Finite Group Databasebeta

← #14925823

Subgroups — #14925823

Order 2816.

1796 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074028C214yesmaximal
2#13073989C211yesmaximal, characteristic
3#13073824C212yesmaximal
4#13073145C214yesmaximal
5#13072451C214yesmaximal
6#13071906C214yesmaximal
7C4⋊Q8×Dic11C214yesmaximal
8#13071183C211yesmaximal, characteristic
9#13071087C214yesmaximal
10C4×#66940C212yesmaximal
11C11×#2551C211yesmaximal, characteristic
12C2×C11×C4⋊Q8C2214yes—
13C2×Q8×Dic11C2214yes—
14C2×#66940C2212yes—
15C2×#66940C2212yes—
16C2×#66940C2212yes—
17C2×#66922C2211yescharacteristic
18C2×C4×Dic22C2212yes—
19C11×#395C2214yes—
20C11×#389C2214yes—
21C11×#384C2211yescharacteristic
22C4×C11×C4⋊C4C2212yes—
23#10622843C2218yes—
24#10622842C2214yes—
25#10622598C2214yes—
26#10622598C2214yes—
27#10622598C2218yes—
28#10622598C2214yes—
29#10622597C2218yes—
30#10622596C2214yes—
31#10622591C2218yes—
32C4⋊C4×Dic11C2218yes—
33C4⋊C4×Dic11C2214yes—
34C4⋊C4×Dic11C2212yes—
35C4⋊C4×Dic11C2212yes—
36#10622587C2214yes—
37#10622587C2212yes—
38#10622586C2214yes—
39#10622548C2214yes—
40C4×Dic11⋊C4C2214yes—
41C42×Dic11C2211yescharacteristic
42C42×Dic11C2214yes—
43#10622542C2214yes—
44#10622274C2214yes—
45#10622269C2218yes—
46#10622268C2218yes—
47#10622262C2214yes—
48#10622262C2214yes—
49#10622261C2214yes—
50C22×Q8×C11C2314yes—
51C22×Dic22C2312yes—
52C22×Dic22C2312yes—
53C11×C4⋊Q8—216no—
54C2×C11×C4⋊C4C2314yes—
55C2×C11×C4⋊C4C2318yes—
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C4⋊C4C2312yes—
59C2×C42×C11C2314yes—
60C2×C42×C11C2311yescharacteristic
61Q8×Dic11—48no—
62C2×C4⋊Dic11C2312yes—
63C2×C4⋊Dic11C2314yes—
64C2×C4⋊Dic11C2318yes—
65C2×C4⋊Dic11C2318yes—
66C2×C4⋊Dic11C2314yes—
67C2×Dic11⋊C4C2314yes—
68C2×Dic11⋊C4C2314yes—
69C2×Dic11⋊C4C2314yes—
70C2×Dic11⋊C4C2314yes—
71C2×C4×Dic11C2314yes—
72C2×C4×Dic11C2311yescharacteristic
73C2×C4×Dic11C2314yes—
74C2×C4×Dic11C2314yes—
75C2×C4×Dic11C2312yes—
76C2×C4×Dic11C2314yes—
77C2×C4×Dic11C2311yescharacteristic
78C2×C4×Dic11C2314yes—
79C2×C4×Dic11C2314yes—
80C2×C4×Dic11C2312yes—
81#66940—28no—
82#66940—44no—
83#66940Q8116yescomplemented
84#66922—24no—
85C4×Dic22—28no—
86C11×#95C2314yes—
87C11×#95C2314yes—
88C11⋊#95C2318yes—
89C11⋊#95C2314yes—
90C11⋊#95C2314yes—
91C11⋊#95C2314yes—
92C11⋊#95C2318yes—
93C11⋊#95C2318yes—
94C11⋊#95C2318yes—
95#34950—111nomaximal, Sylow
96C2×Q8×C11—216no—
97C2×Q8×C11—44no—
98C22×C4×C11C2414yes—
99C22×C4×C11C2414yes—
100C22×C4×C11C2414yes—
101C22×C4×C11C2411yescharacteristic
102C22×C4×C11C2412yes—
103C22×Dic11C2414yes—
104C22×Dic11C2411yescharacteristic
105C22×Dic11C2414yes—
106C22×Dic11C2414yes—
107C22×Dic11C2412yes—
108C22×Dic11C2411yescharacteristic
109C2×Dic22—24no—
110C2×Dic22—24no—
111C2×Dic22—24no—
112C2×Dic22—42no—
113C2×Dic22—42no—
114C2×Dic22C2×Q818yes—
115C11×C4⋊C4—216no—
116C11×C4⋊C4—28no—
117C11×C4⋊C4—42no—
118C11×C4⋊C4C2×Q818yes—
119C11×C4⋊C4#4118yes—
120C42×C11—28no—
121C42×C11#4114yes—
122C4⋊Dic11—24no—
123C4⋊Dic11—28no—
124C4⋊Dic11—48no—
125C4⋊Dic11—48no—
126C4⋊Dic11—44no—
127Dic11⋊C4—28no—
128Dic11⋊C4—28no—
129Dic11⋊C4—44no—
130Dic11⋊C4C2×Q8116yes—
131C4×Dic11—22no—
132C4×Dic11—28no—
133C4×Dic11—28no—
134C4×Dic11—28no—
135C4×Dic11—28no—
136C4×Dic11—24no—
137C4×Dic11—44no—
138C4×Dic11—41no—
139C4×Dic11C2×Q8116yes—
140C4×Dic11C2×Q818yes—
141#2586—114no—
142#2582—111no—
143#2567—112no—
144#2551D1111yescharacteristic
145#2507—114no—
146#2451—114no—
147#2399—114no—
148C4×C4⋊Q8—111no—
149C4×C4⋊Q8—114no—
150#2295—114no—
151C42×Q8—112no—
152C23×C11C2511yescharacteristic
153Q8×C11—416no—
154C2×C4×C11—24no—
155C2×C4×C11—24no—
156C2×C4×C11—24no—
157C2×C4×C11—21no—
158C2×C4×C11—24no—
159C2×C4×C11—21no—
160C2×C4×C11—28no—
161C2×C4×C11—24no—
162C2×C4×C11C22×Q818yes—
163C2×C4×C11C22×Q814yes—
164C2×C4×C11C2×#4118yes—
165C2×C4×C11C2×#4114yes—
166C2×C4×C11C2×#4112yes—
167C2×C4×C11C2×#4114yes—
168C2×Dic11—22no—
169C2×Dic11—24no—
170C2×Dic11—24no—
171C2×Dic11—22no—
172C2×Dic11—22no—
173C2×Dic11—24no—
174C2×Dic11—24no—
175C2×Dic11—21no—
176C2×Dic11—24no—
177C2×Dic11—24no—
178C2×Dic11—24no—
179C2×Dic11—24no—
180C2×Dic11C22×Q814yes—
181C2×Dic11C22×Q818yes—
182C2×Dic11C22×Q814yes—
183C2×Dic11H(5,𝔽2)12yes—
184Dic22—216no—
185Dic22—48no—
186C2×C4⋊Q8—111no—
187C2×C4⋊Q8C2×D1114yes—
188C2×C4×Q8—114no—
189C2×C4×Q8—112no—
190C2×C4×Q8—112no—
191C2×C4×Q8—112no—
192C2×C4×Q8—112no—
193#398—114no—
194#398—118no—
195#398—114no—
196#395—114no—
197#395—118no—
198#395C2×D1114yes—
199#391—118no—
200#391—112no—
201#391—114no—
202#391—114no—
203#389—114no—
204#389—114no—
205#389—118no—
206#389—114no—
207#389—114no—
208#389C2×D1114yes—
209#387—118no—
210#387—118no—
211#384—114no—
212#384C2×D1111yescharacteristic
213C4×C4⋊C4—112no—
214C4×C4⋊C4—114no—
215C4×C4⋊C4—118no—
216C4×C4⋊C4—112no—
217C4×C4⋊C4—114no—
218C4×C4⋊C4—114no—
219C4×C4⋊C4—114no—
220C4×C4⋊C4C2×D1112yes—
221#376—114no—
222C43—111no—
223C43—114no—
224C22×C11C23×Q812yes—
225C22×C11C22×#4112yes—
226C22×C11C22×#4111yescharacteristic
227C22×C11C2×H(5,𝔽2)11yescharacteristic
228C22×C11#58511yescharacteristic
229C4×C11—22no—
230C4×C11—28no—
231C4×C11—28no—
232C4×C11—44no—
233C4×C11#53318yes—
234Dic11—28no—
235Dic11—24no—
236Dic11—44no—
237Dic11—44no—
238Dic11—41no—
239Dic11Q8214yes—
240C22×Q8—112no—
241C22×Q8—112no—
242C22×Q8C22×D1114yes—
243C4⋊Q8—216no—
244C4⋊Q8—224no—
245C4×Q8—1116no—
246C4×Q8—228no—
247C4×Q8—228no—
248C4×Q8—444no—
249C4×Q8—448no—
250C2×C4⋊C4—114no—
251C2×C4⋊C4—112no—
252C2×C4⋊C4—114no—
253C2×C4⋊C4—114no—
254C2×C4⋊C4—114no—
255C2×C4⋊C4—118no—
256C2×C4⋊C4—114no—
257C2×C4⋊C4—114no—
258C2×C4⋊C4—118no—
259C2×C4⋊C4C22×D1114yes—
260C2×C4⋊C4C22×D1118yes—
261C2×C4⋊C4C22×D1112yes—
262C2×C4⋊C4C22×D1112yes—
263C2×C4⋊C4C22×D1112yes—
264C2×C42—112no—
265C2×C42—114no—
266C2×C42—114no—
267C2×C42—111no—
268C2×C42—114no—
269C2×C42—112no—
270C2×C42—114no—
271C2×C42—114no—
272C2×C42—111no—
273C2×C42—114no—
274C2×C42C22×D1114yes—
275C2×C42C22×D1111yescharacteristic
276#95—118no—
277#95—114no—
278#95—114no—
279#95—114no—
280#95—118no—
281#95—118no—
282#95—118no—
283#95C22×D1114yes—
284#95C22×D1114yes—
285C2×C11C2×#53312yes—
286C2×C11#346011yescharacteristic
287C2×C11C2×Q8211yescharacteristic
288C2×C11Q8×#4112yes—
289C2×C11#348111yescharacteristic
290C2×Q8—216no—
291C2×Q8—44no—
292C2×Q8—118no—
293C2×Q8—224no—
294C2×Q8—224no—
295C2×Q8—224no—
296C2×Q8—442no—
297C2×Q8—442no—
298C22×C4—111no—
299C22×C4—114no—
300C22×C4—112no—
301C22×C4—114no—
302C22×C4—111no—
303C22×C4—114no—
304C22×C4C23×D1114yes—
305C22×C4C23×D1114yes—
306C22×C4C23×D1114yes—
307C22×C4C23×D1111yescharacteristic
308C22×C4C23×D1112yes—
309C4⋊C4—216no—
310C4⋊C4—28no—
311C4⋊C4—42no—
312C4⋊C4—1116no—
313C4⋊C4—228no—
314C4⋊C4—228no—
315C4⋊C4—224no—
316C4⋊C4—228no—
317C4⋊C4—444no—
318C4⋊C4—448no—
319C4⋊C4—444no—
320C4⋊C4—448no—
321C4⋊C4#434118yes—
322C4⋊C4Q8×D1118yes—
323C42—28no—
324C42—118no—
325C42—1116no—
326C42—222no—
327C42—228no—
328C42—228no—
329C42—228no—
330C42—224no—
331C42—228no—
332C42—444no—
333C42—441no—
334C42#434314yes—
335C11#3495011yescharacteristic, complemented, Sylow
336C23C24×D1111yescharacteristic
337Q8—416no—
338Q8—2216no—
339Q8—448no—
340C2×C4—24no—
341C2×C4—24no—
342C2×C4—21no—
343C2×C4—24no—
344C2×C4—24no—
345C2×C4—21no—
346C2×C4—28no—
347C2×C4—24no—
348C2×C4—114no—
349C2×C4—112no—
350C2×C4—114no—
351C2×C4—118no—
352C2×C4—222no—
353C2×C4—224no—
354C2×C4—224no—
355C2×C4—222no—
356C2×C4—222no—
357C2×C4—224no—
358C2×C4—224no—
359C2×C4—221no—
360C2×C4—224no—
361C2×C4—224no—
362C2×C4—224no—
363C2×C4—224no—
364C2×C4C2×#434118yes—
365C2×C4C2×#434114yes—
366C2×C4C2×Q8×D1118yes—
367C2×C4C2×Q8×D1114yes—
368C2×C4C2×#434312yes—
369C2×C4C2×#434314yes—
370C22C22×#434112yes—
371C22C22×Q8×D1112yes—
372C22C22×#434311yescharacteristic
373C22D11×H(5,𝔽2)11yescharacteristic
374C22#1062345711yescharacteristic
375C4—28no—
376C4—28no—
377C4—22no—
378C4—44no—
379C4—114no—
380C4—228no—
381C4—224no—
382C4—441no—
383C4—444no—
384C4—444no—
385C4#1062325918yes—
386C2C2×#1062325912yes—
387C2#1308203911yescharacteristic
388C2Q82×D1111yescharacteristic
389C2Q8×#434112yes—
390C2#1308221711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, prime radical, cosocleC23×C11C25
FittingC11×#2551C2
hypercenter#2551D11
hypocenterC11#34950
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2551

Complements

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

NH ≅ G/Ntype
83. #66940Q8semidirect
335. C11#34950semidirect

Maximal subgroups

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

subgroupindex
#130740282
#130739892
#130738242
#130731452
#130724512
#130719062
C4⋊Q8×Dic112
#130711832
#130710872
C4×#669402
C11×#25512
#3495011