D11#4112yes—
170C23×D11#4112yes—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
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×C11C22×C412yes—
213C22×C4×C11C22×C412yes—
214C22×C4×C11C22×C412yes—
215C22×C4×C11C2×D412yes—
216C22×C4×C11C2×D412yes—
217C22×C4×C11C2×D412yes—
218C22×C4×C11C2×Q812yes—
219C22×C4×C11C2×Q812yes—
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C22×Dic11—21no—
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×Dic11C22×C412yes—
258C22×Dic11C22×C412yes—
259C22×Dic11C22×C412yes—
260C22×Dic11C2×D412yes—
261C22×Dic11C2×D412yes—
262C22×Dic11C2×D412yes—
263C22×Dic11C2×D412yes—
264C22×Dic11C2×Q812yes—
265C22×Dic11C2×Q812yes—
266C22×Dic11#4112yes—
267C22×Dic11#4112yes—
268C22×Dic11#4112yes—
269C2×C4×D11—28no—
270C2×C4×D11—28no—
271C2×C4×D11—28no—
272C2×C4×D11—28no—
273C2×C4×D11—28no—
274C2×C4×D11—44no—
275C2×C4×D11—44no—
276C2×C4×D11—44no—
277C2×C4×D11—44no—
278C2×C4×D11—44no—
279C2×C4×D11—44no—
280C2×C4×D11—44no—
281C2×C4×D11—44no—
282C2×C4×D11—44no—
283C2×C4×D11—44no—
284C2×C4×D11—44no—
285C2×C4×D11—44no—
286C2×C4×D11—44no—
287C2×C4×D11—44no—
288C2×C4×D11—44no—
289C2×C4×D11—44no—
290C11×C4⋊C4—44no—
291(C2×D11)⋊C4—28no—
292(C2×D11)⋊C4—28no—
293(C2×D11)⋊C4—44no—
294(C2×D11)⋊C4C4⋊C4116yescomplemented
295C4⋊Dic11—28no—
296C4⋊Dic11—44no—
297Dic11⋊C4—44no—
298Dic11⋊C4—44no—
299Dic11⋊C4—44no—
300Dic11⋊C4—44no—
301Dic11⋊C4—44no—
302C4×Dic11—44no—
303C4×Dic11—44no—
304C2×#389—111no—
305C2×#385—111no—
306C2×#385—111no—
307C2×#385—111no—
308C2×#380—111no—
309C2×C4×C22⋊C4—111no—
310C22×#95—111no—
311#1444—111no—
312#1442D1111yescharacteristic, complemented
313#1441—111no—
314#1441—111no—
315#1436—111no—
316#1436—111no—
317C4⋊#95—111no—
318C22⋊#95—111no—
319C23×C11C23×C411yescharacteristic
320C23×C11C22×D411yescharacteristic
321C23×C11C22×D411yescharacteristic
322C23×C11C22×D411yescharacteristic
323C23×C11C22×Q811yescharacteristic
324C23×C11C22×Q811yescharacteristic
325C23×C11C2×#4111yescharacteristic
326C23×C11C2×#4111yescharacteristic
327C23×C11C2×#4111yescharacteristic
328C23×C11C2×#4111yescharacteristic
329C23×C11C2×#4111yescharacteristic
330C23×C11H(5,𝔽2)11yescharacteristic
331C23×C11H(5,𝔽2)11yescharacteristic
332C23×C11H(5,𝔽2)11yescharacteristic
333C23×C112−1+411yescharacteristic
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—22no—
342C22×D11—22no—
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×D11C2×C4⋊C414yes—
363C22×D11C4×D414yes—
364C22×D11C4×Q814yes—
365C22×D11#12114yes—
366C22×D11C22⋊Q814yes—
367C22×D11#12514yes—
368C22×D11C4⋊Q814yes—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
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—41no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—41no—
398C2×C4×C11—41no—
399C2×C4×C11—41no—
400C2×C4×C11—41no—
401C2×C4×C11—41no—
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×C11C2×C4⋊C414yes—
418C2×Dic11—22no—
419C2×Dic11—22no—
420C2×Dic11—22no—
421C2×Dic11—22no—
422C2×Dic11—22no—
423C2×Dic11—22no—
424C2×Dic11—22no—
425C2×Dic11—22no—
426C2×Dic11—22no—
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×Dic11C2×C4⋊C414yes—
465C2×Dic11C4×D414yes—
466C2×Dic11C22⋊Q814yes—
467C4×D11—416no—
468C4×D11—416no—
469C4×D11—416no—
470C24×C4—111no—
471C24×C4—111no—
472C24×C4—111no—
473C22×C4⋊C4—111no—
474C22×C4⋊C4—111no—
475C22×C4⋊C4—111no—
476C22×C4⋊C4—111no—
477C22×C4⋊C4—111no—
478C22×C4⋊C4—111no—
479C22×C4⋊C4—111no—
480C22×C4⋊C4C2×D1111yescharacteristic
481C22×C22⋊C4—111no—
482C22×C22⋊C4—111no—
483C22×C22⋊C4—111no—
484C22×C22⋊C4—111no—
485C22×C42—111no—
486C22×C42—111no—
487#389—224no—
488#385—118no—
489#385—224no—
490#385—224no—
491#380—224no—
492C4×C22⋊C4—224no—
493C2×#95—111no—
494C2×#95—111no—
495C2×#95—111no—
496C2×#95—111no—
497C2×#95—111no—
498C2×#95—111no—
499C2×#95—111no—
500C2×#95—111no—
501C2×#95—111no—
502C2×#95—111no—
503C2×#95—111no—
504C2×#95—111no—
505C2×#95—224no—
506C2×#95C2×D1111yescharacteristic
507C2×#95C2×D1111yescharacteristic
508C2×#95C2×D1111yescharacteristic
509C2×#95C2×D1111yescharacteristic
510C2×#95C2×D1111yescharacteristic
511C2×#95C2×D1111yescharacteristic
512C22×C11C22×C4⋊C411yescharacteristic
513C22×C11C2×C4×D411yescharacteristic
514C22×C11C2×C4×D411yescharacteristic
515C22×C11C2×C4×Q811yescharacteristic
516C22×C11C4×#4111yescharacteristic
517C22×C11#51811yescharacteristic
518C22×C11#52011yescharacteristic
519C22×C11C2×#12111yescharacteristic
520C22×C11C2×C22⋊Q811yescharacteristic
521C22×C11C2×C22⋊Q811yescharacteristic
522C22×C11#52511yescharacteristic
523C22×C11C2×#12511yescharacteristic
524C22×C11#52911yescharacteristic
525C22×C11C2×C4⋊Q811yescharacteristic
526C22×C11#53311yescharacteristic
527C22×C11#53811yescharacteristic
528C22×C11#53911yescharacteristic
529C22×C11#54311yescharacteristic
530C22×C11#54411yescharacteristic
531C22×C11D4211yescharacteristic
532C22×C11D4211yescharacteristic
533C22×C11#54611yescharacteristic
534C22×C11#54611yescharacteristic
535C22×C11#54611yescharacteristic
536C22×C11#54611yescharacteristic
537C22×C11#54611yescharacteristic
538C22×C11#54711yescharacteristic
539C22×C11#54711yescharacteristic
540C22×C11D4×Q811yescharacteristic
541C22×C11#55111yescharacteristic
542C22×C11#55111yescharacteristic
543C22×C11#55211yescharacteristic
544C22×C11#55411yescharacteristic
545C22×C11#55411yescharacteristic
546C22×C11#55411yescharacteristic
547C2×D11—24no—
548C2×D11—24no—
549C2×D11—24no—
550C2×D11—24no—
551C2×D11—24no—
552C2×D11—24no—
553C2×D11—24no—
554C2×D11—24no—
555C2×D11—24no—
556C2×D11—24no—
557C2×D11—24no—
558C2×D11—24no—
559C2×D11—24no—
560C2×D11—24no—
561C2×D11#38918yescomplemented
562C4×C11—24no—
563C4×C11—42no—
564C4×C11—42no—
565C4×C11—42no—
566C4×C11—42no—
567C4×C11—42no—
568C4×C11—81no—
569Dic11—24no—
570Dic11—24no—
571Dic11—24no—
572Dic11—42no—
573Dic11—42no—
574Dic11—42no—
575Dic11—81no—
576C25—111no—
577C23×C4—111no—
578C23×C4—111no—
579C23×C4—111no—
580C23×C4—111no—
581C23×C4—111no—
582C23×C4—111no—
583C23×C4—114no—
584C23×C4—114no—
585C23×C4—111no—
586C23×C4—222no—
587C23×C4—222no—
588C23×C4—222no—
589C23×C4—222no—
590C23×C4—222no—
591C23×C4—222no—
592C23×C4—222no—
593C23×C4—222no—
594C23×C4—222no—
595C23×C4—222no—
596C23×C4—222no—
597C23×C4—222no—
598C23×C4—222no—
599C23×C4—441no—
600C23×C4—441no—
601C23×C4—441no—
602C23×C4—441no—
603C23×C4—441no—
604C23×C4—441no—
605C23×C4C22×D1111yescharacteristic
606C23×C4C22×D1111yescharacteristic
607C23×C4C22×D1111yescharacteristic
608C23×C4C22×D1111yescharacteristic
609C23×C4C22×D1111yescharacteristic
610C23×C4C22×D1111yescharacteristic
611C23×C4C22×D1111yescharacteristic
612C2×C4⋊C4—22no—
613C2×C4⋊C4—22no—
614C2×C4⋊C4—41no—
615C2×C4⋊C4—114no—
616C2×C4⋊C4—114no—
617C2×C4⋊C4—222no—
618C2×C4⋊C4—222no—
619C2×C4⋊C4—222no—
620C2×C4⋊C4—222no—
621C2×C4⋊C4—222no—
622C2×C4⋊C4—222no—
623C2×C4⋊C4—222no—
624C2×C4⋊C4—222no—
625C2×C4⋊C4—222no—
626C2×C4⋊C4—222no—
627C2×C4⋊C4—222no—
628C2×C4⋊C4—222no—
629C2×C4⋊C4—441no—
630C2×C4⋊C4—441no—
631C2×C4⋊C4—441no—
632C2×C4⋊C4—441no—
633C2×C4⋊C4—441no—
634C2×C4⋊C4—441no—
635C2×C4⋊C4—441no—
636C2×C22⋊C4—114no—
637C2×C22⋊C4—114no—
638C2×C22⋊C4—114no—
639C2×C22⋊C4—114no—
640C2×C22⋊C4—114no—
641C2×C22⋊C4—222no—
642C2×C22⋊C4—222no—
643C2×C22⋊C4—222no—
644C2×C22⋊C4—222no—
645C2×C22⋊C4—222no—
646C2×C22⋊C4—222no—
647C2×C22⋊C4—222no—
648C2×C42—222no—
649C2×C42—222no—
650C2×C42—222no—
651C2×C42—222no—
652C2×C42—441no—
653C2×C42—441no—
654#95—22no—
655#95—22no—
656#95—22no—
657#95—22no—
658#95—41no—
659#95—114no—
660#95—114no—
661#95—222no—
662#95—222no—
663#95—222no—
664#95—222no—
665#95—222no—
666#95—222no—
667#95—222no—
668#95—222no—
669#95—222no—
670#95—441no—
671#95C4×D1114yescomplemented
672C2×C11C2×#38911yescharacteristic
673C2×C11C4×C22⋊Q811yescharacteristic
674C2×C11#232911yescharacteristic
675C2×C11D4×C4⋊C411yescharacteristic
676C2×C11#234911yescharacteristic
677C2×C11#235811yescharacteristic
678C2×C11#235911yescharacteristic
679C2×C11#242411yescharacteristic
680C2×C11#242511yescharacteristic
681C2×C11#243711yescharacteristic
682C2×C11#243811yescharacteristic
683C2×C11#244011yescharacteristic
684C2×C11#247311yescharacteristic
685C2×C11#250511yescharacteristic
686C2×C11#254911yescharacteristic
687D11—28no—
688C24—112no—
689C24—112no—
690C24—112no—
691C24—112no—
692C24—112no—
693C24—112no—
694C24—112no—
695C24—221no—
696C24—221no—
697C24—221no—
698C24—221no—
699C24—221no—
700C24—221no—
701C24—221no—
702C24—221no—
703C24C23×D1111yescharacteristic
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
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—112no—
746C22×C4—112no—
747C22×C4—112no—
748C22×C4—112no—
749C22×C4—112no—
750C22×C4—112no—
751C22×C4—112no—
752C22×C4—112no—
753C22×C4—112no—
754C22×C4—112no—
755C22×C4—112no—
756C22×C4—112no—
757C22×C4—228no—
758C22×C4—228no—
759C22×C4—228no—
760C22×C4—228no—
761C22×C4—228no—
762C22×C4—221no—
763C22×C4—221no—
764C22×C4—221no—
765C22×C4—221no—
766C22×C4—221no—
767C22×C4—221no—
768C22×C4—221no—
769C22×C4—221no—
770C22×C4—221no—
771C22×C4—221no—
772C22×C4—221no—
773C22×C4—221no—
774C22×C4—221no—
775C22×C4—221no—
776C22×C4—221no—
777C22×C4—221no—
778C22×C4—221no—
779C22×C4—221no—
780C22×C4—221no—
781C22×C4—221no—
782C22×C4—221no—
783C22×C4—221no—
784C22×C4—221no—
785C22×C4—221no—
786C22×C4—221no—
787C22×C4—221no—
788C22×C4—221no—
789C22×C4—221no—
790C22×C4—221no—
791C22×C4—221no—
792C22×C4—221no—
793C22×C4—221no—
794C22×C4—221no—
795C22×C4—221no—
796C22×C4—221no—
797C22×C4—221no—
798C22×C4—221no—
799C22×C4—444no—
800C22×C4—444no—
801C22×C4—444no—
802C22×C4—444no—
803C22×C4—444no—
804C22×C4—444no—
805C22×C4—444no—
806C22×C4—444no—
807C22×C4—444no—
808C22×C4—444no—
809C22×C4—444no—
810C22×C4—444no—
811C22×C4—444no—
812C22×C4—444no—
813C22×C4—444no—
814C22×C4—444no—
815C22×C4C2×C4×D1112yes—
816C22×C4C2×C4×D1112yes—
817C22×C4C2×C4×D1112yes—
818C22×C4D4×D1112yes—
819C22×C4D4×D1112yes—
820C22×C4D4×D1112yes—
821C22×C4Q8×D1112yes—
822C22×C4Q8×D1112yes—
823C4⋊C4—44no—
824C4⋊C4—228no—
825C4⋊C4—444no—
826C4⋊C4—444no—
827C4⋊C4—444no—
828C4⋊C4—444no—
829C4⋊C4—444no—
830C4⋊C4—444no—
831C22⋊C4—1116no—
832C22⋊C4—228no—
833C22⋊C4—228no—
834C22⋊C4—444no—
835C42—444no—
836C42—444no—
837C11#1400411yescharacteristic, complemented, Sylow
838C23—114no—
839C23—114no—
840C23—114no—
841C23—114no—
842C23—114no—
843C23—114no—
844C23—114no—
845C23—222no—
846C23—222no—
847C23—222no—
848C23—222no—
849C23—222no—
850C23—222no—
851C23—222no—
852C23—222no—
853C23—222no—
854C23—222no—
855C23—222no—
856C23—222no—
857C23—222no—
858C23—222no—
859C23—222no—
860C23—222no—
861C23—222no—
862C23—222no—
863C23—222no—
864C23—222no—
865C23—222no—
866C23—222no—
867C23—222no—
868C23—222no—
869C23—222no—
870C23—222no—
871C23—222no—
872C23—222no—
873C23C22×C4×D1111yescharacteristic
874C23C2×D4×D1111yescharacteristic
875C23C2×D4×D1111yescharacteristic
876C23C2×D4×D1111yescharacteristic
877C23#6703711yescharacteristic
878C23C2×Q8×D1111yescharacteristic
879C23C2×Q8×D1111yescharacteristic
880C23#41×D1111yescharacteristic
881C23#41×D1111yescharacteristic
882C23#41×D1111yescharacteristic
883C23#41×D1111yescharacteristic
884C23#41×D1111yescharacteristic
885C23#6704211yescharacteristic
886C23#6704211yescharacteristic
887C23#6704311yescharacteristic
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—114no—
937C2×C4—114no—
938C2×C4—114no—
939C2×C4—222no—
940C2×C4—222no—
941C2×C4—222no—
942C2×C4—222no—
943C2×C4—222no—
944C2×C4—222no—
945C2×C4—222no—
946C2×C4—222no—
947C2×C4—222no—
948C2×C4—222no—
949C2×C4—222no—
950C2×C4—222no—
951C2×C4—222no—
952C2×C4—222no—
953C2×C4—222no—
954C2×C4—222no—
955C2×C4—222no—
956C2×C4—222no—
957C2×C4—222no—
958C2×C4—222no—
959C2×C4—222no—
960C2×C4—222no—
961C2×C4—222no—
962C2×C4—222no—
963C2×C4—222no—
964C2×C4—222no—
965C2×C4—222no—
966C2×C4—4416no—
967C2×C4—4416no—
968C2×C4—4416no—
969C2×C4—441no—
970C2×C4—441no—
971C2×C4—441no—
972C2×C4—441no—
973C2×C4—441no—
974C2×C4—441no—
975C2×C4—441no—
976C2×C4—441no—
977C2×C4—441no—
978C2×C4—441no—
979C2×C4—441no—
980C2×C4—441no—
981C2×C4—441no—
982C2×C4—441no—
983C2×C4—441no—
984C2×C4—441no—
985C2×C4—441no—
986C2×C4—441no—
987C2×C4—441no—
988C2×C4C4⋊C4×D1114yes—
989C22—118no—
990C22—224no—
991C22—224no—
992C22—224no—
993C22—224no—
994C22—224no—
995C22—224no—
996C22—224no—
997C22—224no—
998C22—224no—
999C22—224no—
1000C22—224no—
1001C22—224no—
1002C22—224no—
1003C22—224no—
1004C22C2×C4⋊C4×D1111yescharacteristic
1005C22#1062305211yescharacteristic
1006C22#1062305311yescharacteristic
1007C22C4×D4×D1111yescharacteristic
1008C22C4×D4×D1111yescharacteristic
1009C22#1062307711yescharacteristic
1010C22C4×Q8×D1111yescharacteristic
1011C22#1062312111yescharacteristic
1012C22D11×#12111yescharacteristic
1013C22#1062314011yescharacteristic
1014C22#1062314311yescharacteristic
1015C22D11×C22⋊Q811yescharacteristic
1016C22D11×C22⋊Q811yescharacteristic
1017C22#1062316311yescharacteristic
1018C22#1062316511yescharacteristic
1019C22#1062316711yescharacteristic
1020C22#1062318511yescharacteristic
1021C22#1062318611yescharacteristic
1022C22#1062318611yescharacteristic
1023C22#1062318711yescharacteristic
1024C22#1062318811yescharacteristic
1025C22#1062320711yescharacteristic
1026C22#1062320711yescharacteristic
1027C22#1062320711yescharacteristic
1028C22#1062321011yescharacteristic
1029C22D11×#12511yescharacteristic
1030C22#1062321911yescharacteristic
1031C22#1062322011yescharacteristic
1032C22#1062322111yescharacteristic
1033C22#1062322111yescharacteristic
1034C22#1062323611yescharacteristic
1035C22#1062323711yescharacteristic
1036C22#1062323811yescharacteristic
1037C22#1062323911yescharacteristic
1038C22D11×C4⋊Q811yescharacteristic
1039C4—24no—
1040C4—42no—
1041C4—42no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—81no—
1046C4—224no—
1047C4—224no—
1048C4—224no—
1049C4—442no—
1050C4—442no—
1051C4—442no—
1052C4—881no—
1053C2—228no—
1054C2D11×#38911yescharacteristic
1055C2#1307115011yescharacteristic
1056C2#1307134511yescharacteristic
1057C2#1307151411yescharacteristic
1058C2#1307152411yescharacteristic
1059C2#1307159411yescharacteristic
1060C2#1307160511yescharacteristic
1061C2#1307214511yescharacteristic
1062C2#1307217011yescharacteristic
1063C2#1307227611yescharacteristic
1064C2#1307229511yescharacteristic
1065C2#1307231311yescharacteristic
1066C2#1307275211yescharacteristic
1067C2#1307311211yescharacteristic
1068C2#1307362311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1442C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1442D11
hypocenterC11#14004
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
1. C2×#10622586C2semidirect
8. #13066880C2semidirect
9. #13066868C2semidirect
10. #13066867C2semidirect
11. #13066851C2semidirect
12. #13066850C2semidirect
13. Dic11⋊#95C2semidirect
15. C11×#1442C2semidirect
54. #10622281C4semidirect
114. C2×C4⋊Dic11C2×C4semidirect
129. C2×Dic11⋊C4C2×C4semidirect
141. C11×#95C2×C4semidirect
152. C11⋊#95C2×C4semidirect
294. (C2×D11)⋊C4C4⋊C4semidirect
312. #1442D11semidirect
561. C2×D11#389semidirect
671. #95C4×D11semidirect
837. C11#14004semidirect

Maximal subgroups

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

subgroupindex
C2×#106225862
C2×#106222812
C2×#106226022
C2×#106222802
C2×#106222792
C2×D11×#952
#130668802
#130668682
#130668672
#130668512
#130668502
Dic11⋊#952
(C2×D11)⋊#952
C11×#14422
#1400411