Finite Group Databasebeta

← #14769099

Subgroups — #14769099

Order 2816.

1668 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623360C211yesmaximal, characteristic
2C2×#10622853C211yesmaximal, characteristic, complemented
3C2×D11×#99C211yesmaximal, characteristic, complemented
4#13071458C212yesmaximal, complemented
5#13069450C212yesmaximal, complemented
6#13069072C212yesmaximal, complemented
7#13069066C212yesmaximal, complemented
8#13068602C211yesmaximal, characteristic, complemented
9#13068529C211yesmaximal, characteristic, complemented
10#99×Dic11C211yesmaximal, characteristic, complemented
11C11×#1782C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C22×D4×D11C2211yescharacteristic
14#10623360—22no—
15#10623360—22no—
16#10623360—22no—
17#10623360—22no—
18C2×#67000C411yescharacteristic, complemented
19C2×#66999C411yescharacteristic, complemented
20C2×#66992C411yescharacteristic, complemented
21C2×#66992C2211yescharacteristic
22C2×#66990C411yescharacteristic, complemented
23C2×#66990C2211yescharacteristic
24C2×D4×Dic11C2211yescharacteristic
25C2×#66983C411yescharacteristic, complemented
26C2×#66982C411yescharacteristic, complemented
27C2×#66982C2211yescharacteristic
28C2×C4×C22⋊D11C411yescharacteristic, complemented
29C22×(C2×D11)⋊C4C411yescharacteristic, complemented
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C2×#66979C2212yescomplemented
32C2×C22⋊C4×D11C2212yes—
33C2×C11×#99C2211yescharacteristic
34C2×C11×#99C2211yescharacteristic
35C2×C11×#99C2212yescomplemented
36C11×#381C2212yescomplemented
37#10622853—24no—
38C2×#66898C2211yescharacteristic
39C2×#66898C2211yescharacteristic
40C2×#66898C2212yescomplemented
41#10622568C2212yes—
42C2×#66870C2212yes—
43C2×#66870C2212yes—
44#10622555C2212yescomplemented
45C22⋊C4×Dic11C2212yescomplemented
46D11×#99—24no—
47#10622283—22no—
48#10622282—22no—
49#10622281—22no—
50#10622279—22no—
51#10622165C2212yescomplemented
52#10622165C2212yescomplemented
53C24×D11C2×C411yescharacteristic
54C24×D11C2311yescharacteristic
55C2×C11×#41—22no—
56C2×C11×#41—22no—
57C2×C11×#41—22no—
58C2×C11×#41—22no—
59C2×C11×#41—42no—
60C22×Q8×C11C2×C411yescharacteristic, complemented
61C22×D4×C11C2×C411yescharacteristic, complemented
62C22×D4×C11C2311yescharacteristic
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11C2×C411yescharacteristic, complemented
65C23×C4×C11C2×C411yescharacteristic, complemented
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11C2×C411yescharacteristic
68C22×C22⋊D11C2×C411yescharacteristic
69C22×C22⋊D11C2×C411yescharacteristic
70C22×C22⋊D11C2×C411yescharacteristic, complemented
71C22×C22⋊D11C2311yescharacteristic
72C23×Dic11C2×C411yescharacteristic, complemented
73C23×Dic11C2311yescharacteristic
74C2×D4×D11—22no—
75C2×D4×D11—22no—
76C2×D4×D11—22no—
77C2×D4×D11—22no—
78C2×D4×D11—42no—
79C22×D44C2×C411yescharacteristic
80C22×C4×D11—22no—
81C22×C4×D11C2×C411yescharacteristic
82C2×C11×C22⋊C4C2312yes—
83C2×C11×C22⋊C4C2312yes—
84C2×C22⋊Dic11C2×C411yescharacteristic, complemented
85C2×C22⋊Dic11C2×C411yescharacteristic, complemented
86C2×C22⋊Dic11C2312yes—
87C2×C22⋊Dic11C2311yescharacteristic
88C2×C22⋊Dic11C2312yes—
89#67000—22no—
90#67000—22no—
91#66999—22no—
92#66999—22no—
93#66992—22no—
94#66992—22no—
95#66992—22no—
96#66992—22no—
97#66990—22no—
98#66990—22no—
99#66990—22no—
100#66990—22no—
101D4×Dic11—22no—
102D4×Dic11—22no—
103#66983—22no—
104#66983—22no—
105#66982—22no—
106#66982—22no—
107#66982—22no—
108#66982—22no—
109C4×C22⋊D11—21no—
110C4×C22⋊D11—21no—
111C4×C22⋊D11—21no—
112C4×C22⋊D11—21no—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—22no—
118C2×(C2×D11)⋊C4—22no—
119C2×(C2×D11)⋊C4—22no—
120C2×(C2×D11)⋊C4C2×C411yescharacteristic
121C2×(C2×D11)⋊C4C2×C411yescharacteristic
122C2×(C2×D11)⋊C4C2×C411yescharacteristic
123C2×(C2×D11)⋊C4C2×C411yescharacteristic
124C2×(C2×D11)⋊C4C2×C411yescharacteristic
125C2×(C2×D11)⋊C4C2×C411yescharacteristic
126C2×(C2×D11)⋊C4C2×C411yescharacteristic, complemented
127C2×(C2×D11)⋊C4C2×C411yescharacteristic, complemented
128C2×(C2×D11)⋊C4C2×C411yescharacteristic, complemented
129C2×(C2×D11)⋊C4D412yes—
130C2×(C2×D11)⋊C4D412yes—
131C2×(C2×D11)⋊C4D412yes—
132C2×(C2×D11)⋊C4D412yes—
133#66979—24no—
134#66979—42no—
135C2×C4⋊Dic11—22no—
136C2×C4⋊Dic11C2×C411yescharacteristic, complemented
137C2×Dic11⋊C4—22no—
138C2×Dic11⋊C4C2×C411yescharacteristic, complemented
139C2×Dic11⋊C4C2×C411yescharacteristic, complemented
140C2×Dic11⋊C4C2×C411yescharacteristic, complemented
141C2×C4×Dic11—22no—
142C2×C4×Dic11—22no—
143C2×C4×Dic11C2×C411yescharacteristic, complemented
144C22⋊C4×D11—24no—
145C22⋊C4×D11—42no—
146C11×#99—22no—
147C11×#99—22no—
148C11×#99—42no—
149C11×#95—22no—
150C11×#95—22no—
151#66898—22no—
152#66898—24no—
153#66898D414yescomplemented
154C11⋊#95—22no—
155C11⋊#95—22no—
156#66870—24no—
157#66870—42no—
158#22405—111nomaximal, Sylow
159C24×C11C22×C411yescharacteristic
160C24×C11C22×C411yescharacteristic
161C24×C11C2411yescharacteristic
162C23×D11—21no—
163C23×D11—21no—
164C23×D11—22no—
165C23×D11—22no—
166C23×D11—21no—
167C23×D11—21no—
168C23×D11—42no—
169C23×D11—41no—
170C23×D11—42no—
171C23×D11—81no—
172C23×D11—81no—
173C23×D11C22×C411yescharacteristic
174C23×D11C22×C411yescharacteristic
175C23×D11C22×C411yescharacteristic
176C23×D11C2×D412yes—
177C23×D11C2×D412yes—
178C11×#41—44no—
179C11×#41—44no—
180C11×#41—44no—
181C11×#41—44no—
182C2×Q8×C11—22no—
183C2×Q8×C11—22no—
184C2×Q8×C11—41no—
185C2×D4×C11—22no—
186C2×D4×C11—22no—
187C2×D4×C11—22no—
188C2×D4×C11—21no—
189C2×D4×C11—22no—
190C2×D4×C11—21no—
191C2×D4×C11—22no—
192C2×D4×C11—22no—
193C2×D4×C11—41no—
194C2×D4×C11C2×D412yes—
195C2×D4×C11#4112yes—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—41no—
208C22×C4×C11—41no—
209C22×C4×C11C22×C411yescharacteristic
210C22×C4×C11C22×C411yescharacteristic
211C22×C4×C11C22×C411yescharacteristic
212C22×C4×C11C22×C411yescharacteristic
213C22×C4×C11C2×D412yes—
214C22×C4×C11C2×D412yes—
215C2×C22⋊D11—22no—
216C2×C22⋊D11—22no—
217C2×C22⋊D11—21no—
218C2×C22⋊D11—22no—
219C2×C22⋊D11—21no—
220C2×C22⋊D11—22no—
221C2×C22⋊D11—21no—
222C2×C22⋊D11—21no—
223C2×C22⋊D11—22no—
224C2×C22⋊D11—22no—
225C2×C22⋊D11—41no—
226C2×C22⋊D11—42no—
227C2×C22⋊D11—81no—
228C2×C22⋊D11—81no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11—22no—
232C22×Dic11—22no—
233C22×Dic11—81no—
234C22×Dic11—81no—
235C22×Dic11C22×C411yescharacteristic
236C22×Dic11C22×C411yescharacteristic
237C22×Dic11C22×C411yescharacteristic
238C22×Dic11C22×C411yescharacteristic
239C22×Dic11C22×C411yescharacteristic
240C22×Dic11C2×D412yes—
241C22×Dic11C2×D412yes—
242D4×D11—44no—
243D4×D11—44no—
244D4×D11—44no—
245D4×D11—44no—
246C2×D44—22no—
247C2×D44—22no—
248C2×D44—41no—
249C2×C4×D11—21no—
250C2×C4×D11—21no—
251C2×C4×D11—22no—
252C2×C4×D11—41no—
253C2×C4×D11—44no—
254C2×C4×D11—44no—
255C2×C4×D11—82no—
256C11×C22⋊C4—22no—
257C11×C22⋊C4—22no—
258C11×C22⋊C4—22no—
259C11×C22⋊C4—22no—
260C22⋊Dic11—21no—
261C22⋊Dic11—21no—
262C22⋊Dic11—22no—
263C22⋊Dic11—22no—
264C22⋊Dic11—22no—
265C22⋊Dic11—22no—
266C22⋊Dic11—22no—
267C22⋊Dic11C2×D414yes—
268(C2×D11)⋊C4—21no—
269(C2×D11)⋊C4—21no—
270(C2×D11)⋊C4—21no—
271(C2×D11)⋊C4—21no—
272(C2×D11)⋊C4—22no—
273(C2×D11)⋊C4—21no—
274(C2×D11)⋊C4—21no—
275(C2×D11)⋊C4—22no—
276(C2×D11)⋊C4—44no—
277(C2×D11)⋊C4—44no—
278(C2×D11)⋊C4—82no—
279(C2×D11)⋊C4C22⋊C411yescharacteristic
280(C2×D11)⋊C4C22⋊C411yescharacteristic
281(C2×D11)⋊C4C22⋊C411yescharacteristic
282(C2×D11)⋊C4C22⋊C411yescharacteristic
283(C2×D11)⋊C4C22⋊C412yes—
284(C2×D11)⋊C4C22⋊C412yes—
285(C2×D11)⋊C4C22⋊C412yes—
286(C2×D11)⋊C4C22⋊C412yes—
287(C2×D11)⋊C4C22⋊C412yes—
288(C2×D11)⋊C4C22⋊C412yes—
289C4⋊Dic11—22no—
290C4⋊Dic11—44no—
291Dic11⋊C4—22no—
292Dic11⋊C4—21no—
293Dic11⋊C4—21no—
294Dic11⋊C4—22no—
295Dic11⋊C4—82no—
296C4×Dic11—21no—
297C4×Dic11—21no—
298C4×Dic11—44no—
299C4×Dic11—82no—
300C2×#546—111no—
301C2×#410—111no—
302C22×#99—111no—
303#2342—112no—
304#1964—112no—
305#1899—112no—
306#1898—112no—
307#1799—111no—
308#1782D1111yescharacteristic, complemented
309#1781—111no—
310C4×#99—111no—
311C23×C11—21no—
312C23×C11—21no—
313C23×C11—21no—
314C23×C11—21no—
315C23×C11—21no—
316C23×C11—41no—
317C23×C11—41no—
318C23×C11—41no—
319C23×C11—41no—
320C23×C11—41no—
321C23×C11—41no—
322C23×C11C4×D412yes—
323C23×C11C23×C411yescharacteristic
324C23×C11C22×D412yes—
325C23×C11C22×D411yescharacteristic
326C23×C11C2×#4111yescharacteristic
327C23×C11H(5,𝔽2)12yes—
328C22×D11—21no—
329C22×D11—21no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—21no—
333C22×D11—21no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—24no—
337C22×D11—22no—
338C22×D11—21no—
339C22×D11—21no—
340C22×D11—21no—
341C22×D11—42no—
342C22×D11—41no—
343C22×D11—42no—
344C22×D11—41no—
345C22×D11—41no—
346C22×D11—42no—
347C22×D11—42no—
348C22×D11—42no—
349C22×D11—42no—
350C22×D11—42no—
351C22×D11—41no—
352C22×D11—41no—
353C22×D11—81no—
354C22×D11—81no—
355C22×D11—82no—
356C22×D11—84no—
357C22×D11—82no—
358C22×D11—84no—
359C22×D11—84no—
360C22×D11C2×C22⋊C411yescharacteristic
361C22×D11C2×C22⋊C412yes—
362C22×D11C2×C22⋊C411yescharacteristic
363Q8×C11—44no—
364D4×C11—24no—
365D4×C11—24no—
366D4×C11—44no—
367D4×C11—42no—
368D4×C11—42no—
369C2×C4×C11—21no—
370C2×C4×C11—21no—
371C2×C4×C11—21no—
372C2×C4×C11—21no—
373C2×C4×C11—21no—
374C2×C4×C11—21no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—21no—
380C2×C4×C11—21no—
381C2×C4×C11—21no—
382C2×C4×C11—42no—
383C2×C4×C11—42no—
384C2×C4×C11—42no—
385C2×C4×C11—42no—
386C2×C4×C11—42no—
387C2×C4×C11—42no—
388C2×C4×C11—42no—
389C2×C4×C11—42no—
390C2×C4×C11—42no—
391C2×C4×C11—42no—
392C2×C4×C11C2×C22⋊C411yescharacteristic
393C2×C4×C11C2×C22⋊C411yescharacteristic
394C2×C4×C11C2×C22⋊C412yes—
395C2×C4×C11C4×D412yes—
396C22⋊D11—44no—
397C22⋊D11—42no—
398C22⋊D11—42no—
399C22⋊D11—42no—
400C22⋊D11—42no—
401C22⋊D11—82no—
402C22⋊D11—82no—
403C2×Dic11—21no—
404C2×Dic11—21no—
405C2×Dic11—21no—
406C2×Dic11—21no—
407C2×Dic11—21no—
408C2×Dic11—24no—
409C2×Dic11—42no—
410C2×Dic11—42no—
411C2×Dic11—41no—
412C2×Dic11—41no—
413C2×Dic11—42no—
414C2×Dic11—42no—
415C2×Dic11—41no—
416C2×Dic11—41no—
417C2×Dic11—42no—
418C2×Dic11—42no—
419C2×Dic11—42no—
420C2×Dic11—81no—
421C2×Dic11—81no—
422C2×Dic11C2×C22⋊C411yescharacteristic
423C2×Dic11C2×C22⋊C411yescharacteristic
424C2×Dic11C2×C22⋊C412yes—
425D44—44no—
426C4×D11—42no—
427C4×D11—42no—
428C4×D11—88no—
429C22×#41C2×D1111yescharacteristic
430C23×D4—111no—
431#546—222no—
432#546—222no—
433#546—222no—
434#546—222no—
435C2×#124—111no—
436C2×#123—111no—
437C2×#123—111no—
438C2×C22⋊Q8—111no—
439C2×#121—111no—
440C2×#121—111no—
441C2×#121—111no—
442C2×#120—111no—
443C2×#120—111no—
444C2×C4×D4—111no—
445C2×C4×D4—111no—
446C2×#117—112no—
447C22×C22⋊C4—111no—
448C22×C22⋊C4—111no—
449C22×C22⋊C4—112no—
450#410—224no—
451C2×#99—111no—
452C2×#99—111no—
453C2×#99—112no—
454C2×#99—112no—
455C2×#99—112no—
456C2×#99—224no—
457C2×#99C2×D1111yescharacteristic
458C2×#99C2×D1111yescharacteristic
459C2×#99C2×D1112yescomplemented
460#388—222no—
461#388—222no—
462#385—222no—
463#381C2×D1112yescomplemented
464#380—112no—
465#379—112no—
466C4×C22⋊C4—112no—
467C4×C22⋊C4—222no—
468#342—112no—
469#342—112no—
470C22×C11—22no—
471C22×C11—21no—
472C22×C11—22no—
473C22×C11—21no—
474C22×C11—22no—
475C22×C11—41no—
476C22×C11—41no—
477C22×C11—42no—
478C22×C11—42no—
479C22×C11—42no—
480C22×C11—41no—
481C22×C11—41no—
482C22×C11—41no—
483C22×C11—41no—
484C22×C11—41no—
485C22×C11—81no—
486C22×C11—81no—
487C22×C11C22×C22⋊C411yescharacteristic
488C22×C11C2×C4×D411yescharacteristic
489C22×C11#51811yescharacteristic
490C22×C11D4212yes—
491C22×C11#54612yes—
492C2×D11—21no—
493C2×D11—21no—
494C2×D11—21no—
495C2×D11—22no—
496C2×D11—21no—
497C2×D11—22no—
498C2×D11—21no—
499C2×D11—22no—
500C2×D11—44no—
501C2×D11—42no—
502C2×D11—42no—
503C2×D11—44no—
504C2×D11—41no—
505C2×D11—41no—
506C2×D11—41no—
507C2×D11—84no—
508C2×D11—81no—
509C2×D11—81no—
510C2×D11—82no—
511C2×D11—82no—
512C2×D11—84no—
513C2×D11—81no—
514C2×D11—81no—
515C2×D11#41012yescomplemented
516C4×C11—21no—
517C4×C11—21no—
518C4×C11—22no—
519C4×C11—22no—
520C4×C11—41no—
521C4×C11—82no—
522C4×C11—82no—
523Dic11—21no—
524Dic11—21no—
525Dic11—22no—
526Dic11—44no—
527Dic11—41no—
528Dic11—41no—
529Dic11—41no—
530Dic11—82no—
531C25—111no—
532C25—111no—
533C2×#41—22no—
534C2×#41—22no—
535C2×#41—22no—
536C2×#41—22no—
537C2×#41—42no—
538C22×Q8C4×D1111yescharacteristic, complemented
539C22×D4—111no—
540C22×D4—111no—
541C22×D4—111no—
542C22×D4—111no—
543C22×D4—111no—
544C22×D4—111no—
545C22×D4—222no—
546C22×D4—222no—
547C22×D4—222no—
548C22×D4—222no—
549C22×D4—442no—
550C22×D4C4×D1111yescharacteristic, complemented
551C22×D4C22×D1111yescharacteristic
552C22×D4C22×D1111yescharacteristic
553C23×C4—111no—
554C23×C4—111no—
555C23×C4—111no—
556C23×C4—222no—
557C23×C4C4×D1111yescharacteristic, complemented
558C23×C4C4×D1111yescharacteristic, complemented
559C23×C4C22×D1111yescharacteristic
560#124—222no—
561#124—222no—
562#123—222no—
563#123—222no—
564#123—222no—
565#123—222no—
566C22⋊Q8—222no—
567C22⋊Q8—222no—
568#121—222no—
569#121—222no—
570#121—222no—
571#121—222no—
572#121—222no—
573#121—222no—
574#120—222no—
575#120—222no—
576#120—222no—
577#120—222no—
578C4×D4—221no—
579C4×D4—221no—
580C4×D4—221no—
581C4×D4—221no—
582C4×D4—222no—
583C4×D4—222no—
584#117—224no—
585#117—442no—
586C2×C4⋊C4—111no—
587C2×C4⋊C4—111no—
588C2×C4⋊C4—111no—
589C2×C4⋊C4—111no—
590C2×C4⋊C4—222no—
591C2×C4⋊C4—222no—
592C2×C22⋊C4—111no—
593C2×C22⋊C4—111no—
594C2×C22⋊C4—111no—
595C2×C22⋊C4—111no—
596C2×C22⋊C4—112no—
597C2×C22⋊C4—112no—
598C2×C22⋊C4—112no—
599C2×C22⋊C4—112no—
600C2×C22⋊C4—112no—
601C2×C22⋊C4—111no—
602C2×C22⋊C4—111no—
603C2×C22⋊C4—111no—
604C2×C22⋊C4—111no—
605C2×C22⋊C4—111no—
606C2×C22⋊C4—111no—
607C2×C22⋊C4—111no—
608C2×C22⋊C4—111no—
609C2×C22⋊C4—112no—
610C2×C22⋊C4—224no—
611C2×C22⋊C4—221no—
612C2×C22⋊C4—221no—
613C2×C22⋊C4—221no—
614C2×C22⋊C4—221no—
615C2×C22⋊C4—222no—
616C2×C22⋊C4—222no—
617C2×C22⋊C4—222no—
618C2×C22⋊C4—442no—
619C2×C22⋊C4C22×D1112yes—
620C2×C22⋊C4C22×D1112yes—
621C2×C42—111no—
622C2×C42—222no—
623C2×C42—222no—
624#99—22no—
625#99—22no—
626#99—42no—
627#99—114no—
628#99—224no—
629#99—224no—
630#99—222no—
631#99—442no—
632#95—22no—
633#95—22no—
634#95—222no—
635#95—222no—
636C2×C11—22no—
637C2×C11—22no—
638C2×C11—21no—
639C2×C11—21no—
640C2×C11—42no—
641C2×C11—81no—
642C2×C11D4×C22⋊C411yescharacteristic
643C2×C11C2×#41011yescharacteristic
644C2×C11#288311yescharacteristic
645D11—22no—
646D11—42no—
647D11—41no—
648D11—81no—
649C24—111no—
650C24—112no—
651C24—111no—
652C24—112no—
653C24—111no—
654C24—221no—
655C24—221no—
656C24—221no—
657C24—221no—
658C24—222no—
659C24—222no—
660C24—441no—
661C24—442no—
662C24—442no—
663C24—881no—
664C24—881no—
665C24C2×C4×D1111yescharacteristic
666C24C2×C4×D1111yescharacteristic
667C24C23×D1111yescharacteristic
668#41—44no—
669#41—44no—
670#41—44no—
671#41—44no—
672C2×Q8—22no—
673C2×Q8—22no—
674C2×Q8—41no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—21no—
679C2×D4—22no—
680C2×D4—21no—
681C2×D4—22no—
682C2×D4—22no—
683C2×D4—41no—
684C2×D4—222no—
685C2×D4—222no—
686C2×D4—221no—
687C2×D4—221no—
688C2×D4—222no—
689C2×D4—222no—
690C2×D4—221no—
691C2×D4—222no—
692C2×D4—221no—
693C2×D4—222no—
694C2×D4—222no—
695C2×D4—222no—
696C2×D4—441no—
697C2×D4—441no—
698C2×D4—444no—
699C2×D4—444no—
700C2×D4—444no—
701C2×D4—444no—
702C2×D4—442no—
703C2×D4—881no—
704C2×D4—881no—
705C2×D4D4×D1112yes—
706C2×D4#434112yes—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—41no—
719C22×C4—41no—
720C22×C4—111no—
721C22×C4—111no—
722C22×C4—112no—
723C22×C4—112no—
724C22×C4—111no—
725C22×C4—111no—
726C22×C4—111no—
727C22×C4—221no—
728C22×C4—221no—
729C22×C4—221no—
730C22×C4—221no—
731C22×C4—222no—
732C22×C4—222no—
733C22×C4—222no—
734C22×C4—441no—
735C22×C4—444no—
736C22×C4—444no—
737C22×C4—882no—
738C22×C4—881no—
739C22×C4—881no—
740C22×C4C2×C4×D1111yescharacteristic
741C22×C4C2×C4×D1111yescharacteristic
742C22×C4C2×C4×D1111yescharacteristic
743C22×C4C2×C4×D1111yescharacteristic
744C22×C4D4×D1112yes—
745C22×C4D4×D1112yes—
746C4⋊C4—222no—
747C4⋊C4—222no—
748C4⋊C4—221no—
749C4⋊C4—221no—
750C4⋊C4—222no—
751C4⋊C4—444no—
752C4⋊C4—882no—
753C22⋊C4—22no—
754C22⋊C4—22no—
755C22⋊C4—22no—
756C22⋊C4—22no—
757C22⋊C4—111no—
758C22⋊C4—111no—
759C22⋊C4—111no—
760C22⋊C4—111no—
761C22⋊C4—112no—
762C22⋊C4—112no—
763C22⋊C4—112no—
764C22⋊C4—112no—
765C22⋊C4—112no—
766C22⋊C4—112no—
767C22⋊C4—114no—
768C22⋊C4—221no—
769C22⋊C4—221no—
770C22⋊C4—221no—
771C22⋊C4—221no—
772C22⋊C4—222no—
773C22⋊C4—222no—
774C22⋊C4—221no—
775C22⋊C4—221no—
776C22⋊C4—222no—
777C22⋊C4—222no—
778C22⋊C4—221no—
779C22⋊C4—221no—
780C22⋊C4—222no—
781C22⋊C4—222no—
782C22⋊C4—222no—
783C22⋊C4—444no—
784C22⋊C4—444no—
785C22⋊C4—882no—
786C42—221no—
787C42—221no—
788C42—444no—
789C42—882no—
790C11#2240511yescharacteristic, complemented, Sylow
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—111no—
803C23—111no—
804C23—112no—
805C23—224no—
806C23—222no—
807C23—221no—
808C23—221no—
809C23—222no—
810C23—222no—
811C23—221no—
812C23—221no—
813C23—222no—
814C23—222no—
815C23—221no—
816C23—221no—
817C23—221no—
818C23—442no—
819C23—441no—
820C23—442no—
821C23—441no—
822C23—442no—
823C23—441no—
824C23—442no—
825C23—442no—
826C23—441no—
827C23—441no—
828C23—442no—
829C23—442no—
830C23—881no—
831C23—881no—
832C23—882no—
833C23—882no—
834C23—884no—
835C23—884no—
836C23—884no—
837C23(C22⋊D11)⋊C412yes—
838C23C22×C4×D1111yescharacteristic
839C23C2×D4×D1112yes—
840C23C2×D4×D1111yescharacteristic
841C23C2×#434111yescharacteristic
842C23#6703712yes—
843Q8—44no—
844D4—24no—
845D4—24no—
846D4—44no—
847D4—42no—
848D4—42no—
849D4—444no—
850D4—444no—
851D4—442no—
852D4—442no—
853D4—442no—
854D4—442no—
855D4—882no—
856D4—882no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—111no—
881C2×C4—111no—
882C2×C4—112no—
883C2×C4—221no—
884C2×C4—221no—
885C2×C4—221no—
886C2×C4—221no—
887C2×C4—221no—
888C2×C4—224no—
889C2×C4—442no—
890C2×C4—442no—
891C2×C4—442no—
892C2×C4—442no—
893C2×C4—441no—
894C2×C4—441no—
895C2×C4—442no—
896C2×C4—442no—
897C2×C4—441no—
898C2×C4—441no—
899C2×C4—442no—
900C2×C4—442no—
901C2×C4—442no—
902C2×C4—888no—
903C2×C4—881no—
904C2×C4—881no—
905C2×C4C22⋊C4×D1111yescharacteristic
906C2×C4C22⋊C4×D1111yescharacteristic
907C2×C4C22⋊C4×D1112yes—
908C2×C4(C22⋊D11)⋊C412yes—
909C22—22no—
910C22—21no—
911C22—22no—
912C22—21no—
913C22—22no—
914C22—41no—
915C22—41no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—81no—
925C22—81no—
926C22—112no—
927C22—221no—
928C22—221no—
929C22—221no—
930C22—222no—
931C22—221no—
932C22—222no—
933C22—222no—
934C22—221no—
935C22—444no—
936C22—442no—
937C22—442no—
938C22—444no—
939C22—441no—
940C22—441no—
941C22—441no—
942C22—882no—
943C22—882no—
944C22—881no—
945C22—881no—
946C22—881no—
947C22—881no—
948C22—884no—
949C22—884no—
950C22C2×C22⋊C4×D1111yescharacteristic
951C22C2×(C22⋊D11)⋊C411yescharacteristic
952C22#1062301711yescharacteristic
953C22#1062312112yes—
954C22#1062312212yes—
955C4—21no—
956C4—21no—
957C4—22no—
958C4—22no—
959C4—41no—
960C4—82no—
961C4—82no—
962C4—221no—
963C4—221no—
964C4—222no—
965C4—444no—
966C4—441no—
967C4—441no—
968C4—441no—
969C4—882no—
970C2—22no—
971C2—22no—
972C2—21no—
973C2—21no—
974C2—42no—
975C2—81no—
976C2—222no—
977C2—441no—
978C2—442no—
979C2—881no—
980C2#1307143211yescharacteristic
981C2D11×#41011yescharacteristic
982C2#1307707511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC11×#1782C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623360C2
cosocleC24×C11C24
hypercenter#1782D11
hypocenterC11#22405
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1782

Complements

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

NH ≅ G/Ntype
2. C2×#10622853C2semidirect
3. C2×D11×#99C2semidirect
4. #13071458C2semidirect
5. #13069450C2semidirect
6. #13069072C2semidirect
7. #13069066C2semidirect
8. #13068602C2semidirect
9. #13068529C2semidirect
10. #99×Dic11C2semidirect
11. C11×#1782C2semidirect
18. C2×#67000C4semidirect
19. C2×#66999C4semidirect
20. C2×#66992C4semidirect
22. C2×#66990C4semidirect
25. C2×#66983C4semidirect
26. C2×#66982C4semidirect
28. C2×C4×C22⋊D11C4semidirect
29. C22×(C2×D11)⋊C4C4semidirect
31. C2×#66979C22semidirect
35. C2×C11×#99C22semidirect
36. C11×#381C22semidirect
40. C2×#66898C22semidirect
44. #10622555C22semidirect
45. C22⋊C4×Dic11C22semidirect
51. #10622165C22semidirect
52. #10622165C22semidirect
60. C22×Q8×C11C2×C4semidirect
61. C22×D4×C11C2×C4semidirect
64. C23×C4×C11C2×C4semidirect
65. C23×C4×C11C2×C4semidirect
70. C22×C22⋊D11C2×C4semidirect
72. C23×Dic11C2×C4semidirect
84. C2×C22⋊Dic11C2×C4semidirect
85. C2×C22⋊Dic11C2×C4semidirect
126. C2×(C2×D11)⋊C4C2×C4semidirect
127. C2×(C2×D11)⋊C4C2×C4semidirect
128. C2×(C2×D11)⋊C4C2×C4semidirect
136. C2×C4⋊Dic11C2×C4semidirect
138. C2×Dic11⋊C4C2×C4semidirect
139. C2×Dic11⋊C4C2×C4semidirect
140. C2×Dic11⋊C4C2×C4semidirect
143. C2×C4×Dic11C2×C4semidirect
153. #66898D4semidirect
308. #1782D11semidirect
459. C2×#99C2×D11semidirect
463. #381C2×D11semidirect
515. C2×D11#410semidirect
538. C22×Q8C4×D11semidirect
550. C22×D4C4×D11semidirect
557. C23×C4C4×D11semidirect
558. C23×C4C4×D11semidirect
790. C11#22405semidirect

Maximal subgroups

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

subgroupindex
C2×#106233602
C2×#106228532
C2×D11×#992
#130714582
#130694502
#130690722
#130690662
#130686022
#130685292
#99×Dic112
C11×#17822
#2240511