Finite Group Databasebeta

← #14658160

Subgroups — #14658160

Order 2816.

574 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 95 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#13079367C211yesmaximal, characteristic
2#13069451C212yesmaximal, complemented
3#13069042C212yesmaximal, complemented
4#13068793C211yesmaximal, characteristic, complemented
5C11×#1289C211yesmaximal, characteristic, complemented
6C2×#66983C2212yes—
7C23×C11⋊C8C2211yescharacteristic
8C2×C11×C22⋊C8C2211yescharacteristic
9C11×#380C2212yes—
10C4×C22⋊Dic11C2211yescharacteristic
11#10622728—21no—
12#10622728—21no—
13C2×Dic11⋊C8—21no—
14C2×#66873—22no—
15C2×#66870—22no—
16C2×#66870—22no—
17#10622349—22no—
18#10622345—22no—
19#10622188—21no—
20#10622167—22no—
21C23×C4×C11C2311yescharacteristic
22C22×C22⋊D11—22no—
23C22×D44D412yes—
24C22×C8×C11D411yescharacteristic
25C22×C8×C11D411yescharacteristic
26C2×C11×C4⋊C4—22no—
27C2×C11×C22⋊C4—22no—
28C2×C22⋊Dic11D411yescharacteristic
29C2×C22⋊Dic11D411yescharacteristic
30#66983—22no—
31#66983—22no—
32#66983—22no—
33#66983—22no—
34C2×(C2×D11)⋊C4—22no—
35C2×C4⋊Dic11D412yes—
36C2×C4×Dic11—21no—
37C22×C11⋊C8—22no—
38C22×C11⋊C8—21no—
39C22×C11⋊C8—42no—
40C2×D88—21no—
41C2×D88—21no—
42C11×C22⋊C8—22no—
43C11×#95—22no—
44C11⋊#95—21no—
45#66885—22no—
46#66885—22no—
47#66882—21no—
48#66882—21no—
49Dic11⋊C8—42no—
50#66873—44no—
51#66870—44no—
52#66870—44no—
53#10564—111nomaximal, Sylow
54C24×C11C2×D411yescharacteristic
55C23×D11—22no—
56C22×C4×C11—41no—
57C22×C4×C11—41no—
58C22×C4×C11—42no—
59C22×C4×C11C2×D412yes—
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11#4111yescharacteristic
62C22×C4×C11#4112yes—
63C2×C22⋊D11—42no—
64C2×C22⋊D11—42no—
65C2×C22⋊D11—42no—
66C2×C22⋊D11—42no—
67C2×C22⋊D11—42no—
68C2×C22⋊D11—42no—
69C22×Dic11—21no—
70C22×Dic11—21no—
71C22×Dic11—22no—
72C2×D44—22no—
73C2×D44—22no—
74C2×D44—42no—
75C2×D44—42no—
76C2×C8×C11—21no—
77C2×C8×C11—21no—
78C2×C8×C11—41no—
79C2×C8×C11—41no—
80C11×C4⋊C4—42no—
81C11×C4⋊C4—42no—
82C11×C22⋊C4—42no—
83C11×C22⋊C4—42no—
84C22⋊Dic11—21no—
85C22⋊Dic11—22no—
86C22⋊Dic11D812yescomplemented
87(C2×D11)⋊C4—42no—
88(C2×D11)⋊C4—42no—
89C4⋊Dic11—22no—
90C4⋊Dic11—22no—
91C4×Dic11—41no—
92C4×Dic11—41no—
93C2×C11⋊C8—24no—
94C2×C11⋊C8—22no—
95C2×C11⋊C8—41no—
96C2×C11⋊C8—42no—
97C2×C11⋊C8—41no—
98D88—81no—
99D88—81no—
100#3186—111no—
101#1964—112no—
102#1893—112no—
103#1850—111no—
104#1289D1111yescharacteristic, complemented
105C23×C11—41no—
106C23×C11—41no—
107C23×C11#12112yes—
108C23×C11#12111yescharacteristic
109C23×C11C2×D811yescharacteristic
110C23×C11#13511yescharacteristic
111C23×C11AGL(1,ℤ/8)12yes—
112C22×D11—42no—
113C22×D11—42no—
114C22×D11—42no—
115C22×D11—82no—
116C22×D11—82no—
117C2×C4×C11—21no—
118C2×C4×C11—22no—
119C2×C4×C11—21no—
120C2×C4×C11—22no—
121C2×C4×C11—42no—
122C2×C4×C11—41no—
123C2×C4×C11—82no—
124C2×C4×C11—82no—
125C2×C4×C11—82no—
126C2×C4×C11#12011yescharacteristic
127C2×C4×C11#12312yes—
128C2×C4×C11#12411yescharacteristic
129C22⋊D11—82no—
130C22⋊D11—82no—
131C22⋊D11—82no—
132C22⋊D11—82no—
133C2×Dic11—22no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—42no—
139C2×Dic11—42no—
140C2×Dic11—42no—
141C2×Dic11—41no—
142D44—44no—
143D44—42no—
144D44—42no—
145C8×C11—41no—
146C8×C11—41no—
147C11⋊C8—42no—
148C23×C8—111no—
149C2×#121—112no—
150#480—222no—
151#466—221no—
152#466—221no—
153#447—222no—
154C2×C4⋊C8—221no—
155C2×#102—222no—
156C2×#99—222no—
157C2×#99—222no—
158C2×C22⋊C8C2×D1111yescharacteristic
159#380C2×D1112yes—
160C4×C22⋊C4—111no—
161#340—222no—
162#336—221no—
163C22×C11—22no—
164C22×C11—21no—
165C22×C11—22no—
166C22×C11—21no—
167C22×C11—41no—
168C22×C11—41no—
169C22×C11—42no—
170C22×C11#39411yescharacteristic
171C22×C11#45912yes—
172C22×C11#46312yes—
173C22×C11#46611yescharacteristic
174C22×C11#46911yescharacteristic
175C2×D11—82no—
176C2×D11—82no—
177C2×D11—82no—
178C2×D11—162no—
179C2×D11—162no—
180C4×C11—22no—
181C4×C11—21no—
182C4×C11—162no—
183C4×C11B(4,𝔽2)11yescharacteristic
184C4×C11#45811yescharacteristic
185Dic11—42no—
186Dic11—81no—
187Dic11—82no—
188C22×D4—112no—
189C22×D4—222no—
190C23×C4C22×D1111yescharacteristic
191C2×D8—221no—
192C2×D8—221no—
193C22×C8—221no—
194C22×C8—222no—
195C22×C8—442no—
196C22×C8D4411yescharacteristic
197C22×C8D4411yescharacteristic
198#121—222no—
199#121—222no—
200#121—222no—
201#121—222no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4—112no—
204C2×C22⋊C4—22no—
205C2×C22⋊C4—111no—
206C2×C22⋊C4—111no—
207C2×C22⋊C4—222no—
208C2×C42—221no—
209#107—221no—
210#107—221no—
211C4⋊C8—442no—
212#102—222no—
213#102—222no—
214#102—444no—
215#99—444no—
216#99—444no—
217C22⋊C8—22no—
218#95—22no—
219#95—221no—
220C2×C11—21no—
221C2×C11—21no—
222C2×C11—22no—
223C2×C11—22no—
224C2×C11#204411yescharacteristic
225C2×C11#205311yescharacteristic
226C2×C11#205411yescharacteristic
227D11—162no—
228C24—222no—
229C24D4×D1111yescharacteristic
230C2×D4—222no—
231C2×D4—222no—
232C2×D4—442no—
233C2×D4—442no—
234C2×D4—442no—
235C2×D4—442no—
236C2×D4—442no—
237C2×D4—442no—
238C2×D4—442no—
239C2×D4—442no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—42no—
243C22×C4—221no—
244C22×C4—222no—
245C22×C4—221no—
246C22×C4C2×D4411yescharacteristic
247C22×C4#433912yes—
248C22×C4D4×D1112yes—
249C22×C4#434311yescharacteristic
250D8—881no—
251D8—881no—
252C2×C8—21no—
253C2×C8—21no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—224no—
257C2×C8—222no—
258C2×C8—441no—
259C2×C8—442no—
260C2×C8—441no—
261C4⋊C4—42no—
262C4⋊C4—42no—
263C4⋊C4—222no—
264C4⋊C4—222no—
265C22⋊C4—42no—
266C22⋊C4—42no—
267C22⋊C4—112no—
268C22⋊C4—221no—
269C22⋊C4—222no—
270C22⋊C4—442no—
271C22⋊C4—442no—
272C42—441no—
273C42—441no—
274C11#1056411yescharacteristic, complemented, Sylow
275C23—41no—
276C23—41no—
277C23—442no—
278C23—442no—
279C23—442no—
280C23—882no—
281C23—882no—
282C23#6693712yes—
283C23#6694811yescharacteristic
284C23D8×D1111yescharacteristic
285C23#6696712yes—
286C23#6697211yescharacteristic
287D4—444no—
288D4—442no—
289D4—442no—
290D4—882no—
291D4—882no—
292D4—882no—
293D4—882no—
294C2×C4—21no—
295C2×C4—22no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—42no—
299C2×C4—41no—
300C2×C4—82no—
301C2×C4—82no—
302C2×C4—82no—
303C2×C4—222no—
304C2×C4—441no—
305C2×C4—441no—
306C2×C4—441no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4—442no—
310C2×C4—442no—
311C2×C4—442no—
312C2×C4#6692811yescharacteristic
313C2×C4#6693511yescharacteristic
314C2×C4#6694712yes—
315C8—41no—
316C8—41no—
317C8—442no—
318C22—22no—
319C22—21no—
320C22—22no—
321C22—21no—
322C22—41no—
323C22—42no—
324C22—41no—
325C22—882no—
326C22—882no—
327C22—882no—
328C22—1762no—
329C22—1762no—
330C22#1062228511yescharacteristic
331C22#1062239912yes—
332C22#1062243212yes—
333C22#1062247811yescharacteristic
334C22#1062249611yescharacteristic
335C4—21no—
336C4—22no—
337C4—162no—
338C4—442no—
339C4—881no—
340C4—882no—
341C4#1062235411yescharacteristic
342C4#1062235511yescharacteristic
343C2—22no—
344C2—21no—
345C2—21no—
346C2—22no—
347C2—1762no—
348C2#1306986811yescharacteristic
349C2#1306992311yescharacteristic
350C2#1306992811yescharacteristic
subgroupG/H
centerC22#10622285
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1289C2
socleC22×C11#394
prime radical#13079367C2
hypercenter#1289D11
hypocenterC11#10564
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1289

Complements

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

NH ≅ G/Ntype
2. #13069451C2semidirect
3. #13069042C2semidirect
4. #13068793C2semidirect
5. C11×#1289C2semidirect
86. C22⋊Dic11D8semidirect
104. #1289D11semidirect
274. C11#10564semidirect

Maximal subgroups

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

subgroupindex
#130793672
#130694512
#130690422
#130687932
C11×#12892
#1056411