Finite Group Databasebeta

← #14676318

Subgroups — #14676318

Order 2816.

2230 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622824C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
3#13066865C212yesmaximal, complemented
4#13066857C212yesmaximal
5#13066853C212yesmaximal, complemented
6#13066848C212yesmaximal, complemented
7#13066843C212yesmaximal, complemented
8#13066839C212yesmaximal, complemented
9C22×C4×D4×C11C211yesmaximal, characteristic
10C23×D4×C11C2211yescharacteristic
11C24×C4×C11C2211yescharacteristic
12C24×C4×C11C2211yescharacteristic
13C2×C4×D4×C11—24no—
14C2×C4×D4×C11—24no—
15C2×C4×D4×C11C418yescomplemented
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C22×C22⋊Dic11C2212yes—
21C22×C22⋊Dic11C2214yes—
22C22×C22⋊Dic11C2212yes—
23C22×C4×Dic11C2212yes—
24#10622824—24no—
25C4×C22⋊Dic11—24no—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2214yes—
29C2×C11⋊#95C2214yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2214yes—
32C25×C11C2311yescharacteristic
33C25×C11C2311yescharacteristic
34C22×D4×C11—22no—
35C22×D4×C11—22no—
36C22×D4×C11—24no—
37C22×D4×C11—24no—
38C22×D4×C11C2×C414yes—
39C23×C4×C11—22no—
40C23×C4×C11—22no—
41C23×C4×C11—44no—
42C23×C4×C11—44no—
43C23×C4×C11C2×C414yes—
44C23×C4×C11C2×C414yes—
45C23×C4×C11D414yes—
46C23×C4×C11D414yes—
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×Dic11C2314yes—
53C23×Dic11C2314yes—
54C4×D4×C11—232no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4C2×C414yes—
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×C42×C11—22no—
65C2×C42×C11—22no—
66C2×C42×C11C2×C414yes—
67C2×C22⋊Dic11—24no—
68C2×C22⋊Dic11—28no—
69C2×C22⋊Dic11—24no—
70C2×C22⋊Dic11—28no—
71C2×C22⋊Dic11—28no—
72C2×C22⋊Dic11—44no—
73C2×C22⋊Dic11—44no—
74C2×C4×Dic11—24no—
75C2×C4×Dic11—44no—
76C11⋊#95—24no—
77C11⋊#95—24no—
78C11⋊#95—24no—
79C11⋊#95—28no—
80C11⋊#95—28no—
81C11⋊#95—44no—
82#13940—111nomaximal, Sylow
83C24×C11—21no—
84C24×C11—21no—
85C24×C11—24no—
86C24×C11—24no—
87C24×C11—22no—
88C24×C11—22no—
89C24×C11—22no—
90C24×C11—24no—
91C24×C11—24no—
92C24×C11C22×C412yes—
93C24×C11C22×C412yes—
94C24×C11C2×D412yes—
95C24×C11C2×D412yes—
96C24×C11#4114yes—
97C24×C11C2411yescharacteristic
98C2×D4×C11—216no—
99C2×D4×C11—216no—
100C2×D4×C11—28no—
101C2×D4×C11—28no—
102C2×D4×C11—28no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—22no—
106C22×C4×C11—24no—
107C22×C4×C11—24no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—24no—
113C22×C4×C11—24no—
114C22×C4×C11—28no—
115C22×C4×C11—48no—
116C22×C4×C11—48no—
117C22×C4×C11—48no—
118C22×C4×C11—48no—
119C22×C4×C11—48no—
120C22×C4×C11—48no—
121C22×C4×C11C22⋊C4116yescomplemented
122C22×C4×C11C22×C412yes—
123C22×C4×C11C22×C412yes—
124C22×C4×C11C22×C412yes—
125C22×C4×C11C22×C412yes—
126C22×C4×C11C22×C412yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D412yes—
131C22×C4×C11#4114yes—
132C22×Dic11—24no—
133C22×Dic11—24no—
134C22×Dic11—24no—
135C22×Dic11—24no—
136C22×Dic11—24no—
137C22×Dic11—24no—
138C22×Dic11—24no—
139C22×Dic11—24no—
140C22×Dic11—24no—
141C22×Dic11—24no—
142C22×Dic11—24no—
143C22×Dic11—24no—
144C22×Dic11—24no—
145C22×Dic11#4118yes—
146C11×C4⋊C4—28no—
147C11×C22⋊C4—28no—
148C11×C22⋊C4—28no—
149C42×C11—28no—
150C22⋊Dic11—216no—
151C22⋊Dic11—416no—
152C22⋊Dic11—48no—
153C4×Dic11—48no—
154C22×C4×D4D1111yescharacteristic
155C2×#381—111no—
156C2×C4×C22⋊C4—111no—
157#1440—112no—
158#1438—112no—
159#1437—112no—
160#1436—112no—
161#1434—112no—
162C22⋊#95—112no—
163C23×C11—22no—
164C23×C11—22no—
165C23×C11—22no—
166C23×C11—22no—
167C23×C11—24no—
168C23×C11—24no—
169C23×C11—24no—
170C23×C11—24no—
171C23×C11—24no—
172C23×C11—24no—
173C23×C11—24no—
174C23×C11—24no—
175C23×C11—24no—
176C23×C11—24no—
177C23×C11—24no—
178C23×C11—24no—
179C23×C11—28no—
180C23×C11—28no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11—42no—
185C23×C11—44no—
186C23×C11—44no—
187C23×C11—44no—
188C23×C11—44no—
189C23×C11—44no—
190C23×C11—44no—
191C23×C11C2×C22⋊C414yes—
192C23×C11#11714yes—
193C23×C11C23×C411yescharacteristic
194C23×C11C22×D411yescharacteristic
195C23×C11C22×D411yescharacteristic
196C23×C11C2×#4112yes—
197C23×C11C2×#4112yes—
198C23×C11C2×#4114yes—
199C23×C11H(5,𝔽2)14yes—
200D4×C11—232no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—416no—
216C2×C4×C11—416no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11C2×C22⋊C414yes—
222C2×C4×C11C2×C22⋊C414yes—
223C2×C4×C11#11714yes—
224C2×Dic11—28no—
225C2×Dic11—28no—
226C2×Dic11—28no—
227C2×Dic11—44no—
228C2×Dic11—44no—
229C2×Dic11—44no—
230C2×Dic11—44no—
231C2×Dic11—44no—
232C2×Dic11—44no—
233C2×Dic11—44no—
234C2×Dic11—44no—
235C2×Dic11—44no—
236C2×Dic11—44no—
237C2×Dic11—44no—
238C23×D4C2×D1111yescharacteristic
239C24×C4C2×D1111yescharacteristic
240C24×C4C2×D1111yescharacteristic
241C2×C4×D4—24no—
242C2×C4×D4—24no—
243C2×C4×D4Dic1118yescomplemented
244C22×C4⋊C4C2×D1111yescharacteristic
245C22×C22⋊C4—112no—
246C22×C22⋊C4—114no—
247C22×C22⋊C4—112no—
248C22×C22⋊C4C2×D1111yescharacteristic
249C22×C22⋊C4C2×D1111yescharacteristic
250C22×C42—112no—
251C22×C42C2×D1111yescharacteristic
252#381—224no—
253C4×C22⋊C4—224no—
254C2×#95—112no—
255C2×#95—112no—
256C2×#95—114no—
257C2×#95—114no—
258C2×#95—112no—
259C2×#95—114no—
260C22×C11—24no—
261C22×C11—28no—
262C22×C11—24no—
263C22×C11—24no—
264C22×C11—24no—
265C22×C11—42no—
266C22×C11—48no—
267C22×C11—48no—
268C22×C11—48no—
269C22×C11—48no—
270C22×C11—44no—
271C22×C11—44no—
272C22×C11—44no—
273C22×C11—42no—
274C22×C11C22×C22⋊C411yescharacteristic
275C22×C11C2×#11711yescharacteristic
276C22×C11C2×#11711yescharacteristic
277C22×C11C4×#4112yes—
278C22×C11#51812yes—
279C22×C11#52512yes—
280C22×C11#52512yes—
281C22×C11#52512yes—
282C22×C11#53212yes—
283C22×C11#53412yes—
284C22×C11#53412yes—
285C22×C11#55114yes—
286C22×C11#55314yes—
287C22×C11#55314yes—
288C22×C11#55914yes—
289C4×C11—24no—
290C4×C11—24no—
291C4×C11—24no—
292C4×C11—42no—
293C4×C11—42no—
294Dic11—48no—
295Dic11—84no—
296C25C22×D1111yescharacteristic
297C25C22×D1111yescharacteristic
298C22×D4—24no—
299C22×D4—22no—
300C22×D4—22no—
301C22×D4—24no—
302C22×D4C2×Dic1114yes—
303C23×C4—22no—
304C23×C4—22no—
305C23×C4—44no—
306C23×C4—44no—
307C23×C4—114no—
308C23×C4—114no—
309C23×C4C2×Dic1114yes—
310C23×C4C2×Dic1114yes—
311C23×C4C22⋊D1114yes—
312C23×C4C22⋊D1114yes—
313C23×C4C22×D1111yescharacteristic
314C23×C4C22×D1111yescharacteristic
315C23×C4C22×D1111yescharacteristic
316C23×C4C22×D1111yescharacteristic
317C23×C4C22×D1111yescharacteristic
318C4×D4—232no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4C2×Dic1114yes—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—228no—
327C2×C22⋊C4—224no—
328C2×C22⋊C4—228no—
329C2×C22⋊C4—228no—
330C2×C22⋊C4—224no—
331C2×C22⋊C4—444no—
332C2×C22⋊C4—444no—
333C2×C22⋊C4C2×Dic1114yes—
334C2×C22⋊C4C2×Dic1114yes—
335C2×C42—22no—
336C2×C42—22no—
337C2×C42—224no—
338C2×C42—444no—
339C2×C42C2×Dic1114yes—
340#95—228no—
341#95—228no—
342#95—224no—
343#95—224no—
344#95—224no—
345#95—444no—
346C2×C11—44no—
347C2×C11—44no—
348C2×C11#228011yescharacteristic
349C2×C11#229711yescharacteristic
350C2×C11#230811yescharacteristic
351C2×C11#235312yes—
352C2×C11#235712yes—
353C2×C11#260014yes—
354C2×C11#260214yes—
355C24—22no—
356C24—22no—
357C24—22no—
358C24—24no—
359C24—24no—
360C24—24no—
361C24—24no—
362C24—21no—
363C24—21no—
364C24#433914yes—
365C24C22×Dic1112yes—
366C24C22×Dic1112yes—
367C24C2×C22⋊D1112yes—
368C24C2×C22⋊D1112yes—
369C24C23×D1111yescharacteristic
370C2×D4—216no—
371C2×D4—216no—
372C2×D4—28no—
373C2×D4—28no—
374C2×D4—28no—
375C22×C4—22no—
376C22×C4—24no—
377C22×C4—24no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—24no—
381C22×C4—24no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—28no—
387C22×C4—48no—
388C22×C4—48no—
389C22×C4—48no—
390C22×C4—48no—
391C22×C4—48no—
392C22×C4—48no—
393C22×C4—118no—
394C22×C4—224no—
395C22×C4—224no—
396C22×C4—224no—
397C22×C4—224no—
398C22×C4—224no—
399C22×C4—224no—
400C22×C4—224no—
401C22×C4—224no—
402C22×C4—224no—
403C22×C4—224no—
404C22×C4—224no—
405C22×C4—224no—
406C22×C4—224no—
407C22×C4C22⋊Dic11116yescomplemented
408C22×C4#433914yes—
409C22×C4C22×Dic1112yes—
410C22×C4C22×Dic1112yes—
411C22×C4C22×Dic1112yes—
412C22×C4C22×Dic1112yes—
413C22×C4C22×Dic1112yes—
414C22×C4C2×C22⋊D1112yes—
415C22×C4C2×C22⋊D1112yes—
416C22×C4C2×C22⋊D1112yes—
417C22×C4C2×C22⋊D1112yes—
418C4⋊C4—28no—
419C22⋊C4—28no—
420C22⋊C4—28no—
421C22⋊C4—2216no—
422C22⋊C4—4416no—
423C22⋊C4—448no—
424C42—28no—
425C42—448no—
426C11#1394011yescharacteristic, complemented, Sylow
427C23—22no—
428C23—22no—
429C23—22no—
430C23—24no—
431C23—24no—
432C23—24no—
433C23—24no—
434C23—28no—
435C23—24no—
436C23—24no—
437C23—24no—
438C23—24no—
439C23—28no—
440C23—24no—
441C23—24no—
442C23—24no—
443C23—24no—
444C23—22no—
445C23—44no—
446C23—42no—
447C23—42no—
448C23—44no—
449C23—44no—
450C23—44no—
451C23—44no—
452C23—44no—
453C23—42no—
454C23—42no—
455C23#6697914yes—
456C23C2×C22⋊Dic1114yes—
457C23C2×#433912yes—
458C23C2×#433912yes—
459C23#6703714yes—
460C23#41×D1114yes—
461C23C23×Dic1111yescharacteristic
462C23C22×C22⋊D1111yescharacteristic
463C23C22×C22⋊D1111yescharacteristic
464D4—232no—
465C2×C4—22no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—22no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—416no—
480C2×C4—416no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—228no—
486C2×C4—228no—
487C2×C4—228no—
488C2×C4—444no—
489C2×C4—444no—
490C2×C4—444no—
491C2×C4—444no—
492C2×C4—444no—
493C2×C4—444no—
494C2×C4—444no—
495C2×C4—444no—
496C2×C4—444no—
497C2×C4—444no—
498C2×C4—444no—
499C2×C4#6697914yes—
500C2×C4C2×C22⋊Dic1114yes—
501C2×C4C2×C22⋊Dic1114yes—
502C22—24no—
503C22—24no—
504C22—24no—
505C22—24no—
506C22—28no—
507C22—42no—
508C22—48no—
509C22—48no—
510C22—48no—
511C22—48no—
512C22—42no—
513C22—44no—
514C22—44no—
515C22—44no—
516C22#1062307114yes—
517C22#1062308714yes—
518C22#1062308914yes—
519C22#1062309014yes—
520C22C2×#6697911yescharacteristic
521C22C2×#6697911yescharacteristic
522C22#1062332212yes—
523C22#1062332212yes—
524C22#1062332912yes—
525C22#1062333512yes—
526C22#1062333512yes—
527C22#41×Dic1112yes—
528C22#1062335912yes—
529C22#1062336312yes—
530C22C22×C22⋊Dic1111yescharacteristic
531C4—24no—
532C4—24no—
533C4—24no—
534C4—42no—
535C4—42no—
536C4—448no—
537C4—884no—
538C2—44no—
539C2—44no—
540C2#1307099911yescharacteristic
541C2#1307110711yescharacteristic
542C2#1307119411yescharacteristic
543C2#1307155612yes—
544C2#1307158912yes—
545C2#1307419814yes—
546C2#1307422814yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C4×D4×C11C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC22×C4×D4D11
hypocenterC11#13940
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#10622824C2semidirect
2. C2×C4×C22⋊Dic11C2semidirect
3. #13066865C2semidirect
5. #13066853C2semidirect
6. #13066848C2semidirect
7. #13066843C2semidirect
8. #13066839C2semidirect
15. C2×C4×D4×C11C4semidirect
121. C22×C4×C11C22⋊C4semidirect
243. C2×C4×D4Dic11semidirect
407. C22×C4C22⋊Dic11semidirect
426. C11#13940semidirect

Maximal subgroups

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

subgroupindex
C2×#106228242
C2×C4×C22⋊Dic112
#130668652
#130668572
#130668532
#130668482
#130668432
#130668392
C22×C4×D4×C112
#1394011