Finite Group Databasebeta

← #14679263

Subgroups — #14679263

Order 2816.

1786 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×Dic11C211yesmaximal, characteristic
2C2×#10622598C212yesmaximal
3C2×#10622594C211yesmaximal, characteristic
4#13066887C211yesmaximal, characteristic
5#13066881C211yesmaximal, characteristic
6#13066869C211yesmaximal, characteristic
7#13066850C212yesmaximal
8#13066850C212yesmaximal
9#13066848C212yesmaximal
10#95×Dic11C211yesmaximal, characteristic
11C2×C11×#395C211yesmaximal, characteristic
12C23×Q8×C11C2211yescharacteristic
13C22×C11×C4⋊C4C2212yes—
14C22×C11×C4⋊C4C2211yescharacteristic
15C2×Q8×Dic11—28no—
16C2×Q8×Dic11—24no—
17C22×C4⋊Dic11C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2212yes—
20C22×C4⋊Dic11C2212yes—
21C22×C4×Dic11C2212yes—
22C22×C4×Dic11C2212yes—
23C22×C4×Dic11C2211yescharacteristic
24C11×#395C418yescomplemented
25C2×C11×#95C2211yescharacteristic
26C2×C11×#95C2212yes—
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38#10622598—28no—
39#10622594—24no—
40C22×Q8×C11—24no—
41C22×Q8×C11—22no—
42C22×Q8×C11—22no—
43C22×Q8×C11—24no—
44C22×Q8×C11C2×C414yes—
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2312yes—
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2312yes—
50C23×Dic11C2311yescharacteristic
51C23×Dic11C2311yescharacteristic
52C23×Dic11C2312yes—
53C23×Dic11C2312yes—
54C23×Dic11C2311yescharacteristic
55C23×Dic11C2311yescharacteristic
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—24no—
58C2×C11×C4⋊C4—24no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4C2×C414yes—
61C2×C11×C4⋊C4C2×C418yes—
62Q8×Dic11—232no—
63C2×C4⋊Dic11—22no—
64C2×C4⋊Dic11—24no—
65C2×C4⋊Dic11—24no—
66C2×C4⋊Dic11—24no—
67C2×C4⋊Dic11—24no—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11—24no—
70C2×C4⋊Dic11—24no—
71C2×C4⋊Dic11—42no—
72C2×C4⋊Dic11D418yes—
73C2×C4×Dic11—24no—
74C2×C4×Dic11—24no—
75C2×C4×Dic11—24no—
76C2×C4×Dic11—24no—
77C2×C4×Dic11—24no—
78C2×C4×Dic11—24no—
79C2×C4×Dic11—42no—
80C2×C4×Dic11D414yes—
81C11×#95C2×C418yes—
82C11×#95C2×C414yes—
83C11⋊#95—22no—
84C11⋊#95—24no—
85C11⋊#95—22no—
86C11⋊#95—24no—
87C11⋊#95—24no—
88C11⋊#95—22no—
89C11⋊#95—22no—
90C11⋊#95—22no—
91C11⋊#95—24no—
92C11⋊#95—42no—
93C11⋊#95Q818yescomplemented
94#14186—111nomaximal, Sylow
95C24×C11C2411yescharacteristic
96C2×Q8×C11—28no—
97C2×Q8×C11—28no—
98C2×Q8×C11—216no—
99C2×Q8×C11—28no—
100C2×Q8×C11—216no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11C22×C412yes—
122C22×C4×C11C22×C412yes—
123C22×C4×C11C22×C414yes—
124C22×C4×C11C22×C412yes—
125C22×C4×C11C22×C414yes—
126C22×C4×C11C2×D414yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×Q814yes—
129C22×C4×C11#4112yes—
130C22×C4×C11#4114yes—
131C22×C4×C11#4114yes—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—21no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11C2×D414yes—
161C22×Dic11C2×D412yes—
162C22×Dic11C2×D414yes—
163C22×Dic11C2×D412yes—
164C22×Dic11C2×Q814yes—
165C22×Dic11C2×Q814yes—
166C11×C4⋊C4—216no—
167C11×C4⋊C4—28no—
168C4⋊Dic11—28no—
169C4⋊Dic11—216no—
170C4⋊Dic11—48no—
171C4⋊Dic11—44no—
172C4×Dic11—216no—
173C4×Dic11—28no—
174C4×Dic11—48no—
175C22×C4×Q8—111no—
176C2×#395D1111yescharacteristic
177C2×#389—112no—
178C2×#387—111no—
179#1446—111no—
180#1444—111no—
181#1441—111no—
182#1436—112no—
183#1436—112no—
184#1436—112no—
185C4×#95—111no—
186C23×C11C23×C411yescharacteristic
187C23×C11C22×D411yescharacteristic
188C23×C11C22×D412yes—
189C23×C11C22×Q812yes—
190C23×C11C2×#4111yescharacteristic
191C23×C11C2×#4112yes—
192C23×C11C2×#4112yes—
193C23×C11H(5,𝔽2)11yescharacteristic
194C23×C112−1+411yescharacteristic
195C23×C112−1+411yescharacteristic
196C23×C112−1+411yescharacteristic
197Q8×C11—232no—
198C2×C4×C11—24no—
199C2×C4×C11—24no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—24no—
203C2×C4×C11—24no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—24no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—42no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11C4×D414yes—
227C2×C4×C11C4×D418yes—
228C2×C4×C11C4×Q818yescomplemented
229C2×Dic11—22no—
230C2×Dic11—22no—
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—24no—
234C2×Dic11—24no—
235C2×Dic11—24no—
236C2×Dic11—24no—
237C2×Dic11—24no—
238C2×Dic11—24no—
239C2×Dic11—24no—
240C2×Dic11—24no—
241C2×Dic11—24no—
242C2×Dic11—24no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—42no—
258C2×Dic11—42no—
259C2×Dic11—42no—
260C2×Dic11—42no—
261C2×Dic11#12014yes—
262C2×Dic11C4⋊Q814yes—
263C23×Q8C2×D1111yescharacteristic
264C2×C4×Q8—224no—
265C2×C4×Q8—228no—
266C22×C4⋊C4—112no—
267C22×C4⋊C4—111no—
268C22×C4⋊C4—111no—
269C22×C4⋊C4—112no—
270C22×C4⋊C4C2×D1112yes—
271C22×C4⋊C4C2×D1111yescharacteristic
272C22×C42—111no—
273C22×C42—112no—
274C22×C42—112no—
275#395Dic1118yescomplemented
276#389—228no—
277#387—224no—
278C2×#95—112no—
279C2×#95—111no—
280C2×#95—112no—
281C2×#95—112no—
282C2×#95—111no—
283C2×#95—111no—
284C2×#95—111no—
285C2×#95—112no—
286C2×#95—112no—
287C2×#95—111no—
288C2×#95—112no—
289C2×#95C2×D1111yescharacteristic
290C2×#95C2×D1112yes—
291C22×C11C2×C4×D411yescharacteristic
292C22×C11C2×C4×D412yes—
293C22×C11C2×C4×Q812yes—
294C22×C11#51911yescharacteristic
295C22×C11#52011yescharacteristic
296C22×C11C2×#12011yescharacteristic
297C22×C11#52511yescharacteristic
298C22×C11#52512yes—
299C22×C11C2×C4⋊Q811yescharacteristic
300C22×C11#53211yescharacteristic
301C22×C11#53312yes—
302C22×C11#53611yescharacteristic
303C22×C11#53711yescharacteristic
304C22×C11#54111yescharacteristic
305C22×C11#54211yescharacteristic
306C22×C11#54612yes—
307C22×C11#54712yes—
308C22×C11D4×Q812yes—
309C22×C11D4×Q812yes—
310C22×C11#55212yes—
311C22×C11#55412yes—
312C22×C11#55612yes—
313C22×C11#55712yes—
314C4×C11—28no—
315C4×C11—28no—
316C4×C11—24no—
317C4×C11—42no—
318C4×C11—42no—
319Dic11—24no—
320Dic11—24no—
321Dic11—44no—
322Dic11—44no—
323Dic11—81no—
324Dic11—81no—
325C22×Q8—22no—
326C22×Q8—24no—
327C22×Q8—24no—
328C22×Q8—22no—
329C22×Q8C2×Dic1114yes—
330C23×C4—111no—
331C23×C4—111no—
332C23×C4—112no—
333C23×C4—112no—
334C23×C4—111no—
335C23×C4—111no—
336C23×C4C22×D1111yescharacteristic
337C23×C4C22×D1111yescharacteristic
338C23×C4C22×D1111yescharacteristic
339C23×C4C22×D1112yes—
340C23×C4C22×D1112yes—
341C4×Q8—2232no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—118no—
347C2×C4⋊C4—224no—
348C2×C4⋊C4—224no—
349C2×C4⋊C4—224no—
350C2×C4⋊C4—222no—
351C2×C4⋊C4—222no—
352C2×C4⋊C4—224no—
353C2×C4⋊C4—224no—
354C2×C4⋊C4—224no—
355C2×C4⋊C4—442no—
356C2×C4⋊C4C2×Dic1114yes—
357C2×C4⋊C4C2×Dic1118yes—
358C2×C42—114no—
359C2×C42—224no—
360C2×C42—224no—
361C2×C42—224no—
362C2×C42—224no—
363C2×C42—224no—
364C2×C42—224no—
365C2×C42—442no—
366#95—118no—
367#95—222no—
368#95—222no—
369#95—222no—
370#95—224no—
371#95—222no—
372#95—224no—
373#95—222no—
374#95—224no—
375#95—224no—
376#95—442no—
377#95C2×Dic1118yes—
378#95C2×Dic1114yes—
379C2×C11C4×#12011yescharacteristic
380C2×C11C4×C4⋊Q811yescharacteristic
381C2×C11#232311yescharacteristic
382C2×C11#236012yes—
383C2×C11#236512yes—
384C2×C11#243011yescharacteristic
385C2×C11#243411yescharacteristic
386C2×C11#246212yes—
387C2×C11#246512yes—
388C2×C11#258411yescharacteristic
389C2×C11#260411yescharacteristic
390C24C23×D1111yescharacteristic
391C2×Q8—28no—
392C2×Q8—28no—
393C2×Q8—216no—
394C2×Q8—216no—
395C2×Q8—28no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—112no—
417C22×C4—112no—
418C22×C4—114no—
419C22×C4—114no—
420C22×C4—114no—
421C22×C4—114no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—221no—
425C22×C4—221no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—222no—
432C22×C4—222no—
433C22×C4—222no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4—222no—
437C22×C4—222no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4—221no—
441C22×C4—221no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4—222no—
445C22×C4—222no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4D4×D1112yes—
451C22×C4D4×D1114yes—
452C22×C4#434114yes—
453C22×C4#434112yes—
454C22×C4Q8×D1114yes—
455C22×C4#434314yes—
456C22×C4C22×Dic1112yes—
457C22×C4C22×Dic1112yes—
458C22×C4C22×Dic1112yes—
459C22×C4C22×Dic1114yes—
460C22×C4C22×Dic1114yes—
461C4⋊C4—216no—
462C4⋊C4—28no—
463C4⋊C4—2216no—
464C4⋊C4—228no—
465C4⋊C4—448no—
466C4⋊C4—444no—
467C42—228no—
468C42—2216no—
469C42—448no—
470C11#1418611yescharacteristic, complemented, Sylow
471C23C2×D4×D1111yescharacteristic
472C23C2×D4×D1112yes—
473C23C2×#434112yes—
474C23C2×#434111yescharacteristic
475C23C2×Q8×D1112yes—
476C23C2×#434312yes—
477C23#6704011yescharacteristic
478C23#6704011yescharacteristic
479C23#6704211yescharacteristic
480C23#6704311yescharacteristic
481C23C23×Dic1111yescharacteristic
482Q8—232no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—22no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—114no—
512C2×C4—114no—
513C2×C4—222no—
514C2×C4—224no—
515C2×C4—224no—
516C2×C4—222no—
517C2×C4—222no—
518C2×C4—222no—
519C2×C4—224no—
520C2×C4—224no—
521C2×C4—224no—
522C2×C4—224no—
523C2×C4—224no—
524C2×C4—224no—
525C2×C4—224no—
526C2×C4—224no—
527C2×C4—442no—
528C2×C4—442no—
529C2×C4—442no—
530C2×C4—442no—
531C2×C4—442no—
532C2×C4—442no—
533C2×C4—442no—
534C2×C4—442no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—442no—
538C2×C4—442no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—442no—
544C2×C4—442no—
545C2×C4D4×Dic1118yes—
546C2×C4D4×Dic1114yes—
547C2×C4Q8×Dic1118yescomplemented
548C22#1062311711yescharacteristic
549C22#1062311712yes—
550C22D11×#12011yescharacteristic
551C22#1062315611yescharacteristic
552C22#1062315911yescharacteristic
553C22#1062316011yescharacteristic
554C22#1062316112yes—
555C22#1062316312yes—
556C22#1062316612yes—
557C22#1062317312yes—
558C22#1062317411yescharacteristic
559C22#1062325212yes—
560C22D11×C4⋊Q811yescharacteristic
561C22#1062325611yescharacteristic
562C22#1062325712yes—
563C22#1062325812yes—
564C22#1062325912yes—
565C22#1062326312yes—
566C22C2×D4×Dic1112yes—
567C22C2×D4×Dic1111yescharacteristic
568C22C2×Q8×Dic1112yes—
569C22#1062334311yescharacteristic
570C22#1062335811yescharacteristic
571C4—28no—
572C4—24no—
573C4—28no—
574C4—42no—
575C4—42no—
576C4—224no—
577C4—224no—
578C4—444no—
579C4—444no—
580C4—881no—
581C4—881no—
582C2#120×Dic1111yescharacteristic
583C2C4⋊Q8×Dic1111yescharacteristic
584C2#1307130011yescharacteristic
585C2#1307162512yes—
586C2#1307167612yes—
587C2#1307222711yescharacteristic
588C2#1307225511yescharacteristic
589C2#1307259312yes—
590C2#1307263212yes—
591C2#1307399811yescharacteristic
592C2#1307424711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#395C2
socle, prime radical, cosocleC24×C11C24
hypercenterC2×#395D11
hypocenterC11#14186
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
24. C11×#395C4semidirect
93. C11⋊#95Q8semidirect
228. C2×C4×C11C4×Q8semidirect
275. #395Dic11semidirect
470. C11#14186semidirect
547. C2×C4Q8×Dic11semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×Dic112
C2×#106225982
C2×#106225942
#130668872
#130668812
#130668692
#130668502
#130668482
#95×Dic112
C2×C11×#3952
#1418611