Finite Group Databasebeta

← #14683126

Subgroups — #14683126

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×#10622573C211yesmaximal, characteristic
2C2×#10622570C211yesmaximal, characteristic, complemented
3C2×#10622282C211yesmaximal, characteristic, complemented
4C2×#10622826C211yesmaximal, characteristic, complemented
5C2×#10622826C211yesmaximal, characteristic, complemented
6#13066874C211yesmaximal, characteristic, complemented
7#13066864C211yesmaximal, characteristic, complemented
8#13066856C211yesmaximal, characteristic, complemented
9#13066856C211yesmaximal, characteristic, complemented
10#13066855C211yesmaximal, characteristic, complemented
11#13066853C211yesmaximal, characteristic, complemented
12#13066852C211yesmaximal, characteristic, complemented
13#13066852C211yesmaximal, characteristic, complemented
14#13066842C211yesmaximal, characteristic, complemented
15C11×C22⋊#95C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
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
39C2×C11×#95C2211yescharacteristic
40C2×C11×#95C2211yescharacteristic
41#10622826—24no—
42#10622826—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
53#10622573C418yescomplemented
54#10622570—24no—
55#10622282—24no—
56C25×C11C2311yescharacteristic
57C24×D11C2311yescharacteristic
58C24×D11C2311yescharacteristic
59C23×C4×C11—22no—
60C23×C4×C11—22no—
61C23×C4×C11—22no—
62C23×C4×C11—41no—
63C23×C4×C11—41no—
64C23×C4×C11—41no—
65C23×C4×C11—41no—
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C22×C22⋊D11—22no—
73C22×C22⋊D11—22no—
74C22×C22⋊D11—22no—
75C22×C22⋊D11—22no—
76C22×C22⋊D11—22no—
77C22×C22⋊D11—22no—
78C22×C22⋊D11—41no—
79C22×C22⋊D11—41no—
80C22×C22⋊D11—41no—
81C22×C22⋊D11—41no—
82C22×C22⋊D11—41no—
83C22×C22⋊D11—41no—
84C22×C22⋊D11C2×C414yes—
85C22×C22⋊D11C2×C414yes—
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C22×D44—41no—
93C22×D44—41no—
94C22×D44—41no—
95C22×D44—41no—
96C22×D44—41no—
97C22×D44—41no—
98C22×D44C2×C414yescomplemented
99C2×C11×C22⋊C4—22no—
100C2×C11×C22⋊C4—22no—
101C2×C11×C22⋊C4—41no—
102C2×C11×C22⋊C4—41no—
103C2×C11×C22⋊C4—41no—
104C2×C11×C22⋊C4C2×C414yes—
105C2×C22⋊Dic11—22no—
106C2×C22⋊Dic11—22no—
107C2×C22⋊Dic11—41no—
108C2×C22⋊Dic11—41no—
109C2×C22⋊Dic11—41no—
110C2×C22⋊Dic11D414yescomplemented
111C2×(C2×D11)⋊C4—22no—
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—22no—
121C2×(C2×D11)⋊C4—22no—
122C2×(C2×D11)⋊C4—22no—
123C2×(C2×D11)⋊C4—22no—
124C2×(C2×D11)⋊C4—22no—
125C2×(C2×D11)⋊C4—41no—
126C2×(C2×D11)⋊C4—41no—
127C2×(C2×D11)⋊C4—41no—
128C2×(C2×D11)⋊C4—41no—
129C2×(C2×D11)⋊C4—41no—
130C2×(C2×D11)⋊C4—41no—
131C2×(C2×D11)⋊C4—41no—
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)⋊C4C2×C414yescomplemented
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—22no—
151C11×#95—41no—
152C11×#95—41no—
153C11×#95—41no—
154C11⋊#95—22no—
155C11⋊#95—22no—
156C11⋊#95—22no—
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×C11C22×C412yes—
178C24×C11C2×D412yes—
179C24×C11#4112yes—
180C24×C11C2411yescharacteristic
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×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×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×D11C22×C412yes—
210C23×D11C22×C412yes—
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×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—44no—
249C22×C4×C11—44no—
250C22×C4×C11—44no—
251C22×C4×C11—44no—
252C22×C4×C11—44no—
253C22×C4×C11—44no—
254C22×C4×C11—44no—
255C22×C4×C11C22×C412yes—
256C22×C4×C11C22×C412yes—
257C22×C4×C11C2×D412yes—
258C22×C4×C11#4112yes—
259C22×C4×C11#4112yes—
260C2×C22⋊D11—28no—
261C2×C22⋊D11—28no—
262C2×C22⋊D11—28no—
263C2×C22⋊D11—44no—
264C2×C22⋊D11—44no—
265C2×C22⋊D11—44no—
266C2×C22⋊D11—44no—
267C2×C22⋊D11—44no—
268C2×C22⋊D11—44no—
269C2×C22⋊D11—44no—
270C2×C22⋊D11—44no—
271C2×C22⋊D11—44no—
272C2×C22⋊D11—44no—
273C2×C22⋊D11—44no—
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—21no—
308C22×Dic11—21no—
309C22×Dic11C22×C412yes—
310C22×Dic11C22×C412yes—
311C22×Dic11C2×D412yes—
312C22×Dic11C2×D412yes—
313C22×Dic11C2×D412yes—
314C22×Dic11C2×D412yes—
315C22×Dic11#4112yes—
316C2×D44—44no—
317C2×D44—44no—
318C2×D44—44no—
319C2×D44—44no—
320C2×D44—44no—
321C2×D44—44no—
322C2×D44—44no—
323C11×C22⋊C4—44no—
324C11×C22⋊C4—44no—
325C22⋊Dic11—44no—
326C22⋊Dic11—44no—
327(C2×D11)⋊C4—28no—
328(C2×D11)⋊C4—44no—
329(C2×D11)⋊C4—44no—
330(C2×D11)⋊C4—44no—
331(C2×D11)⋊C4—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#1438—111no—
350#1437—111no—
351#1437—111no—
352#1437—111no—
353#1434—111no—
354C22⋊#95D1111yescharacteristic, complemented
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—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×C11—41no—
389C23×C11C4×D414yes—
390C23×C11C23×C411yescharacteristic
391C23×C11C22×D411yescharacteristic
392C23×C11C22×D411yescharacteristic
393C23×C11C2×#4111yescharacteristic
394C23×C11C2×#4111yescharacteristic
395C23×C11C2×#4111yescharacteristic
396C23×C11C2×#4111yescharacteristic
397C23×C11H(5,𝔽2)11yescharacteristic
398C23×C11H(5,𝔽2)11yescharacteristic
399C23×C11H(5,𝔽2)11yescharacteristic
400C23×C11H(5,𝔽2)11yescharacteristic
401C23×C11H(5,𝔽2)11yescharacteristic
402C23×C11H(5,𝔽2)11yescharacteristic
403C23×C11H(5,𝔽2)11yescharacteristic
404C23×C11H(5,𝔽2)11yescharacteristic
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—41no—
420C22×D11—41no—
421C22×D11—41no—
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×D11—41no—
439C22×D11—41no—
440C22×D11—41no—
441C22×D11—41no—
442C22×D11—41no—
443C22×D11—41no—
444C22×D11—41no—
445C22×D11—41no—
446C22×D11—41no—
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—
475C2×C4×C11—22no—
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—22no—
486C2×C4×C11—22no—
487C2×C4×C11—22no—
488C2×C4×C11—22no—
489C2×C4×C11—22no—
490C2×C4×C11—416no—
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—
511C2×C4×C11—41no—
512C2×C4×C11—41no—
513C2×C4×C11—41no—
514C2×C4×C11—41no—
515C2×C4×C11—41no—
516C2×C4×C11—41no—
517C2×C4×C11—41no—
518C22⋊D11—416no—
519C22⋊D11—416no—
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—22no—
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×Dic11C4×D414yes—
562D44—416no—
563C23×D4—111no—
564C23×D4—111no—
565C23×D4—111no—
566C24×C4C2×D1111yescharacteristic
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⋊C4—111no—
579C22×C22⋊C4—111no—
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×#95C2×D1111yescharacteristic
600C2×#95C2×D1111yescharacteristic
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×C11C2×C4×D411yescharacteristic
619C22×C11C2×C4×D411yescharacteristic
620C22×C11C4×#4111yescharacteristic
621C22×C11#51811yescharacteristic
622C22×C11#51811yescharacteristic
623C22×C11#51811yescharacteristic
624C22×C11#51811yescharacteristic
625C22×C11#53411yescharacteristic
626C22×C11#53511yescharacteristic
627C22×C11#53511yescharacteristic
628C22×C11#53511yescharacteristic
629C22×C11#53811yescharacteristic
630C22×C11#53811yescharacteristic
631C22×C11#53811yescharacteristic
632C22×C11#53811yescharacteristic
633C22×C11#54011yescharacteristic
634C22×C11#54011yescharacteristic
635C22×C11#54011yescharacteristic
636C22×C11#54011yescharacteristic
637C22×C11D4211yescharacteristic
638C22×C11#54611yescharacteristic
639C22×C11#54611yescharacteristic
640C22×C11#54611yescharacteristic
641C22×C11#54611yescharacteristic
642C22×C11#54611yescharacteristic
643C22×C11#55011yescharacteristic
644C22×C11#55111yescharacteristic
645C22×C11#55311yescharacteristic
646C22×C11#55311yescharacteristic
647C22×C11#55311yescharacteristic
648C22×C11#55511yescharacteristic
649C22×C11#56011yescharacteristic
650C22×C11#56011yescharacteristic
651C22×C11#56011yescharacteristic
652C22×C11H(3,𝔽4)11yescharacteristic
653C2×D11—42no—
654C2×D11—42no—
655C2×D11—42no—
656C2×D11—42no—
657C2×D11—42no—
658C2×D11—42no—
659C2×D11—42no—
660C2×D11—42no—
661C2×D11—42no—
662C2×D11—42no—
663C2×D11—42no—
664C2×D11—42no—
665C2×D11—42no—
666C2×D11—42no—
667C2×D11—81no—
668C2×D11—81no—
669C2×D11—81no—
670C2×D11—81no—
671C2×D11—81no—
672C2×D11—81no—
673C2×D11—81no—
674C2×D11—81no—
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—42no—
687C4×C11—42no—
688C4×C11—81no—
689Dic11—24no—
690Dic11—42no—
691Dic11—42no—
692Dic11—42no—
693Dic11—42no—
694Dic11—81no—
695C25—111no—
696C25—111no—
697C25C22×D1111yescharacteristic
698C22×D4—114no—
699C22×D4—114no—
700C22×D4—114no—
701C22×D4—222no—
702C22×D4—222no—
703C22×D4—222no—
704C22×D4—222no—
705C22×D4—222no—
706C22×D4—222no—
707C22×D4—441no—
708C22×D4—441no—
709C22×D4—441no—
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×D4—441no—
719C23×C4—22no—
720C23×C4—22no—
721C23×C4—22no—
722C23×C4—41no—
723C23×C4—41no—
724C23×C4—41no—
725C23×C4—41no—
726C23×C4—111no—
727C23×C4—111no—
728C23×C4—111no—
729C23×C4—111no—
730C23×C4—111no—
731C23×C4—111no—
732C23×C4C22×D1111yescharacteristic
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—41no—
744C2×C22⋊C4—41no—
745C2×C22⋊C4—41no—
746C2×C22⋊C4—114no—
747C2×C22⋊C4—114no—
748C2×C22⋊C4—114no—
749C2×C22⋊C4—222no—
750C2×C22⋊C4—222no—
751C2×C22⋊C4—222no—
752C2×C22⋊C4—222no—
753C2×C22⋊C4—222no—
754C2×C22⋊C4—222no—
755C2×C22⋊C4—222no—
756C2×C22⋊C4—222no—
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—441no—
766C2×C22⋊C4—441no—
767C2×C22⋊C4—441no—
768C2×C22⋊C4—441no—
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⋊C4C4×D1114yes—
783C2×C42—222no—
784C2×C42—222no—
785C2×C42—222no—
786C2×C42—441no—
787C2×C42—441no—
788C2×C42—441no—
789#95—22no—
790#95—41no—
791#95—41no—
792#95—41no—
793#95—114no—
794#95—114no—
795#95—222no—
796#95—222no—
797#95—222no—
798#95—441no—
799#95—441no—
800#95—441no—
801#95—441no—
802#95—441no—
803C2×C11—44no—
804C2×C11#232111yescharacteristic
805C2×C11#232811yescharacteristic
806C2×C11#233311yescharacteristic
807C2×C11#235811yescharacteristic
808C2×C11#236311yescharacteristic
809C2×C11#236411yescharacteristic
810C2×C11#237511yescharacteristic
811C2×C11#267011yescharacteristic
812C2×C11#267311yescharacteristic
813C2×C11#269911yescharacteristic
814C2×C11#270311yescharacteristic
815C2×C11#270311yescharacteristic
816C2×C11#271411yescharacteristic
817C2×C11#275311yescharacteristic
818C2×C11#275611yescharacteristic
819D11—82no—
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—112no—
834C24—112no—
835C24—221no—
836C24—221no—
837C24—221no—
838C24—221no—
839C24—221no—
840C24—221no—
841C24—221no—
842C24—221no—
843C24—221no—
844C24—221no—
845C24—221no—
846C24—221no—
847C24—221no—
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—
862C24—221no—
863C24C2×C4×D1112yes—
864C24D4×D1112yes—
865C24#434312yes—
866C24C23×D1111yescharacteristic
867C2×D4—228no—
868C2×D4—228no—
869C2×D4—228no—
870C2×D4—444no—
871C2×D4—444no—
872C2×D4—444no—
873C2×D4—444no—
874C2×D4—444no—
875C2×D4—444no—
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—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—44no—
926C22×C4—44no—
927C22×C4—44no—
928C22×C4—44no—
929C22×C4—44no—
930C22×C4—44no—
931C22×C4—44no—
932C22×C4—112no—
933C22×C4—112no—
934C22×C4—112no—
935C22×C4—112no—
936C22×C4—112no—
937C22×C4—112no—
938C22×C4—112no—
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—221no—
970C22×C4—221no—
971C22×C4—221no—
972C22×C4—221no—
973C22×C4—221no—
974C22×C4C2×C4×D1112yes—
975C22×C4C2×C4×D1112yes—
976C22×C4#433912yes—
977C22×C4#433912yes—
978C22×C4D4×D1112yes—
979C4⋊C4—444no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—228no—
983C22⋊C4—444no—
984C22⋊C4—444no—
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—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—222no—
1032C23—222no—
1033C23—222no—
1034C23—222no—
1035C23—222no—
1036C23—222no—
1037C23—222no—
1038C23—222no—
1039C23—222no—
1040C23—222no—
1041C23—222no—
1042C23—222no—
1043C23—222no—
1044C23—222no—
1045C23—441no—
1046C23—441no—
1047C23—441no—
1048C23—441no—
1049C23—441no—
1050C23—441no—
1051C23—441no—
1052C23—441no—
1053C23—441no—
1054C23—441no—
1055C23—441no—
1056C23—441no—
1057C23—441no—
1058C23—441no—
1059C23—441no—
1060C23—441no—
1061C23—441no—
1062C23—441no—
1063C23—441no—
1064C23—441no—
1065C23—441no—
1066C23—441no—
1067C23—441no—
1068C23—441no—
1069C23—441no—
1070C23—441no—
1071C23—441no—
1072C23—441no—
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#6694614yes—
1102C23C22×C4×D1111yescharacteristic
1103C23C2×#433911yescharacteristic
1104C23C2×#433911yescharacteristic
1105C23C2×D4×D1111yescharacteristic
1106C23C2×D4×D1111yescharacteristic
1107C23#6703711yescharacteristic
1108C23#6703711yescharacteristic
1109C23#6703711yescharacteristic
1110C23#6703711yescharacteristic
1111C23#6703711yescharacteristic
1112C23C2×#434311yescharacteristic
1113C23#41×D1111yescharacteristic
1114C23#6704211yescharacteristic
1115C23#6704211yescharacteristic
1116C23#6704211yescharacteristic
1117D4—4416no—
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—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—416no—
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—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—114no—
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—222no—
1181C2×C4—222no—
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—442no—
1221C22—442no—
1222C22—442no—
1223C22—442no—
1224C22—442no—
1225C22—442no—
1226C22—442no—
1227C22—442no—
1228C22—442no—
1229C22—442no—
1230C22—442no—
1231C22—442no—
1232C22—442no—
1233C22—442no—
1234C22—881no—
1235C22—881no—
1236C22—881no—
1237C22—881no—
1238C22—881no—
1239C22—881no—
1240C22—881no—
1241C22—881no—
1242C22—881no—
1243C22—881no—
1244C22—881no—
1245C22—881no—
1246C22—881no—
1247C22—881no—
1248C22—881no—
1249C22—881no—
1250C22C4×#433911yescharacteristic
1251C22#1062301711yescharacteristic
1252C22#1062302111yescharacteristic
1253C22#1062302111yescharacteristic
1254C22#1062302111yescharacteristic
1255C22#1062302511yescharacteristic
1256C22C2×#6694611yescharacteristic
1257C22#1062304511yescharacteristic
1258C22#1062304511yescharacteristic
1259C22#1062306311yescharacteristic
1260C22#1062306611yescharacteristic
1261C22#1062307111yescharacteristic
1262C22C4×D4×D1111yescharacteristic
1263C22#1062307611yescharacteristic
1264C22#1062307611yescharacteristic
1265C22#1062307611yescharacteristic
1266C22#1062308411yescharacteristic
1267C22#1062309111yescharacteristic
1268C22#1062309311yescharacteristic
1269C22#1062312111yescharacteristic
1270C22#1062312311yescharacteristic
1271C22#1062312311yescharacteristic
1272C22#1062312511yescharacteristic
1273C22#1062313811yescharacteristic
1274C22#1062314611yescharacteristic
1275C22#1062315111yescharacteristic
1276C22#1062315111yescharacteristic
1277C22#1062316111yescharacteristic
1278C22#1062316811yescharacteristic
1279C22#1062317511yescharacteristic
1280C22#1062317511yescharacteristic
1281C22#1062318411yescharacteristic
1282C22#1062318511yescharacteristic
1283C22#1062319411yescharacteristic
1284C22#1062319711yescharacteristic
1285C4—42no—
1286C4—42no—
1287C4—42no—
1288C4—42no—
1289C4—42no—
1290C4—81no—
1291C4—224no—
1292C4—442no—
1293C4—442no—
1294C4—442no—
1295C4—442no—
1296C4—881no—
1297C2—44no—
1298C2—882no—
1299C2—882no—
1300C2#1307127311yescharacteristic
1301C2#1307133711yescharacteristic
1302C2#1307137611yescharacteristic
1303C2#1307159211yescharacteristic
1304C2#1307165511yescharacteristic
1305C2#1307166311yescharacteristic
1306C2#1307175411yescharacteristic
1307C2#1307484211yescharacteristic
1308C2#1307488611yescharacteristic
1309C2#1307520311yescharacteristic
1310C2#1307525911yescharacteristic
1311C2#1307526011yescharacteristic
1312C2#1307541311yescharacteristic
1313C2#1307589411yescharacteristic
1314C2#1307593911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC2×#10622573C2
hypercenterC22⋊#95D11
hypocenterC11#14520
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#10622570C2semidirect
3. C2×#10622282C2semidirect
4. C2×#10622826C2semidirect
5. C2×#10622826C2semidirect
6. #13066874C2semidirect
7. #13066864C2semidirect
8. #13066856C2semidirect
9. #13066856C2semidirect
10. #13066855C2semidirect
11. #13066853C2semidirect
12. #13066852C2semidirect
13. #13066852C2semidirect
14. #13066842C2semidirect
15. C11×C22⋊#95C2semidirect
53. #10622573C4semidirect
98. C22×D44C2×C4semidirect
110. C2×C22⋊Dic11D4semidirect
139. C2×(C2×D11)⋊C4C2×C4semidirect
140. C2×(C2×D11)⋊C4C2×C4semidirect
162. C11⋊#95C2×C4semidirect
163. C11⋊#95D4semidirect
354. C22⋊#95D11semidirect
996. C11#14520semidirect

Maximal subgroups

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

subgroupindex
C2×#106225732
C2×#106225702
C2×#106222822
C2×#106228262
#130668742
#130668642
#130668562
#130668552
#130668532
#130668522
#130668422
C11×C22⋊#952
#1452011