Finite Group Databasebeta

← #14677722

Subgroups — #14677722

Order 2816.

1962 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66930C211yesmaximal, characteristic
2C2×#10622558C211yesmaximal, characteristic
3C2×#10622267C211yesmaximal, characteristic, complemented
4C2×#10622563C211yesmaximal, characteristic
5C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
6#13066879C211yesmaximal, characteristic, complemented
7#13066868C211yesmaximal, characteristic, complemented
8#13066863C211yesmaximal, characteristic
9#13066853C211yesmaximal, characteristic
10#13066850C211yesmaximal, characteristic, complemented
11#13066847C211yesmaximal, characteristic, complemented
12#13066847C211yesmaximal, characteristic, complemented
13#13066842C211yesmaximal, characteristic, complemented
14#13066838C211yesmaximal, characteristic
15C11×#1439C211yesmaximal, characteristic
16C24×Dic11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C2×#66930—24no—
34C2×#66930—24no—
35C2×#66930—24no—
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
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C4⋊C4×Dic11—24no—
55#10622563C418yescomplemented
56#10622558—24no—
57#10622267—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—22no—
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—22no—
90C2×C11×C22⋊C4—41no—
91C2×C11×C22⋊C4C2×C414yes—
92C2×C22⋊Dic11—22no—
93C2×C22⋊Dic11—22no—
94C2×C22⋊Dic11—22no—
95C2×C22⋊Dic11—22no—
96C2×C22⋊Dic11—22no—
97C2×C22⋊Dic11—22no—
98C2×C22⋊Dic11—41no—
99C2×C22⋊Dic11C2×C414yes—
100C2×C22⋊Dic11D414yes—
101C2×C4⋊Dic11—22no—
102C2×C4⋊Dic11—22no—
103C2×C4⋊Dic11—22no—
104C2×C4⋊Dic11—22no—
105C2×C4⋊Dic11C2×C414yes—
106C2×C4⋊Dic11C2×C414yes—
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—41no—
115C2×Dic11⋊C4D414yes—
116C2×C4×Dic11—22no—
117C2×C4×Dic11—22no—
118C2×C4×Dic11—22no—
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—
128#66930—232no—
129C11×#95—22no—
130C11×#95—22no—
131C11×#95—41no—
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—22no—
143C11⋊#95—41no—
144C11⋊#95—41no—
145C11⋊#95C2×C414yes—
146C11⋊#95C2×C414yes—
147#14063—111nomaximal, Sylow
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×C11—21no—
160C24×C11C22×C412yes—
161C24×C11C2×D412yes—
162C24×C11#4112yes—
163C24×C11C2411yescharacteristic
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×C11C22×C412yes—
200C22×C4×C11C22×C412yes—
201C22×C4×C11C2×D412yes—
202C22×C4×C11C2×D412yes—
203C22×C4×C11#4112yes—
204C22×C4×C11#4112yes—
205C22×C4×C11#4112yes—
206C22×Dic11—28no—
207C22×Dic11—28no—
208C22×Dic11—28no—
209C22×Dic11—28no—
210C22×Dic11—28no—
211C22×Dic11—28no—
212C22×Dic11—28no—
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—21no—
252C22×Dic11—21no—
253C22×Dic11—21no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11C22×C412yes—
257C22×Dic11C22×C412yes—
258C22×Dic11C22×C412yes—
259C22×Dic11C22×C412yes—
260C22×Dic11C2×D412yes—
261C22×Dic11C2×D412yes—
262C22×Dic11C2×D412yes—
263C22×Dic11C2×D412yes—
264C22×Dic11C2×D412yes—
265C22×Dic11C2×D412yes—
266C22×Dic11#4112yes—
267C22×Dic11#4112yes—
268C22×Dic11#4112yes—
269C11×C4⋊C4—28no—
270C11×C22⋊C4—28no—
271C11×C22⋊C4—28no—
272C11×C22⋊C4—44no—
273C22⋊Dic11—28no—
274C22⋊Dic11—28no—
275C22⋊Dic11—44no—
276C4⋊Dic11—28no—
277C4⋊Dic11—28no—
278Dic11⋊C4—28no—
279Dic11⋊C4—28no—
280Dic11⋊C4—44no—
281C4×Dic11—28no—
282C4×Dic11—28no—
283C4×Dic11—28no—
284C4×Dic11—44no—
285C22×#117—111no—
286C2×#388—111no—
287C2×#387—111no—
288C2×#385—111no—
289C2×C4×C4⋊C4—111no—
290#1444—111no—
291#1441—111no—
292#1440—111no—
293#1439D1111yescharacteristic
294#1437—111no—
295#1436—111no—
296#1436—111no—
297#1436—111no—
298#1434—111no—
299C22⋊#95—111no—
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—22no—
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×C11—41no—
334C23×C11C4×D414yes—
335C23×C11C23×C411yescharacteristic
336C23×C11C22×D411yescharacteristic
337C23×C11C22×D411yescharacteristic
338C23×C11C22×D411yescharacteristic
339C23×C11C2×#4111yescharacteristic
340C23×C11C2×#4111yescharacteristic
341C23×C11C2×#4111yescharacteristic
342C23×C11C2×#4111yescharacteristic
343C23×C11C2×#4111yescharacteristic
344C23×C11C2×#4111yescharacteristic
345C23×C11C2×#4111yescharacteristic
346C23×C11H(5,𝔽2)11yescharacteristic
347C23×C112−1+411yescharacteristic
348C23×C112−1+411yescharacteristic
349C23×C112−1+411yescharacteristic
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—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—41no—
391C2×C4×C11#11714yescomplemented
392C2×Dic11—232no—
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—22no—
418C2×Dic11—22no—
419C2×Dic11—22no—
420C2×Dic11—22no—
421C2×Dic11—22no—
422C2×Dic11—22no—
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×Dic11C4×D414yes—
447C2×Dic11C4×D414yes—
448C2×Dic11#12014yes—
449C24×C4—111no—
450C2×#117—224no—
451C2×#117—224no—
452C2×#117—224no—
453C22×C4⋊C4—111no—
454C22×C4⋊C4—111no—
455C22×C4⋊C4—111no—
456C22×C4⋊C4—111no—
457C22×C4⋊C4—111no—
458C22×C4⋊C4C2×D1111yescharacteristic
459C22×C22⋊C4—111no—
460C22×C22⋊C4—111no—
461C22×C22⋊C4—111no—
462C22×C22⋊C4C2×D1111yescharacteristic
463C22×C22⋊C4C2×D1111yescharacteristic
464C22×C22⋊C4C2×D1111yescharacteristic
465C22×C42—111no—
466C22×C42—111no—
467C22×C42—111no—
468C22×C42—111no—
469#388—224no—
470#387—224no—
471#385—118no—
472C4×C4⋊C4—224no—
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×#11711yescharacteristic
507C22×C11C2×C4×D411yescharacteristic
508C22×C11C2×C4×D411yescharacteristic
509C22×C11C2×C4×D411yescharacteristic
510C22×C11C4×#4111yescharacteristic
511C22×C11#51911yescharacteristic
512C22×C11#52011yescharacteristic
513C22×C11C2×#12011yescharacteristic
514C22×C11#52511yescharacteristic
515C22×C11#52511yescharacteristic
516C22×C11#52511yescharacteristic
517C22×C11#52511yescharacteristic
518C22×C11#52511yescharacteristic
519C22×C11#52911yescharacteristic
520C22×C11#52911yescharacteristic
521C22×C11#53611yescharacteristic
522C22×C11#53711yescharacteristic
523C22×C11#54111yescharacteristic
524C22×C11#54211yescharacteristic
525C22×C11#54611yescharacteristic
526C22×C11#54711yescharacteristic
527C22×C11#54711yescharacteristic
528C22×C11#54711yescharacteristic
529C22×C11#54711yescharacteristic
530C22×C11#54711yescharacteristic
531C22×C11#54811yescharacteristic
532C22×C11#55011yescharacteristic
533C22×C11#55111yescharacteristic
534C22×C11#55211yescharacteristic
535C22×C11#55211yescharacteristic
536C22×C11#55211yescharacteristic
537C22×C11#55211yescharacteristic
538C22×C11#55511yescharacteristic
539C22×C11#55611yescharacteristic
540C22×C11#55611yescharacteristic
541C4×C11—24no—
542C4×C11—42no—
543C4×C11—42no—
544C4×C11—42no—
545C4×C11—42no—
546C4×C11—81no—
547Dic11—24no—
548Dic11—24no—
549Dic11—24no—
550Dic11—42no—
551Dic11—42no—
552Dic11—42no—
553Dic11—42no—
554Dic11—81no—
555C25C22×D1111yescharacteristic
556C23×C4—111no—
557C23×C4—111no—
558C23×C4—111no—
559C23×C4—114no—
560C23×C4—111no—
561C23×C4—111no—
562C23×C4—111no—
563C23×C4—111no—
564C23×C4—111no—
565C23×C4—222no—
566C23×C4—222no—
567C23×C4—222no—
568C23×C4—222no—
569C23×C4—222no—
570C23×C4—222no—
571C23×C4C22×D1111yescharacteristic
572C23×C4C22×D1111yescharacteristic
573C23×C4C22×D1111yescharacteristic
574C23×C4C22×D1111yescharacteristic
575C23×C4C22×D1111yescharacteristic
576C23×C4C22×D1111yescharacteristic
577#117—2232no—
578C2×C4⋊C4—22no—
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—114no—
582C2×C4⋊C4—114no—
583C2×C4⋊C4—114no—
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—222no—
594C2×C4⋊C4—222no—
595C2×C4⋊C4—441no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—22no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—22no—
602C2×C22⋊C4—22no—
603C2×C22⋊C4—41no—
604C2×C22⋊C4—114no—
605C2×C22⋊C4—114no—
606C2×C22⋊C4—222no—
607C2×C22⋊C4—222no—
608C2×C22⋊C4—222no—
609C2×C22⋊C4—222no—
610C2×C22⋊C4—222no—
611C2×C22⋊C4—222no—
612C2×C22⋊C4—441no—
613C2×C22⋊C4C4×D1114yes—
614C2×C42—114no—
615C2×C42—222no—
616C2×C42—222no—
617C2×C42—222no—
618C2×C42—222no—
619C2×C42—222no—
620C2×C42—222no—
621C2×C42—222no—
622C2×C42—222no—
623C2×C42—222no—
624C2×C42—222no—
625C2×C42—222no—
626#95—22no—
627#95—22no—
628#95—41no—
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—222no—
639#95—222no—
640#95—222no—
641#95—222no—
642#95—441no—
643#95—441no—
644C2×C11—44no—
645C2×C11#229011yescharacteristic
646C2×C11C4×#12011yescharacteristic
647C2×C11#232311yescharacteristic
648C2×C11#234411yescharacteristic
649C2×C11#235411yescharacteristic
650C2×C11#235911yescharacteristic
651C2×C11#236211yescharacteristic
652C2×C11#240611yescharacteristic
653C2×C11#240711yescharacteristic
654C2×C11#247411yescharacteristic
655C2×C11#247511yescharacteristic
656C2×C11#247811yescharacteristic
657C2×C11#247911yescharacteristic
658C2×C11#259911yescharacteristic
659C2×C11#260911yescharacteristic
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24C2×C4×D1112yes—
673C24D4×D1112yes—
674C24#434312yes—
675C24C23×D1111yescharacteristic
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—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—112no—
723C22×C4—112no—
724C22×C4—228no—
725C22×C4—228no—
726C22×C4—228no—
727C22×C4—228no—
728C22×C4—228no—
729C22×C4—228no—
730C22×C4—228no—
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—221no—
774C22×C4C2×C4×D1112yes—
775C22×C4C2×C4×D1112yes—
776C22×C4D4×D1112yes—
777C22×C4D4×D1112yes—
778C22×C4#434112yes—
779C22×C4#434112yes—
780C22×C4#434112yes—
781C4⋊C4—28no—
782C4⋊C4—228no—
783C4⋊C4—228no—
784C4⋊C4—228no—
785C4⋊C4—228no—
786C4⋊C4—444no—
787C22⋊C4—28no—
788C22⋊C4—28no—
789C22⋊C4—44no—
790C22⋊C4—228no—
791C22⋊C4—228no—
792C22⋊C4—444no—
793C42—228no—
794C42—228no—
795C42—228no—
796C42—444no—
797C11#1406311yescharacteristic, complemented, Sylow
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—22no—
815C23—22no—
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—
830C23—41no—
831C23—41no—
832C23#6694614yes—
833C23C22×C4×D1111yescharacteristic
834C23C2×D4×D1111yescharacteristic
835C23C2×D4×D1111yescharacteristic
836C23C2×D4×D1111yescharacteristic
837C23C2×#434111yescharacteristic
838C23C2×#434111yescharacteristic
839C23C2×#434111yescharacteristic
840C23#6703711yescharacteristic
841C23C2×#434311yescharacteristic
842C23#41×D1111yescharacteristic
843C23#41×D1111yescharacteristic
844C23#41×D1111yescharacteristic
845C23#6704311yescharacteristic
846C23#6704311yescharacteristic
847C23#6704311yescharacteristic
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—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—41no—
888C2×C4—41no—
889C2×C4—114no—
890C2×C4—114no—
891C2×C4—114no—
892C2×C4—2232no—
893C2×C4—222no—
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—222no—
919C2×C4—222no—
920C2×C4—222no—
921C2×C4—222no—
922C2×C4—222no—
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#6693014yescomplemented
947C22—24no—
948C22—24no—
949C22—24no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22C2×#6693011yescharacteristic
963C22C2×#6694611yescharacteristic
964C22#1062304711yescharacteristic
965C22C4×#434111yescharacteristic
966C22C4×D4×D1111yescharacteristic
967C22C4×D4×D1111yescharacteristic
968C22#1062307711yescharacteristic
969C22#1062311711yescharacteristic
970C22D11×#12011yescharacteristic
971C22#1062312211yescharacteristic
972C22#1062312811yescharacteristic
973C22#1062312911yescharacteristic
974C22#1062313111yescharacteristic
975C22#1062313711yescharacteristic
976C22#1062314211yescharacteristic
977C22#1062314211yescharacteristic
978C22#1062314211yescharacteristic
979C22#1062314711yescharacteristic
980C22#1062315811yescharacteristic
981C22#1062315811yescharacteristic
982C22#1062316811yescharacteristic
983C22#1062317311yescharacteristic
984C22#1062317311yescharacteristic
985C22#1062317311yescharacteristic
986C22#1062318011yescharacteristic
987C22#1062318611yescharacteristic
988C22#1062318611yescharacteristic
989C22#1062318711yescharacteristic
990C22#1062319311yescharacteristic
991C22#1062320211yescharacteristic
992C22#1062320211yescharacteristic
993C22#1062320611yescharacteristic
994C22#1062323211yescharacteristic
995C22#1062323911yescharacteristic
996C22#1062324911yescharacteristic
997C4—24no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—42no—
1002C4—81no—
1003C4—224no—
1004C4—224no—
1005C4—224no—
1006C4—442no—
1007C4—442no—
1008C4—442no—
1009C4—442no—
1010C4—881no—
1011C2—44no—
1012C2#1307105611yescharacteristic
1013C2#1307111711yescharacteristic
1014C2#1307129111yescharacteristic
1015C2#1307148711yescharacteristic
1016C2#1307156411yescharacteristic
1017C2#1307160611yescharacteristic
1018C2#1307164611yescharacteristic
1019C2#1307194611yescharacteristic
1020C2#1307195411yescharacteristic
1021C2#1307276711yescharacteristic
1022C2#1307279011yescharacteristic
1023C2#1307282711yescharacteristic
1024C2#1307285011yescharacteristic
1025C2#1307418611yescharacteristic
1026C2#1307428911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenter#1439D11
hypocenterC11#14063
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
3. C2×#10622267C2semidirect
5. C2×C4⋊C4×Dic11C2semidirect
6. #13066879C2semidirect
7. #13066868C2semidirect
10. #13066850C2semidirect
11. #13066847C2semidirect
12. #13066847C2semidirect
13. #13066842C2semidirect
55. #10622563C4semidirect
391. C2×C4×C11#117semidirect
797. C11#14063semidirect
946. C2×C4#66930semidirect

Maximal subgroups

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

subgroupindex
C22×#669302
C2×#106225582
C2×#106222672
C2×#106225632
C2×C4⋊C4×Dic112
#130668792
#130668682
#130668632
#130668532
#130668502
#130668472
#130668422
#130668382
C11×#14392
#1406311