Finite Group Databasebeta

← #14675370

Subgroups — #14675370

Order 2816.

2022 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622564C212yesmaximal
2C2×C4⋊C4×Dic11C212yesmaximal, complemented
3C2×C4×C22⋊Dic11C212yesmaximal
4#13066853C211yesmaximal, characteristic
5#13066853C211yesmaximal, characteristic
6#13066850C212yesmaximal, complemented
7#13066848C212yesmaximal, complemented
8#95×Dic11C212yesmaximal, complemented
9C2×C11×#385C211yesmaximal, characteristic
10C24×C4×C11C2211yescharacteristic
11C22×C11×C4⋊C4C2212yes—
12C22×C11×C22⋊C4C2211yescharacteristic
13C22×C11×C22⋊C4C2211yescharacteristic
14C22×C22⋊Dic11C2212yes—
15C22×C22⋊Dic11C2212yes—
16C22×C4⋊Dic11C2212yes—
17C22×C4×Dic11C2211yescharacteristic
18C22×C4×Dic11C2212yes—
19C22×C4×Dic11C2212yes—
20C22×C4×Dic11C2211yescharacteristic
21C22×C4×Dic11C2212yes—
22C11×#385C418yescomplemented
23C2×C11×#95C2212yes—
24C4×C22⋊Dic11—28no—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C4⋊C4×Dic11—28no—
34#10622564C4116yescomplemented
35C25×C11C2311yescharacteristic
36C23×C4×C11—24no—
37C23×C4×C11—24no—
38C23×C4×C11—41no—
39C23×C4×C11—41no—
40C23×C4×C11C2×C414yes—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2312yes—
44C23×C4×C11C2312yes—
45C23×Dic11C2312yes—
46C23×Dic11C2312yes—
47C23×Dic11C2312yes—
48C23×Dic11C2312yes—
49C2×C11×C4⋊C4—24no—
50C2×C11×C4⋊C4—24no—
51C2×C11×C4⋊C4C2×C418yes—
52C2×C11×C22⋊C4—41no—
53C2×C11×C22⋊C4—41no—
54C2×C11×C22⋊C4C2×C418yes—
55C2×C11×C22⋊C4C2×C414yes—
56C2×C11×C22⋊C4C2×C414yes—
57C2×C22⋊Dic11—24no—
58C2×C22⋊Dic11—24no—
59C2×C22⋊Dic11—24no—
60C2×C22⋊Dic11—24no—
61C2×C22⋊Dic11C2×C418yes—
62C2×C22⋊Dic11C2×C418yes—
63C2×C4⋊Dic11—24no—
64C2×C4⋊Dic11—24no—
65C2×C4⋊Dic11C2×C418yescomplemented
66C2×C4×Dic11—24no—
67C2×C4×Dic11—24no—
68C2×C4×Dic11—24no—
69C2×C4×Dic11—24no—
70C2×C4×Dic11—24no—
71C2×C4×Dic11—24no—
72C2×C4×Dic11—24no—
73C2×C4×Dic11—24no—
74C2×C4×Dic11—42no—
75C2×C4×Dic11—42no—
76C2×C4×Dic11—41no—
77C2×C4×Dic11—41no—
78C2×C4×Dic11C2×C418yescomplemented
79C11×#95C2×C418yes—
80C11⋊#95—24no—
81C11⋊#95—24no—
82C11⋊#95—24no—
83C11⋊#95—41no—
84C11⋊#95—41no—
85C11⋊#95C2×C418yescomplemented
86C11⋊#95C2×C418yescomplemented
87C11⋊#95D418yes—
88#13823—111nomaximal, Sylow
89C24×C11—22no—
90C24×C11—22no—
91C24×C11—22no—
92C24×C11—22no—
93C24×C11—21no—
94C24×C11—21no—
95C24×C11—22no—
96C24×C11C22×C414yes—
97C24×C11C22×C412yes—
98C24×C11C2411yescharacteristic
99C22×C4×C11—22no—
100C22×C4×C11—22no—
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—21no—
114C22×C4×C11—21no—
115C22×C4×C11—216no—
116C22×C4×C11—44no—
117C22×C4×C11—44no—
118C22×C4×C11—48no—
119C22×C4×C11—44no—
120C22×C4×C11C22×C412yes—
121C22×C4×C11C22×C412yes—
122C22×C4×C11C22×C414yes—
123C22×C4×C11C22×C414yes—
124C22×C4×C11C22×C414yes—
125C22×C4×C11C22×C414yes—
126C22×C4×C11C2×D414yes—
127C22×C4×C11#4114yes—
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
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×Dic11C22×C414yes—
149C22×Dic11C22×C414yes—
150C22×Dic11C22×C414yes—
151C22×Dic11C22×C414yes—
152C22×Dic11C2×D414yes—
153C22×Dic11C2×D414yes—
154C22×Dic11#4114yes—
155C22×Dic11#4114yes—
156C11×C4⋊C4—216no—
157C11×C22⋊C4—44no—
158C11×C22⋊C4C42116yescomplemented
159C22⋊Dic11—216no—
160C22⋊Dic11—216no—
161C4⋊Dic11—216no—
162C4×Dic11—216no—
163C4×Dic11—48no—
164C4×Dic11—48no—
165C4×Dic11—44no—
166C4×Dic11—44no—
167C2×#388—112no—
168C2×#385D1111yescharacteristic
169C2×C4×C4⋊C4—112no—
170C2×C4×C22⋊C4—112no—
171#1437—111no—
172#1437—111no—
173#1436—112no—
174#1436—112no—
175C4×#95—112no—
176C23×C11—24no—
177C23×C11—24no—
178C23×C11—24no—
179C23×C11—24no—
180C23×C11—24no—
181C23×C11—24no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—24no—
185C23×C11—24no—
186C23×C11—41no—
187C23×C11—42no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11—41no—
191C23×C11—41no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—42no—
195C23×C11—41no—
196C23×C11C2×C4214yes—
197C23×C11C23×C412yes—
198C23×C11C23×C411yescharacteristic
199C23×C11C22×D412yes—
200C23×C11C2×#4112yes—
201C23×C11C2×#4112yes—
202C23×C11C2×#4112yes—
203C23×C11H(5,𝔽2)11yescharacteristic
204C23×C11H(5,𝔽2)11yescharacteristic
205C23×C112−1+412yes—
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—24no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—416no—
223C2×C4×C11—41no—
224C2×C4×C11—42no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—42no—
228C2×C4×C11—41no—
229C2×C4×C11C2×C4218yes—
230C2×C4×C11C4×D418yes—
231C2×Dic11—24no—
232C2×Dic11—24no—
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—24no—
244C2×Dic11—24no—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—24no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11C4×D418yes—
258C2×Dic11C4×D418yes—
259C24×C4C2×D1111yescharacteristic
260C22×C4⋊C4—112no—
261C22×C4⋊C4C2×D1112yes—
262C22×C22⋊C4—112no—
263C22×C22⋊C4—112no—
264C22×C22⋊C4C2×D1111yescharacteristic
265C22×C22⋊C4C2×D1111yescharacteristic
266C22×C42—112no—
267C22×C42—111no—
268C22×C42—112no—
269C22×C42—112no—
270C22×C42—111no—
271#388—1116no—
272#385Dic1118yescomplemented
273C4×C4⋊C4—228no—
274C4×C22⋊C4—228no—
275C2×#95—112no—
276C2×#95—112no—
277C2×#95—112no—
278C2×#95—112no—
279C2×#95—112no—
280C2×#95—112no—
281C2×#95—111no—
282C2×#95—111no—
283C2×#95C2×D1112yes—
284C22×C11—28no—
285C22×C11—24no—
286C22×C11—42no—
287C22×C11—44no—
288C22×C11—44no—
289C22×C11—44no—
290C22×C11—44no—
291C22×C11—44no—
292C22×C11—42no—
293C22×C11C22×C4211yescharacteristic
294C22×C11C2×C4×D412yes—
295C22×C11C2×C4×D412yes—
296C22×C11C2×C4×D412yes—
297C22×C11C4×#4112yes—
298C22×C11C4×#4112yes—
299C22×C11C4×#4112yes—
300C22×C11#51811yescharacteristic
301C22×C11#51911yescharacteristic
302C22×C11#52012yes—
303C22×C11#52012yes—
304C22×C11D4211yescharacteristic
305C22×C11#54612yes—
306C22×C11#54712yes—
307C22×C11#54812yes—
308C22×C11#55111yescharacteristic
309C22×C11#55111yescharacteristic
310C22×C11#55212yes—
311C22×C11#55312yes—
312C22×C11#55612yes—
313C22×C11#55911yescharacteristic
314C4×C11—28no—
315C4×C11—28no—
316C4×C11—42no—
317C4×C11—42no—
318Dic11—28no—
319Dic11—28no—
320Dic11—44no—
321Dic11—44no—
322C25C22×D1111yescharacteristic
323C23×C4—24no—
324C23×C4—24no—
325C23×C4—41no—
326C23×C4—41no—
327C23×C4—112no—
328C23×C4—112no—
329C23×C4—112no—
330C23×C4—112no—
331C23×C4C2×Dic1114yes—
332C23×C4C22×D1111yescharacteristic
333C23×C4C22×D1111yescharacteristic
334C23×C4C22×D1112yes—
335C23×C4C22×D1112yes—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—118no—
339C2×C4⋊C4—224no—
340C2×C4⋊C4—224no—
341C2×C4⋊C4C2×Dic1118yes—
342C2×C22⋊C4—41no—
343C2×C22⋊C4—41no—
344C2×C22⋊C4—118no—
345C2×C22⋊C4—118no—
346C2×C22⋊C4—224no—
347C2×C22⋊C4—224no—
348C2×C22⋊C4—224no—
349C2×C22⋊C4—224no—
350C2×C22⋊C4C4×D1118yes—
351C2×C22⋊C4C2×Dic1114yes—
352C2×C22⋊C4C2×Dic1114yes—
353C2×C42—118no—
354C2×C42—224no—
355C2×C42—224no—
356C2×C42—224no—
357C2×C42—224no—
358C2×C42—224no—
359C2×C42—224no—
360C2×C42—224no—
361C2×C42—224no—
362C2×C42—442no—
363C2×C42—442no—
364C2×C42—441no—
365C2×C42—441no—
366#95—118no—
367#95—118no—
368#95—118no—
369#95—224no—
370#95—224no—
371#95—224no—
372#95—441no—
373#95—441no—
374#95C2×Dic1118yes—
375C2×C11—44no—
376C2×C11C42×D412yes—
377C2×C11#227411yescharacteristic
378C2×C11#235811yescharacteristic
379C2×C11#235912yes—
380C2×C11#236112yes—
381C2×C11#236212yes—
382C2×C11#236712yes—
383C2×C11#237312yes—
384C2×C11#237411yescharacteristic
385C24—22no—
386C24—22no—
387C24—21no—
388C24—21no—
389C24—22no—
390C24—22no—
391C24—22no—
392C24C2×C4×D1114yes—
393C24C22×Dic1112yes—
394C24C23×D1111yescharacteristic
395C22×C4—22no—
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—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—216no—
412C22×C4—44no—
413C22×C4—44no—
414C22×C4—44no—
415C22×C4—48no—
416C22×C4—114no—
417C22×C4—114no—
418C22×C4—114no—
419C22×C4—114no—
420C22×C4—114no—
421C22×C4—114no—
422C22×C4—114no—
423C22×C4—114no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4—222no—
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—222no—
441C22×C4—222no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4C2×C4×D1114yes—
445C22×C4C2×C4×D1114yes—
446C22×C4D4×D1114yes—
447C22×C4#434114yes—
448C22×C4C22×Dic1112yes—
449C22×C4C22×Dic1112yes—
450C22×C4C22×Dic1114yes—
451C22×C4C22×Dic1114yes—
452C4⋊C4—216no—
453C4⋊C4—2216no—
454C22⋊C4—44no—
455C22⋊C4—2216no—
456C22⋊C4—2216no—
457C22⋊C4C4×Dic11116yescomplemented
458C42—2216no—
459C42—448no—
460C42—448no—
461C42—444no—
462C42—444no—
463C11#1382311yescharacteristic, complemented, Sylow
464C23—24no—
465C23—24no—
466C23—24no—
467C23—24no—
468C23—24no—
469C23—22no—
470C23—24no—
471C23—24no—
472C23—22no—
473C23—24no—
474C23—41no—
475C23—41no—
476C23—42no—
477C23—42no—
478C23—42no—
479C23—42no—
480C23—42no—
481C23—41no—
482C23—42no—
483C23—41no—
484C23C2×C4×Dic1114yes—
485C23C22×C4×D1112yes—
486C23C2×D4×D1112yes—
487C23C2×#434112yes—
488C23#6703711yescharacteristic
489C23#6703711yescharacteristic
490C23#6704012yes—
491C23#41×D1112yes—
492C23#41×D1112yes—
493C23C23×Dic1111yescharacteristic
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—416no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—42no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—41no—
517C2×C4—118no—
518C2×C4—118no—
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—224no—
528C2×C4—224no—
529C2×C4—224no—
530C2×C4—224no—
531C2×C4—224no—
532C2×C4—224no—
533C2×C4—224no—
534C2×C4—224no—
535C2×C4—224no—
536C2×C4—224no—
537C2×C4—442no—
538C2×C4—442no—
539C2×C4—442no—
540C2×C4—442no—
541C2×C4—442no—
542C2×C4—442no—
543C2×C4—442no—
544C2×C4—442no—
545C2×C4C2×C4×Dic1118yes—
546C2×C4D4×Dic1118yes—
547C22—28no—
548C22—24no—
549C22—44no—
550C22—44no—
551C22—44no—
552C22—44no—
553C22—42no—
554C22—42no—
555C22—44no—
556C22#1062303512yes—
557C22#1062303512yes—
558C22C4×#434112yes—
559C22C4×#434112yes—
560C22C4×D4×D1112yes—
561C22C4×D4×D1112yes—
562C22#1062311811yescharacteristic
563C22#1062312111yescharacteristic
564C22#1062312212yes—
565C22#1062316212yes—
566C22#1062316412yes—
567C22#1062317012yes—
568C22#1062317212yes—
569C22#1062319011yescharacteristic
570C22#1062319212yes—
571C22#1062319511yescharacteristic
572C22C22×C4×Dic1111yescharacteristic
573C22C2×D4×Dic1112yes—
574C22#1062332911yescharacteristic
575C22#1062334311yescharacteristic
576C22#41×Dic1112yes—
577C4—28no—
578C4—28no—
579C4—42no—
580C4—42no—
581C4—228no—
582C4—228no—
583C4—444no—
584C4—444no—
585C2—44no—
586C2C4×D4×Dic1112yes—
587C2#1307097311yescharacteristic
588C2#1307160011yescharacteristic
589C2#1307161112yes—
590C2#1307163512yes—
591C2#1307164712yes—
592C2#1307168412yes—
593C2#1307173112yes—
594C2#1307175211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC2×C11×#385C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#385D11
hypocenterC11#13823
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×Dic11C2semidirect
6. #13066850C2semidirect
7. #13066848C2semidirect
8. #95×Dic11C2semidirect
22. C11×#385C4semidirect
34. #10622564C4semidirect
65. C2×C4⋊Dic11C2×C4semidirect
78. C2×C4×Dic11C2×C4semidirect
85. C11⋊#95C2×C4semidirect
86. C11⋊#95C2×C4semidirect
158. C11×C22⋊C4C42semidirect
272. #385Dic11semidirect
457. C22⋊C4C4×Dic11semidirect
463. C11#13823semidirect

Maximal subgroups

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

subgroupindex
C2×#106225642
C2×C4⋊C4×Dic112
C2×C4×C22⋊Dic112
#130668532
#130668502
#130668482
#95×Dic112
C2×C11×#3852
#1382311