Finite Group Databasebeta

← #14682720

Subgroups — #14682720

Order 2816.

1918 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622570C211yesmaximal, characteristic
2C2×#10622826C211yesmaximal, characteristic
3C2×#10622569C211yesmaximal, characteristic
4#13066870C211yesmaximal, characteristic, complemented
5#13066867C211yesmaximal, characteristic, complemented
6#13066862C211yesmaximal, characteristic, complemented
7#13066861C211yesmaximal, characteristic, complemented
8#13066860C211yesmaximal, characteristic, complemented
9#13066859C211yesmaximal, characteristic, complemented
10#13066841C211yesmaximal, characteristic, complemented
11#13066840C211yesmaximal, characteristic, complemented
12#13066839C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×C22⋊#95C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C2×C11×#95C2211yescharacteristic
34C2×C11×#95C2211yescharacteristic
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2211yescharacteristic
37#10622826—24no—
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
51C2×C11⋊#95C2211yescharacteristic
52#10622570C418yescomplemented
53#10622569—24no—
54C25×C11C2311yescharacteristic
55C24×D11C2311yescharacteristic
56C23×C4×C11—22no—
57C23×C4×C11—22no—
58C23×C4×C11—22no—
59C23×C4×C11—41no—
60C23×C4×C11—41no—
61C23×C4×C11—41no—
62C23×C4×C11—41no—
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C22×C22⋊D11—41no—
70C22×C22⋊D11—41no—
71C22×C22⋊D11—41no—
72C22×C22⋊D11—41no—
73C22×C22⋊D11C2×C414yes—
74C22×C22⋊D11D414yes—
75C22×C22⋊D11Q814yes—
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C22×C4×D11—22no—
84C22×C4×D11—22no—
85C22×C4×D11—22no—
86C22×C4×D11—41no—
87C22×C4×D11—41no—
88C22×C4×D11—41no—
89C22×C4×D11—41no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—41no—
93C2×C11×C22⋊C4—41no—
94C2×C11×C22⋊C4—41no—
95C2×C11×C22⋊C4C2×C414yescomplemented
96C2×C22⋊Dic11—22no—
97C2×C22⋊Dic11—22no—
98C2×C22⋊Dic11—22no—
99C2×C22⋊Dic11—41no—
100C2×C22⋊Dic11—41no—
101C2×C22⋊Dic11—41no—
102C2×C22⋊Dic11—41no—
103C2×C22⋊Dic11—41no—
104C2×C22⋊Dic11C2×C414yescomplemented
105C2×(C2×D11)⋊C4—22no—
106C2×(C2×D11)⋊C4—22no—
107C2×(C2×D11)⋊C4—22no—
108C2×(C2×D11)⋊C4—22no—
109C2×(C2×D11)⋊C4—22no—
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)⋊C4—41no—
118C2×(C2×D11)⋊C4C2×C414yescomplemented
119C2×(C2×D11)⋊C4C2×C414yescomplemented
120C2×C4⋊Dic11—41no—
121C2×C4⋊Dic11—41no—
122C2×C4⋊Dic11—41no—
123C2×Dic11⋊C4—41no—
124C2×Dic11⋊C4—41no—
125C2×Dic11⋊C4—41no—
126C2×Dic11⋊C4—41no—
127C2×Dic11⋊C4—41no—
128C2×Dic11⋊C4C2×C414yescomplemented
129C2×C4×Dic11—41no—
130C2×C4×Dic11—41no—
131C2×C4×Dic11C2×C414yescomplemented
132C11×#95—22no—
133C11×#95—41no—
134C11×#95—41no—
135C11×#95—41no—
136C11⋊#95—22no—
137C11⋊#95—22no—
138C11⋊#95—22no—
139C11⋊#95—22no—
140C11⋊#95—22no—
141C11⋊#95—22no—
142C11⋊#95—22no—
143C11⋊#95—41no—
144C11⋊#95—41no—
145C11⋊#95—41no—
146C11⋊#95—41no—
147C11⋊#95—41no—
148C11⋊#95—41no—
149C11⋊#95—41no—
150#14486—111nomaximal, Sylow
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×C11—21no—
162C24×C11—21no—
163C24×C11C22×C412yes—
164C24×C11C2×D412yes—
165C24×C11C2×Q812yes—
166C24×C11C2411yescharacteristic
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×D11C22×C412yes—
180C23×D11C2×D412yes—
181C23×D11C2×Q812yes—
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×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—44no—
220C22×C4×C11—44no—
221C22×C4×C11—44no—
222C22×C4×C11—44no—
223C22×C4×C11—44no—
224C22×C4×C11—44no—
225C22×C4×C11—44no—
226C22×C4×C11C22×C412yes—
227C22×C4×C11C22×C412yes—
228C22×C4×C11#4112yes—
229C22×C4×C11#4112yes—
230C22×C4×C11#4112yes—
231C2×C22⋊D11—44no—
232C2×C22⋊D11—44no—
233C2×C22⋊D11—44no—
234C2×C22⋊D11—44no—
235C2×C22⋊D11—44no—
236C2×C22⋊D11—44no—
237C2×C22⋊D11C4⋊C4116yescomplemented
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×Dic11—21no—
274C22×Dic11—21no—
275C22×Dic11—21no—
276C22×Dic11—21no—
277C22×Dic11—21no—
278C22×Dic11—21no—
279C22×Dic11—21no—
280C22×Dic11—21no—
281C22×Dic11C22×C412yes—
282C22×Dic11C22×C412yes—
283C22×Dic11C22×C412yes—
284C22×Dic11C2×D412yes—
285C22×Dic11C2×Q812yes—
286C22×Dic11#4112yes—
287C2×C4×D11—44no—
288C2×C4×D11—44no—
289C2×C4×D11—44no—
290C2×C4×D11—44no—
291C2×C4×D11—44no—
292C2×C4×D11—44no—
293C2×C4×D11—44no—
294C11×C22⋊C4—44no—
295C11×C22⋊C4—44no—
296C22⋊Dic11—44no—
297C22⋊Dic11—44no—
298C22⋊Dic11—44no—
299(C2×D11)⋊C4—44no—
300(C2×D11)⋊C4—44no—
301(C2×D11)⋊C4—44no—
302(C2×D11)⋊C4—44no—
303(C2×D11)⋊C4—44no—
304C4⋊Dic11—44no—
305Dic11⋊C4—44no—
306Dic11⋊C4—44no—
307C4×Dic11—44no—
308C2×#390—111no—
309C2×#386—111no—
310C2×#386—111no—
311#1441—111no—
312#1441—111no—
313#1439—111no—
314#1439—111no—
315#1439—111no—
316#1439—111no—
317#1434—111no—
318#1434—111no—
319C22⋊#95—111no—
320C22⋊#95—111no—
321C22⋊#95—111no—
322C22⋊#95D1111yescharacteristic, complemented
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—22no—
337C23×C11—22no—
338C23×C11—22no—
339C23×C11—22no—
340C23×C11—22no—
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×C11—41no—
357C23×C11C2×C4⋊C414yes—
358C23×C11C23×C411yescharacteristic
359C23×C11C22×D411yescharacteristic
360C23×C11C22×Q811yescharacteristic
361C23×C11C2×#4111yescharacteristic
362C23×C11C2×#4111yescharacteristic
363C23×C11C2×#4111yescharacteristic
364C23×C11C2×#4111yescharacteristic
365C23×C11H(5,𝔽2)11yescharacteristic
366C23×C11H(5,𝔽2)11yescharacteristic
367C23×C11H(5,𝔽2)11yescharacteristic
368C23×C11H(5,𝔽2)11yescharacteristic
369C23×C11H(5,𝔽2)11yescharacteristic
370C23×C11H(5,𝔽2)11yescharacteristic
371C23×C11H(5,𝔽2)11yescharacteristic
372C23×C11H(5,𝔽2)11yescharacteristic
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—22no—
390C22×D11—22no—
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×D11—41no—
406C22×D11—41no—
407C22×D11C2×C4⋊C414yes—
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—416no—
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—
448C2×C4×C11—41no—
449C2×C4×C11—41no—
450C2×C4×C11—41no—
451C22⋊D11—416no—
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—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×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—41no—
497C2×Dic11—41no—
498C2×Dic11—41no—
499C2×Dic11—41no—
500C2×Dic11C2×C4⋊C414yes—
501C4×D11—416no—
502C23×D4—111no—
503C24×C4—111no—
504C24×C4C2×D1111yescharacteristic
505C22×C4⋊C4—111no—
506C22×C4⋊C4—111no—
507C22×C4⋊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×C22⋊C4—111no—
515C22×C22⋊C4—111no—
516C22×C22⋊C4C2×D1111yescharacteristic
517C22×C22⋊C4C2×D1111yescharacteristic
518C22×C42—111no—
519#390—118no—
520#386—224no—
521#386—224no—
522C2×#95—111no—
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
539C2×#95C2×D1111yescharacteristic
540C22×C11—24no—
541C22×C11—24no—
542C22×C11—24no—
543C22×C11—42no—
544C22×C11—42no—
545C22×C11—42no—
546C22×C11—42no—
547C22×C11—42no—
548C22×C11—42no—
549C22×C11—42no—
550C22×C11—42no—
551C22×C11—42no—
552C22×C11—42no—
553C22×C11—42no—
554C22×C11—42no—
555C22×C11C22×C4⋊C411yescharacteristic
556C22×C11C4×#4111yescharacteristic
557C22×C11C4×#4111yescharacteristic
558C22×C11#51811yescharacteristic
559C22×C11#51811yescharacteristic
560C22×C11#51811yescharacteristic
561C22×C11#51811yescharacteristic
562C22×C11#53411yescharacteristic
563C22×C11#53411yescharacteristic
564C22×C11#53811yescharacteristic
565C22×C11#53811yescharacteristic
566C22×C11#53811yescharacteristic
567C22×C11#53811yescharacteristic
568C22×C11#54011yescharacteristic
569C22×C11#54011yescharacteristic
570C22×C11#54011yescharacteristic
571C22×C11#54011yescharacteristic
572C22×C11#54311yescharacteristic
573C22×C11#54311yescharacteristic
574C22×C11#54611yescharacteristic
575C22×C11#54611yescharacteristic
576C22×C11#54611yescharacteristic
577C22×C11#54611yescharacteristic
578C22×C11#55111yescharacteristic
579C22×C11#55111yescharacteristic
580C22×C11#55411yescharacteristic
581C22×C11#55411yescharacteristic
582C22×C11#55411yescharacteristic
583C22×C11#55411yescharacteristic
584C22×C11#55511yescharacteristic
585C22×C11#55511yescharacteristic
586C22×C11#56011yescharacteristic
587C22×C11#56011yescharacteristic
588C22×C11#56011yescharacteristic
589C22×C11#56011yescharacteristic
590C2×D11—24no—
591C2×D11—24no—
592C2×D11—24no—
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—
604C2×D11—42no—
605C4×C11—42no—
606C4×C11—42no—
607C4×C11—42no—
608C4×C11—42no—
609C4×C11—42no—
610C4×C11—81no—
611Dic11—24no—
612Dic11—42no—
613Dic11—42no—
614Dic11—42no—
615Dic11—81no—
616Dic11—81no—
617Dic11—81no—
618C25—111no—
619C25C22×D1111yescharacteristic
620C22×D4—114no—
621C22×D4—114no—
622C22×D4—114no—
623C22×D4—441no—
624C22×D4—441no—
625C22×D4—441no—
626C22×D4—441no—
627C23×C4—22no—
628C23×C4—22no—
629C23×C4—22no—
630C23×C4—41no—
631C23×C4—41no—
632C23×C4—41no—
633C23×C4—41no—
634C23×C4—111no—
635C23×C4—111no—
636C23×C4—111no—
637C23×C4—111no—
638C23×C4—111no—
639C23×C4—111no—
640C23×C4—111no—
641C23×C4—222no—
642C23×C4—222no—
643C23×C4—222no—
644C23×C4—441no—
645C23×C4—441no—
646C23×C4—441no—
647C23×C4—441no—
648C23×C4C22×D1111yescharacteristic
649C23×C4C22×D1111yescharacteristic
650C23×C4C22×D1111yescharacteristic
651C23×C4C22×D1111yescharacteristic
652C23×C4C22×D1111yescharacteristic
653C23×C4C22×D1111yescharacteristic
654C2×C4⋊C4—114no—
655C2×C4⋊C4—441no—
656C2×C4⋊C4—441no—
657C2×C4⋊C4—441no—
658C2×C4⋊C4—441no—
659C2×C4⋊C4—441no—
660C2×C4⋊C4—441no—
661C2×C4⋊C4—441no—
662C2×C4⋊C4—441no—
663C2×C22⋊C4—22no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—41no—
666C2×C22⋊C4—41no—
667C2×C22⋊C4—41no—
668C2×C22⋊C4—114no—
669C2×C22⋊C4—114no—
670C2×C22⋊C4—114no—
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—441no—
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⋊C4—441no—
691C2×C22⋊C4—441no—
692C2×C22⋊C4C4×D1114yescomplemented
693C2×C42—114no—
694C2×C42—441no—
695C2×C42—441no—
696#95—22no—
697#95—41no—
698#95—41no—
699#95—41no—
700#95—222no—
701#95—222no—
702#95—222no—
703#95—222no—
704#95—222no—
705#95—222no—
706#95—222no—
707#95—441no—
708#95—441no—
709#95—441no—
710#95—441no—
711#95—441no—
712#95—441no—
713#95—441no—
714C2×C11—44no—
715C2×C11#231511yescharacteristic
716C2×C11#233311yescharacteristic
717C2×C11#233311yescharacteristic
718C2×C11#234911yescharacteristic
719C2×C11#234911yescharacteristic
720C2×C11#237211yescharacteristic
721C2×C11#238011yescharacteristic
722C2×C11#269711yescharacteristic
723C2×C11#269711yescharacteristic
724C2×C11#269911yescharacteristic
725C2×C11#269911yescharacteristic
726C2×C11#274811yescharacteristic
727C2×C11#274811yescharacteristic
728C2×C11#278411yescharacteristic
729C2×C11#278411yescharacteristic
730D11—44no—
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—112no—
744C24—112no—
745C24—112no—
746C24—221no—
747C24—221no—
748C24—221no—
749C24—221no—
750C24—221no—
751C24—221no—
752C24—221no—
753C24—221no—
754C24—221no—
755C24—221no—
756C24—221no—
757C24—221no—
758C24C2×C4×D1112yes—
759C24D4×D1112yes—
760C24Q8×D1112yes—
761C24C23×D1111yescharacteristic
762C2×D4—1116no—
763C2×D4—444no—
764C2×D4—444no—
765C2×D4—444no—
766C2×D4—444no—
767C2×D4—444no—
768C2×D4—444no—
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—44no—
807C22×C4—44no—
808C22×C4—44no—
809C22×C4—44no—
810C22×C4—44no—
811C22×C4—44no—
812C22×C4—44no—
813C22×C4—112no—
814C22×C4—112no—
815C22×C4—112no—
816C22×C4—112no—
817C22×C4—112no—
818C22×C4—112no—
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—221no—
857C22×C4—221no—
858C22×C4—221no—
859C22×C4—221no—
860C22×C4—221no—
861C22×C4—221no—
862C22×C4—444no—
863C22×C4—444no—
864C22×C4—444no—
865C22×C4—444no—
866C22×C4—444no—
867C22×C4—444no—
868C22×C4—444no—
869C22×C4C2×C4×D1112yes—
870C22×C4C2×C4×D1112yes—
871C22×C4#433912yes—
872C22×C4#433912yes—
873C22×C4#434112yes—
874C4⋊C4—444no—
875C4⋊C4—444no—
876C4⋊C4—444no—
877C22⋊C4—44no—
878C22⋊C4—44no—
879C22⋊C4—444no—
880C22⋊C4—444no—
881C22⋊C4—444no—
882C22⋊C4—444no—
883C22⋊C4—444no—
884C22⋊C4—444no—
885C22⋊C4—444no—
886C22⋊C4—444no—
887C42—444no—
888C11#1448611yescharacteristic, complemented, Sylow
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
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—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—114no—
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—222no—
939C23—222no—
940C23—222no—
941C23—222no—
942C23—441no—
943C23—441no—
944C23—441no—
945C23—441no—
946C23—441no—
947C23—441no—
948C23—441no—
949C23—441no—
950C23—441no—
951C23—441no—
952C23—441no—
953C23—441no—
954C23—441no—
955C23—441no—
956C23—441no—
957C23—441no—
958C23C4⋊C4×D1114yes—
959C23C22×C4×D1111yescharacteristic
960C23C2×#433911yescharacteristic
961C23C2×#433911yescharacteristic
962C23C2×D4×D1111yescharacteristic
963C23C2×#434111yescharacteristic
964C23#6703711yescharacteristic
965C23#6703711yescharacteristic
966C23#6703711yescharacteristic
967C23#6703711yescharacteristic
968C23#6703711yescharacteristic
969C23C2×Q8×D1111yescharacteristic
970C23#41×D1111yescharacteristic
971C23#6704211yescharacteristic
972C23#6704211yescharacteristic
973C23#6704211yescharacteristic
974D4—4416no—
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—416no—
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—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—4416no—
1035C2×C4—441no—
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—
1062C2×C4—441no—
1063C2×C4—441no—
1064C2×C4—441no—
1065C2×C4—441no—
1066C2×C4—441no—
1067C2×C4—441no—
1068C22—24no—
1069C22—24no—
1070C22—24no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—224no—
1084C22—224no—
1085C22—224no—
1086C22—442no—
1087C22—442no—
1088C22—442no—
1089C22—442no—
1090C22—442no—
1091C22—442no—
1092C22—442no—
1093C22—442no—
1094C22—442no—
1095C22—442no—
1096C22—442no—
1097C22—442no—
1098C22C4×#433911yescharacteristic
1099C22#1062301711yescharacteristic
1100C22#1062302111yescharacteristic
1101C22#1062302111yescharacteristic
1102C22#1062302511yescharacteristic
1103C22#1062302611yescharacteristic
1104C22C2×C4⋊C4×D1111yescharacteristic
1105C22#1062304211yescharacteristic
1106C22#1062304211yescharacteristic
1107C22#1062306311yescharacteristic
1108C22#1062306611yescharacteristic
1109C22C4×#434111yescharacteristic
1110C22#1062307611yescharacteristic
1111C22#1062307611yescharacteristic
1112C22#1062307611yescharacteristic
1113C22#1062308711yescharacteristic
1114C22#1062309111yescharacteristic
1115C22#1062309311yescharacteristic
1116C22#1062309411yescharacteristic
1117C22#1062312011yescharacteristic
1118C22#1062312211yescharacteristic
1119C22#1062312411yescharacteristic
1120C22#1062312611yescharacteristic
1121C22#1062314411yescharacteristic
1122C22#1062315011yescharacteristic
1123C22#1062315111yescharacteristic
1124C22#1062315111yescharacteristic
1125C22#1062316511yescharacteristic
1126C22#1062316511yescharacteristic
1127C22#1062316611yescharacteristic
1128C22#1062316711yescharacteristic
1129C22#1062318411yescharacteristic
1130C22#1062318511yescharacteristic
1131C22#1062319411yescharacteristic
1132C22#1062319711yescharacteristic
1133C4—42no—
1134C4—42no—
1135C4—42no—
1136C4—42no—
1137C4—42no—
1138C4—81no—
1139C4—224no—
1140C4—442no—
1141C4—442no—
1142C4—442no—
1143C4—881no—
1144C4—881no—
1145C4—881no—
1146C2—44no—
1147C2—444no—
1148C2#1307122711yescharacteristic
1149C2#1307137611yescharacteristic
1150C2#1307138211yescharacteristic
1151C2#1307152211yescharacteristic
1152C2#1307152311yescharacteristic
1153C2#1307172411yescharacteristic
1154C2#1307179111yescharacteristic
1155C2#1307517911yescharacteristic
1156C2#1307518011yescharacteristic
1157C2#1307520311yescharacteristic
1158C2#1307520511yescharacteristic
1159C2#1307582511yescharacteristic
1160C2#1307582611yescharacteristic
1161C2#1307631311yescharacteristic
1162C2#1307631511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC22⋊#95D11
hypocenterC11#14486
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
4. #13066870C2semidirect
5. #13066867C2semidirect
6. #13066862C2semidirect
7. #13066861C2semidirect
8. #13066860C2semidirect
9. #13066859C2semidirect
10. #13066841C2semidirect
11. #13066840C2semidirect
12. #13066839C2semidirect
13. (C2×D11)⋊#95C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×C22⋊#95C2semidirect
52. #10622570C4semidirect
95. C2×C11×C22⋊C4C2×C4semidirect
104. C2×C22⋊Dic11C2×C4semidirect
118. C2×(C2×D11)⋊C4C2×C4semidirect
119. C2×(C2×D11)⋊C4C2×C4semidirect
128. C2×Dic11⋊C4C2×C4semidirect
131. C2×C4×Dic11C2×C4semidirect
237. C2×C22⋊D11C4⋊C4semidirect
322. C22⋊#95D11semidirect
692. C2×C22⋊C4C4×D11semidirect
888. C11#14486semidirect

Maximal subgroups

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

subgroupindex
C2×#106225702
C2×#106228262
C2×#106225692
#130668702
#130668672
#130668622
#130668612
#130668602
#130668592
#130668412
#130668402
#130668392
(C2×D11)⋊#952
C11×C22⋊#952
#1448611