Finite Group Databasebeta

← #14914222

Subgroups — #14914222

Order 2816.

2310 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623001C211yesmaximal, characteristic
2#13071621C218yesmaximal
3#13071575C214yesmaximal, complemented
4#13071528C214yesmaximal, complemented
5#13071355C214yesmaximal, complemented
6#13071240C212yesmaximal
7#13071183C214yesmaximal, complemented
8#13070973C212yesmaximal
9C4×#66979C211yesmaximal, characteristic
10C2×C11×#384C211yesmaximal, characteristic
11C22×C11×C4⋊C4C2212yes—
12C22×C11×C4⋊C4C2214yes—
13C22×C42×C11C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C2×#66979C2212yes—
16C2×#66979C2211yescharacteristic
17C2×#66977C2214yes—
18C2×#66940C2218yes—
19#10623001C4116yescomplemented
20C2×#66923C2212yes—
21C2×#66922C2212yes—
22C2×C4×Dic22C2214yes—
23C11×#384C2212yes—
24C11×#384C2214yes—
25C11×#384C2212yes—
26#10622823C2218yes—
27C4×C22⋊Dic11C2214yes—
28C4×C22⋊Dic11C2218yes—
29#10622591C22116yes—
30#10622590C2214yes—
31#10622589C2214yes—
32C4⋊C4×Dic11C2218yes—
33C4⋊C4×Dic11C2218yes—
34C4⋊C4×Dic11C2218yes—
35#10622587C2218yes—
36#10622586C2218yes—
37#10622586C2218yes—
38#10622585C22116yes—
39C4×C4⋊Dic11C2212yes—
40C4×C4⋊Dic11C2212yes—
41#10622545C2212yes—
42C42×Dic11C2212yes—
43C23×C4×C11C2312yes—
44C23×C4×C11C2314yes—
45C23×C4×C11C2311yescharacteristic
46C22×Dic22C2314yes—
47C2×C11×C4⋊C4—28no—
48C2×C11×C4⋊C4—48no—
49C2×C11×C4⋊C4C2318yes—
50C2×C11×C4⋊C4C2314yes—
51C2×C11×C4⋊C4C2314yes—
52C2×C11×C4⋊C4C2318yes—
53C2×C42×C11C2×C418yes—
54C2×C42×C11C2312yes—
55C2×C42×C11C2311yescharacteristic
56C2×C42×C11C2311yescharacteristic
57C2×C22⋊Dic11C2312yes—
58C2×C22⋊Dic11C2314yes—
59C2×C22⋊Dic11C2312yes—
60#66979—24no—
61#66979C2×C4116yes—
62#66979Q818yescomplemented
63C2×C4⋊Dic11C2311yescharacteristic
64C2×C4⋊Dic11C2311yescharacteristic
65C2×C4⋊Dic11C2314yes—
66C2×C4⋊Dic11C2314yes—
67C2×C4⋊Dic11C2312yes—
68#66977C2×C4132yes—
69C2×Dic11⋊C4C23116yes—
70C2×Dic11⋊C4C2318yes—
71C2×C4×Dic11C2314yes—
72C2×C4×Dic11C2312yes—
73C2×C4×Dic11C2314yes—
74C2×C4×Dic11C23116yes—
75C2×C4×Dic11C2314yes—
76C2×C4×Dic11C2312yes—
77#66940—416no—
78#66923C2×C4116yescomplemented
79#66922C2×C4116yescomplemented
80C4×Dic22C2×C4132yescomplemented
81C11⋊#95C2314yes—
82C11⋊#95C2314yes—
83C11⋊#95C23116yes—
84C11⋊#95C23116yes—
85#34214—111nomaximal, Sylow
86C24×C11C2411yescharacteristic
87C22×C4×C11—24no—
88C22×C4×C11—24no—
89C22×C4×C11—28no—
90C22×C4×C11—48no—
91C22×C4×C11C22×C418yes—
92C22×C4×C11C22×C414yes—
93C22×C4×C11C2×Q814yes—
94C22×C4×C11#4114yes—
95C22×C4×C11C2418yes—
96C22×C4×C11C2412yes—
97C22×C4×C11C2411yescharacteristic
98C22×C4×C11C2411yescharacteristic
99C22×C4×C11C2412yes—
100C22×Dic11C2412yes—
101C22×Dic11C2412yes—
102C22×Dic11C2418yes—
103C22×Dic11C2414yes—
104C2×Dic22—28no—
105C2×Dic22—28no—
106C2×Dic22C22×C4116yes—
107C11×C4⋊C4—28no—
108C11×C4⋊C4—28no—
109C11×C4⋊C4—216no—
110C11×C4⋊C4—48no—
111C42×C11C22×C418yes—
112C42×C11C22×C414yes—
113C42×C11C22×C414yes—
114C22⋊Dic11—24no—
115C22⋊Dic11C22×C4116yes—
116C22⋊Dic11C2×Q818yes—
117C4⋊Dic11—22no—
118C4⋊Dic11—22no—
119C4⋊Dic11C22×C4116yes—
120C4⋊Dic11C22×C4116yes—
121C4⋊Dic11C2×Q818yes—
122Dic11⋊C4—416no—
123Dic11⋊C4C22×C4132yes—
124C4×Dic11—24no—
125C4×Dic11—28no—
126C4×Dic11—28no—
127C4×Dic11—416no—
128C4×Dic11C22×C4116yes—
129C4×Dic11C2×Q818yes—
130C2×#533—111no—
131#2360—118no—
132#2355—114no—
133Q8×C4⋊C4—114no—
134#2330—114no—
135#2317—112no—
136C4×C4⋊Q8—114no—
137C2×#384D1111yescharacteristic
138#2274—112no—
139C4×#117—111no—
140C23×C11—22no—
141C23×C11—22no—
142C23×C11C23×C412yes—
143C23×C11C22×Q812yes—
144C23×C11C2×#4112yes—
145C23×C11C2511yescharacteristic
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11—216no—
149C2×C4×C11—28no—
150C2×C4×C11—216no—
151C2×C4×C11—88no—
152C2×C4×C11C4×Q8116yescomplemented
153C2×C4×C11C23×C414yes—
154C2×C4×C11C23×C412yes—
155C2×C4×C11C23×C412yes—
156C2×C4×C11C23×C414yes—
157C2×C4×C11C22×Q812yes—
158C2×C4×C11C22×Q812yes—
159C2×C4×C11C2×#4112yes—
160C2×C4×C11C2×#4112yes—
161C2×C4×C11H(5,𝔽2)14yes—
162C2×C4×C112−1+414yes—
163C2×Dic11—24no—
164C2×Dic11—28no—
165C2×Dic11—24no—
166C2×Dic11—28no—
167C2×Dic11—22no—
168C2×Dic11—22no—
169C2×Dic11—24no—
170C2×Dic11—24no—
171C2×Dic11C23×C4116yes—
172C2×Dic11C22×Q818yes—
173Dic22—232no—
174#533—1116no—
175C2×C4⋊Q8—112no—
176C2×#125—112no—
177C2×C22⋊Q8—114no—
178C2×C4×Q8—118no—
179C2×C4×Q8—114no—
180C2×#117—112no—
181C2×#117—111no—
182C2×#117—111no—
183C22×C4⋊C4C2×D1112yes—
184C22×C4⋊C4C2×D1114yes—
185C22×C42C2×D1111yescharacteristic
186#391—118no—
187#389—118no—
188#389—118no—
189#389—1116no—
190#387—1116no—
191#385—118no—
192#384—114no—
193#384C2×D1112yes—
194#384C2×D1112yes—
195#384C2×D1114yes—
196#382—114no—
197C4×C4⋊C4—118no—
198C4×C4⋊C4—118no—
199C4×C4⋊C4—118no—
200C4×C4⋊C4—112no—
201C4×C4⋊C4—112no—
202C4×C22⋊C4—114no—
203C4×C22⋊C4—118no—
204#376—112no—
205C43—112no—
206C22×C11—24no—
207C22×C11—24no—
208C22×C11—22no—
209C22×C11—22no—
210C22×C11C2×C4×Q814yes—
211C22×C11C24×C411yescharacteristic
212C22×C11C23×Q811yescharacteristic
213C22×C11C22×#4111yescharacteristic
214C22×C11C2×H(5,𝔽2)12yes—
215C22×C11C2×2−1+412yes—
216C4×C11—24no—
217C4×C11—48no—
218C4×C11C2×C4×Q814yes—
219C4×C11C2×C4×Q814yes—
220C4×C11#52018yes—
221Dic11—216no—
222Dic11—28no—
223Dic11—42no—
224Dic11—42no—
225C22×Q8—114no—
226C23×C4C22×D1112yes—
227C23×C4C22×D1114yes—
228C23×C4C22×D1111yescharacteristic
229C4⋊Q8—1116no—
230#125—1116no—
231C22⋊Q8—1132no—
232C4×Q8—1132no—
233C4×Q8—4416no—
234#117—1116no—
235#117—118no—
236#117—224no—
237C2×C4⋊C4—28no—
238C2×C4⋊C4—48no—
239C2×C4⋊C4—114no—
240C2×C4⋊C4—112no—
241C2×C4⋊C4—118no—
242C2×C4⋊C4—114no—
243C2×C4⋊C4—111no—
244C2×C4⋊C4—111no—
245C2×C4⋊C4—1116no—
246C2×C4⋊C4C22×D1118yes—
247C2×C4⋊C4C22×D1114yes—
248C2×C4⋊C4C22×D1114yes—
249C2×C4⋊C4C22×D1118yes—
250C2×C22⋊C4—114no—
251C2×C22⋊C4—112no—
252C2×C22⋊C4—112no—
253C2×C42—114no—
254C2×C42—112no—
255C2×C42—112no—
256C2×C42—114no—
257C2×C42—114no—
258C2×C42—1116no—
259C2×C42C4×D1118yes—
260C2×C42C22×D1112yes—
261C2×C42C22×D1111yescharacteristic
262C2×C42C22×D1111yescharacteristic
263#95—114no—
264#95—114no—
265#95—1116no—
266#95—1116no—
267C2×C11—24no—
268C2×C11C22×C4×Q811yescharacteristic
269C2×C11C2×#52012yes—
270C2×C11#350312yes—
271C2×C11#350811yescharacteristic
272C2×C11#350911yescharacteristic
273C24C23×D1111yescharacteristic
274C2×Q8—1116no—
275C2×Q8—228no—
276C2×Q8—228no—
277C22×C4—24no—
278C22×C4—24no—
279C22×C4—28no—
280C22×C4—48no—
281C22×C4—114no—
282C22×C4—118no—
283C22×C4—112no—
284C22×C4—112no—
285C22×C4C2×C4×D1118yes—
286C22×C4C2×C4×D1114yes—
287C22×C4#434114yes—
288C22×C4Q8×D1114yes—
289C22×C4C23×D1118yes—
290C22×C4C23×D1112yes—
291C22×C4C23×D1111yescharacteristic
292C22×C4C23×D1111yescharacteristic
293C22×C4C23×D1112yes—
294C4⋊C4—28no—
295C4⋊C4—28no—
296C4⋊C4—216no—
297C4⋊C4—48no—
298C4⋊C4—1116no—
299C4⋊C4—1132no—
300C4⋊C4—1116no—
301C4⋊C4—118no—
302C4⋊C4—222no—
303C4⋊C4—222no—
304C4⋊C4—4416no—
305C22⋊C4—1116no—
306C22⋊C4—118no—
307C22⋊C4—224no—
308C42—1116no—
309C42—118no—
310C42—224no—
311C42—228no—
312C42—228no—
313C42—4416no—
314C42C2×C4×D1118yes—
315C42C2×C4×D1114yes—
316C42C2×C4×D1114yes—
317C11#3421411yescharacteristic, complemented, Sylow
318C23—22no—
319C23—22no—
320C23C22×C4×D1112yes—
321C23C2×#434112yes—
322C23C2×Q8×D1112yes—
323C23C24×D1111yescharacteristic
324Q8—2232no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—216no—
328C2×C4—28no—
329C2×C4—216no—
330C2×C4—88no—
331C2×C4—1116no—
332C2×C4—118no—
333C2×C4—224no—
334C2×C4—228no—
335C2×C4—224no—
336C2×C4—228no—
337C2×C4—222no—
338C2×C4—222no—
339C2×C4—224no—
340C2×C4—224no—
341C2×C4#66940116yescomplemented
342C2×C4C22×C4×D1114yes—
343C2×C4C22×C4×D1112yes—
344C2×C4C22×C4×D1112yes—
345C2×C4C22×C4×D1114yes—
346C2×C4C2×#434112yes—
347C2×C4C2×#434112yes—
348C2×C4#6703714yes—
349C2×C4C2×Q8×D1112yes—
350C2×C4C2×Q8×D1112yes—
351C2×C4#6704014yes—
352C22—24no—
353C22—22no—
354C22—22no—
355C22—24no—
356C22C2×#6694014yes—
357C22C23×C4×D1111yescharacteristic
358C22C22×#434111yescharacteristic
359C22C2×#6703712yes—
360C22C22×Q8×D1111yescharacteristic
361C22C2×#6704012yes—
362C4—24no—
363C4—48no—
364C4—228no—
365C4—2216no—
366C4—442no—
367C4—442no—
368C4C2×#6694014yes—
369C4C2×#6694014yes—
370C4#1062303518yes—
371C2—24no—
372C2C22×#6694011yescharacteristic
373C2C2×#1062303512yes—
374C2#1308243212yes—
375C2#1308249011yescharacteristic
376C2#1308250011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC2×C11×#384C2
socle, cosocleC23×C11C25
prime radicalC24×C11C24
hypercenterC2×#384D11
hypocenterC11#34214
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#384

Complements

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

NH ≅ G/Ntype
3. #13071575C2semidirect
4. #13071528C2semidirect
5. #13071355C2semidirect
7. #13071183C2semidirect
19. #10623001C4semidirect
62. #66979Q8semidirect
78. #66923C2×C4semidirect
79. #66922C2×C4semidirect
80. C4×Dic22C2×C4semidirect
152. C2×C4×C11C4×Q8semidirect
317. C11#34214semidirect
341. C2×C4#66940semidirect

Maximal subgroups

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

subgroupindex
C2×#106230012
#130716212
#130715752
#130715282
#130713552
#130712402
#130711832
#130709732
C4×#669792
C2×C11×#3842
#3421411