Finite Group Databasebeta

← #14684530

Subgroups — #14684530

Order 2816.

1586 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622572C211yesmaximal, characteristic
2C2×#10622603C211yesmaximal, characteristic, complemented
3C2×#10622557C211yesmaximal, characteristic, complemented
4#13066875C211yesmaximal, characteristic, complemented
5#13066871C211yesmaximal, characteristic, complemented
6#13066870C211yesmaximal, characteristic, complemented
7#13066862C211yesmaximal, characteristic, complemented
8#13066861C211yesmaximal, characteristic, complemented
9#13066860C211yesmaximal, characteristic, complemented
10#13066860C211yesmaximal, characteristic, complemented
11#13066859C211yesmaximal, characteristic, complemented
12#13066855C211yesmaximal, characteristic
13#13066855C211yesmaximal, characteristic
14Dic11⋊#95C211yesmaximal, characteristic, complemented
15C11×#1439C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2211yescharacteristic
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
51#10622603—24no—
52#10622572C418yescomplemented
53#10622557—24no—
54C25×C11C2311yescharacteristic
55C24×D11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—41no—
63C22×C22⋊D11—41no—
64C22×C22⋊D11—41no—
65C22×C22⋊D11—41no—
66C22×C22⋊D11—41no—
67C22×C22⋊D11—41no—
68C22×C22⋊D11C2×C414yes—
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—41no—
78C2×C11×C4⋊C4—41no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—41no—
81C2×C11×C22⋊C4—41no—
82C2×C11×C22⋊C4—41no—
83C2×C11×C22⋊C4—41no—
84C2×C11×C22⋊C4—41no—
85C2×C11×C22⋊C4—41no—
86C2×C11×C22⋊C4—41no—
87C2×C11×C22⋊C4C2×C414yes—
88C2×C22⋊Dic11—22no—
89C2×C22⋊Dic11—22no—
90C2×C22⋊Dic11—22no—
91C2×C22⋊Dic11—41no—
92C2×C22⋊Dic11—41no—
93C2×C22⋊Dic11—41no—
94C2×C22⋊Dic11—41no—
95C2×C22⋊Dic11—41no—
96C2×C22⋊Dic11C2×C414yes—
97C2×(C2×D11)⋊C4—22no—
98C2×(C2×D11)⋊C4—22no—
99C2×(C2×D11)⋊C4—22no—
100C2×(C2×D11)⋊C4—22no—
101C2×(C2×D11)⋊C4—41no—
102C2×(C2×D11)⋊C4—41no—
103C2×(C2×D11)⋊C4—41no—
104C2×(C2×D11)⋊C4—41no—
105C2×(C2×D11)⋊C4—41no—
106C2×(C2×D11)⋊C4—41no—
107C2×(C2×D11)⋊C4—41no—
108C2×(C2×D11)⋊C4—41no—
109C2×(C2×D11)⋊C4—41no—
110C2×(C2×D11)⋊C4—41no—
111C2×(C2×D11)⋊C4—41no—
112C2×(C2×D11)⋊C4—41no—
113C2×(C2×D11)⋊C4C2×C414yes—
114C2×(C2×D11)⋊C4C2×C414yes—
115C2×C4⋊Dic11—41no—
116C2×C4⋊Dic11—41no—
117C2×C4⋊Dic11—41no—
118C2×Dic11⋊C4—22no—
119C2×Dic11⋊C4—22no—
120C2×Dic11⋊C4—41no—
121C2×Dic11⋊C4—41no—
122C2×Dic11⋊C4—41no—
123C2×Dic11⋊C4—41no—
124C2×Dic11⋊C4—41no—
125C2×Dic11⋊C4—41no—
126C2×Dic11⋊C4C2×C414yes—
127C2×C4×Dic11—41no—
128C2×C4×Dic11—41no—
129C2×C4×Dic11D414yescomplemented
130C11×#95—41no—
131C11×#95—41no—
132C11×#95—41no—
133C11⋊#95—22no—
134C11⋊#95—22no—
135C11⋊#95—22no—
136C11⋊#95—22no—
137C11⋊#95—41no—
138C11⋊#95—41no—
139C11⋊#95—41no—
140C11⋊#95—41no—
141C11⋊#95—41no—
142C11⋊#95—41no—
143C11⋊#95—41no—
144C11⋊#95—41no—
145C11⋊#95C2×C414yes—
146#14632—111nomaximal, Sylow
147C24×C11—21no—
148C24×C11—21no—
149C24×C11—21no—
150C24×C11—21no—
151C24×C11—21no—
152C24×C11—21no—
153C24×C11—21no—
154C24×C11—21no—
155C24×C11—21no—
156C24×C11—21no—
157C24×C11—21no—
158C24×C11—21no—
159C24×C11—21no—
160C24×C11—21no—
161C24×C11C22×C412yes—
162C24×C11C2411yescharacteristic
163C23×D11—21no—
164C23×D11—21no—
165C23×D11—21no—
166C23×D11—21no—
167C23×D11—21no—
168C23×D11—21no—
169C23×D11—21no—
170C23×D11—21no—
171C23×D11—21no—
172C23×D11—21no—
173C23×D11—21no—
174C23×D11—21no—
175C23×D11—21no—
176C23×D11—21no—
177C23×D11C22×C412yes—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11C22×C412yes—
218C22×C4×C11C22×C412yes—
219C22×C4×C11C2×D412yes—
220C2×C22⋊D11—44no—
221C2×C22⋊D11—44no—
222C2×C22⋊D11—44no—
223C2×C22⋊D11—44no—
224C2×C22⋊D11—44no—
225C2×C22⋊D11—44no—
226C2×C22⋊D11—44no—
227C22×Dic11—21no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—21no—
233C22×Dic11—21no—
234C22×Dic11—21no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—21no—
239C22×Dic11—21no—
240C22×Dic11—21no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11—21no—
247C22×Dic11—21no—
248C22×Dic11—21no—
249C22×Dic11—21no—
250C22×Dic11—21no—
251C22×Dic11—21no—
252C22×Dic11—21no—
253C22×Dic11—21no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11—21no—
258C22×Dic11—21no—
259C22×Dic11—21no—
260C22×Dic11—21no—
261C22×Dic11—21no—
262C22×Dic11—21no—
263C22×Dic11—21no—
264C22×Dic11—21no—
265C22×Dic11—21no—
266C22×Dic11—21no—
267C22×Dic11—21no—
268C22×Dic11—21no—
269C22×Dic11—21no—
270C22×Dic11C22×C412yes—
271C22×Dic11C22×C412yes—
272C22×Dic11C22×C412yes—
273C22×Dic11C2×D412yes—
274C22×Dic11C2×D412yes—
275C22×Dic11#4112yes—
276C11×C4⋊C4—44no—
277C11×C22⋊C4—44no—
278C11×C22⋊C4—44no—
279C11×C22⋊C4—44no—
280C22⋊Dic11—28no—
281C22⋊Dic11—44no—
282C22⋊Dic11—44no—
283(C2×D11)⋊C4—28no—
284(C2×D11)⋊C4—44no—
285(C2×D11)⋊C4—44no—
286(C2×D11)⋊C4—44no—
287(C2×D11)⋊C4—44no—
288(C2×D11)⋊C4—44no—
289C4⋊Dic11—44no—
290Dic11⋊C4—44no—
291Dic11⋊C4—44no—
292Dic11⋊C4—44no—
293C4×Dic11—44no—
294C2×#394—111no—
295C2×#388—111no—
296C2×#388—111no—
297#1442—111no—
298#1442—111no—
299#1441—111no—
300#1439—111no—
301#1439—111no—
302#1439—111no—
303#1439—111no—
304#1439—111no—
305#1439D1111yescharacteristic, complemented
306#1438—111no—
307#1438—111no—
308C4⋊#95—111no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—41no—
317C23×C11—41no—
318C23×C11—41no—
319C23×C11—41no—
320C23×C11—41no—
321C23×C11—41no—
322C23×C11—41no—
323C23×C11—41no—
324C23×C11—41no—
325C23×C11—41no—
326C23×C11—41no—
327C23×C11—41no—
328C23×C11—41no—
329C23×C11—41no—
330C23×C11—41no—
331C23×C11—41no—
332C23×C11—41no—
333C23×C11—41no—
334C23×C11—41no—
335C23×C11—41no—
336C23×C11—41no—
337C23×C11—41no—
338C23×C11—41no—
339C23×C11—41no—
340C23×C11—41no—
341C23×C11—41no—
342C23×C11—41no—
343C23×C11—41no—
344C23×C11C23×C411yescharacteristic
345C23×C11C22×D411yescharacteristic
346C23×C11C2×#4111yescharacteristic
347C23×C11H(5,𝔽2)11yescharacteristic
348C23×C11H(5,𝔽2)11yescharacteristic
349C23×C11H(5,𝔽2)11yescharacteristic
350C23×C11H(5,𝔽2)11yescharacteristic
351C23×C11H(5,𝔽2)11yescharacteristic
352C23×C11H(5,𝔽2)11yescharacteristic
353C23×C11H(5,𝔽2)11yescharacteristic
354C23×C11H(5,𝔽2)11yescharacteristic
355C23×C11H(5,𝔽2)11yescharacteristic
356C23×C112−1+411yescharacteristic
357C23×C112−1+411yescharacteristic
358C23×C112−1+411yescharacteristic
359C22×D11—22no—
360C22×D11—22no—
361C22×D11—22no—
362C22×D11—22no—
363C22×D11—22no—
364C22×D11—22no—
365C22×D11—22no—
366C22×D11—41no—
367C22×D11—41no—
368C22×D11—41no—
369C22×D11—41no—
370C22×D11—41no—
371C22×D11—41no—
372C22×D11—41no—
373C22×D11—41no—
374C22×D11—41no—
375C22×D11—41no—
376C22×D11—41no—
377C22×D11—41no—
378C22×D11—41no—
379C22×D11—41no—
380C22×D11—41no—
381C22×D11—41no—
382C22×D11—41no—
383C22×D11—41no—
384C22×D11—41no—
385C22×D11—41no—
386C22×D11—41no—
387C22×D11—41no—
388C22×D11—41no—
389C22×D11—41no—
390C22×D11—41no—
391C22×D11—41no—
392C22×D11—41no—
393C22×D11—41no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—41no—
404C2×C4×C11—41no—
405C2×C4×C11—41no—
406C2×C4×C11—41no—
407C2×C4×C11—41no—
408C2×C4×C11—41no—
409C2×C4×C11—41no—
410C2×C4×C11—41no—
411C2×C4×C11—41no—
412C2×C4×C11—41no—
413C2×C4×C11—41no—
414C2×C4×C11—41no—
415C2×C4×C11—41no—
416C2×C4×C11—41no—
417C2×C4×C11—41no—
418C2×C4×C11—41no—
419C2×C4×C11—41no—
420C2×C4×C11—41no—
421C2×C4×C11—41no—
422C2×C4×C11—41no—
423C2×C4×C11—41no—
424C2×C4×C11—41no—
425C2×C4×C11—41no—
426C2×C4×C11—41no—
427C2×C4×C11—41no—
428C2×C4×C11—41no—
429C2×C4×C11—41no—
430C2×C4×C11—41no—
431C2×C4×C11—41no—
432C2×C4×C11—41no—
433C2×C4×C11—41no—
434C2×C4×C11—41no—
435C2×C4×C11—41no—
436C22⋊D11—416no—
437C2×Dic11—22no—
438C2×Dic11—22no—
439C2×Dic11—22no—
440C2×Dic11—22no—
441C2×Dic11—22no—
442C2×Dic11—22no—
443C2×Dic11—22no—
444C2×Dic11—22no—
445C2×Dic11—22no—
446C2×Dic11—22no—
447C2×Dic11—22no—
448C2×Dic11—22no—
449C2×Dic11—22no—
450C2×Dic11—22no—
451C2×Dic11—22no—
452C2×Dic11—41no—
453C2×Dic11—41no—
454C2×Dic11—41no—
455C2×Dic11—41no—
456C2×Dic11—41no—
457C2×Dic11—41no—
458C2×Dic11—41no—
459C2×Dic11—41no—
460C2×Dic11—41no—
461C2×Dic11—41no—
462C2×Dic11—41no—
463C2×Dic11—41no—
464C2×Dic11—41no—
465C2×Dic11—41no—
466C2×Dic11—41no—
467C2×Dic11—41no—
468C2×Dic11—41no—
469C2×Dic11—41no—
470C2×Dic11—41no—
471C2×Dic11—41no—
472C2×Dic11—41no—
473C2×Dic11—41no—
474C2×Dic11—41no—
475C2×Dic11—41no—
476C2×Dic11—41no—
477C2×Dic11—41no—
478C2×Dic11—41no—
479C2×Dic11—41no—
480C2×Dic11—41no—
481C2×Dic11—41no—
482C2×Dic11—41no—
483C2×Dic11—41no—
484C2×Dic11—41no—
485C2×Dic11C4×D414yes—
486C23×D4—111no—
487C22×C4⋊C4—111no—
488C22×C4⋊C4—111no—
489C22×C4⋊C4—111no—
490C22×C4⋊C4—111no—
491C22×C4⋊C4C2×D1111yescharacteristic
492C22×C22⋊C4—111no—
493C22×C22⋊C4—111no—
494C22×C22⋊C4—111no—
495C22×C22⋊C4—111no—
496C22×C22⋊C4—111no—
497C22×C22⋊C4—111no—
498C22×C22⋊C4—111no—
499C22×C22⋊C4—111no—
500C22×C22⋊C4—111no—
501C22×C22⋊C4C2×D1111yescharacteristic
502C22×C22⋊C4C2×D1111yescharacteristic
503C22×C22⋊C4C2×D1111yescharacteristic
504C22×C42—111no—
505#394—118no—
506#388—224no—
507#388—224no—
508C2×#95—111no—
509C2×#95—111no—
510C2×#95—111no—
511C2×#95—111no—
512C2×#95—111no—
513C2×#95—111no—
514C2×#95—111no—
515C2×#95—111no—
516C2×#95—111no—
517C2×#95—111no—
518C2×#95—111no—
519C2×#95—111no—
520C2×#95—111no—
521C2×#95C2×D1111yescharacteristic
522C2×#95C2×D1111yescharacteristic
523C2×#95C2×D1111yescharacteristic
524C22×C11—42no—
525C22×C11—42no—
526C22×C11—42no—
527C22×C11—42no—
528C22×C11—42no—
529C22×C11—42no—
530C22×C11—42no—
531C22×C11—81no—
532C22×C11—81no—
533C22×C11—81no—
534C22×C11—81no—
535C22×C11—81no—
536C22×C11—81no—
537C22×C11—81no—
538C22×C11—81no—
539C22×C11C2×C4×D411yescharacteristic
540C22×C11#51811yescharacteristic
541C22×C11#51811yescharacteristic
542C22×C11#51811yescharacteristic
543C22×C11#52011yescharacteristic
544C22×C11#52011yescharacteristic
545C22×C11#52011yescharacteristic
546C22×C11#53411yescharacteristic
547C22×C11#53511yescharacteristic
548C22×C11#53511yescharacteristic
549C22×C11#53711yescharacteristic
550C22×C11#53711yescharacteristic
551C22×C11#53711yescharacteristic
552C22×C11#53811yescharacteristic
553C22×C11#53911yescharacteristic
554C22×C11#54011yescharacteristic
555C22×C11#54011yescharacteristic
556C22×C11#54211yescharacteristic
557C22×C11#54211yescharacteristic
558C22×C11#56011yescharacteristic
559C22×C11#56011yescharacteristic
560C22×C11#56011yescharacteristic
561C22×C11#56011yescharacteristic
562C22×C11#56011yescharacteristic
563C22×C11H(3,𝔽4)11yescharacteristic
564C22×C11H(3,𝔽4)11yescharacteristic
565C22×C11#56211yescharacteristic
566C22×C11#56211yescharacteristic
567C22×C11#56211yescharacteristic
568C22×C11#56211yescharacteristic
569C22×C11#56211yescharacteristic
570C22×C11#56211yescharacteristic
571C22×C11#56311yescharacteristic
572C22×C11#56311yescharacteristic
573C22×C11#56311yescharacteristic
574C2×D11—42no—
575C2×D11—42no—
576C2×D11—42no—
577C2×D11—42no—
578C2×D11—42no—
579C2×D11—42no—
580C2×D11—42no—
581C2×D11—81no—
582C2×D11—81no—
583C2×D11—81no—
584C2×D11—81no—
585C2×D11—81no—
586C2×D11—81no—
587C2×D11—81no—
588C2×D11—81no—
589C4×C11—42no—
590C4×C11—42no—
591C4×C11—42no—
592C4×C11—81no—
593C4×C11—81no—
594C4×C11—81no—
595Dic11—24no—
596Dic11—42no—
597Dic11—42no—
598Dic11—42no—
599Dic11—81no—
600Dic11—81no—
601Dic11—81no—
602C25—111no—
603C25C22×D1111yescharacteristic
604C22×D4—114no—
605C22×D4—441no—
606C22×D4—441no—
607C22×D4—441no—
608C22×D4—441no—
609C22×D4—441no—
610C22×D4—441no—
611C23×C4—111no—
612C23×C4—111no—
613C23×C4—111no—
614C23×C4—111no—
615C23×C4—111no—
616C23×C4—111no—
617C23×C4—111no—
618C23×C4C22×D1111yescharacteristic
619C23×C4C22×D1111yescharacteristic
620C23×C4C22×D1111yescharacteristic
621C23×C4C22×D1111yescharacteristic
622C23×C4C22×D1111yescharacteristic
623C23×C4C22×D1111yescharacteristic
624C2×C4⋊C4—22no—
625C2×C4⋊C4—41no—
626C2×C4⋊C4—41no—
627C2×C4⋊C4—114no—
628C2×C4⋊C4—222no—
629C2×C4⋊C4—222no—
630C2×C4⋊C4—441no—
631C2×C4⋊C4—441no—
632C2×C4⋊C4—441no—
633C2×C4⋊C4—441no—
634C2×C4⋊C4—441no—
635C2×C4⋊C4—441no—
636C2×C4⋊C4—441no—
637C2×C4⋊C4—441no—
638C2×C4⋊C4—441no—
639C2×C22⋊C4—22no—
640C2×C22⋊C4—41no—
641C2×C22⋊C4—41no—
642C2×C22⋊C4—41no—
643C2×C22⋊C4—41no—
644C2×C22⋊C4—41no—
645C2×C22⋊C4—41no—
646C2×C22⋊C4—41no—
647C2×C22⋊C4—114no—
648C2×C22⋊C4—114no—
649C2×C22⋊C4—114no—
650C2×C22⋊C4—222no—
651C2×C22⋊C4—222no—
652C2×C22⋊C4—222no—
653C2×C22⋊C4—222no—
654C2×C22⋊C4—222no—
655C2×C22⋊C4—222no—
656C2×C22⋊C4—222no—
657C2×C22⋊C4—441no—
658C2×C22⋊C4—441no—
659C2×C22⋊C4—441no—
660C2×C22⋊C4—441no—
661C2×C22⋊C4—441no—
662C2×C22⋊C4—441no—
663C2×C22⋊C4—441no—
664C2×C22⋊C4—441no—
665C2×C22⋊C4—441no—
666C2×C22⋊C4—441no—
667C2×C22⋊C4—441no—
668C2×C22⋊C4—441no—
669C2×C22⋊C4—441no—
670C2×C22⋊C4—441no—
671C2×C22⋊C4—441no—
672C2×C22⋊C4—441no—
673C2×C22⋊C4—441no—
674C2×C22⋊C4C4×D1114yes—
675C2×C42—114no—
676C2×C42—441no—
677C2×C42—441no—
678#95—41no—
679#95—41no—
680#95—41no—
681#95—114no—
682#95—222no—
683#95—222no—
684#95—222no—
685#95—222no—
686#95—441no—
687#95—441no—
688#95—441no—
689#95—441no—
690#95—441no—
691#95—441no—
692#95—441no—
693#95—441no—
694C2×C11—82no—
695C2×C11#232411yescharacteristic
696C2×C11#232411yescharacteristic
697C2×C11#232511yescharacteristic
698C2×C11#237511yescharacteristic
699C2×C11#237611yescharacteristic
700C2×C11#237611yescharacteristic
701C2×C11#237911yescharacteristic
702C2×C11#281311yescharacteristic
703C2×C11#281311yescharacteristic
704C2×C11#281911yescharacteristic
705C2×C11#282311yescharacteristic
706C2×C11#282811yescharacteristic
707C2×C11#283211yescharacteristic
708C2×C11#283711yescharacteristic
709C2×C11#283711yescharacteristic
710D11—82no—
711C24—21no—
712C24—21no—
713C24—21no—
714C24—21no—
715C24—21no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—112no—
726C24—221no—
727C24—221no—
728C24—221no—
729C24—221no—
730C24—221no—
731C24—221no—
732C24—221no—
733C24—221no—
734C24—221no—
735C24—221no—
736C24—221no—
737C24—221no—
738C24—221no—
739C24—221no—
740C24C2×C4×D1112yes—
741C24C23×D1111yescharacteristic
742C2×D4—444no—
743C2×D4—444no—
744C2×D4—444no—
745C2×D4—444no—
746C2×D4—444no—
747C2×D4—444no—
748C2×D4—444no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—112no—
789C22×C4—112no—
790C22×C4—112no—
791C22×C4—112no—
792C22×C4—112no—
793C22×C4—112no—
794C22×C4—221no—
795C22×C4—221no—
796C22×C4—221no—
797C22×C4—221no—
798C22×C4—221no—
799C22×C4—221no—
800C22×C4—221no—
801C22×C4—221no—
802C22×C4—221no—
803C22×C4—221no—
804C22×C4—221no—
805C22×C4—221no—
806C22×C4—221no—
807C22×C4—221no—
808C22×C4—221no—
809C22×C4—221no—
810C22×C4—221no—
811C22×C4—221no—
812C22×C4—221no—
813C22×C4—221no—
814C22×C4—221no—
815C22×C4—221no—
816C22×C4—221no—
817C22×C4—221no—
818C22×C4—221no—
819C22×C4—221no—
820C22×C4—221no—
821C22×C4—221no—
822C22×C4—221no—
823C22×C4—221no—
824C22×C4—221no—
825C22×C4—221no—
826C22×C4—221no—
827C22×C4—221no—
828C22×C4—221no—
829C22×C4—221no—
830C22×C4—221no—
831C22×C4—221no—
832C22×C4—221no—
833C22×C4—221no—
834C22×C4—221no—
835C22×C4—221no—
836C22×C4—221no—
837C22×C4C2×C4×D1112yes—
838C22×C4C2×C4×D1112yes—
839C22×C4D4×D1112yes—
840C4⋊C4—44no—
841C4⋊C4—444no—
842C4⋊C4—444no—
843C4⋊C4—444no—
844C4⋊C4—444no—
845C22⋊C4—44no—
846C22⋊C4—44no—
847C22⋊C4—44no—
848C22⋊C4—228no—
849C22⋊C4—228no—
850C22⋊C4—444no—
851C22⋊C4—444no—
852C22⋊C4—444no—
853C22⋊C4—444no—
854C22⋊C4—444no—
855C22⋊C4—444no—
856C22⋊C4—444no—
857C42—444no—
858C11#1463211yescharacteristic, complemented, Sylow
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—41no—
879C23—41no—
880C23—41no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—222no—
895C23—222no—
896C23—222no—
897C23—222no—
898C23—222no—
899C23—222no—
900C23—222no—
901C23—441no—
902C23—441no—
903C23—441no—
904C23—441no—
905C23—441no—
906C23—441no—
907C23—441no—
908C23—441no—
909C23—441no—
910C23—441no—
911C23—441no—
912C23—441no—
913C23—441no—
914C23—441no—
915C23—441no—
916C23—441no—
917C23—441no—
918C23—441no—
919C23—441no—
920C23—441no—
921C23—441no—
922C23—441no—
923C23—441no—
924C23—441no—
925C23—441no—
926C23—441no—
927C23—441no—
928C23—441no—
929C23C22×C4×D1111yescharacteristic
930C23C2×D4×D1111yescharacteristic
931C23#6703711yescharacteristic
932C23#6703711yescharacteristic
933C23#6703711yescharacteristic
934C23#6703711yescharacteristic
935C23#6703711yescharacteristic
936C23#6703711yescharacteristic
937C23#6704011yescharacteristic
938C23#41×D1111yescharacteristic
939C23#6704211yescharacteristic
940C23#6704211yescharacteristic
941C23#6704211yescharacteristic
942C23#6704311yescharacteristic
943C23#6704311yescharacteristic
944D4—4416no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—114no—
988C2×C4—222no—
989C2×C4—222no—
990C2×C4—222no—
991C2×C4—222no—
992C2×C4—222no—
993C2×C4—222no—
994C2×C4—222no—
995C2×C4—222no—
996C2×C4—222no—
997C2×C4—222no—
998C2×C4—222no—
999C2×C4—222no—
1000C2×C4—222no—
1001C2×C4—222no—
1002C2×C4—222no—
1003C2×C4—441no—
1004C2×C4—441no—
1005C2×C4—441no—
1006C2×C4—441no—
1007C2×C4—441no—
1008C2×C4—441no—
1009C2×C4—441no—
1010C2×C4—441no—
1011C2×C4—441no—
1012C2×C4—441no—
1013C2×C4—441no—
1014C2×C4—441no—
1015C2×C4—441no—
1016C2×C4—441no—
1017C2×C4—441no—
1018C2×C4—441no—
1019C2×C4—441no—
1020C2×C4—441no—
1021C2×C4—441no—
1022C2×C4—441no—
1023C2×C4—441no—
1024C2×C4—441no—
1025C2×C4—441no—
1026C2×C4—441no—
1027C2×C4—441no—
1028C2×C4—441no—
1029C2×C4—441no—
1030C2×C4—441no—
1031C2×C4—441no—
1032C2×C4—441no—
1033C2×C4—441no—
1034C2×C4—441no—
1035C2×C4—441no—
1036C22—42no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—42no—
1042C22—42no—
1043C22—81no—
1044C22—81no—
1045C22—81no—
1046C22—81no—
1047C22—81no—
1048C22—81no—
1049C22—81no—
1050C22—81no—
1051C22—442no—
1052C22—442no—
1053C22—442no—
1054C22—442no—
1055C22—442no—
1056C22—442no—
1057C22—442no—
1058C22—881no—
1059C22—881no—
1060C22—881no—
1061C22—881no—
1062C22—881no—
1063C22—881no—
1064C22—881no—
1065C22—881no—
1066C22#1062301711yescharacteristic
1067C22#1062303511yescharacteristic
1068C22#1062305411yescharacteristic
1069C22C4×D4×D1111yescharacteristic
1070C22#1062307611yescharacteristic
1071C22#1062307611yescharacteristic
1072C22#1062307711yescharacteristic
1073C22#1062312011yescharacteristic
1074C22#1062312311yescharacteristic
1075C22#1062312611yescharacteristic
1076C22#1062312811yescharacteristic
1077C22#1062313911yescharacteristic
1078C22#1062314611yescharacteristic
1079C22#1062315111yescharacteristic
1080C22#1062315111yescharacteristic
1081C22#1062315111yescharacteristic
1082C22#1062315211yescharacteristic
1083C22#1062315211yescharacteristic
1084C22#1062316011yescharacteristic
1085C22#1062316911yescharacteristic
1086C22#1062317711yescharacteristic
1087C22#1062317711yescharacteristic
1088C22#1062317811yescharacteristic
1089C22#1062317811yescharacteristic
1090C22#1062318811yescharacteristic
1091C22#1062319311yescharacteristic
1092C22#1062319411yescharacteristic
1093C22#1062319811yescharacteristic
1094C22#1062319811yescharacteristic
1095C22#1062320511yescharacteristic
1096C22#1062321411yescharacteristic
1097C22#1062321411yescharacteristic
1098C22#1062324111yescharacteristic
1099C22#1062324311yescharacteristic
1100C22#1062325111yescharacteristic
1101C4—42no—
1102C4—42no—
1103C4—42no—
1104C4—81no—
1105C4—81no—
1106C4—81no—
1107C4—224no—
1108C4—442no—
1109C4—442no—
1110C4—442no—
1111C4—881no—
1112C4—881no—
1113C4—881no—
1114C2—82no—
1115C2—882no—
1116C2#1307130411yescharacteristic
1117C2#1307130611yescharacteristic
1118C2#1307131311yescharacteristic
1119C2#1307175311yescharacteristic
1120C2#1307176011yescharacteristic
1121C2#1307176511yescharacteristic
1122C2#1307178511yescharacteristic
1123C2#1307661711yescharacteristic
1124C2#1307662211yescharacteristic
1125C2#1307666411yescharacteristic
1126C2#1307668911yescharacteristic
1127C2#1307673211yescharacteristic
1128C2#1307678011yescharacteristic
1129C2#1307682511yescharacteristic
1130C2#1307683511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenter#1439D11
hypocenterC11#14632
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#10622603C2semidirect
3. C2×#10622557C2semidirect
4. #13066875C2semidirect
5. #13066871C2semidirect
6. #13066870C2semidirect
7. #13066862C2semidirect
8. #13066861C2semidirect
9. #13066860C2semidirect
10. #13066860C2semidirect
11. #13066859C2semidirect
14. Dic11⋊#95C2semidirect
15. C11×#1439C2semidirect
52. #10622572C4semidirect
129. C2×C4×Dic11D4semidirect
305. #1439D11semidirect
858. C11#14632semidirect

Maximal subgroups

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

subgroupindex
C2×#106225722
C2×#106226032
C2×#106225572
#130668752
#130668712
#130668702
#130668622
#130668612
#130668602
#130668592
#130668552
Dic11⋊#952
C11×#14392
#1463211