Finite Group Databasebeta

← #14664296

Subgroups — #14664296

Order 2816.

420 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 71 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#13074309C211yesmaximal, characteristic
2#13068353C211yesmaximal, characteristic
3#13066949C211yesmaximal, characteristic
4#13066644C211yesmaximal, characteristic, complemented
5#13066642C211yesmaximal, characteristic, complemented
6#13066622C211yesmaximal, characteristic, complemented
7C11×#1346C211yesmaximal, characteristic, complemented
8C2×M16×D11—21no—
9C2×#66945C2211yescharacteristic
10C2×#66943C411yescharacteristic
11C11×#398C2211yescharacteristic
12#10622606C411yescharacteristic
13#10622602—21no—
14#10622599C2211yescharacteristic
15#10622598—21no—
16#10622332—21no—
17#10622290C411yescharacteristic
18#10622283—21no—
19#10622267—21no—
20#10622261C411yescharacteristic
21C11×#343C2211yescharacteristic
22C11×#324C2211yescharacteristic
23#10622192—21no—
24#10622168C2211yescharacteristic
25#10622166C2211yescharacteristic
26#10622106—21no—
27C22×C4×D11D411yescharacteristic
28C2×C11×M16—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C11×C4⋊C4C2311yescharacteristic
32C2×(C2×D11)⋊C4—21no—
33C2×(C2×D11)⋊C4—21no—
34C2×(C2×D11)⋊C4C2×C411yescharacteristic
35C2×(C2×D11)⋊C4D411yescharacteristic
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11C2×C411yescharacteristic
39C2×C4⋊Dic11D411yescharacteristic
40C2×Dic11⋊C4—21no—
41C2×C4×Dic11—21no—
42C2×C4×Dic11C2×C411yescharacteristic
43C2×C4×Dic11D411yescharacteristic
44C2×#4318—21no—
45M16×D11—24no—
46M16×D11—42no—
47C2×#4313—41no—
48C2×C8×D11—41no—
49#66945—41no—
50#66945—41no—
51#66943—41no—
52#66943—41no—
53C11×C22⋊C8—21no—
54C11×#95—21no—
55C11×#95C2×C411yescharacteristic
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95C2×C411yescharacteristic
61C22⋊(C11⋊C8)—21no—
62#66879—41no—
63Dic11⋊C8—41no—
64#11767—111nomaximal, Sylow
65C23×D11C22⋊C411yescharacteristic
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×Dic11—21no—
72C22×Dic11—21no—
73C22×Dic11C22⋊C411yescharacteristic
74C22×Dic11C22⋊C411yescharacteristic
75C22×Dic11C22⋊C411yescharacteristic
76C2×C4×D11—21no—
77C2×C4×D11—21no—
78C2×C4×D11—22no—
79C2×C4×D11—21no—
80C2×C4×D11—21no—
81C11×M16—22no—
82C11×M16—41no—
83C2×C8×C11—41no—
84C2×C8×C11—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89(C2×D11)⋊C4—41no—
90(C2×D11)⋊C4—41no—
91(C2×D11)⋊C4—42no—
92(C2×D11)⋊C4—42no—
93C4⋊Dic11—41no—
94C4⋊Dic11—41no—
95C4⋊Dic11—42no—
96C4⋊Dic11—42no—
97Dic11⋊C4—41no—
98Dic11⋊C4—41no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11—42no—
104#4318—22no—
105#4318—41no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108#4313—44no—
109C8×D11—44no—
110#2611—111no—
111#1742—111no—
112#1464—111no—
113#1353—111no—
114#1353—111no—
115#1346—111no—
116#1346D1111yescharacteristic, complemented
117C23×C11C2×C22⋊C411yescharacteristic
118C22×D11—21no—
119C22×D11—21no—
120C22×D11—41no—
121C22×D11—41no—
122C22×D11#10412yes—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—22no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C11#13711yescharacteristic
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—21no—
140C2×Dic11—21no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11#9911yescharacteristic
150C2×Dic11#9911yescharacteristic
151C4×D11—22no—
152C4×D11—22no—
153C4×D11—22no—
154C4×D11—22no—
155C8×C11—42no—
156C8×C11—81no—
157C11⋊C8—42no—
158C11⋊C8—81no—
159C22×M16—221no—
160C2×#125—111no—
161C2×#117—111no—
162#432—221no—
163#400—111no—
164#399—111no—
165#398C2×D1111yescharacteristic
166#397—111no—
167#389—221no—
168#388—221no—
169#387—221no—
170#385—221no—
171#376—111no—
172#343—111no—
173#343—221no—
174#343C2×D1111yescharacteristic
175#324—111no—
176#324C2×D1111yescharacteristic
177#323—221no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11C2×#9911yescharacteristic
181C22×C11#41711yescharacteristic
182C22×C11C2×#10411yescharacteristic
183C2×D11—22no—
184C2×D11—41no—
185C2×D11—41no—
186C2×D11—42no—
187C2×D11—81no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—42no—
191C4×C11—41no—
192C4×C11—41no—
193C4×C11—81no—
194Dic11—21no—
195Dic11—21no—
196Dic11—41no—
197Dic11—41no—
198Dic11—81no—
199Dic11—81no—
200C23×C4—111no—
201C2×M16—21no—
202C2×M16—224no—
203C2×M16—221no—
204C2×M16—441no—
205C2×M16—442no—
206C22×C8—441no—
207#125—441no—
208#125—441no—
209#117—441no—
210#117—441no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—111no—
213C2×C4⋊C4—111no—
214C2×C4⋊C4—221no—
215C2×C4⋊C4—221no—
216C2×C4⋊C4—221no—
217C2×C4⋊C4C4×D1111yescharacteristic
218C2×C4⋊C4C22×D1111yescharacteristic
219C2×C22⋊C4—111no—
220C2×C22⋊C4—111no—
221C2×C22⋊C4—221no—
222C2×C22⋊C4—221no—
223C2×C42—111no—
224C2×C42—111no—
225C2×C42—221no—
226C4⋊C8—441no—
227C22⋊C8—21no—
228C22⋊C8—221no—
229#97—441no—
230#95—21no—
231#95—111no—
232#95—221no—
233#95—221no—
234#95—221no—
235#95—221no—
236#95C4×D1111yescharacteristic
237C2×C11—21no—
238C2×C11—21no—
239C2×C11#150411yescharacteristic
240C2×C11#212311yescharacteristic
241C2×C11#213211yescharacteristic
242D11—42no—
243C24—111no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—111no—
247C22×C4—111no—
248C22×C4—111no—
249C22×C4—221no—
250C22×C4—221no—
251C22×C4—222no—
252C22×C4—221no—
253C22×C4—221no—
254C22×C4—221no—
255C22×C4—221no—
256C22×C4C2×C4×D1111yescharacteristic
257C22×C4D4×D1111yescharacteristic
258C22×C4D4×D1111yescharacteristic
259M16—22no—
260M16—41no—
261M16—222no—
262M16—444no—
263M16—441no—
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—444no—
267C2×C8—441no—
268C2×C8—441no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—441no—
274C4⋊C4—441no—
275C4⋊C4—442no—
276C4⋊C4—441no—
277C4⋊C4—441no—
278C4⋊C4—442no—
279C22⋊C4—441no—
280C22⋊C4—441no—
281C22⋊C4—442no—
282C22⋊C4—442no—
283C42—221no—
284C42—221no—
285C42—221no—
286C42—221no—
287C42—442no—
288C11#1176711yescharacteristic, complemented, Sylow
289C23—112no—
290C23—221no—
291C23—221no—
292C23—441no—
293C23—441no—
294C23C22⋊C4×D1111yescharacteristic
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—111no—
308C2×C4—111no—
309C2×C4—222no—
310C2×C4—222no—
311C2×C4—222no—
312C2×C4—222no—
313C2×C4—221no—
314C2×C4—221no—
315C2×C4—221no—
316C2×C4—221no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—441no—
324C2×C4—441no—
325C2×C4#6696411yescharacteristic
326C2×C4#6696811yescharacteristic
327C8—42no—
328C8—81no—
329C8—442no—
330C8—881no—
331C22—21no—
332C22—21no—
333C22—222no—
334C22—442no—
335C22—441no—
336C22—441no—
337C22—881no—
338C22D11×#9911yescharacteristic
339C22#1062238411yescharacteristic
340C22D11×#10411yescharacteristic
341C4—21no—
342C4—21no—
343C4—42no—
344C4—41no—
345C4—41no—
346C4—81no—
347C4—221no—
348C4—221no—
349C4—441no—
350C4—441no—
351C4—881no—
352C4—881no—
353C2—21no—
354C2—21no—
355C2—442no—
356C2#1306711711yescharacteristic
357C2#1307026811yescharacteristic
358C2#1307030011yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1346C2
socleC22×C11C2×#99
prime radicalC23×D11C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1346D11
hypocenterC11#11767
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1346

Complements

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

NH ≅ G/Ntype
4. #13066644C2semidirect
5. #13066642C2semidirect
6. #13066622C2semidirect
7. C11×#1346C2semidirect
116. #1346D11semidirect
288. C11#11767semidirect

Maximal subgroups

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

subgroupindex
#130743092
#130683532
#130669492
#130666442
#130666422
#130666222
C11×#13462
#1176711