Finite Group Databasebeta

← #14914020

Subgroups — #14914020

Order 2816.

2314 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4341C211yesmaximal, characteristic
2#13071590C212yesmaximal, complemented
3#13071589C211yesmaximal, characteristic, complemented
4#13071584C212yesmaximal, complemented
5#13071536C211yesmaximal, characteristic, complemented
6#13071533C211yesmaximal, characteristic, complemented
7#13071498C214yesmaximal, complemented
8#13071497C212yesmaximal, complemented
9#13071455C212yesmaximal
10#13071257C214yesmaximal, complemented
11#13071253C212yesmaximal, complemented
12#13071012C211yesmaximal, characteristic, complemented
13#13071010C212yesmaximal, complemented
14#13071009C211yesmaximal, characteristic, complemented
15#13071007C212yesmaximal, complemented
16#13070980C212yesmaximal, complemented
17C11×#2357C211yesmaximal, characteristic, complemented
18C22×#4341C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×D4×Dic11C2211yescharacteristic
21C2×C4×C22⋊D11C2212yes—
22C22×C4×Dic11C2212yes—
23C4×#4341C4116yescomplemented
24C2×#66945C2211yescharacteristic
25C2×#66940C2212yes—
26C2×#66940C2211yescharacteristic
27C2×(C22⋊D11)⋊C4C2212yes—
28C2×#66930C2212yes—
29C2×C42×D11C2211yescharacteristic
30C2×C4×Dic22C2212yes—
31C2×C4×Dic22C2211yescharacteristic
32C11×#390C2212yes—
33C11×#388C2214yes—
34C11×#382C2211yescharacteristic
35C11×#381C2212yes—
36C4×C11×C4⋊C4C2212yes—
37C4×C11×C4⋊C4C2211yescharacteristic
38C4×C11×C22⋊C4C2212yes—
39#10622834C2212yes—
40#10622824C2212yes—
41C4×C22⋊Dic11C2212yes—
42#10622600C2212yes—
43#10622600C2212yes—
44#10622590C2212yes—
45C4⋊C4×Dic11C2212yes—
46C4⋊C4×Dic11C2212yes—
47#10622586C2212yes—
48#10622585C2214yes—
49#10622570C2214yes—
50#10622570C2214yes—
51#10622564C2214yes—
52#10622558C2214yes—
53#10622557C2214yes—
54#10622556C2214yes—
55#10622555C2214yes—
56#10622555C2214yes—
57C22⋊C4×Dic11C2214yes—
58#10622553C2214yes—
59C4×(C2×D11)⋊C4C2212yes—
60#10622549C2211yescharacteristic
61C4×C4⋊Dic11C2211yescharacteristic
62#10622545C2212yes—
63#10622545C2214yes—
64C4×Dic11⋊C4C2214yes—
65C4×Dic11⋊C4C2214yes—
66#10622541C2212yes—
67#10622282C2214yes—
68#10622279C2212yes—
69#10622277C2212yes—
70#10622277C2211yescharacteristic
71#10622277C2211yescharacteristic
72#10622264C2211yescharacteristic
73#10622264C2212yes—
74#10622264C2211yescharacteristic
75#10622263C2214yes—
76#10622263C2212yes—
77#10622263C2212yes—
78#10622262C2214yes—
79#10622262C2212yes—
80#10622262C2212yes—
81#10622261C2214yes—
82#10622261C2212yes—
83#10622260C2214yes—
84C22×D4×C11C2311yescharacteristic
85C23×C4×C11C2312yes—
86C22×C22⋊D11C2312yes—
87C23×Dic11C2312yes—
88C23×Dic11C2312yes—
89C2×#4341—24no—
90C2×#4341—24no—
91C2×#4341C2×C418yes—
92C22×C4×D11C2311yescharacteristic
93C22×C4×D11C2311yescharacteristic
94C22×C4×D11C2311yescharacteristic
95C22×Dic22C2311yescharacteristic
96C4×D4×C11C2×C418yes—
97C2×C11×C4⋊C4C2312yes—
98C2×C11×C4⋊C4C2312yes—
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C22⋊C4C2314yes—
101C2×C11×C22⋊C4C2314yes—
102C2×C11×C22⋊C4C2312yes—
103C2×C42×C11C2312yes—
104C2×C42×C11C2314yes—
105C2×C42×C11C2311yescharacteristic
106C2×C22⋊Dic11C2314yes—
107C2×C22⋊Dic11C2314yes—
108C2×C22⋊Dic11C2312yes—
109D4×Dic11C2×C418yes—
110C4×C22⋊D11C2×C4116yes—
111C2×(C2×D11)⋊C4C2314yes—
112C2×(C2×D11)⋊C4C2312yes—
113C2×(C2×D11)⋊C4C2312yes—
114C2×(C2×D11)⋊C4C2312yes—
115C2×C4⋊Dic11C2312yes—
116C2×C4⋊Dic11C2312yes—
117C2×C4⋊Dic11C2311yescharacteristic
118C2×Dic11⋊C4C2314yes—
119C2×Dic11⋊C4C2314yes—
120C2×Dic11⋊C4C2314yes—
121C2×Dic11⋊C4C2314yes—
122C2×Dic11⋊C4C2312yes—
123C2×Dic11⋊C4C2312yes—
124C2×C4×Dic11C2×C4116yes—
125C2×C4×Dic11C2314yes—
126C2×C4×Dic11C2314yes—
127C2×C4×Dic11C2312yes—
128C2×C4×Dic11C2314yes—
129C2×C4×Dic11C2314yes—
130C2×C4×Dic11C2312yes—
131C2×C4×Dic11C2311yescharacteristic
132C2×C4×Dic11C2311yescharacteristic
133C2×C4×Dic11C2311yescharacteristic
134C2×C4×Dic11C2312yes—
135C2×C4×Dic11C2312yes—
136#66945C2×C418yes—
137#66940—28no—
138#66940C2×C418yes—
139(C22⋊D11)⋊C4C2×C4116yes—
140#66930C2×C4116yes—
141C42×D11C2×C418yes—
142C4×Dic22—28no—
143C4×Dic22C2×C418yes—
144C11×#95C2312yes—
145C11×#95C2314yes—
146C11×#95C2311yescharacteristic
147C11×#95C2312yes—
148C11×#95C2311yescharacteristic
149C11⋊#95C2314yes—
150C11⋊#95C2312yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2312yes—
155C11⋊#95C2311yescharacteristic
156C11⋊#95C2312yes—
157C11⋊#95C2312yes—
158C11⋊#95C2311yescharacteristic
159C11⋊#95C2312yes—
160C11⋊#95C2314yes—
161C11⋊#95C2312yes—
162C11⋊#95C2312yes—
163C11⋊#95C2312yes—
164#34197—111nomaximal, Sylow
165C24×C11C2412yes—
166C23×D11C2411yescharacteristic
167C2×D4×C11—22no—
168C2×D4×C11—22no—
169C2×D4×C11C22×C414yes—
170C22×C4×C11—44no—
171C22×C4×C11C22×C418yes—
172C22×C4×C11C2412yes—
173C22×C4×C11C2412yes—
174C22×C4×C11C2414yes—
175C22×C4×C11C2411yescharacteristic
176C22×C4×C11C2412yes—
177C22×C4×C11C2411yescharacteristic
178C22×C4×C11C2411yescharacteristic
179C2×C22⋊D11—24no—
180C2×C22⋊D11—24no—
181C2×C22⋊D11C22×C418yes—
182C22×Dic11—24no—
183C22×Dic11—24no—
184C22×Dic11—44no—
185C22×Dic11C22×C418yes—
186C22×Dic11C22×C418yes—
187C22×Dic11C2412yes—
188C22×Dic11C2412yes—
189C22×Dic11C2414yes—
190C22×Dic11C2411yescharacteristic
191C22×Dic11C2411yescharacteristic
192C22×Dic11C2411yescharacteristic
193C22×Dic11C2412yes—
194C22×Dic11C2412yes—
195#4341—232no—
196C2×C4×D11—22no—
197C2×C4×D11—22no—
198C2×C4×D11—42no—
199C2×C4×D11—42no—
200C2×C4×D11C22×C414yes—
201C2×C4×D11C22×C414yes—
202C2×C4×D11C22×C414yes—
203C2×Dic22C22×C414yes—
204C2×Dic22#4114yes—
205C2×Dic22#4114yes—
206C11×C4⋊C4—24no—
207C11×C4⋊C4—42no—
208C11×C4⋊C4C22×C414yes—
209C11×C22⋊C4—44no—
210C11×C22⋊C4—44no—
211C11×C22⋊C4C22×C418yes—
212C42×C11—24no—
213C42×C11—44no—
214C42×C11C22×C414yes—
215C22⋊Dic11—44no—
216C22⋊Dic11—44no—
217C22⋊Dic11C22×C418yes—
218(C2×D11)⋊C4—44no—
219(C2×D11)⋊C4—42no—
220(C2×D11)⋊C4—42no—
221(C2×D11)⋊C4C22×C418yes—
222C4⋊Dic11—24no—
223C4⋊Dic11—42no—
224C4⋊Dic11C22×C414yes—
225Dic11⋊C4—28no—
226Dic11⋊C4—28no—
227Dic11⋊C4—44no—
228Dic11⋊C4—44no—
229Dic11⋊C4C22×C418yes—
230Dic11⋊C4C22×C418yes—
231C4×Dic11—28no—
232C4×Dic11—28no—
233C4×Dic11—24no—
234C4×Dic11—44no—
235C4×Dic11—44no—
236C4×Dic11C22×C418yes—
237C4×Dic11C22×C414yes—
238C4×Dic11C22×C414yes—
239C4×Dic11C22×C414yes—
240C4×Dic11C22×C418yes—
241C4×Dic11C22×C418yes—
242C2×C4×#41—111no—
243#2357—112no—
244#2357—112no—
245#2357—111no—
246#2357D1111yescharacteristic, complemented
247#2351—111no—
248#2351—111no—
249#2346—114no—
250#2346—112no—
251#2341—112no—
252#2319—112no—
253#2319—114no—
254#2283—111no—
255#2283—112no—
256#2283—111no—
257#2283—112no—
258#2276—112no—
259C23×C11—22no—
260C23×C11—22no—
261C23×C11—24no—
262C23×C11—24no—
263C23×C11C23×C414yes—
264C23×C11C2511yescharacteristic
265C22×D11—21no—
266C22×D11—21no—
267C22×D11—22no—
268C22×D11—22no—
269C22×D11C23×C412yes—
270D4×C11—28no—
271C2×C4×C11—24no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—24no—
276C2×C4×C11—22no—
277C2×C4×C11—24no—
278C2×C4×C11—22no—
279C2×C4×C11—24no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—48no—
284C2×C4×C11C23×C412yes—
285C2×C4×C11C23×C414yes—
286C2×C4×C11C23×C412yes—
287C2×C4×C11C23×C412yes—
288C2×C4×C11C2×#4112yes—
289C2×C4×C11C2×#4112yes—
290C22⋊D11—216no—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—22no—
294C2×Dic11—24no—
295C2×Dic11—22no—
296C2×Dic11—216no—
297C2×Dic11—22no—
298C2×Dic11—22no—
299C2×Dic11—24no—
300C2×Dic11—22no—
301C2×Dic11—24no—
302C2×Dic11—22no—
303C2×Dic11—24no—
304C2×Dic11—22no—
305C2×Dic11—22no—
306C2×Dic11—48no—
307C2×Dic11C23×C412yes—
308C2×Dic11C23×C412yes—
309C2×Dic11C23×C412yes—
310C2×Dic11C23×C414yes—
311C2×Dic11C23×C414yes—
312C2×Dic11C2×#4114yes—
313C2×Dic11C2×#4114yes—
314C4×D11—28no—
315C4×D11—44no—
316C4×D11—44no—
317Dic22#117116yes—
318C22×#41—111no—
319C4×#41—1116no—
320C2×C4×Q8—111no—
321C2×C4×Q8—112no—
322C2×C4×Q8—111no—
323C2×C4×Q8—112no—
324C2×C4×D4—111no—
325C2×C4×D4—112no—
326C2×C4×D4—112no—
327C2×C4×D4C2×D1111yescharacteristic
328C2×#117—111no—
329C2×#117—112no—
330C22×C42—112no—
331C22×C42—111no—
332#390—112no—
333#390—114no—
334#390—114no—
335#390C2×D1112yes—
336#389—114no—
337#389—112no—
338#389—112no—
339#389—114no—
340#388—114no—
341#388—114no—
342#388—114no—
343#388—114no—
344#388—114no—
345#388C2×D1114yes—
346#383—111no—
347#383—112no—
348#383—111no—
349#382—112no—
350#382—111no—
351#382—114no—
352#382—112no—
353#382—112no—
354#382C2×D1111yescharacteristic
355#381—112no—
356#381—114no—
357#381—112no—
358#381—111no—
359#381—111no—
360#381C2×D1112yes—
361#380—112no—
362#380—112no—
363#380—114no—
364#380—114no—
365C4×C4⋊C4—112no—
366C4×C4⋊C4—112no—
367C4×C4⋊C4—114no—
368C4×C4⋊C4—114no—
369C4×C4⋊C4—111no—
370C4×C4⋊C4—114no—
371C4×C4⋊C4—112no—
372C4×C4⋊C4—112no—
373C4×C4⋊C4C2×D1112yes—
374C4×C4⋊C4C2×D1111yescharacteristic
375C4×C22⋊C4—112no—
376C4×C22⋊C4—114no—
377C4×C22⋊C4—112no—
378C4×C22⋊C4—112no—
379C4×C22⋊C4C2×D1112yes—
380#376—112no—
381#376—114no—
382#376—114no—
383#376—112no—
384C22×C11—24no—
385C22×C11—24no—
386C22×C11—24no—
387C22×C11—44no—
388C22×C11—44no—
389C22×C11C24×C411yescharacteristic
390C22×C11C22×#4111yescharacteristic
391C22×C11C22×#4111yescharacteristic
392C22×C11#58512yes—
393C22×C11#58512yes—
394C2×D11—22no—
395C2×D11—22no—
396C2×D11—22no—
397C2×D11—42no—
398C2×D11—42no—
399C4×C11—22no—
400C4×C11—24no—
401C4×C11—22no—
402C4×C11—44no—
403C4×C11—42no—
404C4×C11—42no—
405C4×C11C2×#11714yes—
406Dic11—22no—
407Dic11—22no—
408Dic11—22no—
409Dic11—24no—
410Dic11—42no—
411Dic11—42no—
412Dic11—44no—
413Dic11C2×#11718yes—
414C2×#41—118no—
415C2×#41—224no—
416C2×#41—224no—
417C22×Q8—111no—
418C22×D4—112no—
419C22×D4C22×D1111yescharacteristic
420C23×C4—112no—
421C23×C4—112no—
422C23×C4—111no—
423C23×C4—111no—
424C23×C4—111no—
425C23×C4C22×D1112yes—
426C4×Q8—118no—
427C4×Q8—118no—
428C4×Q8—228no—
429C4×Q8—228no—
430C4×D4—118no—
431C4×D4—1116no—
432C4×D4—1116no—
433C4×D4C4×D1118yes—
434#117—118no—
435#117—1116no—
436C2×C4⋊C4—112no—
437C2×C4⋊C4—112no—
438C2×C4⋊C4—111no—
439C2×C4⋊C4—114no—
440C2×C4⋊C4—114no—
441C2×C4⋊C4—112no—
442C2×C4⋊C4—114no—
443C2×C4⋊C4—114no—
444C2×C4⋊C4—112no—
445C2×C4⋊C4C22×D1112yes—
446C2×C4⋊C4C22×D1112yes—
447C2×C4⋊C4C22×D1111yescharacteristic
448C2×C22⋊C4—112no—
449C2×C22⋊C4—112no—
450C2×C22⋊C4—114no—
451C2×C22⋊C4—114no—
452C2×C22⋊C4—112no—
453C2×C22⋊C4—112no—
454C2×C22⋊C4—114no—
455C2×C22⋊C4C22×D1114yes—
456C2×C22⋊C4C22×D1114yes—
457C2×C22⋊C4C22×D1112yes—
458C2×C42—1116no—
459C2×C42—111no—
460C2×C42—112no—
461C2×C42—112no—
462C2×C42—111no—
463C2×C42—112no—
464C2×C42—111no—
465C2×C42—118no—
466C2×C42—114no—
467C2×C42—114no—
468C2×C42—112no—
469C2×C42—114no—
470C2×C42—114no—
471C2×C42C22×D1112yes—
472C2×C42C22×D1114yes—
473C2×C42C22×D1111yescharacteristic
474#95—112no—
475#95—112no—
476#95—114no—
477#95—112no—
478#95—114no—
479#95—112no—
480#95—112no—
481#95—114no—
482#95—114no—
483#95—114no—
484#95—112no—
485#95—112no—
486#95—112no—
487#95—111no—
488#95—111no—
489#95C22×D1114yes—
490#95C22×D1112yes—
491#95C22×D1112yes—
492#95C22×D1111yescharacteristic
493#95C22×D1111yescharacteristic
494C2×C11—44no—
495C2×C11C22×#11711yescharacteristic
496C2×C11#342811yescharacteristic
497C2×C11#342811yescharacteristic
498C2×C11#352412yes—
499C2×C11#352412yes—
500D11—42no—
501C24—111no—
502C24C23×D1112yes—
503#41—2232no—
504C2×Q8—114no—
505C2×Q8—114no—
506C2×Q8—114no—
507C2×D4—22no—
508C2×D4—22no—
509C2×D4—118no—
510C2×D4—224no—
511C2×D4—224no—
512C2×D4C2×C4×D1114yes—
513C22×C4—44no—
514C22×C4—112no—
515C22×C4—118no—
516C22×C4—111no—
517C22×C4—111no—
518C22×C4—111no—
519C22×C4—112no—
520C22×C4—118no—
521C22×C4—114no—
522C22×C4—114no—
523C22×C4—114no—
524C22×C4—112no—
525C22×C4—112no—
526C22×C4—114no—
527C22×C4—224no—
528C22×C4—224no—
529C22×C4—222no—
530C22×C4—222no—
531C22×C4—442no—
532C22×C4—442no—
533C22×C4—444no—
534C22×C4C2×C4×D1118yes—
535C22×C4C23×D1112yes—
536C22×C4C23×D1112yes—
537C22×C4C23×D1114yes—
538C22×C4C23×D1111yescharacteristic
539C22×C4C23×D1112yes—
540C22×C4C23×D1111yescharacteristic
541C22×C4C23×D1111yescharacteristic
542C4⋊C4—24no—
543C4⋊C4—42no—
544C4⋊C4—118no—
545C4⋊C4—118no—
546C4⋊C4—114no—
547C4⋊C4—228no—
548C4⋊C4—228no—
549C4⋊C4—224no—
550C4⋊C4—444no—
551C4⋊C4—444no—
552C4⋊C4—442no—
553C4⋊C4C2×C4×D1114yes—
554C22⋊C4—44no—
555C22⋊C4—44no—
556C22⋊C4—118no—
557C22⋊C4—118no—
558C22⋊C4—444no—
559C22⋊C4—442no—
560C22⋊C4—442no—
561C22⋊C4—444no—
562C22⋊C4—444no—
563C22⋊C4C2×C4×D1118yes—
564C42—24no—
565C42—44no—
566C42—114no—
567C42—118no—
568C42—114no—
569C42—118no—
570C42—118no—
571C42—114no—
572C42—228no—
573C42—228no—
574C42—224no—
575C42—444no—
576C42—444no—
577C42C2×C4×D1114yes—
578C11#3419711yescharacteristic, complemented, Sylow
579C23—22no—
580C23—22no—
581C23—24no—
582C23—24no—
583C23—112no—
584C23—221no—
585C23—221no—
586C23—222no—
587C23—222no—
588C23C22×C4×D1114yes—
589C23C24×D1111yescharacteristic
590Q8—1116no—
591D4—28no—
592D4—2216no—
593C2×C4—22no—
594C2×C4—24no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—24no—
599C2×C4—22no—
600C2×C4—24no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—24no—
604C2×C4—22no—
605C2×C4—48no—
606C2×C4—114no—
607C2×C4—114no—
608C2×C4—114no—
609C2×C4—112no—
610C2×C4—112no—
611C2×C4—112no—
612C2×C4—114no—
613C2×C4—2216no—
614C2×C4—221no—
615C2×C4—221no—
616C2×C4—224no—
617C2×C4—222no—
618C2×C4—222no—
619C2×C4—228no—
620C2×C4—222no—
621C2×C4—222no—
622C2×C4—224no—
623C2×C4—222no—
624C2×C4—224no—
625C2×C4—222no—
626C2×C4—222no—
627C2×C4—224no—
628C2×C4—222no—
629C2×C4—444no—
630C2×C4—444no—
631C2×C4—448no—
632C2×C4C22×C4×D1112yes—
633C2×C4C22×C4×D1114yes—
634C2×C4C22×C4×D1112yes—
635C2×C4C22×C4×D1112yes—
636C2×C4#41×D1112yes—
637C2×C4#41×D1112yes—
638C22—24no—
639C22—24no—
640C22—24no—
641C22—44no—
642C22—44no—
643C22—222no—
644C22—222no—
645C22—222no—
646C22—442no—
647C22—442no—
648C22C23×C4×D1111yescharacteristic
649C22C2×#41×D1111yescharacteristic
650C22C2×#41×D1111yescharacteristic
651C22#1062345312yes—
652C22#1062345512yes—
653C4—22no—
654C4—24no—
655C4—22no—
656C4—44no—
657C4—42no—
658C4—42no—
659C4—118no—
660C4—222no—
661C4—222no—
662C4—222no—
663C4—224no—
664C4—442no—
665C4—442no—
666C4—444no—
667C4D11×#11714yes—
668C2—44no—
669C2—442no—
670C2C2×D11×#11711yescharacteristic
671C2#1308181411yescharacteristic
672C2#1308181511yescharacteristic
673C2#1308272012yes—
674C2#1308272412yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2357C2
socle, cosocleC23×C11C25
prime radicalC22×#4341C22
hypercenter#2357D11
hypocenterC11#34197
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2357

Complements

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

NH ≅ G/Ntype
2. #13071590C2semidirect
3. #13071589C2semidirect
4. #13071584C2semidirect
5. #13071536C2semidirect
6. #13071533C2semidirect
7. #13071498C2semidirect
8. #13071497C2semidirect
10. #13071257C2semidirect
11. #13071253C2semidirect
12. #13071012C2semidirect
13. #13071010C2semidirect
14. #13071009C2semidirect
15. #13071007C2semidirect
16. #13070980C2semidirect
17. C11×#2357C2semidirect
23. C4×#4341C4semidirect
246. #2357D11semidirect
578. C11#34197semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43412
#130715902
#130715892
#130715842
#130715362
#130715332
#130714982
#130714972
#130714552
#130712572
#130712532
#130710122
#130710102
#130710092
#130710072
#130709802
C11×#23572
#3419711