Finite Group Databasebeta

← #14654407

Subgroups — #14654407

Order 2816.

822 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 822 conjugacy classes of subgroups — too many to draw. Only its 79 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#13077868C212yesmaximal, complemented
2#13076640C211yesmaximal, characteristic, complemented
3#13067144C212yesmaximal, complemented
4#13066524C211yesmaximal, characteristic, complemented
5C11×#1782C211yesmaximal, characteristic, complemented
6C22×C11×#41C2211yescharacteristic
7C2×#67002—22no—
8C2×#66983C2212yes—
9C2×C11×#99—22no—
10C11×#381C2211yescharacteristic
11C11×#381C2211yescharacteristic
12#10622851—24no—
13#10622845—22no—
14#10622840—22no—
15#10622830—22no—
16#10622820C2212yes—
17#10622573—22no—
18#10622287—22no—
19#10622284—22no—
20#10622089—24no—
21C2×C11×#41—22no—
22C2×C11×#41—22no—
23C2×C11×#41—44no—
24C22×Q8×C11D411yescharacteristic, complemented
25C22×D4×C11—21no—
26C22×D4×C11D411yescharacteristic, complemented
27C23×C4×C11—21no—
28C23×C4×C11C2311yescharacteristic
29C22×C22⋊D11—22no—
30C22×D44—22no—
31C22×D44D412yes—
32C2×C11×C22⋊C4—21no—
33C2×C11×C22⋊C4D412yes—
34#67002—48no—
35C2×#4325—24no—
36C2×#4323—24no—
37#66983—22no—
38#66983—22no—
39#66983—22no—
40#66983—22no—
41C2×(C2×D11)⋊C4—22no—
42C2×(C2×D11)⋊C4—24no—
43C2×C4⋊Dic11D412yes—
44C2×#4318—22no—
45C11×#99—44no—
46C11×#95—22no—
47C11×#95—22no—
48#66899—24no—
49#66896—24no—
50C11⋊#95—22no—
51C22⋊(C11⋊C8)—22no—
52C22⋊(C11⋊C8)D414yescomplemented
53#9980—111nomaximal, Sylow
54C24×C11—21no—
55C24×C11C2×D411yescharacteristic
56C23×D11—22no—
57C11×#41—28no—
58C11×#41—44no—
59C11×#41—44no—
60C11×#41—44no—
61C2×Q8×C11—22no—
62C2×Q8×C11—42no—
63C2×D4×C11—24no—
64C2×D4×C11—22no—
65C2×D4×C11—42no—
66C2×D4×C11—42no—
67C2×D4×C11—41no—
68C2×D4×C11—41no—
69C22×C4×C11—21no—
70C22×C4×C11—22no—
71C22×C4×C11—42no—
72C22×C4×C11—42no—
73C22×C4×C11—42no—
74C22×C4×C11—42no—
75C22×C4×C11—41no—
76C22×C4×C11C2×D412yes—
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D412yes—
79C22×C4×C11#4111yescharacteristic
80C2×C22⋊D11—42no—
81C2×C22⋊D11—42no—
82C2×C22⋊D11—84no—
83C22×Dic11—22no—
84C2×D44—22no—
85C2×D44—22no—
86C2×D44—44no—
87C2×D44—84no—
88C2×D44—82no—
89C11×C22⋊C4—42no—
90C11×C22⋊C4—42no—
91#4325—48no—
92#4323—48no—
93(C2×D11)⋊C4—42no—
94(C2×D11)⋊C4—42no—
95(C2×D11)⋊C4—84no—
96C4⋊Dic11—22no—
97C4⋊Dic11—22no—
98#4318—44no—
99C2×C11⋊C8—24no—
100#3006—112no—
101#2815—111no—
102#1782D1111yescharacteristic, complemented
103#1510—112no—
104#1306—111no—
105C23×C11—22no—
106C23×C11—22no—
107C23×C11—42no—
108C23×C11—41no—
109C23×C11—41no—
110C23×C11—82no—
111C23×C11#12011yescharacteristic
112C23×C11#12111yescharacteristic
113C23×C11#12711yescharacteristic
114C22×D11—42no—
115C22×D11—42no—
116C22×D11—44no—
117C22×D11—42no—
118C22×D11—44no—
119Q8×C11—24no—
120Q8×C11—42no—
121D4×C11—24no—
122D4×C11—42no—
123D4×C11—44no—
124D4×C11—44no—
125C2×C4×C11—24no—
126C2×C4×C11—22no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—42no—
130C2×C4×C11—48no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—44no—
134C2×C4×C11—42no—
135C2×C4×C11—81no—
136C2×C4×C11—82no—
137C2×C4×C11#12012yes—
138C2×C4×C11#12112yes—
139C22⋊D11—84no—
140C22⋊D11—84no—
141C2×Dic11—44no—
142C2×Dic11—42no—
143D44—44no—
144D44—82no—
145D44—88no—
146C11⋊C8—44no—
147C22×#41C2×D1111yescharacteristic
148C2×AGL(1,ℤ/8)—222no—
149C2×#121—112no—
150#449—224no—
151#448—222no—
152#447—222no—
153#417—222no—
154C2×#99—22no—
155#407—112no—
156#397—222no—
157#392—222no—
158#392—222no—
159#381C2×D1111yescharacteristic
160#381C2×D1111yescharacteristic
161#327—224no—
162C22×C11—22no—
163C22×C11—22no—
164C22×C11—22no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11—42no—
168C22×C11—82no—
169C22×C11—82no—
170C22×C11—82no—
171C22×C11—82no—
172C22×C11#39211yescharacteristic
173C22×C11B(4,𝔽2)12yes—
174C2×D11—84no—
175C2×D11—84no—
176C2×D11—82no—
177C2×D11—82no—
178C2×D11—82no—
179C4×C11—22no—
180C4×C11—22no—
181C4×C11—42no—
182C4×C11—82no—
183C4×C11—161no—
184Dic11—82no—
185C2×#41—22no—
186C2×#41—22no—
187C2×#41—44no—
188C22×Q8D4411yescharacteristic, complemented
189C22×D4—21no—
190C22×D4—112no—
191C22×D4—222no—
192C22×D4—222no—
193C22×D4D4411yescharacteristic, complemented
194C23×C4—21no—
195C23×C4C22×D1111yescharacteristic
196AGL(1,ℤ/8)—448no—
197C2×SD16—224no—
198C2×D8—224no—
199C2×M16—222no—
200#121—222no—
201#121—222no—
202#121—222no—
203#121—222no—
204C2×C4⋊C4—112no—
205C2×C22⋊C4—21no—
206C2×C22⋊C4—222no—
207C2×C22⋊C4—224no—
208C2×C22⋊C4C22⋊D1112yes—
209#103—224no—
210#102—224no—
211#99—44no—
212C22⋊C8—114no—
213C22⋊C8—222no—
214#95—22no—
215#95—22no—
216#95—222no—
217C2×C11—22no—
218C2×C11—41no—
219C2×C11—41no—
220C2×C11—82no—
221C2×C11#200812yes—
222C2×C11#202111yescharacteristic
223D11—162no—
224C24—21no—
225C24—222no—
226C24C2×C22⋊D1111yescharacteristic
227#41—28no—
228#41—44no—
229#41—44no—
230#41—44no—
231C2×Q8—22no—
232C2×Q8—42no—
233C2×D4—24no—
234C2×D4—22no—
235C2×D4—42no—
236C2×D4—42no—
237C2×D4—41no—
238C2×D4—41no—
239C2×D4—222no—
240C2×D4—222no—
241C2×D4—444no—
242C2×D4—442no—
243C2×D4—442no—
244C2×D4—884no—
245C2×D4—882no—
246C2×D4—884no—
247C22×C4—21no—
248C22×C4—22no—
249C22×C4—42no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4—42no—
253C22×C4—41no—
254C22×C4—222no—
255C22×C4C2×D4411yescharacteristic
256C22×C4#433911yescharacteristic
257C22×C4D4×D1112yes—
258C22×C4D4×D1112yes—
259SD16—448no—
260D8—448no—
261M16—444no—
262C2×C8—224no—
263C4⋊C4—222no—
264C4⋊C4—222no—
265C22⋊C4—42no—
266C22⋊C4—42no—
267C22⋊C4—442no—
268C22⋊C4—442no—
269C22⋊C4—884no—
270C11#998011yescharacteristic, complemented, Sylow
271C23—22no—
272C23—22no—
273C23—42no—
274C23—41no—
275C23—41no—
276C23—82no—
277C23—442no—
278C23—442no—
279C23—444no—
280C23—442no—
281C23—444no—
282C23#6698311yescharacteristic
283C23#6699011yescharacteristic
284C23#6699311yescharacteristic
285Q8—24no—
286Q8—42no—
287D4—24no—
288D4—42no—
289D4—44no—
290D4—44no—
291D4—444no—
292D4—882no—
293D4—888no—
294D4—884no—
295D4—884no—
296C2×C4—24no—
297C2×C4—22no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—48no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—44no—
305C2×C4—42no—
306C2×C4—81no—
307C2×C4—82no—
308C2×C4—444no—
309C2×C4—442no—
310C2×C4#6693512yes—
311C2×C4#6693712yes—
312C8—444no—
313C22—22no—
314C22—22no—
315C22—22no—
316C22—21no—
317C22—21no—
318C22—42no—
319C22—82no—
320C22—82no—
321C22—82no—
322C22—82no—
323C22—884no—
324C22—884no—
325C22—882no—
326C22—882no—
327C22—882no—
328C22#1062257311yescharacteristic
329C22#1062264512yes—
330C4—22no—
331C4—22no—
332C4—42no—
333C4—82no—
334C4—161no—
335C4—882no—
336C2—22no—
337C2—41no—
338C2—41no—
339C2—82no—
340C2—1762no—
341C2#1306966812yes—
342C2#1306974211yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1782C2
socleC22×C11#392
hypercenter#1782D11
hypocenterC11#9980
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1782

Complements

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

NH ≅ G/Ntype
1. #13077868C2semidirect
2. #13076640C2semidirect
3. #13067144C2semidirect
4. #13066524C2semidirect
5. C11×#1782C2semidirect
24. C22×Q8×C11D4semidirect
26. C22×D4×C11D4semidirect
52. C22⋊(C11⋊C8)D4semidirect
102. #1782D11semidirect
188. C22×Q8D44semidirect
193. C22×D4D44semidirect
270. C11#9980semidirect

Maximal subgroups

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

subgroupindex
#130778682
#130766402
#130671442
#130665242
C11×#17822
#998011