Finite Group Databasebeta

← #14645952

Subgroups — #14645952

Order 2816.

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

normal subgroups only

This group has 718 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
1#13068693C211yesmaximal, characteristic, complemented
2#13068687C211yesmaximal, characteristic, complemented
3#13067172C212yesmaximal, complemented
4#13067172C212yesmaximal, complemented
5C11×#3493C211yesmaximal, characteristic
6C11×#556—22no—
7C11×#555—22no—
8C11×#553—22no—
9C11×#552—22no—
10C11×#544C411yescharacteristic, complemented
11C11×#538—22no—
12C11×#537C411yescharacteristic, complemented
13C11×#529—22no—
14C11×#525C2212yes—
15C11×#520C412yescomplemented
16C2×C11×#117C2211yescharacteristic
17#10622824C2212yes—
18C2×C22⋊(C11⋊C8)C2211yescharacteristic
19C2×C22⋊(C11⋊C8)C2211yescharacteristic
20#10622176—22no—
21#10622176—22no—
22#10622175—22no—
23#10622175—22no—
24#10622164—22no—
25#10622162—22no—
26C2×C11×#41C2×C412yes—
27C23×C4×C11C2311yescharacteristic
28C11×C4⋊Q8—22no—
29C11×#126—24no—
30C11×#126—24no—
31C11×#125—22no—
32C11×#125—22no—
33C11×#124—22no—
34C11×#124—24no—
35C11×#123—24no—
36C11×#123—22no—
37C11×C22⋊Q8—22no—
38C11×C22⋊Q8—22no—
39C11×C22⋊Q8D412yes—
40C11×C22⋊Q8D412yes—
41C11×#121—24no—
42C11×#121—22no—
43C11×#121—22no—
44C11×#121D412yes—
45C11×#121D412yes—
46C11×#120—22no—
47C4×Q8×C11—22no—
48C4×Q8×C11—22no—
49C4×D4×C11—22no—
50C4×D4×C11—22no—
51C4×D4×C11—24no—
52C4×D4×C11—22no—
53C4×D4×C11—22no—
54C11×#117—24no—
55C11×#117—22no—
56C11×#117—22no—
57C11×#117—22no—
58C11×#117C2×C412yes—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4C2×C411yescharacteristic
61C2×C11×C4⋊C4C2×C411yescharacteristic
62C2×C11×C22⋊C4D412yes—
63C2×C42×C11D412yes—
64C2×C22⋊Dic11—22no—
65C22×C11⋊C8—21no—
66C22×C11⋊C8—21no—
67C11⋊#95—22no—
68C11⋊#95—22no—
69C22⋊(C11⋊C8)—22no—
70C22⋊(C11⋊C8)—22no—
71#8463—111nomaximal, Sylow
72C24×C11C2×D411yescharacteristic
73C11×#41—44no—
74C2×Q8×C11—22no—
75C2×Q8×C11C22⋊C412yes—
76C2×D4×C11—22no—
77C2×D4×C11—22no—
78C2×D4×C11—22no—
79C2×D4×C11—22no—
80C2×D4×C11C22⋊C412yes—
81C22×C4×C11—24no—
82C22×C4×C11—22no—
83C22×C4×C11—42no—
84C22×C4×C11C22⋊C412yes—
85C22×C4×C11C22⋊C412yes—
86C22×C4×C11C22×C411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D412yes—
89C22×C4×C11C2×D412yes—
90C22×Dic11—42no—
91C11×C4⋊C4—24no—
92C11×C4⋊C4—24no—
93C11×C4⋊C4—22no—
94C11×C4⋊C4—22no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4C22⋊C412yes—
100C11×C4⋊C4C22⋊C412yes—
101C11×C22⋊C4—24no—
102C11×C22⋊C4—24no—
103C11×C22⋊C4—22no—
104C11×C22⋊C4—24no—
105C11×C22⋊C4—22no—
106C11×C22⋊C4—22no—
107C11×C22⋊C4—22no—
108C11×C22⋊C4—22no—
109C42×C11—24no—
110C42×C11—22no—
111C42×C11—22no—
112C42×C11—22no—
113C22⋊Dic11—44no—
114C2×C11⋊C8—42no—
115C2×C11⋊C8—42no—
116C2×C11⋊C8—41no—
117C2×C11⋊C8—41no—
118#3493D1111yescharacteristic
119#1820—111no—
120#1818—111no—
121#1516—112no—
122#1516—112no—
123C23×C11—22no—
124C23×C11—22no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11C2×C22⋊C411yescharacteristic
128C23×C11#12012yes—
129Q8×C11—42no—
130Q8×C11—82no—
131D4×C11—42no—
132D4×C11—44no—
133D4×C11—82no—
134D4×C11—82no—
135D4×C11—82no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—44no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—84no—
149C2×C4×C11C2×C22⋊C412yes—
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12011yescharacteristic
152C2×Dic11—82no—
153C2×Dic11—82no—
154C2×Dic11—82no—
155C11⋊C8—81no—
156C11⋊C8—81no—
157#556—22no—
158#555—22no—
159#553—22no—
160#552—22no—
161#544Dic1111yescharacteristic, complemented
162#538—22no—
163#537Dic1111yescharacteristic, complemented
164#529—22no—
165#525C2×D1112yes—
166#520Dic1112yescomplemented
167C2×#117C2×D1111yescharacteristic
168C2×C22⋊C8—111no—
169C2×C22⋊C8—111no—
170#381—112no—
171#342—222no—
172#336—222no—
173#328—222no—
174#328—222no—
175#327—222no—
176#327—222no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—22no—
180C22×C11—22no—
181C22×C11—22no—
182C22×C11—42no—
183C22×C11—42no—
184C22×C11—42no—
185C22×C11—82no—
186C22×C11#37911yescharacteristic
187C22×C11#41012yes—
188C4×C11—22no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—42no—
192C4×C11—42no—
193C4×C11—42no—
194C4×C11—42no—
195C4×C11—42no—
196Dic11—162no—
197C2×#41C2×Dic1112yes—
198C23×C4C22×D1111yescharacteristic
199C22×C8—221no—
200C22×C8—221no—
201C4⋊Q8—22no—
202#126—24no—
203#126—24no—
204#125—22no—
205#125—22no—
206#124—22no—
207#124—24no—
208#123—24no—
209#123—22no—
210C22⋊Q8—22no—
211C22⋊Q8—22no—
212C22⋊Q8C22⋊D1112yes—
213C22⋊Q8C22⋊D1112yes—
214#121—24no—
215#121—22no—
216#121—22no—
217#121C22⋊D1112yes—
218#121C22⋊D1112yes—
219#120—22no—
220C4×Q8—22no—
221C4×Q8—22no—
222C4×D4—22no—
223C4×D4—22no—
224C4×D4—24no—
225C4×D4—22no—
226C4×D4—22no—
227#117—24no—
228#117—22no—
229#117—22no—
230#117—22no—
231#117C2×Dic1112yes—
232C2×C4⋊C4—22no—
233C2×C4⋊C4C2×Dic1111yescharacteristic
234C2×C4⋊C4C2×Dic1111yescharacteristic
235C2×C22⋊C4—222no—
236C2×C22⋊C4C22⋊D1112yes—
237C2×C42C22⋊D1112yes—
238C22⋊C8—222no—
239C22⋊C8—222no—
240#95—222no—
241#95—222no—
242C2×C11—22no—
243C2×C11—42no—
244C2×C11—82no—
245C2×C11#178211yescharacteristic
246C2×C11#179411yescharacteristic
247C2×C11#179411yescharacteristic
248C24C2×C22⋊D1111yescharacteristic
249#41—44no—
250C2×Q8—22no—
251C2×Q8C22⋊Dic1112yes—
252C2×D4—22no—
253C2×D4—22no—
254C2×D4—22no—
255C2×D4—22no—
256C2×D4C22⋊Dic1112yes—
257C22×C4—24no—
258C22×C4—22no—
259C22×C4—42no—
260C22×C4—442no—
261C22×C4C22⋊Dic1112yes—
262C22×C4C22⋊Dic1112yes—
263C22×C4C22×Dic1111yescharacteristic
264C22×C4C2×C22⋊D1111yescharacteristic
265C22×C4C2×C22⋊D1112yes—
266C22×C4C2×C22⋊D1112yes—
267C2×C8—442no—
268C2×C8—442no—
269C2×C8—441no—
270C2×C8—441no—
271C4⋊C4—24no—
272C4⋊C4—24no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4C22⋊Dic1112yes—
280C4⋊C4C22⋊Dic1112yes—
281C22⋊C4—24no—
282C22⋊C4—24no—
283C22⋊C4—22no—
284C22⋊C4—24no—
285C22⋊C4—22no—
286C22⋊C4—22no—
287C22⋊C4—22no—
288C22⋊C4—22no—
289C22⋊C4—444no—
290C42—24no—
291C42—22no—
292C42—22no—
293C42—22no—
294C11#846311yescharacteristic, complemented, Sylow
295C23—22no—
296C23—22no—
297C23—41no—
298C23—41no—
299C23C2×C22⋊Dic1111yescharacteristic
300C23#6700612yes—
301Q8—42no—
302Q8—82no—
303D4—42no—
304D4—44no—
305D4—82no—
306D4—82no—
307D4—82no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—44no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—84no—
321C2×C4—882no—
322C2×C4—882no—
323C2×C4—882no—
324C2×C4C2×C22⋊Dic1112yes—
325C2×C4#6700611yescharacteristic
326C2×C4#6700611yescharacteristic
327C8—881no—
328C8—881no—
329C22—21no—
330C22—21no—
331C22—22no—
332C22—22no—
333C22—22no—
334C22—42no—
335C22—42no—
336C22—42no—
337C22—82no—
338C22#1062285312yes—
339C22#1062286011yescharacteristic
340C4—21no—
341C4—21no—
342C4—22no—
343C4—42no—
344C4—42no—
345C4—42no—
346C4—42no—
347C4—42no—
348C4—1762no—
349C2—22no—
350C2—42no—
351C2—82no—
352C2#1306853411yescharacteristic
353C2#1306858011yescharacteristic
354C2#1306858011yescharacteristic
subgroupG/H
centerC22#10622860
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
Fitting, prime radicalC11×#3493C2
socleC22×C11#379
cosocleC23×C4×C11C23
hypercenter#3493D11
hypocenterC11#8463
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3493

Complements

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

NH ≅ G/Ntype
1. #13068693C2semidirect
2. #13068687C2semidirect
3. #13067172C2semidirect
4. #13067172C2semidirect
10. C11×#544C4semidirect
12. C11×#537C4semidirect
15. C11×#520C4semidirect
161. #544Dic11semidirect
163. #537Dic11semidirect
166. #520Dic11semidirect
294. C11#8463semidirect

Maximal subgroups

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

subgroupindex
#130686932
#130686872
#130671722
C11×#34932
#846311