Finite Group Databasebeta

← #14655555

Subgroups — #14655555

Order 2816.

544 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 103 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#13079762C211yesmaximal, characteristic, complemented
2#13078990C211yesmaximal, characteristic
3C2×#10622683C211yesmaximal, characteristic
4#13069459C211yesmaximal, characteristic, complemented
5#13067070C211yesmaximal, characteristic, complemented
6#13066452C211yesmaximal, characteristic, complemented
7C11×#1545C211yesmaximal, characteristic
8C2×C11×#127C2211yescharacteristic
9#10623001C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#423C2211yescharacteristic
13#10622828—22no—
14C2×#66896—22no—
15C2×#66888—22no—
16#10622684—22no—
17#10622683—22no—
18#10622683—21no—
19#10622683—21no—
20#10622683—22no—
21C4×#4318C2211yescharacteristic
22C2×C4×C11⋊C8C2211yescharacteristic
23#10622464—22no—
24#10622334—22no—
25#10622294—21no—
26#10622293—21no—
27C11×#331—22no—
28#10622122—22no—
29C22×D4×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×Dic22—21no—
33C2×C11×M16—21no—
34C11×#127—21no—
35C11×#127—21no—
36C11×#127—21no—
37C11×#127D412yes—
38C2×C42×C11C2311yescharacteristic
39#66979—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11D412yes—
42#66977—21no—
43#66977—21no—
44C2×#4318D412yes—
45C22×C11⋊C8—21no—
46#66923—21no—
47#66922—21no—
48#66922—21no—
49#66922—21no—
50#66922—21no—
51#66922D411yescharacteristic
52#66922D411yescharacteristic
53C4×Dic22—21no—
54C4×Dic22—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8D412yes—
58C11×C22⋊C8—21no—
59C4×C8×C11—21no—
60#66896—28no—
61#66896—24no—
62#66896—24no—
63#66888—44no—
64#66881—24no—
65#66880—24no—
66#66867—21no—
67C4×C11⋊C8—21no—
68C4×C11⋊C8—21no—
69C4×C11⋊C8D412yes—
70#10151—111nomaximal, Sylow
71C24×C11—41no—
72C2×D4×C11—22no—
73C2×D4×C11—22no—
74C2×D4×C11—22no—
75C2×D4×C11—44no—
76C2×D4×C11—41no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C2×D4×C11—42no—
80C2×D4×C11—42no—
81C2×D4×C11—82no—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11#4111yescharacteristic
85C22×Dic11—22no—
86C2×Dic22—21no—
87C2×Dic22—21no—
88C2×Dic22—41no—
89C2×Dic22—41no—
90C2×Dic22—42no—
91C2×Dic22—42no—
92C11×M16—42no—
93C2×C8×C11—22no—
94C2×C8×C11—41no—
95C42×C11C2×D411yescharacteristic
96C42×C11C2×D411yescharacteristic
97C42×C11C2×D411yescharacteristic
98C42×C11C2×D411yescharacteristic
99C22⋊Dic11—41no—
100C4⋊Dic11—22no—
101C4⋊Dic11—21no—
102C4⋊Dic11—22no—
103C4⋊Dic11—21no—
104C4⋊Dic11—21no—
105C4⋊Dic11—21no—
106C4⋊Dic11—41no—
107C4⋊Dic11—41no—
108Dic11⋊C4—41no—
109Dic11⋊C4—41no—
110C4×Dic11—41no—
111#4318—22no—
112#4318—22no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—42no—
116#3229—111no—
117#3138—111no—
118C2×#486—111no—
119#1966—111no—
120#1545D1111yescharacteristic
121#1493—111no—
122#1278—111no—
123C23×C11—42no—
124C23×C11—82no—
125C23×C11—82no—
126C23×C11—82no—
127C23×C11#12111yescharacteristic
128D4×C11—44no—
129D4×C11—44no—
130D4×C11—82no—
131D4×C11—82no—
132D4×C11—82no—
133D4×C11—81no—
134D4×C11—81no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11#12011yescharacteristic
138C2×C4×C11#12011yescharacteristic
139C2×C4×C11#12011yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12111yescharacteristic
142C2×C4×C11#12711yescharacteristic
143C2×C4×C11#13512yes—
144C2×C4×C11AGL(1,ℤ/8)12yes—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—42no—
148C2×Dic11—44no—
149Dic22—42no—
150Dic22—42no—
151Dic22—82no—
152Dic22—81no—
153Dic22—81no—
154C8×C11—42no—
155C8×C11—81no—
156C11⋊C8—42no—
157C11⋊C8—42no—
158#533—111no—
159C2×C4⋊Q8—111no—
160C2×#127C2×D1111yescharacteristic
161#498—221no—
162#490—222no—
163#487—221no—
164#486—222no—
165#486—221no—
166#486—221no—
167#486—222no—
168#483—222no—
169#475—222no—
170#431C2×D1111yescharacteristic
171#423C2×D1111yescharacteristic
172#418—222no—
173C2×#102—222no—
174C2×#101—222no—
175C4×M16—111no—
176C2×C4×C8—111no—
177#331—22no—
178Q8⋊C8—222no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—82no—
182C22×C11—82no—
183C22×C11—82no—
184C22×C11—164no—
185C22×C11#39211yescharacteristic
186C22×C11#46312yes—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11#44912yes—
190C4×C11#45412yes—
191C4×C11#47112yes—
192C4×C11#49511yescharacteristic
193C4×C11#49611yescharacteristic
194Dic11—81no—
195Dic11—82no—
196Dic11—81no—
197C22×Q8—221no—
198C22×D4—21no—
199C22×D4—21no—
200C22×D4—21no—
201C2×M16—21no—
202C2×M16—112no—
203C22×C8—221no—
204C4⋊Q8—111no—
205C4⋊Q8—111no—
206C4⋊Q8—221no—
207C4⋊Q8—221no—
208C4⋊Q8—221no—
209C4⋊Q8—221no—
210#127—21no—
211#127—21no—
212#127—21no—
213#127D4412yes—
214#125—221no—
215C22⋊Q8—221no—
216C22⋊Q8—221no—
217C4×Q8—221no—
218C4×Q8—221no—
219#117—221no—
220C2×C4⋊C4—112no—
221C2×C4⋊C4—221no—
222C2×C42C22×D1111yescharacteristic
223#106—224no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8C22⋊D1112yes—
227#103—224no—
228#102—228no—
229#102—224no—
230#102—224no—
231#101—444no—
232C22⋊C8—21no—
233#97—221no—
234C4×C8—21no—
235C4×C8—112no—
236C4×C8—221no—
237C4×C8—221no—
238C2×C11—22no—
239C2×C11—162no—
240C2×C11#200311yescharacteristic
241C2×C11#201211yescharacteristic
242C2×C11#201911yescharacteristic
243C24—41no—
244C2×Q8—221no—
245C2×Q8—221no—
246C2×Q8—441no—
247C2×Q8—442no—
248C2×Q8—442no—
249C2×Q8—441no—
250C2×D4—22no—
251C2×D4—22no—
252C2×D4—22no—
253C2×D4—44no—
254C2×D4—41no—
255C2×D4—42no—
256C2×D4—42no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—82no—
260C22×C4—222no—
261C22×C4#433911yescharacteristic
262C22×C4D4×D1111yescharacteristic
263C22×C4D4×D1111yescharacteristic
264M16—42no—
265M16—222no—
266M16—222no—
267C2×C8—22no—
268C2×C8—41no—
269C2×C8—222no—
270C2×C8—222no—
271C2×C8—442no—
272C4⋊C4—222no—
273C4⋊C4—221no—
274C4⋊C4—221no—
275C4⋊C4—221no—
276C4⋊C4—222no—
277C4⋊C4—221no—
278C4⋊C4—441no—
279C4⋊C4—441no—
280C4⋊C4—441no—
281C4⋊C4—441no—
282C22⋊C4—441no—
283C42—441no—
284C42C2×D4411yescharacteristic
285C42D4×D1111yescharacteristic
286C42D4×D1111yescharacteristic
287C42C2×C22⋊D1111yescharacteristic
288C11#1015111yescharacteristic, complemented, Sylow
289C23—42no—
290C23—82no—
291C23—82no—
292C23—82no—
293C23#6693711yescharacteristic
294Q8—442no—
295Q8—442no—
296Q8—881no—
297Q8—881no—
298Q8—882no—
299D4—44no—
300D4—44no—
301D4—82no—
302D4—81no—
303D4—81no—
304D4—82no—
305D4—82no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4—442no—
311C2×C4—444no—
312C2×C4#6693511yescharacteristic
313C2×C4#6693511yescharacteristic
314C2×C4#6693711yescharacteristic
315C2×C4#6696412yes—
316C2×C4#6696912yes—
317C2×C4#6698311yescharacteristic
318C2×C4#6699011yescharacteristic
319C2×C4#6699311yescharacteristic
320C8—42no—
321C8—81no—
322C8—442no—
323C8—442no—
324C22—21no—
325C22—21no—
326C22—82no—
327C22—82no—
328C22—82no—
329C22—164no—
330C22#1062240012yes—
331C22#1062257311yescharacteristic
332C4—21no—
333C4—21no—
334C4—881no—
335C4—882no—
336C4—881no—
337C4#1062236112yes—
338C4#1062239412yes—
339C4#1062276711yescharacteristic
340C4#1062278111yescharacteristic
341C4#1062281412yes—
342C2—22no—
343C2—162no—
344C2#1306963911yescharacteristic
345C2#1306969511yescharacteristic
346C2#1306973211yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1545C2
socleC22×C11#392
prime radicalC2×C11×#127C22
hypercenter#1545D11
hypocenterC11#10151
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1545

Complements

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

NH ≅ G/Ntype
1. #13079762C2semidirect
4. #13069459C2semidirect
5. #13067070C2semidirect
6. #13066452C2semidirect
288. C11#10151semidirect

Maximal subgroups

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

subgroupindex
#130797622
#130789902
C2×#106226832
#130694592
#130670702
#130664522
C11×#15452
#1015111