Finite Group Databasebeta

← #14681111

Subgroups — #14681111

Order 2816.

2594 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66991C211yesmaximal, characteristic
2C2×#10622570C211yesmaximal, characteristic, complemented
3C2×#10622557C211yesmaximal, characteristic, complemented
4C2×#10622833C211yesmaximal, characteristic, complemented
5C2×#10622571C211yesmaximal, characteristic, complemented
6C2×#10622559C211yesmaximal, characteristic, complemented
7C2×#10622280C211yesmaximal, characteristic, complemented
8#13066868C211yesmaximal, characteristic, complemented
9#13066859C211yesmaximal, characteristic, complemented
10#13066859C211yesmaximal, characteristic, complemented
11#13066855C211yesmaximal, characteristic, complemented
12#13066855C211yesmaximal, characteristic, complemented
13#13066850C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×#1438C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C2×#66991—24no—
31C2×#66991—24no—
32C2×#66991C418yescomplemented
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×C4⋊Dic11C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×C4×Dic11C2211yescharacteristic
42C2×C11×#95C2211yescharacteristic
43C2×C11×#95C2211yescharacteristic
44#10622833—24no—
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
55#10622571—24no—
56#10622570—24no—
57#10622559—24no—
58#10622557—24no—
59#10622280—24no—
60C25×C11C2311yescharacteristic
61C25×C11C2311yescharacteristic
62C24×D11C2311yescharacteristic
63C22×D4×C11—22no—
64C22×D4×C11—22no—
65C22×D4×C11—22no—
66C22×D4×C11—22no—
67C22×D4×C11—41no—
68C22×D4×C11—41no—
69C22×D4×C11C2×C414yes—
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C22×C22⋊D11—22no—
76C22×C22⋊D11—22no—
77C22×C22⋊D11—22no—
78C22×C22⋊D11—22no—
79C22×C22⋊D11—22no—
80C22×C22⋊D11—22no—
81C22×C22⋊D11—22no—
82C22×C22⋊D11—22no—
83C22×C22⋊D11—41no—
84C22×C22⋊D11—41no—
85C22×C22⋊D11—41no—
86C22×C22⋊D11—41no—
87C22×C22⋊D11C2×C414yes—
88C22×C22⋊D11C2×C414yescomplemented
89C23×Dic11—22no—
90C23×Dic11—22no—
91C23×Dic11—22no—
92C23×Dic11—41no—
93C23×Dic11—41no—
94C23×Dic11—41no—
95C23×Dic11—41no—
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2311yescharacteristic
103C22×C4×D11—22no—
104C22×C4×D11—22no—
105C22×C4×D11—22no—
106C22×C4×D11—22no—
107C22×C4×D11—41no—
108C22×C4×D11—41no—
109C22×C4×D11C2×C414yescomplemented
110C2×C11×C22⋊C4—22no—
111C2×C11×C22⋊C4—22no—
112C2×C11×C22⋊C4—22no—
113C2×C11×C22⋊C4—22no—
114C2×C11×C22⋊C4—41no—
115C2×C11×C22⋊C4—41no—
116C2×C11×C22⋊C4—41no—
117C2×C11×C22⋊C4—41no—
118C2×C11×C22⋊C4—41no—
119C2×C11×C22⋊C4—41no—
120C2×C11×C22⋊C4—41no—
121C2×C11×C22⋊C4—41no—
122C2×C22⋊Dic11—22no—
123C2×C22⋊Dic11—22no—
124C2×C22⋊Dic11—22no—
125C2×C22⋊Dic11—22no—
126C2×C22⋊Dic11—22no—
127C2×C22⋊Dic11—22no—
128C2×C22⋊Dic11—22no—
129C2×C22⋊Dic11—41no—
130C2×C22⋊Dic11—41no—
131C2×C22⋊Dic11—41no—
132C2×C22⋊Dic11—41no—
133C2×C22⋊Dic11C2×C414yes—
134C2×C22⋊Dic11C2×C414yescomplemented
135C2×C22⋊Dic11D414yes—
136C2×C22⋊Dic11D414yes—
137#66991—232no—
138C2×(C2×D11)⋊C4—22no—
139C2×(C2×D11)⋊C4—22no—
140C2×(C2×D11)⋊C4—22no—
141C2×(C2×D11)⋊C4—22no—
142C2×(C2×D11)⋊C4—22no—
143C2×(C2×D11)⋊C4—41no—
144C2×(C2×D11)⋊C4—41no—
145C2×(C2×D11)⋊C4—41no—
146C2×(C2×D11)⋊C4—41no—
147C2×(C2×D11)⋊C4—41no—
148C2×(C2×D11)⋊C4—41no—
149C2×(C2×D11)⋊C4D414yescomplemented
150C2×C4⋊Dic11—22no—
151C2×C4⋊Dic11—22no—
152C2×C4⋊Dic11C2×C414yescomplemented
153C2×Dic11⋊C4—22no—
154C2×Dic11⋊C4—22no—
155C2×Dic11⋊C4—22no—
156C2×Dic11⋊C4—22no—
157C2×Dic11⋊C4—22no—
158C2×Dic11⋊C4—22no—
159C2×Dic11⋊C4—41no—
160C2×Dic11⋊C4—41no—
161C2×Dic11⋊C4—41no—
162C2×C4×Dic11—22no—
163C2×C4×Dic11—22no—
164C2×C4×Dic11—41no—
165C11×#95—22no—
166C11×#95—22no—
167C11⋊#95—22no—
168C11⋊#95—22no—
169C11⋊#95—22no—
170C11⋊#95—22no—
171C11⋊#95—22no—
172C11⋊#95—22no—
173C11⋊#95—22no—
174C11⋊#95—41no—
175C11⋊#95—41no—
176C11⋊#95D414yescomplemented
177#14361—111nomaximal, Sylow
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×C11—21no—
192C24×C11—21no—
193C24×C11—21no—
194C24×C11—21no—
195C24×C11—21no—
196C24×C11—21no—
197C24×C11—21no—
198C24×C11—21no—
199C24×C11—21no—
200C24×C11—21no—
201C24×C11—21no—
202C24×C11—21no—
203C24×C11—21no—
204C24×C11C22×C412yes—
205C24×C11C22×C412yes—
206C24×C11C2×D412yes—
207C24×C11C2×D412yes—
208C24×C11C2411yescharacteristic
209C23×D11—21no—
210C23×D11—21no—
211C23×D11—21no—
212C23×D11—21no—
213C23×D11—21no—
214C23×D11—21no—
215C23×D11—21no—
216C23×D11—21no—
217C23×D11—21no—
218C23×D11—21no—
219C23×D11—21no—
220C23×D11—21no—
221C23×D11C22×C412yes—
222C23×D11C2×D412yes—
223C23×D11#4112yes—
224C2×D4×C11—28no—
225C2×D4×C11—28no—
226C2×D4×C11—44no—
227C2×D4×C11—44no—
228C2×D4×C11—44no—
229C2×D4×C11—44no—
230C2×D4×C11—44no—
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×C11—21no—
251C22×C4×C11—21no—
252C22×C4×C11—21no—
253C22×C4×C11—21no—
254C22×C4×C11—21no—
255C22×C4×C11—21no—
256C22×C4×C11—21no—
257C22×C4×C11—21no—
258C22×C4×C11—21no—
259C22×C4×C11—21no—
260C22×C4×C11—21no—
261C22×C4×C11—21no—
262C22×C4×C11C22×C412yes—
263C22×C4×C11C2×D412yes—
264C22×C4×C11C2×D412yes—
265C22×C4×C11#4112yes—
266C2×C22⋊D11—28no—
267C2×C22⋊D11—28no—
268C2×C22⋊D11—28no—
269C2×C22⋊D11—28no—
270C2×C22⋊D11—44no—
271C2×C22⋊D11—44no—
272C2×C22⋊D11—44no—
273C2×C22⋊D11—44no—
274C2×C22⋊D11—44no—
275C2×C22⋊D11—44no—
276C2×C22⋊D11—44no—
277C2×C22⋊D11—44no—
278C2×C22⋊D11—44no—
279C2×C22⋊D11—44no—
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×Dic11—21no—
310C22×Dic11—21no—
311C22×Dic11—21no—
312C22×Dic11—21no—
313C22×Dic11—21no—
314C22×Dic11—21no—
315C22×Dic11—21no—
316C22×Dic11—21no—
317C22×Dic11—21no—
318C22×Dic11—21no—
319C22×Dic11—44no—
320C22×Dic11—44no—
321C22×Dic11—44no—
322C22×Dic11—44no—
323C22×Dic11—44no—
324C22×Dic11—44no—
325C22×Dic11—44no—
326C22×Dic11C22×C412yes—
327C22×Dic11C22×C412yes—
328C22×Dic11C22×C412yes—
329C22×Dic11C2×D412yes—
330C22×Dic11C2×D412yes—
331C22×Dic11C2×D412yes—
332C22×Dic11C2×D412yes—
333C22×Dic11C2×D412yes—
334C22×Dic11C2×D412yes—
335C22×Dic11C2×D412yes—
336C2×C4×D11—28no—
337C2×C4×D11—28no—
338C2×C4×D11—44no—
339C2×C4×D11—44no—
340C2×C4×D11—44no—
341C2×C4×D11—44no—
342C2×C4×D11—44no—
343C11×C22⋊C4—44no—
344C11×C22⋊C4—44no—
345C11×C22⋊C4—44no—
346C11×C22⋊C4—44no—
347C22⋊Dic11—28no—
348C22⋊Dic11—44no—
349C22⋊Dic11—44no—
350C22⋊Dic11—44no—
351C22⋊Dic11C22⋊C4116yescomplemented
352(C2×D11)⋊C4—44no—
353(C2×D11)⋊C4—44no—
354(C2×D11)⋊C4—44no—
355(C2×D11)⋊C4—44no—
356C4⋊Dic11—28no—
357Dic11⋊C4—44no—
358Dic11⋊C4—44no—
359Dic11⋊C4—44no—
360C4×Dic11—44no—
361C22×#121—111no—
362C2×#390—111no—
363C2×#388—111no—
364C2×#386—111no—
365C2×#386—111no—
366C2×#385—111no—
367C2×#380—111no—
368#1441—111no—
369#1439—111no—
370#1439—111no—
371#1438—111no—
372#1438—111no—
373#1438D1111yescharacteristic, complemented
374#1436—111no—
375C22⋊#95—111no—
376C23×C11—22no—
377C23×C11—22no—
378C23×C11—22no—
379C23×C11—22no—
380C23×C11—22no—
381C23×C11—22no—
382C23×C11—22no—
383C23×C11—22no—
384C23×C11—22no—
385C23×C11—22no—
386C23×C11—22no—
387C23×C11—22no—
388C23×C11—22no—
389C23×C11—22no—
390C23×C11—22no—
391C23×C11—22no—
392C23×C11—22no—
393C23×C11—22no—
394C23×C11—22no—
395C23×C11—22no—
396C23×C11—22no—
397C23×C11—22no—
398C23×C11—22no—
399C23×C11—22no—
400C23×C11—22no—
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×C11—41no—
425C23×C11—41no—
426C23×C11—41no—
427C23×C11—41no—
428C23×C11—41no—
429C23×C11—41no—
430C23×C11—41no—
431C23×C11—41no—
432C23×C11—41no—
433C23×C11—41no—
434C23×C11—41no—
435C23×C11—41no—
436C23×C11—41no—
437C23×C11—41no—
438C23×C11—41no—
439C23×C11—41no—
440C23×C11—41no—
441C23×C11—41no—
442C23×C11—41no—
443C23×C11—41no—
444C23×C11—41no—
445C23×C11C2×C22⋊C414yes—
446C23×C11C23×C411yescharacteristic
447C23×C11C22×D411yescharacteristic
448C23×C11C22×D411yescharacteristic
449C23×C11C22×D411yescharacteristic
450C23×C11C22×D411yescharacteristic
451C23×C11C2×#4111yescharacteristic
452C23×C11C2×#4111yescharacteristic
453C23×C11H(5,𝔽2)11yescharacteristic
454C23×C11H(5,𝔽2)11yescharacteristic
455C23×C11H(5,𝔽2)11yescharacteristic
456C23×C11H(5,𝔽2)11yescharacteristic
457C23×C11H(5,𝔽2)11yescharacteristic
458C23×C11H(5,𝔽2)11yescharacteristic
459C23×C112−1+411yescharacteristic
460C23×C112−1+411yescharacteristic
461C22×D11—22no—
462C22×D11—22no—
463C22×D11—22no—
464C22×D11—22no—
465C22×D11—22no—
466C22×D11—22no—
467C22×D11—22no—
468C22×D11—22no—
469C22×D11—22no—
470C22×D11—22no—
471C22×D11—22no—
472C22×D11—22no—
473C22×D11—22no—
474C22×D11—22no—
475C22×D11—22no—
476C22×D11—22no—
477C22×D11—22no—
478C22×D11—22no—
479C22×D11—41no—
480C22×D11—41no—
481C22×D11—41no—
482C22×D11—41no—
483C22×D11—41no—
484C22×D11—41no—
485C22×D11—41no—
486C22×D11—41no—
487C22×D11—41no—
488C22×D11—41no—
489C22×D11—41no—
490C22×D11—41no—
491C22×D11—41no—
492C22×D11—41no—
493C22×D11—41no—
494C22×D11—41no—
495C22×D11C4×D414yes—
496D4×C11—416no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—22no—
501C2×C4×C11—22no—
502C2×C4×C11—22no—
503C2×C4×C11—22no—
504C2×C4×C11—22no—
505C2×C4×C11—22no—
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—
518C2×C4×C11—41no—
519C2×C4×C11—41no—
520C2×C4×C11—41no—
521C2×C4×C11—41no—
522C2×C4×C11—41no—
523C2×C4×C11—41no—
524C2×C4×C11—41no—
525C2×C4×C11—41no—
526C2×C4×C11—41no—
527C2×C4×C11—41no—
528C2×C4×C11—41no—
529C2×C4×C11—41no—
530C2×C4×C11—41no—
531C2×C4×C11C4×D414yes—
532C22⋊D11—416no—
533C22⋊D11—416no—
534C2×Dic11—22no—
535C2×Dic11—22no—
536C2×Dic11—22no—
537C2×Dic11—22no—
538C2×Dic11—22no—
539C2×Dic11—22no—
540C2×Dic11—22no—
541C2×Dic11—22no—
542C2×Dic11—22no—
543C2×Dic11—22no—
544C2×Dic11—22no—
545C2×Dic11—22no—
546C2×Dic11—22no—
547C2×Dic11—22no—
548C2×Dic11—22no—
549C2×Dic11—22no—
550C2×Dic11—22no—
551C2×Dic11—22no—
552C2×Dic11—22no—
553C2×Dic11—22no—
554C2×Dic11—22no—
555C2×Dic11—22no—
556C2×Dic11—22no—
557C2×Dic11—22no—
558C2×Dic11—416no—
559C2×Dic11—41no—
560C2×Dic11—41no—
561C2×Dic11—41no—
562C2×Dic11—41no—
563C2×Dic11—41no—
564C2×Dic11—41no—
565C2×Dic11—41no—
566C2×Dic11—41no—
567C2×Dic11—41no—
568C2×Dic11—41no—
569C2×Dic11—41no—
570C2×Dic11—41no—
571C2×Dic11—41no—
572C2×Dic11—41no—
573C2×Dic11—41no—
574C2×Dic11—41no—
575C2×Dic11—41no—
576C2×Dic11—41no—
577C2×Dic11—41no—
578C2×Dic11—41no—
579C2×Dic11—41no—
580C2×Dic11—41no—
581C2×Dic11—41no—
582C2×Dic11C2×C22⋊C414yes—
583C2×Dic11C2×C22⋊C414yes—
584C4×D11—416no—
585C23×D4—111no—
586C23×D4—111no—
587C23×D4C2×D1111yescharacteristic
588C24×C4—111no—
589C24×C4—111no—
590C2×#121—118no—
591C2×#121—224no—
592C2×#121—224no—
593C22×C4⋊C4—111no—
594C22×C4⋊C4—111no—
595C22×C4⋊C4—111no—
596C22×C4⋊C4—111no—
597C22×C22⋊C4—111no—
598C22×C22⋊C4—111no—
599C22×C22⋊C4—111no—
600C22×C22⋊C4—111no—
601C22×C22⋊C4—111no—
602C22×C22⋊C4—111no—
603C22×C22⋊C4—111no—
604C22×C22⋊C4—111no—
605C22×C22⋊C4—111no—
606C22×C22⋊C4C2×D1111yescharacteristic
607C22×C22⋊C4C2×D1111yescharacteristic
608C22×C22⋊C4C2×D1111yescharacteristic
609C22×C22⋊C4C2×D1111yescharacteristic
610C22×C42—111no—
611#390—224no—
612#388—224no—
613#386—224no—
614#386—224no—
615#385—224no—
616#380—224no—
617C2×#95—111no—
618C2×#95—111no—
619C2×#95—111no—
620C2×#95—111no—
621C2×#95—111no—
622C2×#95—111no—
623C2×#95—111no—
624C2×#95—111no—
625C2×#95—111no—
626C2×#95—111no—
627C2×#95C2×D1111yescharacteristic
628C2×#95C2×D1111yescharacteristic
629C22×C11—24no—
630C22×C11—24no—
631C22×C11—24no—
632C22×C11—42no—
633C22×C11—42no—
634C22×C11—42no—
635C22×C11—42no—
636C22×C11—42no—
637C22×C11—42no—
638C22×C11—42no—
639C22×C11—42no—
640C22×C11—42no—
641C22×C11—42no—
642C22×C11—42no—
643C22×C11—42no—
644C22×C11—42no—
645C22×C11—42no—
646C22×C11—42no—
647C22×C11—42no—
648C22×C11—42no—
649C22×C11—42no—
650C22×C11—42no—
651C22×C11—81no—
652C22×C11—81no—
653C22×C11—81no—
654C22×C11—81no—
655C22×C11—81no—
656C22×C11—81no—
657C22×C11—81no—
658C22×C11—81no—
659C22×C11C22×C22⋊C411yescharacteristic
660C22×C11C2×C4×D411yescharacteristic
661C22×C11C2×C4×D411yescharacteristic
662C22×C11#51811yescharacteristic
663C22×C11#51811yescharacteristic
664C22×C11#52011yescharacteristic
665C22×C11#52011yescharacteristic
666C22×C11#53411yescharacteristic
667C22×C11#53511yescharacteristic
668C22×C11#53511yescharacteristic
669C22×C11#53611yescharacteristic
670C22×C11#53711yescharacteristic
671C22×C11#53711yescharacteristic
672C22×C11#53711yescharacteristic
673C22×C11#53711yescharacteristic
674C22×C11#53811yescharacteristic
675C22×C11#53911yescharacteristic
676C22×C11#54011yescharacteristic
677C22×C11#54211yescharacteristic
678C22×C11D4211yescharacteristic
679C22×C11D4211yescharacteristic
680C22×C11D4211yescharacteristic
681C22×C11D4211yescharacteristic
682C22×C11D4211yescharacteristic
683C22×C11#54611yescharacteristic
684C22×C11#54611yescharacteristic
685C22×C11#54611yescharacteristic
686C22×C11#54611yescharacteristic
687C22×C11#54711yescharacteristic
688C22×C11#54811yescharacteristic
689C22×C11#55311yescharacteristic
690C22×C11#56011yescharacteristic
691C22×C11#56011yescharacteristic
692C22×C11#56211yescharacteristic
693C22×C11#56211yescharacteristic
694C2×D11—24no—
695C2×D11—24no—
696C2×D11—24no—
697C2×D11—42no—
698C2×D11—42no—
699C2×D11—42no—
700C2×D11—42no—
701C2×D11—42no—
702C2×D11—42no—
703C2×D11—42no—
704C2×D11—42no—
705C2×D11—42no—
706C2×D11—42no—
707C2×D11—42no—
708C2×D11—42no—
709C4×C11—24no—
710C4×C11—42no—
711C4×C11—81no—
712C4×C11—81no—
713C4×C11—81no—
714Dic11—24no—
715Dic11—24no—
716Dic11—42no—
717Dic11—42no—
718Dic11—42no—
719Dic11—42no—
720Dic11—81no—
721C25—111no—
722C25C22×D1111yescharacteristic
723C25C22×D1111yescharacteristic
724C22×D4—22no—
725C22×D4—22no—
726C22×D4—22no—
727C22×D4—22no—
728C22×D4—41no—
729C22×D4—41no—
730C22×D4—114no—
731C22×D4—114no—
732C22×D4—222no—
733C22×D4—222no—
734C22×D4—222no—
735C22×D4—222no—
736C22×D4—222no—
737C22×D4—222no—
738C22×D4—222no—
739C22×D4—222no—
740C22×D4—441no—
741C22×D4—441no—
742C22×D4—441no—
743C22×D4—441no—
744C22×D4C4×D1114yes—
745C23×C4—111no—
746C23×C4—111no—
747C23×C4—111no—
748C23×C4—111no—
749C23×C4—111no—
750C23×C4—111no—
751C23×C4—114no—
752C23×C4—111no—
753C23×C4—222no—
754C23×C4—222no—
755C23×C4—222no—
756C23×C4—222no—
757C23×C4—222no—
758C23×C4—222no—
759C23×C4—222no—
760C23×C4—441no—
761C23×C4—441no—
762C23×C4—441no—
763C23×C4—441no—
764C23×C4—441no—
765C23×C4—441no—
766C23×C4C22×D1111yescharacteristic
767C23×C4C22×D1111yescharacteristic
768C23×C4C22×D1111yescharacteristic
769C23×C4C22×D1111yescharacteristic
770C23×C4C22×D1111yescharacteristic
771#121—2232no—
772C2×C4⋊C4—114no—
773C2×C4⋊C4—222no—
774C2×C4⋊C4—222no—
775C2×C4⋊C4—222no—
776C2×C4⋊C4—222no—
777C2×C4⋊C4—222no—
778C2×C4⋊C4—222no—
779C2×C4⋊C4—222no—
780C2×C4⋊C4—222no—
781C2×C4⋊C4—441no—
782C2×C4⋊C4—441no—
783C2×C4⋊C4—441no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—41no—
789C2×C22⋊C4—41no—
790C2×C22⋊C4—41no—
791C2×C22⋊C4—41no—
792C2×C22⋊C4—41no—
793C2×C22⋊C4—41no—
794C2×C22⋊C4—41no—
795C2×C22⋊C4—41no—
796C2×C22⋊C4—114no—
797C2×C22⋊C4—114no—
798C2×C22⋊C4—114no—
799C2×C22⋊C4—114no—
800C2×C22⋊C4—114no—
801C2×C22⋊C4—222no—
802C2×C22⋊C4—222no—
803C2×C22⋊C4—222no—
804C2×C22⋊C4—222no—
805C2×C22⋊C4—222no—
806C2×C22⋊C4—222no—
807C2×C22⋊C4—222no—
808C2×C22⋊C4—222no—
809C2×C22⋊C4—222no—
810C2×C22⋊C4—222no—
811C2×C22⋊C4—222no—
812C2×C22⋊C4—222no—
813C2×C22⋊C4—441no—
814C2×C22⋊C4—441no—
815C2×C22⋊C4—441no—
816C2×C22⋊C4—441no—
817C2×C22⋊C4—441no—
818C2×C22⋊C4—441no—
819C2×C22⋊C4—441no—
820C2×C22⋊C4—441no—
821C2×C22⋊C4—441no—
822C2×C22⋊C4—441no—
823C2×C42—222no—
824C2×C42—222no—
825C2×C42—441no—
826#95—22no—
827#95—22no—
828#95—114no—
829#95—222no—
830#95—222no—
831#95—222no—
832#95—222no—
833#95—222no—
834#95—222no—
835#95—222no—
836#95—441no—
837#95—441no—
838C2×C11—44no—
839C2×C11—82no—
840C2×C11#231111yescharacteristic
841C2×C11#232411yescharacteristic
842C2×C11#232511yescharacteristic
843C2×C11D4×C22⋊C411yescharacteristic
844C2×C11D4×C22⋊C411yescharacteristic
845C2×C11#236111yescharacteristic
846C2×C11#237711yescharacteristic
847C2×C11#266911yescharacteristic
848C2×C11#267111yescharacteristic
849C2×C11#267211yescharacteristic
850C2×C11#267511yescharacteristic
851C2×C11#267611yescharacteristic
852C2×C11#268111yescharacteristic
853C2×C11#269111yescharacteristic
854C2×C11#270311yescharacteristic
855D11—44no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24—112no—
883C24—112no—
884C24—112no—
885C24—221no—
886C24—221no—
887C24—221no—
888C24—221no—
889C24—221no—
890C24—221no—
891C24—221no—
892C24—221no—
893C24—221no—
894C24—221no—
895C24—221no—
896C24—221no—
897C24C2×C4×D1112yes—
898C24C2×C4×D1112yes—
899C24D4×D1112yes—
900C24D4×D1112yes—
901C24C23×D1111yescharacteristic
902C2×D4—28no—
903C2×D4—28no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—44no—
908C2×D4—44no—
909C2×D4—228no—
910C2×D4—228no—
911C2×D4—228no—
912C2×D4—228no—
913C2×D4—444no—
914C2×D4—444no—
915C2×D4—444no—
916C2×D4—444no—
917C2×D4—444no—
918C2×D4—444no—
919C2×D4—444no—
920C2×D4—444no—
921C2×D4—444no—
922C2×D4—444no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—112no—
955C22×C4—112no—
956C22×C4—112no—
957C22×C4—112no—
958C22×C4—112no—
959C22×C4—112no—
960C22×C4—112no—
961C22×C4—112no—
962C22×C4—112no—
963C22×C4—112no—
964C22×C4—228no—
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×C4—221no—
975C22×C4—221no—
976C22×C4—221no—
977C22×C4—221no—
978C22×C4—221no—
979C22×C4—221no—
980C22×C4—221no—
981C22×C4—221no—
982C22×C4—221no—
983C22×C4—221no—
984C22×C4—221no—
985C22×C4—221no—
986C22×C4—221no—
987C22×C4—221no—
988C22×C4—221no—
989C22×C4—221no—
990C22×C4—221no—
991C22×C4—221no—
992C22×C4—221no—
993C22×C4—221no—
994C22×C4—221no—
995C22×C4—221no—
996C22×C4—221no—
997C22×C4—228no—
998C22×C4—221no—
999C22×C4—221no—
1000C22×C4—221no—
1001C22×C4—221no—
1002C22×C4—221no—
1003C22×C4—221no—
1004C22×C4—221no—
1005C22×C4—444no—
1006C22×C4—444no—
1007C22×C4—444no—
1008C22×C4—444no—
1009C22×C4—444no—
1010C22×C4—444no—
1011C22×C4—444no—
1012C22×C4—444no—
1013C22×C4—444no—
1014C22×C4—444no—
1015C22×C4—444no—
1016C22×C4—444no—
1017C22×C4C2×C4×D1112yes—
1018C22×C4D4×D1112yes—
1019C22×C4D4×D1112yes—
1020C22×C4#434112yes—
1021C4⋊C4—228no—
1022C4⋊C4—444no—
1023C4⋊C4—444no—
1024C4⋊C4—444no—
1025C22⋊C4—44no—
1026C22⋊C4—44no—
1027C22⋊C4—44no—
1028C22⋊C4—44no—
1029C22⋊C4—1116no—
1030C22⋊C4—228no—
1031C22⋊C4—444no—
1032C22⋊C4—444no—
1033C22⋊C4—444no—
1034C22⋊C4—444no—
1035C22⋊C4—444no—
1036C22⋊C4—444no—
1037C22⋊C4—444no—
1038C42—444no—
1039C11#1436111yescharacteristic, complemented, Sylow
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—114no—
1110C23—222no—
1111C23—222no—
1112C23—222no—
1113C23—222no—
1114C23—222no—
1115C23—222no—
1116C23—222no—
1117C23—222no—
1118C23—222no—
1119C23—222no—
1120C23—222no—
1121C23—222no—
1122C23—222no—
1123C23—222no—
1124C23—222no—
1125C23—222no—
1126C23—222no—
1127C23—222no—
1128C23—441no—
1129C23—441no—
1130C23—441no—
1131C23—441no—
1132C23—441no—
1133C23—441no—
1134C23—441no—
1135C23—441no—
1136C23—441no—
1137C23—441no—
1138C23—441no—
1139C23—441no—
1140C23—441no—
1141C23—441no—
1142C23—441no—
1143C23—441no—
1144C23C22⋊C4×D1114yes—
1145C23C22×C4×D1111yescharacteristic
1146C23C2×D4×D1111yescharacteristic
1147C23C2×D4×D1111yescharacteristic
1148C23C2×D4×D1111yescharacteristic
1149C23C2×D4×D1111yescharacteristic
1150C23C2×#434111yescharacteristic
1151C23#6703711yescharacteristic
1152C23#6703711yescharacteristic
1153C23#6703711yescharacteristic
1154C23#6703711yescharacteristic
1155C23#6703711yescharacteristic
1156C23#41×D1111yescharacteristic
1157C23#6704211yescharacteristic
1158C23#6704311yescharacteristic
1159C23#6704311yescharacteristic
1160D4—416no—
1161D4—4416no—
1162D4—4416no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—114no—
1198C2×C4—114no—
1199C2×C4—222no—
1200C2×C4—222no—
1201C2×C4—222no—
1202C2×C4—222no—
1203C2×C4—222no—
1204C2×C4—222no—
1205C2×C4—222no—
1206C2×C4—222no—
1207C2×C4—222no—
1208C2×C4—222no—
1209C2×C4—222no—
1210C2×C4—222no—
1211C2×C4—222no—
1212C2×C4—222no—
1213C2×C4—222no—
1214C2×C4—222no—
1215C2×C4—222no—
1216C2×C4—222no—
1217C2×C4—222no—
1218C2×C4—222no—
1219C2×C4—222no—
1220C2×C4—222no—
1221C2×C4—222no—
1222C2×C4—222no—
1223C2×C4—4416no—
1224C2×C4—4416no—
1225C2×C4—441no—
1226C2×C4—441no—
1227C2×C4—441no—
1228C2×C4—441no—
1229C2×C4—441no—
1230C2×C4—441no—
1231C2×C4—441no—
1232C2×C4—441no—
1233C2×C4—441no—
1234C2×C4—441no—
1235C2×C4—441no—
1236C2×C4—441no—
1237C2×C4—441no—
1238C2×C4—441no—
1239C2×C4—441no—
1240C2×C4—441no—
1241C2×C4—441no—
1242C2×C4—441no—
1243C2×C4—441no—
1244C2×C4—441no—
1245C2×C4—441no—
1246C2×C4—441no—
1247C2×C4—441no—
1248C2×C4(C22⋊D11)⋊C414yes—
1249C22—24no—
1250C22—24no—
1251C22—24no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—224no—
1280C22—224no—
1281C22—224no—
1282C22—442no—
1283C22—442no—
1284C22—442no—
1285C22—442no—
1286C22—442no—
1287C22—442no—
1288C22—442no—
1289C22—442no—
1290C22—442no—
1291C22—442no—
1292C22—442no—
1293C22—442no—
1294C22C2×C22⋊C4×D1111yescharacteristic
1295C22C2×(C22⋊D11)⋊C411yescharacteristic
1296C22#1062301711yescharacteristic
1297C22C4×D4×D1111yescharacteristic
1298C22#1062307611yescharacteristic
1299C22#1062307711yescharacteristic
1300C22#1062307711yescharacteristic
1301C22#1062312011yescharacteristic
1302C22#1062312111yescharacteristic
1303C22#1062312111yescharacteristic
1304C22#1062312111yescharacteristic
1305C22#1062312211yescharacteristic
1306C22#1062312211yescharacteristic
1307C22#1062312311yescharacteristic
1308C22#1062312611yescharacteristic
1309C22#1062312811yescharacteristic
1310C22#1062312811yescharacteristic
1311C22#1062313811yescharacteristic
1312C22#1062313911yescharacteristic
1313C22#1062313911yescharacteristic
1314C22#1062314011yescharacteristic
1315C22#1062314111yescharacteristic
1316C22#1062314211yescharacteristic
1317C22#1062314411yescharacteristic
1318C22#1062314511yescharacteristic
1319C22#1062315111yescharacteristic
1320C22#1062315211yescharacteristic
1321C22#1062317911yescharacteristic
1322C22#1062318511yescharacteristic
1323C22#1062319111yescharacteristic
1324C22#1062319811yescharacteristic
1325C22#1062320811yescharacteristic
1326C22#1062321311yescharacteristic
1327C22#1062324811yescharacteristic
1328C22#1062325011yescharacteristic
1329C4—24no—
1330C4—42no—
1331C4—81no—
1332C4—81no—
1333C4—81no—
1334C4—224no—
1335C4—224no—
1336C4—442no—
1337C4—442no—
1338C4—442no—
1339C4—442no—
1340C4—881no—
1341C2—44no—
1342C2—82no—
1343C2—444no—
1344C2#1307120311yescharacteristic
1345C2#1307131211yescharacteristic
1346C2#1307131811yescharacteristic
1347C2#1307143211yescharacteristic
1348C2#1307143411yescharacteristic
1349C2#1307163711yescharacteristic
1350C2#1307176811yescharacteristic
1351C2#1307483511yescharacteristic
1352C2#1307485411yescharacteristic
1353C2#1307487311yescharacteristic
1354C2#1307490811yescharacteristic
1355C2#1307491911yescharacteristic
1356C2#1307497011yescharacteristic
1357C2#1307509611yescharacteristic
1358C2#1307526611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1438C2
socle, cosocleC24×C11C24
prime radicalC22×#66991C2
hypercenter#1438D11
hypocenterC11#14361
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. C2×#10622559C2semidirect
7. C2×#10622280C2semidirect
8. #13066868C2semidirect
9. #13066859C2semidirect
10. #13066859C2semidirect
11. #13066855C2semidirect
12. #13066855C2semidirect
13. #13066850C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1438C2semidirect
32. C2×#66991C4semidirect
88. C22×C22⋊D11C2×C4semidirect
109. C22×C4×D11C2×C4semidirect
134. C2×C22⋊Dic11C2×C4semidirect
149. C2×(C2×D11)⋊C4D4semidirect
152. C2×C4⋊Dic11C2×C4semidirect
176. C11⋊#95D4semidirect
351. C22⋊Dic11C22⋊C4semidirect
373. #1438D11semidirect
1039. C11#14361semidirect

Maximal subgroups

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

subgroupindex
C22×#669912
C2×#106225702
C2×#106225572
C2×#106228332
C2×#106225712
C2×#106225592
C2×#106222802
#130668682
#130668592
#130668552
#130668502
(C2×D11)⋊#952
C11×#14382
#1436111