Finite Group Databasebeta

← #14651695

Subgroups — #14651695

Order 2816.

660 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 660 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072894C211yesmaximal, characteristic
2#13071214C211yesmaximal, characteristic
3#13068688C212yesmaximal
4C11⋊#1304C212yesmaximal
5C11×#1819C211yesmaximal, characteristic
6C22×C11×C22⋊C4C2211yescharacteristic
7C22×C22⋊Dic11C2211yescharacteristic
8C11×#379C2212yes—
9#10622860C2211yescharacteristic
10#10622860C2212yes—
11#10622825—21no—
12#10622824—21no—
13#10622823—21no—
14C4×C22⋊Dic11—21no—
15#10622565—22no—
16#10622564—24no—
17#10622559C412yescomplemented
18#10622556C412yescomplemented
19C11×#342—22no—
20#10622165—24no—
21C25×C11C2311yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C23×Dic11C2×C411yescharacteristic
25C23×Dic11C2×C411yescharacteristic
26C2×C11×C22⋊C4—22no—
27C2×C11×C22⋊C4—22no—
28C2×C11×C22⋊C4—22no—
29C2×C11×C22⋊C4—22no—
30C2×C11×C22⋊C4—22no—
31C2×C11×C22⋊C4C2×C412yes—
32C2×C11×C22⋊C4D412yes—
33C2×C22⋊Dic11—21no—
34C2×C22⋊Dic11—22no—
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—22no—
38C2×C22⋊Dic11—22no—
39C2×C22⋊Dic11—22no—
40C2×C22⋊Dic11—21no—
41C2×C22⋊Dic11C2×C412yes—
42C2×C22⋊Dic11D414yes—
43C2×C4⋊Dic11—22no—
44C2×Dic11⋊C4—22no—
45C2×C4×Dic11—22no—
46C11⋊#95—22no—
47C11⋊#95—22no—
48C11⋊#95—22no—
49C11⋊#95—22no—
50C11⋊#95—22no—
51#9500—111nomaximal, Sylow
52C24×C11—42no—
53C24×C11—42no—
54C24×C11—81no—
55C24×C11C22×C411yescharacteristic
56C24×C11C2×D411yescharacteristic
57C24×C11C2×D411yescharacteristic
58C24×C11C2×D412yes—
59C24×C11#4112yes—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—42no—
65C22×C4×C11—42no—
66C22×C4×C11—81no—
67C22×C4×C11C22⋊C412yes—
68C22×C4×C11C22⋊C412yes—
69C22×Dic11—21no—
70C22×Dic11—22no—
71C22×Dic11—21no—
72C22×Dic11—22no—
73C22×Dic11—22no—
74C22×Dic11—24no—
75C22×Dic11—42no—
76C22×Dic11—81no—
77C11×C22⋊C4—24no—
78C11×C22⋊C4—24no—
79C11×C22⋊C4—44no—
80C11×C22⋊C4—44no—
81C11×C22⋊C4—82no—
82C22⋊Dic11—42no—
83C22⋊Dic11—44no—
84C22⋊Dic11—44no—
85C22⋊Dic11—42no—
86C22⋊Dic11—41no—
87C22⋊Dic11—42no—
88C22⋊Dic11—41no—
89C22⋊Dic11—81no—
90C22⋊Dic11—82no—
91C4⋊Dic11—82no—
92Dic11⋊C4—82no—
93C4×Dic11—82no—
94#2483—111no—
95#2312—111no—
96#1819—112no—
97#1819D1111yescharacteristic
98#1304—112no—
99C23×C11—22no—
100C23×C11—22no—
101C23×C11—22no—
102C23×C11—22no—
103C23×C11—24no—
104C23×C11—41no—
105C23×C11—41no—
106C23×C11—41no—
107C23×C11—42no—
108C23×C11—41no—
109C23×C11—42no—
110C23×C11—42no—
111C23×C11—41no—
112C23×C11—42no—
113C23×C11—42no—
114C23×C11—88no—
115C23×C11C2×C22⋊C411yescharacteristic
116C23×C11C4×D412yes—
117C23×C11#12011yescharacteristic
118C23×C11#12112yes—
119C23×C11#12311yescharacteristic
120C2×C4×C11—22no—
121C2×C4×C11—22no—
122C2×C4×C11—42no—
123C2×C4×C11—42no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—81no—
127C2×C4×C11—81no—
128C2×C4×C11—82no—
129C2×C4×C11—82no—
130C2×C4×C11—82no—
131C2×Dic11—42no—
132C2×Dic11—42no—
133C2×Dic11—44no—
134C2×Dic11—42no—
135C2×Dic11—44no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—42no—
139C2×Dic11—42no—
140C2×Dic11—44no—
141C2×Dic11—82no—
142C2×Dic11—82no—
143C22×C22⋊C4—111no—
144C22×C22⋊C4C2×D1111yescharacteristic
145#397—222no—
146#388—224no—
147#385—112no—
148#385—221no—
149#381—112no—
150#381—221no—
151#380—221no—
152#379—112no—
153#379—111no—
154#379C2×D1112yes—
155C4×C22⋊C4—221no—
156#342—22no—
157#342—224no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—22no—
163C22×C11—21no—
164C22×C11—22no—
165C22×C11—22no—
166C22×C11—22no—
167C22×C11—21no—
168C22×C11—22no—
169C22×C11—21no—
170C22×C11—22no—
171C22×C11—44no—
172C22×C11—44no—
173C22×C11—84no—
174C22×C11—82no—
175C22×C11—84no—
176C22×C11#38611yescharacteristic
177C22×C11#41012yes—
178C22×C11#45812yes—
179C4×C11—42no—
180C4×C11—42no—
181C4×C11—162no—
182Dic11—84no—
183Dic11—82no—
184Dic11—81no—
185Dic11—81no—
186C25C22×D1111yescharacteristic
187C23×C4—111no—
188C23×C4—111no—
189C23×C4D4411yescharacteristic
190C23×C4D4411yescharacteristic
191C2×C4⋊C4—222no—
192C2×C4⋊C4—222no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—22no—
195C2×C22⋊C4—22no—
196C2×C22⋊C4—22no—
197C2×C22⋊C4—22no—
198C2×C22⋊C4—112no—
199C2×C22⋊C4—114no—
200C2×C22⋊C4—221no—
201C2×C22⋊C4—222no—
202C2×C22⋊C4—221no—
203C2×C22⋊C4—222no—
204C2×C22⋊C4—222no—
205C2×C22⋊C4—221no—
206C2×C22⋊C4—222no—
207C2×C22⋊C4—221no—
208C2×C22⋊C4C4×D1112yes—
209C2×C22⋊C4C22⋊D1112yes—
210C2×C42—222no—
211#95—222no—
212#95—222no—
213#95—222no—
214#95—222no—
215#95—222no—
216C2×C11—22no—
217C2×C11—22no—
218C2×C11—42no—
219C2×C11—41no—
220C2×C11—42no—
221C2×C11#189011yescharacteristic
222C2×C11#189911yescharacteristic
223C2×C11#191311yescharacteristic
224C24—42no—
225C24—42no—
226C24—81no—
227C24C2×C4×D1111yescharacteristic
228C24C2×D4411yescharacteristic
229C24D4×D1112yes—
230C24#434112yes—
231C24C2×C22⋊D1111yescharacteristic
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4—81no—
239C22×C4—224no—
240C22×C4—221no—
241C22×C4—222no—
242C22×C4—221no—
243C22×C4—222no—
244C22×C4—222no—
245C22×C4—442no—
246C22×C4—881no—
247C22×C4(C2×D11)⋊C412yes—
248C22×C4(C2×D11)⋊C412yes—
249C4⋊C4—882no—
250C4⋊C4—882no—
251C22⋊C4—24no—
252C22⋊C4—24no—
253C22⋊C4—44no—
254C22⋊C4—44no—
255C22⋊C4—82no—
256C22⋊C4—442no—
257C22⋊C4—444no—
258C22⋊C4—441no—
259C22⋊C4—441no—
260C22⋊C4—442no—
261C22⋊C4—444no—
262C22⋊C4—442no—
263C22⋊C4—882no—
264C22⋊C4—881no—
265C42—882no—
266C11#950011yescharacteristic, complemented, Sylow
267C23—22no—
268C23—22no—
269C23—22no—
270C23—24no—
271C23—22no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23—42no—
276C23—42no—
277C23—41no—
278C23—42no—
279C23—42no—
280C23—42no—
281C23—41no—
282C23—88no—
283C23(C22⋊D11)⋊C412yes—
284C23#6693511yescharacteristic
285C23#6693911yescharacteristic
286C23C2×(C2×D11)⋊C411yescharacteristic
287C23#6699212yes—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—82no—
297C2×C4—82no—
298C2×C4—82no—
299C2×C4—444no—
300C2×C4—442no—
301C2×C4—444no—
302C2×C4—442no—
303C2×C4—442no—
304C2×C4—441no—
305C2×C4—441no—
306C2×C4—444no—
307C2×C4—442no—
308C2×C4—442no—
309C2×C4—882no—
310C2×C4—882no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—22no—
316C22—22no—
317C22—21no—
318C22—21no—
319C22—22no—
320C22—22no—
321C22—21no—
322C22—22no—
323C22—22no—
324C22—44no—
325C22—44no—
326C22—84no—
327C22—82no—
328C22—84no—
329C22#1062235512yes—
330C22#1062257111yescharacteristic
331C22#1062261912yes—
332C4—42no—
333C4—42no—
334C4—162no—
335C4—884no—
336C4—882no—
337C4—881no—
338C4—881no—
339C2—22no—
340C2—22no—
341C2—42no—
342C2—42no—
343C2—41no—
344C2#1306902711yescharacteristic
345C2#1306907211yescharacteristic
346C2#1306915611yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC24×C11C22×C4
FrattiniC25C22×D11
FittingC11×#1819C2
socleC22×C11#386
prime radical, cosocleC25×C11C23
hypercenter#1819D11
hypocenterC11#9500
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C25 ◁ #1819

Complements

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

NH ≅ G/Ntype
17. #10622559C4semidirect
18. #10622556C4semidirect
266. C11#9500semidirect

Maximal subgroups

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

subgroupindex
#130728942
#130712142
#130686882
C11⋊#13042
C11×#18192
#950011