Finite Group Databasebeta

← #14676781

Subgroups — #14676781

Order 2816.

1746 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622268C211yesmaximal, characteristic, complemented
2C2×#10622823C211yesmaximal, characteristic
3C2×#10622825C211yesmaximal, characteristic
4C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
5#13066880C211yesmaximal, characteristic, complemented
6#13066870C211yesmaximal, characteristic, complemented
7#13066859C211yesmaximal, characteristic
8#13066859C211yesmaximal, characteristic
9#13066853C211yesmaximal, characteristic
10#13066853C211yesmaximal, characteristic
11#13066850C211yesmaximal, characteristic, complemented
12#13066849C211yesmaximal, characteristic, complemented
13#13066849C211yesmaximal, characteristic, complemented
14#13066843C211yesmaximal, characteristic, complemented
15C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
16C24×C4×C11C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
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×Dic11⋊C4C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C4×C11×C22⋊C4—24no—
34C2×C11×#95C2211yescharacteristic
35C2×C11×#95C2211yescharacteristic
36#10622825—24no—
37#10622823C418yescomplemented
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×Dic11⋊C4—24no—
55#10622268—24no—
56C25×C11C2311yescharacteristic
57C23×C4×C11—22no—
58C23×C4×C11—22no—
59C23×C4×C11—22no—
60C23×C4×C11—22no—
61C23×C4×C11—41no—
62C23×C4×C11—41no—
63C23×C4×C11C2×C414yes—
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4Q814yes—
84C2×C42×C11—22no—
85C2×C42×C11—22no—
86C2×C42×C11—22no—
87C2×C42×C11—22no—
88C2×C42×C11—41no—
89C2×C42×C11—41no—
90C2×C22⋊Dic11—22no—
91C2×C22⋊Dic11—22no—
92C2×C22⋊Dic11—22no—
93C2×C22⋊Dic11—22no—
94C2×C22⋊Dic11—22no—
95C2×C22⋊Dic11—22no—
96C2×C22⋊Dic11—41no—
97C2×C22⋊Dic11—41no—
98C2×C22⋊Dic11—41no—
99C2×C22⋊Dic11—41no—
100C2×C22⋊Dic11C2×C414yes—
101C2×C22⋊Dic11C2×C414yes—
102C2×C4⋊Dic11—22no—
103C2×C4⋊Dic11—22no—
104C2×C4⋊Dic11—22no—
105C2×C4⋊Dic11—22no—
106C2×C4⋊Dic11—41no—
107C2×C4⋊Dic11—41no—
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—22no—
116C2×Dic11⋊C4—41no—
117C2×Dic11⋊C4—41no—
118C2×Dic11⋊C4C2×C414yes—
119C2×Dic11⋊C4C2×C414yes—
120C2×C4×Dic11—22no—
121C2×C4×Dic11—22no—
122C2×C4×Dic11—22no—
123C2×C4×Dic11—22no—
124C2×C4×Dic11—22no—
125C2×C4×Dic11—41no—
126C11×#95—22no—
127C11×#95D414yes—
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—41no—
137C11⋊#95—41no—
138C11⋊#95—41no—
139C11⋊#95—41no—
140C11⋊#95—41no—
141C11⋊#95C2×C414yes—
142C11⋊#95C2×C414yes—
143C11⋊#95D414yes—
144#13987—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—28no—
192C22×C4×C11—28no—
193C22×C4×C11—44no—
194C22×C4×C11—44no—
195C22×C4×C11—44no—
196C22×C4×C11—44no—
197C22×C4×C11—44no—
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×C11C2×Q812yes—
205C22×C4×C11C2×Q812yes—
206C22×C4×C11#4112yes—
207C22×C4×C11#4112yes—
208C22×C4×C11#4112yes—
209C22×C4×C11#4112yes—
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—21no—
252C22×Dic11—21no—
253C22×Dic11—21no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11—21no—
258C22×Dic11C22×C412yes—
259C22×Dic11C22×C412yes—
260C22×Dic11C22×C412yes—
261C22×Dic11C22×C412yes—
262C22×Dic11C2×D412yes—
263C22×Dic11C2×D412yes—
264C22×Dic11#4112yes—
265C22×Dic11#4112yes—
266C11×C22⋊C4—28no—
267C11×C22⋊C4—28no—
268C42×C11—44no—
269C42×C11—44no—
270C22⋊Dic11—28no—
271C22⋊Dic11—44no—
272C22⋊Dic11—44no—
273C22⋊Dic11—44no—
274C4⋊Dic11—44no—
275C4⋊Dic11—44no—
276Dic11⋊C4—28no—
277Dic11⋊C4—28no—
278Dic11⋊C4—28no—
279Dic11⋊C4—44no—
280C4×Dic11—28no—
281C4×Dic11—44no—
282C2×#387—111no—
283C2×#385—111no—
284C2×#380—111no—
285C2×C4×C4⋊C4—111no—
286C2×C4×C22⋊C4D1111yescharacteristic
287#1444—111no—
288#1441—111no—
289#1439—111no—
290#1439—111no—
291#1437—111no—
292#1437—111no—
293#1436—111no—
294#1436—111no—
295#1436—111no—
296#1434—111no—
297C23×C11—22no—
298C23×C11—22no—
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—41no—
316C23×C11—41no—
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×C11C4×Q814yes—
332C23×C11C23×C411yescharacteristic
333C23×C11C22×D411yescharacteristic
334C23×C11C22×D411yescharacteristic
335C23×C11C22×Q811yescharacteristic
336C23×C11C2×#4111yescharacteristic
337C23×C11C2×#4111yescharacteristic
338C23×C11C2×#4111yescharacteristic
339C23×C11C2×#4111yescharacteristic
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×C112−1+411yescharacteristic
347C2×C4×C11—22no—
348C2×C4×C11—22no—
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—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—416no—
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×C11C4×D414yes—
388C2×C4×C11C4×D414yes—
389C2×C4×C11C22⋊Q814yes—
390C2×Dic11—22no—
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—22no—
410C2×Dic11—22no—
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—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#11714yes—
446C24×C4C2×D1111yescharacteristic
447C22×C4⋊C4—111no—
448C22×C4⋊C4—111no—
449C22×C4⋊C4—111no—
450C22×C4⋊C4—111no—
451C22×C4⋊C4—111no—
452C22×C4⋊C4—111no—
453C22×C22⋊C4—111no—
454C22×C22⋊C4—111no—
455C22×C22⋊C4—111no—
456C22×C22⋊C4—111no—
457C22×C22⋊C4C2×D1111yescharacteristic
458C22×C22⋊C4C2×D1111yescharacteristic
459C22×C42—111no—
460C22×C42—111no—
461C22×C42C2×D1111yescharacteristic
462C22×C42C2×D1111yescharacteristic
463#387—224no—
464#385—118no—
465#380—224no—
466C4×C4⋊C4—224no—
467C4×C22⋊C4—24no—
468C2×#95—111no—
469C2×#95—111no—
470C2×#95—111no—
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×#95C2×D1111yescharacteristic
485C2×#95C2×D1111yescharacteristic
486C22×C11—24no—
487C22×C11—24no—
488C22×C11—24no—
489C22×C11—42no—
490C22×C11—42no—
491C22×C11—42no—
492C22×C11—42no—
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×C11C2×#11711yescharacteristic
502C22×C11C2×C4×D411yescharacteristic
503C22×C11C2×C4×D411yescharacteristic
504C22×C11C2×C4×Q811yescharacteristic
505C22×C11C4×#4111yescharacteristic
506C22×C11#51811yescharacteristic
507C22×C11#52011yescharacteristic
508C22×C11C2×C22⋊Q811yescharacteristic
509C22×C11#52511yescharacteristic
510C22×C11#52511yescharacteristic
511C22×C11#52511yescharacteristic
512C22×C11#52911yescharacteristic
513C22×C11#52911yescharacteristic
514C22×C11#52911yescharacteristic
515C22×C11#53311yescharacteristic
516C22×C11#53811yescharacteristic
517C22×C11#53911yescharacteristic
518C22×C11#54011yescharacteristic
519C22×C11#54211yescharacteristic
520C22×C11D4211yescharacteristic
521C22×C11#54611yescharacteristic
522C22×C11#54611yescharacteristic
523C22×C11#54611yescharacteristic
524C22×C11#54711yescharacteristic
525C22×C11D4×Q811yescharacteristic
526C22×C11#55011yescharacteristic
527C22×C11#55111yescharacteristic
528C22×C11#55211yescharacteristic
529C22×C11#55311yescharacteristic
530C22×C11#55311yescharacteristic
531C22×C11#55411yescharacteristic
532C22×C11#55411yescharacteristic
533C22×C11#55411yescharacteristic
534C22×C11#55511yescharacteristic
535C22×C11#55611yescharacteristic
536C4×C11—24no—
537C4×C11—24no—
538C4×C11—24no—
539C4×C11—42no—
540C4×C11—42no—
541C4×C11—42no—
542Dic11—24no—
543Dic11—42no—
544Dic11—42no—
545Dic11—42no—
546Dic11—42no—
547Dic11—42no—
548Dic11—81no—
549Dic11—81no—
550C25C22×D1111yescharacteristic
551C23×C4—22no—
552C23×C4—22no—
553C23×C4—22no—
554C23×C4—22no—
555C23×C4—41no—
556C23×C4—41no—
557C23×C4—111no—
558C23×C4—111no—
559C23×C4—111no—
560C23×C4—111no—
561C23×C4—111no—
562C23×C4—111no—
563C23×C4—111no—
564C23×C4—111no—
565C23×C4C4×D1114yes—
566C23×C4C22×D1111yescharacteristic
567C23×C4C22×D1111yescharacteristic
568C23×C4C22×D1111yescharacteristic
569C23×C4C22×D1111yescharacteristic
570C23×C4C22×D1111yescharacteristic
571C23×C4C22×D1111yescharacteristic
572C2×C4⋊C4—114no—
573C2×C4⋊C4—114no—
574C2×C4⋊C4—222no—
575C2×C4⋊C4—222no—
576C2×C4⋊C4—222no—
577C2×C4⋊C4—222no—
578C2×C4⋊C4—222no—
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—441no—
587C2×C4⋊C4—441no—
588C2×C4⋊C4—441no—
589C2×C4⋊C4—441no—
590C2×C22⋊C4—22no—
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
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—441no—
604C2×C22⋊C4—441no—
605C2×C22⋊C4—441no—
606C2×C22⋊C4—441no—
607C2×C22⋊C4Dic2214yes—
608C2×C42—22no—
609C2×C42—22no—
610C2×C42—22no—
611C2×C42—22no—
612C2×C42—41no—
613C2×C42—41no—
614C2×C42—222no—
615C2×C42—222no—
616C2×C42—222no—
617C2×C42—222no—
618C2×C42—222no—
619C2×C42—441no—
620#95—22no—
621#95—114no—
622#95—114no—
623#95—114no—
624#95—222no—
625#95—222no—
626#95—222no—
627#95—222no—
628#95—222no—
629#95—222no—
630#95—222no—
631#95—222no—
632#95—441no—
633#95—441no—
634#95—441no—
635#95—441no—
636#95—441no—
637#95C22⋊D1114yes—
638C2×C11—44no—
639C2×C11#229011yescharacteristic
640C2×C11C4×C22⋊Q811yescharacteristic
641C2×C11#233511yescharacteristic
642C2×C11#234511yescharacteristic
643C2×C11#235411yescharacteristic
644C2×C11#235811yescharacteristic
645C2×C11#236011yescharacteristic
646C2×C11#244911yescharacteristic
647C2×C11#245411yescharacteristic
648C2×C11#245611yescharacteristic
649C2×C11#246511yescharacteristic
650C2×C11#246811yescharacteristic
651C2×C11#247611yescharacteristic
652C2×C11#257411yescharacteristic
653C2×C11#257711yescharacteristic
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24C2×Dic2212yes—
667C24C2×C4×D1112yes—
668C24#433912yes—
669C24C23×D1111yescharacteristic
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
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—28no—
701C22×C4—28no—
702C22×C4—44no—
703C22×C4—44no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—112no—
708C22×C4—112no—
709C22×C4—112no—
710C22×C4—112no—
711C22×C4—112no—
712C22×C4—112no—
713C22×C4—112no—
714C22×C4—112no—
715C22×C4—221no—
716C22×C4—221no—
717C22×C4—221no—
718C22×C4—221no—
719C22×C4—221no—
720C22×C4—221no—
721C22×C4—221no—
722C22×C4—221no—
723C22×C4—221no—
724C22×C4—221no—
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×C4C2×Dic2212yes—
764C22×C4C2×Dic2212yes—
765C22×C4C2×C4×D1112yes—
766C22×C4C2×C4×D1112yes—
767C22×C4#433912yes—
768C22×C4#433912yes—
769C22×C4#433912yes—
770C22×C4D4×D1112yes—
771C22×C4#434112yes—
772C22×C4C2×C22⋊D1112yes—
773C22×C4C2×C22⋊D1112yes—
774C22×C4C2×C22⋊D1112yes—
775C4⋊C4—228no—
776C4⋊C4—228no—
777C4⋊C4—228no—
778C4⋊C4—444no—
779C4⋊C4—444no—
780C4⋊C4—444no—
781C22⋊C4—28no—
782C22⋊C4—28no—
783C22⋊C4—228no—
784C22⋊C4—444no—
785C22⋊C4—444no—
786C22⋊C4—444no—
787C42—44no—
788C42—44no—
789C42—228no—
790C42—444no—
791C11#1398711yescharacteristic, complemented, Sylow
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
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—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C4×Dic2214yes—
827C23C22×Dic2211yescharacteristic
828C23C22×C4×D1111yescharacteristic
829C23C2×#433911yescharacteristic
830C23C2×#433911yescharacteristic
831C23C2×#433911yescharacteristic
832C23C2×#433911yescharacteristic
833C23C2×D4×D1111yescharacteristic
834C23C2×#434111yescharacteristic
835C23#6703711yescharacteristic
836C23#6703711yescharacteristic
837C23#41×D1111yescharacteristic
838C23#41×D1111yescharacteristic
839C23#6704211yescharacteristic
840C23#6704311yescharacteristic
841C23C22×C22⋊D1111yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
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—22no—
868C2×C4—22no—
869C2×C4—416no—
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—114no—
883C2×C4—222no—
884C2×C4—222no—
885C2×C4—222no—
886C2×C4—222no—
887C2×C4—222no—
888C2×C4—222no—
889C2×C4—222no—
890C2×C4—222no—
891C2×C4—222no—
892C2×C4—222no—
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—441no—
905C2×C4—441no—
906C2×C4—441no—
907C2×C4—441no—
908C2×C4—441no—
909C2×C4—441no—
910C2×C4—441no—
911C2×C4—441no—
912C2×C4—441no—
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(C22⋊D11)⋊C414yes—
939C2×C4#6697714yes—
940C2×C4C4×C22⋊D1114yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C2×C4×Dic2211yescharacteristic
957C22#1062300111yescharacteristic
958C22C4×#433911yescharacteristic
959C22#1062301011yescharacteristic
960C22C2×(C22⋊D11)⋊C411yescharacteristic
961C22#1062301711yescharacteristic
962C22#1062302111yescharacteristic
963C22#1062302611yescharacteristic
964C22D11×#11711yescharacteristic
965C22#1062305411yescharacteristic
966C22#1062306311yescharacteristic
967C22#1062306411yescharacteristic
968C22D4×Dic2211yescharacteristic
969C22#1062307011yescharacteristic
970C22#1062307011yescharacteristic
971C22#1062307111yescharacteristic
972C22#1062307111yescharacteristic
973C22#1062307211yescharacteristic
974C22#1062307411yescharacteristic
975C22#1062307811yescharacteristic
976C22#1062307811yescharacteristic
977C22#1062308111yescharacteristic
978C22#1062308811yescharacteristic
979C22#1062308811yescharacteristic
980C22#1062309111yescharacteristic
981C22#1062309211yescharacteristic
982C22#1062309311yescharacteristic
983C22#1062309511yescharacteristic
984C22C2×#6697711yescharacteristic
985C22C2×C4×C22⋊D1111yescharacteristic
986C22#1062332211yescharacteristic
987C22D4×C22⋊D1111yescharacteristic
988C22#1062333711yescharacteristic
989C22#1062335511yescharacteristic
990C22#1062336511yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—224no—
998C4—442no—
999C4—442no—
1000C4—442no—
1001C4—442no—
1002C4—442no—
1003C4—881no—
1004C4—881no—
1005C2—44no—
1006C2#1307106211yescharacteristic
1007C2C4×#6697711yescharacteristic
1008C2#1307140611yescharacteristic
1009C2#1307149411yescharacteristic
1010C2#1307156611yescharacteristic
1011C2#1307159511yescharacteristic
1012C2#1307161911yescharacteristic
1013C2#1307241911yescharacteristic
1014C2#1307248211yescharacteristic
1015C2#1307250211yescharacteristic
1016C2#1307263711yescharacteristic
1017C2#1307267611yescharacteristic
1018C2#1307280211yescharacteristic
1019C2#1307389011yescharacteristic
1020C2#1307393511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C4×C11×C22⋊C4C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#13987
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10622268C2semidirect
4. C2×C4×Dic11⋊C4C2semidirect
5. #13066880C2semidirect
6. #13066870C2semidirect
11. #13066850C2semidirect
12. #13066849C2semidirect
13. #13066849C2semidirect
14. #13066843C2semidirect
37. #10622823C4semidirect
791. C11#13987semidirect

Maximal subgroups

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

subgroupindex
C2×#106222682
C2×#106228232
C2×#106228252
C2×C4×Dic11⋊C42
#130668802
#130668702
#130668592
#130668532
#130668502
#130668492
#130668432
C2×C4×C11×C22⋊C42
#1398711