Finite Group Databasebeta

← #14680421

Subgroups — #14680421

Order 2816.

1978 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622825C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
3#13066869C212yesmaximal, complemented
4#13066865C212yesmaximal, complemented
5#13066861C212yesmaximal, complemented
6#13066857C212yesmaximal
7#13066853C212yesmaximal, complemented
8#13066848C212yesmaximal, complemented
9C22×C11×#123C211yesmaximal, characteristic
10C23×D4×C11C2211yescharacteristic
11C24×C4×C11C2211yescharacteristic
12C2×C11×#123—24no—
13C2×C11×#123—24no—
14C2×C11×#123C418yescomplemented
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C22⋊Dic11C2212yes—
21C22×C22⋊Dic11C2214yes—
22C22×C22⋊Dic11C2212yes—
23C22×C4⋊Dic11C2212yes—
24C22×C4×Dic11C2212yes—
25#10622825—24no—
26C4×C22⋊Dic11—24no—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2214yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2214yes—
31C2×C11⋊#95C2214yes—
32C25×C11C2311yescharacteristic
33C25×C11C2311yescharacteristic
34C22×D4×C11—22no—
35C22×D4×C11—22no—
36C22×D4×C11—44no—
37C22×D4×C11C2×C414yes—
38C23×C4×C11—44no—
39C23×C4×C11C2×C414yes—
40C23×C4×C11D414yes—
41C23×C4×C11D414yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×Dic11C2314yes—
48C23×Dic11C2314yes—
49C11×#123—232no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4C2×C414yes—
55C2×C11×C4⋊C4C2×C414yes—
56C2×C11×C22⋊C4—22no—
57C2×C11×C22⋊C4—22no—
58C2×C11×C22⋊C4—22no—
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4C2×C414yes—
63C2×C11×C22⋊C4C2×C414yes—
64C2×C11×C22⋊C4C2×C414yes—
65C2×C22⋊Dic11—24no—
66C2×C22⋊Dic11—28no—
67C2×C22⋊Dic11—24no—
68C2×C22⋊Dic11—28no—
69C2×C22⋊Dic11—44no—
70C2×C22⋊Dic11—44no—
71C2×C22⋊Dic11—44no—
72C2×C4⋊Dic11—24no—
73C2×C4⋊Dic11—44no—
74C2×C4×Dic11—24no—
75C2×C4×Dic11—44no—
76C11⋊#95—24no—
77C11⋊#95—24no—
78C11⋊#95—28no—
79C11⋊#95—44no—
80C11⋊#95—44no—
81#14287—111nomaximal, Sylow
82C24×C11—24no—
83C24×C11—22no—
84C24×C11—24no—
85C24×C11—22no—
86C24×C11—21no—
87C24×C11—21no—
88C24×C11—24no—
89C24×C11—22no—
90C24×C11—24no—
91C24×C11—22no—
92C24×C11C22×C412yes—
93C24×C11C22×C412yes—
94C24×C11C2×D412yes—
95C24×C11C2×D412yes—
96C24×C11C2411yescharacteristic
97C2×D4×C11—28no—
98C2×D4×C11—48no—
99C2×D4×C11—48no—
100C2×D4×C11—48no—
101C22×C4×C11—24no—
102C22×C4×C11—24no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—24no—
110C22×C4×C11—22no—
111C22×C4×C11—24no—
112C22×C4×C11—22no—
113C22×C4×C11—48no—
114C22×C4×C11—48no—
115C22×C4×C11—48no—
116C22×C4×C11C22⋊C4116yescomplemented
117C22×C4×C11C22×C412yes—
118C22×C4×C11C22×C412yes—
119C22×C4×C11C22×C412yes—
120C22×C4×C11C22×C412yes—
121C22×C4×C11C22×C412yes—
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D412yes—
126C22×Dic11—24no—
127C22×Dic11—24no—
128C22×Dic11—24no—
129C22×Dic11—24no—
130C22×Dic11—24no—
131C22×Dic11—24no—
132C22×Dic11—24no—
133C22×Dic11—24no—
134C22×Dic11—24no—
135C22×Dic11—24no—
136C22×Dic11—24no—
137C22×Dic11—24no—
138C22×Dic11—24no—
139C22×Dic11#4118yes—
140C11×C4⋊C4—28no—
141C11×C4⋊C4—28no—
142C11×C22⋊C4—28no—
143C11×C22⋊C4—28no—
144C11×C22⋊C4—28no—
145C22⋊Dic11—216no—
146C22⋊Dic11—48no—
147C22⋊Dic11—416no—
148C4⋊Dic11—48no—
149C4×Dic11—48no—
150C22×#123D1111yescharacteristic
151C2×#380—111no—
152C2×C4×C22⋊C4—111no—
153#1441—112no—
154#1440—112no—
155#1439—112no—
156#1438—112no—
157#1437—112no—
158#1436—112no—
159C23×C11—24no—
160C23×C11—24no—
161C23×C11—24no—
162C23×C11—24no—
163C23×C11—24no—
164C23×C11—24no—
165C23×C11—24no—
166C23×C11—22no—
167C23×C11—22no—
168C23×C11—24no—
169C23×C11—22no—
170C23×C11—24no—
171C23×C11—24no—
172C23×C11—24no—
173C23×C11—44no—
174C23×C11—44no—
175C23×C11—44no—
176C23×C11—44no—
177C23×C11—42no—
178C23×C11—42no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11—42no—
184C23×C11—44no—
185C23×C11—44no—
186C23×C11—44no—
187C23×C11—44no—
188C23×C11C2×C22⋊C414yes—
189C23×C11C23×C411yescharacteristic
190C23×C11C22×D411yescharacteristic
191C23×C11C22×D411yescharacteristic
192C23×C11C2×#4114yes—
193C23×C11H(5,𝔽2)14yes—
194C23×C11H(5,𝔽2)12yes—
195C23×C112−1+412yes—
196D4×C11—416no—
197C2×C4×C11—24no—
198C2×C4×C11—24no—
199C2×C4×C11—24no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—24no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—416no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—42no—
217C2×C4×C11C2×C22⋊C414yes—
218C2×C4×C11C2×C22⋊C414yes—
219C2×Dic11—28no—
220C2×Dic11—28no—
221C2×Dic11—28no—
222C2×Dic11—44no—
223C2×Dic11—44no—
224C2×Dic11—44no—
225C2×Dic11—44no—
226C2×Dic11—44no—
227C2×Dic11—44no—
228C2×Dic11—44no—
229C2×Dic11—44no—
230C2×Dic11—44no—
231C2×Dic11—44no—
232C2×Dic11—44no—
233C23×D4C2×D1111yescharacteristic
234C24×C4C2×D1111yescharacteristic
235C2×#123—24no—
236C2×#123—24no—
237C2×#123Dic1118yescomplemented
238C22×C4⋊C4—112no—
239C22×C4⋊C4C2×D1111yescharacteristic
240C22×C4⋊C4C2×D1111yescharacteristic
241C22×C22⋊C4—112no—
242C22×C22⋊C4—114no—
243C22×C22⋊C4—112no—
244C22×C22⋊C4C2×D1111yescharacteristic
245C22×C22⋊C4C2×D1111yescharacteristic
246C22×C22⋊C4C2×D1111yescharacteristic
247C22×C42—112no—
248#380—224no—
249C4×C22⋊C4—224no—
250C2×#95—112no—
251C2×#95—114no—
252C2×#95—112no—
253C2×#95—114no—
254C2×#95—114no—
255C22×C11—24no—
256C22×C11—24no—
257C22×C11—24no—
258C22×C11—48no—
259C22×C11—48no—
260C22×C11—44no—
261C22×C11—44no—
262C22×C11—42no—
263C22×C11—42no—
264C22×C11—48no—
265C22×C11—42no—
266C22×C11—84no—
267C22×C11—82no—
268C22×C11—82no—
269C22×C11C22×C22⋊C411yescharacteristic
270C22×C11C4×#4112yes—
271C22×C11#51812yes—
272C22×C11#52012yes—
273C22×C11#52512yes—
274C22×C11#53212yes—
275C22×C11#53412yes—
276C22×C11#53412yes—
277C22×C11#53511yescharacteristic
278C22×C11#53611yescharacteristic
279C22×C11#53712yes—
280C22×C11#53814yes—
281C22×C11#53914yes—
282C22×C11#54014yes—
283C22×C11#54214yes—
284C4×C11—24no—
285C4×C11—24no—
286C4×C11—42no—
287C4×C11—42no—
288C4×C11—42no—
289Dic11—48no—
290Dic11—84no—
291C25C22×D1111yescharacteristic
292C25C22×D1111yescharacteristic
293C22×D4—22no—
294C22×D4—22no—
295C22×D4—44no—
296C22×D4C2×Dic1114yes—
297C23×C4—44no—
298C23×C4—114no—
299C23×C4—114no—
300C23×C4C2×Dic1114yes—
301C23×C4C22⋊D1114yes—
302C23×C4C22⋊D1114yes—
303C23×C4C22×D1111yescharacteristic
304C23×C4C22×D1111yescharacteristic
305C23×C4C22×D1111yescharacteristic
306C23×C4C22×D1111yescharacteristic
307C23×C4C22×D1111yescharacteristic
308#123—232no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—224no—
314C2×C4⋊C4—444no—
315C2×C4⋊C4C2×Dic1114yes—
316C2×C4⋊C4C2×Dic1114yes—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—228no—
324C2×C22⋊C4—224no—
325C2×C22⋊C4—228no—
326C2×C22⋊C4—224no—
327C2×C22⋊C4—444no—
328C2×C22⋊C4—444no—
329C2×C22⋊C4—444no—
330C2×C22⋊C4C2×Dic1114yes—
331C2×C22⋊C4C2×Dic1114yes—
332C2×C22⋊C4C2×Dic1114yes—
333C2×C42—224no—
334C2×C42—444no—
335#95—228no—
336#95—224no—
337#95—224no—
338#95—444no—
339#95—444no—
340C2×C11—44no—
341C2×C11—82no—
342C2×C11#229711yescharacteristic
343C2×C11#230811yescharacteristic
344C2×C11#231111yescharacteristic
345C2×C11#233514yes—
346C2×C11#263014yes—
347C2×C11#266112yes—
348C2×C11#266312yes—
349C24—24no—
350C24—24no—
351C24—22no—
352C24—22no—
353C24—24no—
354C24—24no—
355C24—22no—
356C24—22no—
357C24—21no—
358C24—21no—
359C24C22×Dic1112yes—
360C24C22×Dic1112yes—
361C24C2×C22⋊D1112yes—
362C24C2×C22⋊D1112yes—
363C24C23×D1111yescharacteristic
364C2×D4—28no—
365C2×D4—48no—
366C2×D4—48no—
367C2×D4—48no—
368C22×C4—24no—
369C22×C4—24no—
370C22×C4—24no—
371C22×C4—24no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—48no—
381C22×C4—48no—
382C22×C4—48no—
383C22×C4—118no—
384C22×C4—224no—
385C22×C4—224no—
386C22×C4—224no—
387C22×C4—224no—
388C22×C4—224no—
389C22×C4—224no—
390C22×C4—224no—
391C22×C4—224no—
392C22×C4—224no—
393C22×C4—224no—
394C22×C4—224no—
395C22×C4—224no—
396C22×C4—224no—
397C22×C4C22⋊Dic11116yescomplemented
398C22×C4C22×Dic1112yes—
399C22×C4C22×Dic1112yes—
400C22×C4C22×Dic1112yes—
401C22×C4C22×Dic1112yes—
402C22×C4C22×Dic1112yes—
403C22×C4C2×C22⋊D1112yes—
404C22×C4C2×C22⋊D1112yes—
405C22×C4C2×C22⋊D1112yes—
406C22×C4C2×C22⋊D1112yes—
407C4⋊C4—28no—
408C4⋊C4—28no—
409C4⋊C4—448no—
410C22⋊C4—28no—
411C22⋊C4—28no—
412C22⋊C4—28no—
413C22⋊C4—2216no—
414C22⋊C4—4416no—
415C22⋊C4—448no—
416C42—448no—
417C11#1428711yescharacteristic, complemented, Sylow
418C23—24no—
419C23—24no—
420C23—24no—
421C23—22no—
422C23—24no—
423C23—24no—
424C23—24no—
425C23—22no—
426C23—24no—
427C23—24no—
428C23—24no—
429C23—24no—
430C23—24no—
431C23—22no—
432C23—44no—
433C23—44no—
434C23—44no—
435C23—44no—
436C23—42no—
437C23—42no—
438C23—41no—
439C23—42no—
440C23—41no—
441C23—42no—
442C23—42no—
443C23—44no—
444C23—44no—
445C23—44no—
446C23—44no—
447C23C2×C22⋊Dic1114yes—
448C23#6703714yes—
449C23#41×D1114yes—
450C23#6704212yes—
451C23#6704312yes—
452C23C23×Dic1111yescharacteristic
453C23C22×C22⋊D1111yescharacteristic
454C23C22×C22⋊D1111yescharacteristic
455D4—416no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—416no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—228no—
477C2×C4—228no—
478C2×C4—228no—
479C2×C4—444no—
480C2×C4—444no—
481C2×C4—444no—
482C2×C4—444no—
483C2×C4—444no—
484C2×C4—444no—
485C2×C4—444no—
486C2×C4—444no—
487C2×C4—444no—
488C2×C4—444no—
489C2×C4—444no—
490C2×C4C2×C22⋊Dic1114yes—
491C2×C4C2×C22⋊Dic1114yes—
492C22—24no—
493C22—24no—
494C22—24no—
495C22—48no—
496C22—48no—
497C22—44no—
498C22—44no—
499C22—42no—
500C22—48no—
501C22—42no—
502C22—42no—
503C22—84no—
504C22—82no—
505C22—82no—
506C22#1062318814yes—
507C22#1062319114yes—
508C22#1062319314yes—
509C22#1062319414yes—
510C22#1062332912yes—
511C22#1062333512yes—
512C22#1062333512yes—
513C22#1062335611yescharacteristic
514C22#41×Dic1112yes—
515C22#1062335812yes—
516C22#1062335912yes—
517C22#1062336111yescharacteristic
518C22#1062336312yes—
519C22#1062336412yes—
520C22C22×C22⋊Dic1111yescharacteristic
521C4—24no—
522C4—24no—
523C4—42no—
524C4—42no—
525C4—42no—
526C4—448no—
527C4—884no—
528C2—44no—
529C2—82no—
530C2#1307110711yescharacteristic
531C2#1307119411yescharacteristic
532C2#1307120811yescharacteristic
533C2#1307141014yes—
534C2#1307445514yes—
535C2#1307474412yes—
536C2#1307476612yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C11×#123C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC22×#123D11
hypocenterC11#14287
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C2×#10622825C2semidirect
2. C2×C4×C22⋊Dic11C2semidirect
3. #13066869C2semidirect
4. #13066865C2semidirect
5. #13066861C2semidirect
7. #13066853C2semidirect
8. #13066848C2semidirect
14. C2×C11×#123C4semidirect
116. C22×C4×C11C22⋊C4semidirect
237. C2×#123Dic11semidirect
397. C22×C4C22⋊Dic11semidirect
417. C11#14287semidirect

Maximal subgroups

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

subgroupindex
C2×#106228252
C2×C4×C22⋊Dic112
#130668692
#130668652
#130668612
#130668572
#130668532
#130668482
C22×C11×#1232
#1428711