Finite Group Databasebeta

← #14683128

Subgroups — #14683128

Order 2816.

2182 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622836C211yesmaximal, characteristic
2C2×#10622570C211yesmaximal, characteristic, complemented
3C2×#10622557C211yesmaximal, characteristic, complemented
4C2×#10622833C211yesmaximal, characteristic, complemented
5C2×#10622571C211yesmaximal, characteristic, complemented
6#13066871C211yesmaximal, characteristic, complemented
7#13066864C211yesmaximal, characteristic, complemented
8#13066855C211yesmaximal, characteristic, complemented
9#13066855C211yesmaximal, characteristic, complemented
10#13066853C211yesmaximal, characteristic, complemented
11#13066853C211yesmaximal, characteristic, complemented
12#13066852C211yesmaximal, characteristic, complemented
13#13066842C211yesmaximal, characteristic, complemented
14#13066838C211yesmaximal, characteristic, complemented
15C11×#1438C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×C4×Dic11C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
38C2×C11×#95C2211yescharacteristic
39#10622836C418yescomplemented
40#10622833—24no—
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
53#10622571—24no—
54#10622570—24no—
55#10622557—24no—
56C25×C11C2311yescharacteristic
57C25×C11C2311yescharacteristic
58C24×D11C2311yescharacteristic
59C22×D4×C11—22no—
60C22×D4×C11—22no—
61C22×D4×C11—41no—
62C22×D4×C11—41no—
63C22×D4×C11—41no—
64C22×D4×C11—41no—
65C22×D4×C11C2×C414yes—
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C22×C22⋊D11—22no—
72C22×C22⋊D11—22no—
73C22×C22⋊D11—22no—
74C22×C22⋊D11—22no—
75C22×C22⋊D11—41no—
76C22×C22⋊D11—41no—
77C22×C22⋊D11—41no—
78C22×C22⋊D11—41no—
79C22×C22⋊D11—41no—
80C22×C22⋊D11—41no—
81C22×C22⋊D11—41no—
82C22×C22⋊D11—41no—
83C22×C22⋊D11C2×C414yes—
84C22×C22⋊D11C2×C414yescomplemented
85C23×Dic11—22no—
86C23×Dic11—22no—
87C23×Dic11—22no—
88C23×Dic11—41no—
89C23×Dic11—41no—
90C23×Dic11—41no—
91C23×Dic11—41no—
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C2×C11×C22⋊C4—22no—
100C2×C11×C22⋊C4—22no—
101C2×C11×C22⋊C4—22no—
102C2×C11×C22⋊C4—22no—
103C2×C11×C22⋊C4—22no—
104C2×C11×C22⋊C4—22no—
105C2×C11×C22⋊C4—41no—
106C2×C11×C22⋊C4—41no—
107C2×C11×C22⋊C4—41no—
108C2×C11×C22⋊C4—41no—
109C2×C11×C22⋊C4—41no—
110C2×C11×C22⋊C4—41no—
111C2×C22⋊Dic11—22no—
112C2×C22⋊Dic11—22no—
113C2×C22⋊Dic11—22no—
114C2×C22⋊Dic11—22no—
115C2×C22⋊Dic11—22no—
116C2×C22⋊Dic11—22no—
117C2×C22⋊Dic11—41no—
118C2×C22⋊Dic11—41no—
119C2×C22⋊Dic11—41no—
120C2×C22⋊Dic11—41no—
121C2×C22⋊Dic11—41no—
122C2×C22⋊Dic11—41no—
123C2×C22⋊Dic11C2×C414yes—
124C2×C22⋊Dic11C2×C414yescomplemented
125C2×C22⋊Dic11D414yescomplemented
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—41no—
133C2×(C2×D11)⋊C4—41no—
134C2×(C2×D11)⋊C4—41no—
135C2×(C2×D11)⋊C4—41no—
136C2×(C2×D11)⋊C4—41no—
137C2×(C2×D11)⋊C4—41no—
138C2×(C2×D11)⋊C4—41no—
139C2×(C2×D11)⋊C4—41no—
140C2×(C2×D11)⋊C4C2×C414yescomplemented
141C2×Dic11⋊C4—22no—
142C2×Dic11⋊C4—22no—
143C2×Dic11⋊C4—41no—
144C2×C4×Dic11—22no—
145C2×C4×Dic11—22no—
146C2×C4×Dic11—22no—
147C2×C4×Dic11—41no—
148C2×C4×Dic11—41no—
149C2×C4×Dic11—41no—
150C11×#95—41no—
151C11×#95—41no—
152C11⋊#95—22no—
153C11⋊#95—22no—
154C11⋊#95—22no—
155C11⋊#95—22no—
156C11⋊#95—41no—
157C11⋊#95—41no—
158C11⋊#95—41no—
159C11⋊#95—41no—
160C11⋊#95—41no—
161C11⋊#95—41no—
162C11⋊#95C2×C414yescomplemented
163C11⋊#95D414yescomplemented
164#14520—111nomaximal, Sylow
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×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×C11—21no—
185C24×C11—21no—
186C24×C11—21no—
187C24×C11—21no—
188C24×C11—21no—
189C24×C11—21no—
190C24×C11—21no—
191C24×C11C22×C412yes—
192C24×C11C22×C412yes—
193C24×C11C2×D412yes—
194C24×C11#4112yes—
195C24×C11C2411yescharacteristic
196C23×D11—21no—
197C23×D11—21no—
198C23×D11—21no—
199C23×D11—21no—
200C23×D11—21no—
201C23×D11—21no—
202C23×D11—21no—
203C23×D11—21no—
204C23×D11—21no—
205C23×D11—21no—
206C23×D11—21no—
207C23×D11—21no—
208C23×D11—21no—
209C23×D11—21no—
210C23×D11C22×C412yes—
211C2×D4×C11—28no—
212C2×D4×C11—44no—
213C2×D4×C11—44no—
214C2×D4×C11—44no—
215C2×D4×C11—44no—
216C2×D4×C11—44no—
217C2×D4×C11—44no—
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×C11—21no—
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—21no—
249C22×C4×C11—21no—
250C22×C4×C11C22×C412yes—
251C22×C4×C11C2×D412yes—
252C22×C4×C11#4112yes—
253C2×C22⋊D11—28no—
254C2×C22⋊D11—28no—
255C2×C22⋊D11—44no—
256C2×C22⋊D11—44no—
257C2×C22⋊D11—44no—
258C2×C22⋊D11—44no—
259C2×C22⋊D11—44no—
260C2×C22⋊D11—44no—
261C2×C22⋊D11—44no—
262C2×C22⋊D11—44no—
263C2×C22⋊D11—44no—
264C2×C22⋊D11—44no—
265C2×C22⋊D11—44no—
266C2×C22⋊D11—44no—
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—21no—
292C22×Dic11—21no—
293C22×Dic11—21no—
294C22×Dic11—21no—
295C22×Dic11—21no—
296C22×Dic11—21no—
297C22×Dic11—21no—
298C22×Dic11—21no—
299C22×Dic11—21no—
300C22×Dic11—21no—
301C22×Dic11—21no—
302C22×Dic11—21no—
303C22×Dic11—21no—
304C22×Dic11—21no—
305C22×Dic11—21no—
306C22×Dic11—21no—
307C22×Dic11—44no—
308C22×Dic11—44no—
309C22×Dic11—44no—
310C22×Dic11—44no—
311C22×Dic11—44no—
312C22×Dic11—44no—
313C22×Dic11—44no—
314C22×Dic11C22×C412yes—
315C22×Dic11C22×C412yes—
316C22×Dic11C22×C412yes—
317C22×Dic11C2×D412yes—
318C22×Dic11C2×D412yes—
319C22×Dic11C2×D412yes—
320C22×Dic11C2×D412yes—
321C22×Dic11#4112yes—
322C22×Dic11#4112yes—
323C11×C22⋊C4—44no—
324C11×C22⋊C4—44no—
325C11×C22⋊C4—44no—
326C11×C22⋊C4—44no—
327C22⋊Dic11—28no—
328C22⋊Dic11—44no—
329C22⋊Dic11—44no—
330C22⋊Dic11—44no—
331C22⋊Dic11—44no—
332(C2×D11)⋊C4—44no—
333(C2×D11)⋊C4—44no—
334(C2×D11)⋊C4—44no—
335(C2×D11)⋊C4—44no—
336(C2×D11)⋊C4—44no—
337Dic11⋊C4—44no—
338C4×Dic11—44no—
339C4×Dic11—44no—
340C2×#392—111no—
341C2×#390—111no—
342C2×#388—111no—
343C2×#386—111no—
344C2×#386—111no—
345#1442—111no—
346#1440—111no—
347#1438—111no—
348#1438—111no—
349#1438D1111yescharacteristic, complemented
350#1437—111no—
351#1437—111no—
352#1437—111no—
353#1434—111no—
354C22⋊#95—111no—
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—22no—
373C23×C11—22no—
374C23×C11—22no—
375C23×C11—22no—
376C23×C11—22no—
377C23×C11—22no—
378C23×C11—22no—
379C23×C11—22no—
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×C11—41no—
389C23×C11—41no—
390C23×C11—41no—
391C23×C11—41no—
392C23×C11—41no—
393C23×C11—41no—
394C23×C11—41no—
395C23×C11—41no—
396C23×C11—41no—
397C23×C11—41no—
398C23×C11—41no—
399C23×C11—41no—
400C23×C11—41no—
401C23×C11—41no—
402C23×C11—41no—
403C23×C11—41no—
404C23×C11—41no—
405C23×C11—41no—
406C23×C11—41no—
407C23×C11—41no—
408C23×C11—41no—
409C23×C11—41no—
410C23×C11—41no—
411C23×C11—41no—
412C23×C11—41no—
413C23×C11—41no—
414C23×C11—41no—
415C23×C11—41no—
416C23×C11—41no—
417C23×C11—41no—
418C23×C11—41no—
419C23×C11—41no—
420C23×C11—41no—
421C23×C11—41no—
422C23×C11—41no—
423C23×C11—41no—
424C23×C11C4×D414yes—
425C23×C11C23×C411yescharacteristic
426C23×C11C22×D411yescharacteristic
427C23×C11C22×D411yescharacteristic
428C23×C11C2×#4111yescharacteristic
429C23×C11C2×#4111yescharacteristic
430C23×C11C2×#4111yescharacteristic
431C23×C11C2×#4111yescharacteristic
432C23×C11H(5,𝔽2)11yescharacteristic
433C23×C11H(5,𝔽2)11yescharacteristic
434C23×C11H(5,𝔽2)11yescharacteristic
435C23×C11H(5,𝔽2)11yescharacteristic
436C23×C11H(5,𝔽2)11yescharacteristic
437C23×C11H(5,𝔽2)11yescharacteristic
438C23×C11H(5,𝔽2)11yescharacteristic
439C23×C11H(5,𝔽2)11yescharacteristic
440C22×D11—22no—
441C22×D11—22no—
442C22×D11—22no—
443C22×D11—22no—
444C22×D11—22no—
445C22×D11—22no—
446C22×D11—22no—
447C22×D11—41no—
448C22×D11—41no—
449C22×D11—41no—
450C22×D11—41no—
451C22×D11—41no—
452C22×D11—41no—
453C22×D11—41no—
454C22×D11—41no—
455C22×D11—41no—
456C22×D11—41no—
457C22×D11—41no—
458C22×D11—41no—
459C22×D11—41no—
460C22×D11—41no—
461C22×D11—41no—
462C22×D11—41no—
463C22×D11—41no—
464C22×D11—41no—
465C22×D11—41no—
466C22×D11—41no—
467C22×D11—41no—
468C22×D11—41no—
469C22×D11—41no—
470C22×D11—41no—
471C22×D11—41no—
472C22×D11—41no—
473C22×D11—41no—
474C22×D11—41no—
475D4×C11—416no—
476C2×C4×C11—22no—
477C2×C4×C11—22no—
478C2×C4×C11—22no—
479C2×C4×C11—22no—
480C2×C4×C11—22no—
481C2×C4×C11—22no—
482C2×C4×C11—22no—
483C2×C4×C11—22no—
484C2×C4×C11—22no—
485C2×C4×C11—41no—
486C2×C4×C11—41no—
487C2×C4×C11—41no—
488C2×C4×C11—41no—
489C2×C4×C11—41no—
490C2×C4×C11—41no—
491C2×C4×C11—41no—
492C2×C4×C11—41no—
493C2×C4×C11—41no—
494C2×C4×C11—41no—
495C2×C4×C11—41no—
496C2×C4×C11—41no—
497C2×C4×C11—41no—
498C2×C4×C11—41no—
499C2×C4×C11—41no—
500C2×C4×C11—41no—
501C2×C4×C11—41no—
502C2×C4×C11—41no—
503C2×C4×C11—41no—
504C2×C4×C11—41no—
505C2×C4×C11—41no—
506C2×C4×C11—41no—
507C2×C4×C11—41no—
508C2×C4×C11—41no—
509C2×C4×C11—41no—
510C2×C4×C11—41no—
511C22⋊D11—416no—
512C22⋊D11—416no—
513C2×Dic11—22no—
514C2×Dic11—22no—
515C2×Dic11—22no—
516C2×Dic11—22no—
517C2×Dic11—22no—
518C2×Dic11—22no—
519C2×Dic11—22no—
520C2×Dic11—22no—
521C2×Dic11—22no—
522C2×Dic11—22no—
523C2×Dic11—22no—
524C2×Dic11—22no—
525C2×Dic11—22no—
526C2×Dic11—22no—
527C2×Dic11—22no—
528C2×Dic11—22no—
529C2×Dic11—22no—
530C2×Dic11—22no—
531C2×Dic11—22no—
532C2×Dic11—22no—
533C2×Dic11—22no—
534C2×Dic11—22no—
535C2×Dic11—22no—
536C2×Dic11—22no—
537C2×Dic11—416no—
538C2×Dic11—41no—
539C2×Dic11—41no—
540C2×Dic11—41no—
541C2×Dic11—41no—
542C2×Dic11—41no—
543C2×Dic11—41no—
544C2×Dic11—41no—
545C2×Dic11—41no—
546C2×Dic11—41no—
547C2×Dic11—41no—
548C2×Dic11—41no—
549C2×Dic11—41no—
550C2×Dic11—41no—
551C2×Dic11—41no—
552C2×Dic11—41no—
553C2×Dic11—41no—
554C2×Dic11—41no—
555C2×Dic11—41no—
556C2×Dic11—41no—
557C2×Dic11—41no—
558C2×Dic11—41no—
559C2×Dic11—41no—
560C2×Dic11—41no—
561C2×Dic11—41no—
562C2×Dic11C4×D414yes—
563C23×D4—111no—
564C23×D4—111no—
565C23×D4C2×D1111yescharacteristic
566C24×C4—111no—
567C22×C4⋊C4—111no—
568C22×C22⋊C4—111no—
569C22×C22⋊C4—111no—
570C22×C22⋊C4—111no—
571C22×C22⋊C4—111no—
572C22×C22⋊C4—111no—
573C22×C22⋊C4—111no—
574C22×C22⋊C4—111no—
575C22×C22⋊C4—111no—
576C22×C22⋊C4—111no—
577C22×C22⋊C4—111no—
578C22×C22⋊C4C2×D1111yescharacteristic
579C22×C22⋊C4C2×D1111yescharacteristic
580C22×C22⋊C4C2×D1111yescharacteristic
581C22×C22⋊C4C2×D1111yescharacteristic
582C22×C42—111no—
583C22×C42—111no—
584#392—118no—
585#390—224no—
586#388—224no—
587#386—224no—
588#386—224no—
589C2×#95—111no—
590C2×#95—111no—
591C2×#95—111no—
592C2×#95—111no—
593C2×#95—111no—
594C2×#95—111no—
595C2×#95—111no—
596C2×#95—111no—
597C2×#95—111no—
598C2×#95—111no—
599C2×#95—111no—
600C2×#95—111no—
601C2×#95C2×D1111yescharacteristic
602C2×#95C2×D1111yescharacteristic
603C22×C11—24no—
604C22×C11—24no—
605C22×C11—24no—
606C22×C11—42no—
607C22×C11—42no—
608C22×C11—42no—
609C22×C11—42no—
610C22×C11—42no—
611C22×C11—42no—
612C22×C11—42no—
613C22×C11—42no—
614C22×C11—42no—
615C22×C11—42no—
616C22×C11—42no—
617C22×C11—42no—
618C22×C11—42no—
619C22×C11—42no—
620C22×C11—42no—
621C22×C11—42no—
622C22×C11—42no—
623C22×C11—42no—
624C22×C11—42no—
625C22×C11—81no—
626C22×C11—81no—
627C22×C11—81no—
628C22×C11—81no—
629C22×C11—81no—
630C22×C11—81no—
631C22×C11—81no—
632C22×C11—81no—
633C22×C11C2×C4×D411yescharacteristic
634C22×C11C2×C4×D411yescharacteristic
635C22×C11C4×#4111yescharacteristic
636C22×C11#51811yescharacteristic
637C22×C11#51811yescharacteristic
638C22×C11#51811yescharacteristic
639C22×C11#51811yescharacteristic
640C22×C11#53411yescharacteristic
641C22×C11#53511yescharacteristic
642C22×C11#53511yescharacteristic
643C22×C11#53511yescharacteristic
644C22×C11#53811yescharacteristic
645C22×C11#53811yescharacteristic
646C22×C11#53811yescharacteristic
647C22×C11#53811yescharacteristic
648C22×C11#54011yescharacteristic
649C22×C11#54011yescharacteristic
650C22×C11#54011yescharacteristic
651C22×C11#54011yescharacteristic
652C22×C11D4211yescharacteristic
653C22×C11#54611yescharacteristic
654C22×C11#54611yescharacteristic
655C22×C11#54611yescharacteristic
656C22×C11#54611yescharacteristic
657C22×C11#54611yescharacteristic
658C22×C11#55011yescharacteristic
659C22×C11#55111yescharacteristic
660C22×C11#55311yescharacteristic
661C22×C11#55311yescharacteristic
662C22×C11#55311yescharacteristic
663C22×C11#55511yescharacteristic
664C22×C11#56011yescharacteristic
665C22×C11#56011yescharacteristic
666C22×C11#56011yescharacteristic
667C22×C11H(3,𝔽4)11yescharacteristic
668C2×D11—42no—
669C2×D11—42no—
670C2×D11—42no—
671C2×D11—42no—
672C2×D11—42no—
673C2×D11—42no—
674C2×D11—42no—
675C2×D11—81no—
676C2×D11—81no—
677C2×D11—81no—
678C2×D11—81no—
679C2×D11—81no—
680C2×D11—81no—
681C2×D11—81no—
682C2×D11—81no—
683C4×C11—42no—
684C4×C11—42no—
685C4×C11—42no—
686C4×C11—81no—
687C4×C11—81no—
688Dic11—24no—
689Dic11—42no—
690Dic11—42no—
691Dic11—42no—
692Dic11—42no—
693Dic11—42no—
694Dic11—42no—
695C25—111no—
696C25C22×D1111yescharacteristic
697C25C22×D1111yescharacteristic
698C22×D4—22no—
699C22×D4—22no—
700C22×D4—41no—
701C22×D4—41no—
702C22×D4—41no—
703C22×D4—41no—
704C22×D4—114no—
705C22×D4—114no—
706C22×D4—222no—
707C22×D4—222no—
708C22×D4—222no—
709C22×D4—222no—
710C22×D4—441no—
711C22×D4—441no—
712C22×D4—441no—
713C22×D4—441no—
714C22×D4—441no—
715C22×D4—441no—
716C22×D4—441no—
717C22×D4—441no—
718C22×D4C4×D1114yes—
719C23×C4—111no—
720C23×C4—111no—
721C23×C4—111no—
722C23×C4—111no—
723C23×C4—111no—
724C23×C4—111no—
725C23×C4—111no—
726C23×C4—222no—
727C23×C4—222no—
728C23×C4—222no—
729C23×C4—441no—
730C23×C4—441no—
731C23×C4—441no—
732C23×C4—441no—
733C23×C4C22×D1111yescharacteristic
734C23×C4C22×D1111yescharacteristic
735C23×C4C22×D1111yescharacteristic
736C23×C4C22×D1111yescharacteristic
737C23×C4C22×D1111yescharacteristic
738C2×C4⋊C4—222no—
739C2×C4⋊C4—222no—
740C2×C4⋊C4—441no—
741C2×C22⋊C4—22no—
742C2×C22⋊C4—22no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—22no—
746C2×C22⋊C4—22no—
747C2×C22⋊C4—41no—
748C2×C22⋊C4—41no—
749C2×C22⋊C4—41no—
750C2×C22⋊C4—41no—
751C2×C22⋊C4—41no—
752C2×C22⋊C4—41no—
753C2×C22⋊C4—114no—
754C2×C22⋊C4—114no—
755C2×C22⋊C4—114no—
756C2×C22⋊C4—114no—
757C2×C22⋊C4—222no—
758C2×C22⋊C4—222no—
759C2×C22⋊C4—222no—
760C2×C22⋊C4—222no—
761C2×C22⋊C4—222no—
762C2×C22⋊C4—222no—
763C2×C22⋊C4—222no—
764C2×C22⋊C4—222no—
765C2×C22⋊C4—222no—
766C2×C22⋊C4—222no—
767C2×C22⋊C4—222no—
768C2×C22⋊C4—222no—
769C2×C22⋊C4—441no—
770C2×C22⋊C4—441no—
771C2×C22⋊C4—441no—
772C2×C22⋊C4—441no—
773C2×C22⋊C4—441no—
774C2×C22⋊C4—441no—
775C2×C22⋊C4—441no—
776C2×C22⋊C4—441no—
777C2×C22⋊C4—441no—
778C2×C22⋊C4—441no—
779C2×C22⋊C4—441no—
780C2×C22⋊C4—441no—
781C2×C22⋊C4—441no—
782C2×C22⋊C4—441no—
783C2×C42—222no—
784C2×C42—222no—
785C2×C42—222no—
786C2×C42—441no—
787C2×C42—441no—
788C2×C42—441no—
789#95—41no—
790#95—41no—
791#95—114no—
792#95—114no—
793#95—222no—
794#95—222no—
795#95—222no—
796#95—222no—
797#95—441no—
798#95—441no—
799#95—441no—
800#95—441no—
801#95—441no—
802#95—441no—
803C2×C11—44no—
804C2×C11—82no—
805C2×C11#232111yescharacteristic
806C2×C11#232811yescharacteristic
807C2×C11#233311yescharacteristic
808C2×C11#235811yescharacteristic
809C2×C11#236311yescharacteristic
810C2×C11#236411yescharacteristic
811C2×C11#237511yescharacteristic
812C2×C11#267011yescharacteristic
813C2×C11#267311yescharacteristic
814C2×C11#269911yescharacteristic
815C2×C11#270311yescharacteristic
816C2×C11#270311yescharacteristic
817C2×C11#271411yescharacteristic
818C2×C11#275311yescharacteristic
819C2×C11#275611yescharacteristic
820D11—82no—
821C24—21no—
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—112no—
848C24—221no—
849C24—221no—
850C24—221no—
851C24—221no—
852C24—221no—
853C24—221no—
854C24—221no—
855C24—221no—
856C24—221no—
857C24—221no—
858C24—221no—
859C24—221no—
860C24—221no—
861C24—221no—
862C24C2×C4×D1112yes—
863C24C2×C4×D1112yes—
864C24D4×D1112yes—
865C24#434112yes—
866C24C23×D1111yescharacteristic
867C2×D4—28no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—228no—
875C2×D4—228no—
876C2×D4—444no—
877C2×D4—444no—
878C2×D4—444no—
879C2×D4—444no—
880C2×D4—444no—
881C2×D4—444no—
882C2×D4—444no—
883C2×D4—444no—
884C2×D4—444no—
885C2×D4—444no—
886C2×D4—444no—
887C2×D4—444no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—112no—
921C22×C4—112no—
922C22×C4—112no—
923C22×C4—112no—
924C22×C4—112no—
925C22×C4—112no—
926C22×C4—112no—
927C22×C4—112no—
928C22×C4—112no—
929C22×C4—221no—
930C22×C4—221no—
931C22×C4—221no—
932C22×C4—221no—
933C22×C4—221no—
934C22×C4—221no—
935C22×C4—221no—
936C22×C4—221no—
937C22×C4—221no—
938C22×C4—221no—
939C22×C4—221no—
940C22×C4—221no—
941C22×C4—221no—
942C22×C4—221no—
943C22×C4—221no—
944C22×C4—221no—
945C22×C4—221no—
946C22×C4—221no—
947C22×C4—221no—
948C22×C4—221no—
949C22×C4—221no—
950C22×C4—221no—
951C22×C4—221no—
952C22×C4—221no—
953C22×C4—221no—
954C22×C4—221no—
955C22×C4—221no—
956C22×C4—221no—
957C22×C4—221no—
958C22×C4—221no—
959C22×C4—221no—
960C22×C4—221no—
961C22×C4—221no—
962C22×C4—221no—
963C22×C4—221no—
964C22×C4—221no—
965C22×C4—221no—
966C22×C4—221no—
967C22×C4—221no—
968C22×C4—221no—
969C22×C4—444no—
970C22×C4—444no—
971C22×C4—444no—
972C22×C4—444no—
973C22×C4—444no—
974C22×C4—444no—
975C22×C4—444no—
976C22×C4C2×C4×D1112yes—
977C22×C4D4×D1112yes—
978C22×C4#434112yes—
979C4⋊C4—444no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—228no—
985C22⋊C4—444no—
986C22⋊C4—444no—
987C22⋊C4—444no—
988C22⋊C4—444no—
989C22⋊C4—444no—
990C22⋊C4—444no—
991C22⋊C4—444no—
992C22⋊C4—444no—
993C22⋊C4—444no—
994C42—444no—
995C42—444no—
996C11#1452011yescharacteristic, complemented, Sylow
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—222no—
1067C23—222no—
1068C23—222no—
1069C23—222no—
1070C23—222no—
1071C23—222no—
1072C23—222no—
1073C23—441no—
1074C23—441no—
1075C23—441no—
1076C23—441no—
1077C23—441no—
1078C23—441no—
1079C23—441no—
1080C23—441no—
1081C23—441no—
1082C23—441no—
1083C23—441no—
1084C23—441no—
1085C23—441no—
1086C23—441no—
1087C23—441no—
1088C23—441no—
1089C23—441no—
1090C23—441no—
1091C23—441no—
1092C23—441no—
1093C23—441no—
1094C23—441no—
1095C23—441no—
1096C23—441no—
1097C23—441no—
1098C23—441no—
1099C23—441no—
1100C23—441no—
1101C23(C22⋊D11)⋊C414yes—
1102C23C22×C4×D1111yescharacteristic
1103C23C2×D4×D1111yescharacteristic
1104C23C2×D4×D1111yescharacteristic
1105C23C2×#434111yescharacteristic
1106C23C2×#434111yescharacteristic
1107C23#6703711yescharacteristic
1108C23#6703711yescharacteristic
1109C23#6703711yescharacteristic
1110C23#6703711yescharacteristic
1111C23#6703711yescharacteristic
1112C23#6703711yescharacteristic
1113C23#41×D1111yescharacteristic
1114C23#41×D1111yescharacteristic
1115C23#6704211yescharacteristic
1116C23#6704211yescharacteristic
1117D4—416no—
1118D4—4416no—
1119D4—4416no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—114no—
1156C2×C4—222no—
1157C2×C4—222no—
1158C2×C4—222no—
1159C2×C4—222no—
1160C2×C4—222no—
1161C2×C4—222no—
1162C2×C4—222no—
1163C2×C4—222no—
1164C2×C4—222no—
1165C2×C4—222no—
1166C2×C4—222no—
1167C2×C4—222no—
1168C2×C4—222no—
1169C2×C4—222no—
1170C2×C4—222no—
1171C2×C4—222no—
1172C2×C4—222no—
1173C2×C4—222no—
1174C2×C4—222no—
1175C2×C4—222no—
1176C2×C4—222no—
1177C2×C4—222no—
1178C2×C4—222no—
1179C2×C4—222no—
1180C2×C4—4416no—
1181C2×C4—441no—
1182C2×C4—441no—
1183C2×C4—441no—
1184C2×C4—441no—
1185C2×C4—441no—
1186C2×C4—441no—
1187C2×C4—441no—
1188C2×C4—441no—
1189C2×C4—441no—
1190C2×C4—441no—
1191C2×C4—441no—
1192C2×C4—441no—
1193C2×C4—441no—
1194C2×C4—441no—
1195C2×C4—441no—
1196C2×C4—441no—
1197C2×C4—441no—
1198C2×C4—441no—
1199C2×C4—441no—
1200C2×C4—441no—
1201C2×C4—441no—
1202C2×C4—441no—
1203C2×C4—441no—
1204C2×C4—441no—
1205C22—24no—
1206C22—24no—
1207C22—24no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—442no—
1236C22—442no—
1237C22—442no—
1238C22—442no—
1239C22—442no—
1240C22—442no—
1241C22—442no—
1242C22—881no—
1243C22—881no—
1244C22—881no—
1245C22—881no—
1246C22—881no—
1247C22—881no—
1248C22—881no—
1249C22—881no—
1250C22C2×(C22⋊D11)⋊C411yescharacteristic
1251C22#1062301711yescharacteristic
1252C22#1062301711yescharacteristic
1253C22C4×#434111yescharacteristic
1254C22C4×D4×D1111yescharacteristic
1255C22#1062307611yescharacteristic
1256C22#1062307611yescharacteristic
1257C22#1062312011yescharacteristic
1258C22#1062312211yescharacteristic
1259C22#1062312211yescharacteristic
1260C22#1062312311yescharacteristic
1261C22#1062312311yescharacteristic
1262C22#1062312411yescharacteristic
1263C22#1062312411yescharacteristic
1264C22#1062312411yescharacteristic
1265C22#1062313211yescharacteristic
1266C22#1062313211yescharacteristic
1267C22#1062313811yescharacteristic
1268C22#1062314011yescharacteristic
1269C22#1062314111yescharacteristic
1270C22#1062314111yescharacteristic
1271C22#1062314611yescharacteristic
1272C22#1062314611yescharacteristic
1273C22#1062314911yescharacteristic
1274C22#1062315011yescharacteristic
1275C22#1062315111yescharacteristic
1276C22#1062315111yescharacteristic
1277C22#1062318511yescharacteristic
1278C22#1062318811yescharacteristic
1279C22#1062318911yescharacteristic
1280C22#1062319411yescharacteristic
1281C22#1062320111yescharacteristic
1282C22#1062321411yescharacteristic
1283C22#1062324911yescharacteristic
1284C22#1062325111yescharacteristic
1285C4—42no—
1286C4—42no—
1287C4—42no—
1288C4—81no—
1289C4—81no—
1290C4—224no—
1291C4—442no—
1292C4—442no—
1293C4—442no—
1294C4—442no—
1295C4—442no—
1296C4—442no—
1297C2—44no—
1298C2—82no—
1299C2—882no—
1300C2#1307127111yescharacteristic
1301C2#1307133711yescharacteristic
1302C2#1307137711yescharacteristic
1303C2#1307159611yescharacteristic
1304C2#1307165111yescharacteristic
1305C2#1307166411yescharacteristic
1306C2#1307175311yescharacteristic
1307C2#1307484411yescharacteristic
1308C2#1307488811yescharacteristic
1309C2#1307520411yescharacteristic
1310C2#1307526411yescharacteristic
1311C2#1307526411yescharacteristic
1312C2#1307541411yescharacteristic
1313C2#1307588611yescharacteristic
1314C2#1307593111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1438C2
socle, cosocleC24×C11C24
prime radicalC2×#10622836C2
hypercenter#1438D11
hypocenterC11#14520
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C2×#10622570C2semidirect
3. C2×#10622557C2semidirect
4. C2×#10622833C2semidirect
5. C2×#10622571C2semidirect
6. #13066871C2semidirect
7. #13066864C2semidirect
8. #13066855C2semidirect
9. #13066855C2semidirect
10. #13066853C2semidirect
11. #13066853C2semidirect
12. #13066852C2semidirect
13. #13066842C2semidirect
14. #13066838C2semidirect
15. C11×#1438C2semidirect
39. #10622836C4semidirect
84. C22×C22⋊D11C2×C4semidirect
124. C2×C22⋊Dic11C2×C4semidirect
125. C2×C22⋊Dic11D4semidirect
140. C2×(C2×D11)⋊C4C2×C4semidirect
162. C11⋊#95C2×C4semidirect
163. C11⋊#95D4semidirect
349. #1438D11semidirect
996. C11#14520semidirect

Maximal subgroups

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

subgroupindex
C2×#106228362
C2×#106225702
C2×#106225572
C2×#106228332
C2×#106225712
#130668712
#130668642
#130668552
#130668532
#130668522
#130668422
#130668382
C11×#14382
#1452011