Finite Group Databasebeta

← #14925861

Subgroups — #14925861

Order 2816.

2402 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623153C211yesmaximal, characteristic
2C22×#66940C211yesmaximal, characteristic
3#13074002C214yesmaximal, complemented
4#13073997C211yesmaximal, characteristic
5#13073996C211yesmaximal, characteristic
6#13073991C211yesmaximal, characteristic
7#13073820C212yesmaximal, complemented
8#13073600C212yesmaximal, complemented
9#13073092C212yesmaximal
10#13072258C212yesmaximal
11#13071908C212yesmaximal, complemented
12#13071906C212yesmaximal, complemented
13#13071187C214yesmaximal, complemented
14#13071095C212yesmaximal
15#13071095C212yesmaximal
16C4×#66930C211yesmaximal, characteristic
17C11×#2583C211yesmaximal, characteristic
18C23×Dic22C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic
22C2×#66997C2211yescharacteristic
23C2×#66977C2211yescharacteristic
24C22×Dic11⋊C4C2211yescharacteristic
25C22×Dic11⋊C4C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27C22×C4×Dic11C2211yescharacteristic
28C22×C4×Dic11C2211yescharacteristic
29#10623153—28no—
30C2×#66942C2212yes—
31C2×#66941C2211yescharacteristic
32C2×#66941C2214yes—
33C2×#66940—28no—
34C2×#66940C2212yes—
35C2×#66940C2211yescharacteristic
36C2×#66940C2212yes—
37C2×#66940C2212yes—
38C2×#66940C2212yes—
39C2×#66940C2212yes—
40C2×#66931C2212yes—
41C2×#66930C2212yes—
42C2×#66930C2212yes—
43C11×#398C2212yes—
44C11×#395C2212yes—
45C11×#389C2214yes—
46C11×#385C2212yes—
47C11×#385C2212yes—
48C4×C11×C22⋊C4C2211yescharacteristic
49#10622842C2212yes—
50#10622823C2212yes—
51#10622823C2212yes—
52C4×C22⋊Dic11C2211yescharacteristic
53#10622597C2214yes—
54#10622596C2212yes—
55#10622593C2212yes—
56#10622592C2212yes—
57#10622592C2214yes—
58#10622589C2214yes—
59C4⋊C4×Dic11C2214yes—
60C4⋊C4×Dic11C2214yes—
61#10622585C2214yes—
62#10622585C2214yes—
63#10622585C2214yes—
64#10622585C2214yes—
65#10622563C2212yes—
66#10622563C2212yes—
67#10622559C2212yes—
68#10622559C2212yes—
69C22⋊C4×Dic11C2212yes—
70C4×Dic11⋊C4C2212yes—
71C42×Dic11C2212yes—
72#10622541C2214yes—
73#10622274C2212yes—
74#10622270C2214yes—
75#10622269C2214yes—
76#10622269C2212yes—
77#10622262C2214yes—
78#10622262C2214yes—
79#10622262C2212yes—
80#10622261C2212yes—
81#10622260C2214yes—
82#10622260C2214yes—
83#10622259C2214yes—
84#10622259C2214yes—
85C22×Q8×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C22×Dic22—24no—
94C22×Dic22—28no—
95C22×Dic22C2312yes—
96C22×Dic22C2312yes—
97C22×Dic22C2312yes—
98C22×Dic22C2311yescharacteristic
99C11×C22⋊Q8—24no—
100C2×C11×C4⋊C4—24no—
101C2×C11×C4⋊C4C2312yes—
102C2×C11×C4⋊C4C2312yes—
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C4⋊C4C2312yes—
105C2×C11×C4⋊C4C2314yes—
106C2×C11×C4⋊C4C2314yes—
107C2×C11×C22⋊C4C2312yes—
108C2×C11×C22⋊C4C2312yes—
109C2×C42×C11C2312yes—
110C2×C22⋊Dic11C2312yes—
111C2×C22⋊Dic11C2312yes—
112Q8×Dic11—24no—
113#66997—24no—
114C2×C4⋊Dic11C2312yes—
115C2×C4⋊Dic11C2314yes—
116C2×C4⋊Dic11C2311yescharacteristic
117C2×C4⋊Dic11C2314yes—
118#66977—24no—
119C2×Dic11⋊C4—24no—
120C2×Dic11⋊C4—24no—
121C2×Dic11⋊C4C2312yes—
122C2×Dic11⋊C4C2312yes—
123C2×Dic11⋊C4C2312yes—
124C2×Dic11⋊C4C2312yes—
125C2×Dic11⋊C4C2312yes—
126C2×Dic11⋊C4C2312yes—
127C2×Dic11⋊C4C2312yes—
128C2×Dic11⋊C4C2312yes—
129C2×Dic11⋊C4C2312yes—
130C2×Dic11⋊C4C2314yes—
131C2×Dic11⋊C4C2314yes—
132C2×Dic11⋊C4C2314yes—
133C2×Dic11⋊C4C2314yes—
134C2×Dic11⋊C4C2314yes—
135C2×C4×Dic11—24no—
136C2×C4×Dic11—24no—
137C2×C4×Dic11D418yes—
138C2×C4×Dic11C2312yes—
139C2×C4×Dic11C2312yes—
140C2×C4×Dic11C2314yes—
141C2×C4×Dic11C2312yes—
142C2×C4×Dic11C2312yes—
143C2×C4×Dic11C2312yes—
144C2×C4×Dic11C2312yes—
145C2×C4×Dic11C2312yes—
146C2×C4×Dic11C2311yescharacteristic
147C2×C4×Dic11C2311yescharacteristic
148C2×C4×Dic11C2311yescharacteristic
149C2×C4×Dic11C2311yescharacteristic
150C2×C4×Dic11C2314yes—
151#66942—28no—
152#66941—216no—
153#66941—24no—
154#66940—28no—
155#66940—28no—
156#66940—28no—
157#66940—28no—
158#66940—24no—
159#66940—28no—
160#66931—28no—
161#66930—28no—
162#66930Q8116yescomplemented
163C11×#95C2314yes—
164C11×#95C2314yes—
165C11×#95C2312yes—
166C11⋊#95C2314yes—
167C11⋊#95C2314yes—
168C11⋊#95C2314yes—
169C11⋊#95C2314yes—
170C11⋊#95C2314yes—
171C11⋊#95C2314yes—
172C11⋊#95C2312yes—
173C11⋊#95C2314yes—
174#34953—111nomaximal, Sylow
175C24×C11C2411yescharacteristic
176C2×Q8×C11—22no—
177C2×Q8×C11—42no—
178C22×C4×C11—22no—
179C22×C4×C11—24no—
180C22×C4×C11—22no—
181C22×C4×C11—42no—
182C22×C4×C11—42no—
183C22×C4×C11C2×D414yes—
184C22×C4×C11C2412yes—
185C22×C4×C11C2412yes—
186C22×C4×C11C2412yes—
187C22×C4×C11C2411yescharacteristic
188C22×C4×C11C2411yescharacteristic
189C22×C4×C11C2414yes—
190C22×C4×C11C2412yes—
191C22×Dic11—24no—
192C22×Dic11—24no—
193C22×Dic11—22no—
194C22×Dic11—22no—
195C22×Dic11—42no—
196C22×Dic11C2×D414yes—
197C22×Dic11C2×D414yes—
198C22×Dic11C2×Q818yes—
199C22×Dic11C2412yes—
200C22×Dic11C2412yes—
201C22×Dic11C2412yes—
202C22×Dic11C2411yescharacteristic
203C22×Dic11C2414yes—
204C22×Dic11C2412yes—
205C22×Dic11C2411yescharacteristic
206C22×Dic11C2411yescharacteristic
207C22×Dic11C2411yescharacteristic
208C2×Dic22—232no—
209C2×Dic22—24no—
210C2×Dic22—24no—
211C2×Dic22—24no—
212C2×Dic22—24no—
213C2×Dic22—24no—
214C2×Dic22—28no—
215C2×Dic22—22no—
216C2×Dic22—24no—
217C2×Dic22—42no—
218C2×Dic22#4118yes—
219C11×C4⋊C4—24no—
220C11×C4⋊C4—24no—
221C11×C4⋊C4—22no—
222C11×C4⋊C4—24no—
223C11×C4⋊C4—28no—
224C11×C4⋊C4—44no—
225C11×C22⋊C4—24no—
226C11×C22⋊C4C2×Q818yes—
227C42×C11—42no—
228C22⋊Dic11—24no—
229C22⋊Dic11C2×Q818yes—
230C4⋊Dic11—24no—
231C4⋊Dic11—28no—
232C4⋊Dic11—22no—
233C4⋊Dic11—44no—
234Dic11⋊C4—24no—
235Dic11⋊C4—24no—
236Dic11⋊C4—24no—
237Dic11⋊C4—24no—
238Dic11⋊C4—24no—
239Dic11⋊C4—24no—
240Dic11⋊C4—28no—
241Dic11⋊C4—24no—
242Dic11⋊C4—24no—
243Dic11⋊C4—24no—
244Dic11⋊C4—28no—
245Dic11⋊C4—44no—
246Dic11⋊C4—44no—
247Dic11⋊C4C2×Q8116yescomplemented
248C4×Dic11—24no—
249C4×Dic11—24no—
250C4×Dic11—24no—
251C4×Dic11—24no—
252C4×Dic11—24no—
253C4×Dic11—24no—
254C4×Dic11—28no—
255C4×Dic11—42no—
256C4×Dic11C2×D414yes—
257C4×Dic11C2×D414yes—
258C4×Dic11C2×D414yes—
259C4×Dic11C2×D414yes—
260C4×Dic11C2×Q8116yescomplemented
261C2×#533—111no—
262C22×C4×Q8—111no—
263#2584—114no—
264#2583—111no—
265#2583—111no—
266#2583—111no—
267#2583D1111yescharacteristic
268#2567—112no—
269#2546—112no—
270#2502—112no—
271#2434—112no—
272#2399—112no—
273#2399—112no—
274C4×C4⋊Q8—114no—
275#2296—112no—
276#2296—112no—
277C4×#117—111no—
278C23×C11—22no—
279C23×C11—22no—
280C23×C11C22×D412yes—
281C23×C11C22×Q814yes—
282C23×C11C2511yescharacteristic
283Q8×C11—44no—
284C2×C4×C11—28no—
285C2×C4×C11—22no—
286C2×C4×C11—24no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—24no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—24no—
295C2×C4×C11—24no—
296C2×C4×C11—24no—
297C2×C4×C11—44no—
298C2×C4×C11—44no—
299C2×C4×C11C22×D412yes—
300C2×C4×C11C22×D412yes—
301C2×C4×C11C22×Q818yes—
302C2×C4×C11C2×#4114yes—
303C2×Dic11—28no—
304C2×Dic11—22no—
305C2×Dic11—24no—
306C2×Dic11—22no—
307C2×Dic11—22no—
308C2×Dic11—24no—
309C2×Dic11—28no—
310C2×Dic11—22no—
311C2×Dic11—22no—
312C2×Dic11—22no—
313C2×Dic11—24no—
314C2×Dic11—24no—
315C2×Dic11—24no—
316C2×Dic11—44no—
317C2×Dic11C4⋊Q8116yescomplemented
318C2×Dic11C22×D412yes—
319C2×Dic11C22×D412yes—
320C2×Dic11C22×D412yes—
321C2×Dic11C22×D412yes—
322C2×Dic11C22×Q818yes—
323C2×Dic11C22×Q814yes—
324C2×Dic11C22×Q814yes—
325C2×Dic11C2×#4114yes—
326C2×Dic11C2×#4114yes—
327Dic22—216no—
328Dic22—216no—
329Dic22—44no—
330Dic22—48no—
331C23×Q8—111no—
332#533—228no—
333C2×C4⋊Q8—111no—
334C2×C4⋊Q8—114no—
335C2×C4⋊Q8—111no—
336C2×#125—112no—
337C2×C22⋊Q8—111no—
338C2×C22⋊Q8—112no—
339C2×C22⋊Q8C2×D1111yescharacteristic
340C2×C4×Q8—111no—
341C2×C4×Q8—112no—
342C2×C4×Q8—112no—
343C2×C4×Q8—112no—
344C2×C4×Q8—112no—
345C2×C4×Q8—112no—
346C2×C4×Q8—111no—
347C2×C4×Q8—228no—
348C2×#117—112no—
349C2×#117—112no—
350C22×C4⋊C4—111no—
351C22×C4⋊C4—111no—
352C22×C4⋊C4C2×D1111yescharacteristic
353C22×C42—111no—
354C22×C42—111no—
355C22×C42—111no—
356#398—112no—
357#398—112no—
358#398—114no—
359#398—112no—
360#398—114no—
361#398C2×D1112yes—
362#395—112no—
363#395—112no—
364#395—114no—
365#395—112no—
366#395—114no—
367#395C2×D1112yes—
368#391—114no—
369#391—114no—
370#389—114no—
371#389—114no—
372#389—114no—
373#389—114no—
374#389—114no—
375#389—114no—
376#389—114no—
377#389C2×D1114yes—
378#385—112no—
379#385—112no—
380#385—112no—
381#385—112no—
382#385—112no—
383#385—112no—
384#385C2×D1112yes—
385#385C2×D1112yes—
386#384—114no—
387C4×C4⋊C4—114no—
388C4×C4⋊C4—114no—
389C4×C4⋊C4—112no—
390C4×C4⋊C4—114no—
391C4×C4⋊C4—114no—
392C4×C4⋊C4—112no—
393C4×C22⋊C4—111no—
394C4×C22⋊C4—112no—
395C4×C22⋊C4C2×D1111yescharacteristic
396#376—112no—
397C43—112no—
398C22×C11—22no—
399C22×C11—22no—
400C22×C11—28no—
401C22×C11C2×C4⋊Q814yes—
402C22×C11C23×D411yescharacteristic
403C22×C11C23×Q812yes—
404C22×C11C22×#4112yes—
405C22×C11#58512yes—
406C4×C11—24no—
407C4×C11—22no—
408C4×C11—22no—
409C4×C11—28no—
410C4×C11—42no—
411C4×C11—42no—
412C4×C11—42no—
413Dic11—22no—
414Dic11—24no—
415Dic11—28no—
416Dic11—42no—
417Dic11—42no—
418Dic11—42no—
419Dic11#52514yes—
420Dic11C2×C4⋊Q814yes—
421Dic11C2×C4⋊Q814yes—
422C22×Q8—112no—
423C22×Q8—112no—
424C22×Q8—112no—
425C22×Q8—111no—
426C22×Q8—224no—
427C22×Q8—228no—
428C22×Q8C22×D1111yescharacteristic
429C23×C4—111no—
430C23×C4—111no—
431C23×C4—111no—
432C23×C4—111no—
433C23×C4C22×D1111yescharacteristic
434C23×C4C22×D1111yescharacteristic
435C23×C4C22×D1111yescharacteristic
436C4⋊Q8—224no—
437C4⋊Q8—224no—
438C4⋊Q8—2216no—
439#125—228no—
440C22⋊Q8—24no—
441C22⋊Q8—228no—
442C22⋊Q8—224no—
443C4×Q8—228no—
444C4×Q8—228no—
445C4×Q8—228no—
446C4×Q8—228no—
447C4×Q8—228no—
448C4×Q8—224no—
449C4×Q8—224no—
450#117—1116no—
451#117—228no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—114no—
454C2×C4⋊C4—112no—
455C2×C4⋊C4—112no—
456C2×C4⋊C4—112no—
457C2×C4⋊C4—112no—
458C2×C4⋊C4—112no—
459C2×C4⋊C4—112no—
460C2×C4⋊C4—112no—
461C2×C4⋊C4—112no—
462C2×C4⋊C4—112no—
463C2×C4⋊C4—112no—
464C2×C4⋊C4—111no—
465C2×C4⋊C4—114no—
466C2×C4⋊C4—114no—
467C2×C4⋊C4—114no—
468C2×C4⋊C4—114no—
469C2×C4⋊C4—114no—
470C2×C4⋊C4—114no—
471C2×C4⋊C4—224no—
472C2×C4⋊C4—224no—
473C2×C4⋊C4C22×D1112yes—
474C2×C4⋊C4C22×D1112yes—
475C2×C4⋊C4C22×D1112yes—
476C2×C4⋊C4C22×D1111yescharacteristic
477C2×C4⋊C4C22×D1114yes—
478C2×C4⋊C4C22×D1114yes—
479C2×C22⋊C4—112no—
480C2×C22⋊C4—112no—
481C2×C22⋊C4C22×D1112yes—
482C2×C22⋊C4C22×D1112yes—
483C2×C42—118no—
484C2×C42—114no—
485C2×C42—111no—
486C2×C42—111no—
487C2×C42—111no—
488C2×C42—111no—
489C2×C42—112no—
490C2×C42—112no—
491C2×C42—112no—
492C2×C42—112no—
493C2×C42—112no—
494C2×C42—112no—
495C2×C42—114no—
496C2×C42—112no—
497C2×C42—224no—
498C2×C42—224no—
499C2×C42C22×D1112yes—
500#95—112no—
501#95—114no—
502#95—114no—
503#95—114no—
504#95—114no—
505#95—114no—
506#95—114no—
507#95—114no—
508#95C22×D1112yes—
509#95C22×D1114yes—
510#95C22×D1114yes—
511C2×C11—24no—
512C2×C11C2×#52511yescharacteristic
513C2×C11C22×C4⋊Q811yescharacteristic
514C2×C11#344911yescharacteristic
515C2×C11Q8×#4114yes—
516C24C23×D1111yescharacteristic
517C2×Q8—22no—
518C2×Q8—42no—
519C2×Q8—118no—
520C2×Q8—224no—
521C2×Q8—224no—
522C2×Q8—224no—
523C2×Q8—224no—
524C2×Q8—224no—
525C2×Q8—228no—
526C2×Q8—2232no—
527C2×Q8—222no—
528C2×Q8—224no—
529C2×Q8—442no—
530C22×C4—22no—
531C22×C4—24no—
532C22×C4—22no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—114no—
536C22×C4—118no—
537C22×C4—111no—
538C22×C4—111no—
539C22×C4—111no—
540C22×C4—114no—
541C22×C4—114no—
542C22×C4—111no—
543C22×C4—112no—
544C22×C4—112no—
545C22×C4—112no—
546C22×C4—112no—
547C22×C4—224no—
548C22×C4—224no—
549C22×C4—222no—
550C22×C4—222no—
551C22×C4—442no—
552C22×C4D4×D1114yes—
553C22×C4C23×D1112yes—
554C22×C4C23×D1112yes—
555C22×C4C23×D1112yes—
556C22×C4C23×D1111yescharacteristic
557C22×C4C23×D1111yescharacteristic
558C22×C4C23×D1114yes—
559C22×C4C23×D1112yes—
560C4⋊C4—24no—
561C4⋊C4—24no—
562C4⋊C4—24no—
563C4⋊C4—22no—
564C4⋊C4—28no—
565C4⋊C4—44no—
566C4⋊C4—1116no—
567C4⋊C4—224no—
568C4⋊C4—224no—
569C4⋊C4—224no—
570C4⋊C4—224no—
571C4⋊C4—224no—
572C4⋊C4—224no—
573C4⋊C4—224no—
574C4⋊C4—228no—
575C4⋊C4—228no—
576C4⋊C4—224no—
577C4⋊C4—224no—
578C4⋊C4—224no—
579C4⋊C4—222no—
580C4⋊C4—228no—
581C4⋊C4—444no—
582C4⋊C4—444no—
583C4⋊C4—444no—
584C22⋊C4—24no—
585C22⋊C4—118no—
586C22⋊C4—224no—
587C22⋊C4Q8×D1118yes—
588C42—42no—
589C42—114no—
590C42—114no—
591C42—114no—
592C42—114no—
593C42—1116no—
594C42—224no—
595C42—224no—
596C42—224no—
597C42—224no—
598C42—224no—
599C42—224no—
600C42—228no—
601C42—442no—
602C11#3495311yescharacteristic, complemented, Sylow
603C23—22no—
604C23—22no—
605C23C2×D4×D1112yes—
606C23C2×Q8×D1114yes—
607C23C24×D1111yescharacteristic
608Q8—44no—
609Q8—2216no—
610Q8—2216no—
611Q8—444no—
612Q8—448no—
613C2×C4—28no—
614C2×C4—22no—
615C2×C4—24no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—24no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—44no—
627C2×C4—44no—
628C2×C4—1116no—
629C2×C4—112no—
630C2×C4—112no—
631C2×C4—112no—
632C2×C4—114no—
633C2×C4—114no—
634C2×C4—114no—
635C2×C4—112no—
636C2×C4—118no—
637C2×C4—114no—
638C2×C4—228no—
639C2×C4—228no—
640C2×C4—222no—
641C2×C4—224no—
642C2×C4—222no—
643C2×C4—222no—
644C2×C4—224no—
645C2×C4—222no—
646C2×C4—222no—
647C2×C4—222no—
648C2×C4—224no—
649C2×C4—224no—
650C2×C4—224no—
651C2×C4—444no—
652C2×C4C2×D4×D1112yes—
653C2×C4C2×D4×D1112yes—
654C2×C4C2×Q8×D1118yes—
655C2×C4#41×D1114yes—
656C22—28no—
657C22—22no—
658C22—22no—
659C22D11×C4⋊Q814yes—
660C22C22×D4×D1111yescharacteristic
661C22C22×Q8×D1112yes—
662C22C2×#41×D1112yes—
663C22#1062345512yes—
664C4—28no—
665C4—22no—
666C4—22no—
667C4—24no—
668C4—42no—
669C4—42no—
670C4—42no—
671C4—114no—
672C4—114no—
673C4—114no—
674C4—228no—
675C4—222no—
676C4—224no—
677C4—442no—
678C4—442no—
679C4—442no—
680C2—24no—
681C2D11×#52511yescharacteristic
682C2C2×D11×C4⋊Q811yescharacteristic
683C2#1308194211yescharacteristic
684C2#1308219514yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2583C2
prime radicalC24×C11C24
hypercenter#2583D11
hypocenterC11#34953
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2583

Complements

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

NH ≅ G/Ntype
3. #13074002C2semidirect
7. #13073820C2semidirect
8. #13073600C2semidirect
11. #13071908C2semidirect
12. #13071906C2semidirect
13. #13071187C2semidirect
162. #66930Q8semidirect
247. Dic11⋊C4C2×Q8semidirect
260. C4×Dic11C2×Q8semidirect
317. C2×Dic11C4⋊Q8semidirect
602. C11#34953semidirect

Maximal subgroups

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

subgroupindex
C2×#106231532
C22×#669402
#130740022
#130739972
#130739962
#130739912
#130738202
#130736002
#130730922
#130722582
#130719082
#130719062
#130711872
#130710952
C4×#669302
C11×#25832
#3495311