Finite Group Databasebeta

← #14782483

Subgroups — #14782483

Order 2816.

1102 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622734C211yesmaximal, characteristic
2C2×#10622731C211yesmaximal, characteristic
3C2×#10622838C211yesmaximal, characteristic
4#13071098C211yesmaximal, characteristic
5C2×#10622843C211yesmaximal, characteristic
6#13070009C214yesmaximal, complemented
7#13069995C214yesmaximal, complemented
8#13068337C211yesmaximal, characteristic
9C2×C11×#419C211yesmaximal, characteristic
10C23×Q8×C11C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15C22×C4×Dic11C2211yescharacteristic
16C22×#4318C2211yescharacteristic
17C11×#419—24no—
18C2×C11×#103C2214yes—
19#10622843—21no—
20#10622843—21no—
21#10622843C2214yes—
22#10622838—24no—
23C2×#66899C2212yes—
24C2×#66899C2212yes—
25C2×C11⋊#95—22no—
26#10622734—24no—
27#10622731—24no—
28C2×#66882C2212yes—
29C2×#66881C2212yes—
30C2×Dic11⋊C8C2214yes—
31#10622586C2212yes—
32#10622586C2212yes—
33#10622559—22no—
34C4×Dic11⋊C4—21no—
35C4×Dic11⋊C4—21no—
36#10622167C2214yes—
37C22×Q8×C11—21no—
38C22×Q8×C11—22no—
39C22×Q8×C11—22no—
40C22×Q8×C11—22no—
41C22×Q8×C11—22no—
42C22×Q8×C11—22no—
43C22×Q8×C11Q814yes—
44C22×Q8×C11C2312yes—
45C23×C4×C11—21no—
46C23×C4×C11C2311yescharacteristic
47C23×Dic11—21no—
48C23×Dic11D412yes—
49C2×C11×M16—22no—
50C2×C11×M16—22no—
51C2×C11×M16D414yes—
52C22×C8×C11C2312yes—
53C11×#117—22no—
54C11×#117—22no—
55C2×C11×C4⋊C4C2312yes—
56C2×C11×C22⋊C4—21no—
57C2×C42×C11—21no—
58C2×C22⋊Dic11—21no—
59#66979—22no—
60#66979D414yes—
61C2×C4⋊Dic11—22no—
62C2×C4⋊Dic11—22no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11C2312yes—
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4⋊Dic11C2311yescharacteristic
67C2×Dic11⋊C4—22no—
68C2×Dic11⋊C4—22no—
69C2×C4×Dic11—22no—
70C2×C4×Dic11—21no—
71C2×C4×Dic11—22no—
72C2×C4×Dic11D411yescharacteristic
73C2×C4×Dic11D411yescharacteristic
74C2×C4×Dic11C2312yes—
75C2×#4318—22no—
76C2×#4318—22no—
77C2×#4318—22no—
78C22×C11⋊C8C2312yes—
79C11×#103—28no—
80#66899—24no—
81#66899—24no—
82C11⋊#95—22no—
83C11⋊#95—22no—
84C11⋊#95—24no—
85C11⋊#95—24no—
86#66882—24no—
87#66881—24no—
88Dic11⋊C8—28no—
89#23619—111nomaximal, Sylow
90C24×C11C2×D411yescharacteristic
91C2×Q8×C11—24no—
92C2×Q8×C11—22no—
93C2×Q8×C11—28no—
94C2×Q8×C11—28no—
95C2×Q8×C11—22no—
96C2×Q8×C11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11—22no—
99C2×Q8×C11—42no—
100C2×Q8×C11—42no—
101C2×Q8×C11—44no—
102C2×Q8×C11—44no—
103C2×Q8×C11C2×Q814yes—
104C22×C4×C11—24no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—42no—
108C22×C4×C11—42no—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2×Q812yes—
113C22×C4×C11#4112yes—
114C22×C4×C11#4112yes—
115C22×C4×C11#4112yes—
116C22×C4×C11C2411yescharacteristic
117C22×Dic11—24no—
118C22×Dic11—24no—
119C22×Dic11—21no—
120C22×Dic11—21no—
121C22×Dic11—22no—
122C22×Dic11—42no—
123C22×Dic11—44no—
124C22×Dic11—42no—
125C22×Dic11C2×D412yes—
126C22×Dic11C2×D412yes—
127C11×M16—28no—
128C2×C8×C11—22no—
129C2×C8×C11—22no—
130C2×C8×C11C2×D414yes—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C22⋊C4—42no—
134C42×C11—42no—
135C22⋊Dic11—24no—
136C4⋊Dic11—22no—
137C4⋊Dic11—21no—
138C4⋊Dic11—21no—
139C4⋊Dic11—22no—
140C4⋊Dic11—42no—
141C4⋊Dic11C2×D412yes—
142C4⋊Dic11C2×D412yes—
143Dic11⋊C4—44no—
144Dic11⋊C4—44no—
145C4×Dic11—22no—
146C4×Dic11—22no—
147C4×Dic11—24no—
148C4×Dic11—22no—
149C4×Dic11—22no—
150#4318—44no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—22no—
153C2×C11⋊C8—22no—
154C2×#428—111no—
155C2×#423—111no—
156C2×#419—111no—
157C2×#419D1111yescharacteristic
158#2296—111no—
159C2×#391—111no—
160#2068—114no—
161#2066—114no—
162#1736—111no—
163C23×C11—22no—
164C23×C11—22no—
165C23×C11#12112yes—
166C23×C11#12112yes—
167C23×C11C22⋊Q812yes—
168C23×C11C22×D411yescharacteristic
169Q8×C11—24no—
170Q8×C11—24no—
171Q8×C11—42no—
172Q8×C11—42no—
173Q8×C11—48no—
174C2×C4×C11—24no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—48no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11#12112yes—
182C2×C4×C11#12112yes—
183C2×C4×C11#12114yes—
184C2×C4×C11C22⋊Q814yes—
185C2×C4×C11C22⋊Q812yes—
186C2×C4×C11C22⋊Q814yes—
187C2×C4×C11#12614yes—
188C2×C4×C11C22×D411yescharacteristic
189C2×C4×C11C22×D411yescharacteristic
190C2×C4×C11C22×Q811yescharacteristic
191C2×C4×C11C2×#4111yescharacteristic
192C2×C4×C11C2×#4111yescharacteristic
193C2×C4×C11C2×#4111yescharacteristic
194C2×Dic11—22no—
195C2×Dic11—22no—
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—22no—
199C2×Dic11—22no—
200C2×Dic11—22no—
201C2×Dic11—48no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—44no—
206C2×Dic11—84no—
207C2×Dic11#13714yes—
208C8×C11—24no—
209C11⋊C8—42no—
210C23×Q8C2×D1111yescharacteristic
211C22×M16—111no—
212C22×M16C2×D1111yescharacteristic
213C2×#117—111no—
214C2×#117C2×D1111yescharacteristic
215C22×C4⋊C4—111no—
216C22×C42—111no—
217#428—224no—
218C2×#107—112no—
219C2×#106—112no—
220#423—224no—
221C2×C4⋊C8—114no—
222#419—24no—
223#419—224no—
224C2×#103—112no—
225C2×#103—112no—
226C2×#103C2×D1114yes—
227#391—114no—
228#391—221no—
229#391—221no—
230#389—112no—
231#389—112no—
232#385—222no—
233C4×C4⋊C4—221no—
234C4×C4⋊C4—221no—
235C2×#95—222no—
236#340—114no—
237C22×C11—24no—
238C22×C11—22no—
239C22×C11—22no—
240C22×C11—24no—
241C22×C11#39614yes—
242C22×C11C2×#12111yescharacteristic
243C22×C11C2×#12111yescharacteristic
244C22×C11C2×C22⋊Q811yescharacteristic
245C22×C11C2×#13712yes—
246C22×C11#57512yes—
247C4×C11—44no—
248C4×C11—82no—
249C4×C11#39614yes—
250C4×C11C2×#12111yescharacteristic
251C4×C11C2×C22⋊Q811yescharacteristic
252C4×C11C2×C22⋊Q811yescharacteristic
253C4×C11C2×#12611yescharacteristic
254Dic11—24no—
255Dic11—42no—
256Dic11—42no—
257Dic11—42no—
258Dic11—82no—
259C22×Q8—21no—
260C22×Q8—22no—
261C22×Q8—22no—
262C22×Q8—22no—
263C22×Q8—22no—
264C22×Q8—22no—
265C22×Q8Dic2214yes—
266C22×Q8C22×D1112yes—
267C23×C4—21no—
268C23×C4—112no—
269C23×C4—221no—
270C23×C4C22×D1111yescharacteristic
271C2×M16—22no—
272C2×M16—22no—
273C2×M16—222no—
274C2×M16—222no—
275C2×M16—222no—
276C2×M16C22⋊D1114yes—
277C22×C8—112no—
278C22×C8C22×D1112yes—
279#117—22no—
280#117—22no—
281#117—114no—
282#117—222no—
283C2×C4⋊C4—111no—
284C2×C4⋊C4—111no—
285C2×C4⋊C4—112no—
286C2×C4⋊C4—222no—
287C2×C4⋊C4—222no—
288C2×C4⋊C4—222no—
289C2×C4⋊C4—222no—
290C2×C4⋊C4—221no—
291C2×C4⋊C4C22×D1112yes—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—221no—
294C2×C42—21no—
295C2×C42—111no—
296C2×C42—111no—
297C2×C42—112no—
298C2×C42—221no—
299C2×C42—222no—
300C2×C42—222no—
301#107—224no—
302#106—224no—
303C4⋊C8—228no—
304#103—28no—
305#103—224no—
306#103—224no—
307#95—224no—
308#95—224no—
309#95—222no—
310#95—222no—
311C2×C11—24no—
312C2×C11C2×#39611yescharacteristic
313C2×C11#303911yescharacteristic
314C2×C11#304011yescharacteristic
315C2×C11#305612yes—
316C2×C11#307812yes—
317C24D4×D1111yescharacteristic
318C2×Q8—24no—
319C2×Q8—22no—
320C2×Q8—28no—
321C2×Q8—28no—
322C2×Q8—22no—
323C2×Q8—22no—
324C2×Q8—22no—
325C2×Q8—22no—
326C2×Q8—44no—
327C2×Q8—42no—
328C2×Q8—42no—
329C2×Q8—44no—
330C2×Q8C2×Dic2214yes—
331C22×C4—24no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—42no—
335C22×C4—42no—
336C22×C4—112no—
337C22×C4—112no—
338C22×C4—224no—
339C22×C4—224no—
340C22×C4—221no—
341C22×C4—221no—
342C22×C4—222no—
343C22×C4—442no—
344C22×C4—444no—
345C22×C4—442no—
346C22×C4C2×Dic2212yes—
347C22×C4#433912yes—
348C22×C4D4×D1111yescharacteristic
349C22×C4D4×D1112yes—
350C22×C4#434112yes—
351C22×C4#434112yes—
352C22×C4C2×C22⋊D1112yes—
353C22×C4C23×D1111yescharacteristic
354M16—28no—
355M16—444no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—222no—
359C2×C8—222no—
360C2×C8—222no—
361C2×C8C2×C22⋊D1114yes—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—112no—
365C4⋊C4—112no—
366C4⋊C4—221no—
367C4⋊C4—221no—
368C4⋊C4—222no—
369C4⋊C4—222no—
370C4⋊C4—444no—
371C4⋊C4—444no—
372C4⋊C4—442no—
373C22⋊C4—42no—
374C22⋊C4—224no—
375C42—42no—
376C42—224no—
377C42—222no—
378C42—222no—
379C42—222no—
380C42—222no—
381C11#2361911yescharacteristic, complemented, Sylow
382C23—22no—
383C23—22no—
384C23#6693112yes—
385C23#6693712yes—
386C23#6699112yes—
387C23C2×D4×D1111yescharacteristic
388Q8—24no—
389Q8—24no—
390Q8—42no—
391Q8—48no—
392Q8—42no—
393C2×C4—24no—
394C2×C4—42no—
395C2×C4—48no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—114no—
401C2×C4—222no—
402C2×C4—222no—
403C2×C4—222no—
404C2×C4—222no—
405C2×C4—222no—
406C2×C4—222no—
407C2×C4—222no—
408C2×C4—448no—
409C2×C4—442no—
410C2×C4—442no—
411C2×C4—442no—
412C2×C4—444no—
413C2×C4—884no—
414C2×C4#6693114yes—
415C2×C4#6693112yes—
416C2×C4#6693214yes—
417C2×C4#6693712yes—
418C2×C4#6697714yes—
419C2×C4#6699112yes—
420C2×C4#6699214yes—
421C2×C4C22×Dic2211yescharacteristic
422C2×C4C2×#433911yescharacteristic
423C2×C4C2×D4×D1111yescharacteristic
424C2×C4C2×#434111yescharacteristic
425C2×C4C2×#434111yescharacteristic
426C2×C4C22×C22⋊D1111yescharacteristic
427C8—24no—
428C8—442no—
429C22—22no—
430C22—22no—
431C22—24no—
432C22—24no—
433C22#1062256114yes—
434C22C2×#6693111yescharacteristic
435C22C2×#6693711yescharacteristic
436C22D11×#13712yes—
437C22#1062330812yes—
438C22C2×#6699111yescharacteristic
439C4—44no—
440C4—82no—
441C4—224no—
442C4—442no—
443C4—442no—
444C4—442no—
445C4—882no—
446C4#1062256114yes—
447C4C2×#6693111yescharacteristic
448C4C2×#6693211yescharacteristic
449C4C2×#6697711yescharacteristic
450C4C2×#6699211yescharacteristic
451C2—24no—
452C2C2×#1062256111yescharacteristic
453C2#1307810211yescharacteristic
454C2#1307811311yescharacteristic
455C2#1307824012yes—
456C2#1307841812yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#419C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenterC2×#419D11
hypocenterC11#23619
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
6. #13070009C2semidirect
7. #13069995C2semidirect
381. C11#23619semidirect

Maximal subgroups

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

subgroupindex
C2×#106227342
C2×#106227312
C2×#106228382
#130710982
C2×#106228432
#130700092
#130699952
#130683372
C2×C11×#4192
#2361911