Finite Group Databasebeta

← #14681915

Subgroups — #14681915

Order 2816.

2386 conjugacy classes of subgroups.

The subgroup lattice has 1334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66937C211yesmaximal, characteristic
2C2×#10622601C211yesmaximal, characteristic, complemented
3C2×#10622570C211yesmaximal, characteristic, complemented
4C2×#10622265C211yesmaximal, characteristic, complemented
5C2×#10622591C211yesmaximal, characteristic, complemented
6#13066860C211yesmaximal, characteristic, complemented
7#13066856C211yesmaximal, characteristic, complemented
8#13066855C211yesmaximal, characteristic, complemented
9#13066855C211yesmaximal, characteristic, complemented
10#13066855C211yesmaximal, characteristic, complemented
11#13066853C211yesmaximal, characteristic, complemented
12#13066852C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×#1439C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C22×C4×Dic11C2211yescharacteristic
38C22×C4×Dic11C2211yescharacteristic
39C2×#66937—24no—
40C2×#66937—24no—
41C2×#66937C418yescomplemented
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
53C2×C11⋊#95C2211yescharacteristic
54#10622601—24no—
55#10622591—24no—
56#10622570—24no—
57#10622265—24no—
58C25×C11C2311yescharacteristic
59C24×D11C2311yescharacteristic
60C24×D11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11—22no—
68C22×C22⋊D11—22no—
69C22×C22⋊D11—22no—
70C22×C22⋊D11—22no—
71C22×C22⋊D11—22no—
72C22×C22⋊D11—22no—
73C22×C22⋊D11—41no—
74C22×C22⋊D11—41no—
75C22×C22⋊D11—41no—
76C22×C22⋊D11—41no—
77C22×C22⋊D11—41no—
78C22×C22⋊D11—41no—
79C22×C22⋊D11C2×C414yes—
80C22×C22⋊D11C2×C414yes—
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C22×D44—22no—
88C22×D44—22no—
89C22×D44—22no—
90C22×D44—22no—
91C22×D44—41no—
92C22×D44—41no—
93C22×D44C2×C414yes—
94C22×C4×D11—22no—
95C22×C4×D11—22no—
96C22×C4×D11—41no—
97C22×C4×D11—41no—
98C22×C4×D11—41no—
99C22×C4×D11—41no—
100C22×C4×D11C2×C414yes—
101C2×C11×C4⋊C4—22no—
102C2×C11×C4⋊C4—22no—
103C2×C11×C4⋊C4—41no—
104C2×C11×C22⋊C4—22no—
105C2×C11×C22⋊C4—22no—
106C2×C11×C22⋊C4—22no—
107C2×C11×C22⋊C4—41no—
108C2×C11×C22⋊C4—41no—
109C2×C11×C22⋊C4—41no—
110C2×C11×C22⋊C4—41no—
111C2×C11×C22⋊C4—41no—
112C2×C11×C22⋊C4C2×C414yes—
113C2×C22⋊Dic11—22no—
114C2×C22⋊Dic11—22no—
115C2×C22⋊Dic11—22no—
116C2×C22⋊Dic11—41no—
117C2×C22⋊Dic11—41no—
118C2×C22⋊Dic11—41no—
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—22no—
126C2×(C2×D11)⋊C4—22no—
127C2×(C2×D11)⋊C4—22no—
128C2×(C2×D11)⋊C4—22no—
129C2×(C2×D11)⋊C4—22no—
130C2×(C2×D11)⋊C4—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)⋊C4—41no—
140C2×(C2×D11)⋊C4—41no—
141C2×(C2×D11)⋊C4—41no—
142C2×(C2×D11)⋊C4—41no—
143C2×(C2×D11)⋊C4—41no—
144C2×(C2×D11)⋊C4C2×C414yes—
145C2×(C2×D11)⋊C4D414yescomplemented
146C2×Dic11⋊C4—22no—
147C2×Dic11⋊C4—22no—
148C2×Dic11⋊C4—41no—
149C2×Dic11⋊C4C2×C414yes—
150C2×Dic11⋊C4D414yes—
151C2×Dic11⋊C4D414yes—
152C2×C4×Dic11—22no—
153C2×C4×Dic11—22no—
154C2×C4×Dic11—22no—
155C2×C4×Dic11—22no—
156C2×C4×Dic11—41no—
157C2×C4×Dic11—41no—
158#66937—232no—
159C11×#95—22no—
160C11×#95—41no—
161C11×#95—41no—
162C11⋊#95—22no—
163C11⋊#95—22no—
164C11⋊#95—22no—
165C11⋊#95—22no—
166C11⋊#95—22no—
167C11⋊#95—22no—
168C11⋊#95—22no—
169C11⋊#95—41no—
170C11⋊#95—41no—
171#14418—111nomaximal, Sylow
172C24×C11—21no—
173C24×C11—21no—
174C24×C11—21no—
175C24×C11—21no—
176C24×C11—21no—
177C24×C11—21no—
178C24×C11—21no—
179C24×C11—21no—
180C24×C11—21no—
181C24×C11—21no—
182C24×C11—21no—
183C24×C11—21no—
184C24×C11—21no—
185C24×C11—21no—
186C24×C11C22×C412yes—
187C24×C11C2411yescharacteristic
188C23×D11—21no—
189C23×D11—21no—
190C23×D11—21no—
191C23×D11—21no—
192C23×D11—21no—
193C23×D11—21no—
194C23×D11—21no—
195C23×D11—21no—
196C23×D11—21no—
197C23×D11—21no—
198C23×D11—21no—
199C23×D11—21no—
200C23×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×D11—21no—
211C23×D11—21no—
212C23×D11—21no—
213C23×D11—21no—
214C23×D11C22×C412yes—
215C23×D11C22×C412yes—
216C23×D11C2×D412yes—
217C23×D11#4112yes—
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×C11—21no—
251C22×C4×C11—21no—
252C22×C4×C11—21no—
253C22×C4×C11—21no—
254C22×C4×C11—21no—
255C22×C4×C11C22×C412yes—
256C22×C4×C11C22×C412yes—
257C22×C4×C11C2×D412yes—
258C22×C4×C11C2×D412yes—
259C22×C4×C11C2×D412yes—
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×Dic11C22×C412yes—
308C22×Dic11C22×C412yes—
309C22×Dic11C2×D412yes—
310C22×Dic11C2×D412yes—
311C22×Dic11C2×D412yes—
312C22×Dic11C2×D412yes—
313C22×Dic11C2×D412yes—
314C22×Dic11#4112yes—
315C22×Dic11#4112yes—
316C2×D44—28no—
317C2×D44—28no—
318C2×D44—44no—
319C2×D44—44no—
320C2×D44—44no—
321C2×D44—44no—
322C2×D44—44no—
323C2×C4×D11—28no—
324C2×C4×D11—44no—
325C2×C4×D11—44no—
326C2×C4×D11—44no—
327C2×C4×D11—44no—
328C2×C4×D11—44no—
329C2×C4×D11—44no—
330C11×C4⋊C4—44no—
331C11×C22⋊C4—28no—
332C11×C22⋊C4—44no—
333C11×C22⋊C4—44no—
334C22⋊Dic11—44no—
335C22⋊Dic11—44no—
336(C2×D11)⋊C4—28no—
337(C2×D11)⋊C4—44no—
338(C2×D11)⋊C4—44no—
339(C2×D11)⋊C4—44no—
340(C2×D11)⋊C4—44no—
341(C2×D11)⋊C4—44no—
342(C2×D11)⋊C4—44no—
343(C2×D11)⋊C4—44no—
344(C2×D11)⋊C4—44no—
345Dic11⋊C4—44no—
346Dic11⋊C4C22⋊C4116yescomplemented
347C4×Dic11—44no—
348C4×Dic11—44no—
349C22×#121—111no—
350C2×#390—111no—
351C2×#390—111no—
352C2×#387—111no—
353C2×#387—111no—
354#1439—111no—
355#1439D1111yescharacteristic, complemented
356#1438—111no—
357#1438—111no—
358#1438—111no—
359#1438—111no—
360#1437—111no—
361#1437—111no—
362C22⋊#95—111no—
363C22⋊#95—111no—
364C23×C11—22no—
365C23×C11—22no—
366C23×C11—22no—
367C23×C11—22no—
368C23×C11—22no—
369C23×C11—22no—
370C23×C11—22no—
371C23×C11—41no—
372C23×C11—41no—
373C23×C11—41no—
374C23×C11—41no—
375C23×C11—41no—
376C23×C11—41no—
377C23×C11—41no—
378C23×C11—41no—
379C23×C11—41no—
380C23×C11—41no—
381C23×C11—41no—
382C23×C11—41no—
383C23×C11—41no—
384C23×C11—41no—
385C23×C11—41no—
386C23×C11—41no—
387C23×C11—41no—
388C23×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×C11C23×C411yescharacteristic
400C23×C11C22×D411yescharacteristic
401C23×C11C22×D411yescharacteristic
402C23×C11C22×D411yescharacteristic
403C23×C11C2×#4111yescharacteristic
404C23×C11C2×#4111yescharacteristic
405C23×C11C2×#4111yescharacteristic
406C23×C11H(5,𝔽2)11yescharacteristic
407C23×C11H(5,𝔽2)11yescharacteristic
408C23×C11H(5,𝔽2)11yescharacteristic
409C23×C11H(5,𝔽2)11yescharacteristic
410C23×C11H(5,𝔽2)11yescharacteristic
411C23×C11H(5,𝔽2)11yescharacteristic
412C23×C11H(5,𝔽2)11yescharacteristic
413C23×C112−1+411yescharacteristic
414C22×D11—22no—
415C22×D11—22no—
416C22×D11—22no—
417C22×D11—22no—
418C22×D11—22no—
419C22×D11—22no—
420C22×D11—22no—
421C22×D11—22no—
422C22×D11—22no—
423C22×D11—22no—
424C22×D11—22no—
425C22×D11—22no—
426C22×D11—22no—
427C22×D11—22no—
428C22×D11—22no—
429C22×D11—22no—
430C22×D11—22no—
431C22×D11—22no—
432C22×D11—22no—
433C22×D11—22no—
434C22×D11—22no—
435C22×D11—22no—
436C22×D11—22no—
437C22×D11—22no—
438C22×D11—22no—
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—
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×D11C4×D414yes—
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—22no—
491C2×C4×C11—22no—
492C2×C4×C11—22no—
493C2×C4×C11—22no—
494C2×C4×C11—22no—
495C2×C4×C11—22no—
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—
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×C11C2×C22⋊C414yes—
526C22⋊D11—416no—
527C22⋊D11—416no—
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—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—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×Dic11—41no—
563C2×Dic11—41no—
564C2×Dic11—41no—
565C2×Dic11—41no—
566C2×Dic11—41no—
567C2×Dic11—41no—
568C2×Dic11C2×C22⋊C414yes—
569C2×Dic11C2×C22⋊C414yes—
570D44—416no—
571C4×D11—416no—
572C23×D4—111no—
573C23×D4—111no—
574C23×D4—111no—
575C24×C4—111no—
576C2×#121—118no—
577C2×#121—224no—
578C2×#121—224no—
579C22×C4⋊C4—111no—
580C22×C4⋊C4—111no—
581C22×C4⋊C4C2×D1111yescharacteristic
582C22×C22⋊C4—111no—
583C22×C22⋊C4—111no—
584C22×C22⋊C4—111no—
585C22×C22⋊C4—111no—
586C22×C22⋊C4—111no—
587C22×C22⋊C4—111no—
588C22×C22⋊C4—111no—
589C22×C22⋊C4—111no—
590C22×C22⋊C4—111no—
591C22×C22⋊C4—111no—
592C22×C22⋊C4—111no—
593C22×C22⋊C4C2×D1111yescharacteristic
594C22×C22⋊C4C2×D1111yescharacteristic
595C22×C22⋊C4C2×D1111yescharacteristic
596C22×C42—111no—
597C22×C42—111no—
598#390—224no—
599#390—224no—
600#387—224no—
601#387—224no—
602C2×#95—111no—
603C2×#95—111no—
604C2×#95—111no—
605C2×#95—111no—
606C2×#95—111no—
607C2×#95—111no—
608C2×#95—111no—
609C2×#95—111no—
610C2×#95—111no—
611C2×#95C2×D1111yescharacteristic
612C2×#95C2×D1111yescharacteristic
613C2×#95C2×D1111yescharacteristic
614C22×C11—42no—
615C22×C11—42no—
616C22×C11—42no—
617C22×C11—42no—
618C22×C11—42no—
619C22×C11—42no—
620C22×C11—42no—
621C22×C11—81no—
622C22×C11—81no—
623C22×C11—81no—
624C22×C11—81no—
625C22×C11—81no—
626C22×C11—81no—
627C22×C11—81no—
628C22×C11—81no—
629C22×C11C22×C22⋊C411yescharacteristic
630C22×C11C2×C4×D411yescharacteristic
631C22×C11C4×#4111yescharacteristic
632C22×C11#51811yescharacteristic
633C22×C11#51811yescharacteristic
634C22×C11#51811yescharacteristic
635C22×C11#52011yescharacteristic
636C22×C11#53411yescharacteristic
637C22×C11#53511yescharacteristic
638C22×C11#53511yescharacteristic
639C22×C11#53511yescharacteristic
640C22×C11#53511yescharacteristic
641C22×C11#53711yescharacteristic
642C22×C11#53811yescharacteristic
643C22×C11#53811yescharacteristic
644C22×C11#53811yescharacteristic
645C22×C11#53911yescharacteristic
646C22×C11#54011yescharacteristic
647C22×C11#54011yescharacteristic
648C22×C11D4211yescharacteristic
649C22×C11D4211yescharacteristic
650C22×C11#54611yescharacteristic
651C22×C11#54611yescharacteristic
652C22×C11#54611yescharacteristic
653C22×C11#54611yescharacteristic
654C22×C11#54811yescharacteristic
655C22×C11#54811yescharacteristic
656C22×C11#55011yescharacteristic
657C22×C11#55011yescharacteristic
658C22×C11#55311yescharacteristic
659C22×C11#55311yescharacteristic
660C22×C11#56011yescharacteristic
661C22×C11#56011yescharacteristic
662C22×C11#56211yescharacteristic
663C22×C11#56211yescharacteristic
664C2×D11—24no—
665C2×D11—24no—
666C2×D11—24no—
667C2×D11—42no—
668C2×D11—42no—
669C2×D11—42no—
670C2×D11—42no—
671C2×D11—42no—
672C2×D11—42no—
673C2×D11—42no—
674C2×D11—42no—
675C2×D11—42no—
676C2×D11—42no—
677C2×D11—42no—
678C2×D11—42no—
679C2×D11—42no—
680C2×D11—42no—
681C2×D11—42no—
682C2×D11—42no—
683C2×D11—42no—
684C2×D11—42no—
685C2×D11—42no—
686C2×D11—81no—
687C2×D11—81no—
688C2×D11—81no—
689C2×D11—81no—
690C2×D11—81no—
691C2×D11—81no—
692C2×D11—81no—
693C2×D11—81no—
694C4×C11—24no—
695C4×C11—42no—
696C4×C11—42no—
697C4×C11—81no—
698C4×C11—81no—
699C4×C11—81no—
700Dic11—24no—
701Dic11—24no—
702Dic11—42no—
703Dic11—42no—
704Dic11—42no—
705Dic11—81no—
706C25—111no—
707C25—111no—
708C25C22×D1111yescharacteristic
709C22×D4—114no—
710C22×D4—114no—
711C22×D4—114no—
712C22×D4—222no—
713C22×D4—222no—
714C22×D4—222no—
715C22×D4—222no—
716C22×D4—222no—
717C22×D4—222no—
718C22×D4—222no—
719C22×D4—222no—
720C22×D4—222no—
721C22×D4—222no—
722C22×D4—441no—
723C22×D4—441no—
724C22×D4—441no—
725C22×D4—441no—
726C22×D4—441no—
727C22×D4—441no—
728C22×D4—441no—
729C22×D4—441no—
730C23×C4—111no—
731C23×C4—111no—
732C23×C4—111no—
733C23×C4—111no—
734C23×C4—111no—
735C23×C4—114no—
736C23×C4—111no—
737C23×C4—222no—
738C23×C4—222no—
739C23×C4—441no—
740C23×C4—441no—
741C23×C4—441no—
742C23×C4—441no—
743C23×C4C22×D1111yescharacteristic
744C23×C4C22×D1111yescharacteristic
745C23×C4C22×D1111yescharacteristic
746C23×C4C22×D1111yescharacteristic
747C23×C4C22×D1111yescharacteristic
748C23×C4C22×D1111yescharacteristic
749#121—2232no—
750C2×C4⋊C4—22no—
751C2×C4⋊C4—22no—
752C2×C4⋊C4—41no—
753C2×C4⋊C4—114no—
754C2×C4⋊C4—114no—
755C2×C4⋊C4—114no—
756C2×C4⋊C4—222no—
757C2×C4⋊C4—222no—
758C2×C4⋊C4—441no—
759C2×C22⋊C4—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—41no—
763C2×C22⋊C4—41no—
764C2×C22⋊C4—41no—
765C2×C22⋊C4—41no—
766C2×C22⋊C4—41no—
767C2×C22⋊C4—114no—
768C2×C22⋊C4—114no—
769C2×C22⋊C4—222no—
770C2×C22⋊C4—222no—
771C2×C22⋊C4—222no—
772C2×C22⋊C4—222no—
773C2×C22⋊C4—222no—
774C2×C22⋊C4—222no—
775C2×C22⋊C4—222no—
776C2×C22⋊C4—222no—
777C2×C22⋊C4—222no—
778C2×C22⋊C4—222no—
779C2×C22⋊C4—222no—
780C2×C22⋊C4—222no—
781C2×C22⋊C4—222no—
782C2×C22⋊C4—222no—
783C2×C22⋊C4—441no—
784C2×C22⋊C4—441no—
785C2×C22⋊C4—441no—
786C2×C22⋊C4—441no—
787C2×C22⋊C4—441no—
788C2×C22⋊C4—441no—
789C2×C22⋊C4—441no—
790C2×C22⋊C4—441no—
791C2×C22⋊C4—441no—
792C2×C22⋊C4—441no—
793C2×C22⋊C4—441no—
794C2×C22⋊C4—441no—
795C2×C22⋊C4—441no—
796C2×C22⋊C4—441no—
797C2×C22⋊C4—441no—
798C2×C22⋊C4—441no—
799C2×C22⋊C4—441no—
800C2×C22⋊C4C4×D1114yes—
801C2×C42—222no—
802C2×C42—222no—
803C2×C42—222no—
804C2×C42—222no—
805C2×C42—441no—
806C2×C42—441no—
807#95—22no—
808#95—41no—
809#95—41no—
810#95—222no—
811#95—222no—
812#95—222no—
813#95—222no—
814#95—222no—
815#95—222no—
816#95—222no—
817#95—441no—
818#95—441no—
819C2×C11—82no—
820C2×C11#230911yescharacteristic
821C2×C11#232511yescharacteristic
822C2×C11#233311yescharacteristic
823C2×C11D4×C22⋊C411yescharacteristic
824C2×C11#234111yescharacteristic
825C2×C11#236411yescharacteristic
826C2×C11#237711yescharacteristic
827C2×C11#267311yescharacteristic
828C2×C11#267311yescharacteristic
829C2×C11#267611yescharacteristic
830C2×C11#267611yescharacteristic
831C2×C11#271111yescharacteristic
832C2×C11#271111yescharacteristic
833C2×C11#271411yescharacteristic
834C2×C11#271411yescharacteristic
835D11—44no—
836D11—82no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—112no—
852C24—112no—
853C24—112no—
854C24—112no—
855C24—221no—
856C24—221no—
857C24—221no—
858C24—221no—
859C24—221no—
860C24—221no—
861C24—221no—
862C24—221no—
863C24—221no—
864C24—221no—
865C24—221no—
866C24—221no—
867C24—221no—
868C24—221no—
869C24—221no—
870C24—221no—
871C24—221no—
872C24—221no—
873C24—221no—
874C24—221no—
875C24—221no—
876C24—221no—
877C24—221no—
878C24—221no—
879C24—221no—
880C24—221no—
881C24C2×C4×D1112yes—
882C24C23×D1111yescharacteristic
883C2×D4—228no—
884C2×D4—228no—
885C2×D4—228no—
886C2×D4—228no—
887C2×D4—228no—
888C2×D4—444no—
889C2×D4—444no—
890C2×D4—444no—
891C2×D4—444no—
892C2×D4—444no—
893C2×D4—444no—
894C2×D4—444no—
895C2×D4—444no—
896C2×D4—444no—
897C2×D4—444no—
898C2×D4—444no—
899C2×D4—444no—
900C2×D4—444no—
901C2×D4—444no—
902C2×D4—444no—
903C2×D4—444no—
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—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—112no—
942C22×C4—112no—
943C22×C4—112no—
944C22×C4—112no—
945C22×C4—112no—
946C22×C4—112no—
947C22×C4—112no—
948C22×C4—112no—
949C22×C4—112no—
950C22×C4—228no—
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×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—444no—
985C22×C4—444no—
986C22×C4—444no—
987C22×C4—444no—
988C22×C4—444no—
989C22×C4—444no—
990C22×C4C2×C4×D1112yes—
991C22×C4C2×C4×D1112yes—
992C22×C4D4×D1112yes—
993C22×C4D4×D1112yes—
994C22×C4D4×D1112yes—
995C4⋊C4—44no—
996C4⋊C4—1116no—
997C4⋊C4—444no—
998C22⋊C4—28no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—228no—
1002C22⋊C4—444no—
1003C22⋊C4—444no—
1004C22⋊C4—444no—
1005C22⋊C4—444no—
1006C22⋊C4—444no—
1007C22⋊C4—444no—
1008C22⋊C4—444no—
1009C22⋊C4—444no—
1010C22⋊C4—444no—
1011C22⋊C4—444no—
1012C42—444no—
1013C42—444no—
1014C11#1441811yescharacteristic, complemented, Sylow
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—114no—
1051C23—222no—
1052C23—222no—
1053C23—222no—
1054C23—222no—
1055C23—222no—
1056C23—222no—
1057C23—222no—
1058C23—222no—
1059C23—222no—
1060C23—222no—
1061C23—222no—
1062C23—222no—
1063C23—222no—
1064C23—222no—
1065C23—222no—
1066C23—222no—
1067C23—222no—
1068C23—222no—
1069C23—222no—
1070C23—222no—
1071C23—222no—
1072C23—222no—
1073C23—222no—
1074C23—222no—
1075C23—222no—
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—441no—
1102C23—441no—
1103C23—441no—
1104C23—441no—
1105C23—441no—
1106C23—441no—
1107C23—441no—
1108C23—441no—
1109C23—441no—
1110C23—441no—
1111C23—441no—
1112C23—441no—
1113C23—441no—
1114C23—441no—
1115C23—441no—
1116C23—441no—
1117C23—441no—
1118C23—441no—
1119C23—441no—
1120C23C22×C4×D1111yescharacteristic
1121C23C2×D4×D1111yescharacteristic
1122C23C2×D4×D1111yescharacteristic
1123C23C2×D4×D1111yescharacteristic
1124C23#6703711yescharacteristic
1125C23#6703711yescharacteristic
1126C23#6703711yescharacteristic
1127C23#6703711yescharacteristic
1128C23#6704011yescharacteristic
1129C23#41×D1111yescharacteristic
1130C23#41×D1111yescharacteristic
1131C23#41×D1111yescharacteristic
1132C23#6704211yescharacteristic
1133C23#6704211yescharacteristic
1134C23#6704211yescharacteristic
1135D4—4416no—
1136D4—4416no—
1137D4—4416no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
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—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—114no—
1180C2×C4—114no—
1181C2×C4—222no—
1182C2×C4—222no—
1183C2×C4—222no—
1184C2×C4—222no—
1185C2×C4—222no—
1186C2×C4—222no—
1187C2×C4—222no—
1188C2×C4—222no—
1189C2×C4—222no—
1190C2×C4—222no—
1191C2×C4—222no—
1192C2×C4—222no—
1193C2×C4—222no—
1194C2×C4—222no—
1195C2×C4—222no—
1196C2×C4—222no—
1197C2×C4—222no—
1198C2×C4—222no—
1199C2×C4—222no—
1200C2×C4—222no—
1201C2×C4—222no—
1202C2×C4—4416no—
1203C2×C4—441no—
1204C2×C4—441no—
1205C2×C4—441no—
1206C2×C4—441no—
1207C2×C4—441no—
1208C2×C4—441no—
1209C2×C4—441no—
1210C2×C4—441no—
1211C2×C4—441no—
1212C2×C4—441no—
1213C2×C4—441no—
1214C2×C4—441no—
1215C2×C4—441no—
1216C2×C4—441no—
1217C2×C4—441no—
1218C2×C4—441no—
1219C2×C4—441no—
1220C2×C4—441no—
1221C2×C4—441no—
1222C2×C4C22⋊C4×D1114yes—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—224no—
1239C22—224no—
1240C22—224no—
1241C22—442no—
1242C22—442no—
1243C22—442no—
1244C22—442no—
1245C22—442no—
1246C22—442no—
1247C22—442no—
1248C22—442no—
1249C22—442no—
1250C22—442no—
1251C22—442no—
1252C22—442no—
1253C22—442no—
1254C22—442no—
1255C22—442no—
1256C22—442no—
1257C22—442no—
1258C22—442no—
1259C22—442no—
1260C22—881no—
1261C22—881no—
1262C22—881no—
1263C22—881no—
1264C22—881no—
1265C22—881no—
1266C22—881no—
1267C22—881no—
1268C22C2×C22⋊C4×D1111yescharacteristic
1269C22#1062303511yescharacteristic
1270C22#1062305311yescharacteristic
1271C22C4×D4×D1111yescharacteristic
1272C22#1062307611yescharacteristic
1273C22#1062307611yescharacteristic
1274C22#1062307611yescharacteristic
1275C22#1062312011yescharacteristic
1276C22#1062312111yescharacteristic
1277C22#1062312611yescharacteristic
1278C22#1062313011yescharacteristic
1279C22#1062313011yescharacteristic
1280C22#1062313811yescharacteristic
1281C22#1062313811yescharacteristic
1282C22#1062314011yescharacteristic
1283C22#1062314111yescharacteristic
1284C22#1062314111yescharacteristic
1285C22#1062314611yescharacteristic
1286C22#1062316011yescharacteristic
1287C22#1062316411yescharacteristic
1288C22#1062316411yescharacteristic
1289C22#1062316911yescharacteristic
1290C22#1062317811yescharacteristic
1291C22#1062317811yescharacteristic
1292C22#1062318511yescharacteristic
1293C22#1062318811yescharacteristic
1294C22#1062319211yescharacteristic
1295C22#1062319411yescharacteristic
1296C22#1062319711yescharacteristic
1297C22#1062320511yescharacteristic
1298C22#1062320711yescharacteristic
1299C22#1062320911yescharacteristic
1300C22#1062323511yescharacteristic
1301C22#1062324011yescharacteristic
1302C22#1062324611yescharacteristic
1303C4—24no—
1304C4—42no—
1305C4—42no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—224no—
1310C4—224no—
1311C4—442no—
1312C4—442no—
1313C4—442no—
1314C4—881no—
1315C2—82no—
1316C2—444no—
1317C2—882no—
1318C2#1307119511yescharacteristic
1319C2#1307131311yescharacteristic
1320C2#1307137911yescharacteristic
1321C2#1307143411yescharacteristic
1322C2#1307145311yescharacteristic
1323C2#1307166011yescharacteristic
1324C2#1307177211yescharacteristic
1325C2#1307488411yescharacteristic
1326C2#1307488911yescharacteristic
1327C2#1307491611yescharacteristic
1328C2#1307492311yescharacteristic
1329C2#1307537211yescharacteristic
1330C2#1307537911yescharacteristic
1331C2#1307541111yescharacteristic
1332C2#1307541811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC22×#66937C2
hypercenter#1439D11
hypocenterC11#14418
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#10622601C2semidirect
3. C2×#10622570C2semidirect
4. C2×#10622265C2semidirect
5. C2×#10622591C2semidirect
6. #13066860C2semidirect
7. #13066856C2semidirect
8. #13066855C2semidirect
9. #13066855C2semidirect
10. #13066855C2semidirect
11. #13066853C2semidirect
12. #13066852C2semidirect
13. (C2×D11)⋊#95C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1439C2semidirect
41. C2×#66937C4semidirect
145. C2×(C2×D11)⋊C4D4semidirect
346. Dic11⋊C4C22⋊C4semidirect
355. #1439D11semidirect
1014. C11#14418semidirect

Maximal subgroups

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

subgroupindex
C22×#669372
C2×#106226012
C2×#106225702
C2×#106222652
C2×#106225912
#130668602
#130668562
#130668552
#130668532
#130668522
(C2×D11)⋊#952
C11×#14392
#1441811