Finite Group Databasebeta

← #14645113

Subgroups — #14645113

Order 2816.

1482 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 1482 conjugacy classes of subgroups — too many to draw. Only its 183 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
1C22×C4×D44C211yesmaximal, characteristic
2#13068684C211yesmaximal, characteristic, complemented
3C2×#10622106C214yesmaximal, complemented
4C11×#1817C211yesmaximal, characteristic, complemented
5C23×D44C411yescharacteristic
6C23×C4×D11C412yes—
7C22×C42×C11C2211yescharacteristic
8C22×(C2×D11)⋊C4C2212yes—
9C22×C4⋊Dic11C411yescharacteristic
10C2×C4×D44—22no—
11C2×C4×D44—22no—
12C2×C4×D44—28no—
13C2×C11×C22⋊C8C2212yes—
14C2×C22⋊(C11⋊C8)C2212yes—
15C11×#336—22no—
16#10622162—22no—
17#10622106—28no—
18C24×D11C2×C412yes—
19C23×C4×C11C2×C411yescharacteristic
20C23×C4×C11C2×C411yescharacteristic
21C23×C4×C11C2311yescharacteristic
22C23×Dic11C2×C412yes—
23C22×D44—24no—
24C22×D44—24no—
25C22×D44—22no—
26C22×D44—22no—
27C22×D44C814yescomplemented
28C22×C4×D11—24no—
29C22×C4×D11—24no—
30C22×C4×D11—24no—
31C22×C4×D11—48no—
32C22×C8×C11—22no—
33C2×C42×C11—24no—
34C2×C42×C11D412yes—
35C2×C42×C11D412yes—
36C2×(C2×D11)⋊C4—22no—
37C2×(C2×D11)⋊C4—24no—
38C2×(C2×D11)⋊C4—22no—
39C2×(C2×D11)⋊C4D418yes—
40C2×C4⋊Dic11—22no—
41C2×C4⋊Dic11—24no—
42C22×C11⋊C8—22no—
43C4×D44—216no—
44C4×D44—216no—
45C11×C22⋊C8—24no—
46C22⋊(C11⋊C8)—24no—
47#8302—111nomaximal, Sylow
48C24×C11C22×C411yescharacteristic
49C23×D11—22no—
50C23×D11—22no—
51C23×D11—22no—
52C23×D11—22no—
53C23×D11—44no—
54C23×D11—44no—
55C23×D11C22⋊C414yes—
56C23×D11C2×C814yes—
57C23×D11M1614yes—
58C22×C4×C11—22no—
59C22×C4×C11—22no—
60C22×C4×C11—22no—
61C22×C4×C11—24no—
62C22×C4×C11—42no—
63C22×C4×C11C22⋊C412yes—
64C22×C4×C11C22⋊C412yes—
65C22×C4×C11C2×C812yes—
66C22×C4×C11M1612yes—
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D414yes—
70C22×Dic11—22no—
71C22×Dic11—22no—
72C22×Dic11—44no—
73C22×Dic11C22⋊C414yes—
74C2×D44—28no—
75C2×D44—28no—
76C2×D44—216no—
77C2×D44—216no—
78C2×D44—28no—
79C2×C4×D11—216no—
80C2×C4×D11—416no—
81C2×C4×D11—416no—
82C2×C4×D11—48no—
83C2×C4×D11—48no—
84C2×C8×C11—44no—
85C2×C8×C11—42no—
86C42×C11—24no—
87C42×C11—24no—
88(C2×D11)⋊C4—28no—
89(C2×D11)⋊C4—28no—
90C4⋊Dic11—28no—
91C2×C11⋊C8—44no—
92C2×C11⋊C8—42no—
93C22×C4×D4—111no—
94#1817—111no—
95#1817D1111yescharacteristic, complemented
96C2×#323—114no—
97C23×C11—22no—
98C23×C11—22no—
99C23×C11C2×C22⋊C412yes—
100C23×C11C2×C22⋊C411yescharacteristic
101C23×C11C22×C811yescharacteristic
102C23×C11C2×M1611yescharacteristic
103C23×C11C2×M1612yes—
104C22×D11—24no—
105C22×D11—24no—
106C22×D11—24no—
107C22×D11—24no—
108C22×D11—24no—
109C22×D11—24no—
110C22×D11—44no—
111C22×D11—48no—
112C22×D11—48no—
113C22×D11—44no—
114C22×D11—44no—
115C22×D11—44no—
116C22×D11—44no—
117C22×D11—44no—
118C22×D11—48no—
119C22×D11—48no—
120C22×D11C22⋊C818yes—
121C2×C4×C11—28no—
122C2×C4×C11—22no—
123C2×C4×C11—22no—
124C2×C4×C11—24no—
125C2×C4×C11—22no—
126C2×C4×C11—24no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11—44no—
131C2×C4×C11C22⋊C814yes—
132C2×C4×C11#10014yes—
133C2×C4×C11#12012yes—
134C2×C4×C11#12012yes—
135C2×Dic11—24no—
136C2×Dic11—44no—
137C2×Dic11—44no—
138C2×Dic11—44no—
139D44—232no—
140C4×D11—432no—
141C8×C11—82no—
142C11⋊C8—82no—
143C23×D4—111no—
144C24×C4—112no—
145C2×C4×D4—228no—
146C2×C4×D4—222no—
147C2×C4×D4—222no—
148C22×C4⋊C4—111no—
149C22×C22⋊C4—112no—
150C22×C42C2×D1111yescharacteristic
151C2×C22⋊C8—112no—
152C2×C22⋊C8C2×D1112yes—
153#336—22no—
154#336—222no—
155#323—228no—
156C22×C11—22no—
157C22×C11—22no—
158C22×C11—24no—
159C22×C11—22no—
160C22×C11—22no—
161C22×C11#37911yescharacteristic
162C22×C11C2×C22⋊C811yescharacteristic
163C22×C11C2×C22⋊C812yes—
164C22×C11#40711yescharacteristic
165C22×C11#40712yes—
166C22×C11#41012yes—
167C22×C11C2×#10012yes—
168C2×D11—28no—
169C2×D11—48no—
170C2×D11—48no—
171C2×D11—48no—
172C2×D11—48no—
173C2×D11—48no—
174C2×D11—44no—
175C2×D11—44no—
176C2×D11—48no—
177C4×C11—24no—
178C4×C11—22no—
179C4×C11—22no—
180C4×C11—24no—
181Dic11—44no—
182C25—112no—
183C22×D4—114no—
184C22×D4—224no—
185C22×D4—224no—
186C22×D4—222no—
187C22×D4—222no—
188C23×C4—112no—
189C23×C4—224no—
190C23×C4—224no—
191C23×C4—224no—
192C23×C4—448no—
193C23×C4C4×D1111yescharacteristic
194C23×C4C4×D1111yescharacteristic
195C23×C4C22×D1111yescharacteristic
196C22×C8—22no—
197C22×C8—222no—
198C4×D4—2216no—
199C4×D4—2216no—
200C2×C4⋊C4—224no—
201C2×C4⋊C4—222no—
202C2×C22⋊C4—118no—
203C2×C22⋊C4—222no—
204C2×C22⋊C4—224no—
205C2×C22⋊C4—222no—
206C2×C42—24no—
207C2×C42D4412yes—
208C2×C42C22⋊D1112yes—
209C22⋊C8—24no—
210C22⋊C8—224no—
211C2×C11—22no—
212C2×C11—22no—
213C2×C11#146012yes—
214C2×C11#146612yes—
215C2×C11#177911yescharacteristic
216C2×C11#178211yescharacteristic
217C2×C11#178311yescharacteristic
218D11—48no—
219C24—114no—
220C24—114no—
221C24—114no—
222C24—222no—
223C24—222no—
224C24—222no—
225C24—222no—
226C24—444no—
227C24—444no—
228C24C2×C4×D1111yescharacteristic
229C2×D4—2216no—
230C2×D4—228no—
231C2×D4—228no—
232C2×D4—2216no—
233C2×D4—228no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—24no—
238C22×C4—42no—
239C22×C4—114no—
240C22×C4—2216no—
241C22×C4—222no—
242C22×C4—222no—
243C22×C4—4416no—
244C22×C4—4416no—
245C22×C4—448no—
246C22×C4—448no—
247C22×C4—444no—
248C22×C4C8×D1112yes—
249C22×C4#431312yes—
250C22×C4(C2×D11)⋊C412yes—
251C22×C4(C2×D11)⋊C412yes—
252C22×C4C2×D4411yescharacteristic
253C22×C4D4×D1114yes—
254C22×C4C2×C22⋊D1111yescharacteristic
255C2×C8—44no—
256C2×C8—42no—
257C2×C8—444no—
258C2×C8—442no—
259C4⋊C4—228no—
260C22⋊C4—228no—
261C22⋊C4—228no—
262C42—24no—
263C42—24no—
264C11#830211yescharacteristic, complemented, Sylow
265C23—22no—
266C23—22no—
267C23—118no—
268C23—224no—
269C23—224no—
270C23—224no—
271C23—224no—
272C23—224no—
273C23—224no—
274C23—444no—
275C23—448no—
276C23—448no—
277C23—444no—
278C23—444no—
279C23—448no—
280C23—448no—
281C23—444no—
282C23—444no—
283C23—444no—
284C23C22⋊C4×D1112yes—
285C23C2×C8×D1111yescharacteristic
286C23C2×#431311yescharacteristic
287C23M16×D1112yes—
288C23C2×(C2×D11)⋊C411yescharacteristic
289D4—2232no—
290C2×C4—28no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—24no—
296C2×C4—24no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—44no—
300C2×C4—224no—
301C2×C4—4432no—
302C2×C4—444no—
303C2×C4—444no—
304C2×C4—444no—
305C2×C4(C2×D11)⋊C814yes—
306C2×C4#6688714yes—
307C2×C4#6693512yes—
308C2×C4#6699012yes—
309C8—82no—
310C8—882no—
311C22—22no—
312C22—22no—
313C22—24no—
314C22—22no—
315C22—22no—
316C22—228no—
317C22—448no—
318C22—448no—
319C22—448no—
320C22—448no—
321C22—448no—
322C22—448no—
323C22—444no—
324C22—444no—
325C22D11×C22⋊C812yes—
326C22#1062233912yes—
327C22#1062256811yescharacteristic
328C22#1062261912yes—
329C22C2×(C2×D11)⋊C811yescharacteristic
330C22#1062273911yescharacteristic
331C22C2×#6688712yes—
332C4—24no—
333C4—22no—
334C4—22no—
335C4—24no—
336C4—444no—
337C2—22no—
338C2—22no—
339C2—448no—
340C2#1306693612yes—
341C2#1306695612yes—
342C2#1306852511yescharacteristic
343C2#1306853311yescharacteristic
344C2#1306853611yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC23×C11C22×C8
FrattiniC23×C4C22×D11
FittingC11×#1817C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D44C4
cosocleC23×C4×C11C23
hypercenter#1817D11
hypocenterC11#8302
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

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

NH ≅ G/Ntype
2. #13068684C2semidirect
3. C2×#10622106C2semidirect
4. C11×#1817C2semidirect
27. C22×D44C8semidirect
95. #1817D11semidirect
264. C11#8302semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D442
#130686842
C2×#106221062
C11×#18172
#830211