Finite Group Databasebeta

← #14684733

Subgroups — #14684733

Order 2816.

1030 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13066884C212yesmaximal
2#13066884C211yesmaximal, characteristic
3#13066878C212yesmaximal
4#13066878C212yesmaximal
5#13066869C212yesmaximal
6#13066869C212yesmaximal
7#13066850C212yesmaximal
8#13066848C211yesmaximal, characteristic
9C2×C11×#398C211yesmaximal, characteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C11×C4⋊C4C2212yes—
13C22×C4⋊Dic11C2212yes—
14C22×C4×Dic11C2211yescharacteristic
15C11×#398C418yescomplemented
16C2×C11×#95C2212yes—
17C2×C11×#95C2211yescharacteristic
18C2×C11⋊#95C2212yes—
19C2×C11⋊#95C2212yes—
20C2×C11⋊#95C2212yes—
21C2×C11⋊#95C2211yescharacteristic
22C2×C11⋊#95C2212yes—
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2211yescharacteristic
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32C23×C4×C11C2311yescharacteristic
33C23×C4×C11C2312yes—
34C23×C4×C11C2312yes—
35C23×C4×C11C2311yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C23×Dic11C2312yes—
38C23×Dic11C2312yes—
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C2×C11×C4⋊C4—41no—
42C2×C11×C4⋊C4—41no—
43C2×C11×C4⋊C4—42no—
44C2×C11×C4⋊C4—41no—
45C2×C11×C4⋊C4—42no—
46C2×C11×C4⋊C4—41no—
47C2×C11×C4⋊C4C2×C414yes—
48C2×C11×C4⋊C4C2×C418yes—
49C2×C11×C4⋊C4C2×C414yes—
50C2×C4⋊Dic11—24no—
51C2×C4⋊Dic11—42no—
52C2×C4⋊Dic11—42no—
53C2×C4×Dic11—42no—
54C2×C4×Dic11—41no—
55C11×#95C2×C418yes—
56C11×#95C2×C414yes—
57C11⋊#95—24no—
58C11⋊#95—24no—
59C11⋊#95—42no—
60C11⋊#95—42no—
61C11⋊#95—42no—
62C11⋊#95—42no—
63C11⋊#95—42no—
64C11⋊#95—42no—
65C11⋊#95—41no—
66C11⋊#95—42no—
67C11⋊#95—42no—
68C11⋊#95—41no—
69C11⋊#95—42no—
70C11⋊#95—41no—
71#14650—111nomaximal, Sylow
72C24×C11C2411yescharacteristic
73C22×C4×C11—22no—
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—21no—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—21no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11C22×C414yes—
98C22×C4×C11C22×C412yes—
99C22×C4×C11C22×C414yes—
100C22×C4×C11C22×C412yes—
101C22×C4×C11C22×C412yes—
102C22×Dic11—22no—
103C22×Dic11—22no—
104C22×Dic11—22no—
105C22×Dic11—22no—
106C22×Dic11—22no—
107C22×Dic11—22no—
108C22×Dic11—22no—
109C22×Dic11—22no—
110C22×Dic11—22no—
111C22×Dic11—22no—
112C22×Dic11—22no—
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11—22no—
116C22×Dic11—22no—
117C22×Dic11—22no—
118C22×Dic11—22no—
119C22×Dic11—22no—
120C22×Dic11—22no—
121C22×Dic11—22no—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11—22no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11#4114yes—
130C11×C4⋊C4—48no—
131C11×C4⋊C4—44no—
132C11×C4⋊C4—44no—
133C4⋊Dic11—48no—
134C4×Dic11—44no—
135C2×#398D1111yescharacteristic
136#1445—111no—
137#1445—112no—
138#1443—112no—
139#1443—112no—
140#1441—112no—
141#1441—112no—
142#1436—112no—
143#1436—111no—
144C23×C11C23×C411yescharacteristic
145C23×C11C2×#4112yes—
146C23×C11H(5,𝔽2)11yescharacteristic
147C23×C11H(5,𝔽2)12yes—
148C23×C11H(5,𝔽2)11yescharacteristic
149C23×C11H(5,𝔽2)12yes—
150C23×C112−1+412yes—
151C23×C112−1+412yes—
152C23×C112−1+412yes—
153C2×C4×C11—22no—
154C2×C4×C11—24no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—24no—
159C2×C4×C11—24no—
160C2×C4×C11—22no—
161C2×C4×C11—24no—
162C2×C4×C11—24no—
163C2×C4×C11—24no—
164C2×C4×C11—24no—
165C2×C4×C11—24no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×Dic11—24no—
183C2×Dic11—24no—
184C2×Dic11—24no—
185C2×Dic11—42no—
186C2×Dic11—42no—
187C2×Dic11—42no—
188C2×Dic11—42no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193C2×Dic11—42no—
194C2×Dic11—42no—
195C2×Dic11—42no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C22×C4⋊C4—112no—
211C22×C4⋊C4C2×D1111yescharacteristic
212C22×C4⋊C4C2×D1111yescharacteristic
213C22×C4⋊C4C2×D1112yes—
214C22×C42—111no—
215#398Dic1118yescomplemented
216C2×#95—112no—
217C2×#95—112no—
218C2×#95—112no—
219C2×#95—112no—
220C2×#95—111no—
221C2×#95—112no—
222C2×#95—112no—
223C2×#95—112no—
224C2×#95—111no—
225C2×#95—112no—
226C2×#95—112no—
227C2×#95—112no—
228C2×#95—112no—
229C2×#95—111no—
230C2×#95C2×D1112yes—
231C2×#95C2×D1111yescharacteristic
232C22×C11C4×#4111yescharacteristic
233C22×C11#51811yescharacteristic
234C22×C11#51811yescharacteristic
235C22×C11#51912yes—
236C22×C11#52012yes—
237C22×C11#53812yes—
238C22×C11#53912yes—
239C22×C11#53912yes—
240C22×C11#54012yes—
241C22×C11#54112yes—
242C22×C11#54112yes—
243C22×C11#56011yescharacteristic
244C22×C11#56212yes—
245C22×C11#56212yes—
246C22×C11#56212yes—
247C22×C11#56312yes—
248C22×C11#56311yescharacteristic
249C22×C11#56311yescharacteristic
250C22×C11#56312yes—
251C22×C11#56312yes—
252C22×C11#56311yescharacteristic
253C4×C11—42no—
254C4×C11—44no—
255C4×C11—42no—
256C4×C11—42no—
257C4×C11—44no—
258Dic11—44no—
259Dic11—82no—
260Dic11—82no—
261Dic11—82no—
262C23×C4—112no—
263C23×C4—112no—
264C23×C4—112no—
265C23×C4—112no—
266C23×C4C22×D1112yes—
267C23×C4C22×D1111yescharacteristic
268C23×C4C22×D1111yescharacteristic
269C23×C4C22×D1112yes—
270C23×C4C22×D1111yescharacteristic
271C2×C4⋊C4—41no—
272C2×C4⋊C4—41no—
273C2×C4⋊C4—42no—
274C2×C4⋊C4—41no—
275C2×C4⋊C4—42no—
276C2×C4⋊C4—41no—
277C2×C4⋊C4—224no—
278C2×C4⋊C4—442no—
279C2×C4⋊C4—442no—
280C2×C4⋊C4C2×Dic1114yes—
281C2×C4⋊C4C2×Dic1118yes—
282C2×C4⋊C4C2×Dic1114yes—
283C2×C42—441no—
284C2×C42—442no—
285#95—224no—
286#95—224no—
287#95—442no—
288#95—441no—
289#95—442no—
290#95—442no—
291#95—441no—
292#95—442no—
293#95—441no—
294#95—442no—
295#95—442no—
296#95—442no—
297#95—442no—
298#95—442no—
299#95C2×Dic1118yes—
300#95C2×Dic1114yes—
301C2×C11#233311yescharacteristic
302C2×C11#233612yes—
303C2×C11#237611yescharacteristic
304C2×C11#237812yes—
305C2×C11#238111yescharacteristic
306C2×C11#282712yes—
307C2×C11#283312yes—
308C2×C11#283612yes—
309C2×C11#283612yes—
310C24C23×D1111yescharacteristic
311C22×C4—21no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—21no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—22no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—114no—
336C22×C4—222no—
337C22×C4—222no—
338C22×C4—222no—
339C22×C4—222no—
340C22×C4—222no—
341C22×C4—222no—
342C22×C4—222no—
343C22×C4—222no—
344C22×C4—222no—
345C22×C4—222no—
346C22×C4—222no—
347C22×C4—222no—
348C22×C4—222no—
349C22×C4—222no—
350C22×C4—222no—
351C22×C4—222no—
352C22×C4—222no—
353C22×C4—222no—
354C22×C4—222no—
355C22×C4—222no—
356C22×C4—222no—
357C22×C4—222no—
358C22×C4—222no—
359C22×C4—222no—
360C22×C4—222no—
361C22×C4—222no—
362C22×C4—222no—
363C22×C4C22×Dic1114yes—
364C22×C4C22×Dic1112yes—
365C22×C4C22×Dic1112yes—
366C22×C4C22×Dic1114yes—
367C22×C4C22×Dic1112yes—
368C4⋊C4—48no—
369C4⋊C4—44no—
370C4⋊C4—44no—
371C4⋊C4—448no—
372C42—444no—
373C11#1465011yescharacteristic, complemented, Sylow
374C23#6703711yescharacteristic
375C23#6703711yescharacteristic
376C23#6703712yes—
377C23#6704012yes—
378C23#6704012yes—
379C23#41×D1112yes—
380C23#6704212yes—
381C23#6704312yes—
382C23C23×Dic1111yescharacteristic
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—24no—
387C2×C4—24no—
388C2×C4—22no—
389C2×C4—24no—
390C2×C4—24no—
391C2×C4—22no—
392C2×C4—24no—
393C2×C4—24no—
394C2×C4—24no—
395C2×C4—24no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—224no—
413C2×C4—224no—
414C2×C4—224no—
415C2×C4—442no—
416C2×C4—442no—
417C2×C4—442no—
418C2×C4—442no—
419C2×C4—442no—
420C2×C4—442no—
421C2×C4—442no—
422C2×C4—442no—
423C2×C4—442no—
424C2×C4—442no—
425C2×C4—442no—
426C2×C4—442no—
427C2×C4—442no—
428C2×C4—442no—
429C2×C4—442no—
430C2×C4—442no—
431C2×C4—442no—
432C2×C4—442no—
433C2×C4—442no—
434C2×C4—442no—
435C2×C4—442no—
436C2×C4—442no—
437C2×C4—442no—
438C2×C4—442no—
439C2×C4—442no—
440C22#1062314412yes—
441C22#1062314612yes—
442C22#1062317712yes—
443C22#1062317712yes—
444C22#1062317812yes—
445C22#1062317812yes—
446C22#1062318211yescharacteristic
447C22#1062319711yescharacteristic
448C22#1062319812yes—
449C22#1062322312yes—
450C22#1062322312yes—
451C22#1062322712yes—
452C22#1062322712yes—
453C22#1062326612yes—
454C22#1062326611yescharacteristic
455C22#1062326611yescharacteristic
456C22#1062332911yescharacteristic
457C22#1062332911yescharacteristic
458C22#1062334312yes—
459C22#41×Dic1111yescharacteristic
460C22#1062335812yes—
461C4—42no—
462C4—44no—
463C4—42no—
464C4—42no—
465C4—44no—
466C4—444no—
467C4—882no—
468C4—882no—
469C4—882no—
470C2#1307138311yescharacteristic
471C2#1307142212yes—
472C2#1307176411yescharacteristic
473C2#1307178212yes—
474C2#1307179711yescharacteristic
475C2#1307671912yes—
476C2#1307679112yes—
477C2#1307681212yes—
478C2#1307682212yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#398C2
socle, prime radical, cosocleC24×C11C24
hypercenterC2×#398D11
hypocenterC11#14650
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
15. C11×#398C4semidirect
215. #398Dic11semidirect
373. C11#14650semidirect

Maximal subgroups

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

subgroupindex
#130668842
#130668782
#130668692
#130668502
#130668482
C2×C11×#3982
#1465011