Finite Group Databasebeta

← #14652794

Subgroups — #14652794

Order 2816.

596 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 123 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#13076973C211yesmaximal, characteristic
2#13068365C211yesmaximal, characteristic, complemented
3C2×#10622102C214yesmaximal, complemented
4C11×#1767C211yesmaximal, characteristic, complemented
5C2×#66928C412yes—
6C2×#66928C2212yes—
7C2×#66927C411yescharacteristic
8C2×#66922C411yescharacteristic
9C2×C11×C4⋊C8—21no—
10C2×C11×#97C2212yes—
11C43×C11C2211yescharacteristic
12#10622552—21no—
13#10622552—21no—
14#10622552—21no—
15#10622552—21no—
16C2×#66867C2212yes—
17C11×#336—21no—
18#10622162—21no—
19#10622162—21no—
20#10622102—28no—
21C22×D44—21no—
22C22×D44—21no—
23C22×D44C2×C412yes—
24C22×Dic22C2×C412yes—
25C22×C8×C11—22no—
26C2×C42×C11C2×C411yescharacteristic
27C2×C42×C11C2×C411yescharacteristic
28C2×C42×C11D411yescharacteristic
29C2×C42×C11D411yescharacteristic
30C2×C42×C11D411yescharacteristic
31C2×C42×C11D411yescharacteristic
32C2×C42×C11C2311yescharacteristic
33C2×(C2×D11)⋊C4—22no—
34C2×(C2×D11)⋊C4—22no—
35C2×(C2×D11)⋊C4—22no—
36C2×(C2×D11)⋊C4—22no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C22×C11⋊C8—22no—
40#66928—24no—
41#66928—24no—
42#66928—44no—
43#66927—42no—
44#66922—42no—
45C11×C4⋊C8—24no—
46C11×#97—24no—
47#66867—22no—
48#66867D414yescomplemented
49#9689—111nomaximal, Sylow
50C23×D11—22no—
51C22×C4×C11C22⋊C411yescharacteristic
52C22×C4×C11C22⋊C411yescharacteristic
53C22×C4×C11C22⋊C411yescharacteristic
54C22×C4×C11C22⋊C411yescharacteristic
55C22×C4×C11C22×C411yescharacteristic
56C22×C4×C11C2×D411yescharacteristic
57C22×C4×C11C2×D411yescharacteristic
58C22×Dic11—22no—
59C2×D44—24no—
60C2×D44—42no—
61C2×D44—42no—
62C2×D44—42no—
63C2×D44—42no—
64C2×D44—42no—
65C2×D44—42no—
66C2×D44—42no—
67C2×D44—42no—
68C2×Dic22—24no—
69C2×Dic22—42no—
70C2×Dic22—42no—
71C2×C8×C11—24no—
72C2×C8×C11—42no—
73C2×C8×C11—42no—
74C42×C11—22no—
75C42×C11—22no—
76C42×C11—22no—
77C42×C11—41no—
78C42×C11—41no—
79C42×C11—41no—
80C42×C11C2×D412yes—
81C42×C11#4112yes—
82(C2×D11)⋊C4—44no—
83(C2×D11)⋊C4—44no—
84(C2×D11)⋊C4—44no—
85(C2×D11)⋊C4—42no—
86(C2×D11)⋊C4—42no—
87C4⋊Dic11—42no—
88C4⋊Dic11—42no—
89C2×C11⋊C8—24no—
90C2×C11⋊C8—42no—
91C2×C11⋊C8—42no—
92#2858—111no—
93#1767D1111yescharacteristic, complemented
94#1745—111no—
95C2×#329—114no—
96C23×C11C2×C22⋊C411yescharacteristic
97C22×D11—42no—
98C22×D11—42no—
99C22×D11—42no—
100C22×D11—42no—
101C22×D11—42no—
102C22×D11—42no—
103C22×D11—42no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11#10012yes—
120C2×C4×C11#10012yes—
121C2×C4×C11#10412yes—
122C2×C4×C11C4×D412yes—
123C2×C4×C11#12112yes—
124C2×C4×C11#12411yescharacteristic
125C2×C4×C11#12711yescharacteristic
126C2×Dic11—42no—
127C2×Dic11—42no—
128C2×Dic11—42no—
129D44—84no—
130D44—84no—
131D44—84no—
132Dic22—84no—
133C8×C11—44no—
134C11⋊C8—44no—
135C2×C4⋊Q8—111no—
136C2×#127—111no—
137C2×#124—112no—
138C2×#124—112no—
139C2×C4⋊C8—21no—
140C2×#97—112no—
141C2×#97C2×D1112yes—
142#390—221no—
143#390—221no—
144#390—221no—
145#390—221no—
146C43C2×D1111yescharacteristic
147#336—21no—
148#336—221no—
149#336—221no—
150#329—228no—
151C22×C11#39011yescharacteristic
152C22×C11C2×#10011yescharacteristic
153C22×C11C2×#10011yescharacteristic
154C22×C11C2×#10411yescharacteristic
155C22×C11#42111yescharacteristic
156C22×C11#42111yescharacteristic
157C22×C11#42111yescharacteristic
158C2×D11—82no—
159C2×D11—82no—
160C2×D11—82no—
161C2×D11—82no—
162C2×D11—82no—
163C2×D11—82no—
164C2×D11—82no—
165C4×C11—22no—
166C4×C11—22no—
167C4×C11—21no—
168C4×C11—21no—
169C4×C11—22no—
170C4×C11—22no—
171C4×C11—22no—
172C4×C11—41no—
173Dic11—82no—
174C22×Q8—112no—
175C22×D4—112no—
176C22×D4—221no—
177C22×D4—221no—
178C22×C8—22no—
179C22×C8—222no—
180C4⋊Q8—442no—
181#127—442no—
182#124—224no—
183#124—224no—
184#124—444no—
185C2×C4⋊C4—221no—
186C2×C4⋊C4—221no—
187C2×C22⋊C4—222no—
188C2×C22⋊C4—222no—
189C2×C22⋊C4—222no—
190C2×C22⋊C4—222no—
191C2×C42C4×D1111yescharacteristic
192C2×C42C4×D1111yescharacteristic
193C2×C42D4411yescharacteristic
194C2×C42D4411yescharacteristic
195C2×C42C22⋊D1111yescharacteristic
196C2×C42C22⋊D1111yescharacteristic
197C2×C42C22×D1111yescharacteristic
198C4⋊C8—24no—
199#97—24no—
200#97—114no—
201#97—222no—
202C2×C11#152711yescharacteristic
203C2×C11#153011yescharacteristic
204C2×C11#153311yescharacteristic
205C2×C11#153611yescharacteristic
206C2×C11#196311yescharacteristic
207C2×C11#196511yescharacteristic
208C2×C11#198011yescharacteristic
209D11—162no—
210C24—222no—
211C2×Q8—224no—
212C2×Q8—442no—
213C2×Q8—442no—
214C2×D4—224no—
215C2×D4—442no—
216C2×D4—442no—
217C2×D4—442no—
218C2×D4—442no—
219C2×D4—442no—
220C2×D4—442no—
221C2×D4—442no—
222C2×D4—442no—
223C22×C4—222no—
224C22×C4(C2×D11)⋊C411yescharacteristic
225C22×C4(C2×D11)⋊C411yescharacteristic
226C22×C4(C2×D11)⋊C411yescharacteristic
227C22×C4(C2×D11)⋊C411yescharacteristic
228C22×C4C2×C4×D1111yescharacteristic
229C22×C4C2×D4411yescharacteristic
230C22×C4C2×C22⋊D1111yescharacteristic
231C2×C8—24no—
232C2×C8—42no—
233C2×C8—42no—
234C2×C8—224no—
235C2×C8—442no—
236C2×C8—442no—
237C4⋊C4—442no—
238C4⋊C4—442no—
239C22⋊C4—444no—
240C22⋊C4—444no—
241C22⋊C4—444no—
242C22⋊C4—442no—
243C22⋊C4—442no—
244C42—22no—
245C42—22no—
246C42—22no—
247C42—41no—
248C42—41no—
249C42—41no—
250C42D4×D1112yes—
251C42#434312yes—
252C11#968911yescharacteristic, complemented, Sylow
253C23—442no—
254C23—442no—
255C23—442no—
256C23—442no—
257C23—442no—
258C23—442no—
259C23—442no—
260C23C2×(C2×D11)⋊C411yescharacteristic
261Q8—884no—
262D4—884no—
263D4—884no—
264D4—884no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—442no—
281C2×C4—442no—
282C2×C4—442no—
283C2×C4#6686912yes—
284C2×C4#6688712yes—
285C2×C4#6688712yes—
286C2×C4#6694612yes—
287C2×C4#6694812yes—
288C2×C4#6699311yescharacteristic
289C2×C4#6700011yescharacteristic
290C8—44no—
291C8—444no—
292C22—882no—
293C22—882no—
294C22—882no—
295C22—882no—
296C22—882no—
297C22—882no—
298C22—882no—
299C22C2×#6686911yescharacteristic
300C22#1062260111yescharacteristic
301C22#1062261811yescharacteristic
302C22C2×#6688711yescharacteristic
303C22C2×#6688711yescharacteristic
304C22#1062275211yescharacteristic
305C22#1062275211yescharacteristic
306C4—22no—
307C4—22no—
308C4—22no—
309C4—22no—
310C4—21no—
311C4—21no—
312C4—22no—
313C4—41no—
314C4—882no—
315C2—1762no—
316C2#1306721311yescharacteristic
317C2#1306722611yescharacteristic
318C2#1306723911yescharacteristic
319C2#1306725011yescharacteristic
320C2#1306944711yescharacteristic
321C2#1306945511yescharacteristic
322C2#1306953411yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1767C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#66927C4
cosocleC2×C42×C11C23
hypercenter#1767D11
hypocenterC11#9689
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ #1767

Complements

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

NH ≅ G/Ntype
2. #13068365C2semidirect
3. C2×#10622102C2semidirect
4. C11×#1767C2semidirect
48. #66867D4semidirect
93. #1767D11semidirect
252. C11#9689semidirect

Maximal subgroups

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

subgroupindex
#130769732
#130683652
C2×#106221022
C11×#17672
#968911