Finite Group Databasebeta

← #14681636

Subgroups — #14681636

Order 2816.

1866 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622570C211yesmaximal, characteristic
2C2×#10622603C211yesmaximal, characteristic, complemented
3C2×#10622557C211yesmaximal, characteristic, complemented
4C2×#10622569C211yesmaximal, characteristic
5C2×#10622280C211yesmaximal, characteristic, complemented
6#13066879C211yesmaximal, characteristic, complemented
7#13066865C211yesmaximal, characteristic, complemented
8#13066864C211yesmaximal, characteristic, complemented
9#13066859C211yesmaximal, characteristic, complemented
10#13066855C211yesmaximal, characteristic
11#13066851C211yesmaximal, characteristic, complemented
12#13066851C211yesmaximal, characteristic, complemented
13#13066842C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×#1439C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
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#10622570—24no—
53#10622569C418yescomplemented
54#10622557—24no—
55#10622280—24no—
56C25×C11C2311yescharacteristic
57C24×D11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11—22no—
65C22×C22⋊D11—22no—
66C22×C22⋊D11—22no—
67C22×C22⋊D11—22no—
68C22×C22⋊D11—41no—
69C22×C22⋊D11—41no—
70C22×C22⋊D11C2×C414yes—
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C22×C4×D11—22no—
79C22×C4×D11—22no—
80C22×C4×D11—41no—
81C22×C4×D11—41no—
82C22×C4×D11—41no—
83C22×C4×D11—41no—
84C22×C4×D11C2×C414yes—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4—41no—
87C2×C11×C4⋊C4—41no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—41no—
91C2×C11×C22⋊C4—41no—
92C2×C11×C22⋊C4—41no—
93C2×C11×C22⋊C4—41no—
94C2×C11×C22⋊C4—41no—
95C2×C11×C22⋊C4—41no—
96C2×C11×C22⋊C4C2×C414yes—
97C2×C22⋊Dic11—22no—
98C2×C22⋊Dic11—22no—
99C2×C22⋊Dic11—22no—
100C2×C22⋊Dic11—22no—
101C2×C22⋊Dic11—41no—
102C2×C22⋊Dic11—41no—
103C2×C22⋊Dic11—41no—
104C2×C22⋊Dic11—41no—
105C2×C22⋊Dic11C2×C414yes—
106C2×(C2×D11)⋊C4—22no—
107C2×(C2×D11)⋊C4—22no—
108C2×(C2×D11)⋊C4—22no—
109C2×(C2×D11)⋊C4—22no—
110C2×(C2×D11)⋊C4—22no—
111C2×(C2×D11)⋊C4—22no—
112C2×(C2×D11)⋊C4—22no—
113C2×(C2×D11)⋊C4—41no—
114C2×(C2×D11)⋊C4—41no—
115C2×(C2×D11)⋊C4—41no—
116C2×(C2×D11)⋊C4—41no—
117C2×(C2×D11)⋊C4—41no—
118C2×(C2×D11)⋊C4—41no—
119C2×(C2×D11)⋊C4C2×C414yes—
120C2×(C2×D11)⋊C4D414yes—
121C2×Dic11⋊C4—22no—
122C2×Dic11⋊C4—22no—
123C2×Dic11⋊C4—22no—
124C2×Dic11⋊C4—41no—
125C2×Dic11⋊C4—41no—
126C2×Dic11⋊C4—41no—
127C2×Dic11⋊C4—41no—
128C2×Dic11⋊C4—41no—
129C2×Dic11⋊C4D414yescomplemented
130C2×C4×Dic11—22no—
131C2×C4×Dic11—22no—
132C2×C4×Dic11—22no—
133C2×C4×Dic11—22no—
134C2×C4×Dic11—41no—
135C2×C4×Dic11—41no—
136C11×#95—22no—
137C11×#95—41no—
138C11×#95—41no—
139C11⋊#95—22no—
140C11⋊#95—22no—
141C11⋊#95—22no—
142C11⋊#95—22no—
143C11⋊#95—22no—
144C11⋊#95—22no—
145C11⋊#95—22no—
146C11⋊#95—22no—
147C11⋊#95—41no—
148C11⋊#95—41no—
149C11⋊#95—41no—
150C11⋊#95C2×C414yes—
151C11⋊#95C2×C414yes—
152#14397—111nomaximal, Sylow
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×C11—21no—
162C24×C11—21no—
163C24×C11—21no—
164C24×C11—21no—
165C24×C11—21no—
166C24×C11—21no—
167C24×C11C22×C412yes—
168C24×C11C2411yescharacteristic
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×D11—21no—
178C23×D11—21no—
179C23×D11—21no—
180C23×D11—21no—
181C23×D11C22×C412yes—
182C23×D11C2×D412yes—
183C23×D11#4112yes—
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×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11C22×C412yes—
223C22×C4×C11C22×C412yes—
224C22×C4×C11C2×D412yes—
225C22×C4×C11C2×D412yes—
226C2×C22⋊D11—28no—
227C2×C22⋊D11—28no—
228C2×C22⋊D11—44no—
229C2×C22⋊D11—44no—
230C2×C22⋊D11—44no—
231C2×C22⋊D11—44no—
232C2×C22⋊D11—44no—
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×Dic11—21no—
271C22×Dic11—21no—
272C22×Dic11—21no—
273C22×Dic11C22×C412yes—
274C22×Dic11C22×C412yes—
275C22×Dic11C22×C412yes—
276C22×Dic11C2×D412yes—
277C22×Dic11C2×D412yes—
278C22×Dic11C2×D412yes—
279C22×Dic11#4112yes—
280C22×Dic11#4112yes—
281C22×Dic11#4112yes—
282C2×C4×D11—28no—
283C2×C4×D11—44no—
284C2×C4×D11—44no—
285C2×C4×D11—44no—
286C2×C4×D11—44no—
287C2×C4×D11—44no—
288C2×C4×D11—44no—
289C11×C4⋊C4—44no—
290C11×C22⋊C4—44no—
291C11×C22⋊C4—44no—
292C11×C22⋊C4—44no—
293C22⋊Dic11—28no—
294C22⋊Dic11—44no—
295C22⋊Dic11—44no—
296(C2×D11)⋊C4—28no—
297(C2×D11)⋊C4—44no—
298(C2×D11)⋊C4—44no—
299(C2×D11)⋊C4—44no—
300(C2×D11)⋊C4—44no—
301Dic11⋊C4—44no—
302Dic11⋊C4—44no—
303Dic11⋊C4—44no—
304C4×Dic11—44no—
305C4×Dic11—44no—
306C2×#390—111no—
307C2×#388—111no—
308C2×#388—111no—
309C2×#386—111no—
310C2×#380—111no—
311#1444—111no—
312#1440—111no—
313#1440—111no—
314#1439—111no—
315#1439D1111yescharacteristic, complemented
316#1438—111no—
317#1436—111no—
318#1436—111no—
319#1434—111no—
320C22⋊#95—111no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
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×C11—41no—
345C23×C11—41no—
346C23×C11—41no—
347C23×C11—41no—
348C23×C11—41no—
349C23×C11—41no—
350C23×C11—41no—
351C23×C11—41no—
352C23×C11—41no—
353C23×C11—41no—
354C23×C11—41no—
355C23×C11—41no—
356C23×C11C23×C411yescharacteristic
357C23×C11C22×D411yescharacteristic
358C23×C11C22×D411yescharacteristic
359C23×C11C2×#4111yescharacteristic
360C23×C11C2×#4111yescharacteristic
361C23×C11C2×#4111yescharacteristic
362C23×C11C2×#4111yescharacteristic
363C23×C11H(5,𝔽2)11yescharacteristic
364C23×C11H(5,𝔽2)11yescharacteristic
365C23×C11H(5,𝔽2)11yescharacteristic
366C23×C11H(5,𝔽2)11yescharacteristic
367C23×C11H(5,𝔽2)11yescharacteristic
368C23×C11H(5,𝔽2)11yescharacteristic
369C23×C112−1+411yescharacteristic
370C23×C112−1+411yescharacteristic
371C22×D11—22no—
372C22×D11—22no—
373C22×D11—22no—
374C22×D11—22no—
375C22×D11—22no—
376C22×D11—22no—
377C22×D11—22no—
378C22×D11—22no—
379C22×D11—22no—
380C22×D11—22no—
381C22×D11—22no—
382C22×D11—22no—
383C22×D11—22no—
384C22×D11—22no—
385C22×D11—22no—
386C22×D11—22no—
387C22×D11—22no—
388C22×D11—22no—
389C22×D11—41no—
390C22×D11—41no—
391C22×D11—41no—
392C22×D11—41no—
393C22×D11—41no—
394C22×D11—41no—
395C22×D11—41no—
396C22×D11—41no—
397C22×D11—41no—
398C22×D11—41no—
399C22×D11—41no—
400C22×D11—41no—
401C22×D11—41no—
402C22×D11—41no—
403C22×D11—41no—
404C22×D11—41no—
405C22×D11C4×D414yes—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
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—
436C2×C4×C11—41no—
437C2×C4×C11—41no—
438C2×C4×C11—41no—
439C2×C4×C11—41no—
440C2×C4×C11—41no—
441C2×C4×C11—41no—
442C2×C4×C11—41no—
443C2×C4×C11—41no—
444C2×C4×C11—41no—
445C2×C4×C11—41no—
446C2×C4×C11—41no—
447C2×C4×C11—41no—
448C22⋊D11—416no—
449C2×Dic11—22no—
450C2×Dic11—22no—
451C2×Dic11—22no—
452C2×Dic11—22no—
453C2×Dic11—22no—
454C2×Dic11—22no—
455C2×Dic11—22no—
456C2×Dic11—22no—
457C2×Dic11—22no—
458C2×Dic11—22no—
459C2×Dic11—22no—
460C2×Dic11—22no—
461C2×Dic11—22no—
462C2×Dic11—22no—
463C2×Dic11—22no—
464C2×Dic11—22no—
465C2×Dic11—22no—
466C2×Dic11—22no—
467C2×Dic11—22no—
468C2×Dic11—22no—
469C2×Dic11—22no—
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×Dic11—41no—
486C2×Dic11—41no—
487C2×Dic11—41no—
488C2×Dic11—41no—
489C2×Dic11—41no—
490C2×Dic11—41no—
491C2×Dic11—41no—
492C2×Dic11—41no—
493C2×Dic11—41no—
494C2×Dic11—41no—
495C2×Dic11—41no—
496C2×Dic11#11714yes—
497C2×Dic11C4×D414yes—
498C4×D11—416no—
499C23×D4—111no—
500C24×C4—111no—
501C22×C4⋊C4—111no—
502C22×C4⋊C4—111no—
503C22×C4⋊C4—111no—
504C22×C4⋊C4C2×D1111yescharacteristic
505C22×C22⋊C4—111no—
506C22×C22⋊C4—111no—
507C22×C22⋊C4—111no—
508C22×C22⋊C4—111no—
509C22×C22⋊C4—111no—
510C22×C22⋊C4—111no—
511C22×C22⋊C4—111no—
512C22×C22⋊C4—111no—
513C22×C22⋊C4C2×D1111yescharacteristic
514C22×C22⋊C4C2×D1111yescharacteristic
515C22×C22⋊C4C2×D1111yescharacteristic
516C22×C42—111no—
517C22×C42—111no—
518#390—224no—
519#388—224no—
520#388—224no—
521#386—118no—
522#380—224no—
523C2×#95—111no—
524C2×#95—111no—
525C2×#95—111no—
526C2×#95—111no—
527C2×#95—111no—
528C2×#95—111no—
529C2×#95—111no—
530C2×#95—111no—
531C2×#95—111no—
532C2×#95—111no—
533C2×#95—111no—
534C2×#95—111no—
535C2×#95—111no—
536C2×#95C2×D1111yescharacteristic
537C2×#95C2×D1111yescharacteristic
538C2×#95C2×D1111yescharacteristic
539C22×C11—42no—
540C22×C11—42no—
541C22×C11—42no—
542C22×C11—42no—
543C22×C11—42no—
544C22×C11—42no—
545C22×C11—42no—
546C22×C11—81no—
547C22×C11—81no—
548C22×C11—81no—
549C22×C11—81no—
550C22×C11—81no—
551C22×C11—81no—
552C22×C11—81no—
553C22×C11—81no—
554C22×C11C2×#11711yescharacteristic
555C22×C11C2×C4×D411yescharacteristic
556C22×C11C2×C4×D411yescharacteristic
557C22×C11#51811yescharacteristic
558C22×C11#51811yescharacteristic
559C22×C11#52011yescharacteristic
560C22×C11#52011yescharacteristic
561C22×C11#53411yescharacteristic
562C22×C11#53411yescharacteristic
563C22×C11#53511yescharacteristic
564C22×C11#53711yescharacteristic
565C22×C11#53811yescharacteristic
566C22×C11#53811yescharacteristic
567C22×C11#53811yescharacteristic
568C22×C11#53911yescharacteristic
569C22×C11#54011yescharacteristic
570C22×C11#54011yescharacteristic
571C22×C11#54211yescharacteristic
572C22×C11#54211yescharacteristic
573C22×C11D4211yescharacteristic
574C22×C11#54611yescharacteristic
575C22×C11#54611yescharacteristic
576C22×C11#54711yescharacteristic
577C22×C11#54711yescharacteristic
578C22×C11#54811yescharacteristic
579C22×C11#55011yescharacteristic
580C22×C11#55111yescharacteristic
581C22×C11#55111yescharacteristic
582C22×C11#55311yescharacteristic
583C22×C11#55511yescharacteristic
584C22×C11#55611yescharacteristic
585C22×C11#56011yescharacteristic
586C22×C11#56211yescharacteristic
587C22×C11#56211yescharacteristic
588C22×C11#56311yescharacteristic
589C2×D11—24no—
590C2×D11—24no—
591C2×D11—24no—
592C2×D11—42no—
593C2×D11—42no—
594C2×D11—42no—
595C2×D11—42no—
596C2×D11—42no—
597C2×D11—42no—
598C2×D11—42no—
599C2×D11—42no—
600C2×D11—42no—
601C2×D11—42no—
602C2×D11—42no—
603C2×D11—42no—
604C4×C11—42no—
605C4×C11—42no—
606C4×C11—42no—
607C4×C11—42no—
608C4×C11—81no—
609C4×C11—81no—
610Dic11—24no—
611Dic11—24no—
612Dic11—42no—
613Dic11—42no—
614Dic11—42no—
615Dic11—81no—
616Dic11—81no—
617C25—111no—
618C25C22×D1111yescharacteristic
619C22×D4—114no—
620C22×D4—222no—
621C22×D4—222no—
622C22×D4—222no—
623C22×D4—222no—
624C22×D4—441no—
625C22×D4—441no—
626C23×C4—111no—
627C23×C4—111no—
628C23×C4—111no—
629C23×C4—111no—
630C23×C4—111no—
631C23×C4—114no—
632C23×C4—111no—
633C23×C4—111no—
634C23×C4—222no—
635C23×C4—222no—
636C23×C4—441no—
637C23×C4—441no—
638C23×C4—441no—
639C23×C4—441no—
640C23×C4C22×D1111yescharacteristic
641C23×C4C22×D1111yescharacteristic
642C23×C4C22×D1111yescharacteristic
643C23×C4C22×D1111yescharacteristic
644C23×C4C22×D1111yescharacteristic
645C23×C4C22×D1111yescharacteristic
646C2×C4⋊C4—22no—
647C2×C4⋊C4—41no—
648C2×C4⋊C4—41no—
649C2×C4⋊C4—114no—
650C2×C4⋊C4—222no—
651C2×C4⋊C4—222no—
652C2×C4⋊C4—222no—
653C2×C4⋊C4—441no—
654C2×C4⋊C4—441no—
655C2×C4⋊C4—441no—
656C2×C4⋊C4—441no—
657C2×C4⋊C4—441no—
658C2×C22⋊C4—22no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—41no—
661C2×C22⋊C4—41no—
662C2×C22⋊C4—41no—
663C2×C22⋊C4—41no—
664C2×C22⋊C4—41no—
665C2×C22⋊C4—41no—
666C2×C22⋊C4—114no—
667C2×C22⋊C4—114no—
668C2×C22⋊C4—114no—
669C2×C22⋊C4—222no—
670C2×C22⋊C4—222no—
671C2×C22⋊C4—222no—
672C2×C22⋊C4—222no—
673C2×C22⋊C4—222no—
674C2×C22⋊C4—222no—
675C2×C22⋊C4—222no—
676C2×C22⋊C4—222no—
677C2×C22⋊C4—222no—
678C2×C22⋊C4—222no—
679C2×C22⋊C4—222no—
680C2×C22⋊C4—441no—
681C2×C22⋊C4—441no—
682C2×C22⋊C4—441no—
683C2×C22⋊C4—441no—
684C2×C22⋊C4—441no—
685C2×C22⋊C4—441no—
686C2×C22⋊C4—441no—
687C2×C22⋊C4—441no—
688C2×C22⋊C4—441no—
689C2×C22⋊C4—441no—
690C2×C22⋊C4C4×D1114yes—
691C2×C42—222no—
692C2×C42—222no—
693C2×C42—222no—
694C2×C42—222no—
695C2×C42—441no—
696C2×C42—441no—
697#95—22no—
698#95—41no—
699#95—41no—
700#95—114no—
701#95—114no—
702#95—222no—
703#95—222no—
704#95—222no—
705#95—222no—
706#95—222no—
707#95—222no—
708#95—222no—
709#95—222no—
710#95—441no—
711#95—441no—
712#95—441no—
713C2×C11—82no—
714C2×C11#231911yescharacteristic
715C2×C11#232111yescharacteristic
716C2×C11#232511yescharacteristic
717C2×C11#234211yescharacteristic
718C2×C11#235411yescharacteristic
719C2×C11#236111yescharacteristic
720C2×C11#237611yescharacteristic
721C2×C11#267111yescharacteristic
722C2×C11#267311yescharacteristic
723C2×C11#268611yescharacteristic
724C2×C11#271511yescharacteristic
725C2×C11#272311yescharacteristic
726C2×C11#273011yescharacteristic
727C2×C11#275611yescharacteristic
728C2×C11#278611yescharacteristic
729D11—44no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—112no—
745C24—112no—
746C24—112no—
747C24—221no—
748C24—221no—
749C24—221no—
750C24—221no—
751C24—221no—
752C24—221no—
753C24—221no—
754C24—221no—
755C24—221no—
756C24—221no—
757C24—221no—
758C24—221no—
759C24C2×C4×D1112yes—
760C24C23×D1111yescharacteristic
761C2×D4—228no—
762C2×D4—228no—
763C2×D4—444no—
764C2×D4—444no—
765C2×D4—444no—
766C2×D4—444no—
767C2×D4—444no—
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—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—112no—
807C22×C4—112no—
808C22×C4—112no—
809C22×C4—112no—
810C22×C4—112no—
811C22×C4—112no—
812C22×C4—112no—
813C22×C4—112no—
814C22×C4—112no—
815C22×C4—228no—
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×C4—221no—
838C22×C4—221no—
839C22×C4—221no—
840C22×C4—221no—
841C22×C4—221no—
842C22×C4—221no—
843C22×C4—221no—
844C22×C4—221no—
845C22×C4—221no—
846C22×C4—221no—
847C22×C4—221no—
848C22×C4—221no—
849C22×C4—221no—
850C22×C4—221no—
851C22×C4—221no—
852C22×C4—221no—
853C22×C4—221no—
854C22×C4—221no—
855C22×C4—221no—
856C22×C4—444no—
857C22×C4—444no—
858C22×C4—444no—
859C22×C4—444no—
860C22×C4—444no—
861C22×C4—444no—
862C22×C4C2×C4×D1112yes—
863C22×C4C2×C4×D1112yes—
864C22×C4D4×D1112yes—
865C22×C4D4×D1112yes—
866C4⋊C4—44no—
867C4⋊C4—444no—
868C4⋊C4—444no—
869C4⋊C4—444no—
870C22⋊C4—44no—
871C22⋊C4—44no—
872C22⋊C4—44no—
873C22⋊C4—228no—
874C22⋊C4—228no—
875C22⋊C4—444no—
876C22⋊C4—444no—
877C22⋊C4—444no—
878C22⋊C4—444no—
879C22⋊C4—444no—
880C22⋊C4—444no—
881C42—444no—
882C42—444no—
883C11#1439711yescharacteristic, complemented, Sylow
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—114no—
920C23—222no—
921C23—222no—
922C23—222no—
923C23—222no—
924C23—222no—
925C23—222no—
926C23—222no—
927C23—222no—
928C23—222no—
929C23—222no—
930C23—222no—
931C23—222no—
932C23—222no—
933C23—222no—
934C23—222no—
935C23—222no—
936C23—222no—
937C23—222no—
938C23—441no—
939C23—441no—
940C23—441no—
941C23—441no—
942C23—441no—
943C23—441no—
944C23—441no—
945C23—441no—
946C23—441no—
947C23—441no—
948C23—441no—
949C23—441no—
950C23—441no—
951C23—441no—
952C23—441no—
953C23—441no—
954C23C22×C4×D1111yescharacteristic
955C23C2×D4×D1111yescharacteristic
956C23C2×D4×D1111yescharacteristic
957C23#6703711yescharacteristic
958C23#6703711yescharacteristic
959C23#6703711yescharacteristic
960C23#6703711yescharacteristic
961C23#6703711yescharacteristic
962C23#6704011yescharacteristic
963C23#41×D1111yescharacteristic
964C23#41×D1111yescharacteristic
965C23#41×D1111yescharacteristic
966C23#41×D1111yescharacteristic
967C23#6704211yescharacteristic
968C23#6704311yescharacteristic
969D4—4416no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—114no—
1013C2×C4—114no—
1014C2×C4—222no—
1015C2×C4—222no—
1016C2×C4—222no—
1017C2×C4—222no—
1018C2×C4—222no—
1019C2×C4—222no—
1020C2×C4—222no—
1021C2×C4—222no—
1022C2×C4—222no—
1023C2×C4—222no—
1024C2×C4—222no—
1025C2×C4—222no—
1026C2×C4—222no—
1027C2×C4—222no—
1028C2×C4—222no—
1029C2×C4—222no—
1030C2×C4—222no—
1031C2×C4—222no—
1032C2×C4—222no—
1033C2×C4—222no—
1034C2×C4—222no—
1035C2×C4—4416no—
1036C2×C4—441no—
1037C2×C4—441no—
1038C2×C4—441no—
1039C2×C4—441no—
1040C2×C4—441no—
1041C2×C4—441no—
1042C2×C4—441no—
1043C2×C4—441no—
1044C2×C4—441no—
1045C2×C4—441no—
1046C2×C4—441no—
1047C2×C4—441no—
1048C2×C4—441no—
1049C2×C4—441no—
1050C2×C4—441no—
1051C2×C4—441no—
1052C2×C4—441no—
1053C2×C4—441no—
1054C2×C4—441no—
1055C2×C4—441no—
1056C2×C4—441no—
1057C2×C4—441no—
1058C2×C4—441no—
1059C2×C4—441no—
1060C2×C4—441no—
1061C2×C4—441no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—81no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22—81no—
1077C22—224no—
1078C22—224no—
1079C22—224no—
1080C22—442no—
1081C22—442no—
1082C22—442no—
1083C22—442no—
1084C22—442no—
1085C22—442no—
1086C22—442no—
1087C22—442no—
1088C22—442no—
1089C22—442no—
1090C22—442no—
1091C22—442no—
1092C22#1062301711yescharacteristic
1093C22#1062303511yescharacteristic
1094C22D11×#11711yescharacteristic
1095C22C4×D4×D1111yescharacteristic
1096C22C4×D4×D1111yescharacteristic
1097C22#1062307611yescharacteristic
1098C22#1062307711yescharacteristic
1099C22#1062312011yescharacteristic
1100C22#1062312111yescharacteristic
1101C22#1062312611yescharacteristic
1102C22#1062313011yescharacteristic
1103C22#1062313611yescharacteristic
1104C22#1062313911yescharacteristic
1105C22#1062314111yescharacteristic
1106C22#1062314411yescharacteristic
1107C22#1062314411yescharacteristic
1108C22#1062314611yescharacteristic
1109C22#1062314611yescharacteristic
1110C22#1062316211yescharacteristic
1111C22#1062316411yescharacteristic
1112C22#1062317111yescharacteristic
1113C22#1062317111yescharacteristic
1114C22#1062317711yescharacteristic
1115C22#1062317811yescharacteristic
1116C22#1062318611yescharacteristic
1117C22#1062319011yescharacteristic
1118C22#1062319111yescharacteristic
1119C22#1062319211yescharacteristic
1120C22#1062319811yescharacteristic
1121C22#1062320111yescharacteristic
1122C22#1062320711yescharacteristic
1123C22#1062320911yescharacteristic
1124C22#1062323311yescharacteristic
1125C22#1062323611yescharacteristic
1126C22#1062324611yescharacteristic
1127C4—42no—
1128C4—42no—
1129C4—42no—
1130C4—42no—
1131C4—81no—
1132C4—81no—
1133C4—224no—
1134C4—224no—
1135C4—442no—
1136C4—442no—
1137C4—442no—
1138C4—881no—
1139C4—881no—
1140C2—82no—
1141C2—444no—
1142C2#1307125811yescharacteristic
1143C2#1307127511yescharacteristic
1144C2#1307131811yescharacteristic
1145C2#1307146411yescharacteristic
1146C2#1307156211yescharacteristic
1147C2#1307163511yescharacteristic
1148C2#1307176511yescharacteristic
1149C2#1307485111yescharacteristic
1150C2#1307488411yescharacteristic
1151C2#1307502711yescharacteristic
1152C2#1307543311yescharacteristic
1153C2#1307552811yescharacteristic
1154C2#1307561211yescharacteristic
1155C2#1307594311yescharacteristic
1156C2#1307633111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenter#1439D11
hypocenterC11#14397
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
5. C2×#10622280C2semidirect
6. #13066879C2semidirect
7. #13066865C2semidirect
8. #13066864C2semidirect
9. #13066859C2semidirect
11. #13066851C2semidirect
12. #13066851C2semidirect
13. #13066842C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1439C2semidirect
53. #10622569C4semidirect
129. C2×Dic11⋊C4D4semidirect
315. #1439D11semidirect
883. C11#14397semidirect

Maximal subgroups

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

subgroupindex
C2×#106225702
C2×#106226032
C2×#106225572
C2×#106225692
C2×#106222802
#130668792
#130668652
#130668642
#130668592
#130668552
#130668512
#130668422
(C2×D11)⋊#952
C11×#14392
#1439711