Finite Group Databasebeta

← #14655682

Subgroups — #14655682

Order 2816.

556 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 105 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#13078998C211yesmaximal, characteristic, complemented
2C2×#10622683C211yesmaximal, characteristic
3#13069457C211yesmaximal, characteristic
4#13067287C211yesmaximal, characteristic, complemented
5#13067071C211yesmaximal, characteristic, complemented
6#13066452C211yesmaximal, characteristic, complemented
7C11×#3208C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C11×#127C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#492—21no—
12C11×#486—21no—
13C11×#460—22no—
14C11×#450—22no—
15C11×#431C2211yescharacteristic
16C2×#66897—22no—
17C2×#66896—22no—
18#10622706—21no—
19#10622706—21no—
20#10622683—22no—
21#10622683—22no—
22#10622682—22no—
23#10622617—22no—
24#10622537C2211yescharacteristic
25C4×#4318C2211yescharacteristic
26C2×C4×C11⋊C8C2211yescharacteristic
27Q8⋊(C11⋊C8)—22no—
28#10622124—22no—
29C22×D4×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11D412yes—
32C22×Dic22—21no—
33C2×C11×SD16—24no—
34C11×C4⋊Q8D411yescharacteristic
35C11×C4⋊Q8D411yescharacteristic
36C11×#127—21no—
37C11×#127—21no—
38C11×#127—21no—
39C11×#127—21no—
40C11×#125—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C11×#117—21no—
46C2×C42×C11C2311yescharacteristic
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11—21no—
49C2×#4318—21no—
50C2×#4318D412yes—
51C22×C11⋊C8—21no—
52#66922—21no—
53#66922—21no—
54#66922—21no—
55#66922D412yes—
56C11×C4⋊C8D412yes—
57C11×#102—24no—
58C11×C22⋊C8—21no—
59C4×C8×C11—21no—
60#66897—44no—
61#66896—28no—
62#66874—24no—
63#66874—24no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66#66867—21no—
67C4×C11⋊C8—21no—
68C4×C11⋊C8—21no—
69C4×C11⋊C8D412yes—
70#10169—111nomaximal, Sylow
71C24×C11—22no—
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C2×D4×C11—22no—
75C2×D4×C11—22no—
76C2×D4×C11—44no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C2×D4×C11—41no—
80C2×D4×C11—41no—
81C2×D4×C11—42no—
82C2×D4×C11—42no—
83C2×D4×C11—82no—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11#4111yescharacteristic
87C22×Dic11—41no—
88C2×Dic22—22no—
89C2×Dic22—41no—
90C2×Dic22—42no—
91C2×Dic22—42no—
92C11×SD16—84no—
93C2×C8×C11—22no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C22⋊C4—41no—
101C42×C11—41no—
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C4⋊Dic11—22no—
107C4⋊Dic11—22no—
108C4⋊Dic11—41no—
109C4⋊Dic11—41no—
110#4318—22no—
111#4318—22no—
112#4318—42no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—42no—
116C2×C11⋊C8—41no—
117#3208D1111yescharacteristic
118#3139—111no—
119C2×#486—111no—
120#1965—111no—
121#1546—111no—
122#1493—111no—
123#1278—111no—
124C23×C11—42no—
125C23×C11—44no—
126C23×C11—82no—
127C23×C11—82no—
128C23×C11#12111yescharacteristic
129Q8×C11—42no—
130Q8×C11—42no—
131D4×C11—44no—
132D4×C11—44no—
133D4×C11—82no—
134D4×C11—82no—
135D4×C11—82no—
136D4×C11—81no—
137D4×C11—81no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12011yescharacteristic
144C2×C4×C11#12011yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12711yescharacteristic
148C2×C4×C11#13512yes—
149C2×C4×C11AGL(1,ℤ/8)12yes—
150C2×Dic11—42no—
151C2×Dic11—82no—
152Dic22—44no—
153Dic22—81no—
154Dic22—81no—
155C8×C11—42no—
156C11⋊C8—42no—
157C11⋊C8—42no—
158C11⋊C8—81no—
159#533C2×D1111yescharacteristic
160C2×C4⋊Q8—111no—
161C2×#127C2×D1111yescharacteristic
162#492—21no—
163#491—222no—
164#487—221no—
165#487—221no—
166#486—21no—
167#486—222no—
168#486—222no—
169#460—22no—
170#450—22no—
171#431C2×D1111yescharacteristic
172#423—111no—
173#419—222no—
174C2×#102—222no—
175C2×#100—222no—
176C4×M16—111no—
177C2×C4×C8—111no—
178#332—222no—
179Q8⋊C8—222no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—82no—
183C22×C11—82no—
184C22×C11—82no—
185C22×C11—164no—
186C22×C11#39211yescharacteristic
187C22×C11#46312yes—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—81no—
191C4×C11—81no—
192C4×C11#44912yes—
193C4×C11#45512yes—
194C4×C11#47112yes—
195C4×C11#49511yescharacteristic
196C4×C11#49611yescharacteristic
197Dic11—82no—
198C22×Q8—221no—
199C22×D4—21no—
200C22×D4—21no—
201C22×D4C22⋊D1112yes—
202C2×SD16—24no—
203C2×M16—112no—
204C2×M16—221no—
205C22×C8—221no—
206C4⋊Q8—112no—
207C4⋊Q8—221no—
208C4⋊Q8—221no—
209C4⋊Q8—221no—
210C4⋊Q8C22⋊D1111yescharacteristic
211C4⋊Q8C22⋊D1111yescharacteristic
212#127—21no—
213#127—21no—
214#127—21no—
215#127—21no—
216#125—21no—
217C22⋊Q8—21no—
218C22⋊Q8—21no—
219C4×Q8—21no—
220C4×Q8—21no—
221#117—21no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4—221no—
224C2×C42C22×D1111yescharacteristic
225C4⋊C8—221no—
226C4⋊C8—221no—
227C4⋊C8C22⋊D1112yes—
228#103—224no—
229#103—224no—
230#102—24no—
231#102—228no—
232#100—444no—
233C22⋊C8—21no—
234#97—221no—
235C4×C8—21no—
236C4×C8—112no—
237C4×C8—221no—
238C4×C8—221no—
239C2×C11—22no—
240C2×C11—162no—
241C2×C11#200411yescharacteristic
242C2×C11#201211yescharacteristic
243C2×C11#201911yescharacteristic
244C24—22no—
245C2×Q8—21no—
246C2×Q8—21no—
247C2×Q8—222no—
248C2×Q8—441no—
249C2×Q8—442no—
250C2×Q8—442no—
251C2×D4—22no—
252C2×D4—22no—
253C2×D4—44no—
254C2×D4—42no—
255C2×D4—42no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—41no—
260C2×D4—82no—
261C22×C4—441no—
262C22×C4D4×D1111yescharacteristic
263C22×C4#434111yescharacteristic
264C22×C4C2×C22⋊D1111yescharacteristic
265SD16—84no—
266M16—222no—
267M16—222no—
268M16—442no—
269C2×C8—22no—
270C2×C8—222no—
271C2×C8—222no—
272C2×C8—442no—
273C2×C8—441no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—222no—
281C4⋊C4—222no—
282C4⋊C4—441no—
283C4⋊C4—441no—
284C22⋊C4—41no—
285C42—41no—
286C42D4×D1111yescharacteristic
287C42D4×D1111yescharacteristic
288C42C2×C22⋊D1111yescharacteristic
289C42C2×C22⋊D1111yescharacteristic
290C11#1016911yescharacteristic, complemented, Sylow
291C23—42no—
292C23—44no—
293C23—82no—
294C23—82no—
295C23#6699211yescharacteristic
296Q8—42no—
297Q8—42no—
298Q8—444no—
299Q8—881no—
300Q8—881no—
301D4—44no—
302D4—44no—
303D4—82no—
304D4—81no—
305D4—82no—
306D4—81no—
307D4—82no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—442no—
313C2×C4—882no—
314C2×C4#6696712yes—
315C2×C4#6696912yes—
316C2×C4#6699011yescharacteristic
317C2×C4#6699011yescharacteristic
318C2×C4#6699111yescharacteristic
319C2×C4#6699211yescharacteristic
320C2×C4#6699311yescharacteristic
321C2×C4#6700611yescharacteristic
322C8—42no—
323C8—442no—
324C8—442no—
325C8—881no—
326C22—21no—
327C22—21no—
328C22—82no—
329C22—82no—
330C22—82no—
331C22—164no—
332C22#1062277812yes—
333C22#1062283611yescharacteristic
334C4—21no—
335C4—21no—
336C4—81no—
337C4—81no—
338C4—882no—
339C4#1062278111yescharacteristic
340C4#1062278512yes—
341C4#1062278911yescharacteristic
342C4#1062281312yes—
343C4#1062285512yes—
344C2—22no—
345C2—162no—
346C2#1306964311yescharacteristic
347C2#1306969011yescharacteristic
348C2#1306973011yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3208C2
socleC22×C11#392
prime radicalC2×C11×#127C22
hypercenter#3208D11
hypocenterC11#10169
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3208

Complements

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

NH ≅ G/Ntype
1. #13078998C2semidirect
4. #13067287C2semidirect
5. #13067071C2semidirect
6. #13066452C2semidirect
290. C11#10169semidirect

Maximal subgroups

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

subgroupindex
#130789982
C2×#106226832
#130694572
#130672872
#130670712
#130664522
C11×#32082
#1016911