Finite Group Databasebeta

← #14677927

Subgroups — #14677927

Order 2816.

1946 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×#10622601C211yesmaximal, characteristic
2C2×#10622283C211yesmaximal, characteristic, complemented
3C2×#10622283C211yesmaximal, characteristic, complemented
4C2×#10622278C211yesmaximal, characteristic
5C2×#10622279C211yesmaximal, characteristic, complemented
6#13066864C211yesmaximal, characteristic, complemented
7#13066864C211yesmaximal, characteristic, complemented
8#13066856C211yesmaximal, characteristic
9#13066852C211yesmaximal, characteristic, complemented
10#13066852C211yesmaximal, characteristic, complemented
11#13066850C211yesmaximal, characteristic, complemented
12#13066848C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
14#95×Dic11C211yesmaximal, characteristic, complemented
15C11×#1442C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
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×C4×Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
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#10622601—24no—
52#10622283—24no—
53#10622283—24no—
54#10622279—24no—
55#10622278C418yescomplemented
56C24×D11C2311yescharacteristic
57C24×D11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C22×D44—22no—
72C22×D44—22no—
73C22×D44—22no—
74C22×D44—22no—
75C22×D44—41no—
76C22×D44—41no—
77C22×D44C2×C414yes—
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—22no—
87C2×C11×C4⋊C4—41no—
88C2×(C2×D11)⋊C4—22no—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4—22no—
91C2×(C2×D11)⋊C4—22no—
92C2×(C2×D11)⋊C4—22no—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—22no—
95C2×(C2×D11)⋊C4—22no—
96C2×(C2×D11)⋊C4—22no—
97C2×(C2×D11)⋊C4—22no—
98C2×(C2×D11)⋊C4—22no—
99C2×(C2×D11)⋊C4—22no—
100C2×(C2×D11)⋊C4—22no—
101C2×(C2×D11)⋊C4—22no—
102C2×(C2×D11)⋊C4—22no—
103C2×(C2×D11)⋊C4—22no—
104C2×(C2×D11)⋊C4—22no—
105C2×(C2×D11)⋊C4—22no—
106C2×(C2×D11)⋊C4—22no—
107C2×(C2×D11)⋊C4—22no—
108C2×(C2×D11)⋊C4—22no—
109C2×(C2×D11)⋊C4—41no—
110C2×(C2×D11)⋊C4—41no—
111C2×(C2×D11)⋊C4—41no—
112C2×(C2×D11)⋊C4—41no—
113C2×(C2×D11)⋊C4—41no—
114C2×(C2×D11)⋊C4—41no—
115C2×(C2×D11)⋊C4—41no—
116C2×(C2×D11)⋊C4—41no—
117C2×(C2×D11)⋊C4C2×C414yes—
118C2×(C2×D11)⋊C4C2×C414yes—
119C2×(C2×D11)⋊C4C2×C414yes—
120C2×(C2×D11)⋊C4D414yes—
121C2×C4⋊Dic11—22no—
122C2×C4⋊Dic11—22no—
123C2×C4⋊Dic11—22no—
124C2×C4×Dic11—22no—
125C2×C4×Dic11—22no—
126C2×C4×Dic11—22no—
127C2×C4×Dic11—22no—
128C2×C4×Dic11—22no—
129C2×C4×Dic11—41no—
130C2×C4×Dic11—41no—
131C2×C4×Dic11—41no—
132C2×C4×Dic11—41no—
133C2×C4×Dic11—41no—
134C2×C4×Dic11—41no—
135C2×C4×Dic11D414yescomplemented
136C11×#95—22no—
137C11×#95—22no—
138C11×#95—22no—
139C11×#95—22no—
140C11×#95—41no—
141C11×#95C2×C414yes—
142C11⋊#95—22no—
143C11⋊#95—22no—
144C11⋊#95—22no—
145C11⋊#95—22no—
146C11⋊#95—22no—
147C11⋊#95—22no—
148C11⋊#95—22no—
149C11⋊#95—41no—
150C11⋊#95—41no—
151C11⋊#95C2×C414yes—
152#14076—111nomaximal, Sylow
153C24×C11C2411yescharacteristic
154C23×D11—21no—
155C23×D11—21no—
156C23×D11—21no—
157C23×D11—21no—
158C23×D11—21no—
159C23×D11—21no—
160C23×D11—21no—
161C23×D11—21no—
162C23×D11—21no—
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×D11—21no—
178C23×D11—21no—
179C23×D11—21no—
180C23×D11C22×C412yes—
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×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11C22×C412yes—
226C22×C4×C11C22×C412yes—
227C22×C4×C11C22×C412yes—
228C22×C4×C11C2×D412yes—
229C22×C4×C11C2×D412yes—
230C22×C4×C11#4112yes—
231C22×C4×C11#4112yes—
232C22×C4×C11#4112yes—
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×Dic11C22×C412yes—
267C22×Dic11C22×C412yes—
268C22×Dic11C2×D412yes—
269C22×Dic11C2×D412yes—
270C22×Dic11C2×D412yes—
271C22×Dic11#4112yes—
272C22×Dic11#4112yes—
273C22×Dic11#4112yes—
274C22×Dic11#4112yes—
275C2×D44—28no—
276C2×D44—28no—
277C2×D44—44no—
278C2×D44—44no—
279C2×D44—44no—
280C2×D44—44no—
281C2×D44—44no—
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—
290(C2×D11)⋊C4—28no—
291(C2×D11)⋊C4—28no—
292(C2×D11)⋊C4—28no—
293(C2×D11)⋊C4—28no—
294(C2×D11)⋊C4—44no—
295(C2×D11)⋊C4—44no—
296(C2×D11)⋊C4—44no—
297(C2×D11)⋊C4—44no—
298(C2×D11)⋊C4—44no—
299(C2×D11)⋊C4—44no—
300(C2×D11)⋊C4—44no—
301C4⋊Dic11—44no—
302C4×Dic11—44no—
303C4×Dic11—44no—
304C4×Dic11—44no—
305C4×Dic11—44no—
306C2×#390—111no—
307C2×#388—111no—
308C2×#388—111no—
309C2×#386—111no—
310C2×C4×C22⋊C4—111no—
311#1442D1111yescharacteristic, complemented
312#1440—111no—
313#1440—111no—
314#1438—111no—
315#1437—111no—
316#1437—111no—
317#1436—111no—
318#1436—111no—
319C22⋊#95—111no—
320C4×#95—111no—
321C23×C11C23×C411yescharacteristic
322C23×C11C22×D411yescharacteristic
323C23×C11C22×D411yescharacteristic
324C23×C11C2×#4111yescharacteristic
325C23×C11C2×#4111yescharacteristic
326C23×C11C2×#4111yescharacteristic
327C23×C11C2×#4111yescharacteristic
328C23×C11C2×#4111yescharacteristic
329C23×C11C2×#4111yescharacteristic
330C23×C11C2×#4111yescharacteristic
331C23×C11C2×#4111yescharacteristic
332C23×C11H(5,𝔽2)11yescharacteristic
333C23×C11H(5,𝔽2)11yescharacteristic
334C23×C11H(5,𝔽2)11yescharacteristic
335C23×C11H(5,𝔽2)11yescharacteristic
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—22no—
342C22×D11—22no—
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—22no—
346C22×D11—22no—
347C22×D11—22no—
348C22×D11—22no—
349C22×D11—22no—
350C22×D11—22no—
351C22×D11—22no—
352C22×D11—22no—
353C22×D11—22no—
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—22no—
358C22×D11—22no—
359C22×D11—22no—
360C22×D11—22no—
361C22×D11—41no—
362C22×D11—41no—
363C22×D11—41no—
364C22×D11—41no—
365C22×D11—41no—
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—
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—22no—
419C2×C4×C11—22no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
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—
448C2×C4×C11—41no—
449C2×C4×C11—41no—
450C2×C4×C11—41no—
451C2×C4×C11—41no—
452C2×C4×C11—41no—
453C2×C4×C11—41no—
454C2×C4×C11#11714yes—
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—22no—
471C2×Dic11—22no—
472C2×Dic11—22no—
473C2×Dic11—22no—
474C2×Dic11—22no—
475C2×Dic11—22no—
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×Dic11C4×D414yes—
496C2×Dic11#12114yes—
497D44—416no—
498C4×D11—416no—
499C23×D4—111no—
500C24×C4—111no—
501C22×C4⋊C4—111no—
502C22×C4⋊C4C2×D1111yescharacteristic
503C22×C22⋊C4—111no—
504C22×C22⋊C4—111no—
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⋊C4—111no—
514C22×C42—111no—
515C22×C42—111no—
516C22×C42—111no—
517C22×C42—111no—
518#390—224no—
519#388—224no—
520#388—224no—
521#386—118no—
522C4×C22⋊C4—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×#95C2×D1111yescharacteristic
534C2×#95C2×D1111yescharacteristic
535C2×#95C2×D1111yescharacteristic
536C2×#95C2×D1111yescharacteristic
537C2×#95C2×D1111yescharacteristic
538C2×#95C2×D1111yescharacteristic
539C22×C11C2×#11711yescharacteristic
540C22×C11C2×C4×D411yescharacteristic
541C22×C11C2×C4×D411yescharacteristic
542C22×C11C4×#4111yescharacteristic
543C22×C11C4×#4111yescharacteristic
544C22×C11#51811yescharacteristic
545C22×C11#51811yescharacteristic
546C22×C11C2×#12111yescharacteristic
547C22×C11#52511yescharacteristic
548C22×C11#52911yescharacteristic
549C22×C11#52911yescharacteristic
550C22×C11#52911yescharacteristic
551C22×C11#53211yescharacteristic
552C22×C11#53211yescharacteristic
553C22×C11#53211yescharacteristic
554C22×C11#53411yescharacteristic
555C22×C11#53511yescharacteristic
556C22×C11#53811yescharacteristic
557C22×C11#53811yescharacteristic
558C22×C11#54611yescharacteristic
559C22×C11#54611yescharacteristic
560C22×C11#54611yescharacteristic
561C22×C11#54611yescharacteristic
562C22×C11#55111yescharacteristic
563C22×C11#55111yescharacteristic
564C22×C11#55111yescharacteristic
565C22×C11#55311yescharacteristic
566C22×C11#55311yescharacteristic
567C22×C11#55311yescharacteristic
568C22×C11#55311yescharacteristic
569C22×C11#55311yescharacteristic
570C22×C11#55311yescharacteristic
571C22×C11#55911yescharacteristic
572C22×C11#55911yescharacteristic
573C22×C11#55911yescharacteristic
574C2×D11—24no—
575C2×D11—24no—
576C2×D11—24no—
577C2×D11—42no—
578C2×D11—42no—
579C2×D11—42no—
580C2×D11—42no—
581C2×D11—42no—
582C2×D11—42no—
583C2×D11—42no—
584C2×D11—42no—
585C2×D11—42no—
586C2×D11—42no—
587C2×D11—42no—
588C2×D11—42no—
589C2×D11—42no—
590C2×D11—42no—
591C2×D11—42no—
592C2×D11—42no—
593C2×D11—42no—
594C2×D11—42no—
595C2×D11—42no—
596C2×D11—81no—
597C2×D11—81no—
598C2×D11—81no—
599C2×D11—81no—
600C2×D11—81no—
601C2×D11—81no—
602C2×D11—81no—
603C2×D11—81no—
604C4×C11—24no—
605C4×C11—42no—
606C4×C11—42no—
607C4×C11—42no—
608C4×C11—42no—
609C4×C11—42no—
610C4×C11—81no—
611Dic11—24no—
612Dic11—24no—
613Dic11—42no—
614Dic11—42no—
615Dic11—42no—
616Dic11—81no—
617C25—111no—
618C25—111no—
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—222no—
634C23×C4—222no—
635C23×C4—441no—
636C23×C4—441no—
637C23×C4—441no—
638C23×C4—441no—
639C23×C4C22×D1111yescharacteristic
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—22no—
648C2×C4⋊C4—41no—
649C2×C4⋊C4—222no—
650C2×C4⋊C4—222no—
651C2×C4⋊C4—222no—
652C2×C22⋊C4—114no—
653C2×C22⋊C4—114no—
654C2×C22⋊C4—114no—
655C2×C22⋊C4—114no—
656C2×C22⋊C4—222no—
657C2×C22⋊C4—222no—
658C2×C22⋊C4—222no—
659C2×C22⋊C4—222no—
660C2×C22⋊C4—222no—
661C2×C22⋊C4—222no—
662C2×C22⋊C4—222no—
663C2×C22⋊C4—222no—
664C2×C22⋊C4—222no—
665C2×C22⋊C4—222no—
666C2×C22⋊C4—222no—
667C2×C22⋊C4—222no—
668C2×C22⋊C4—222no—
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—441no—
678C2×C22⋊C4—441no—
679C2×C22⋊C4—441no—
680C2×C22⋊C4—441no—
681C2×C22⋊C4—441no—
682C2×C22⋊C4—441no—
683C2×C22⋊C4—441no—
684C2×C22⋊C4—441no—
685C2×C42—114no—
686C2×C42—222no—
687C2×C42—222no—
688C2×C42—222no—
689C2×C42—222no—
690C2×C42—222no—
691C2×C42—441no—
692C2×C42—441no—
693C2×C42—441no—
694C2×C42—441no—
695C2×C42—441no—
696C2×C42—441no—
697#95—22no—
698#95—22no—
699#95—22no—
700#95—22no—
701#95—41no—
702#95—114no—
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#95C4×D1114yes—
713C2×C11#229311yescharacteristic
714C2×C11C4×#12111yescharacteristic
715C2×C11#232111yescharacteristic
716C2×C11#234211yescharacteristic
717C2×C11#235711yescharacteristic
718C2×C11#236411yescharacteristic
719C2×C11#237411yescharacteristic
720C2×C11#254311yescharacteristic
721C2×C11#254411yescharacteristic
722C2×C11#255711yescharacteristic
723C2×C11#255911yescharacteristic
724C2×C11#259511yescharacteristic
725C2×C11#259711yescharacteristic
726C2×C11#260211yescharacteristic
727C2×C11#260311yescharacteristic
728D11—44no—
729D11—82no—
730C24—112no—
731C24—112no—
732C24—112no—
733C24—112no—
734C24—221no—
735C24—221no—
736C24—221no—
737C24—221no—
738C24—221no—
739C24—221no—
740C24—221no—
741C24—221no—
742C24—221no—
743C24—221no—
744C24—221no—
745C24—221no—
746C24—221no—
747C24—221no—
748C24—221no—
749C24—221no—
750C24—221no—
751C24—221no—
752C24—221no—
753C24—221no—
754C24—221no—
755C24—221no—
756C24—221no—
757C24—221no—
758C24—221no—
759C24—221no—
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—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—112no—
810C22×C4—112no—
811C22×C4—112no—
812C22×C4—112no—
813C22×C4—112no—
814C22×C4—112no—
815C22×C4—112no—
816C22×C4—112no—
817C22×C4—112no—
818C22×C4—228no—
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—444no—
853C22×C4—444no—
854C22×C4—444no—
855C22×C4—444no—
856C22×C4—444no—
857C22×C4—444no—
858C22×C4C2×C4×D1112yes—
859C22×C4C2×C4×D1112yes—
860C22×C4C2×C4×D1112yes—
861C22×C4D4×D1112yes—
862C22×C4D4×D1112yes—
863C22×C4#434112yes—
864C22×C4#434312yes—
865C22×C4#434312yes—
866C4⋊C4—44no—
867C4⋊C4—444no—
868C22⋊C4—228no—
869C22⋊C4—228no—
870C22⋊C4—228no—
871C22⋊C4—228no—
872C22⋊C4—444no—
873C22⋊C4—444no—
874C22⋊C4—444no—
875C22⋊C4—444no—
876C22⋊C4—444no—
877C22⋊C4—444no—
878C22⋊C4—444no—
879C42—444no—
880C42—444no—
881C42—444no—
882C42—444no—
883C11#1407611yescharacteristic, complemented, Sylow
884C23—114no—
885C23—222no—
886C23—222no—
887C23—222no—
888C23—222no—
889C23—222no—
890C23—222no—
891C23—222no—
892C23—222no—
893C23—222no—
894C23—222no—
895C23—222no—
896C23—222no—
897C23—222no—
898C23—222no—
899C23—222no—
900C23—222no—
901C23—222no—
902C23—222no—
903C23—222no—
904C23—222no—
905C23—222no—
906C23—222no—
907C23—222no—
908C23—222no—
909C23—222no—
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—
929C23—441no—
930C23—441no—
931C23—441no—
932C23—441no—
933C23—441no—
934C23—441no—
935C23—441no—
936C23—441no—
937C23—441no—
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
957C23C2×#434111yescharacteristic
958C23#6703711yescharacteristic
959C23C2×#434311yescharacteristic
960C23C2×#434311yescharacteristic
961C23#41×D1111yescharacteristic
962C23#41×D1111yescharacteristic
963C23#41×D1111yescharacteristic
964C23#41×D1111yescharacteristic
965C23#41×D1111yescharacteristic
966C23#6704211yescharacteristic
967C23#6704211yescharacteristic
968C23#6704211yescharacteristic
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—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
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—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—114no—
1019C2×C4—114no—
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—222no—
1036C2×C4—222no—
1037C2×C4—222no—
1038C2×C4—222no—
1039C2×C4—222no—
1040C2×C4—222no—
1041C2×C4—4416no—
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#6694514yes—
1062C22—224no—
1063C22—224no—
1064C22—224no—
1065C22—442no—
1066C22—442no—
1067C22—442no—
1068C22—442no—
1069C22—442no—
1070C22—442no—
1071C22—442no—
1072C22—442no—
1073C22—442no—
1074C22—442no—
1075C22—442no—
1076C22—442no—
1077C22—442no—
1078C22—442no—
1079C22—442no—
1080C22—442no—
1081C22—442no—
1082C22—442no—
1083C22—442no—
1084C22—881no—
1085C22—881no—
1086C22—881no—
1087C22—881no—
1088C22—881no—
1089C22—881no—
1090C22—881no—
1091C22—881no—
1092C22C2×#6694511yescharacteristic
1093C22#1062305211yescharacteristic
1094C22#1062305311yescharacteristic
1095C22C4×D4×D1111yescharacteristic
1096C22C4×D4×D1111yescharacteristic
1097C22#1062307611yescharacteristic
1098C22C4×#434311yescharacteristic
1099C22#1062312211yescharacteristic
1100C22#1062312711yescharacteristic
1101C22D11×#12111yescharacteristic
1102C22#1062313811yescharacteristic
1103C22#1062315511yescharacteristic
1104C22#1062316111yescharacteristic
1105C22#1062316111yescharacteristic
1106C22#1062316811yescharacteristic
1107C22#1062316811yescharacteristic
1108C22#1062318411yescharacteristic
1109C22#1062318511yescharacteristic
1110C22#1062318711yescharacteristic
1111C22#1062318911yescharacteristic
1112C22#1062319511yescharacteristic
1113C22#1062319911yescharacteristic
1114C22#1062320911yescharacteristic
1115C22#1062321211yescharacteristic
1116C22#1062321211yescharacteristic
1117C22#1062322211yescharacteristic
1118C22#1062322611yescharacteristic
1119C22#1062322611yescharacteristic
1120C22#1062322611yescharacteristic
1121C22#1062322611yescharacteristic
1122C22#1062323511yescharacteristic
1123C22#1062323711yescharacteristic
1124C22#1062324011yescharacteristic
1125C22#1062324011yescharacteristic
1126C22#1062325611yescharacteristic
1127C4—24no—
1128C4—42no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—81no—
1134C4—224no—
1135C4—224no—
1136C4—442no—
1137C4—442no—
1138C4—442no—
1139C4—881no—
1140C2—444no—
1141C2—882no—
1142C2#1307107411yescharacteristic
1143C2#1307112811yescharacteristic
1144C2#1307127811yescharacteristic
1145C2#1307146311yescharacteristic
1146C2#1307159111yescharacteristic
1147C2#1307166211yescharacteristic
1148C2#1307174811yescharacteristic
1149C2#1307357711yescharacteristic
1150C2#1307358211yescharacteristic
1151C2#1307371611yescharacteristic
1152C2#1307374811yescharacteristic
1153C2#1307413011yescharacteristic
1154C2#1307416211yescharacteristic
1155C2#1307422311yescharacteristic
1156C2#1307424411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1442C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1442D11
hypocenterC11#14076
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
2. C2×#10622283C2semidirect
3. C2×#10622283C2semidirect
5. C2×#10622279C2semidirect
6. #13066864C2semidirect
7. #13066864C2semidirect
9. #13066852C2semidirect
10. #13066852C2semidirect
11. #13066850C2semidirect
12. #13066848C2semidirect
13. (C2×D11)⋊#95C2semidirect
14. #95×Dic11C2semidirect
15. C11×#1442C2semidirect
55. #10622278C4semidirect
135. C2×C4×Dic11D4semidirect
311. #1442D11semidirect
883. C11#14076semidirect

Maximal subgroups

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

subgroupindex
C2×#106226012
C2×#106222832
C2×#106222782
C2×#106222792
#130668642
#130668562
#130668522
#130668502
#130668482
(C2×D11)⋊#952
#95×Dic112
C11×#14422
#1407611