Finite Group Databasebeta

← #14677221

Subgroups — #14677221

Order 2816.

3166 conjugacy classes of subgroups.

The subgroup lattice has 1398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66983C211yesmaximal, characteristic
2C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
3C2×#10622278C211yesmaximal, characteristic, complemented
4C2×#10622571C211yesmaximal, characteristic, complemented
5C2×#10622571C211yesmaximal, characteristic, complemented
6C2×#10622571C211yesmaximal, characteristic, complemented
7C22×C11⋊#95C211yesmaximal, characteristic, complemented
8#13066868C211yesmaximal, characteristic, complemented
9#13066864C211yesmaximal, characteristic, complemented
10#13066860C211yesmaximal, characteristic, complemented
11#13066856C211yesmaximal, characteristic, complemented
12#13066852C211yesmaximal, characteristic, complemented
13#13066850C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×C22⋊#95C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic
20C24×Dic11C2211yescharacteristic
21C23×D44C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C2×#66983—24no—
26C2×#66983—24no—
27C2×#66983C418yescomplemented
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×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×C4⋊Dic11C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40C2×(C22⋊D11)⋊C4—24no—
41C2×(C22⋊D11)⋊C4—24no—
42C2×(C22⋊D11)⋊C4—24no—
43C2×C11×#95C2211yescharacteristic
44C2×C11×#95C2211yescharacteristic
45C2×C11×#95C2211yescharacteristic
46C2×C11×#95C2211yescharacteristic
47C2×C11⋊#95—24no—
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
57C2×C11⋊#95C2211yescharacteristic
58#10622571—24no—
59#10622571—24no—
60#10622571—24no—
61#10622278—24no—
62C25×C11C2311yescharacteristic
63C24×D11C2311yescharacteristic
64C24×D11C2311yescharacteristic
65C23×C4×C11—22no—
66C23×C4×C11—22no—
67C23×C4×C11—22no—
68C23×C4×C11—22no—
69C23×C4×C11—41no—
70C23×C4×C11—41no—
71C23×C4×C11C2×C414yescomplemented
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C22×C22⋊D11—22no—
79C22×C22⋊D11—22no—
80C22×C22⋊D11—22no—
81C22×C22⋊D11—22no—
82C22×C22⋊D11—22no—
83C22×C22⋊D11—22no—
84C22×C22⋊D11—22no—
85C22×C22⋊D11—22no—
86C22×C22⋊D11—22no—
87C22×C22⋊D11—22no—
88C22×C22⋊D11C2×C414yes—
89C22×C22⋊D11C2×C414yescomplemented
90C22×C22⋊D11D414yes—
91C22×C22⋊D11D414yes—
92C23×Dic11—22no—
93C23×Dic11—22no—
94C23×Dic11—22no—
95C23×Dic11—22no—
96C23×Dic11—22no—
97C23×Dic11—22no—
98C23×Dic11—22no—
99C23×Dic11—22no—
100C23×Dic11—22no—
101C23×Dic11—41no—
102C23×Dic11—41no—
103C23×Dic11—41no—
104C23×Dic11—41no—
105C23×Dic11D414yescomplemented
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2311yescharacteristic
108C23×Dic11C2311yescharacteristic
109C23×Dic11C2311yescharacteristic
110C23×Dic11C2311yescharacteristic
111C23×Dic11C2311yescharacteristic
112C22×D44—22no—
113C22×D44—22no—
114C22×D44—22no—
115C22×D44—22no—
116C22×D44—41no—
117C22×D44—41no—
118C22×D44C2×C414yescomplemented
119C22×C4×D11—22no—
120C22×C4×D11—22no—
121C22×C4×D11—22no—
122C22×C4×D11—22no—
123C22×C4×D11—22no—
124C22×C4×D11—41no—
125C22×C4×D11—41no—
126C2×C11×C22⋊C4—22no—
127C2×C11×C22⋊C4—22no—
128C2×C11×C22⋊C4—22no—
129C2×C11×C22⋊C4—22no—
130C2×C11×C22⋊C4—22no—
131C2×C11×C22⋊C4D414yescomplemented
132#66983—232no—
133C2×(C2×D11)⋊C4—22no—
134C2×(C2×D11)⋊C4—22no—
135C2×(C2×D11)⋊C4—22no—
136C2×(C2×D11)⋊C4—22no—
137C2×(C2×D11)⋊C4—22no—
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—22no—
144C2×(C2×D11)⋊C4—22no—
145C2×(C2×D11)⋊C4—22no—
146C2×(C2×D11)⋊C4—22no—
147C2×(C2×D11)⋊C4—22no—
148C2×(C2×D11)⋊C4—22no—
149C2×(C2×D11)⋊C4—22no—
150C2×(C2×D11)⋊C4—22no—
151C2×(C2×D11)⋊C4—22no—
152C2×(C2×D11)⋊C4—41no—
153C2×(C2×D11)⋊C4—41no—
154C2×(C2×D11)⋊C4—41no—
155C2×(C2×D11)⋊C4—41no—
156C2×(C2×D11)⋊C4—41no—
157C2×(C2×D11)⋊C4—41no—
158C2×(C2×D11)⋊C4C2×C414yescomplemented
159C2×(C2×D11)⋊C4C2×C414yescomplemented
160C2×C4⋊Dic11—22no—
161C2×C4⋊Dic11—22no—
162C2×C4⋊Dic11C2×C414yescomplemented
163C2×Dic11⋊C4—22no—
164C2×Dic11⋊C4—22no—
165C2×Dic11⋊C4—22no—
166C2×C4×Dic11—22no—
167C2×C4×Dic11—22no—
168C2×C4×Dic11—22no—
169(C22⋊D11)⋊C4—232no—
170C11×#95—22no—
171C11×#95—22no—
172C11×#95—41no—
173C11×#95—41no—
174C11⋊#95—22no—
175C11⋊#95—22no—
176C11⋊#95—22no—
177C11⋊#95—22no—
178C11⋊#95—22no—
179C11⋊#95—22no—
180C11⋊#95—22no—
181C11⋊#95—22no—
182C11⋊#95—22no—
183C11⋊#95D414yescomplemented
184#14023—111nomaximal, Sylow
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×C11C22×C412yes—
194C24×C11C2×D412yes—
195C24×C11C2×D412yes—
196C24×C11C2×D412yes—
197C24×C11C2×D412yes—
198C24×C11#4112yes—
199C24×C11#4112yes—
200C24×C11C2411yescharacteristic
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×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×D11—21no—
222C23×D11—21no—
223C23×D11—21no—
224C23×D11—21no—
225C23×D11—21no—
226C23×D11—21no—
227C23×D11C22×C412yes—
228C23×D11C22×C412yes—
229C23×D11C2×D412yes—
230C23×D11C2×D412yes—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—28no—
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—28no—
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×C11—21no—
263C22×C4×C11—21no—
264C22×C4×C11—21no—
265C22×C4×C11—21no—
266C22×C4×C11—21no—
267C22×C4×C11—21no—
268C22×C4×C11—21no—
269C22×C4×C11—44no—
270C22×C4×C11—44no—
271C22×C4×C11—44no—
272C22×C4×C11—44no—
273C22×C4×C11—44no—
274C22×C4×C11C22×C412yes—
275C22×C4×C11C22×C412yes—
276C22×C4×C11C2×D412yes—
277C22×C4×C11C2×D412yes—
278C22×C4×C11C2×D412yes—
279C22×C4×C11#4112yes—
280C2×C22⋊D11—28no—
281C2×C22⋊D11—28no—
282C2×C22⋊D11—28no—
283C2×C22⋊D11—28no—
284C2×C22⋊D11—28no—
285C2×C22⋊D11—28no—
286C2×C22⋊D11—28no—
287C2×C22⋊D11—28no—
288C2×C22⋊D11—28no—
289C2×C22⋊D11—44no—
290C2×C22⋊D11—44no—
291C2×C22⋊D11—44no—
292C2×C22⋊D11—44no—
293C2×C22⋊D11C22⋊C4116yescomplemented
294C22×Dic11—28no—
295C22×Dic11—28no—
296C22×Dic11—28no—
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—21no—
320C22×Dic11—21no—
321C22×Dic11—21no—
322C22×Dic11—21no—
323C22×Dic11—21no—
324C22×Dic11—21no—
325C22×Dic11—21no—
326C22×Dic11—21no—
327C22×Dic11—21no—
328C22×Dic11—21no—
329C22×Dic11—44no—
330C22×Dic11—44no—
331C22×Dic11—44no—
332C22×Dic11—44no—
333C22×Dic11—44no—
334C22×Dic11—44no—
335C22×Dic11—44no—
336C22×Dic11—44no—
337C22×Dic11—44no—
338C22×Dic11—44no—
339C22×Dic11—44no—
340C22×Dic11C22×C412yes—
341C22×Dic11C22×C412yes—
342C22×Dic11C2×D412yes—
343C22×Dic11C2×D412yes—
344C22×Dic11C2×D412yes—
345C22×Dic11C2×D412yes—
346C22×Dic11C2×D412yes—
347C22×Dic11C2×D412yes—
348C22×Dic11#4112yes—
349C22×Dic11#4112yes—
350C2×D44—28no—
351C2×D44—28no—
352C2×D44—44no—
353C2×D44—44no—
354C2×D44—44no—
355C2×D44—44no—
356C2×D44—44no—
357C2×C4×D11—28no—
358C2×C4×D11—44no—
359C2×C4×D11—44no—
360C2×C4×D11—44no—
361C2×C4×D11—44no—
362C2×C4×D11—44no—
363C2×C4×D11—44no—
364C11×C22⋊C4—28no—
365C11×C22⋊C4—44no—
366(C2×D11)⋊C4—28no—
367(C2×D11)⋊C4—28no—
368(C2×D11)⋊C4—28no—
369(C2×D11)⋊C4—44no—
370(C2×D11)⋊C4—44no—
371(C2×D11)⋊C4—44no—
372(C2×D11)⋊C4—44no—
373(C2×D11)⋊C4—44no—
374(C2×D11)⋊C4—44no—
375C4⋊Dic11—28no—
376Dic11⋊C4—28no—
377C4×Dic11—28no—
378C22×#121—111no—
379C22×C4×D4—111no—
380C2×#386—111no—
381C2×#386—111no—
382C2×#386—111no—
383C2×#386—111no—
384C22×#95—111no—
385#1441—111no—
386#1440—111no—
387#1439—111no—
388#1438—111no—
389#1437—111no—
390#1436—111no—
391C22⋊#95—111no—
392C22⋊#95D1111yescharacteristic, complemented
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—22no—
402C23×C11—22no—
403C23×C11—22no—
404C23×C11—22no—
405C23×C11—22no—
406C23×C11—22no—
407C23×C11—22no—
408C23×C11—22no—
409C23×C11—22no—
410C23×C11—22no—
411C23×C11—22no—
412C23×C11—22no—
413C23×C11—22no—
414C23×C11—22no—
415C23×C11—22no—
416C23×C11—22no—
417C23×C11—22no—
418C23×C11—22no—
419C23×C11—22no—
420C23×C11—22no—
421C23×C11C2×C22⋊C414yes—
422C23×C11C4×D414yes—
423C23×C11C4×D414yes—
424C23×C11#12014yes—
425C23×C11#12114yes—
426C23×C11#12114yes—
427C23×C11#12314yes—
428C23×C11C23×C411yescharacteristic
429C23×C11C22×D411yescharacteristic
430C23×C11C22×D411yescharacteristic
431C23×C11C22×D411yescharacteristic
432C23×C11C22×D411yescharacteristic
433C23×C11C22×D411yescharacteristic
434C23×C11C2×#4111yescharacteristic
435C23×C11C2×#4111yescharacteristic
436C23×C11C2×#4111yescharacteristic
437C23×C11C2×#4111yescharacteristic
438C23×C11C2×#4111yescharacteristic
439C23×C11H(5,𝔽2)11yescharacteristic
440C23×C11H(5,𝔽2)11yescharacteristic
441C23×C11H(5,𝔽2)11yescharacteristic
442C23×C112−1+411yescharacteristic
443C22×D11—22no—
444C22×D11—22no—
445C22×D11—22no—
446C22×D11—22no—
447C22×D11—22no—
448C22×D11—22no—
449C22×D11—22no—
450C22×D11—22no—
451C22×D11—22no—
452C22×D11—22no—
453C22×D11—22no—
454C22×D11—22no—
455C22×D11—22no—
456C22×D11—22no—
457C22×D11—22no—
458C22×D11—22no—
459C22×D11—22no—
460C22×D11—22no—
461C22×D11—22no—
462C22×D11—22no—
463C22×D11—22no—
464C22×D11—22no—
465C22×D11—22no—
466C22×D11—22no—
467C22×D11—22no—
468C22×D11—41no—
469C22×D11—41no—
470C22×D11—41no—
471C22×D11—41no—
472C22×D11—41no—
473C22×D11—41no—
474C22×D11—41no—
475C22×D11—41no—
476C22×D11—41no—
477C22×D11—41no—
478C22×D11—41no—
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×D11—41no—
496C22×D11—41no—
497C22×D11—41no—
498C22×D11—41no—
499C22×D11—41no—
500C22×D11—41no—
501C22×D11—41no—
502C22×D11—41no—
503C22×D11—41no—
504C22×D11—41no—
505C22×D11—41no—
506C22×D11—41no—
507C22×D11—41no—
508C22×D11—41no—
509C22×D11—41no—
510C22×D11—41no—
511C22×D11—41no—
512C22×D11C2×C22⋊C414yes—
513C2×C4×C11—22no—
514C2×C4×C11—22no—
515C2×C4×C11—22no—
516C2×C4×C11—22no—
517C2×C4×C11—22no—
518C2×C4×C11—22no—
519C2×C4×C11—22no—
520C2×C4×C11—22no—
521C2×C4×C11—22no—
522C2×C4×C11—22no—
523C2×C4×C11—22no—
524C2×C4×C11—22no—
525C2×C4×C11—22no—
526C2×C4×C11—22no—
527C2×C4×C11—22no—
528C2×C4×C11—416no—
529C2×C4×C11—41no—
530C2×C4×C11—41no—
531C2×C4×C11—41no—
532C2×C4×C11—41no—
533C2×C4×C11—41no—
534C2×C4×C11—41no—
535C2×C4×C11—41no—
536C2×C4×C11—41no—
537C2×C4×C11—41no—
538C2×C4×C11—41no—
539C2×C4×C11—41no—
540C2×C4×C11—41no—
541C2×C4×C11—41no—
542C2×C4×C11—41no—
543C2×C4×C11—41no—
544C2×C4×C11—41no—
545C2×C4×C11—41no—
546C2×C4×C11—41no—
547C2×C4×C11—41no—
548C2×C4×C11—41no—
549C2×C4×C11—41no—
550C2×C4×C11—41no—
551C2×C4×C11—41no—
552C2×C4×C11—41no—
553C2×C4×C11—41no—
554C2×C4×C11—41no—
555C2×C4×C11C4×D414yescomplemented
556C22⋊D11—232no—
557C22⋊D11—416no—
558C2×Dic11—22no—
559C2×Dic11—22no—
560C2×Dic11—22no—
561C2×Dic11—22no—
562C2×Dic11—22no—
563C2×Dic11—22no—
564C2×Dic11—22no—
565C2×Dic11—22no—
566C2×Dic11—22no—
567C2×Dic11—22no—
568C2×Dic11—22no—
569C2×Dic11—22no—
570C2×Dic11—22no—
571C2×Dic11—22no—
572C2×Dic11—22no—
573C2×Dic11—22no—
574C2×Dic11—22no—
575C2×Dic11—22no—
576C2×Dic11—22no—
577C2×Dic11—22no—
578C2×Dic11—22no—
579C2×Dic11—22no—
580C2×Dic11—22no—
581C2×Dic11—22no—
582C2×Dic11—416no—
583C2×Dic11—416no—
584C2×Dic11—41no—
585C2×Dic11—41no—
586C2×Dic11—41no—
587C2×Dic11—41no—
588C2×Dic11—41no—
589C2×Dic11—41no—
590C2×Dic11—41no—
591C2×Dic11—41no—
592C2×Dic11—41no—
593C2×Dic11—41no—
594C2×Dic11—41no—
595C2×Dic11—41no—
596C2×Dic11—41no—
597C2×Dic11—41no—
598C2×Dic11—41no—
599C2×Dic11—41no—
600C2×Dic11C2×C22⋊C414yes—
601C2×Dic11#12114yescomplemented
602D44—416no—
603C4×D11—416no—
604C23×D4—111no—
605C23×D4—111no—
606C23×D4—111no—
607C24×C4—111no—
608C24×C4—111no—
609C24×C4—111no—
610C24×C4C2×D1111yescharacteristic
611C2×#121—118no—
612C2×#121—224no—
613C2×#121—224no—
614C2×C4×D4—224no—
615C2×C4×D4—224no—
616C2×C4×D4—224no—
617C22×C4⋊C4—111no—
618C22×C4⋊C4—111no—
619C22×C22⋊C4—111no—
620C22×C22⋊C4—111no—
621C22×C22⋊C4—111no—
622C22×C22⋊C4—111no—
623C22×C22⋊C4—111no—
624C22×C22⋊C4—111no—
625C22×C22⋊C4—111no—
626C22×C22⋊C4—111no—
627C22×C22⋊C4—111no—
628C22×C22⋊C4C2×D1111yescharacteristic
629C22×C22⋊C4C2×D1111yescharacteristic
630C22×C42—111no—
631#386—224no—
632#386—224no—
633#386—224no—
634#386—224no—
635C2×#95—111no—
636C2×#95—111no—
637C2×#95—111no—
638C2×#95—111no—
639C2×#95—111no—
640C2×#95—111no—
641C2×#95—111no—
642C2×#95—111no—
643C2×#95—111no—
644C2×#95—111no—
645C2×#95—224no—
646C2×#95C2×D1111yescharacteristic
647C2×#95C2×D1111yescharacteristic
648C2×#95C2×D1111yescharacteristic
649C2×#95C2×D1111yescharacteristic
650C22×C11—24no—
651C22×C11—24no—
652C22×C11—24no—
653C22×C11—24no—
654C22×C11—24no—
655C22×C11—24no—
656C22×C11—24no—
657C22×C11—24no—
658C22×C11—24no—
659C22×C11—24no—
660C22×C11—24no—
661C22×C11—24no—
662C22×C11—24no—
663C22×C11—24no—
664C22×C11#38618yescomplemented
665C22×C11C22×C22⋊C411yescharacteristic
666C22×C11C2×C4×D411yescharacteristic
667C22×C11C2×C4×D411yescharacteristic
668C22×C11C2×C4×D411yescharacteristic
669C22×C11C4×#4111yescharacteristic
670C22×C11#51811yescharacteristic
671C22×C11#52011yescharacteristic
672C22×C11C2×#12011yescharacteristic
673C22×C11C2×#12111yescharacteristic
674C22×C11C2×#12111yescharacteristic
675C22×C11C2×#12111yescharacteristic
676C22×C11C2×#12311yescharacteristic
677C22×C11#52511yescharacteristic
678C22×C11#52911yescharacteristic
679C22×C11#53211yescharacteristic
680C22×C11#53411yescharacteristic
681C22×C11#53711yescharacteristic
682C22×C11#53811yescharacteristic
683C22×C11#53911yescharacteristic
684C22×C11D4211yescharacteristic
685C22×C11D4211yescharacteristic
686C22×C11D4211yescharacteristic
687C22×C11#54611yescharacteristic
688C22×C11#54611yescharacteristic
689C22×C11#54611yescharacteristic
690C22×C11#54611yescharacteristic
691C22×C11#54611yescharacteristic
692C22×C11#54611yescharacteristic
693C22×C11#54711yescharacteristic
694C22×C11#54711yescharacteristic
695C22×C11#54711yescharacteristic
696C22×C11#54811yescharacteristic
697C22×C11#55311yescharacteristic
698C22×C11#55311yescharacteristic
699C22×C11#55311yescharacteristic
700C2×D11—24no—
701C2×D11—24no—
702C2×D11—24no—
703C2×D11—42no—
704C2×D11—42no—
705C2×D11—42no—
706C2×D11—42no—
707C2×D11—42no—
708C2×D11—42no—
709C2×D11—42no—
710C2×D11—42no—
711C2×D11—42no—
712C2×D11—42no—
713C2×D11—42no—
714C2×D11—42no—
715C2×D11—42no—
716C2×D11—42no—
717C2×D11—42no—
718C2×D11—42no—
719C2×D11—42no—
720C2×D11—42no—
721C2×D11—42no—
722C2×D11—81no—
723C2×D11—81no—
724C2×D11—81no—
725C2×D11—81no—
726C2×D11—81no—
727C2×D11—81no—
728C2×D11—81no—
729C2×D11—81no—
730C4×C11—24no—
731C4×C11—42no—
732C4×C11—42no—
733C4×C11—42no—
734C4×C11—81no—
735C4×C11—81no—
736Dic11—24no—
737Dic11—24no—
738Dic11—42no—
739Dic11—42no—
740Dic11—42no—
741Dic11—42no—
742C25—111no—
743C25—111no—
744C25C22×D1111yescharacteristic
745C22×D4—114no—
746C22×D4—114no—
747C22×D4—114no—
748C22×D4—114no—
749C22×D4—114no—
750C22×D4—222no—
751C22×D4—222no—
752C22×D4—222no—
753C22×D4—222no—
754C22×D4—222no—
755C22×D4—222no—
756C22×D4—222no—
757C22×D4—222no—
758C22×D4—222no—
759C22×D4—222no—
760C22×D4—222no—
761C22×D4—222no—
762C22×D4—222no—
763C22×D4—222no—
764C22×D4—441no—
765C22×D4—441no—
766C23×C4—22no—
767C23×C4—22no—
768C23×C4—22no—
769C23×C4—22no—
770C23×C4—41no—
771C23×C4—41no—
772C23×C4—111no—
773C23×C4—111no—
774C23×C4—111no—
775C23×C4—111no—
776C23×C4—111no—
777C23×C4—111no—
778C23×C4—114no—
779C23×C4—222no—
780C23×C4—222no—
781C23×C4—222no—
782C23×C4—222no—
783C23×C4—222no—
784C23×C4—222no—
785C23×C4—222no—
786C23×C4—222no—
787C23×C4—222no—
788C23×C4—222no—
789C23×C4—222no—
790C23×C4—222no—
791C23×C4—222no—
792C23×C4—222no—
793C23×C4—441no—
794C23×C4—441no—
795C23×C4—441no—
796C23×C4—441no—
797C23×C4—441no—
798C23×C4—441no—
799C23×C4C4×D1114yescomplemented
800C23×C4C22×D1111yescharacteristic
801C23×C4C22×D1111yescharacteristic
802C23×C4C22×D1111yescharacteristic
803C23×C4C22×D1111yescharacteristic
804C23×C4C22×D1111yescharacteristic
805C23×C4C22×D1111yescharacteristic
806#121—2232no—
807C4×D4—2232no—
808C2×C4⋊C4—114no—
809C2×C4⋊C4—222no—
810C2×C4⋊C4—222no—
811C2×C4⋊C4—222no—
812C2×C4⋊C4—222no—
813C2×C4⋊C4—222no—
814C2×C22⋊C4—22no—
815C2×C22⋊C4—22no—
816C2×C22⋊C4—22no—
817C2×C22⋊C4—22no—
818C2×C22⋊C4—22no—
819C2×C22⋊C4—114no—
820C2×C22⋊C4—114no—
821C2×C22⋊C4—222no—
822C2×C22⋊C4—222no—
823C2×C22⋊C4—222no—
824C2×C22⋊C4—222no—
825C2×C22⋊C4—222no—
826C2×C22⋊C4—222no—
827C2×C22⋊C4—222no—
828C2×C22⋊C4—222no—
829C2×C22⋊C4—222no—
830C2×C22⋊C4—222no—
831C2×C22⋊C4—222no—
832C2×C22⋊C4—222no—
833C2×C22⋊C4—222no—
834C2×C22⋊C4—222no—
835C2×C22⋊C4—222no—
836C2×C22⋊C4—222no—
837C2×C22⋊C4—222no—
838C2×C22⋊C4—222no—
839C2×C22⋊C4—222no—
840C2×C22⋊C4—441no—
841C2×C22⋊C4—441no—
842C2×C22⋊C4—441no—
843C2×C22⋊C4—441no—
844C2×C22⋊C4—441no—
845C2×C22⋊C4—441no—
846C2×C22⋊C4D4414yescomplemented
847C2×C42—222no—
848C2×C42—222no—
849C2×C42—222no—
850#95—22no—
851#95—22no—
852#95—41no—
853#95—41no—
854#95—114no—
855#95—222no—
856#95—222no—
857#95—222no—
858#95—222no—
859#95—222no—
860#95—222no—
861#95—222no—
862#95—222no—
863#95—222no—
864C2×C11—28no—
865C2×C11C2×#38611yescharacteristic
866C2×C11C4×#12111yescharacteristic
867C2×C11#232511yescharacteristic
868C2×C11D4×C22⋊C411yescharacteristic
869C2×C11#233911yescharacteristic
870C2×C11#236111yescharacteristic
871C2×C11#236411yescharacteristic
872C2×C11#241011yescharacteristic
873C2×C11#241611yescharacteristic
874C2×C11#242411yescharacteristic
875C2×C11#242511yescharacteristic
876C2×C11#243011yescharacteristic
877C2×C11#244311yescharacteristic
878C2×C11#244411yescharacteristic
879C2×C11#254311yescharacteristic
880D11—44no—
881D11—82no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—112no—
891C24—112no—
892C24—112no—
893C24—112no—
894C24—221no—
895C24—221no—
896C24—221no—
897C24—221no—
898C24—221no—
899C24—221no—
900C24—221no—
901C24—221no—
902C24—221no—
903C24—221no—
904C24—221no—
905C24—221no—
906C24—221no—
907C24—221no—
908C24—221no—
909C24—221no—
910C24—221no—
911C24—221no—
912C24—221no—
913C24—221no—
914C24—221no—
915C24—221no—
916C24—221no—
917C24—221no—
918C24—221no—
919C24—221no—
920C24C2×C4×D1112yes—
921C24C2×D4412yes—
922C24#433912yes—
923C24D4×D1112yes—
924C24D4×D1112yes—
925C24D4×D1112yes—
926C24#434312yes—
927C24C23×D1111yescharacteristic
928C2×D4—1116no—
929C2×D4—228no—
930C2×D4—228no—
931C2×D4—228no—
932C2×D4—228no—
933C2×D4—228no—
934C2×D4—228no—
935C2×D4—228no—
936C2×D4—228no—
937C2×D4—228no—
938C2×D4—228no—
939C2×D4—228no—
940C2×D4—444no—
941C2×D4—444no—
942C2×D4—444no—
943C2×D4—444no—
944C2×D4—444no—
945C2×D4—444no—
946C2×D4—444no—
947C2×D4—444no—
948C2×D4—444no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—28no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—28no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—112no—
993C22×C4—112no—
994C22×C4—112no—
995C22×C4—112no—
996C22×C4—112no—
997C22×C4—112no—
998C22×C4—112no—
999C22×C4—112no—
1000C22×C4—112no—
1001C22×C4—112no—
1002C22×C4—228no—
1003C22×C4—228no—
1004C22×C4—221no—
1005C22×C4—221no—
1006C22×C4—221no—
1007C22×C4—221no—
1008C22×C4—221no—
1009C22×C4—221no—
1010C22×C4—221no—
1011C22×C4—221no—
1012C22×C4—228no—
1013C22×C4—228no—
1014C22×C4—221no—
1015C22×C4—221no—
1016C22×C4—221no—
1017C22×C4—221no—
1018C22×C4—221no—
1019C22×C4—221no—
1020C22×C4—221no—
1021C22×C4—221no—
1022C22×C4—221no—
1023C22×C4—221no—
1024C22×C4—221no—
1025C22×C4—221no—
1026C22×C4—221no—
1027C22×C4—221no—
1028C22×C4—221no—
1029C22×C4—221no—
1030C22×C4—221no—
1031C22×C4—221no—
1032C22×C4—221no—
1033C22×C4—221no—
1034C22×C4—221no—
1035C22×C4—221no—
1036C22×C4—221no—
1037C22×C4—221no—
1038C22×C4—444no—
1039C22×C4—444no—
1040C22×C4—444no—
1041C22×C4—444no—
1042C22×C4—444no—
1043C22×C4—444no—
1044C22×C4—444no—
1045C22×C4—444no—
1046C22×C4—444no—
1047C22×C4—444no—
1048C22×C4—444no—
1049C22×C4—444no—
1050C22×C4—444no—
1051C22×C4—444no—
1052C22×C4—444no—
1053C22×C4—444no—
1054C22×C4—444no—
1055C22×C4C2×C4×D1112yes—
1056C22×C4C2×C4×D1112yes—
1057C22×C4C2×D4412yes—
1058C22×C4C2×D4412yes—
1059C22×C4D4×D1112yes—
1060C22×C4#434112yes—
1061C4⋊C4—228no—
1062C4⋊C4—228no—
1063C22⋊C4—28no—
1064C22⋊C4—44no—
1065C22⋊C4—228no—
1066C22⋊C4—228no—
1067C22⋊C4—228no—
1068C22⋊C4—444no—
1069C22⋊C4—444no—
1070C22⋊C4—444no—
1071C22⋊C4—444no—
1072C22⋊C4—444no—
1073C22⋊C4—444no—
1074C42—228no—
1075C11#1402311yescharacteristic, complemented, Sylow
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—22no—
1090C23—22no—
1091C23—22no—
1092C23—22no—
1093C23—22no—
1094C23—22no—
1095C23—22no—
1096C23—22no—
1097C23—22no—
1098C23—22no—
1099C23—22no—
1100C23—22no—
1101C23—22no—
1102C23—22no—
1103C23—22no—
1104C23—114no—
1105C23—222no—
1106C23—222no—
1107C23—222no—
1108C23—222no—
1109C23—222no—
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—222no—
1129C23—222no—
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—
1144C23—441no—
1145C23—441no—
1146C23—441no—
1147C23—441no—
1148C23—441no—
1149C23—441no—
1150C23—441no—
1151C23—441no—
1152C23—441no—
1153C23—441no—
1154C23—441no—
1155C23—441no—
1156C23—441no—
1157C23—441no—
1158C23—441no—
1159C23—441no—
1160C23—441no—
1161C23—441no—
1162C23—441no—
1163C23—441no—
1164C23—441no—
1165C23—441no—
1166C23—441no—
1167C23—441no—
1168C23—441no—
1169C23—441no—
1170C23—441no—
1171C23—441no—
1172C23—441no—
1173C23—441no—
1174C23C4×D4414yes—
1175C23C22⋊C4×D1114yes—
1176C23#6693514yes—
1177C23#6693714yes—
1178C23#6694614yes—
1179C23#6694714yes—
1180C23#6694814yes—
1181C23C22×C4×D1111yescharacteristic
1182C23C22×D4411yescharacteristic
1183C23C2×#433911yescharacteristic
1184C23C2×D4×D1111yescharacteristic
1185C23C2×D4×D1111yescharacteristic
1186C23C2×D4×D1111yescharacteristic
1187C23C2×D4×D1111yescharacteristic
1188C23C2×#434111yescharacteristic
1189C23#6703711yescharacteristic
1190C23#6703711yescharacteristic
1191C23C2×#434311yescharacteristic
1192C23#41×D1111yescharacteristic
1193C23#41×D1111yescharacteristic
1194C23#6704211yescharacteristic
1195C23#6704311yescharacteristic
1196D4—2232no—
1197D4—4416no—
1198D4—4416no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—416no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—114no—
1242C2×C4—114no—
1243C2×C4—222no—
1244C2×C4—222no—
1245C2×C4—222no—
1246C2×C4—222no—
1247C2×C4—222no—
1248C2×C4—222no—
1249C2×C4—222no—
1250C2×C4—222no—
1251C2×C4—222no—
1252C2×C4—222no—
1253C2×C4—222no—
1254C2×C4—222no—
1255C2×C4—222no—
1256C2×C4—222no—
1257C2×C4—222no—
1258C2×C4—222no—
1259C2×C4—222no—
1260C2×C4—222no—
1261C2×C4—222no—
1262C2×C4—222no—
1263C2×C4—222no—
1264C2×C4—222no—
1265C2×C4—222no—
1266C2×C4—222no—
1267C2×C4—4416no—
1268C2×C4—4416no—
1269C2×C4—4416no—
1270C2×C4—441no—
1271C2×C4—441no—
1272C2×C4—441no—
1273C2×C4—441no—
1274C2×C4—441no—
1275C2×C4—441no—
1276C2×C4—441no—
1277C2×C4—441no—
1278C2×C4—441no—
1279C2×C4—441no—
1280C2×C4—441no—
1281C2×C4—441no—
1282C2×C4—441no—
1283C2×C4—441no—
1284C2×C4—441no—
1285C2×C4—441no—
1286C2×C4(C22⋊D11)⋊C414yescomplemented
1287C22—24no—
1288C22—24no—
1289C22—24no—
1290C22—24no—
1291C22—24no—
1292C22—24no—
1293C22—24no—
1294C22—24no—
1295C22—24no—
1296C22—24no—
1297C22—24no—
1298C22—24no—
1299C22—24no—
1300C22—24no—
1301C22—224no—
1302C22—224no—
1303C22—224no—
1304C22—442no—
1305C22—442no—
1306C22—442no—
1307C22—442no—
1308C22—442no—
1309C22—442no—
1310C22—442no—
1311C22—442no—
1312C22—442no—
1313C22—442no—
1314C22—442no—
1315C22—442no—
1316C22—442no—
1317C22—442no—
1318C22—442no—
1319C22—442no—
1320C22—442no—
1321C22—442no—
1322C22—442no—
1323C22—881no—
1324C22—881no—
1325C22—881no—
1326C22—881no—
1327C22—881no—
1328C22—881no—
1329C22—881no—
1330C22—881no—
1331C22#1062227818yescomplemented
1332C22C2×C4×D4411yescharacteristic
1333C22C2×C22⋊C4×D1111yescharacteristic
1334C22C2×(C22⋊D11)⋊C411yescharacteristic
1335C22#1062301711yescharacteristic
1336C22C2×#6693511yescharacteristic
1337C22C2×#6693711yescharacteristic
1338C22C2×#6694611yescharacteristic
1339C22C2×#6694711yescharacteristic
1340C22C2×#6694811yescharacteristic
1341C22#1062305311yescharacteristic
1342C22#1062305411yescharacteristic
1343C22#1062307111yescharacteristic
1344C22#1062307111yescharacteristic
1345C22D4×D4411yescharacteristic
1346C22#1062308311yescharacteristic
1347C22#1062308511yescharacteristic
1348C22#1062308511yescharacteristic
1349C22#1062308611yescharacteristic
1350C22#1062309611yescharacteristic
1351C22#1062312111yescharacteristic
1352C22#1062312111yescharacteristic
1353C22#1062312211yescharacteristic
1354C22#1062312211yescharacteristic
1355C22#1062312711yescharacteristic
1356C22#1062312811yescharacteristic
1357C22D11×#12111yescharacteristic
1358C22#1062313611yescharacteristic
1359C22#1062315511yescharacteristic
1360C22#1062315811yescharacteristic
1361C22#1062317511yescharacteristic
1362C22#1062317611yescharacteristic
1363C22#1062318511yescharacteristic
1364C22#1062318511yescharacteristic
1365C22#1062318611yescharacteristic
1366C22#1062318611yescharacteristic
1367C4—24no—
1368C4—42no—
1369C4—42no—
1370C4—42no—
1371C4—81no—
1372C4—81no—
1373C4—224no—
1374C4—224no—
1375C4—442no—
1376C4—442no—
1377C4—442no—
1378C4—442no—
1379C2—28no—
1380C2—444no—
1381C2—882no—
1382C2C2×#1062227811yescharacteristic
1383C2#1307112211yescharacteristic
1384C2#1307131611yescharacteristic
1385C2#1307143211yescharacteristic
1386C2#1307144011yescharacteristic
1387C2#1307163011yescharacteristic
1388C2#1307166611yescharacteristic
1389C2#1307198911yescharacteristic
1390C2#1307205511yescharacteristic
1391C2#1307215011yescharacteristic
1392C2#1307216511yescharacteristic
1393C2#1307222411yescharacteristic
1394C2#1307235511yescharacteristic
1395C2#1307237011yescharacteristic
1396C2#1307358011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC22×#66983C2
hypercenterC22⋊#95D11
hypocenterC11#14023
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C22×(C22⋊D11)⋊C4C2semidirect
3. C2×#10622278C2semidirect
4. C2×#10622571C2semidirect
5. C2×#10622571C2semidirect
6. C2×#10622571C2semidirect
7. C22×C11⋊#95C2semidirect
8. #13066868C2semidirect
9. #13066864C2semidirect
10. #13066860C2semidirect
11. #13066856C2semidirect
12. #13066852C2semidirect
13. #13066850C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×C22⋊#95C2semidirect
27. C2×#66983C4semidirect
71. C23×C4×C11C2×C4semidirect
89. C22×C22⋊D11C2×C4semidirect
105. C23×Dic11D4semidirect
118. C22×D44C2×C4semidirect
131. C2×C11×C22⋊C4D4semidirect
158. C2×(C2×D11)⋊C4C2×C4semidirect
159. C2×(C2×D11)⋊C4C2×C4semidirect
162. C2×C4⋊Dic11C2×C4semidirect
183. C11⋊#95D4semidirect
293. C2×C22⋊D11C22⋊C4semidirect
392. C22⋊#95D11semidirect
555. C2×C4×C11C4×D4semidirect
601. C2×Dic11#121semidirect
664. C22×C11#386semidirect
799. C23×C4C4×D11semidirect
846. C2×C22⋊C4D44semidirect
1075. C11#14023semidirect
1286. C2×C4(C22⋊D11)⋊C4semidirect
1331. C22#10622278semidirect

Maximal subgroups

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

subgroupindex
C22×#669832
C22×(C22⋊D11)⋊C42
C2×#106222782
C2×#106225712
C22×C11⋊#952
#130668682
#130668642
#130668602
#130668562
#130668522
#130668502
(C2×D11)⋊#952
C11×C22⋊#952
#1402311