Finite Group Databasebeta

← #14676871

Subgroups — #14676871

Order 2816.

1802 conjugacy classes of subgroups.

The subgroup lattice has 1026 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622585C211yesmaximal, characteristic, complemented
2C2×#10622557C211yesmaximal, characteristic
3C2×#10622555C211yesmaximal, characteristic
4C2×#10622555C211yesmaximal, characteristic
5C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
6C2×C22⋊C4×Dic11C211yesmaximal, characteristic
7#13066875C211yesmaximal, characteristic, complemented
8#13066874C211yesmaximal, characteristic, complemented
9#13066865C211yesmaximal, characteristic
10#13066863C211yesmaximal, characteristic
11Dic11⋊#95C211yesmaximal, characteristic, complemented
12Dic11⋊#95C211yesmaximal, characteristic, complemented
13#13066843C211yesmaximal, characteristic, complemented
14#13066840C211yesmaximal, characteristic, complemented
15C2×C11×#388C211yesmaximal, characteristic
16C24×Dic11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
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×Dic11⋊C4C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C11×#388—24no—
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
51C2×C11⋊#95C2211yescharacteristic
52#10622585—24no—
53#10622557—24no—
54#10622555—24no—
55#10622555C418yescomplemented
56C22⋊C4×Dic11—24no—
57C4×Dic11⋊C4—24no—
58C25×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×Dic11—22no—
66C23×Dic11—22no—
67C23×Dic11—22no—
68C23×Dic11—22no—
69C23×Dic11—22no—
70C23×Dic11—22no—
71C23×Dic11C2×C414yes—
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—41no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
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⋊C4C2×C414yes—
91C2×C11×C22⋊C4D414yes—
92C2×C42×C11—22no—
93C2×C42×C11—22no—
94C2×C42×C11—22no—
95C2×C22⋊Dic11—22no—
96C2×C22⋊Dic11—22no—
97C2×C22⋊Dic11—22no—
98C2×C22⋊Dic11—22no—
99C2×C22⋊Dic11—22no—
100C2×C22⋊Dic11—22no—
101C2×C22⋊Dic11—22no—
102C2×C22⋊Dic11—41no—
103C2×C22⋊Dic11C2×C414yes—
104C2×Dic11⋊C4—22no—
105C2×Dic11⋊C4—22no—
106C2×Dic11⋊C4—22no—
107C2×Dic11⋊C4—22no—
108C2×Dic11⋊C4—22no—
109C2×Dic11⋊C4—22no—
110C2×Dic11⋊C4—22no—
111C2×Dic11⋊C4—22no—
112C2×Dic11⋊C4—22no—
113C2×Dic11⋊C4—22no—
114C2×Dic11⋊C4—22no—
115C2×Dic11⋊C4—41no—
116C2×Dic11⋊C4C2×C414yes—
117C2×Dic11⋊C4C2×C414yes—
118C2×Dic11⋊C4D414yes—
119C2×C4×Dic11—22no—
120C2×C4×Dic11—22no—
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×Dic11D414yes—
128C11×#95—22no—
129C11×#95—22no—
130C11⋊#95—22no—
131C11⋊#95—22no—
132C11⋊#95—22no—
133C11⋊#95—22no—
134C11⋊#95—22no—
135C11⋊#95—22no—
136C11⋊#95—22no—
137C11⋊#95—22no—
138C11⋊#95—22no—
139C11⋊#95—22no—
140C11⋊#95—22no—
141C11⋊#95—22no—
142C11⋊#95—41no—
143C11⋊#95—41no—
144C11⋊#95C2×C414yes—
145C11⋊#95C2×C414yes—
146#13994—111nomaximal, Sylow
147C24×C11—21no—
148C24×C11—21no—
149C24×C11—21no—
150C24×C11—21no—
151C24×C11—21no—
152C24×C11—21no—
153C24×C11—21no—
154C24×C11—21no—
155C24×C11—21no—
156C24×C11—21no—
157C24×C11—21no—
158C24×C11—21no—
159C24×C11C22×C412yes—
160C24×C11C2×D412yes—
161C24×C11#4112yes—
162C24×C11C2411yescharacteristic
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×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11C22×C412yes—
199C22×C4×C11C22×C412yes—
200C22×C4×C11C2×D412yes—
201C22×C4×C11C2×D412yes—
202C22×C4×C11C2×D412yes—
203C22×C4×C11C2×D412yes—
204C22×C4×C11#4112yes—
205C22×Dic11—28no—
206C22×Dic11—28no—
207C22×Dic11—28no—
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—21no—
251C22×Dic11—44no—
252C22×Dic11—44no—
253C22×Dic11—44no—
254C22×Dic11—44no—
255C22×Dic11C22×C412yes—
256C22×Dic11C22×C412yes—
257C22×Dic11C22×C412yes—
258C22×Dic11C22×C412yes—
259C22×Dic11C2×D412yes—
260C22×Dic11C2×D412yes—
261C22×Dic11C2×D412yes—
262C22×Dic11C2×D412yes—
263C22×Dic11#4112yes—
264C22×Dic11#4112yes—
265C22×Dic11#4112yes—
266C22×Dic11#4112yes—
267C22×Dic11#4112yes—
268C11×C4⋊C4—44no—
269C11×C22⋊C4—28no—
270C11×C22⋊C4—28no—
271C11×C22⋊C4—44no—
272C42×C11—44no—
273C22⋊Dic11—28no—
274C22⋊Dic11—28no—
275C22⋊Dic11—44no—
276Dic11⋊C4—28no—
277Dic11⋊C4—28no—
278Dic11⋊C4—28no—
279Dic11⋊C4—44no—
280Dic11⋊C4—44no—
281C4×Dic11—28no—
282C4×Dic11—44no—
283C4×Dic11—44no—
284C2×#389—111no—
285C2×#388—111no—
286C2×#388D1111yescharacteristic
287C2×#380—111no—
288C2×#380—111no—
289C2×C4×C4⋊C4—111no—
290C2×C4×C22⋊C4—111no—
291#1442—111no—
292#1442—111no—
293#1440—111no—
294#1440—111no—
295C4⋊#95—111no—
296C4⋊#95—111no—
297#1434—111no—
298#1434—111no—
299C23×C11—22no—
300C23×C11—22no—
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—41no—
318C23×C11—41no—
319C23×C11—41no—
320C23×C11—41no—
321C23×C11—41no—
322C23×C11—41no—
323C23×C11—41no—
324C23×C11—41no—
325C23×C11—41no—
326C23×C11—41no—
327C23×C11—41no—
328C23×C11—41no—
329C23×C11—41no—
330C23×C11—41no—
331C23×C11—41no—
332C23×C11—41no—
333C23×C11C4×D414yes—
334C23×C11C23×C411yescharacteristic
335C23×C11C22×D411yescharacteristic
336C23×C11C22×D411yescharacteristic
337C23×C11C22×D411yescharacteristic
338C23×C11C2×#4111yescharacteristic
339C23×C11C2×#4111yescharacteristic
340C23×C11C2×#4111yescharacteristic
341C23×C11C2×#4111yescharacteristic
342C23×C11C2×#4111yescharacteristic
343C23×C11C2×#4111yescharacteristic
344C23×C11C2×#4111yescharacteristic
345C23×C11H(5,𝔽2)11yescharacteristic
346C23×C112−1+411yescharacteristic
347C23×C112−1+411yescharacteristic
348C23×C112−1+411yescharacteristic
349C2×C4×C11—22no—
350C2×C4×C11—22no—
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—41no—
368C2×C4×C11—41no—
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#12114yes—
391C2×Dic11—22no—
392C2×Dic11—22no—
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—41no—
410C2×Dic11—41no—
411C2×Dic11—41no—
412C2×Dic11—41no—
413C2×Dic11—41no—
414C2×Dic11—41no—
415C2×Dic11—41no—
416C2×Dic11—41no—
417C2×Dic11—41no—
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—416no—
434C2×Dic11—41no—
435C2×Dic11—41no—
436C2×Dic11—41no—
437C2×Dic11—41no—
438C2×Dic11—41no—
439C2×Dic11—41no—
440C2×Dic11—41no—
441C2×Dic11#11714yes—
442C2×Dic11C4×D414yes—
443C2×Dic11C4×D414yes—
444C2×Dic11#12114yes—
445C2×Dic11#12314yes—
446C2×Dic11#12414yes—
447C2×Dic11#12614yes—
448C24×C4—111no—
449C22×C4⋊C4—111no—
450C22×C4⋊C4—111no—
451C22×C4⋊C4—111no—
452C22×C4⋊C4—111no—
453C22×C4⋊C4—111no—
454C22×C4⋊C4C2×D1111yescharacteristic
455C22×C22⋊C4—111no—
456C22×C22⋊C4—111no—
457C22×C22⋊C4—111no—
458C22×C22⋊C4C2×D1111yescharacteristic
459C22×C22⋊C4C2×D1111yescharacteristic
460C22×C22⋊C4C2×D1111yescharacteristic
461C22×C42—111no—
462C22×C42—111no—
463C22×C42—111no—
464C22×C42C2×D1111yescharacteristic
465#389—224no—
466#388—24no—
467#388—224no—
468#380—118no—
469#380—224no—
470C4×C4⋊C4—224no—
471C4×C22⋊C4—224no—
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
490C22×C11—24no—
491C22×C11—24no—
492C22×C11—24no—
493C22×C11—42no—
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×C11C2×#11711yescharacteristic
506C22×C11C2×C4×D411yescharacteristic
507C22×C11C2×C4×D411yescharacteristic
508C22×C11C2×C4×D411yescharacteristic
509C22×C11C4×#4111yescharacteristic
510C22×C11#51911yescharacteristic
511C22×C11#52011yescharacteristic
512C22×C11C2×#12111yescharacteristic
513C22×C11C2×#12111yescharacteristic
514C22×C11C2×#12311yescharacteristic
515C22×C11#52511yescharacteristic
516C22×C11C2×#12411yescharacteristic
517C22×C11C2×#12611yescharacteristic
518C22×C11#52911yescharacteristic
519C22×C11#53211yescharacteristic
520C22×C11#53611yescharacteristic
521C22×C11#53711yescharacteristic
522C22×C11#54111yescharacteristic
523C22×C11#54211yescharacteristic
524C22×C11D4211yescharacteristic
525C22×C11#54711yescharacteristic
526C22×C11#54711yescharacteristic
527C22×C11#54711yescharacteristic
528C22×C11#54711yescharacteristic
529C22×C11#54811yescharacteristic
530C22×C11#54811yescharacteristic
531C22×C11#55211yescharacteristic
532C22×C11#55211yescharacteristic
533C22×C11#55211yescharacteristic
534C22×C11#55211yescharacteristic
535C22×C11#55211yescharacteristic
536C22×C11#55311yescharacteristic
537C22×C11#55511yescharacteristic
538C22×C11#55511yescharacteristic
539C22×C11#55611yescharacteristic
540C4×C11—24no—
541C4×C11—42no—
542C4×C11—42no—
543C4×C11—42no—
544C4×C11—42no—
545C4×C11—81no—
546Dic11—42no—
547Dic11—42no—
548Dic11—42no—
549Dic11—42no—
550Dic11—42no—
551Dic11—42no—
552Dic11—81no—
553Dic11#38818yescomplemented
554C25C22×D1111yescharacteristic
555C23×C4—111no—
556C23×C4—114no—
557C23×C4—111no—
558C23×C4—111no—
559C23×C4—111no—
560C23×C4—111no—
561C23×C4—111no—
562C23×C4—111no—
563C23×C4—111no—
564C23×C4—222no—
565C23×C4—222no—
566C23×C4—222no—
567C23×C4—222no—
568C23×C4—222no—
569C23×C4—222no—
570C23×C4C22×D1111yescharacteristic
571C23×C4C22×D1111yescharacteristic
572C23×C4C22×D1111yescharacteristic
573C23×C4C22×D1111yescharacteristic
574C23×C4C22×D1111yescharacteristic
575C23×C4C22×D1111yescharacteristic
576C2×C4⋊C4—22no—
577C2×C4⋊C4—22no—
578C2×C4⋊C4—41no—
579C2×C4⋊C4—114no—
580C2×C4⋊C4—114no—
581C2×C4⋊C4—114no—
582C2×C4⋊C4—222no—
583C2×C4⋊C4—222no—
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—222no—
591C2×C4⋊C4—222no—
592C2×C4⋊C4—222no—
593C2×C4⋊C4—441no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—22no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—41no—
601C2×C22⋊C4—114no—
602C2×C22⋊C4—222no—
603C2×C22⋊C4—222no—
604C2×C22⋊C4—222no—
605C2×C22⋊C4—222no—
606C2×C22⋊C4—222no—
607C2×C22⋊C4—222no—
608C2×C22⋊C4—222no—
609C2×C22⋊C4—441no—
610C2×C22⋊C4C4×D1114yes—
611C2×C22⋊C4C22⋊D1114yes—
612C2×C42—22no—
613C2×C42—22no—
614C2×C42—22no—
615C2×C42—114no—
616C2×C42—222no—
617C2×C42—222no—
618C2×C42—222no—
619C2×C42—222no—
620C2×C42—222no—
621C2×C42—222no—
622C2×C42—222no—
623C2×C42—222no—
624#95—22no—
625#95—22no—
626#95—114no—
627#95—114no—
628#95—222no—
629#95—222no—
630#95—222no—
631#95—222no—
632#95—222no—
633#95—222no—
634#95—222no—
635#95—222no—
636#95—222no—
637#95—222no—
638#95—222no—
639#95—222no—
640#95—441no—
641#95—441no—
642C2×C11—44no—
643C2×C11C2×#38811yescharacteristic
644C2×C11C4×#12111yescharacteristic
645C2×C11#232311yescharacteristic
646C2×C11#234411yescharacteristic
647C2×C11#234611yescharacteristic
648C2×C11#236111yescharacteristic
649C2×C11#236211yescharacteristic
650C2×C11#248511yescharacteristic
651C2×C11#248611yescharacteristic
652C2×C11#248911yescharacteristic
653C2×C11#249111yescharacteristic
654C2×C11#249511yescharacteristic
655C2×C11#249611yescharacteristic
656C2×C11#253611yescharacteristic
657C2×C11#253711yescharacteristic
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24C2×C4×D1112yes—
671C24#433912yes—
672C24C2×C22⋊D1112yes—
673C24C23×D1111yescharacteristic
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
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—112no—
710C22×C4—112no—
711C22×C4—112no—
712C22×C4—112no—
713C22×C4—112no—
714C22×C4—112no—
715C22×C4—112no—
716C22×C4—112no—
717C22×C4—112no—
718C22×C4—112no—
719C22×C4—112no—
720C22×C4—112no—
721C22×C4—112no—
722C22×C4—228no—
723C22×C4—228no—
724C22×C4—228no—
725C22×C4—221no—
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—444no—
769C22×C4—444no—
770C22×C4—444no—
771C22×C4—444no—
772C22×C4C2×C4×D1112yes—
773C22×C4C2×C4×D1112yes—
774C22×C4D4×D1112yes—
775C22×C4D4×D1112yes—
776C22×C4#434112yes—
777C22×C4C2×C22⋊D1112yes—
778C22×C4C2×C22⋊D1112yes—
779C4⋊C4—44no—
780C4⋊C4—228no—
781C4⋊C4—228no—
782C4⋊C4—228no—
783C4⋊C4—444no—
784C4⋊C4—444no—
785C22⋊C4—28no—
786C22⋊C4—28no—
787C22⋊C4—44no—
788C22⋊C4—228no—
789C22⋊C4—228no—
790C22⋊C4—444no—
791C42—44no—
792C42—228no—
793C42—444no—
794C42—444no—
795C11#1399411yescharacteristic, complemented, Sylow
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
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—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23C4×C22⋊D1114yes—
831C23C22×C4×D1111yescharacteristic
832C23C2×#433911yescharacteristic
833C23C2×D4×D1111yescharacteristic
834C23C2×D4×D1111yescharacteristic
835C23C2×#434111yescharacteristic
836C23#6703711yescharacteristic
837C23#41×D1111yescharacteristic
838C23#41×D1111yescharacteristic
839C23#41×D1111yescharacteristic
840C23#41×D1111yescharacteristic
841C23#41×D1111yescharacteristic
842C23#6704311yescharacteristic
843C23#6704311yescharacteristic
844C23#6704311yescharacteristic
845C23C22×C22⋊D1111yescharacteristic
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
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—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
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—114no—
888C2×C4—114no—
889C2×C4—114no—
890C2×C4—114no—
891C2×C4—114no—
892C2×C4—114no—
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—4416no—
913C2×C4—441no—
914C2×C4—441no—
915C2×C4—441no—
916C2×C4—441no—
917C2×C4—441no—
918C2×C4—441no—
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#6699214yes—
945C22—24no—
946C22—24no—
947C22—24no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22#1062304711yescharacteristic
961C22D11×#11711yescharacteristic
962C22#1062306211yescharacteristic
963C22#1062306211yescharacteristic
964C22C4×#434111yescharacteristic
965C22#1062306911yescharacteristic
966C22#1062307111yescharacteristic
967C22C4×D4×D1111yescharacteristic
968C22C4×D4×D1111yescharacteristic
969C22#1062307711yescharacteristic
970C22#1062307811yescharacteristic
971C22#1062308311yescharacteristic
972C22D11×#12111yescharacteristic
973C22#1062313911yescharacteristic
974C22#1062314211yescharacteristic
975C22#1062314711yescharacteristic
976C22#1062317911yescharacteristic
977C22#1062318111yescharacteristic
978C22#1062318111yescharacteristic
979C22D11×#12311yescharacteristic
980C22#1062320011yescharacteristic
981C22#1062320111yescharacteristic
982C22D11×#12411yescharacteristic
983C22#1062320811yescharacteristic
984C22#1062323211yescharacteristic
985C22#1062323311yescharacteristic
986C22D11×#12611yescharacteristic
987C22#1062323911yescharacteristic
988C22C2×C4×C22⋊D1111yescharacteristic
989C22D4×C22⋊D1111yescharacteristic
990C22C2×#6699211yescharacteristic
991C22#1062335511yescharacteristic
992C22#1062335511yescharacteristic
993C22#1062335511yescharacteristic
994C22#1062336311yescharacteristic
995C4—24no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—81no—
1001C4—118no—
1002C4—442no—
1003C4—442no—
1004C4—442no—
1005C4—442no—
1006C4—442no—
1007C4—442no—
1008C4—881no—
1009C2—44no—
1010C2D11×#38811yescharacteristic
1011C2C4×#6699211yescharacteristic
1012C2#1307129511yescharacteristic
1013C2#1307148611yescharacteristic
1014C2#1307149811yescharacteristic
1015C2#1307163311yescharacteristic
1016C2#1307164011yescharacteristic
1017C2#1307291011yescharacteristic
1018C2#1307292111yescharacteristic
1019C2#1307295411yescharacteristic
1020C2#1307297611yescharacteristic
1021C2#1307302411yescharacteristic
1022C2#1307303511yescharacteristic
1023C2#1307352411yescharacteristic
1024C2#1307353011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#388C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#388D11
hypocenterC11#13994
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C2×#10622585C2semidirect
5. C2×C4×Dic11⋊C4C2semidirect
7. #13066875C2semidirect
8. #13066874C2semidirect
11. Dic11⋊#95C2semidirect
12. Dic11⋊#95C2semidirect
13. #13066843C2semidirect
14. #13066840C2semidirect
55. #10622555C4semidirect
553. Dic11#388semidirect
795. C11#13994semidirect

Maximal subgroups

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

subgroupindex
C2×#106225852
C2×#106225572
C2×#106225552
C2×C4×Dic11⋊C42
C2×C22⋊C4×Dic112
#130668752
#130668742
#130668652
#130668632
Dic11⋊#952
#130668432
#130668402
C2×C11×#3882
#1399411