Finite Group Databasebeta

← #14673234

Subgroups — #14673234

Order 2816.

512 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 75 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#13075642C211yesmaximal, characteristic
2C2×#10622115C212yesmaximal, complemented
3#13069019C212yesmaximal, complemented
4#13066743C211yesmaximal, characteristic, complemented
5C11×#1857C211yesmaximal, characteristic, complemented
6C11×#519C2211yescharacteristic
7C2×#67000C2212yes—
8C11×#428—21no—
9C2×C11×#101C2211yescharacteristic
10C11×#391C2211yescharacteristic
11C2×#66900C2212yes—
12#10622614—22no—
13#10622604—21no—
14#10622552—21no—
15#10622284—22no—
16#10622283—22no—
17C11×#339—21no—
18#10622170—22no—
19#10622115—24no—
20C22×Q8×C11C2311yescharacteristic
21C22×D44—21no—
22C22×D44—21no—
23C22×D44D412yes—
24C2×C11×M16—21no—
25C4×Q8×C11—41no—
26C4×Q8×C11—41no—
27C11×#117—21no—
28C11×#117—22no—
29C2×C11×C4⋊C4D411yescharacteristic
30C2×C42×C11D411yescharacteristic
31#67000—22no—
32#67000—22no—
33#67000—22no—
34#67000—22no—
35C2×(C2×D11)⋊C4—22no—
36C2×(C2×D11)⋊C4—22no—
37C2×(C2×D11)⋊C4—22no—
38C2×(C2×D11)⋊C4—22no—
39C2×C4⋊Dic11—21no—
40C2×C4×Dic11D412yes—
41C2×#4318—22no—
42C11×#107—41no—
43C11×#106—41no—
44C11×#101—21no—
45C11×#101D412yescomplemented
46C11×#95—22no—
47#66900—22no—
48#66900—22no—
49C11⋊#95—21no—
50#66873—42no—
51#66873—42no—
52#13426—111nomaximal, Sylow
53C23×D11—22no—
54C2×Q8×C11—41no—
55C2×Q8×C11—41no—
56C2×Q8×C11C2×D411yescharacteristic
57C2×Q8×C11#4111yescharacteristic
58C2×Q8×C11#4112yes—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11C2×D412yes—
62C22×C4×C11C2×D411yescharacteristic
63C22×Dic11—22no—
64C2×D44—22no—
65C2×D44—22no—
66C2×D44—42no—
67C2×D44—42no—
68C2×D44—42no—
69C2×D44—81no—
70C2×D44—81no—
71C2×D44—82no—
72C2×D44—81no—
73C11×M16—22no—
74C11×M16—41no—
75C2×C8×C11—41no—
76C11×C4⋊C4—22no—
77C11×C4⋊C4—22no—
78C11×C4⋊C4—21no—
79C11×C4⋊C4—21no—
80C11×C4⋊C4—41no—
81C11×C22⋊C4—41no—
82C42×C11—42no—
83C42×C11—41no—
84C42×C11—41no—
85(C2×D11)⋊C4—44no—
86(C2×D11)⋊C4—42no—
87(C2×D11)⋊C4—42no—
88(C2×D11)⋊C4—42no—
89(C2×D11)⋊C4—42no—
90(C2×D11)⋊C4—82no—
91C4⋊Dic11—81no—
92C4×Dic11—22no—
93C4×Dic11—22no—
94#4318—42no—
95#4318—42no—
96C2×C11⋊C8—42no—
97#2733—111no—
98C2×#355—112no—
99#1888—112no—
100#1857D1111yescharacteristic, complemented
101#1394—111no—
102C23×C11#12011yescharacteristic
103C22×D11—42no—
104C22×D11—42no—
105C22×D11—42no—
106C22×D11—42no—
107C22×D11—42no—
108C22×D11—42no—
109C22×D11—42no—
110Q8×C11—41no—
111Q8×C11—41no—
112Q8×C11—42no—
113C2×C4×C11—22no—
114C2×C4×C11—21no—
115C2×C4×C11—22no—
116C2×C4×C11—21no—
117C2×C4×C11—22no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—42no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11#12112yes—
125C2×C4×C11#12111yescharacteristic
126C2×C4×C11#12312yes—
127C2×C4×C11#12411yescharacteristic
128C2×Dic11—42no—
129C2×Dic11—42no—
130C2×Dic11—42no—
131D44—44no—
132D44—82no—
133D44—84no—
134D44—84no—
135C8×C11—42no—
136C11⋊C8—82no—
137C2×#124—112no—
138#519C2×D1111yescharacteristic
139#428—21no—
140#418—222no—
141C2×#101—112no—
142C2×#101C2×D1111yescharacteristic
143#394—221no—
144#392—222no—
145#391C2×D1111yescharacteristic
146#390—221no—
147#388—222no—
148#355—224no—
149#339—21no—
150#339—222no—
151C22×C11—21no—
152C22×C11—21no—
153C22×C11#39411yescharacteristic
154C22×C11B(4,𝔽2)11yescharacteristic
155C22×C11#45811yescharacteristic
156C2×D11—82no—
157C2×D11—82no—
158C2×D11—82no—
159C2×D11—82no—
160C2×D11—82no—
161C2×D11—82no—
162C2×D11—82no—
163C4×C11—22no—
164C4×C11—21no—
165C4×C11—22no—
166C4×C11—21no—
167C4×C11—42no—
168C4×C11—81no—
169C4×C11—81no—
170C4×C11—81no—
171Dic11—82no—
172C22×Q8C22×D1111yescharacteristic
173C22×D4—112no—
174C22×D4—221no—
175C22×D4—221no—
176C2×M16—21no—
177C2×M16—222no—
178#124—222no—
179#124—222no—
180#124—222no—
181#124—222no—
182C4×Q8—41no—
183C4×Q8—41no—
184#117—22no—
185#117—21no—
186C2×C4⋊C4—221no—
187C2×C4⋊C4C22⋊D1111yescharacteristic
188C2×C22⋊C4—222no—
189C2×C22⋊C4—222no—
190C2×C22⋊C4—222no—
191C2×C22⋊C4—222no—
192C2×C42—112no—
193C2×C42C22⋊D1111yescharacteristic
194#107—41no—
195#106—41no—
196#102—442no—
197#102—442no—
198#101—21no—
199#101—222no—
200#101—222no—
201#101D4412yescomplemented
202#95—22no—
203#95—221no—
204C2×C11—21no—
205C2×C11—21no—
206C2×C11#204411yescharacteristic
207C2×C11#220211yescharacteristic
208C2×C11#220411yescharacteristic
209D11—162no—
210C24—222no—
211C2×Q8—41no—
212C2×Q8—41no—
213C2×Q8C2×D4411yescharacteristic
214C2×Q8#433911yescharacteristic
215C2×Q8#434312yes—
216C2×D4—222no—
217C2×D4—222no—
218C2×D4—442no—
219C2×D4—442no—
220C2×D4—442no—
221C2×D4—881no—
222C2×D4—881no—
223C2×D4—882no—
224C2×D4—881no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—222no—
228C22×C4D4×D1112yes—
229C22×C4C2×C22⋊D1111yescharacteristic
230M16—22no—
231M16—41no—
232M16—442no—
233M16—442no—
234C2×C8—41no—
235C2×C8—442no—
236C4⋊C4—22no—
237C4⋊C4—22no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—41no—
241C4⋊C4—881no—
242C22⋊C4—41no—
243C22⋊C4—444no—
244C22⋊C4—442no—
245C22⋊C4—442no—
246C22⋊C4—442no—
247C22⋊C4—442no—
248C22⋊C4—882no—
249C42—41no—
250C42—41no—
251C42—42no—
252C42—222no—
253C42—222no—
254C11#1342611yescharacteristic, complemented, Sylow
255C23—442no—
256C23—442no—
257C23—442no—
258C23—442no—
259C23—442no—
260C23—442no—
261C23—442no—
262C23#6699011yescharacteristic
263Q8—41no—
264Q8—41no—
265Q8—42no—
266D4—444no—
267D4—882no—
268D4—884no—
269D4—884no—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—21no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—42no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—442no—
282C2×C4—442no—
283C2×C4—442no—
284C2×C4#6694712yes—
285C2×C4#6694812yes—
286C2×C4#6698311yescharacteristic
287C2×C4#6700011yescharacteristic
288C8—42no—
289C8—882no—
290C22—21no—
291C22—21no—
292C22—882no—
293C22—882no—
294C22—882no—
295C22—882no—
296C22—882no—
297C22—882no—
298C22—882no—
299C22#1062260411yescharacteristic
300C22#1062264511yescharacteristic
301C22#1062266611yescharacteristic
302C4—21no—
303C4—22no—
304C4—22no—
305C4—21no—
306C4—42no—
307C4—81no—
308C4—81no—
309C4—81no—
310C4—882no—
311C2—21no—
312C2—21no—
313C2—1762no—
314C2#1306986711yescharacteristic
315C2#1307063211yescharacteristic
316C2#1307064111yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC22×Q8×C11C23
FrattiniC22×Q8C22×D11
FittingC11×#1857C2
socleC22×C11B(4,𝔽2)
prime radical#13075642C2
hypercenter#1857D11
hypocenterC11#13426
LCSG ▷ C22×Q8×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1857

Complements

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

NH ≅ G/Ntype
2. C2×#10622115C2semidirect
3. #13069019C2semidirect
4. #13066743C2semidirect
5. C11×#1857C2semidirect
45. C11×#101D4semidirect
100. #1857D11semidirect
201. #101D44semidirect
254. C11#13426semidirect

Maximal subgroups

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

subgroupindex
#130756422
C2×#106221152
#130690192
#130667432
C11×#18572
#1342611