Finite Group Databasebeta

← #14656422

Subgroups — #14656422

Order 2816.

626 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 626 conjugacy classes of subgroups — too many to draw. Only its 113 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#13079744C211yesmaximal, characteristic
2#13079541C211yesmaximal, characteristic
3#13069444C211yesmaximal, characteristic
4#13067301C211yesmaximal, characteristic, complemented
5#13067297C211yesmaximal, characteristic, complemented
6#13066449C211yesmaximal, characteristic, complemented
7C11×#2868C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8—22no—
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11#10623008C2211yescharacteristic
12C11×#384—22no—
13C11×#384—22no—
14C43×C11C2211yescharacteristic
15#10622840—22no—
16#10622701—21no—
17#10622698—21no—
18#10622697—22no—
19#10622696—22no—
20#10622694—21no—
21#10622692—21no—
22#10622581—22no—
23C2×#66869—22no—
24#10622538C2211yescharacteristic
25#10622538C2211yescharacteristic
26#10622537C2211yescharacteristic
27#10622185—22no—
28#10622184—22no—
29C22×Q8×C11—21no—
30C22×Q8×C11D412yes—
31C2×#4339—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—48no—
41C2×C11×C4⋊C4—28no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4D412yes—
46C2×C42×C11—21no—
47C2×C42×C11—21no—
48C2×C42×C11D412yes—
49C2×C42×C11C2311yescharacteristic
50C2×#4325—24no—
51#66983—21no—
52#66983—21no—
53C2×#4318—21no—
54#66928—21no—
55#66927D411yescharacteristic
56C4×D44—21no—
57C4×D44—21no—
58#66922D411yescharacteristic
59#66899—24no—
60C22⋊(C11⋊C8)—21no—
61C22⋊(C11⋊C8)—21no—
62#66873—24no—
63#66872—24no—
64#66869—44no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)D412yes—
68C4⋊(C11⋊C8)D412yes—
69C4×C11⋊C8—21no—
70C4×C11⋊C8—21no—
71#10283—111nomaximal, Sylow
72C2×Q8×C11—22no—
73C2×Q8×C11—22no—
74C2×Q8×C11—44no—
75C2×Q8×C11—44no—
76C2×Q8×C11—41no—
77C2×Q8×C11—41no—
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11—22no—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C2×C22⋊D11—41no—
85#4339—42no—
86#4339—42no—
87C2×D44—21no—
88C2×D44—21no—
89C2×D44—21no—
90C2×C4×D11—41no—
91C2×Dic22—21no—
92C11×C4⋊C4—22no—
93C11×C4⋊C4—22no—
94C11×C4⋊C4—416no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C42×C11—24no—
102C42×C11—24no—
103C42×C11—22no—
104C42×C11SD1614yescomplemented
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11#4111yescharacteristic
109#4325—84no—
110(C2×D11)⋊C4—41no—
111(C2×D11)⋊C4—41no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114#4318—42no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8—41no—
118#3227—111no—
119#3206—111no—
120#2868D1111yescharacteristic, complemented
121#1962—111no—
122#1549—111no—
123#1548—111no—
124#1276—111no—
125C23×C11#12011yescharacteristic
126C22×D11—41no—
127Q8×C11—44no—
128Q8×C11—82no—
129Q8×C11—82no—
130Q8×C11—82no—
131C2×C4×C11—24no—
132C2×C4×C11—24no—
133C2×C4×C11—24no—
134C2×C4×C11—22no—
135C2×C4×C11—22no—
136C2×C4×C11—44no—
137C2×C4×C11—44no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11#12011yescharacteristic
141C2×C4×C11#12011yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12711yescharacteristic
146C2×C4×C11C2×SD1612yes—
147C2×C4×C11#13712yes—
148C22⋊D11—82no—
149C2×Dic11—41no—
150D44—42no—
151D44—42no—
152D44—42no—
153C4×D11—81no—
154C4×D11—81no—
155Dic22—42no—
156C11⋊C8—42no—
157C11⋊C8—42no—
158C11⋊C8—81no—
159#532—111no—
160C2×C4⋊Q8—22no—
161C2×C4⋊Q8C2×D1111yescharacteristic
162C2×C4⋊Q8C2×D1111yescharacteristic
163#498—221no—
164#492—221no—
165#487—221no—
166#486—221no—
167#481—222no—
168#476—222no—
169#461—222no—
170#448—222no—
171#431—111no—
172#431—111no—
173#423—111no—
174C2×#104—222no—
175#384—22no—
176#384—22no—
177C43C2×D1111yescharacteristic
178#333—222no—
179#332—222no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11#39211yescharacteristic
183C22×C11#44812yes—
184C2×D11—81no—
185C2×D11—81no—
186C2×D11—81no—
187C4×C11—28no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—82no—
191C4×C11—82no—
192C4×C11#45312yes—
193C4×C11#45612yes—
194C4×C11#46112yes—
195C4×C11#49211yescharacteristic
196C4×C11#49711yescharacteristic
197Dic11—81no—
198C2×#41—221no—
199C22×Q8—21no—
200C22×Q8C22⋊D1112yes—
201C2×SD16—224no—
202C2×M16—221no—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—48no—
212C4⋊Q8—111no—
213#127—111no—
214#124—221no—
215#121—221no—
216#121—221no—
217C4×D4—221no—
218C4×D4—221no—
219C2×C4⋊C4—28no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4C22⋊D1112yes—
224C2×C42—21no—
225C2×C42—21no—
226C2×C42C22⋊D1112yes—
227C2×C42C22×D1111yescharacteristic
228#106—224no—
229C4⋊C8—112no—
230C4⋊C8—112no—
231C4⋊C8—221no—
232C4⋊C8—221no—
233#104—444no—
234#103—224no—
235#102—224no—
236C22⋊C8—221no—
237C22⋊C8—221no—
238C4×C8—221no—
239C4×C8—221no—
240C2×C11—22no—
241C2×C11#200211yescharacteristic
242C2×C11#200511yescharacteristic
243C2×C11#201311yescharacteristic
244D11—161no—
245#41—442no—
246#41—442no—
247C2×Q8—22no—
248C2×Q8—22no—
249C2×Q8—44no—
250C2×Q8—44no—
251C2×Q8—41no—
252C2×Q8—41no—
253C2×Q8—221no—
254C2×D4—221no—
255C2×D4—221no—
256C2×D4—221no—
257C2×D4—441no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—441no—
262C22×C4C2×C22⋊D1111yescharacteristic
263C22×C4C2×C22⋊D1111yescharacteristic
264C22×C4C2×C22⋊D1111yescharacteristic
265SD16—884no—
266M16—442no—
267C2×C8—222no—
268C2×C8—222no—
269C2×C8—441no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—416no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—221no—
280C4⋊C4—221no—
281C22⋊C4—441no—
282C22⋊C4—441no—
283C42—24no—
284C42—24no—
285C42—22no—
286C42#432514yescomplemented
287C42D4×D1111yescharacteristic
288C42D4×D1111yescharacteristic
289C42D4×D1111yescharacteristic
290C42#434111yescharacteristic
291C11#1028311yescharacteristic, complemented, Sylow
292C23—441no—
293C23#6700611yescharacteristic
294Q8—44no—
295Q8—82no—
296Q8—82no—
297Q8—82no—
298Q8—442no—
299D4—442no—
300D4—442no—
301D4—442no—
302D4—882no—
303C2×C4—24no—
304C2×C4—24no—
305C2×C4—24no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—44no—
309C2×C4—44no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—441no—
313C2×C4—881no—
314C2×C4—881no—
315C2×C4#6699011yescharacteristic
316C2×C4#6699011yescharacteristic
317C2×C4#6699111yescharacteristic
318C2×C4#6699211yescharacteristic
319C2×C4#6699211yescharacteristic
320C2×C4#6699311yescharacteristic
321C2×C4C2×#432512yes—
322C2×C4#6699512yes—
323C8—442no—
324C8—442no—
325C8—881no—
326C22—21no—
327C22—21no—
328C22—881no—
329C22—881no—
330C22—881no—
331C22#1062283611yescharacteristic
332C22#1062284012yes—
333C4—28no—
334C4—21no—
335C4—21no—
336C4—82no—
337C4—82no—
338C4—881no—
339C4#1062269012yes—
340C4#1062269612yes—
341C4#1062269811yescharacteristic
342C4#1062269911yescharacteristic
343C4#1062270812yes—
344C2—22no—
345C2—1761no—
346C2#1306963111yescharacteristic
347C2#1306965211yescharacteristic
348C2#1306969911yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2868C2
socleC22×C11#392
prime radical#10623008C22
hypercenter#2868D11
hypocenterC11#10283
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2868

Complements

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

NH ≅ G/Ntype
4. #13067301C2semidirect
5. #13067297C2semidirect
6. #13066449C2semidirect
7. C11×#2868C2semidirect
104. C42×C11SD16semidirect
120. #2868D11semidirect
286. C42#4325semidirect
291. C11#10283semidirect

Maximal subgroups

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

subgroupindex
#130797442
#130795412
#130694442
#130673012
#130672972
#130664492
C11×#28682
#1028311