Finite Group Databasebeta

← #14676873

Subgroups — #14676873

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×#10622260C211yesmaximal, characteristic, complemented
2C2×#10622283C211yesmaximal, characteristic
3C2×#10622553C211yesmaximal, characteristic
4C2×#10622280C211yesmaximal, characteristic
5C2×#10622280C211yesmaximal, characteristic
6C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
7C2×#10622279C211yesmaximal, characteristic
8#13066874C211yesmaximal, characteristic, complemented
9#13066873C211yesmaximal, characteristic, complemented
10#13066864C211yesmaximal, characteristic
11#13066864C211yesmaximal, characteristic
12Dic11⋊#95C211yesmaximal, characteristic, complemented
13Dic11⋊#95C211yesmaximal, characteristic, complemented
14#13066840C211yesmaximal, characteristic, complemented
15C11×#1434C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C22×(C2×D11)⋊C4C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×C4⋊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
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#10622553—24no—
52C4×Dic11⋊C4—24no—
53#10622283—24no—
54#10622280—24no—
55#10622280C418yescomplemented
56#10622279—24no—
57#10622260—24no—
58C24×D11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C22×C4×D11—22no—
74C22×C4×D11—22no—
75C22×C4×D11—22no—
76C22×C4×D11—22no—
77C22×C4×D11—22no—
78C22×C4×D11—22no—
79C22×C4×D11C2×C414yes—
80C2×C42×C11—22no—
81C2×C42×C11—22no—
82C2×C42×C11—22no—
83C2×(C2×D11)⋊C4—22no—
84C2×(C2×D11)⋊C4—22no—
85C2×(C2×D11)⋊C4—22no—
86C2×(C2×D11)⋊C4—22no—
87C2×(C2×D11)⋊C4—22no—
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—41no—
97C2×(C2×D11)⋊C4—41no—
98C2×(C2×D11)⋊C4C2×C414yes—
99C2×(C2×D11)⋊C4C2×C414yes—
100C2×(C2×D11)⋊C4D414yes—
101C2×C4⋊Dic11—22no—
102C2×C4⋊Dic11—22no—
103C2×C4⋊Dic11—41no—
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×#95C2×C414yes—
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—22no—
143C11⋊#95—41no—
144C11⋊#95—41no—
145C11⋊#95C2×C414yes—
146#13994—111nomaximal, Sylow
147C24×C11C2411yescharacteristic
148C23×D11—21no—
149C23×D11—21no—
150C23×D11—21no—
151C23×D11—21no—
152C23×D11—21no—
153C23×D11—21no—
154C23×D11—21no—
155C23×D11—21no—
156C23×D11—21no—
157C23×D11—21no—
158C23×D11—21no—
159C23×D11—21no—
160C23×D11C22×C412yes—
161C23×D11C2×D412yes—
162C23×D11#4112yes—
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×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11C22×C412yes—
205C22×C4×C11C22×C412yes—
206C22×C4×C11C22×C412yes—
207C22×C4×C11C2×D412yes—
208C22×C4×C11C2×D412yes—
209C22×C4×C11C2×D412yes—
210C22×C4×C11#4112yes—
211C22×C4×C11#4112yes—
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×Dic11C22×C412yes—
250C22×Dic11C22×C412yes—
251C22×Dic11C22×C412yes—
252C22×Dic11C2×D412yes—
253C22×Dic11C2×D412yes—
254C22×Dic11C2×D412yes—
255C22×Dic11C2×D412yes—
256C22×Dic11C2×D412yes—
257C22×Dic11#4112yes—
258C22×Dic11#4112yes—
259C22×Dic11#4112yes—
260C22×Dic11#4112yes—
261C2×C4×D11—28no—
262C2×C4×D11—28no—
263C2×C4×D11—28no—
264C2×C4×D11—44no—
265C2×C4×D11—44no—
266C2×C4×D11—44no—
267C2×C4×D11—44no—
268C42×C11—44no—
269(C2×D11)⋊C4—28no—
270(C2×D11)⋊C4—28no—
271(C2×D11)⋊C4—28no—
272(C2×D11)⋊C4—28no—
273(C2×D11)⋊C4—44no—
274(C2×D11)⋊C4—44no—
275C4⋊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×#388—111no—
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#1434D1111yescharacteristic, complemented
299C23×C11C23×C411yescharacteristic
300C23×C11C22×D411yescharacteristic
301C23×C11C22×D411yescharacteristic
302C23×C11C22×D411yescharacteristic
303C23×C11C2×#4111yescharacteristic
304C23×C11C2×#4111yescharacteristic
305C23×C11C2×#4111yescharacteristic
306C23×C11C2×#4111yescharacteristic
307C23×C11C2×#4111yescharacteristic
308C23×C11C2×#4111yescharacteristic
309C23×C11C2×#4111yescharacteristic
310C23×C11H(5,𝔽2)11yescharacteristic
311C23×C112−1+411yescharacteristic
312C23×C112−1+411yescharacteristic
313C23×C112−1+411yescharacteristic
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—41no—
333C22×D11—41no—
334C22×D11—41no—
335C22×D11—41no—
336C22×D11—41no—
337C22×D11—41no—
338C22×D11—41no—
339C22×D11—41no—
340C22×D11—41no—
341C22×D11—41no—
342C22×D11—41no—
343C22×D11—41no—
344C22×D11—41no—
345C22×D11—41no—
346C22×D11—41no—
347C22×D11—41no—
348C22×D11C4×D414yes—
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—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
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×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11#12114yes—
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—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—41no—
434C2×Dic11—41no—
435C2×Dic11—41no—
436C2×Dic11—41no—
437C2×Dic11—41no—
438C2×Dic11—41no—
439C2×Dic11—41no—
440C2×Dic11#11714yes—
441C2×Dic11C4×D414yes—
442C2×Dic11C4×D414yes—
443C2×Dic11#12114yes—
444C2×Dic11#12314yes—
445C2×Dic11#12414yes—
446C2×Dic11#12614yes—
447C4×D11—416no—
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⋊C4—111no—
455C22×C22⋊C4—111no—
456C22×C22⋊C4—111no—
457C22×C22⋊C4—111no—
458C22×C22⋊C4—111no—
459C22×C22⋊C4—111no—
460C22×C22⋊C4—111no—
461C22×C42—111no—
462C22×C42—111no—
463C22×C42—111no—
464C22×C42C2×D1111yescharacteristic
465#389—224no—
466#388—224no—
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×#95C2×D1111yescharacteristic
485C2×#95C2×D1111yescharacteristic
486C2×#95C2×D1111yescharacteristic
487C2×#95C2×D1111yescharacteristic
488C2×#95C2×D1111yescharacteristic
489C2×#95C2×D1111yescharacteristic
490C22×C11C2×#11711yescharacteristic
491C22×C11C2×C4×D411yescharacteristic
492C22×C11C2×C4×D411yescharacteristic
493C22×C11C2×C4×D411yescharacteristic
494C22×C11C4×#4111yescharacteristic
495C22×C11#51911yescharacteristic
496C22×C11#52011yescharacteristic
497C22×C11C2×#12111yescharacteristic
498C22×C11C2×#12111yescharacteristic
499C22×C11C2×#12311yescharacteristic
500C22×C11#52511yescharacteristic
501C22×C11C2×#12411yescharacteristic
502C22×C11C2×#12611yescharacteristic
503C22×C11#52911yescharacteristic
504C22×C11#53211yescharacteristic
505C22×C11#53611yescharacteristic
506C22×C11#53711yescharacteristic
507C22×C11#54111yescharacteristic
508C22×C11#54211yescharacteristic
509C22×C11D4211yescharacteristic
510C22×C11#54711yescharacteristic
511C22×C11#54711yescharacteristic
512C22×C11#54711yescharacteristic
513C22×C11#54711yescharacteristic
514C22×C11#54811yescharacteristic
515C22×C11#54811yescharacteristic
516C22×C11#55211yescharacteristic
517C22×C11#55211yescharacteristic
518C22×C11#55211yescharacteristic
519C22×C11#55211yescharacteristic
520C22×C11#55211yescharacteristic
521C22×C11#55311yescharacteristic
522C22×C11#55511yescharacteristic
523C22×C11#55511yescharacteristic
524C22×C11#55611yescharacteristic
525C2×D11—24no—
526C2×D11—24no—
527C2×D11—24no—
528C2×D11—42no—
529C2×D11—42no—
530C2×D11—42no—
531C2×D11—42no—
532C2×D11—42no—
533C2×D11—42no—
534C2×D11—42no—
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—42no—
538C2×D11—42no—
539C2×D11—42no—
540C4×C11—24no—
541C4×C11—42no—
542C4×C11—42no—
543C4×C11—42no—
544C4×C11—42no—
545C4×C11—42no—
546C4×C11—81no—
547Dic11—42no—
548Dic11—42no—
549Dic11—42no—
550Dic11—42no—
551Dic11—42no—
552Dic11—81no—
553Dic11#38818yescomplemented
554C25—111no—
555C23×C4—111no—
556C23×C4—111no—
557C23×C4—111no—
558C23×C4—111no—
559C23×C4—111no—
560C23×C4—111no—
561C23×C4—114no—
562C23×C4—111no—
563C23×C4—222no—
564C23×C4—222no—
565C23×C4—222no—
566C23×C4—222no—
567C23×C4—222no—
568C23×C4—222no—
569C23×C4C22×D1111yescharacteristic
570C23×C4C22×D1111yescharacteristic
571C23×C4C22×D1111yescharacteristic
572C23×C4C22×D1111yescharacteristic
573C23×C4C22×D1111yescharacteristic
574C23×C4C22×D1111yescharacteristic
575C23×C4C22×D1111yescharacteristic
576C2×C4⋊C4—114no—
577C2×C4⋊C4—114no—
578C2×C4⋊C4—114no—
579C2×C4⋊C4—222no—
580C2×C4⋊C4—222no—
581C2×C4⋊C4—222no—
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—441no—
593C2×C4⋊C4—441no—
594C2×C22⋊C4—114no—
595C2×C22⋊C4—114no—
596C2×C22⋊C4—114no—
597C2×C22⋊C4—222no—
598C2×C22⋊C4—222no—
599C2×C22⋊C4—222no—
600C2×C22⋊C4—222no—
601C2×C22⋊C4—222no—
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—222no—
610C2×C22⋊C4—441no—
611C2×C22⋊C4—441no—
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—22no—
627#95—22no—
628#95—22no—
629#95—114no—
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—441no—
640#95—441no—
641#95C4×D1114yes—
642C2×C11C2×#38811yescharacteristic
643C2×C11C4×#12111yescharacteristic
644C2×C11#232311yescharacteristic
645C2×C11#234411yescharacteristic
646C2×C11#234611yescharacteristic
647C2×C11#236111yescharacteristic
648C2×C11#236211yescharacteristic
649C2×C11#248511yescharacteristic
650C2×C11#248611yescharacteristic
651C2×C11#248911yescharacteristic
652C2×C11#249111yescharacteristic
653C2×C11#249511yescharacteristic
654C2×C11#249611yescharacteristic
655C2×C11#253611yescharacteristic
656C2×C11#253711yescharacteristic
657D11—44no—
658C24—112no—
659C24—112no—
660C24—112no—
661C24—221no—
662C24—221no—
663C24—221no—
664C24—221no—
665C24—221no—
666C24—221no—
667C24—221no—
668C24—221no—
669C24—221no—
670C24—221no—
671C24—221no—
672C24—221no—
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—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—112no—
716C22×C4—112no—
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—112no—
727C22×C4—228no—
728C22×C4—228no—
729C22×C4—228no—
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—444no—
768C22×C4—444no—
769C22×C4—444no—
770C22×C4—444no—
771C22×C4C2×C4×D1112yes—
772C22×C4C2×C4×D1112yes—
773C22×C4C2×C4×D1112yes—
774C22×C4#433912yes—
775C22×C4#433912yes—
776C22×C4D4×D1112yes—
777C22×C4D4×D1112yes—
778C22×C4D4×D1112yes—
779C4⋊C4—228no—
780C4⋊C4—228no—
781C4⋊C4—228no—
782C4⋊C4—444no—
783C4⋊C4—444no—
784C4⋊C4—444no—
785C22⋊C4—228no—
786C22⋊C4—228no—
787C22⋊C4—228no—
788C22⋊C4—228no—
789C22⋊C4—444no—
790C22⋊C4—444no—
791C42—44no—
792C42—228no—
793C42—444no—
794C42—444no—
795C11#1399411yescharacteristic, complemented, Sylow
796C23—114no—
797C23—222no—
798C23—222no—
799C23—222no—
800C23—222no—
801C23—222no—
802C23—222no—
803C23—222no—
804C23—222no—
805C23—222no—
806C23—222no—
807C23—222no—
808C23—222no—
809C23—222no—
810C23—222no—
811C23—222no—
812C23—222no—
813C23—222no—
814C23—222no—
815C23—441no—
816C23—441no—
817C23—441no—
818C23—441no—
819C23—441no—
820C23—441no—
821C23—441no—
822C23—441no—
823C23—441no—
824C23—441no—
825C23—441no—
826C23—441no—
827C23—441no—
828C23—441no—
829C23—441no—
830C23—441no—
831C23C22×C4×D1111yescharacteristic
832C23C2×#433911yescharacteristic
833C23C2×#433911yescharacteristic
834C23C2×D4×D1111yescharacteristic
835C23C2×D4×D1111yescharacteristic
836C23C2×D4×D1111yescharacteristic
837C23#6704011yescharacteristic
838C23#41×D1111yescharacteristic
839C23#41×D1111yescharacteristic
840C23#41×D1111yescharacteristic
841C23#41×D1111yescharacteristic
842C23#41×D1111yescharacteristic
843C23#6704211yescharacteristic
844C23#6704311yescharacteristic
845C23#6704311yescharacteristic
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—22no—
865C2×C4—22no—
866C2×C4—22no—
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—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—114no—
895C2×C4—114no—
896C2×C4—114no—
897C2×C4—114no—
898C2×C4—114no—
899C2×C4—114no—
900C2×C4—114no—
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—4416no—
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#6693714yes—
945C22—224no—
946C22—224no—
947C22—224no—
948C22—442no—
949C22—442no—
950C22—442no—
951C22—442no—
952C22—442no—
953C22—442no—
954C22—442no—
955C22—442no—
956C22—442no—
957C22—442no—
958C22—442no—
959C22—442no—
960C22C4×#433911yescharacteristic
961C22C2×#6693711yescharacteristic
962C22#1062303811yescharacteristic
963C22D11×#11711yescharacteristic
964C22#1062305411yescharacteristic
965C22#1062305911yescharacteristic
966C22#1062306211yescharacteristic
967C22#1062306211yescharacteristic
968C22#1062306211yescharacteristic
969C22#1062306311yescharacteristic
970C22#1062306311yescharacteristic
971C22C4×D4×D1111yescharacteristic
972C22C4×D4×D1111yescharacteristic
973C22C4×D4×D1111yescharacteristic
974C22#1062307811yescharacteristic
975C22#1062307911yescharacteristic
976C22#1062308311yescharacteristic
977C22#1062309911yescharacteristic
978C22#1062310311yescharacteristic
979C22D11×#12111yescharacteristic
980C22#1062314011yescharacteristic
981C22#1062316011yescharacteristic
982C22#1062316211yescharacteristic
983C22#1062317911yescharacteristic
984C22D11×#12311yescharacteristic
985C22#1062318611yescharacteristic
986C22#1062318611yescharacteristic
987C22D11×#12411yescharacteristic
988C22#1062320811yescharacteristic
989C22#1062322411yescharacteristic
990C22#1062322711yescharacteristic
991C22D11×#12611yescharacteristic
992C22#1062323911yescharacteristic
993C22#1062324011yescharacteristic
994C22#1062324111yescharacteristic
995C4—24no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—81no—
1002C4—118no—
1003C4—442no—
1004C4—442no—
1005C4—442no—
1006C4—442no—
1007C4—442no—
1008C4—881no—
1009C2—444no—
1010C2D11×#38811yescharacteristic
1011C2C4×#6693711yescharacteristic
1012C2#1307129711yescharacteristic
1013C2#1307148211yescharacteristic
1014C2#1307150211yescharacteristic
1015C2#1307162911yescharacteristic
1016C2#1307164411yescharacteristic
1017C2#1307291211yescharacteristic
1018C2#1307292311yescharacteristic
1019C2#1307295611yescharacteristic
1020C2#1307297811yescharacteristic
1021C2#1307302611yescharacteristic
1022C2#1307303711yescharacteristic
1023C2#1307352411yescharacteristic
1024C2#1307353111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1434C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1434D11
hypocenterC11#13994
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
1. C2×#10622260C2semidirect
6. C2×C4×Dic11⋊C4C2semidirect
8. #13066874C2semidirect
9. #13066873C2semidirect
12. Dic11⋊#95C2semidirect
13. Dic11⋊#95C2semidirect
14. #13066840C2semidirect
15. C11×#1434C2semidirect
55. #10622280C4semidirect
298. #1434D11semidirect
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×#106222602
C2×#106222832
C2×#106225532
C2×#106222802
C2×C4×Dic11⋊C42
C2×#106222792
#130668742
#130668732
#130668642
Dic11⋊#952
#130668402
C11×#14342
#1399411