Finite Group Databasebeta

← #14683868

Subgroups — #14683868

Order 2816.

1706 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622560C211yesmaximal, characteristic
2C2×#10622542C211yesmaximal, characteristic, complemented
3C2×#10622259C211yesmaximal, characteristic, complemented
4C2×#10622563C211yesmaximal, characteristic
5C2×#10622559C211yesmaximal, characteristic
6#13066880C211yesmaximal, characteristic, complemented
7#13066880C211yesmaximal, characteristic, complemented
8#13066874C211yesmaximal, characteristic, complemented
9#13066872C211yesmaximal, characteristic, complemented
10#13066859C211yesmaximal, characteristic
11#13066853C211yesmaximal, characteristic
12#13066843C211yesmaximal, characteristic, complemented
13#13066842C211yesmaximal, characteristic, complemented
14#13066838C211yesmaximal, characteristic
15C11×#1437C211yesmaximal, characteristic
16C24×Dic11C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C2×C11×#95C2211yescharacteristic
32C2×C11×#95C2211yescharacteristic
33C2×C11×#95C2211yescharacteristic
34C2×C11⋊#95C2211yescharacteristic
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#10622563—24no—
52#10622560C418yescomplemented
53#10622559—24no—
54#10622542—24no—
55#10622259—24no—
56C25×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×Dic11—22no—
64C23×Dic11—22no—
65C23×Dic11—22no—
66C23×Dic11—41no—
67C23×Dic11—41no—
68C23×Dic11—41no—
69C23×Dic11—41no—
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C22×Dic22—22no—
79C22×Dic22—22no—
80C22×Dic22—22no—
81C22×Dic22—22no—
82C22×Dic22—41no—
83C22×Dic22—41no—
84C22×Dic22C2×C414yescomplemented
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—41no—
90C2×C11×C22⋊C4—41no—
91C2×C11×C22⋊C4—41no—
92C2×C11×C22⋊C4C2×C414yes—
93C2×C11×C22⋊C4Q814yescomplemented
94C2×C42×C11—22no—
95C2×C42×C11—22no—
96C2×C42×C11—41no—
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⋊Dic11C2×C414yes—
105C2×C22⋊Dic11C2×C414yes—
106C2×C4⋊Dic11—22no—
107C2×C4⋊Dic11—22no—
108C2×C4⋊Dic11—22no—
109C2×C4⋊Dic11—41no—
110C2×C4⋊Dic11—41no—
111C2×C4⋊Dic11—41no—
112C2×Dic11⋊C4—22no—
113C2×Dic11⋊C4—22no—
114C2×Dic11⋊C4—22no—
115C2×Dic11⋊C4—41no—
116C2×Dic11⋊C4—41no—
117C2×Dic11⋊C4—41no—
118C2×Dic11⋊C4—41no—
119C2×Dic11⋊C4—41no—
120C2×Dic11⋊C4—41no—
121C2×C4×Dic11—22no—
122C2×C4×Dic11—22no—
123C2×C4×Dic11—41no—
124C11×#95—22no—
125C11×#95—41no—
126C11×#95—41no—
127C11⋊#95—22no—
128C11⋊#95—22no—
129C11⋊#95—22no—
130C11⋊#95—22no—
131C11⋊#95—22no—
132C11⋊#95—22no—
133C11⋊#95—22no—
134C11⋊#95—41no—
135C11⋊#95—41no—
136C11⋊#95—41no—
137C11⋊#95—41no—
138C11⋊#95—41no—
139C11⋊#95C2×C414yescomplemented
140C11⋊#95C2×C414yescomplemented
141C11⋊#95C2×C414yescomplemented
142C11⋊#95D414yes—
143C11⋊#95D414yes—
144#14575—111nomaximal, Sylow
145C24×C11—21no—
146C24×C11—21no—
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×C11C22×C412yes—
158C24×C11C2×Q812yes—
159C24×C11#4112yes—
160C24×C11C2411yescharacteristic
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
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×C11C22×C412yes—
197C22×C4×C11C22×C412yes—
198C22×C4×C11C2×D412yes—
199C22×C4×C11C2×D412yes—
200C22×C4×C11C2×Q812yes—
201C22×C4×C11C2×Q812yes—
202C22×C4×C11#4112yes—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—21no—
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C22×Dic11—21no—
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—44no—
251C22×Dic11—44no—
252C22×Dic11—44no—
253C22×Dic11—44no—
254C22×Dic11—44no—
255C22×Dic11—44no—
256C22×Dic11—44no—
257C22×Dic11C22×C412yes—
258C22×Dic11C22×C412yes—
259C22×Dic11C22×C412yes—
260C22×Dic11C22×C412yes—
261C22×Dic11C2×D412yes—
262C22×Dic11C2×D412yes—
263C22×Dic11C2×D412yes—
264C22×Dic11C2×D412yes—
265C22×Dic11#4112yes—
266C2×Dic22—28no—
267C2×Dic22—28no—
268C2×Dic22—44no—
269C2×Dic22—44no—
270C2×Dic22—44no—
271C2×Dic22—44no—
272C2×Dic22—44no—
273C11×C22⋊C4—28no—
274C11×C22⋊C4—44no—
275C11×C22⋊C4—44no—
276C42×C11—44no—
277C22⋊Dic11—28no—
278C22⋊Dic11—44no—
279C22⋊Dic11—44no—
280C4⋊Dic11—44no—
281C4⋊Dic11—44no—
282Dic11⋊C4—44no—
283Dic11⋊C4—44no—
284Dic11⋊C4—44no—
285C4×Dic11—44no—
286C2×#393—111no—
287C2×#391—111no—
288C2×#391—111no—
289C2×#385—111no—
290C2×#385—111no—
291#1444—111no—
292#1444—111no—
293#1442—111no—
294#1442—111no—
295#1439—111no—
296#1437—111no—
297#1437D1111yescharacteristic
298#1434—111no—
299#1434—111no—
300C22⋊#95—111no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—22no—
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×C11C4×Q814yes—
336C23×C11C23×C411yescharacteristic
337C23×C11C22×D411yescharacteristic
338C23×C11C22×D411yescharacteristic
339C23×C11C22×Q811yescharacteristic
340C23×C11C2×#4111yescharacteristic
341C23×C11C2×#4111yescharacteristic
342C23×C11C2×#4111yescharacteristic
343C23×C11H(5,𝔽2)11yescharacteristic
344C23×C11H(5,𝔽2)11yescharacteristic
345C23×C11H(5,𝔽2)11yescharacteristic
346C23×C11H(5,𝔽2)11yescharacteristic
347C23×C11H(5,𝔽2)11yescharacteristic
348C23×C112−1+411yescharacteristic
349C23×C112−1+411yescharacteristic
350C23×C112−1+411yescharacteristic
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11—41no—
372C2×C4×C11—41no—
373C2×C4×C11—41no—
374C2×C4×C11—41no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11C4×D414yes—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—22no—
403C2×Dic11—22no—
404C2×Dic11—22no—
405C2×Dic11—22no—
406C2×Dic11—22no—
407C2×Dic11—22no—
408C2×Dic11—22no—
409C2×Dic11—22no—
410C2×Dic11—22no—
411C2×Dic11—22no—
412C2×Dic11—22no—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—22no—
416C2×Dic11—22no—
417C2×Dic11—416no—
418C2×Dic11—41no—
419C2×Dic11—41no—
420C2×Dic11—41no—
421C2×Dic11—41no—
422C2×Dic11—41no—
423C2×Dic11—41no—
424C2×Dic11—41no—
425C2×Dic11—41no—
426C2×Dic11—41no—
427C2×Dic11—41no—
428C2×Dic11—41no—
429C2×Dic11—41no—
430C2×Dic11—41no—
431C2×Dic11—41no—
432C2×Dic11—41no—
433C2×Dic11—41no—
434C2×Dic11—41no—
435C2×Dic11—41no—
436C2×Dic11—41no—
437C2×Dic11—41no—
438C2×Dic11—41no—
439C2×Dic11—41no—
440C2×Dic11—41no—
441C2×Dic11—41no—
442C2×Dic11—41no—
443C2×Dic11—41no—
444C2×Dic11—41no—
445C2×Dic11—41no—
446C2×Dic11—41no—
447C2×Dic11—41no—
448C2×Dic11—41no—
449C2×Dic11C4×D414yes—
450Dic22—416no—
451C23×Q8—111no—
452C24×C4—111no—
453C22×C4⋊C4—111no—
454C22×C4⋊C4—111no—
455C22×C4⋊C4—111no—
456C22×C4⋊C4—111no—
457C22×C4⋊C4—111no—
458C22×C22⋊C4—111no—
459C22×C22⋊C4—111no—
460C22×C22⋊C4—111no—
461C22×C22⋊C4C2×D1111yescharacteristic
462C22×C22⋊C4C2×D1111yescharacteristic
463C22×C22⋊C4C2×D1111yescharacteristic
464C22×C42—111no—
465C22×C42C2×D1111yescharacteristic
466#393—118no—
467#391—224no—
468#391—224no—
469#385—224no—
470#385—224no—
471C2×#95—111no—
472C2×#95—111no—
473C2×#95—111no—
474C2×#95—111no—
475C2×#95—111no—
476C2×#95—111no—
477C2×#95—111no—
478C2×#95—111no—
479C2×#95—111no—
480C2×#95—111no—
481C2×#95—111no—
482C2×#95—111no—
483C2×#95—111no—
484C2×#95—111no—
485C2×#95—111no—
486C2×#95—111no—
487C2×#95—111no—
488C2×#95C2×D1111yescharacteristic
489C2×#95C2×D1111yescharacteristic
490C2×#95C2×D1111yescharacteristic
491C22×C11—24no—
492C22×C11—24no—
493C22×C11—24no—
494C22×C11—42no—
495C22×C11—42no—
496C22×C11—42no—
497C22×C11—42no—
498C22×C11—42no—
499C22×C11—42no—
500C22×C11—42no—
501C22×C11—42no—
502C22×C11—42no—
503C22×C11—42no—
504C22×C11—42no—
505C22×C11—42no—
506C22×C11C2×C4×D411yescharacteristic
507C22×C11C2×C4×D411yescharacteristic
508C22×C11C2×C4×Q811yescharacteristic
509C22×C11#51811yescharacteristic
510C22×C11#52011yescharacteristic
511C22×C11#52011yescharacteristic
512C22×C11#52011yescharacteristic
513C22×C11#53511yescharacteristic
514C22×C11#53511yescharacteristic
515C22×C11#53611yescharacteristic
516C22×C11#53611yescharacteristic
517C22×C11#53811yescharacteristic
518C22×C11#53911yescharacteristic
519C22×C11#54211yescharacteristic
520C22×C11#54211yescharacteristic
521C22×C11#54211yescharacteristic
522C22×C11#54211yescharacteristic
523C22×C11#54311yescharacteristic
524C22×C11#54411yescharacteristic
525C22×C11D4211yescharacteristic
526C22×C11#54611yescharacteristic
527C22×C11#54611yescharacteristic
528C22×C11#54611yescharacteristic
529C22×C11#54611yescharacteristic
530C22×C11D4×Q811yescharacteristic
531C22×C11D4×Q811yescharacteristic
532C22×C11#55111yescharacteristic
533C22×C11#55211yescharacteristic
534C22×C11#55211yescharacteristic
535C22×C11#55411yescharacteristic
536C22×C11#55411yescharacteristic
537C22×C11H(3,𝔽4)11yescharacteristic
538C22×C11#56211yescharacteristic
539C22×C11#56211yescharacteristic
540C22×C11#56311yescharacteristic
541C4×C11—24no—
542C4×C11—42no—
543C4×C11—42no—
544C4×C11—42no—
545C4×C11—42no—
546C4×C11—81no—
547Dic11—24no—
548Dic11—42no—
549Dic11—42no—
550Dic11—42no—
551Dic11—42no—
552Dic11—42no—
553Dic11—42no—
554Dic11—81no—
555C25C22×D1111yescharacteristic
556C22×Q8—114no—
557C22×Q8—222no—
558C22×Q8—222no—
559C22×Q8—222no—
560C22×Q8—222no—
561C22×Q8—441no—
562C22×Q8—441no—
563C23×C4—111no—
564C23×C4—111no—
565C23×C4—111no—
566C23×C4—111no—
567C23×C4—111no—
568C23×C4—111no—
569C23×C4—111no—
570C23×C4—111no—
571C23×C4—222no—
572C23×C4—222no—
573C23×C4—222no—
574C23×C4—441no—
575C23×C4—441no—
576C23×C4—441no—
577C23×C4—441no—
578C23×C4C22×D1111yescharacteristic
579C23×C4C22×D1111yescharacteristic
580C23×C4C22×D1111yescharacteristic
581C23×C4C22×D1111yescharacteristic
582C23×C4C22×D1111yescharacteristic
583C23×C4C22×D1111yescharacteristic
584C2×C4⋊C4—222no—
585C2×C4⋊C4—222no—
586C2×C4⋊C4—222no—
587C2×C4⋊C4—222no—
588C2×C4⋊C4—222no—
589C2×C4⋊C4—222no—
590C2×C4⋊C4—441no—
591C2×C4⋊C4—441no—
592C2×C4⋊C4—441no—
593C2×C4⋊C4—441no—
594C2×C4⋊C4—441no—
595C2×C4⋊C4—441no—
596C2×C4⋊C4—441no—
597C2×C4⋊C4—441no—
598C2×C4⋊C4—441no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—22no—
602C2×C22⋊C4—22no—
603C2×C22⋊C4—41no—
604C2×C22⋊C4—41no—
605C2×C22⋊C4—41no—
606C2×C22⋊C4—114no—
607C2×C22⋊C4—114no—
608C2×C22⋊C4—222no—
609C2×C22⋊C4—222no—
610C2×C22⋊C4—222no—
611C2×C22⋊C4—222no—
612C2×C22⋊C4—441no—
613C2×C22⋊C4—441no—
614C2×C22⋊C4—441no—
615C2×C22⋊C4Dic2214yescomplemented
616C2×C22⋊C4C4×D1114yes—
617C2×C42—22no—
618C2×C42—22no—
619C2×C42—41no—
620C2×C42—222no—
621C2×C42—222no—
622C2×C42—441no—
623#95—22no—
624#95—41no—
625#95—41no—
626#95—114no—
627#95—114no—
628#95—114no—
629#95—114no—
630#95—114no—
631#95—222no—
632#95—222no—
633#95—222no—
634#95—222no—
635#95—222no—
636#95—222no—
637#95—222no—
638#95—441no—
639#95—441no—
640#95—441no—
641#95—441no—
642#95—441no—
643C2×C11—44no—
644C2×C11#232611yescharacteristic
645C2×C11#232611yescharacteristic
646C2×C11#232911yescharacteristic
647C2×C11#235811yescharacteristic
648C2×C11#236011yescharacteristic
649C2×C11#236011yescharacteristic
650C2×C11#237911yescharacteristic
651C2×C11#267011yescharacteristic
652C2×C11#267711yescharacteristic
653C2×C11#268711yescharacteristic
654C2×C11#268711yescharacteristic
655C2×C11#269211yescharacteristic
656C2×C11#269211yescharacteristic
657C2×C11#276311yescharacteristic
658C2×C11#276411yescharacteristic
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24C2×Dic2212yes—
672C24C2×C4×D1112yes—
673C24#433912yes—
674C24C23×D1111yescharacteristic
675C2×Q8—228no—
676C2×Q8—228no—
677C2×Q8—444no—
678C2×Q8—444no—
679C2×Q8—444no—
680C2×Q8—444no—
681C2×Q8—444no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—112no—
718C22×C4—112no—
719C22×C4—112no—
720C22×C4—112no—
721C22×C4—112no—
722C22×C4—112no—
723C22×C4—112no—
724C22×C4—112no—
725C22×C4—112no—
726C22×C4—221no—
727C22×C4—221no—
728C22×C4—221no—
729C22×C4—221no—
730C22×C4—221no—
731C22×C4—221no—
732C22×C4—221no—
733C22×C4—221no—
734C22×C4—221no—
735C22×C4—221no—
736C22×C4—221no—
737C22×C4—221no—
738C22×C4—221no—
739C22×C4—221no—
740C22×C4—221no—
741C22×C4—221no—
742C22×C4—221no—
743C22×C4—221no—
744C22×C4—221no—
745C22×C4—221no—
746C22×C4—221no—
747C22×C4—221no—
748C22×C4—221no—
749C22×C4—221no—
750C22×C4—221no—
751C22×C4—221no—
752C22×C4—221no—
753C22×C4—221no—
754C22×C4—221no—
755C22×C4—221no—
756C22×C4—221no—
757C22×C4—221no—
758C22×C4—221no—
759C22×C4—221no—
760C22×C4—221no—
761C22×C4—221no—
762C22×C4—221no—
763C22×C4—221no—
764C22×C4—221no—
765C22×C4—221no—
766C22×C4—221no—
767C22×C4—221no—
768C22×C4—221no—
769C22×C4—221no—
770C22×C4—221no—
771C22×C4—221no—
772C22×C4—221no—
773C22×C4—444no—
774C22×C4—444no—
775C22×C4—444no—
776C22×C4—444no—
777C22×C4—444no—
778C22×C4—444no—
779C22×C4—444no—
780C22×C4C2×Dic2212yes—
781C22×C4C2×Dic2212yes—
782C22×C4C2×C4×D1112yes—
783C22×C4C2×C4×D1112yes—
784C22×C4D4×D1112yes—
785C22×C4D4×D1112yes—
786C22×C4#434112yes—
787C4⋊C4—444no—
788C4⋊C4—444no—
789C4⋊C4—444no—
790C4⋊C4—444no—
791C4⋊C4—444no—
792C22⋊C4—28no—
793C22⋊C4—44no—
794C22⋊C4—44no—
795C22⋊C4—228no—
796C22⋊C4—444no—
797C22⋊C4—444no—
798C42—44no—
799C42—444no—
800C11#1457511yescharacteristic, complemented, Sylow
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23C4×Dic2214yes—
836C23C22×Dic2211yescharacteristic
837C23C22×C4×D1111yescharacteristic
838C23C2×#433911yescharacteristic
839C23C2×D4×D1111yescharacteristic
840C23C2×D4×D1111yescharacteristic
841C23C2×#434111yescharacteristic
842C23#6703711yescharacteristic
843C23#6703711yescharacteristic
844C23#6703711yescharacteristic
845C23#41×D1111yescharacteristic
846C23#6704211yescharacteristic
847C23#6704211yescharacteristic
848C23#6704311yescharacteristic
849C23#6704311yescharacteristic
850C23#6704311yescharacteristic
851Q8—4416no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—114no—
894C2×C4—222no—
895C2×C4—222no—
896C2×C4—222no—
897C2×C4—222no—
898C2×C4—222no—
899C2×C4—222no—
900C2×C4—222no—
901C2×C4—222no—
902C2×C4—222no—
903C2×C4—222no—
904C2×C4—222no—
905C2×C4—222no—
906C2×C4—222no—
907C2×C4—222no—
908C2×C4—222no—
909C2×C4—222no—
910C2×C4—222no—
911C2×C4—222no—
912C2×C4—222no—
913C2×C4—222no—
914C2×C4—222no—
915C2×C4—222no—
916C2×C4—222no—
917C2×C4—222no—
918C2×C4—4416no—
919C2×C4—441no—
920C2×C4—441no—
921C2×C4—441no—
922C2×C4—441no—
923C2×C4—441no—
924C2×C4—441no—
925C2×C4—441no—
926C2×C4—441no—
927C2×C4—441no—
928C2×C4—441no—
929C2×C4—441no—
930C2×C4—441no—
931C2×C4—441no—
932C2×C4—441no—
933C2×C4—441no—
934C2×C4—441no—
935C2×C4—441no—
936C2×C4—441no—
937C2×C4—441no—
938C2×C4—441no—
939C2×C4—441no—
940C2×C4—441no—
941C2×C4—441no—
942C2×C4—441no—
943C2×C4—441no—
944C2×C4—441no—
945C2×C4—441no—
946C2×C4—441no—
947C2×C4—441no—
948C2×C4—441no—
949C2×C4—441no—
950C2×C4(C22⋊D11)⋊C414yes—
951C22—24no—
952C22—24no—
953C22—24no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22C2×C4×Dic2211yescharacteristic
967C22#1062301411yescharacteristic
968C22C2×(C22⋊D11)⋊C411yescharacteristic
969C22#1062302111yescharacteristic
970C22#1062305011yescharacteristic
971C22#1062305411yescharacteristic
972C22#1062306211yescharacteristic
973C22D4×Dic2211yescharacteristic
974C22D4×Dic2211yescharacteristic
975C22#1062307011yescharacteristic
976C22#1062307211yescharacteristic
977C22#1062307411yescharacteristic
978C22C4×D4×D1111yescharacteristic
979C22#1062307611yescharacteristic
980C22#1062307711yescharacteristic
981C22#1062307711yescharacteristic
982C22#1062308111yescharacteristic
983C22#1062309111yescharacteristic
984C22#1062309511yescharacteristic
985C22#1062312211yescharacteristic
986C22#1062313411yescharacteristic
987C22#1062313411yescharacteristic
988C22#1062313811yescharacteristic
989C22#1062314011yescharacteristic
990C22#1062314111yescharacteristic
991C22#1062315211yescharacteristic
992C22#1062317911yescharacteristic
993C22#1062318911yescharacteristic
994C22#1062319811yescharacteristic
995C22#1062320011yescharacteristic
996C22#1062320611yescharacteristic
997C22#1062321411yescharacteristic
998C22#1062324111yescharacteristic
999C22#1062324311yescharacteristic
1000C22#1062324611yescharacteristic
1001C4—24no—
1002C4—42no—
1003C4—42no—
1004C4—42no—
1005C4—42no—
1006C4—81no—
1007C4—224no—
1008C4—442no—
1009C4—442no—
1010C4—442no—
1011C4—442no—
1012C4—442no—
1013C4—442no—
1014C4—881no—
1015C2—44no—
1016C2#1307132511yescharacteristic
1017C2#1307132611yescharacteristic
1018C2#1307134411yescharacteristic
1019C2#1307159611yescharacteristic
1020C2#1307161911yescharacteristic
1021C2#1307162211yescharacteristic
1022C2#1307178511yescharacteristic
1023C2#1307483911yescharacteristic
1024C2#1307492811yescharacteristic
1025C2#1307503411yescharacteristic
1026C2#1307504111yescharacteristic
1027C2#1307510911yescharacteristic
1028C2#1307511611yescharacteristic
1029C2#1307603211yescharacteristic
1030C2#1307604111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1437C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenter#1437D11
hypocenterC11#14575
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. C2×#10622542C2semidirect
3. C2×#10622259C2semidirect
6. #13066880C2semidirect
7. #13066880C2semidirect
8. #13066874C2semidirect
9. #13066872C2semidirect
12. #13066843C2semidirect
13. #13066842C2semidirect
52. #10622560C4semidirect
84. C22×Dic22C2×C4semidirect
93. C2×C11×C22⋊C4Q8semidirect
139. C11⋊#95C2×C4semidirect
140. C11⋊#95C2×C4semidirect
141. C11⋊#95C2×C4semidirect
615. C2×C22⋊C4Dic22semidirect
800. C11#14575semidirect

Maximal subgroups

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

subgroupindex
C2×#106225602
C2×#106225422
C2×#106222592
C2×#106225632
C2×#106225592
#130668802
#130668742
#130668722
#130668592
#130668532
#130668432
#130668422
#130668382
C11×#14372
#1457511