Finite Group Databasebeta

← #14656425

Subgroups — #14656425

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#13079746C211yesmaximal, characteristic
2#13079543C211yesmaximal, characteristic
3#13077014C211yesmaximal, characteristic, complemented
4#13069444C211yesmaximal, characteristic
5#13067300C211yesmaximal, characteristic, complemented
6#13067296C211yesmaximal, characteristic, complemented
7C11×#1276C211yesmaximal, characteristic, complemented
8#10623008C2211yescharacteristic
9C2×#66922—22no—
10C2×#66922C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C11×#431C2211yescharacteristic
14C43×C11C2211yescharacteristic
15#10622548—22no—
16#10622548—22no—
17C2×#66869—22no—
18#10622537C2211yescharacteristic
19#10622455—22no—
20#10622454—22no—
21#10622351—22no—
22#10622348—22no—
23#10622307—21no—
24#10622306—21no—
25#10622294—21no—
26#10622293—21no—
27#10622120—22no—
28#10622119—22no—
29C2×#4339—21no—
30C22×Dic22—21no—
31C22×Dic22D412yes—
32C2×C42×C11—21no—
33C2×C42×C11—21no—
34C2×C42×C11D412yes—
35C2×C42×C11C2311yescharacteristic
36#66983—21no—
37#66983—21no—
38C2×C4⋊Dic11—28no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11D412yes—
43C2×#4318—21no—
44C2×#4314—24no—
45#66928—21no—
46#66927D411yescharacteristic
47C4×D44—21no—
48C4×D44—21no—
49#66922—21no—
50#66922—21no—
51#66922—21no—
52#66922—21no—
53#66922—21no—
54#66922—21no—
55#66922—21no—
56#66922—21no—
57#66922—48no—
58#66922D411yescharacteristic
59C11×C4⋊C8D412yes—
60C11×C4⋊C8D412yes—
61C11×C22⋊C8—21no—
62C11×C22⋊C8—21no—
63C4×C8×C11—21no—
64C4×C8×C11—21no—
65#66885—24no—
66#66881—24no—
67#66880—24no—
68#66869—44no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)—21no—
71#10283—111nomaximal, Sylow
72C22×C4×C11—22no—
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C2×C22⋊D11—41no—
77C22×Dic11—22no—
78C22×Dic11—22no—
79#4339—42no—
80#4339—42no—
81C2×D44—21no—
82C2×D44—21no—
83C2×D44—21no—
84C2×C4×D11—41no—
85C2×Dic22—22no—
86C2×Dic22—21no—
87C2×Dic22—22no—
88C2×Dic22—44no—
89C2×Dic22—44no—
90C2×Dic22—41no—
91C2×Dic22—41no—
92C2×C8×C11—22no—
93C2×C8×C11—22no—
94C42×C11—24no—
95C42×C11—24no—
96C42×C11—22no—
97C42×C11SD1614yescomplemented
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11#4111yescharacteristic
102(C2×D11)⋊C4—41no—
103(C2×D11)⋊C4—41no—
104C4⋊Dic11—21no—
105C4⋊Dic11—21no—
106C4⋊Dic11—22no—
107C4⋊Dic11—22no—
108C4⋊Dic11—416no—
109C4⋊Dic11—41no—
110C4⋊Dic11—41no—
111C4⋊Dic11—41no—
112C4⋊Dic11—41no—
113C4⋊Dic11—41no—
114C4⋊Dic11—41no—
115#4318—42no—
116C2×C11⋊C8—41no—
117#4314—84no—
118#3227—111no—
119#3206—111no—
120#2868—111no—
121#1962—111no—
122#1549—111no—
123#1548—111no—
124#1276D1111yescharacteristic, complemented
125C23×C11#12011yescharacteristic
126C22×D11—41no—
127C2×C4×C11—24no—
128C2×C4×C11—24no—
129C2×C4×C11—24no—
130C2×C4×C11—22no—
131C2×C4×C11—22no—
132C2×C4×C11#12011yescharacteristic
133C2×C4×C11#12011yescharacteristic
134C2×C4×C11#12111yescharacteristic
135C2×C4×C11#12111yescharacteristic
136C2×C4×C11#12111yescharacteristic
137C2×C4×C11#12711yescharacteristic
138C2×C4×C11C2×SD1612yes—
139C2×C4×C11#13712yes—
140C22⋊D11—82no—
141C2×Dic11—44no—
142C2×Dic11—44no—
143C2×Dic11—42no—
144C2×Dic11—41no—
145C2×Dic11—42no—
146D44—42no—
147D44—42no—
148D44—42no—
149C4×D11—81no—
150C4×D11—81no—
151Dic22—44no—
152Dic22—42no—
153Dic22—82no—
154Dic22—82no—
155Dic22—82no—
156C8×C11—42no—
157C8×C11—42no—
158C11⋊C8—81no—
159#532—111no—
160C2×C4⋊Q8—111no—
161C2×C4⋊Q8—111no—
162C2×C4⋊Q8—222no—
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#431C2×D1111yescharacteristic
172#431C2×D1111yescharacteristic
173#423—111no—
174C2×#104—222no—
175#384—222no—
176#384—222no—
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#45312yes—
191C4×C11#45612yes—
192C4×C11#46112yes—
193C4×C11#49211yescharacteristic
194C4×C11#49711yescharacteristic
195Dic11—82no—
196Dic11—82no—
197Dic11—81no—
198C2×#41—221no—
199C22×Q8—112no—
200C22×Q8—221no—
201C2×SD16—224no—
202C2×M16—221no—
203C4⋊Q8—111no—
204C4⋊Q8—221no—
205C4⋊Q8—221no—
206C4⋊Q8—221no—
207C4⋊Q8—221no—
208C4⋊Q8—221no—
209C4⋊Q8—221no—
210C4⋊Q8—221no—
211C4⋊Q8—221no—
212C4⋊Q8—448no—
213#127—111no—
214#124—221no—
215#121—221no—
216#121—221no—
217C4×D4—221no—
218C4×D4—221no—
219C2×C4⋊C4—112no—
220C2×C4⋊C4—228no—
221C2×C4⋊C4—221no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4—221no—
224C2×C42—21no—
225C2×C42—21no—
226C2×C42D4412yes—
227C2×C42C22×D1111yescharacteristic
228#106—224no—
229C4⋊C8—221no—
230C4⋊C8—221no—
231C4⋊C8D4412yes—
232C4⋊C8D4412yes—
233#104—444no—
234#103—224no—
235#102—224no—
236C22⋊C8—21no—
237C22⋊C8—21no—
238C4×C8—21no—
239C4×C8—21no—
240C2×C11—22no—
241C2×C11#200211yescharacteristic
242C2×C11#200511yescharacteristic
243C2×C11#201311yescharacteristic
244D11—161no—
245#41—442no—
246#41—442no—
247C2×Q8—222no—
248C2×Q8—221no—
249C2×Q8—222no—
250C2×Q8—444no—
251C2×Q8—444no—
252C2×Q8—441no—
253C2×Q8—441no—
254C2×D4—221no—
255C2×D4—221no—
256C2×D4—221no—
257C2×D4—441no—
258C22×C4—22no—
259C22×C4—222no—
260C22×C4—222no—
261C22×C4—441no—
262C22×C4C2×D4411yescharacteristic
263C22×C4D4×D1111yescharacteristic
264C22×C4D4×D1111yescharacteristic
265SD16—884no—
266M16—442no—
267C2×C8—22no—
268C2×C8—22no—
269C2×C8—441no—
270C4⋊C4—222no—
271C4⋊C4—221no—
272C4⋊C4—221no—
273C4⋊C4—222no—
274C4⋊C4—4416no—
275C4⋊C4—441no—
276C4⋊C4—441no—
277C4⋊C4—441no—
278C4⋊C4—441no—
279C4⋊C4—441no—
280C4⋊C4—441no—
281C22⋊C4—441no—
282C22⋊C4—441no—
283C42—24no—
284C42—24no—
285C42—22no—
286C42#431414yescomplemented
287C42C2×D4411yescharacteristic
288C42C2×D4411yescharacteristic
289C42D4×D1111yescharacteristic
290C42#434311yescharacteristic
291C11#1028311yescharacteristic, complemented, Sylow
292C23—441no—
293C23#6693511yescharacteristic
294Q8—444no—
295Q8—442no—
296Q8—882no—
297Q8—882no—
298Q8—882no—
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—444no—
309C2×C4—444no—
310C2×C4—441no—
311C2×C4—442no—
312C2×C4—442no—
313C2×C4—881no—
314C2×C4—881no—
315C2×C4#6692711yescharacteristic
316C2×C4#6693511yescharacteristic
317C2×C4#6693511yescharacteristic
318C2×C4#6694811yescharacteristic
319C2×C4#6694811yescharacteristic
320C2×C4#6694811yescharacteristic
321C2×C4C2×#431412yes—
322C2×C4#6696212yes—
323C8—42no—
324C8—42no—
325C8—881no—
326C22—21no—
327C22—21no—
328C22—881no—
329C22—881no—
330C22—881no—
331C22#1062228411yescharacteristic
332C22#1062235112yes—
333C4—28no—
334C4—21no—
335C4—21no—
336C4—882no—
337C4—882no—
338C4—881no—
339C4#1062230611yescharacteristic
340C4#1062232811yescharacteristic
341C4#1062243512yes—
342C4#1062243912yes—
343C4#1062245412yes—
344C2—22no—
345C2—1761no—
346C2#1306963411yescharacteristic
347C2#1306965511yescharacteristic
348C2#1306970111yescharacteristic
subgroupG/H
centerC22#10622284
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1276C2
socleC22×C11#392
prime radical#10623008C22
hypercenter#1276D11
hypocenterC11#10283
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
3. #13077014C2semidirect
5. #13067300C2semidirect
6. #13067296C2semidirect
7. C11×#1276C2semidirect
97. C42×C11SD16semidirect
124. #1276D11semidirect
286. C42#4314semidirect
291. C11#10283semidirect

Maximal subgroups

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

subgroupindex
#130797462
#130795432
#130770142
#130694442
#130673002
#130672962
C11×#12762
#1028311