Finite Group Databasebeta

← #14690496

Subgroups — #14690496

Order 2816.

1566 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622597C214yesmaximal
2C2×#10622598C211yesmaximal, characteristic
3C2×#10622589C211yesmaximal, characteristic
4C2×#10622589C211yesmaximal, characteristic
5#13066879C214yesmaximal
6#13066846C211yesmaximal, characteristic
7#13066845C211yesmaximal, characteristic
8C4×C11⋊#95C211yesmaximal, characteristic
9C2×C11×#384C211yesmaximal, characteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C22×C11×C4⋊C4C2214yes—
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15C22×C4⋊Dic11C2211yescharacteristic
16C22×C4⋊Dic11C2212yes—
17C22×Dic11⋊C4C2212yes—
18C22×Dic11⋊C4C2214yes—
19C22×Dic11⋊C4C2212yes—
20C22×C4×Dic11C2211yescharacteristic
21C22×C4×Dic11C2211yescharacteristic
22C11×#384—24no—
23C2×C11⋊#95C2214yes—
24C2×C11⋊#95C2214yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28#10622598—24no—
29#10622597—216no—
30#10622589—24no—
31#10622589—24no—
32C23×C4×C11C2312yes—
33C23×C4×C11C2312yes—
34C23×C4×C11C2312yes—
35C23×C4×C11C2311yescharacteristic
36C23×Dic11C2312yes—
37C23×Dic11C2312yes—
38C23×Dic11C2311yescharacteristic
39C23×Dic11C2312yes—
40C23×Dic11C2311yescharacteristic
41C2×C11×C4⋊C4—22no—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4—22no—
44C2×C11×C4⋊C4—28no—
45C2×C11×C4⋊C4—28no—
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4—44no—
49C2×C11×C4⋊C4D414yes—
50C2×C42×C11—22no—
51C2×C42×C11—22no—
52C2×C42×C11Q814yes—
53C2×C4⋊Dic11—22no—
54C2×C4⋊Dic11—22no—
55C2×C4⋊Dic11—22no—
56C2×C4⋊Dic11—22no—
57C2×C4⋊Dic11—22no—
58C2×C4⋊Dic11—22no—
59C2×C4⋊Dic11—28no—
60C2×C4⋊Dic11—24no—
61C2×Dic11⋊C4—28no—
62C2×Dic11⋊C4—24no—
63C2×Dic11⋊C4—24no—
64C2×Dic11⋊C4—28no—
65C2×Dic11⋊C4—28no—
66C2×Dic11⋊C4—44no—
67C2×Dic11⋊C4—44no—
68C2×C4×Dic11—22no—
69C2×C4×Dic11—22no—
70C2×C4×Dic11—22no—
71C2×C4×Dic11—22no—
72C2×C4×Dic11D414yes—
73C2×C4×Dic11Q814yes—
74C11⋊#95—28no—
75C11⋊#95—28no—
76C11⋊#95—24no—
77C11⋊#95D418yes—
78C11⋊#95Q818yes—
79#15145—111nomaximal, Sylow
80C24×C11C2411yescharacteristic
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—24no—
87C22×C4×C11—22no—
88C22×C4×C11—24no—
89C22×C4×C11—24no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—24no—
94C22×C4×C11C2×D414yes—
95C22×C4×C11C2×D414yes—
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×Q814yes—
99C22×C4×C11C2×Q814yes—
100C22×C4×C11C2×Q812yes—
101C22×C4×C11C2×Q812yes—
102C22×C4×C11#4112yes—
103C22×C4×C11#4112yes—
104C22×C4×C11#4112yes—
105C22×Dic11—22no—
106C22×Dic11—24no—
107C22×Dic11—24no—
108C22×Dic11—22no—
109C22×Dic11—22no—
110C22×Dic11—22no—
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11—22no—
114C22×Dic11—21no—
115C22×Dic11—21no—
116C22×Dic11—22no—
117C22×Dic11—22no—
118C22×Dic11—22no—
119C22×Dic11—22no—
120C22×Dic11—22no—
121C22×Dic11—24no—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—24no—
125C22×Dic11C2×D414yes—
126C22×Dic11C2×D412yes—
127C22×Dic11C2×D414yes—
128C22×Dic11C2×D412yes—
129C22×Dic11C2×Q814yes—
130C22×Dic11C2×Q814yes—
131C22×Dic11C2×Q814yes—
132C11×C4⋊C4—28no—
133C11×C4⋊C4—416no—
134C11×C4⋊C4—44no—
135C42×C11—28no—
136C4⋊Dic11—48no—
137C4⋊Dic11—44no—
138C4⋊Dic11—44no—
139Dic11⋊C4—416no—
140Dic11⋊C4—48no—
141Dic11⋊C4—48no—
142C4×Dic11—28no—
143C4×Dic11—28no—
144C2×#398—114no—
145C2×#389—111no—
146C2×#384—111no—
147C2×#384—111no—
148C2×#384D1111yescharacteristic
149#1444—114no—
150C4⋊#95—111no—
151C4⋊#95—111no—
152C4×#95—111no—
153C23×C11C22×D411yescharacteristic
154C23×C11C22×D412yes—
155C23×C11C22×D411yescharacteristic
156C23×C11C22×Q811yescharacteristic
157C23×C11C22×Q811yescharacteristic
158C23×C11C22×Q812yes—
159C23×C11C2×#4111yescharacteristic
160C23×C11C2×#4111yescharacteristic
161C23×C11C2×#4111yescharacteristic
162C23×C11H(5,𝔽2)12yes—
163C23×C112−1+412yes—
164C2×C4×C11—24no—
165C2×C4×C11—24no—
166C2×C4×C11—24no—
167C2×C4×C11—24no—
168C2×C4×C11—24no—
169C2×C4×C11—24no—
170C2×C4×C11—24no—
171C2×C4×C11—28no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—44no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—44no—
179C2×C4×C11—44no—
180C2×C4×C11#12114yes—
181C2×C4×C11C22⋊Q814yes—
182C2×C4×C11C22⋊Q814yes—
183C2×C4×C11#12314yes—
184C2×C4×C11#12514yes—
185C2×C4×C11#12514yes—
186C2×C4×C11C4⋊Q818yes—
187C2×C4×C11C4⋊Q814yes—
188C2×Dic11—24no—
189C2×Dic11—22no—
190C2×Dic11—22no—
191C2×Dic11—22no—
192C2×Dic11—22no—
193C2×Dic11—24no—
194C2×Dic11—24no—
195C2×Dic11—24no—
196C2×Dic11—24no—
197C2×Dic11—24no—
198C2×Dic11—24no—
199C2×Dic11—24no—
200C2×Dic11—24no—
201C2×Dic11—24no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—44no—
209C2×Dic11—44no—
210C2×Dic11—44no—
211C2×Dic11—44no—
212C2×Dic11#12714yes—
213C2×Dic11C4⋊Q818yes—
214C2×Dic11C4⋊Q814yes—
215C22×C4⋊C4—112no—
216C22×C4⋊C4—112no—
217C22×C4⋊C4—111no—
218C22×C4⋊C4—111no—
219C22×C4⋊C4—114no—
220C22×C4⋊C4—112no—
221C22×C4⋊C4C2×D1111yescharacteristic
222C22×C4⋊C4C2×D1114yes—
223C22×C4⋊C4C2×D1111yescharacteristic
224C22×C42—111no—
225C22×C42—111no—
226C22×C42C2×D1111yescharacteristic
227#398—2216no—
228#389—224no—
229#384—24no—
230#384—224no—
231#384—224no—
232C2×#95—112no—
233C2×#95—112no—
234C2×#95—114no—
235C2×#95—114no—
236C2×#95—112no—
237C22×C11C2×#12111yescharacteristic
238C22×C11C2×C22⋊Q811yescharacteristic
239C22×C11C2×C22⋊Q811yescharacteristic
240C22×C11C2×#12311yescharacteristic
241C22×C11C2×#12511yescharacteristic
242C22×C11C2×#12511yescharacteristic
243C22×C11C2×#12711yescharacteristic
244C22×C11C2×C4⋊Q812yes—
245C22×C11C2×C4⋊Q811yescharacteristic
246C22×C11C2×C4⋊Q811yescharacteristic
247C22×C11C2×C4⋊Q812yes—
248C22×C11#53511yescharacteristic
249C22×C11#53611yescharacteristic
250C22×C11#54412yes—
251C22×C11#54412yes—
252C22×C11D4212yes—
253C22×C11#54712yes—
254C22×C11#54712yes—
255C22×C11D4×Q812yes—
256C22×C11#55012yes—
257C22×C11#55412yes—
258C22×C11#55412yes—
259C22×C11#55712yes—
260C4×C11—28no—
261C4×C11—44no—
262C4×C11—82no—
263C4×C11#39818yescomplemented
264Dic11—28no—
265Dic11—24no—
266Dic11—24no—
267Dic11—82no—
268Dic11—82no—
269C23×C4—111no—
270C23×C4—112no—
271C23×C4—111no—
272C23×C4—112no—
273C23×C4—112no—
274C23×C4C22×D1112yes—
275C23×C4C22×D1112yes—
276C23×C4C22×D1112yes—
277C23×C4C22×D1111yescharacteristic
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—28no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—28no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—44no—
286C2×C4⋊C4—224no—
287C2×C4⋊C4—224no—
288C2×C4⋊C4—224no—
289C2×C4⋊C4—228no—
290C2×C4⋊C4—228no—
291C2×C4⋊C4—228no—
292C2×C4⋊C4—222no—
293C2×C4⋊C4—222no—
294C2×C4⋊C4—222no—
295C2×C4⋊C4—222no—
296C2×C4⋊C4—222no—
297C2×C4⋊C4—228no—
298C2×C4⋊C4—222no—
299C2×C4⋊C4—444no—
300C2×C4⋊C4—444no—
301C2×C4⋊C4C22⋊D1114yes—
302C2×C42—22no—
303C2×C42—22no—
304C2×C42—114no—
305C2×C42—114no—
306C2×C42—222no—
307C2×C42—222no—
308C2×C42—222no—
309C2×C42—222no—
310C2×C42Dic2214yes—
311#95—118no—
312#95—118no—
313#95—224no—
314#95—228no—
315#95—228no—
316C2×C11C2×#39811yescharacteristic
317C2×C11#244012yes—
318C2×C11#244012yes—
319C2×C11#250111yescharacteristic
320C2×C11#250211yescharacteristic
321C2×C11#254111yescharacteristic
322C2×C11#254611yescharacteristic
323C2×C11#255212yes—
324C2×C11#255212yes—
325C2×C11#266011yescharacteristic
326C2×C11#286811yescharacteristic
327C24C23×D1111yescharacteristic
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—24no—
334C22×C4—22no—
335C22×C4—24no—
336C22×C4—24no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—24no—
340C22×C4—22no—
341C22×C4—114no—
342C22×C4—114no—
343C22×C4—112no—
344C22×C4—112no—
345C22×C4—114no—
346C22×C4—114no—
347C22×C4—114no—
348C22×C4—221no—
349C22×C4—221no—
350C22×C4—222no—
351C22×C4—222no—
352C22×C4—221no—
353C22×C4—222no—
354C22×C4—221no—
355C22×C4—222no—
356C22×C4—222no—
357C22×C4—222no—
358C22×C4—222no—
359C22×C4—224no—
360C22×C4—224no—
361C22×C4—222no—
362C22×C4—222no—
363C22×C4—222no—
364C22×C4—224no—
365C22×C4—222no—
366C22×C4—224no—
367C22×C4—222no—
368C22×C4C2×Dic2214yes—
369C22×C4C2×Dic2212yes—
370C22×C4#433912yes—
371C22×C4D4×D1114yes—
372C22×C4D4×D1112yes—
373C22×C4#434112yes—
374C22×C4Q8×D1114yes—
375C22×C4Q8×D1112yes—
376C22×C4#434312yes—
377C22×C4C2×C22⋊D1114yes—
378C22×C4C2×C22⋊D1112yes—
379C4⋊C4—28no—
380C4⋊C4—416no—
381C4⋊C4—44no—
382C4⋊C4—4416no—
383C4⋊C4—448no—
384C4⋊C4—448no—
385C4⋊C4—448no—
386C4⋊C4—444no—
387C4⋊C4—444no—
388C42—28no—
389C42—228no—
390C42—228no—
391C11#1514511yescharacteristic, complemented, Sylow
392C23C22×Dic2211yescharacteristic
393C23C2×#433911yescharacteristic
394C23C2×D4×D1111yescharacteristic
395C23C2×D4×D1112yes—
396C23C2×#434111yescharacteristic
397C23#6703712yes—
398C23C2×Q8×D1112yes—
399C23C2×Q8×D1111yescharacteristic
400C23C2×#434311yescharacteristic
401C23#6704012yes—
402C23C22×C22⋊D1111yescharacteristic
403C2×C4—24no—
404C2×C4—24no—
405C2×C4—24no—
406C2×C4—24no—
407C2×C4—24no—
408C2×C4—24no—
409C2×C4—28no—
410C2×C4—24no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—44no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—44no—
417C2×C4—44no—
418C2×C4—42no—
419C2×C4—114no—
420C2×C4—118no—
421C2×C4—114no—
422C2×C4—222no—
423C2×C4—222no—
424C2×C4—224no—
425C2×C4—224no—
426C2×C4—224no—
427C2×C4—224no—
428C2×C4—224no—
429C2×C4—222no—
430C2×C4—222no—
431C2×C4—224no—
432C2×C4—224no—
433C2×C4—224no—
434C2×C4—224no—
435C2×C4—224no—
436C2×C4—442no—
437C2×C4—442no—
438C2×C4—442no—
439C2×C4—444no—
440C2×C4—442no—
441C2×C4—444no—
442C2×C4—442no—
443C2×C4—444no—
444C2×C4—444no—
445C2×C4—442no—
446C2×C4#6694118yes—
447C2×C4#6694114yes—
448C2×C4#6694214yes—
449C2×C4#6694314yes—
450C2×C4#6694714yes—
451C2×C4#6697714yes—
452C2×C4#6699214yes—
453C2×C4#6699914yes—
454C22C2×#6694111yescharacteristic
455C22C2×#6694112yes—
456C22C2×#6694211yescharacteristic
457C22C2×#6694311yescharacteristic
458C22#1062303112yes—
459C22C2×#6694711yescharacteristic
460C22#1062303812yes—
461C22#1062304212yes—
462C22D11×#12711yescharacteristic
463C22#1062324611yescharacteristic
464C22#1062324912yes—
465C22#1062325212yes—
466C22D11×C4⋊Q812yes—
467C22D11×C4⋊Q811yescharacteristic
468C22#1062325511yescharacteristic
469C22#1062325712yes—
470C22#1062326012yes—
471C22#1062326112yes—
472C22C2×#6697711yescharacteristic
473C22D4×C22⋊D1112yes—
474C22C2×#6699211yescharacteristic
475C22C2×#6699911yescharacteristic
476C22Q8×C22⋊D1112yes—
477C4—28no—
478C4—44no—
479C4—82no—
480C4—228no—
481C4—224no—
482C4—224no—
483C4—882no—
484C4—882no—
485C4#1062259718yescomplemented
486C2C2×#1062259711yescharacteristic
487C2#1307231212yes—
488C2#1307231412yes—
489C2#1307308411yescharacteristic
490C2#1307309111yescharacteristic
491C2#1307356011yescharacteristic
492C2#1307360211yescharacteristic
493C2#1307364912yes—
494C2#1307365212yes—
495C2#1307473811yescharacteristic
496C2#1307701311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, prime radical, cosocleC24×C11C24
FittingC2×C11×#384C2
hypercenterC2×#384D11
hypocenterC11#15145
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#384

Complements

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

NH ≅ G/Ntype
263. C4×C11#398semidirect
391. C11#15145semidirect
485. C4#10622597semidirect

Maximal subgroups

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

subgroupindex
C2×#106225972
C2×#106225982
C2×#106225892
#130668792
#130668462
#130668452
C4×C11⋊#952
C2×C11×#3842
#1514511