Finite Group Databasebeta

← #14656433

Subgroups — #14656433

Order 2816.

542 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 109 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#13079741C211yesmaximal, characteristic
2#13076993C211yesmaximal, characteristic, complemented
3#13069445C211yesmaximal, characteristic
4#13067301C211yesmaximal, characteristic, complemented
5#13067300C211yesmaximal, characteristic, complemented
6#13066448C211yesmaximal, characteristic, complemented
7C11×#3227C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#498—21no—
12C11×#486—21no—
13C11×#481—22no—
14C11×#476—22no—
15C11×#431C2211yescharacteristic
16C2×#66901—22no—
17#10622843—22no—
18#10622692—21no—
19#10622683—21no—
20#10622647—22no—
21#10622621—22no—
22#10622590—22no—
23#10622587—22no—
24C42×Dic11C2211yescharacteristic
25#10622538C2211yescharacteristic
26#10622537C2211yescharacteristic
27#10622185—22no—
28#10622120—22no—
29C2×C11×#41—21no—
30C22×Q8×C11—21no—
31C22×Dic22—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8D411yescharacteristic
37C11×#127D411yescharacteristic
38C11×#124—21no—
39C11×#121—21no—
40C11×#121—21no—
41C4×D4×C11—21no—
42C4×D4×C11—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4D412yes—
45C2×C42×C11C2311yescharacteristic
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11D412yes—
48C2×C4×Dic11—21no—
49C2×C4×Dic11—21no—
50C2×C4×Dic11D412yes—
51C2×#4318—21no—
52#66922—21no—
53#66922—21no—
54#66922—21no—
55#66922—21no—
56C11×#106—24no—
57C11×C4⋊C8D412yes—
58C11×#102—24no—
59C11×C22⋊C8—21no—
60C4×C8×C11—21no—
61#66901—44no—
62#66896—24no—
63C11⋊#95—28no—
64C22⋊(C11⋊C8)—21no—
65#66872—24no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)D412yes—
69C4×C11⋊C8—21no—
70#10285—111nomaximal, Sylow
71C11×#41—42no—
72C11×#41—42no—
73C2×Q8×C11—21no—
74C2×Q8×C11—44no—
75C2×Q8×C11—41no—
76C2×Q8×C11—41no—
77C2×D4×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—41no—
81C22×C4×C11—22no—
82C22×C4×C11—41no—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×Dic11—22no—
87C22×Dic11—22no—
88C2×Dic22—44no—
89C2×Dic22—41no—
90C2×Dic22—41no—
91C2×C8×C11—22no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—22no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—41no—
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11C2×D411yescharacteristic
103C42×C11#4111yescharacteristic
104C4⋊Dic11—22no—
105C4⋊Dic11—22no—
106C4⋊Dic11—41no—
107C4⋊Dic11—41no—
108C4×Dic11—22no—
109C4×Dic11—42no—
110C4×Dic11—42no—
111C4×Dic11SD1614yes—
112#4318—42no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—41no—
115#3227—111no—
116#3227D1111yescharacteristic
117#2862—111no—
118#1962—111no—
119#1549—111no—
120#1549—111no—
121#1276—111no—
122C23×C11—41no—
123C23×C11#12011yescharacteristic
124Q8×C11—42no—
125Q8×C11—82no—
126Q8×C11—82no—
127D4×C11—42no—
128D4×C11—42no—
129D4×C11—42no—
130D4×C11—82no—
131C2×C4×C11—22no—
132C2×C4×C11—22no—
133C2×C4×C11—44no—
134C2×C4×C11—41no—
135C2×C4×C11—42no—
136C2×C4×C11—81no—
137C2×C4×C11—81no—
138C2×C4×C11#12011yescharacteristic
139C2×C4×C11#12011yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12111yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11#12711yescharacteristic
144C2×C4×C11C2×SD1612yes—
145C2×C4×C11#13712yes—
146C2×Dic11—24no—
147C2×Dic11—42no—
148C2×Dic11—42no—
149C2×Dic11—44no—
150C2×Dic11—42no—
151Dic22—82no—
152Dic22—82no—
153C8×C11—42no—
154C11⋊C8—42no—
155C11⋊C8—81no—
156#532C2×D1111yescharacteristic
157C2×C4⋊Q8—111no—
158C2×C4⋊Q8C2×D1111yescharacteristic
159#498—21no—
160#498—221no—
161#486—21no—
162#486—221no—
163#481—22no—
164#481—222no—
165#476—22no—
166#476—222no—
167#431—111no—
168#431C2×D1111yescharacteristic
169#423—111no—
170C2×#104—222no—
171#391—222no—
172#391—222no—
173#382—222no—
174C43—111no—
175#332—222no—
176#332—222no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—81no—
180C22×C11—81no—
181C22×C11—81no—
182C22×C11#39211yescharacteristic
183C22×C11#44812yes—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—82no—
187C4×C11—81no—
188C4×C11#45412yes—
189C4×C11#45412yes—
190C4×C11#46112yes—
191C4×C11#49211yescharacteristic
192C4×C11#49711yescharacteristic
193Dic11—44no—
194Dic11—82no—
195C2×#41—21no—
196C22×Q8—21no—
197C22×Q8—221no—
198C2×M16—221no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—221no—
204C4⋊Q8—221no—
205C4⋊Q8—221no—
206C4⋊Q8—221no—
207C4⋊Q8C22⋊D1111yescharacteristic
208#127C22⋊D1111yescharacteristic
209#124—21no—
210#121—21no—
211#121—21no—
212C4×D4—21no—
213C4×D4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—112no—
216C2×C4⋊C4—221no—
217C2×C4⋊C4C22⋊D1112yes—
218C2×C42—112no—
219C2×C42—221no—
220C2×C42—221no—
221C2×C42C22×D1111yescharacteristic
222#106—24no—
223#106—224no—
224C4⋊C8—112no—
225C4⋊C8—221no—
226C4⋊C8—221no—
227C4⋊C8C22⋊D1112yes—
228#104—444no—
229#102—24no—
230#102—224no—
231C22⋊C8—21no—
232C22⋊C8—221no—
233C4×C8—21no—
234C4×C8—221no—
235#95—228no—
236C2×C11—22no—
237C2×C11—161no—
238C2×C11#200311yescharacteristic
239C2×C11#200311yescharacteristic
240C2×C11#201311yescharacteristic
241#41—42no—
242#41—42no—
243C2×Q8—21no—
244C2×Q8—44no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—444no—
248C2×Q8—441no—
249C2×Q8—441no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—41no—
254C22×C4—22no—
255C22×C4—41no—
256C22×C4—222no—
257C22×C4—222no—
258C22×C4D4×D1111yescharacteristic
259C22×C4D4×D1111yescharacteristic
260C22×C4C2×C22⋊D1111yescharacteristic
261M16—442no—
262C2×C8—22no—
263C2×C8—222no—
264C2×C8—441no—
265C4⋊C4—21no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—21no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—222no—
272C4⋊C4—222no—
273C4⋊C4—441no—
274C4⋊C4—441no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C42—114no—
278C42—222no—
279C42—442no—
280C42—442no—
281C42D4×D1111yescharacteristic
282C42#434111yescharacteristic
283C42C2×C22⋊D1111yescharacteristic
284C42C2×C22⋊D1111yescharacteristic
285C11#1028511yescharacteristic, complemented, Sylow
286C23—41no—
287C23#6699011yescharacteristic
288Q8—42no—
289Q8—82no—
290Q8—82no—
291Q8—882no—
292Q8—882no—
293D4—42no—
294D4—42no—
295D4—42no—
296D4—82no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—44no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—224no—
305C2×C4—442no—
306C2×C4—442no—
307C2×C4—444no—
308C2×C4—442no—
309C2×C4SD16×D1112yes—
310C2×C4#6696812yes—
311C2×C4#6699011yescharacteristic
312C2×C4#6699111yescharacteristic
313C2×C4#6699211yescharacteristic
314C2×C4#6699211yescharacteristic
315C2×C4#6699311yescharacteristic
316C2×C4#6700611yescharacteristic
317C8—42no—
318C8—442no—
319C8—881no—
320C22—21no—
321C22—21no—
322C22—81no—
323C22—81no—
324C22—81no—
325C22#1062278312yes—
326C22#1062283611yescharacteristic
327C4—21no—
328C4—21no—
329C4—82no—
330C4—81no—
331C4—444no—
332C4—882no—
333C4#1062277512yes—
334C4#1062278011yescharacteristic
335C4#1062278811yescharacteristic
336C4#1062281412yes—
337C4#1062285812yes—
338C2—22no—
339C2—161no—
340C2#1306963511yescharacteristic
341C2#1306963611yescharacteristic
342C2#1306969711yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3227C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#3227D11
hypocenterC11#10285
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3227

Complements

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

NH ≅ G/Ntype
2. #13076993C2semidirect
4. #13067301C2semidirect
5. #13067300C2semidirect
6. #13066448C2semidirect
285. C11#10285semidirect

Maximal subgroups

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

subgroupindex
#130797412
#130769932
#130694452
#130673012
#130673002
#130664482
C11×#32272
#1028511