Finite Group Databasebeta

← #14683133

Subgroups — #14683133

Order 2816.

2282 conjugacy classes of subgroups.

The subgroup lattice has 1332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622573C211yesmaximal, characteristic
2C2×#10622552C211yesmaximal, characteristic, complemented
3C2×#10622570C211yesmaximal, characteristic, complemented
4C2×#10622603C211yesmaximal, characteristic, complemented
5C2×#10622278C211yesmaximal, characteristic, complemented
6C2×#10622569C211yesmaximal, characteristic, complemented
7#13066861C211yesmaximal, characteristic, complemented
8#13066860C211yesmaximal, characteristic, complemented
9#13066858C211yesmaximal, characteristic, complemented
10#13066855C211yesmaximal, characteristic, complemented
11#13066855C211yesmaximal, characteristic, complemented
12#13066850C211yesmaximal, characteristic, complemented
13#13066849C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C2×C11×#388C211yesmaximal, 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×C42×C11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
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×(C2×D11)⋊C4C2211yescharacteristic
36C22×C4⋊Dic11C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38C22×C4×Dic11C2211yescharacteristic
39C11×#388—24no—
40C2×C11×#95C2211yescharacteristic
41C2×C11×#95C2211yescharacteristic
42C2×C11⋊#95C2211yescharacteristic
43C2×C11⋊#95C2211yescharacteristic
44C2×C11⋊#95C2211yescharacteristic
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52#10622603—24no—
53#10622573C418yescomplemented
54#10622570—24no—
55#10622569—24no—
56#10622552—24no—
57#10622278—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—41no—
72C22×C22⋊D11—41no—
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×C414yescomplemented
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—22no—
97C22×C4×D11—41no—
98C22×C4×D11—41no—
99C22×C4×D11—41no—
100C22×C4×D11—41no—
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—22no—
108C2×C11×C22⋊C4—22no—
109C2×C11×C22⋊C4—22no—
110C2×C11×C22⋊C4—41no—
111C2×C11×C22⋊C4—41no—
112C2×C11×C22⋊C4C2×C414yescomplemented
113C2×C42×C11—22no—
114C2×C42×C11—22no—
115C2×C42×C11—41no—
116C2×C22⋊Dic11—22no—
117C2×C22⋊Dic11—22no—
118C2×C22⋊Dic11—41no—
119C2×C22⋊Dic11—41no—
120C2×C22⋊Dic11—41no—
121C2×C22⋊Dic11—41no—
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—22no—
131C2×(C2×D11)⋊C4—22no—
132C2×(C2×D11)⋊C4—22no—
133C2×(C2×D11)⋊C4—22no—
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)⋊C4—41no—
145C2×(C2×D11)⋊C4—41no—
146C2×(C2×D11)⋊C4C2×C414yes—
147C2×(C2×D11)⋊C4C2×C414yescomplemented
148C2×(C2×D11)⋊C4D414yescomplemented
149C2×C4⋊Dic11—22no—
150C2×C4⋊Dic11—22no—
151C2×C4⋊Dic11—41no—
152C2×Dic11⋊C4—22no—
153C2×Dic11⋊C4—22no—
154C2×Dic11⋊C4—41no—
155C2×C4×Dic11—22no—
156C2×C4×Dic11—22no—
157C2×C4×Dic11—41no—
158C11×#95—22no—
159C11×#95D414yescomplemented
160C11⋊#95—22no—
161C11⋊#95—22no—
162C11⋊#95—22no—
163C11⋊#95—41no—
164C11⋊#95—41no—
165C11⋊#95—41no—
166C11⋊#95—41no—
167C11⋊#95—41no—
168C11⋊#95C2×C414yescomplemented
169C11⋊#95D414yescomplemented
170#14521—111nomaximal, Sylow
171C24×C11—21no—
172C24×C11—21no—
173C24×C11—21no—
174C24×C11—21no—
175C24×C11—21no—
176C24×C11—21no—
177C24×C11—21no—
178C24×C11—21no—
179C24×C11—21no—
180C24×C11—21no—
181C24×C11—21no—
182C24×C11—21no—
183C24×C11—21no—
184C24×C11—21no—
185C24×C11C22×C412yes—
186C24×C11C2411yescharacteristic
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×D11—21no—
210C23×D11—21no—
211C23×D11—21no—
212C23×D11—21no—
213C23×D11C22×C412yes—
214C23×D11C22×C412yes—
215C23×D11C2×D412yes—
216C23×D11#4112yes—
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—21no—
249C22×C4×C11—21no—
250C22×C4×C11—21no—
251C22×C4×C11C22×C412yes—
252C22×C4×C11C22×C412yes—
253C22×C4×C11C2×D412yes—
254C22×C4×C11C2×D412yes—
255C22×C4×C11C2×D412yes—
256C22×C4×C11C2×D412yes—
257C22×C4×C11C2×D412yes—
258C22×C4×C11#4112yes—
259C2×C22⋊D11—28no—
260C2×C22⋊D11—28no—
261C2×C22⋊D11—44no—
262C2×C22⋊D11—44no—
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—
273C22×Dic11—21no—
274C22×Dic11—21no—
275C22×Dic11—21no—
276C22×Dic11—21no—
277C22×Dic11—21no—
278C22×Dic11—21no—
279C22×Dic11—21no—
280C22×Dic11—21no—
281C22×Dic11—21no—
282C22×Dic11—21no—
283C22×Dic11—21no—
284C22×Dic11—21no—
285C22×Dic11—21no—
286C22×Dic11—21no—
287C22×Dic11—21no—
288C22×Dic11—21no—
289C22×Dic11—21no—
290C22×Dic11—21no—
291C22×Dic11—21no—
292C22×Dic11—21no—
293C22×Dic11—21no—
294C22×Dic11—21no—
295C22×Dic11—21no—
296C22×Dic11—21no—
297C22×Dic11—21no—
298C22×Dic11—21no—
299C22×Dic11—21no—
300C22×Dic11—21no—
301C22×Dic11—21no—
302C22×Dic11—21no—
303C22×Dic11—21no—
304C22×Dic11—21no—
305C22×Dic11—21no—
306C22×Dic11—21no—
307C22×Dic11—21no—
308C22×Dic11—21no—
309C22×Dic11C22×C412yes—
310C22×Dic11C22×C412yes—
311C22×Dic11C2×D412yes—
312C22×Dic11C2×D412yes—
313C22×Dic11C2×D412yes—
314C22×Dic11#4112yes—
315C2×D44—28no—
316C2×D44—28no—
317C2×D44—44no—
318C2×D44—44no—
319C2×D44—44no—
320C2×D44—44no—
321C2×D44—44no—
322C2×C4×D11—44no—
323C2×C4×D11—44no—
324C2×C4×D11—44no—
325C2×C4×D11—44no—
326C2×C4×D11—44no—
327C2×C4×D11—44no—
328C2×C4×D11—44no—
329C11×C4⋊C4—44no—
330C11×C22⋊C4—28no—
331C11×C22⋊C4—44no—
332C11×C22⋊C4—44no—
333C42×C11—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—
345C4⋊Dic11—44no—
346Dic11⋊C4—44no—
347C4×Dic11—44no—
348C2×#392—111no—
349C2×#390—111no—
350C2×#390—111no—
351C2×#388—111no—
352C2×#388D1111yescharacteristic, complemented
353C2×#386—111no—
354C2×#386—111no—
355#1439—111no—
356#1439—111no—
357#1439—111no—
358#1438—111no—
359#1438—111no—
360#1436—111no—
361#1436—111no—
362C22⋊#95—111no—
363C23×C11—22no—
364C23×C11—22no—
365C23×C11—22no—
366C23×C11—22no—
367C23×C11—22no—
368C23×C11—22no—
369C23×C11—22no—
370C23×C11—41no—
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×C11C23×C411yescharacteristic
399C23×C11C22×D411yescharacteristic
400C23×C11C22×D411yescharacteristic
401C23×C11C22×D411yescharacteristic
402C23×C11C2×#4111yescharacteristic
403C23×C11C2×#4111yescharacteristic
404C23×C11C2×#4111yescharacteristic
405C23×C11H(5,𝔽2)11yescharacteristic
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×C112−1+411yescharacteristic
413C22×D11—22no—
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—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—
475C22×D11—41no—
476C22×D11—41no—
477C22×D11—41no—
478C22×D11—41no—
479C22×D11—41no—
480C22×D11—41no—
481C22×D11—41no—
482C22×D11C4×D414yes—
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—22no—
491C2×C4×C11—22no—
492C2×C4×C11—22no—
493C2×C4×C11—22no—
494C2×C4×C11—22no—
495C2×C4×C11—22no—
496C2×C4×C11—22no—
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—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×C11C4×D414yes—
525C22⋊D11—416no—
526C22⋊D11—416no—
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—22no—
539C2×Dic11—22no—
540C2×Dic11—22no—
541C2×Dic11—22no—
542C2×Dic11—41no—
543C2×Dic11—41no—
544C2×Dic11—41no—
545C2×Dic11—41no—
546C2×Dic11—41no—
547C2×Dic11—41no—
548C2×Dic11—41no—
549C2×Dic11—41no—
550C2×Dic11—41no—
551C2×Dic11—41no—
552C2×Dic11—41no—
553C2×Dic11—41no—
554C2×Dic11—41no—
555C2×Dic11—41no—
556C2×Dic11—41no—
557C2×Dic11—41no—
558C2×Dic11—41no—
559C2×Dic11—41no—
560C2×Dic11—41no—
561C2×Dic11—41no—
562C2×Dic11—41no—
563C2×Dic11—41no—
564C2×Dic11—41no—
565C2×Dic11—41no—
566C2×Dic11—41no—
567C2×Dic11—41no—
568C2×Dic11C4×D414yes—
569D44—416no—
570C4×D11—416no—
571C23×D4—111no—
572C23×D4—111no—
573C23×D4—111no—
574C24×C4—111no—
575C22×C4⋊C4—111no—
576C22×C4⋊C4—111no—
577C22×C4⋊C4C2×D1111yescharacteristic
578C22×C22⋊C4—111no—
579C22×C22⋊C4—111no—
580C22×C22⋊C4—111no—
581C22×C22⋊C4—111no—
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⋊C4C2×D1111yescharacteristic
590C22×C22⋊C4C2×D1111yescharacteristic
591C22×C22⋊C4C2×D1111yescharacteristic
592C22×C42—111no—
593C22×C42C2×D1111yescharacteristic
594#392—118no—
595#390—224no—
596#390—224no—
597#388—24no—
598#388—224no—
599#386—224no—
600#386—224no—
601C2×#95—111no—
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
613C22×C11—42no—
614C22×C11—42no—
615C22×C11—42no—
616C22×C11—42no—
617C22×C11—42no—
618C22×C11—42no—
619C22×C11—42no—
620C22×C11—81no—
621C22×C11—81no—
622C22×C11—81no—
623C22×C11—81no—
624C22×C11—81no—
625C22×C11—81no—
626C22×C11—81no—
627C22×C11—81no—
628C22×C11C2×C4×D411yescharacteristic
629C22×C11C2×C4×D411yescharacteristic
630C22×C11C2×C4×D411yescharacteristic
631C22×C11#51811yescharacteristic
632C22×C11#51811yescharacteristic
633C22×C11#51811yescharacteristic
634C22×C11#52011yescharacteristic
635C22×C11#53411yescharacteristic
636C22×C11#53511yescharacteristic
637C22×C11#53511yescharacteristic
638C22×C11#53711yescharacteristic
639C22×C11#53711yescharacteristic
640C22×C11#53711yescharacteristic
641C22×C11#53811yescharacteristic
642C22×C11#53911yescharacteristic
643C22×C11#54011yescharacteristic
644C22×C11#54011yescharacteristic
645C22×C11#54211yescharacteristic
646C22×C11#54211yescharacteristic
647C22×C11D4211yescharacteristic
648C22×C11D4211yescharacteristic
649C22×C11D4211yescharacteristic
650C22×C11#54611yescharacteristic
651C22×C11#54611yescharacteristic
652C22×C11#54611yescharacteristic
653C22×C11#54611yescharacteristic
654C22×C11#55011yescharacteristic
655C22×C11#55011yescharacteristic
656C22×C11#55111yescharacteristic
657C22×C11#55111yescharacteristic
658C22×C11#55911yescharacteristic
659C22×C11#56011yescharacteristic
660C22×C11#56011yescharacteristic
661C22×C11#56011yescharacteristic
662C22×C11H(3,𝔽4)11yescharacteristic
663C2×D11—24no—
664C2×D11—24no—
665C2×D11—24no—
666C2×D11—42no—
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—81no—
686C2×D11—81no—
687C2×D11—81no—
688C2×D11—81no—
689C2×D11—81no—
690C2×D11—81no—
691C2×D11—81no—
692C2×D11—81no—
693C4×C11—24no—
694C4×C11—42no—
695C4×C11—42no—
696C4×C11—42no—
697C4×C11—42no—
698C4×C11—42no—
699Dic11—24no—
700Dic11—42no—
701Dic11—42no—
702Dic11—42no—
703Dic11—81no—
704Dic11—81no—
705C25—111no—
706C25—111no—
707C25C22×D1111yescharacteristic
708C22×D4—114no—
709C22×D4—114no—
710C22×D4—114no—
711C22×D4—222no—
712C22×D4—222no—
713C22×D4—222no—
714C22×D4—222no—
715C22×D4—222no—
716C22×D4—222no—
717C22×D4—222no—
718C22×D4—222no—
719C22×D4—441no—
720C22×D4—441no—
721C22×D4—441no—
722C22×D4—441no—
723C22×D4—441no—
724C22×D4—441no—
725C22×D4—441no—
726C22×D4—441no—
727C22×D4—441no—
728C22×D4—441no—
729C23×C4—111no—
730C23×C4—111no—
731C23×C4—111no—
732C23×C4—111no—
733C23×C4—111no—
734C23×C4—111no—
735C23×C4—222no—
736C23×C4—222no—
737C23×C4—222no—
738C23×C4—441no—
739C23×C4—441no—
740C23×C4—441no—
741C23×C4—441no—
742C23×C4C22×D1111yescharacteristic
743C23×C4C22×D1111yescharacteristic
744C23×C4C22×D1111yescharacteristic
745C23×C4C22×D1111yescharacteristic
746C23×C4C22×D1111yescharacteristic
747C23×C4C22×D1111yescharacteristic
748C2×C4⋊C4—22no—
749C2×C4⋊C4—22no—
750C2×C4⋊C4—41no—
751C2×C4⋊C4—222no—
752C2×C4⋊C4—222no—
753C2×C4⋊C4—222no—
754C2×C4⋊C4—222no—
755C2×C4⋊C4—441no—
756C2×C4⋊C4—441no—
757C2×C22⋊C4—22no—
758C2×C22⋊C4—22no—
759C2×C22⋊C4—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—41no—
764C2×C22⋊C4—41no—
765C2×C22⋊C4—114no—
766C2×C22⋊C4—114no—
767C2×C22⋊C4—114no—
768C2×C22⋊C4—222no—
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—441no—
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⋊C4C4×D1114yescomplemented
799C2×C42—22no—
800C2×C42—22no—
801C2×C42—41no—
802C2×C42—222no—
803C2×C42—222no—
804C2×C42—441no—
805#95—22no—
806#95—114no—
807#95—114no—
808#95—222no—
809#95—222no—
810#95—222no—
811#95—441no—
812#95—441no—
813#95—441no—
814#95—441no—
815#95—441no—
816#95C22⋊D1114yescomplemented
817C2×C11—82no—
818C2×C11#232411yescharacteristic
819C2×C11#232411yescharacteristic
820C2×C11#232511yescharacteristic
821C2×C11#235811yescharacteristic
822C2×C11#235811yescharacteristic
823C2×C11#236611yescharacteristic
824C2×C11#237511yescharacteristic
825C2×C11#267011yescharacteristic
826C2×C11#267311yescharacteristic
827C2×C11#267311yescharacteristic
828C2×C11#267511yescharacteristic
829C2×C11#270511yescharacteristic
830C2×C11#270511yescharacteristic
831C2×C11#271211yescharacteristic
832C2×C11#275211yescharacteristic
833D11—44no—
834D11—82no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—112no—
850C24—112no—
851C24—112no—
852C24—112no—
853C24—221no—
854C24—221no—
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—
879C24C2×C4×D1112yes—
880C24C23×D1111yescharacteristic
881C2×D4—228no—
882C2×D4—228no—
883C2×D4—228no—
884C2×D4—228no—
885C2×D4—444no—
886C2×D4—444no—
887C2×D4—444no—
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—
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—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—112no—
937C22×C4—112no—
938C22×C4—112no—
939C22×C4—112no—
940C22×C4—112no—
941C22×C4—112no—
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×C4—221no—
975C22×C4—221no—
976C22×C4—221no—
977C22×C4—221no—
978C22×C4—444no—
979C22×C4—444no—
980C22×C4—444no—
981C22×C4—444no—
982C22×C4—444no—
983C22×C4—444no—
984C22×C4—444no—
985C22×C4C2×C4×D1112yes—
986C22×C4C2×C4×D1112yes—
987C22×C4#433912yes—
988C22×C4D4×D1112yes—
989C22×C4D4×D1112yes—
990C22×C4C2×C22⋊D1112yes—
991C22×C4C2×C22⋊D1112yes—
992C22×C4C2×C22⋊D1112yes—
993C4⋊C4—44no—
994C4⋊C4—444no—
995C4⋊C4—444no—
996C22⋊C4—28no—
997C22⋊C4—44no—
998C22⋊C4—44no—
999C22⋊C4—228no—
1000C22⋊C4—444no—
1001C22⋊C4—444no—
1002C22⋊C4—444no—
1003C22⋊C4—444no—
1004C22⋊C4—444no—
1005C22⋊C4—444no—
1006C22⋊C4—444no—
1007C22⋊C4—444no—
1008C22⋊C4—444no—
1009C22⋊C4—444no—
1010C42—44no—
1011C42—444no—
1012C11#1452111yescharacteristic, complemented, Sylow
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—41no—
1021C23—41no—
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—114no—
1049C23—222no—
1050C23—222no—
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—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—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—
1118C23C22×C4×D1111yescharacteristic
1119C23C2×#433911yescharacteristic
1120C23C2×D4×D1111yescharacteristic
1121C23C2×D4×D1111yescharacteristic
1122C23#6703711yescharacteristic
1123C23#6703711yescharacteristic
1124C23#41×D1111yescharacteristic
1125C23#41×D1111yescharacteristic
1126C23#6704211yescharacteristic
1127C23#6704211yescharacteristic
1128C23#6704211yescharacteristic
1129C23#6704211yescharacteristic
1130C23#6704211yescharacteristic
1131C23#6704311yescharacteristic
1132C23C22×C22⋊D1111yescharacteristic
1133D4—4416no—
1134D4—4416no—
1135D4—4416no—
1136C2×C4—22no—
1137C2×C4—22no—
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—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
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—114no—
1178C2×C4—222no—
1179C2×C4—222no—
1180C2×C4—222no—
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—4416no—
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—
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×C4C4×C22⋊D1114yes—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—224no—
1237C22—224no—
1238C22—224no—
1239C22—442no—
1240C22—442no—
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—881no—
1259C22—881no—
1260C22—881no—
1261C22—881no—
1262C22—881no—
1263C22—881no—
1264C22—881no—
1265C22—881no—
1266C22#1062305211yescharacteristic
1267C22#1062305411yescharacteristic
1268C22#1062306511yescharacteristic
1269C22#1062306611yescharacteristic
1270C22C4×D4×D1111yescharacteristic
1271C22C4×D4×D1111yescharacteristic
1272C22#1062307611yescharacteristic
1273C22#1062307611yescharacteristic
1274C22#1062308111yescharacteristic
1275C22#1062308411yescharacteristic
1276C22#1062308711yescharacteristic
1277C22#1062309011yescharacteristic
1278C22#1062312811yescharacteristic
1279C22#1062313911yescharacteristic
1280C22#1062314011yescharacteristic
1281C22#1062315111yescharacteristic
1282C22#1062318411yescharacteristic
1283C22#1062318511yescharacteristic
1284C22#1062319411yescharacteristic
1285C22#1062319711yescharacteristic
1286C22#1062320511yescharacteristic
1287C22#1062320711yescharacteristic
1288C22#1062320911yescharacteristic
1289C22#1062321411yescharacteristic
1290C22#1062323611yescharacteristic
1291C22#1062323811yescharacteristic
1292C22#1062324111yescharacteristic
1293C22#1062324211yescharacteristic
1294C22C2×C4×C22⋊D1111yescharacteristic
1295C22D4×C22⋊D1111yescharacteristic
1296C22D4×C22⋊D1111yescharacteristic
1297C22#1062336011yescharacteristic
1298C22#1062336111yescharacteristic
1299C22#1062336411yescharacteristic
1300C22#1062336511yescharacteristic
1301C4—24no—
1302C4—42no—
1303C4—42no—
1304C4—42no—
1305C4—42no—
1306C4—42no—
1307C4—224no—
1308C4—442no—
1309C4—442no—
1310C4—442no—
1311C4—881no—
1312C4—881no—
1313C2—82no—
1314C2—444no—
1315C2—882no—
1316C2#1307130411yescharacteristic
1317C2#1307130911yescharacteristic
1318C2#1307132011yescharacteristic
1319C2#1307159311yescharacteristic
1320C2#1307159411yescharacteristic
1321C2#1307167811yescharacteristic
1322C2#1307175611yescharacteristic
1323C2#1307483711yescharacteristic
1324C2#1307488211yescharacteristic
1325C2#1307488311yescharacteristic
1326C2#1307490611yescharacteristic
1327C2#1307528311yescharacteristic
1328C2#1307528611yescharacteristic
1329C2#1307538811yescharacteristic
1330C2#1307588111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#388C2
socle, cosocleC24×C11C24
prime radicalC2×#10622573C2
hypercenterC2×#388D11
hypocenterC11#14521
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#10622552C2semidirect
3. C2×#10622570C2semidirect
4. C2×#10622603C2semidirect
5. C2×#10622278C2semidirect
6. C2×#10622569C2semidirect
7. #13066861C2semidirect
8. #13066860C2semidirect
9. #13066858C2semidirect
10. #13066855C2semidirect
11. #13066855C2semidirect
12. #13066850C2semidirect
13. #13066849C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C2×C11×#388C2semidirect
53. #10622573C4semidirect
80. C22×C22⋊D11C2×C4semidirect
112. C2×C11×C22⋊C4C2×C4semidirect
147. C2×(C2×D11)⋊C4C2×C4semidirect
148. C2×(C2×D11)⋊C4D4semidirect
159. C11×#95D4semidirect
168. C11⋊#95C2×C4semidirect
169. C11⋊#95D4semidirect
352. C2×#388D11semidirect
798. C2×C22⋊C4C4×D11semidirect
816. #95C22⋊D11semidirect
1012. C11#14521semidirect

Maximal subgroups

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

subgroupindex
C2×#106225732
C2×#106225522
C2×#106225702
C2×#106226032
C2×#106222782
C2×#106225692
#130668612
#130668602
#130668582
#130668552
#130668502
#130668492
(C2×D11)⋊#952
C2×C11×#3882
#1452111