Finite Group Databasebeta

← #14650372

Subgroups — #14650372

Order 2816.

456 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 95 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#13079545C211yesmaximal, characteristic
2#13077692C211yesmaximal, characteristic, complemented
3#13067123C211yesmaximal, characteristic, complemented
4#13067084C211yesmaximal, characteristic, complemented
5#13066477C211yesmaximal, characteristic, complemented
6#13066445C211yesmaximal, characteristic, complemented
7C11×#1505C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9#10623008C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#376C2211yescharacteristic
12#10622847—22no—
13#10622706C411yescharacteristic, complemented
14#10622701C411yescharacteristic, complemented
15#10622689C411yescharacteristic, complemented
16#10622686C411yescharacteristic, complemented
17#10622650—22no—
18#10622629—22no—
19#10622625—21no—
20#10622624—22no—
21D4×C11⋊C8—21no—
22#10622539C2211yescharacteristic
23#10622538C2211yescharacteristic
24#10622538C2211yescharacteristic
25C11×#327—22no—
26#10622121—21no—
27#10622121—21no—
28#10622089—22no—
29C2×C11×#41—21no—
30C2×#4339—21no—
31C11×C4⋊Q8C2×C411yescharacteristic
32C11×#127C2×C411yescharacteristic
33C11×#124—21no—
34C11×#121—21no—
35C11×#121D412yes—
36C4×D4×C11—21no—
37C4×D4×C11D412yes—
38C2×C42×C11—21no—
39C2×C42×C11C2311yescharacteristic
40C2×#4324—22no—
41C2×#4323—22no—
42#66983—21no—
43#66983—21no—
44C2×#4318—22no—
45C22×C11⋊C8—22no—
46#66928—21no—
47#66927C2×C411yescharacteristic
48C4×D44—21no—
49C4×D44—21no—
50#66922C2×C411yescharacteristic
51C11×C4⋊C8—21no—
52C11×C22⋊C8—21no—
53C11×#97—21no—
54C11×#95—21no—
55C11×#95—21no—
56C22⋊(C11⋊C8)—22no—
57C22⋊(C11⋊C8)—22no—
58C22⋊(C11⋊C8)—21no—
59C22⋊(C11⋊C8)—21no—
60C22⋊(C11⋊C8)D412yes—
61#66874—22no—
62#66873—22no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66#66867—21no—
67C4×C11⋊C8C2×C411yescharacteristic
68C4×C11⋊C8C2×C411yescharacteristic
69C4×C11⋊C8D411yescharacteristic
70C4×C11⋊C8D411yescharacteristic
71#9281—111nomaximal, Sylow
72C11×#41—82no—
73C2×Q8×C11—21no—
74C2×D4×C11—22no—
75C2×D4×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11C22⋊C412yes—
78C22×C4×C11—22no—
79C22×C4×C11—41no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11#4111yescharacteristic
83C2×C22⋊D11—41no—
84#4339—82no—
85C2×D44—21no—
86C2×D44—21no—
87C2×D44—21no—
88C2×C4×D11—41no—
89C2×Dic22—21no—
90C2×C8×C11—41no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4C22⋊C412yes—
93C11×C22⋊C4—22no—
94C11×C22⋊C4—22no—
95C42×C11—22no—
96C42×C11—41no—
97C42×C11C22×C411yescharacteristic
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11#4111yescharacteristic
101#4324—82no—
102#4323—82no—
103(C2×D11)⋊C4—41no—
104(C2×D11)⋊C4—41no—
105C4⋊Dic11—21no—
106C4⋊Dic11—21no—
107#4318—82no—
108C2×C11⋊C8—21no—
109C2×C11⋊C8—21no—
110C2×C11⋊C8—21no—
111C2×C11⋊C8—21no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8—82no—
114#3207—111no—
115#2981—111no—
116#1505—111no—
117#1505D1111yescharacteristic, complemented
118#1496—111no—
119#1287—111no—
120#1274—111no—
121C23×C11—22no—
122C23×C11#12111yescharacteristic
123C22×D11—41no—
124Q8×C11—81no—
125D4×C11—42no—
126D4×C11—41no—
127D4×C11—41no—
128D4×C11—81no—
129D4×C11—82no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—22no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—81no—
139C2×C4×C11—81no—
140C2×C4×C11C2×C22⋊C411yescharacteristic
141C2×C4×C11C4×D411yescharacteristic
142C2×C4×C11C4×D411yescharacteristic
143C2×C4×C11#12011yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12311yescharacteristic
146C22⋊D11—82no—
147C2×Dic11—41no—
148D44—42no—
149D44—41no—
150D44—41no—
151D44—81no—
152C4×D11—82no—
153Dic22—42no—
154C8×C11—81no—
155C11⋊C8—41no—
156C11⋊C8—42no—
157C11⋊C8—41no—
158C11⋊C8—41no—
159C11⋊C8—41no—
160#532—111no—
161#532C2×D1111yescharacteristic
162#493—111no—
163#492—111no—
164#487—111no—
165#486—111no—
166#463—222no—
167#449—222no—
168#436—221no—
169#435—222no—
170C8×D4—221no—
171#432—111no—
172#432C2×D1111yescharacteristic
173#431—111no—
174#431—111no—
175#408—222no—
176#376C2×D1111yescharacteristic
177#327—22no—
178#327—222no—
179D4⋊C8—221no—
180D4⋊C8—221no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—42no—
185C22×C11—42no—
186C22×C11—42no—
187C22×C11#38611yescharacteristic
188C2×D11—81no—
189C2×D11—81no—
190C2×D11—81no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—42no—
197C4×C11—82no—
198C4×C11#44311yescharacteristic
199C4×C11#44411yescharacteristic
200Dic11—81no—
201C2×#41—21no—
202C2×#41—221no—
203C2×SD16—222no—
204C2×D8—222no—
205C2×M16—222no—
206C22×C8—222no—
207C4⋊Q8—111no—
208C4⋊Q8C4×D1111yescharacteristic
209#127—111no—
210#127C4×D1111yescharacteristic
211#124—21no—
212#124—221no—
213#121—21no—
214#121—221no—
215#121—221no—
216#121C22⋊D1112yes—
217C4×D4—21no—
218C4×D4—221no—
219C4×D4—221no—
220C4×D4D4412yes—
221C2×C42—21no—
222C2×C42C22×D1111yescharacteristic
223C4⋊C8—21no—
224C4⋊C8—221no—
225C4⋊C8—221no—
226C4⋊C8—221no—
227#103—222no—
228#102—222no—
229C22⋊C8—21no—
230C22⋊C8—112no—
231C22⋊C8—222no—
232C22⋊C8—222no—
233C22⋊C8—221no—
234C22⋊C8—221no—
235#97—21no—
236#97—221no—
237C4×C8—111no—
238C4×C8—111no—
239C4×C8—111no—
240C4×C8—111no—
241#95—21no—
242#95—21no—
243C2×C11—41no—
244C2×C11—82no—
245C2×C11#187611yescharacteristic
246C2×C11#190411yescharacteristic
247C2×C11#191011yescharacteristic
248D11—161no—
249#41—82no—
250#41—882no—
251C2×Q8—21no—
252C2×Q8—221no—
253C2×D4—22no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—221no—
257C2×D4—221no—
258C2×D4—221no—
259C2×D4—441no—
260C2×D4(C2×D11)⋊C412yes—
261C22×C4—22no—
262C22×C4—41no—
263C22×C4—441no—
264C22×C4D4×D1111yescharacteristic
265C22×C4#434111yescharacteristic
266C22×C4C2×C22⋊D1111yescharacteristic
267SD16—882no—
268D8—882no—
269M16—882no—
270C2×C8—41no—
271C2×C8—221no—
272C2×C8—221no—
273C2×C8—222no—
274C2×C8—221no—
275C2×C8—221no—
276C2×C8—882no—
277C4⋊C4—21no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4(C2×D11)⋊C412yes—
281C22⋊C4—22no—
282C22⋊C4—22no—
283C22⋊C4—441no—
284C22⋊C4—441no—
285C42—22no—
286C42—41no—
287C42C2×C4×D1111yescharacteristic
288C42C2×D4411yescharacteristic
289C42D4×D1111yescharacteristic
290C42#434111yescharacteristic
291C11#928111yescharacteristic, complemented, Sylow
292C23—22no—
293C23—441no—
294C23#6699211yescharacteristic
295Q8—81no—
296Q8—442no—
297D4—42no—
298D4—41no—
299D4—41no—
300D4—81no—
301D4—82no—
302D4—442no—
303D4—441no—
304D4—441no—
305D4—881no—
306D4—882no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—441no—
318C2×C4—882no—
319C2×C4(C22⋊D11)⋊C411yescharacteristic
320C2×C4(C22⋊D11)⋊C411yescharacteristic
321C2×C4#6693511yescharacteristic
322C2×C4#6693911yescharacteristic
323C2×C4C2×(C2×D11)⋊C411yescharacteristic
324C2×C4#6699211yescharacteristic
325C8—81no—
326C8—441no—
327C8—442no—
328C8—441no—
329C8—441no—
330C8—441no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—42no—
335C22—42no—
336C22—42no—
337C22—881no—
338C22—881no—
339C22—881no—
340C22#1062257111yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—42no—
347C4—82no—
348C4—881no—
349C4#1062243611yescharacteristic
350C4#1062243711yescharacteristic
351C2—41no—
352C2—82no—
353C2—1761no—
354C2#1306894111yescharacteristic
355C2#1306910111yescharacteristic
356C2#1306914111yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1505C2
socleC22×C11#386
prime radical#13079545C2
cosocleC2×C42×C11C23
hypercenter#1505D11
hypocenterC11#9281
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1505

Complements

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

NH ≅ G/Ntype
2. #13077692C2semidirect
3. #13067123C2semidirect
4. #13067084C2semidirect
5. #13066477C2semidirect
6. #13066445C2semidirect
7. C11×#1505C2semidirect
13. #10622706C4semidirect
14. #10622701C4semidirect
15. #10622689C4semidirect
16. #10622686C4semidirect
117. #1505D11semidirect
291. C11#9281semidirect

Maximal subgroups

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

subgroupindex
#130795452
#130776922
#130671232
#130670842
#130664772
#130664452
C11×#15052
#928111