Finite Group Databasebeta

← #14645487

Subgroups — #14645487

Order 2816.

1050 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 1050 conjugacy classes of subgroups — too many to draw. Only its 131 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
1C2×#10623084C211yesmaximal, characteristic
2#13067285C212yesmaximal, complemented
3#13067044C212yesmaximal, complemented
4#13066937C211yesmaximal, characteristic, complemented
5C11×#1800C211yesmaximal, characteristic, complemented
6C22×#4339C412yes—
7C2×C4×D4×C11C2211yescharacteristic
8C2×#66993—21no—
9C2×#66983C412yes—
10#10623084—24no—
11#10623084—24no—
12C2×#66946—21no—
13C2×#66937—22no—
14C2×#66927C2211yescharacteristic
15C2×C4×Dic22C2211yescharacteristic
16C11×#423C2212yes—
17C2×C11×#100—21no—
18#10622538C2212yes—
19C11×#343—21no—
20#10622163—22no—
21#10622123—24no—
22#10622122—24no—
23C22×D4×C11D411yescharacteristic
24C23×C4×C11C2×C412yes—
25C22×C22⋊D11—22no—
26C22×C22⋊D11—22no—
27C2×#4339—24no—
28C2×#4339—24no—
29C2×#4339—48no—
30C22×D44—21no—
31C22×D44—21no—
32C22×D44C2×C412yes—
33C22×C4×D11—22no—
34C22×Dic22C2×C411yescharacteristic
35C2×C11×M16—22no—
36C4×D4×C11—22no—
37C4×D4×C11—22no—
38C2×C11×C4⋊C4D411yescharacteristic
39C2×C11×C22⋊C4D412yes—
40C2×C42×C11C2311yescharacteristic
41#66993—28no—
42#66983—24no—
43#66983—24no—
44C2×(C2×D11)⋊C4—22no—
45C2×C4⋊Dic11C2×C411yescharacteristic
46C2×Dic11⋊C4—21no—
47C2×C4×Dic11—21no—
48#66946—28no—
49#66937—216no—
50#66927—22no—
51#66927D414yes—
52C4×Dic22—22no—
53C4×Dic22D414yes—
54C11×C4⋊C8—22no—
55C11×C4⋊C8—22no—
56C11×#100—42no—
57C22⋊(C11⋊C8)—22no—
58C4⋊(C11⋊C8)—22no—
59C4×C11⋊C8—22no—
60#8385—111nomaximal, Sylow
61C24×C11C22⋊C412yes—
62C23×D11—22no—
63C2×D4×C11—22no—
64C2×D4×C11—22no—
65C2×D4×C11—21no—
66C2×D4×C11—21no—
67C22×C4×C11—22no—
68C22×C4×C11—22no—
69C22×C4×C11—44no—
70C22×C4×C11C22⋊C412yes—
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C2×C22⋊D11—28no—
75C2×C22⋊D11—28no—
76C2×C22⋊D11—48no—
77C2×C22⋊D11—84no—
78C22×Dic11—21no—
79C22×Dic11—21no—
80#4339—416no—
81#4339—48no—
82#4339—48no—
83C2×D44—22no—
84C2×D44—24no—
85C2×D44—24no—
86C2×D44—44no—
87C2×D44—42no—
88C2×D44—41no—
89C2×D44—41no—
90C2×D44—82no—
91C2×D44C22⋊C414yes—
92C2×C4×D11—28no—
93C2×C4×D11—48no—
94C2×Dic22—24no—
95C2×Dic22—21no—
96C2×Dic22C22⋊C412yes—
97C11×M16—42no—
98C11×M16—42no—
99C2×C8×C11—42no—
100C11×C4⋊C4—22no—
101C11×C22⋊C4—24no—
102C42×C11C2×D412yes—
103C42×C11C2×D412yes—
104(C2×D11)⋊C4—28no—
105C4⋊Dic11—21no—
106C4⋊Dic11C22⋊C412yes—
107Dic11⋊C4—24no—
108C4×Dic11—24no—
109C2×C11⋊C8—42no—
110C2×#550—111no—
111#1800D1111yescharacteristic, complemented
112#1545—112no—
113#1487—112no—
114#1460—111no—
115C23×C11—22no—
116C23×C11—22no—
117C23×C11—22no—
118C23×C11—42no—
119C23×C11—42no—
120C23×C11C2×C22⋊C411yescharacteristic
121C22×D11—24no—
122C22×D11—44no—
123C22×D11—44no—
124C22×D11—42no—
125C22×D11—42no—
126D4×C11—42no—
127D4×C11—42no—
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11—41no—
131C2×C4×C11—44no—
132C2×C4×C11—44no—
133C2×C4×C11—42no—
134C2×C4×C11C2×C22⋊C411yescharacteristic
135C2×C4×C11C2×C22⋊C411yescharacteristic
136C2×C4×C11#12012yes—
137C2×C4×C11#12012yes—
138C2×C4×C11#13512yes—
139C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C11#13711yescharacteristic
141C22⋊D11—416no—
142C22⋊D11—88no—
143C2×Dic11—24no—
144C2×Dic11—22no—
145C2×Dic11—22no—
146C2×Dic11—42no—
147D44—44no—
148D44—44no—
149D44—44no—
150D44—44no—
151D44—84no—
152C4×D11—416no—
153Dic22—24no—
154Dic22—22no—
155Dic22#10014yescomplemented
156C8×C11—82no—
157C11⋊C8—82no—
158C22×#41—112no—
159#550—224no—
160#550—224no—
161C2×#127—111no—
162C2×#127—221no—
163C2×#121—112no—
164C2×#121—222no—
165C2×C4×Q8—111no—
166C2×C4×D4—221no—
167C2×C4×D4C2×D1111yescharacteristic
168#431—112no—
169#423C2×D1112yes—
170C2×#100—21no—
171#343—21no—
172#331—224no—
173Q8⋊C8—224no—
174#323—222no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—42no—
178C22×C11—42no—
179C22×C11—42no—
180C22×C11—82no—
181C22×C11—82no—
182C22×C11#37911yescharacteristic
183C22×C11#41611yescharacteristic
184C22×C11#41711yescharacteristic
185C2×D11—44no—
186C2×D11—44no—
187C2×D11—44no—
188C2×D11—84no—
189C2×D11—84no—
190C4×C11—22no—
191C4×C11—21no—
192C4×C11—42no—
193C4×C11C2×#10012yes—
194C4×C11#44912yes—
195C4×C11#45212yes—
196Dic11—24no—
197Dic11—42no—
198C2×#41—224no—
199C2×#41—224no—
200C2×#41—448no—
201C22×Q8—111no—
202C22×D4—112no—
203C22×D4—222no—
204C22×D4—222no—
205C22×D4—221no—
206C22×D4—221no—
207C22×D4C22⋊D1111yescharacteristic
208C23×C4—222no—
209C23×C4C4×D1112yes—
210C2×M16—22no—
211#127—114no—
212#127—228no—
213#127—222no—
214#121—2216no—
215#121—224no—
216#121—224no—
217C4×Q8—114no—
218C4×Q8—222no—
219C4×D4—22no—
220C4×D4—22no—
221C4×D4—228no—
222C2×C4⋊C4—111no—
223C2×C4⋊C4—221no—
224C2×C4⋊C4C22⋊D1111yescharacteristic
225C2×C22⋊C4—222no—
226C2×C22⋊C4D4412yes—
227C2×C42—221no—
228C2×C42C22×D1111yescharacteristic
229C4⋊C8—22no—
230C4⋊C8—22no—
231C4⋊C8—222no—
232#100—42no—
233C22⋊C8—222no—
234C4×C8—222no—
235C2×C11—21no—
236C2×C11—21no—
237C2×C11—82no—
238C2×C11#178311yescharacteristic
239C2×C11#178811yescharacteristic
240C2×C11#179511yescharacteristic
241D11—84no—
242C24—222no—
243C24(C2×D11)⋊C412yes—
244#41—448no—
245#41—4416no—
246#41—448no—
247C2×Q8—112no—
248C2×Q8—224no—
249C2×Q8—221no—
250C2×D4—21no—
251C2×D4—22no—
252C2×D4—21no—
253C2×D4—22no—
254C2×D4—114no—
255C2×D4—228no—
256C2×D4—228no—
257C2×D4—222no—
258C2×D4—224no—
259C2×D4—224no—
260C2×D4—444no—
261C2×D4—448no—
262C2×D4—441no—
263C2×D4—441no—
264C2×D4—442no—
265C2×D4—882no—
266C2×D4—884no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—44no—
270C22×C4—228no—
271C22×C4—221no—
272C22×C4—221no—
273C22×C4—448no—
274C22×C4(C2×D11)⋊C412yes—
275C22×C4C2×C4×D1111yescharacteristic
276C22×C4C2×D4411yescharacteristic
277C22×C4C2×C22⋊D1111yescharacteristic
278M16—42no—
279M16—42no—
280C2×C8—42no—
281C2×C8—442no—
282C4⋊C4—22no—
283C4⋊C4—112no—
284C4⋊C4—221no—
285C4⋊C4—224no—
286C22⋊C4—24no—
287C22⋊C4—228no—
288C42—224no—
289C42D4×D1112yes—
290C42D4×D1112yes—
291C11#838511yescharacteristic, complemented, Sylow
292C23—22no—
293C23—22no—
294C23—22no—
295C23—42no—
296C23—42no—
297C23—224no—
298C23—444no—
299C23—444no—
300C23—442no—
301C23—442no—
302C23C2×(C2×D11)⋊C411yescharacteristic
303Q8—114no—
304Q8—224no—
305Q8—222no—
306D4—42no—
307D4—42no—
308D4—444no—
309D4—4416no—
310D4—444no—
311D4—444no—
312D4—444no—
313D4—884no—
314D4—888no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—41no—
318C2×C4—44no—
319C2×C4—44no—
320C2×C4—42no—
321C2×C4—224no—
322C2×C4—222no—
323C2×C4—222no—
324C2×C4—4416no—
325C2×C4—442no—
326C2×C4C22⋊C4×D1111yescharacteristic
327C2×C4C22⋊C4×D1111yescharacteristic
328C2×C4#6693512yes—
329C2×C4#6698511yescharacteristic
330C2×C4#6699012yes—
331C2×C4#6699511yescharacteristic
332C2×C4#6700312yes—
333C8—82no—
334C8—882no—
335C22—21no—
336C22—21no—
337C22—42no—
338C22—42no—
339C22—42no—
340C22—82no—
341C22—82no—
342C22—444no—
343C22—444no—
344C22—444no—
345C22—884no—
346C22—884no—
347C22#1062256811yescharacteristic
348C22#1062257911yescharacteristic
349C22#1062261511yescharacteristic
350C4—22no—
351C4—21no—
352C4—42no—
353C4—224no—
354C4—442no—
355C4D11×#10012yes—
356C4#1062265012yes—
357C4#1062266012yes—
358C2—21no—
359C2—21no—
360C2—82no—
361C2—884no—
362C2#1306853511yescharacteristic
363C2#1306855411yescharacteristic
364C2#1306858711yescharacteristic
subgroupG/H
centerC22#10622568
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1800C2
socleC22×C11#379
prime radicalC2×#10623084C2
cosocleC2×C42×C11C23
hypercenter#1800D11
hypocenterC11#8385
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1800

Complements

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

NH ≅ G/Ntype
2. #13067285C2semidirect
3. #13067044C2semidirect
4. #13066937C2semidirect
5. C11×#1800C2semidirect
111. #1800D11semidirect
155. Dic22#100semidirect
291. C11#8385semidirect

Maximal subgroups

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

subgroupindex
C2×#106230842
#130672852
#130670442
#130669372
C11×#18002
#838511