Finite Group Databasebeta

← #14685228

Subgroups — #14685228

Order 2816.

2558 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66931C211yesmaximal, characteristic, complemented
2C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic
3C2×#10622592C211yesmaximal, characteristic, complemented
4C2×#10622286C211yesmaximal, characteristic, complemented
5C2×#10622281C211yesmaximal, characteristic, complemented
6C2×#10622602C211yesmaximal, characteristic, complemented
7#13066867C211yesmaximal, characteristic, complemented
8#13066860C211yesmaximal, characteristic, complemented
9#13066859C211yesmaximal, characteristic, complemented
10#13066855C211yesmaximal, characteristic
11#13066855C211yesmaximal, characteristic
12#13066850C211yesmaximal, characteristic, complemented
13#13066847C211yesmaximal, characteristic, complemented
14#13066838C211yesmaximal, characteristic, complemented
15C11×#1439C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C24×Dic11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C23×Dic22C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
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×Dic11⋊C4C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37C2×(C22⋊D11)⋊C4—24no—
38C2×(C22⋊D11)⋊C4—24no—
39C2×(C22⋊D11)⋊C4—24no—
40C2×#66931—24no—
41C2×#66931—24no—
42C2×#66931—24no—
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
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57#10622602—24no—
58#10622592—24no—
59#10622286—24no—
60#10622281—24no—
61C25×C11C2311yescharacteristic
62C24×D11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C22×C22⋊D11—22no—
70C22×C22⋊D11—22no—
71C22×C22⋊D11—22no—
72C22×C22⋊D11—22no—
73C22×C22⋊D11—22no—
74C22×C22⋊D11—22no—
75C22×C22⋊D11Q814yescomplemented
76C23×Dic11—22no—
77C23×Dic11—22no—
78C23×Dic11—22no—
79C23×Dic11—22no—
80C23×Dic11—41no—
81C23×Dic11—41no—
82C23×Dic11D414yes—
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C22×C4×D11—22no—
91C22×C4×D11—22no—
92C22×C4×D11—22no—
93C22×C4×D11—22no—
94C22×C4×D11—22no—
95C22×C4×D11—41no—
96C22×C4×D11—41no—
97C22×Dic22—22no—
98C22×Dic22—22no—
99C22×Dic22—22no—
100C22×Dic22—22no—
101C22×Dic22—22no—
102C22×Dic22—41no—
103C22×Dic22—41no—
104C2×C11×C4⋊C4—22no—
105C2×C11×C4⋊C4—22no—
106C2×C11×C4⋊C4—41no—
107C2×C11×C22⋊C4—22no—
108C2×C11×C22⋊C4—22no—
109C2×C11×C22⋊C4—22no—
110C2×C11×C22⋊C4—22no—
111C2×C11×C22⋊C4—22no—
112C2×C11×C22⋊C4—22no—
113C2×C11×C22⋊C4—22no—
114C2×C11×C22⋊C4—22no—
115C2×C11×C22⋊C4—41no—
116C2×C22⋊Dic11—22no—
117C2×C22⋊Dic11—22no—
118C2×C22⋊Dic11—22no—
119C2×C22⋊Dic11—22no—
120C2×C22⋊Dic11—22no—
121C2×C22⋊Dic11—41no—
122C2×(C2×D11)⋊C4—22no—
123C2×(C2×D11)⋊C4—22no—
124C2×(C2×D11)⋊C4—22no—
125C2×(C2×D11)⋊C4—22no—
126C2×(C2×D11)⋊C4—22no—
127C2×(C2×D11)⋊C4—22no—
128C2×(C2×D11)⋊C4—22no—
129C2×(C2×D11)⋊C4—22no—
130C2×(C2×D11)⋊C4—22no—
131C2×(C2×D11)⋊C4—22no—
132C2×(C2×D11)⋊C4—22no—
133C2×(C2×D11)⋊C4—22no—
134C2×(C2×D11)⋊C4—41no—
135C2×(C2×D11)⋊C4—41no—
136C2×(C2×D11)⋊C4D414yes—
137C2×C4⋊Dic11—22no—
138C2×C4⋊Dic11—22no—
139C2×C4⋊Dic11D414yescomplemented
140C2×Dic11⋊C4—22no—
141C2×Dic11⋊C4—22no—
142C2×Dic11⋊C4—22no—
143C2×Dic11⋊C4—22no—
144C2×Dic11⋊C4—22no—
145C2×Dic11⋊C4—22no—
146C2×Dic11⋊C4—22no—
147C2×Dic11⋊C4—22no—
148C2×Dic11⋊C4—22no—
149C2×Dic11⋊C4—41no—
150C2×Dic11⋊C4D414yes—
151C2×Dic11⋊C4D414yescomplemented
152C2×C4×Dic11—22no—
153C2×C4×Dic11—22no—
154C2×C4×Dic11—22no—
155(C22⋊D11)⋊C4—232no—
156#66931—232no—
157C11×#95—22no—
158C11×#95—22no—
159C11×#95—22no—
160C11⋊#95—22no—
161C11⋊#95—22no—
162C11⋊#95—22no—
163C11⋊#95—22no—
164C11⋊#95—22no—
165C11⋊#95—22no—
166C11⋊#95—22no—
167C11⋊#95—22no—
168C11⋊#95—22no—
169C11⋊#95—22no—
170C11⋊#95—22no—
171#14723—111nomaximal, Sylow
172C24×C11—21no—
173C24×C11—21no—
174C24×C11—21no—
175C24×C11—21no—
176C24×C11—21no—
177C24×C11—21no—
178C24×C11—21no—
179C24×C11—21no—
180C24×C11—21no—
181C24×C11—21no—
182C24×C11—21no—
183C24×C11—21no—
184C24×C11C2×D412yes—
185C24×C11C2×Q812yes—
186C24×C11#4112yes—
187C24×C11C2411yescharacteristic
188C23×D11—21no—
189C23×D11—21no—
190C23×D11—21no—
191C23×D11—21no—
192C23×D11—21no—
193C23×D11—21no—
194C23×D11—21no—
195C23×D11—21no—
196C23×D11—21no—
197C23×D11—21no—
198C23×D11—21no—
199C23×D11—21no—
200C23×D11C2×D412yes—
201C23×D11C2×Q812yes—
202C23×D11#4112yes—
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×C11—21no—
237C22×C4×C11—21no—
238C22×C4×C11—21no—
239C22×C4×C11—21no—
240C22×C4×C11C2×D412yes—
241C22×C4×C11C2×D412yes—
242C22×C4×C11C2×D412yes—
243C22×C4×C11C2×D412yes—
244C22×C4×C11#4112yes—
245C2×C22⋊D11—28no—
246C2×C22⋊D11—28no—
247C2×C22⋊D11—28no—
248C2×C22⋊D11—28no—
249C2×C22⋊D11—28no—
250C2×C22⋊D11—28no—
251C2×C22⋊D11—28no—
252C22×Dic11—28no—
253C22×Dic11—28no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11—21no—
258C22×Dic11—21no—
259C22×Dic11—21no—
260C22×Dic11—21no—
261C22×Dic11—21no—
262C22×Dic11—21no—
263C22×Dic11—21no—
264C22×Dic11—21no—
265C22×Dic11—21no—
266C22×Dic11—21no—
267C22×Dic11—21no—
268C22×Dic11—21no—
269C22×Dic11—21no—
270C22×Dic11—21no—
271C22×Dic11—21no—
272C22×Dic11—21no—
273C22×Dic11—21no—
274C22×Dic11—21no—
275C22×Dic11—21no—
276C22×Dic11—21no—
277C22×Dic11—21no—
278C22×Dic11—21no—
279C22×Dic11—21no—
280C22×Dic11—21no—
281C22×Dic11—21no—
282C22×Dic11—21no—
283C22×Dic11—21no—
284C22×Dic11—21no—
285C22×Dic11—21no—
286C22×Dic11—21no—
287C22×Dic11—21no—
288C22×Dic11—21no—
289C22×Dic11—21no—
290C22×Dic11—21no—
291C22×Dic11—44no—
292C22×Dic11—44no—
293C22×Dic11—44no—
294C22×Dic11—44no—
295C22×Dic11—44no—
296C22×Dic11C2×D412yes—
297C22×Dic11C2×D412yes—
298C22×Dic11C2×D412yes—
299C22×Dic11C2×D412yes—
300C22×Dic11C2×D412yes—
301C22×Dic11C2×D412yes—
302C22×Dic11C2×D412yes—
303C22×Dic11C2×D412yes—
304C22×Dic11C2×D412yes—
305C22×Dic11C2×Q812yes—
306C22×Dic11#4112yes—
307C22×Dic11#4112yes—
308C2×C4×D11—28no—
309C2×C4×D11—44no—
310C2×C4×D11—44no—
311C2×C4×D11—44no—
312C2×C4×D11—44no—
313C2×C4×D11—44no—
314C2×C4×D11—44no—
315C2×Dic22—28no—
316C2×Dic22—44no—
317C2×Dic22—44no—
318C2×Dic22—44no—
319C2×Dic22—44no—
320C2×Dic22—44no—
321C2×Dic22—44no—
322C11×C4⋊C4—44no—
323C11×C22⋊C4—28no—
324C11×C22⋊C4—28no—
325C11×C22⋊C4—44no—
326C22⋊Dic11—28no—
327C22⋊Dic11—44no—
328(C2×D11)⋊C4—28no—
329(C2×D11)⋊C4—28no—
330(C2×D11)⋊C4—28no—
331(C2×D11)⋊C4—44no—
332(C2×D11)⋊C4—44no—
333C4⋊Dic11—28no—
334Dic11⋊C4—28no—
335Dic11⋊C4—28no—
336Dic11⋊C4—28no—
337Dic11⋊C4—44no—
338C4×Dic11—28no—
339C22×C22⋊Q8—111no—
340C22×C4×D4—111no—
341C2×#395—111no—
342C2×#393—111no—
343C2×#385—111no—
344C2×#385—111no—
345#1441—111no—
346#1439—111no—
347#1439—111no—
348#1439D1111yescharacteristic, complemented
349#1438—111no—
350#1438—111no—
351#1436—111no—
352#1436—111no—
353C22⋊#95—111no—
354C23×C11—22no—
355C23×C11—22no—
356C23×C11—22no—
357C23×C11—22no—
358C23×C11—22no—
359C23×C11—22no—
360C23×C11—22no—
361C23×C11—22no—
362C23×C11—22no—
363C23×C11—22no—
364C23×C11—22no—
365C23×C11—22no—
366C23×C11—22no—
367C23×C11—22no—
368C23×C11—22no—
369C23×C11—22no—
370C23×C11—22no—
371C23×C11—22no—
372C23×C11—41no—
373C23×C11—41no—
374C23×C11—41no—
375C23×C11—41no—
376C23×C11—41no—
377C23×C11—41no—
378C23×C11—41no—
379C23×C11—41no—
380C23×C11—41no—
381C23×C11—41no—
382C23×C11—41no—
383C23×C11—41no—
384C23×C11—41no—
385C23×C11—41no—
386C23×C11—41no—
387C23×C11—41no—
388C23×C11C22⋊Q814yes—
389C23×C11C22×D411yescharacteristic
390C23×C11C22×D411yescharacteristic
391C23×C11C22×D411yescharacteristic
392C23×C11C22×D411yescharacteristic
393C23×C11C22×D411yescharacteristic
394C23×C11C22×Q811yescharacteristic
395C23×C11C2×#4111yescharacteristic
396C23×C11C2×#4111yescharacteristic
397C23×C11C2×#4111yescharacteristic
398C23×C11C2×#4111yescharacteristic
399C23×C11C2×#4111yescharacteristic
400C23×C11H(5,𝔽2)11yescharacteristic
401C23×C11H(5,𝔽2)11yescharacteristic
402C23×C112−1+411yescharacteristic
403C23×C112−1+411yescharacteristic
404C22×D11—22no—
405C22×D11—22no—
406C22×D11—22no—
407C22×D11—22no—
408C22×D11—22no—
409C22×D11—22no—
410C22×D11—22no—
411C22×D11—22no—
412C22×D11—22no—
413C22×D11—22no—
414C22×D11—22no—
415C22×D11—22no—
416C22×D11—22no—
417C22×D11—22no—
418C22×D11—22no—
419C22×D11—22no—
420C22×D11—22no—
421C22×D11—22no—
422C22×D11—41no—
423C22×D11—41no—
424C22×D11—41no—
425C22×D11—41no—
426C22×D11—41no—
427C22×D11—41no—
428C22×D11—41no—
429C22×D11—41no—
430C22×D11—41no—
431C22×D11—41no—
432C22×D11—41no—
433C22×D11—41no—
434C22×D11—41no—
435C22×D11—41no—
436C22×D11—41no—
437C22×D11—41no—
438C22×D11C22⋊Q814yescomplemented
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—22no—
452C2×C4×C11—22no—
453C2×C4×C11—22no—
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×C11—41no—
475C2×C4×C11—41no—
476C2×C4×C11—41no—
477C2×C4×C11—41no—
478C2×C4×C11—41no—
479C2×C4×C11—41no—
480C2×C4×C11—41no—
481C22⋊D11—232no—
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—22no—
504C2×Dic11—22no—
505C2×Dic11—22no—
506C2×Dic11—22no—
507C2×Dic11—22no—
508C2×Dic11—22no—
509C2×Dic11—416no—
510C2×Dic11—41no—
511C2×Dic11—41no—
512C2×Dic11—41no—
513C2×Dic11—41no—
514C2×Dic11—41no—
515C2×Dic11—41no—
516C2×Dic11—41no—
517C2×Dic11—41no—
518C2×Dic11—41no—
519C2×Dic11—41no—
520C2×Dic11—41no—
521C2×Dic11—41no—
522C2×Dic11—41no—
523C2×Dic11—41no—
524C2×Dic11—41no—
525C2×Dic11—41no—
526C2×Dic11—41no—
527C2×Dic11—41no—
528C2×Dic11—41no—
529C2×Dic11#12014yes—
530C2×Dic11#12014yes—
531C2×Dic11C22⋊Q814yescomplemented
532C4×D11—416no—
533Dic22—416no—
534C23×Q8—111no—
535C23×D4—111no—
536C24×C4—111no—
537C24×C4—111no—
538C2×C22⋊Q8—224no—
539C2×C22⋊Q8—224no—
540C2×C22⋊Q8—224no—
541C2×C4×D4—224no—
542C2×C4×D4—224no—
543C2×C4×D4—224no—
544C22×C4⋊C4—111no—
545C22×C4⋊C4—111no—
546C22×C4⋊C4—111no—
547C22×C4⋊C4—111no—
548C22×C4⋊C4—111no—
549C22×C4⋊C4C2×D1111yescharacteristic
550C22×C22⋊C4—111no—
551C22×C22⋊C4—111no—
552C22×C22⋊C4—111no—
553C22×C22⋊C4—111no—
554C22×C22⋊C4—111no—
555C22×C22⋊C4—111no—
556C22×C22⋊C4—111no—
557C22×C22⋊C4C2×D1111yescharacteristic
558C22×C22⋊C4C2×D1111yescharacteristic
559C22×C22⋊C4C2×D1111yescharacteristic
560C22×C42—111no—
561#395—224no—
562#393—224no—
563#385—224no—
564#385—224no—
565C2×#95—111no—
566C2×#95—111no—
567C2×#95—111no—
568C2×#95—111no—
569C2×#95—111no—
570C2×#95—111no—
571C2×#95—111no—
572C2×#95—111no—
573C2×#95—111no—
574C2×#95—111no—
575C2×#95—111no—
576C2×#95C2×D1111yescharacteristic
577C2×#95C2×D1111yescharacteristic
578C2×#95C2×D1111yescharacteristic
579C22×C11—24no—
580C22×C11—24no—
581C22×C11—24no—
582C22×C11—42no—
583C22×C11—42no—
584C22×C11—42no—
585C22×C11—42no—
586C22×C11—42no—
587C22×C11—42no—
588C22×C11—42no—
589C22×C11—42no—
590C22×C11—42no—
591C22×C11—42no—
592C22×C11—42no—
593C22×C11—42no—
594C22×C11C2×#12011yescharacteristic
595C22×C11C2×#12011yescharacteristic
596C22×C11C2×C22⋊Q811yescharacteristic
597C22×C11C2×C22⋊Q811yescharacteristic
598C22×C11C2×C22⋊Q811yescharacteristic
599C22×C11#52511yescharacteristic
600C22×C11#52511yescharacteristic
601C22×C11#52511yescharacteristic
602C22×C11#52511yescharacteristic
603C22×C11#52511yescharacteristic
604C22×C11#53211yescharacteristic
605C22×C11#53211yescharacteristic
606C22×C11#53211yescharacteristic
607C22×C11#53411yescharacteristic
608C22×C11#53611yescharacteristic
609C22×C11#53911yescharacteristic
610C22×C11#53911yescharacteristic
611C22×C11#54211yescharacteristic
612C22×C11#54211yescharacteristic
613C22×C11D4211yescharacteristic
614C22×C11D4211yescharacteristic
615C22×C11D4211yescharacteristic
616C22×C11D4211yescharacteristic
617C22×C11#54711yescharacteristic
618C22×C11#54711yescharacteristic
619C22×C11#54811yescharacteristic
620C22×C11#54811yescharacteristic
621C22×C11#54811yescharacteristic
622C22×C11#54811yescharacteristic
623C22×C11D4×Q811yescharacteristic
624C22×C11D4×Q811yescharacteristic
625C22×C11#55111yescharacteristic
626C22×C11#55111yescharacteristic
627C22×C11#55411yescharacteristic
628C22×C11#55411yescharacteristic
629C2×D11—24no—
630C2×D11—24no—
631C2×D11—24no—
632C2×D11—42no—
633C2×D11—42no—
634C2×D11—42no—
635C2×D11—42no—
636C2×D11—42no—
637C2×D11—42no—
638C2×D11—42no—
639C2×D11—42no—
640C2×D11—42no—
641C2×D11—42no—
642C2×D11—42no—
643C2×D11—42no—
644C4×C11—42no—
645C4×C11—42no—
646C4×C11—42no—
647C4×C11—42no—
648C4×C11—42no—
649C4×C11—81no—
650Dic11—24no—
651Dic11—24no—
652Dic11—24no—
653Dic11—42no—
654Dic11—42no—
655Dic11—42no—
656Dic11—81no—
657C25—111no—
658C25C22×D1111yescharacteristic
659C22×Q8—222no—
660C22×Q8—222no—
661C22×Q8—222no—
662C22×Q8—222no—
663C22×Q8—222no—
664C22×Q8—441no—
665C22×Q8—441no—
666C22×D4—114no—
667C22×D4—222no—
668C22×D4—222no—
669C22×D4—222no—
670C22×D4—222no—
671C22×D4—222no—
672C22×D4—222no—
673C23×C4—111no—
674C23×C4—111no—
675C23×C4—111no—
676C23×C4—111no—
677C23×C4—111no—
678C23×C4—111no—
679C23×C4—114no—
680C23×C4—111no—
681C23×C4—222no—
682C23×C4—222no—
683C23×C4—222no—
684C23×C4—222no—
685C23×C4—222no—
686C23×C4—222no—
687C23×C4—222no—
688C23×C4—222no—
689C23×C4—222no—
690C23×C4—441no—
691C23×C4—441no—
692C23×C4—441no—
693C23×C4—441no—
694C23×C4C22×D1111yescharacteristic
695C23×C4C22×D1111yescharacteristic
696C23×C4C22×D1111yescharacteristic
697C23×C4C22×D1111yescharacteristic
698C23×C4C22×D1111yescharacteristic
699C23×C4C22×D1111yescharacteristic
700C22⋊Q8—2232no—
701C4×D4—2232no—
702C2×C4⋊C4—22no—
703C2×C4⋊C4—22no—
704C2×C4⋊C4—41no—
705C2×C4⋊C4—114no—
706C2×C4⋊C4—114no—
707C2×C4⋊C4—114no—
708C2×C4⋊C4—222no—
709C2×C4⋊C4—222no—
710C2×C4⋊C4—222no—
711C2×C4⋊C4—222no—
712C2×C4⋊C4—222no—
713C2×C4⋊C4—222no—
714C2×C4⋊C4—222no—
715C2×C4⋊C4—222no—
716C2×C4⋊C4—222no—
717C2×C4⋊C4—222no—
718C2×C4⋊C4—222no—
719C2×C4⋊C4—441no—
720C2×C22⋊C4—22no—
721C2×C22⋊C4—22no—
722C2×C22⋊C4—22no—
723C2×C22⋊C4—22no—
724C2×C22⋊C4—22no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4—22no—
728C2×C22⋊C4—41no—
729C2×C22⋊C4—114no—
730C2×C22⋊C4—222no—
731C2×C22⋊C4—222no—
732C2×C22⋊C4—222no—
733C2×C22⋊C4—222no—
734C2×C22⋊C4—222no—
735C2×C22⋊C4—222no—
736C2×C22⋊C4—222no—
737C2×C22⋊C4—222no—
738C2×C22⋊C4—222no—
739C2×C22⋊C4—222no—
740C2×C22⋊C4—222no—
741C2×C22⋊C4—222no—
742C2×C22⋊C4—222no—
743C2×C22⋊C4—222no—
744C2×C22⋊C4—222no—
745C2×C22⋊C4—222no—
746C2×C22⋊C4—222no—
747C2×C22⋊C4—441no—
748C2×C22⋊C4—441no—
749C2×C22⋊C4—441no—
750C2×C42—222no—
751C2×C42—222no—
752C2×C42—222no—
753#95—22no—
754#95—22no—
755#95—22no—
756#95—222no—
757#95—222no—
758#95—222no—
759#95—222no—
760#95—222no—
761#95—222no—
762#95—222no—
763#95—222no—
764#95—222no—
765#95—222no—
766#95—222no—
767C2×C11—44no—
768C2×C11#238811yescharacteristic
769C2×C11#240311yescharacteristic
770C2×C11#240911yescharacteristic
771C2×C11#243211yescharacteristic
772C2×C11#244911yescharacteristic
773C2×C11#244911yescharacteristic
774C2×C11#245211yescharacteristic
775C2×C11#245211yescharacteristic
776C2×C11#246111yescharacteristic
777C2×C11#246111yescharacteristic
778C2×C11#246311yescharacteristic
779C2×C11#246311yescharacteristic
780C2×C11#256411yescharacteristic
781C2×C11#263811yescharacteristic
782C2×C11#284811yescharacteristic
783D11—44no—
784C24—21no—
785C24—21no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—21no—
795C24—21no—
796C24—112no—
797C24—112no—
798C24—112no—
799C24—221no—
800C24—221no—
801C24—221no—
802C24—221no—
803C24—221no—
804C24—221no—
805C24—221no—
806C24—221no—
807C24—221no—
808C24—221no—
809C24—221no—
810C24—221no—
811C24#433912yes—
812C24D4×D1112yes—
813C24Q8×D1112yes—
814C24C23×D1111yescharacteristic
815C2×Q8—228no—
816C2×Q8—444no—
817C2×Q8—444no—
818C2×Q8—444no—
819C2×Q8—444no—
820C2×Q8—444no—
821C2×Q8—444no—
822C2×D4—228no—
823C2×D4—228no—
824C2×D4—228no—
825C2×D4—228no—
826C2×D4—228no—
827C2×D4—228no—
828C2×D4—228no—
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—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—112no—
867C22×C4—112no—
868C22×C4—112no—
869C22×C4—112no—
870C22×C4—112no—
871C22×C4—112no—
872C22×C4—112no—
873C22×C4—112no—
874C22×C4—112no—
875C22×C4—112no—
876C22×C4—112no—
877C22×C4—112no—
878C22×C4—228no—
879C22×C4—228no—
880C22×C4—228no—
881C22×C4—221no—
882C22×C4—221no—
883C22×C4—221no—
884C22×C4—221no—
885C22×C4—221no—
886C22×C4—221no—
887C22×C4—221no—
888C22×C4—221no—
889C22×C4—221no—
890C22×C4—221no—
891C22×C4—221no—
892C22×C4—221no—
893C22×C4—221no—
894C22×C4—221no—
895C22×C4—221no—
896C22×C4—221no—
897C22×C4—221no—
898C22×C4—221no—
899C22×C4—221no—
900C22×C4—221no—
901C22×C4—221no—
902C22×C4—221no—
903C22×C4—221no—
904C22×C4—221no—
905C22×C4—221no—
906C22×C4—221no—
907C22×C4—221no—
908C22×C4—221no—
909C22×C4—221no—
910C22×C4—221no—
911C22×C4—221no—
912C22×C4—221no—
913C22×C4—221no—
914C22×C4—221no—
915C22×C4—221no—
916C22×C4—221no—
917C22×C4—221no—
918C22×C4—444no—
919C22×C4—444no—
920C22×C4—444no—
921C22×C4—444no—
922C22×C4—444no—
923C22×C4—444no—
924C22×C4—444no—
925C22×C4—444no—
926C22×C4—444no—
927C22×C4—444no—
928C22×C4—444no—
929C22×C4D4×D1112yes—
930C22×C4D4×D1112yes—
931C22×C4D4×D1112yes—
932C22×C4D4×D1112yes—
933C22×C4#434112yes—
934C4⋊C4—44no—
935C4⋊C4—228no—
936C4⋊C4—228no—
937C4⋊C4—228no—
938C4⋊C4—228no—
939C4⋊C4—444no—
940C22⋊C4—28no—
941C22⋊C4—28no—
942C22⋊C4—44no—
943C22⋊C4—228no—
944C22⋊C4—228no—
945C22⋊C4—228no—
946C22⋊C4—228no—
947C22⋊C4—444no—
948C22⋊C4—444no—
949C22⋊C4—444no—
950C42—228no—
951C11#1472311yescharacteristic, complemented, Sylow
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—114no—
987C23—222no—
988C23—222no—
989C23—222no—
990C23—222no—
991C23—222no—
992C23—222no—
993C23—222no—
994C23—222no—
995C23—222no—
996C23—222no—
997C23—222no—
998C23—222no—
999C23—222no—
1000C23—222no—
1001C23—222no—
1002C23—222no—
1003C23—222no—
1004C23—222no—
1005C23—441no—
1006C23—441no—
1007C23—441no—
1008C23—441no—
1009C23—441no—
1010C23—441no—
1011C23—441no—
1012C23—441no—
1013C23—441no—
1014C23—441no—
1015C23—441no—
1016C23—441no—
1017C23—441no—
1018C23—441no—
1019C23—441no—
1020C23—441no—
1021C23#6694914yes—
1022C23C2×#433911yescharacteristic
1023C23C2×D4×D1111yescharacteristic
1024C23C2×D4×D1111yescharacteristic
1025C23C2×D4×D1111yescharacteristic
1026C23C2×D4×D1111yescharacteristic
1027C23C2×D4×D1111yescharacteristic
1028C23C2×#434111yescharacteristic
1029C23#6703711yescharacteristic
1030C23C2×Q8×D1111yescharacteristic
1031C23#41×D1111yescharacteristic
1032C23#41×D1111yescharacteristic
1033C23#41×D1111yescharacteristic
1034C23#6704211yescharacteristic
1035C23#6704311yescharacteristic
1036C23#6704311yescharacteristic
1037Q8—4416no—
1038D4—2232no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—114no—
1082C2×C4—114no—
1083C2×C4—114no—
1084C2×C4—222no—
1085C2×C4—222no—
1086C2×C4—222no—
1087C2×C4—222no—
1088C2×C4—222no—
1089C2×C4—222no—
1090C2×C4—222no—
1091C2×C4—222no—
1092C2×C4—222no—
1093C2×C4—222no—
1094C2×C4—222no—
1095C2×C4—222no—
1096C2×C4—222no—
1097C2×C4—222no—
1098C2×C4—222no—
1099C2×C4—222no—
1100C2×C4—222no—
1101C2×C4—222no—
1102C2×C4—222no—
1103C2×C4—222no—
1104C2×C4—222no—
1105C2×C4—222no—
1106C2×C4—222no—
1107C2×C4—222no—
1108C2×C4—222no—
1109C2×C4—222no—
1110C2×C4—222no—
1111C2×C4—4416no—
1112C2×C4—4416no—
1113C2×C4—441no—
1114C2×C4—441no—
1115C2×C4—441no—
1116C2×C4—441no—
1117C2×C4—441no—
1118C2×C4—441no—
1119C2×C4—441no—
1120C2×C4—441no—
1121C2×C4—441no—
1122C2×C4—441no—
1123C2×C4—441no—
1124C2×C4—441no—
1125C2×C4—441no—
1126C2×C4—441no—
1127C2×C4—441no—
1128C2×C4—441no—
1129C2×C4—441no—
1130C2×C4—441no—
1131C2×C4—441no—
1132C22—24no—
1133C22—24no—
1134C22—24no—
1135C22—42no—
1136C22—42no—
1137C22—42no—
1138C22—42no—
1139C22—42no—
1140C22—42no—
1141C22—42no—
1142C22—42no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—42no—
1147C22—224no—
1148C22—224no—
1149C22—224no—
1150C22—442no—
1151C22—442no—
1152C22—442no—
1153C22—442no—
1154C22—442no—
1155C22—442no—
1156C22—442no—
1157C22—442no—
1158C22—442no—
1159C22—442no—
1160C22—442no—
1161C22—442no—
1162C22#1062302611yescharacteristic
1163C22C2×#6694911yescharacteristic
1164C22#1062305811yescharacteristic
1165C22#1062307811yescharacteristic
1166C22#1062307811yescharacteristic
1167C22#1062308311yescharacteristic
1168C22#1062308311yescharacteristic
1169C22D11×#12011yescharacteristic
1170C22D11×#12011yescharacteristic
1171C22#1062312111yescharacteristic
1172C22#1062312711yescharacteristic
1173C22#1062312711yescharacteristic
1174C22#1062312911yescharacteristic
1175C22#1062313611yescharacteristic
1176C22#1062313711yescharacteristic
1177C22#1062314011yescharacteristic
1178C22#1062314011yescharacteristic
1179C22#1062314211yescharacteristic
1180C22D11×C22⋊Q811yescharacteristic
1181C22D11×C22⋊Q811yescharacteristic
1182C22#1062316311yescharacteristic
1183C22#1062316311yescharacteristic
1184C22#1062316611yescharacteristic
1185C22#1062316711yescharacteristic
1186C22#1062317911yescharacteristic
1187C22#1062318611yescharacteristic
1188C22#1062318711yescharacteristic
1189C22#1062318711yescharacteristic
1190C22#1062319111yescharacteristic
1191C22#1062319911yescharacteristic
1192C22#1062320011yescharacteristic
1193C22#1062320811yescharacteristic
1194C22#1062323811yescharacteristic
1195C22#1062324111yescharacteristic
1196C22#1062324811yescharacteristic
1197C4—42no—
1198C4—42no—
1199C4—42no—
1200C4—42no—
1201C4—42no—
1202C4—81no—
1203C4—224no—
1204C4—224no—
1205C4—224no—
1206C4—442no—
1207C4—442no—
1208C4—442no—
1209C4—881no—
1210C2—44no—
1211C2—444no—
1212C2#1307183011yescharacteristic
1213C2#1307192511yescharacteristic
1214C2#1307198011yescharacteristic
1215C2#1307223911yescharacteristic
1216C2#1307242611yescharacteristic
1217C2#1307242811yescharacteristic
1218C2#1307245911yescharacteristic
1219C2#1307246111yescharacteristic
1220C2#1307258711yescharacteristic
1221C2#1307258911yescharacteristic
1222C2#1307261011yescharacteristic
1223C2#1307261411yescharacteristic
1224C2#1307379411yescharacteristic
1225C2#1307453511yescharacteristic
1226C2#1307690211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC11×#1439C2
prime radicalC23×C22⋊D11C22
hypercenter#1439D11
hypocenterC11#14723
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C22×#66931C2semidirect
3. C2×#10622592C2semidirect
4. C2×#10622286C2semidirect
5. C2×#10622281C2semidirect
6. C2×#10622602C2semidirect
7. #13066867C2semidirect
8. #13066860C2semidirect
9. #13066859C2semidirect
12. #13066850C2semidirect
13. #13066847C2semidirect
14. #13066838C2semidirect
15. C11×#1439C2semidirect
75. C22×C22⋊D11Q8semidirect
139. C2×C4⋊Dic11D4semidirect
151. C2×Dic11⋊C4D4semidirect
348. #1439D11semidirect
438. C22×D11C22⋊Q8semidirect
531. C2×Dic11C22⋊Q8semidirect
951. C11#14723semidirect

Maximal subgroups

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

subgroupindex
C22×#669312
C22×(C22⋊D11)⋊C42
C2×#106225922
C2×#106222862
C2×#106222812
C2×#106226022
#130668672
#130668602
#130668592
#130668552
#130668502
#130668472
#130668382
C11×#14392
#1472311