Finite Group Databasebeta

← #14663156

Subgroups — #14663156

Order 2816.

586 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 586 conjugacy classes of subgroups — too many to draw. Only its 77 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#13071105C211yesmaximal, characteristic
2#13066949C212yesmaximal, complemented
3#13066550C211yesmaximal, characteristic, complemented
4#13066547C212yesmaximal, complemented
5C11×#1319C211yesmaximal, characteristic, complemented
6C22×#4343C411yescharacteristic
7C2×#66945C2211yescharacteristic
8C2×C42×D11C411yescharacteristic
9C11×#391C2211yescharacteristic
10#10622843C411yescharacteristic
11#10622601C2211yescharacteristic
12#10622552C411yescharacteristic
13#10622332—22no—
14#10622279—22no—
15#10622278—22no—
16C11×#324C2212yes—
17#10622166C2212yes—
18#10622106—22no—
19C22×Q8×C11C2×C411yescharacteristic
20C2×#4343—22no—
21C2×#4343—22no—
22C2×#4343—42no—
23C2×#4343—41no—
24C2×#4343—41no—
25C22×D44—21no—
26C22×D44C2×C411yescharacteristic
27C22×C4×D11—21no—
28C22×C4×D11—21no—
29C22×C4×D11C2×C411yescharacteristic
30C2×C11×C4⋊C4C2311yescharacteristic
31C2×C42×C11C2×C411yescharacteristic
32C2×(C2×D11)⋊C4—22no—
33C2×(C2×D11)⋊C4—22no—
34C2×(C2×D11)⋊C4D412yes—
35C2×C4⋊Dic11C2×C411yescharacteristic
36C2×C4×Dic11—21no—
37C2×C4×Dic11C2×C411yescharacteristic
38C2×C4×Dic11D412yes—
39#66945—41no—
40#66945—41no—
41C42×D11—42no—
42C11×C22⋊C8—22no—
43C11×#95—22no—
44C11⋊#95—22no—
45C22⋊(C11⋊C8)—22no—
46#66879—42no—
47Dic11⋊C8—42no—
48#11507—111nomaximal, Sylow
49C23×D11—21no—
50C23×D11C22⋊C411yescharacteristic
51C2×Q8×C11—21no—
52C2×Q8×C11—41no—
53C2×Q8×C11—41no—
54C2×Q8×C11M1612yes—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11C22×C411yescharacteristic
58C22×C4×C11C2×D412yes—
59C22×Dic11—21no—
60C22×Dic11C22⋊C411yescharacteristic
61C22×Dic11C22⋊C412yes—
62#4343—44no—
63#4343—44no—
64#4343—44no—
65#4343—44no—
66C2×D44—24no—
67C2×D44—21no—
68C2×D44—41no—
69C2×D44—41no—
70C2×D44—42no—
71C2×D44—42no—
72C2×D44M1612yes—
73C2×C4×D11—21no—
74C2×C4×D11—21no—
75C2×C4×D11—24no—
76C2×C4×D11—22no—
77C2×C4×D11—21no—
78C2×C4×D11—21no—
79C2×C4×D11—42no—
80C2×C4×D11—42no—
81C2×C4×D11—42no—
82C2×C4×D11—41no—
83C2×C4×D11—41no—
84C2×C4×D11—42no—
85C2×C8×C11—42no—
86C11×C4⋊C4—41no—
87C42×C11—41no—
88(C2×D11)⋊C4—42no—
89(C2×D11)⋊C4—44no—
90(C2×D11)⋊C4—44no—
91C4⋊Dic11—41no—
92C4×Dic11—22no—
93C4×Dic11—22no—
94C4×Dic11—41no—
95C4×Dic11—42no—
96C2×C11⋊C8—42no—
97#2297—111no—
98#1464—112no—
99#1319—111no—
100#1319D1111yescharacteristic, complemented
101#1318—112no—
102C23×C11C2×C22⋊C411yescharacteristic
103C22×D11—21no—
104C22×D11—21no—
105C22×D11—22no—
106C22×D11—41no—
107C22×D11—41no—
108C22×D11—42no—
109C22×D11—42no—
110C22×D11—41no—
111C22×D11—41no—
112C22×D11#10012yes—
113Q8×C11—42no—
114Q8×C11—42no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—22no—
118C2×C4×C11—22no—
119C2×C4×C11—22no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—42no—
125C2×C4×C11C2×M1611yescharacteristic
126C2×C4×C11C2×M1611yescharacteristic
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11—22no—
130C2×Dic11—22no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—42no—
134C2×Dic11#9911yescharacteristic
135C2×Dic11#9911yescharacteristic
136D44—42no—
137D44—42no—
138D44—48no—
139C4×D11—22no—
140C4×D11—22no—
141C4×D11—22no—
142C4×D11—22no—
143C4×D11—44no—
144C4×D11—44no—
145C4×D11—48no—
146C8×C11—82no—
147C11⋊C8—82no—
148C22×#41—111no—
149C2×#117—111no—
150C22×C42—111no—
151#432—222no—
152#391—111no—
153#391C2×D1111yescharacteristic
154#390—111no—
155#390—111no—
156#386—222no—
157C4×C22⋊C4—222no—
158#324—112no—
159#324C2×D1112yes—
160#323—222no—
161C22×C11—21no—
162C22×C11—21no—
163C22×C11#40711yescharacteristic
164C22×C11C2×#9911yescharacteristic
165C22×C11C2×#10011yescharacteristic
166C2×D11—22no—
167C2×D11—42no—
168C2×D11—41no—
169C2×D11—41no—
170C2×D11—42no—
171C2×D11—44no—
172C2×D11—42no—
173C2×D11—82no—
174C2×D11—81no—
175C2×D11—81no—
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—42no—
179C4×C11—42no—
180C4×C11—42no—
181Dic11—21no—
182Dic11—21no—
183Dic11—42no—
184Dic11—42no—
185C2×#41—222no—
186C2×#41—222no—
187C2×#41—442no—
188C2×#41—441no—
189C2×#41—441no—
190C22×Q8C4×D1111yescharacteristic
191C22×D4—111no—
192C22×D4—221no—
193C23×C4—111no—
194C23×C4—221no—
195C23×C4—221no—
196#117—441no—
197#117—441no—
198C2×C4⋊C4—111no—
199C2×C4⋊C4C22×D1111yescharacteristic
200C2×C22⋊C4—112no—
201C2×C22⋊C4—222no—
202C2×C22⋊C4—222no—
203C2×C42—112no—
204C2×C42—111no—
205C2×C42—221no—
206C2×C42—442no—
207C2×C42C4×D1111yescharacteristic
208C4⋊C8—442no—
209C22⋊C8—22no—
210C22⋊C8—222no—
211#97—442no—
212#95—22no—
213#95—222no—
214C2×C11—21no—
215C2×C11—21no—
216C2×C11#146211yescharacteristic
217C2×C11#212611yescharacteristic
218C2×C11#213211yescharacteristic
219D11—42no—
220D11—82no—
221C24—111no—
222C24—221no—
223#41—444no—
224#41—444no—
225#41—444no—
226#41—444no—
227C2×Q8—21no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8#431312yes—
231C2×D4—112no—
232C2×D4—224no—
233C2×D4—221no—
234C2×D4—441no—
235C2×D4—441no—
236C2×D4—442no—
237C2×D4—442no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—111no—
241C22×C4—112no—
242C22×C4—221no—
243C22×C4—221no—
244C22×C4—222no—
245C22×C4—224no—
246C22×C4—221no—
247C22×C4—221no—
248C22×C4—221no—
249C22×C4—442no—
250C22×C4—441no—
251C22×C4—441no—
252C22×C4—442no—
253C22×C4—442no—
254C22×C4—442no—
255C22×C4C2×C4×D1111yescharacteristic
256C22×C4D4×D1112yes—
257C2×C8—42no—
258C2×C8—442no—
259C4⋊C4—41no—
260C4⋊C4—441no—
261C22⋊C4—442no—
262C22⋊C4—444no—
263C22⋊C4—444no—
264C42—41no—
265C42—222no—
266C42—222no—
267C42—441no—
268C42—442no—
269C11#1150711yescharacteristic, complemented, Sylow
270C23—112no—
271C23—221no—
272C23—221no—
273C23—222no—
274C23—441no—
275C23—441no—
276C23—442no—
277C23—442no—
278C23—441no—
279C23—441no—
280C23C22⋊C4×D1111yescharacteristic
281Q8—42no—
282Q8—42no—
283D4—442no—
284D4—442no—
285D4—448no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4—111no—
297C2×C4—111no—
298C2×C4—222no—
299C2×C4—222no—
300C2×C4—222no—
301C2×C4—222no—
302C2×C4—221no—
303C2×C4—221no—
304C2×C4—222no—
305C2×C4—222no—
306C2×C4—444no—
307C2×C4—444no—
308C2×C4—448no—
309C2×C4—441no—
310C2×C4—441no—
311C2×C4—442no—
312C2×C4C2×#431311yescharacteristic
313C2×C4M16×D1111yescharacteristic
314C8—82no—
315C8—882no—
316C22—21no—
317C22—21no—
318C22—222no—
319C22—442no—
320C22—442no—
321C22—444no—
322C22—441no—
323C22—441no—
324C22—442no—
325C22—882no—
326C22—881no—
327C22—881no—
328C22#1062233911yescharacteristic
329C22D11×#9911yescharacteristic
330C22D11×#10011yescharacteristic
331C4—21no—
332C4—21no—
333C4—42no—
334C4—42no—
335C4—42no—
336C4—221no—
337C4—221no—
338C4—442no—
339C4—442no—
340C2—21no—
341C2—21no—
342C2—442no—
343C2—882no—
344C2#1306694111yescharacteristic
345C2#1307028011yescharacteristic
346C2#1307030011yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1319C2
socleC22×C11C2×#99
prime radicalC22×#4343C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1319D11
hypocenterC11#11507
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1319

Complements

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

NH ≅ G/Ntype
2. #13066949C2semidirect
3. #13066550C2semidirect
4. #13066547C2semidirect
5. C11×#1319C2semidirect
100. #1319D11semidirect
269. C11#11507semidirect

Maximal subgroups

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

subgroupindex
#130711052
#130669492
#130665502
#130665472
C11×#13192
#1150711