Finite Group Databasebeta

← #14923637

Subgroups — #14923637

Order 2816.

2926 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66979C211yesmaximal, characteristic, complemented
2#13072933C212yesmaximal, complemented
3#13072924C212yesmaximal, complemented
4#13072913C214yesmaximal, complemented
5#13072903C212yesmaximal, complemented
6#13072894C212yesmaximal, complemented
7#13072890C212yesmaximal, complemented
8#13071939C212yesmaximal
9#13071875C214yesmaximal, complemented
10C4×#66988C214yesmaximal, complemented
11#13071099C212yesmaximal, complemented
12#13070999C211yesmaximal, characteristic, complemented
13#13070999C212yesmaximal, complemented
14C22×C4×D4×C11C211yesmaximal, characteristic
15C23×D4×C11C2211yescharacteristic
16C24×C4×C11C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C2×C4×D4×C11—28no—
19C2×C4×D4×C11C2212yes—
20C2×C4×D4×C11C2212yes—
21C2×C4×D4×C11C2212yes—
22C2×C4×D4×C11C2212yes—
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C42×C11C2211yescharacteristic
27C22×C22⋊Dic11C2212yes—
28C2×#66988C2214yes—
29C2×#66979—28no—
30C2×#66979C2212yes—
31C2×#66979C2212yes—
32C2×#66979C2212yes—
33C2×#66979C2212yescomplemented
34C2×#66979C2212yescomplemented
35C22×C4⋊Dic11C2211yescharacteristic, complemented
36C22×C4⋊Dic11C2211yescharacteristic, complemented
37C22×C4×Dic11C2212yescomplemented
38#10622860C2214yes—
39#10622860C2212yes—
40#10622835C2218yes—
41#10622833C2214yes—
42#10622825C2212yescomplemented
43#10622825C2214yescomplemented
44#10622825C2214yescomplemented
45#10622825C2212yescomplemented
46#10622824C2212yes—
47#10622824C2214yes—
48#10622823C2214yes—
49#10622823C2214yes—
50C4×C22⋊Dic11C2212yescomplemented
51C4×C22⋊Dic11C2218yescomplemented
52C4×C22⋊Dic11C2212yescomplemented
53#10622599C2214yescomplemented
54#10622596C2214yescomplemented
55#10622591C2218yescomplemented
56#10622566C2214yescomplemented
57#10622565C2218yescomplemented
58#10622562C2214yescomplemented
59#10622559C2214yescomplemented
60#10622557C2218yescomplemented
61#10622556C2214yescomplemented
62C4×Dic11⋊C4C2218yescomplemented
63#10622541C2214yescomplemented
64#10622541C2214yescomplemented
65C25×C11C2311yescharacteristic
66C25×C11C2311yescharacteristic
67C22×D4×C11—24no—
68C22×D4×C11—28no—
69C22×D4×C11C2312yes—
70C22×D4×C11C2312yes—
71C23×C4×C11—28no—
72C23×C4×C11—24no—
73C23×C4×C11—28no—
74C23×C4×C11D418yes—
75C23×C4×C11C2312yes—
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2312yes—
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×Dic11C2312yes—
87C23×Dic11C2312yes—
88C4×D4×C11—28no—
89C4×D4×C11—28no—
90C4×D4×C11—28no—
91C4×D4×C11—28no—
92C2×C11×C4⋊C4—24no—
93C2×C11×C4⋊C4C2312yes—
94C2×C11×C4⋊C4C2312yes—
95C2×C11×C22⋊C4—24no—
96C2×C11×C22⋊C4—24no—
97C2×C11×C22⋊C4C2312yes—
98C2×C11×C22⋊C4C2312yes—
99C2×C11×C22⋊C4C2312yes—
100C2×C11×C22⋊C4C2312yes—
101C2×C42×C11—24no—
102C2×C42×C11C2312yes—
103C2×C42×C11C2312yes—
104C2×C22⋊Dic11—28no—
105C2×C22⋊Dic11C2314yes—
106C2×C22⋊Dic11C2314yes—
107C2×C22⋊Dic11C2314yes—
108C2×C22⋊Dic11C2314yes—
109C2×C22⋊Dic11C2318yes—
110C2×C22⋊Dic11C2318yes—
111C2×C22⋊Dic11C2314yes—
112#66988—216no—
113#66979—28no—
114#66979—28no—
115#66979—28no—
116#66979—28no—
117#66979—28no—
118C2×C4⋊Dic11—24no—
119C2×C4⋊Dic11—24no—
120C2×C4⋊Dic11C2312yes—
121C2×C4⋊Dic11C2312yes—
122C2×C4⋊Dic11C2314yes—
123C2×C4⋊Dic11C2312yes—
124C2×C4⋊Dic11C2312yes—
125C2×Dic11⋊C4C2318yes—
126C2×Dic11⋊C4C2318yes—
127C2×C4×Dic11—28no—
128C2×C4×Dic11C2314yes—
129C2×C4×Dic11C2314yes—
130C2×C4×Dic11C2314yes—
131C11⋊#95C2318yes—
132C11⋊#95C2318yes—
133C11⋊#95C2318yes—
134C11⋊#95C2314yes—
135C11⋊#95C2318yes—
136C11⋊#95C2314yes—
137#34809—111nomaximal, Sylow
138C24×C11—22no—
139C24×C11—24no—
140C24×C11—24no—
141C24×C11—24no—
142C24×C11—24no—
143C24×C11—42no—
144C24×C11—42no—
145C24×C11C2×D414yes—
146C24×C11C2411yescharacteristic
147C24×C11C2412yes—
148C24×C11C2411yescharacteristic
149C24×C11C2411yescharacteristic
150C2×D4×C11—232no—
151C2×D4×C11—24no—
152C2×D4×C11—24no—
153C2×D4×C11—24no—
154C2×D4×C11—24no—
155C2×D4×C11—24no—
156C2×D4×C11#4118yes—
157C22×C4×C11—22no—
158C22×C4×C11—24no—
159C22×C4×C11—232no—
160C22×C4×C11—24no—
161C22×C4×C11—24no—
162C22×C4×C11—24no—
163C22×C4×C11—24no—
164C22×C4×C11—24no—
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—24no—
168C22×C4×C11—24no—
169C22×C4×C11—24no—
170C22×C4×C11—28no—
171C22×C4×C11—28no—
172C22×C4×C11—42no—
173C22×C4×C11—416no—
174C22×C4×C11C2×D414yes—
175C22×C4×C11C2×D414yes—
176C22×C4×C11C2×D414yes—
177C22×C4×C11C2×D414yes—
178C22×C4×C11C2×D414yes—
179C22×C4×C11C2×D414yes—
180C22×C4×C11#4118yes—
181C22×C4×C11C2412yes—
182C22×C4×C11C2412yes—
183C22×C4×C11C2411yescharacteristic
184C22×C4×C11C2411yescharacteristic
185C22×C4×C11C2412yes—
186C22×C4×C11C2411yescharacteristic
187C22×C4×C11C2411yescharacteristic
188C22×Dic11—24no—
189C22×Dic11—24no—
190C22×Dic11—28no—
191C22×Dic11—44no—
192C22×Dic11C2418yes—
193C22×Dic11C2414yes—
194C22×Dic11C2414yes—
195C11×C4⋊C4—24no—
196C11×C4⋊C4—24no—
197C11×C22⋊C4—24no—
198C11×C22⋊C4—24no—
199C11×C22⋊C4—24no—
200C11×C22⋊C4—24no—
201C42×C11—24no—
202C42×C11—24no—
203C22⋊Dic11—28no—
204C22⋊Dic11—28no—
205C22⋊Dic11—28no—
206C22⋊Dic11—216no—
207C22⋊Dic11—28no—
208C22⋊Dic11—44no—
209C22⋊Dic11—48no—
210C4⋊Dic11—24no—
211C4⋊Dic11—24no—
212C4⋊Dic11—24no—
213C4⋊Dic11—24no—
214C4⋊Dic11—28no—
215Dic11⋊C4—216no—
216Dic11⋊C4—48no—
217C4×Dic11—28no—
218C4×Dic11—28no—
219C4×Dic11—28no—
220C22×C4×D4D1111yescharacteristic
221C22×#117—111no—
222#2487—112no—
223#2486—112no—
224#2485—114no—
225#2484—112no—
226#2483—112no—
227#2482—112no—
228#2405—112no—
229#2395—114no—
230C4×#123—114no—
231#2296—112no—
232#2280—112no—
233#2280—111no—
234C23×C11—22no—
235C23×C11—22no—
236C23×C11—22no—
237C23×C11—22no—
238C23×C11—28no—
239C23×C11—28no—
240C23×C11—28no—
241C23×C11—22no—
242C23×C11—22no—
243C23×C11—24no—
244C23×C11—22no—
245C23×C11—22no—
246C23×C11—22no—
247C23×C11—24no—
248C23×C11—44no—
249C23×C11—416no—
250C23×C11—416no—
251C23×C11—44no—
252C23×C11—44no—
253C23×C11C22×D412yes—
254C23×C11C22×D412yes—
255C23×C11C22×D412yes—
256C23×C11C2×#4114yes—
257C23×C11C2×#4114yes—
258C23×C11C2×#4114yes—
259C23×C11C2511yescharacteristic
260D4×C11—216no—
261D4×C11—216no—
262C2×C4×C11—28no—
263C2×C4×C11—28no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—28no—
269C2×C4×C11—28no—
270C2×C4×C11—28no—
271C2×C4×C11—28no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—24no—
275C2×C4×C11—24no—
276C2×C4×C11—44no—
277C2×C4×C11—44no—
278C2×C4×C11—48no—
279C2×C4×C11—48no—
280C2×C4×C11#123116yescomplemented
281C2×C4×C11C22×D412yes—
282C2×C4×C11C22×D412yes—
283C2×C4×C11C22×D412yes—
284C2×C4×C11C22×D412yes—
285C2×C4×C11C2×#4114yes—
286C2×C4×C11C2×#4114yes—
287C2×C4×C11C2×#4114yes—
288C2×Dic11—24no—
289C2×Dic11—24no—
290C2×Dic11—28no—
291C2×Dic11—28no—
292C2×Dic11—28no—
293C2×Dic11—28no—
294C2×Dic11—28no—
295C2×Dic11—48no—
296C2×Dic11—48no—
297C23×D4C2×D1111yescharacteristic
298C24×C4C2×D1111yescharacteristic
299C24×C4C2×D1111yescharacteristic
300C2×#123—114no—
301C2×C4×D4—28no—
302C2×C4×D4C2×D1112yes—
303C2×C4×D4C2×D1112yes—
304C2×C4×D4C2×D1112yes—
305C2×C4×D4C2×D1112yes—
306C2×#117—112no—
307C2×#117—112no—
308C2×#117—112no—
309C2×#117—112no—
310C2×#117—112no—
311C2×#117—228no—
312C22×C4⋊C4—111no—
313C22×C4⋊C4—111no—
314C22×C4⋊C4C2×D1111yescharacteristic
315C22×C22⋊C4—112no—
316C22×C22⋊C4C2×D1111yescharacteristic
317C22×C22⋊C4C2×D1111yescharacteristic
318C22×C42—112no—
319C22×C42C2×D1111yescharacteristic
320#400—114no—
321#399—114no—
322#398—114no—
323#397—118no—
324#397—114no—
325#394—118no—
326#389—114no—
327#389—114no—
328#388—118no—
329#387—118no—
330#386—114no—
331#385—114no—
332#385—114no—
333#385—114no—
334#381—112no—
335#381—114no—
336#381—114no—
337#380—112no—
338#380—114no—
339#380—114no—
340#380—112no—
341#379—114no—
342#379—112no—
343C4×C4⋊C4—118no—
344C4×C22⋊C4—112no—
345C4×C22⋊C4—118no—
346C4×C22⋊C4—112no—
347C22×C11—22no—
348C22×C11—22no—
349C22×C11—22no—
350C22×C11—22no—
351C22×C11—28no—
352C22×C11—28no—
353C22×C11—22no—
354C22×C11—22no—
355C22×C11—24no—
356C22×C11—22no—
357C22×C11—28no—
358C22×C11—416no—
359C22×C11—416no—
360C22×C11—42no—
361C22×C11—42no—
362C22×C11—44no—
363C22×C11—44no—
364C22×C11C2×#12314yes—
365C22×C11#52514yes—
366C22×C11C23×D411yescharacteristic
367C22×C11C22×#4112yes—
368C22×C11C22×#4112yes—
369C22×C11#58512yes—
370C4×C11—22no—
371C4×C11—22no—
372C4×C11—24no—
373C4×C11—42no—
374C4×C11—42no—
375C4×C11C2×#12314yes—
376C4×C11C2×#12314yes—
377Dic11—44no—
378Dic11—44no—
379Dic11—48no—
380C25C22×D1111yescharacteristic
381C25C22×D1111yescharacteristic
382C22×D4—24no—
383C22×D4—28no—
384C22×D4C22×D1112yes—
385C22×D4C22×D1112yes—
386C23×C4—28no—
387C23×C4—28no—
388C23×C4—24no—
389C23×C4—112no—
390C23×C4—112no—
391C23×C4C22⋊D1118yes—
392C23×C4C22×D1111yescharacteristic
393C23×C4C22×D1111yescharacteristic
394C23×C4C22×D1112yes—
395C23×C4C22×D1112yes—
396C23×C4C22×D1111yescharacteristic
397C23×C4C22×D1111yescharacteristic
398C23×C4C22×D1111yescharacteristic
399C23×C4C22×D1111yescharacteristic
400C23×C4C22×D1111yescharacteristic
401C23×C4C22×D1111yescharacteristic
402C23×C4C22×D1111yescharacteristic
403#123—2216no—
404C4×D4—28no—
405C4×D4—28no—
406C4×D4—28no—
407C4×D4—28no—
408#117—228no—
409#117—228no—
410#117—228no—
411#117—228no—
412#117—228no—
413C2×C4⋊C4—24no—
414C2×C4⋊C4—112no—
415C2×C4⋊C4—112no—
416C2×C4⋊C4—112no—
417C2×C4⋊C4—112no—
418C2×C4⋊C4—114no—
419C2×C4⋊C4—118no—
420C2×C4⋊C4—118no—
421C2×C4⋊C4—224no—
422C2×C4⋊C4—224no—
423C2×C4⋊C4C22×D1112yes—
424C2×C4⋊C4C22×D1112yes—
425C2×C22⋊C4—24no—
426C2×C22⋊C4—24no—
427C2×C22⋊C4—114no—
428C2×C22⋊C4—114no—
429C2×C22⋊C4—114no—
430C2×C22⋊C4—114no—
431C2×C22⋊C4—118no—
432C2×C22⋊C4—118no—
433C2×C22⋊C4—114no—
434C2×C22⋊C4—228no—
435C2×C22⋊C4C22×D1112yes—
436C2×C22⋊C4C22×D1112yes—
437C2×C22⋊C4C22×D1112yes—
438C2×C22⋊C4C22×D1112yes—
439C2×C42—24no—
440C2×C42—114no—
441C2×C42—114no—
442C2×C42—114no—
443C2×C42—228no—
444C2×C42C22×D1112yes—
445C2×C42C22×D1112yes—
446#95—118no—
447#95—118no—
448#95—114no—
449#95—114no—
450#95—118no—
451#95—118no—
452C2×C11—24no—
453C2×C11—24no—
454C2×C11—42no—
455C2×C11—44no—
456C2×C11C22×#12311yescharacteristic
457C2×C11C2×#52511yescharacteristic
458C2×C11#344911yescharacteristic
459C2×C11#347514yes—
460C24—24no—
461C24—24no—
462C24—24no—
463C24—22no—
464C24—24no—
465C24—42no—
466C24—42no—
467C24C2×C22⋊D1114yes—
468C24C23×D1112yes—
469C24C23×D1111yescharacteristic
470C24C23×D1111yescharacteristic
471C24C23×D1111yescharacteristic
472C2×D4—232no—
473C2×D4—24no—
474C2×D4—24no—
475C2×D4—24no—
476C2×D4—24no—
477C2×D4—24no—
478C2×D4#433918yes—
479C22×C4—24no—
480C22×C4—22no—
481C22×C4—232no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—28no—
491C22×C4—28no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—42no—
495C22×C4—416no—
496C22×C4—118no—
497C22×C4—114no—
498C22×C4—114no—
499C22×C4—228no—
500C22×C4—224no—
501C22×C4—224no—
502C22×C4—444no—
503C22×C4#434118yes—
504C22×C4C2×C22⋊D1114yes—
505C22×C4C2×C22⋊D1114yes—
506C22×C4C2×C22⋊D1114yes—
507C22×C4C2×C22⋊D1114yes—
508C22×C4C2×C22⋊D1114yes—
509C22×C4C2×C22⋊D1114yes—
510C22×C4C23×D1112yes—
511C22×C4C23×D1112yes—
512C22×C4C23×D1112yes—
513C22×C4C23×D1111yescharacteristic
514C22×C4C23×D1111yescharacteristic
515C22×C4C23×D1111yescharacteristic
516C22×C4C23×D1111yescharacteristic
517C4⋊C4—24no—
518C4⋊C4—24no—
519C4⋊C4—2216no—
520C4⋊C4—228no—
521C4⋊C4—224no—
522C4⋊C4—224no—
523C4⋊C4—224no—
524C4⋊C4—224no—
525C4⋊C4—448no—
526C22⋊C4—24no—
527C22⋊C4—24no—
528C22⋊C4—24no—
529C22⋊C4—24no—
530C22⋊C4—228no—
531C22⋊C4—2216no—
532C22⋊C4—228no—
533C22⋊C4—228no—
534C22⋊C4—228no—
535C22⋊C4—444no—
536C22⋊C4—448no—
537C42—24no—
538C42—24no—
539C42—228no—
540C42—228no—
541C42—228no—
542C11#3480911yescharacteristic, complemented, Sylow
543C23—22no—
544C23—22no—
545C23—22no—
546C23—22no—
547C23—28no—
548C23—28no—
549C23—28no—
550C23—22no—
551C23—22no—
552C23—24no—
553C23—22no—
554C23—24no—
555C23—22no—
556C23—22no—
557C23—44no—
558C23—416no—
559C23—416no—
560C23—44no—
561C23—44no—
562C23C2×#433914yes—
563C23C2×#433914yes—
564C23C2×#434114yes—
565C23C22×C22⋊D1112yes—
566C23C22×C22⋊D1112yes—
567C23C22×C22⋊D1112yes—
568C23C24×D1111yescharacteristic
569D4—216no—
570D4—216no—
571C2×C4—28no—
572C2×C4—28no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—28no—
578C2×C4—28no—
579C2×C4—28no—
580C2×C4—28no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—44no—
586C2×C4—44no—
587C2×C4—48no—
588C2×C4—48no—
589C2×C4—228no—
590C2×C4—228no—
591C2×C4—228no—
592C2×C4—228no—
593C2×C4—228no—
594C2×C4—224no—
595C2×C4—224no—
596C2×C4—448no—
597C2×C4—448no—
598C2×C4#66988116yescomplemented
599C2×C4C2×#433914yes—
600C2×C4C2×#434114yes—
601C2×C4C2×#434114yes—
602C2×C4C22×C22⋊D1112yes—
603C2×C4C22×C22⋊D1112yes—
604C2×C4C22×C22⋊D1112yes—
605C2×C4C22×C22⋊D1112yes—
606C22—22no—
607C22—28no—
608C22—28no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—24no—
613C22—22no—
614C22—28no—
615C22—22no—
616C22—22no—
617C22—416no—
618C22—416no—
619C22—44no—
620C22—44no—
621C22—42no—
622C22—42no—
623C22#1062332214yes—
624C22C2×#6698814yes—
625C22C22×#433912yes—
626C22C22×#434112yes—
627C22#1062345312yes—
628C22C23×C22⋊D1111yescharacteristic
629C4—24no—
630C4—22no—
631C4—22no—
632C4—42no—
633C4—42no—
634C4—444no—
635C4—448no—
636C4—444no—
637C4C2×#6698814yes—
638C4C2×#6698814yes—
639C2—24no—
640C2—24no—
641C2—44no—
642C2—42no—
643C2C22×#6698811yescharacteristic
644C2C2×#1062332211yescharacteristic
645C2#1308194511yescharacteristic
646C2#1308217414yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C4×D4×C11C2
prime radicalC23×D4×C11C22
hypercenterC22×C4×D4D11
hypocenterC11#34809
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×#66979C2semidirect
2. #13072933C2semidirect
3. #13072924C2semidirect
4. #13072913C2semidirect
5. #13072903C2semidirect
6. #13072894C2semidirect
7. #13072890C2semidirect
9. #13071875C2semidirect
10. C4×#66988C2semidirect
11. #13071099C2semidirect
12. #13070999C2semidirect
13. #13070999C2semidirect
33. C2×#66979C22semidirect
34. C2×#66979C22semidirect
35. C22×C4⋊Dic11C22semidirect
36. C22×C4⋊Dic11C22semidirect
37. C22×C4×Dic11C22semidirect
42. #10622825C22semidirect
43. #10622825C22semidirect
44. #10622825C22semidirect
45. #10622825C22semidirect
50. C4×C22⋊Dic11C22semidirect
51. C4×C22⋊Dic11C22semidirect
52. C4×C22⋊Dic11C22semidirect
53. #10622599C22semidirect
54. #10622596C22semidirect
55. #10622591C22semidirect
56. #10622566C22semidirect
57. #10622565C22semidirect
58. #10622562C22semidirect
59. #10622559C22semidirect
60. #10622557C22semidirect
61. #10622556C22semidirect
62. C4×Dic11⋊C4C22semidirect
63. #10622541C22semidirect
64. #10622541C22semidirect
280. C2×C4×C11#123semidirect
542. C11#34809semidirect
598. C2×C4#66988semidirect

Maximal subgroups

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

subgroupindex
C22×#669792
#130729332
#130729242
#130729132
#130729032
#130728942
#130728902
#130719392
#130718752
C4×#669882
#130710992
#130709992
C22×C4×D4×C112
#3480911