Finite Group Databasebeta

← #14669800

Subgroups — #14669800

Order 2816.

420 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 97 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#13077334C211yesmaximal, characteristic
2#13070281C211yesmaximal, characteristic
3#13068660C212yesmaximal, complemented
4#13066736C212yesmaximal, complemented
5C11×#2126C211yesmaximal, characteristic
6C11×#532C2211yescharacteristic
7C2×#67001C411yescharacteristic, complemented
8C2×#67001C2211yescharacteristic
9C11×#410C2212yes—
10#10622853C2212yes—
11#10622847C411yescharacteristic, complemented
12#10622847C2211yescharacteristic
13#10622624—22no—
14#10622624—22no—
15#10622611—22no—
16#10622537C411yescharacteristic, complemented
17C2×#66867C411yescharacteristic, complemented
18C11×#354—21no—
19C11×#353—21no—
20#10622183—21no—
21#10622179—21no—
22#10622169—22no—
23C2×C11×#41C2×C411yescharacteristic
24C2×C11×#41C2311yescharacteristic
25C11×C4⋊Q8Q811yescharacteristic
26C11×#127D411yescharacteristic
27C11×#124D411yescharacteristic
28C11×#124Q811yescharacteristic
29C11×#121—22no—
30C4×D4×C11—22no—
31C11×#117—22no—
32C2×C42×C11C2×C411yescharacteristic
33#67001—42no—
34#67001—42no—
35#66979—22no—
36C2×#4318—21no—
37C2×#4318C2×C411yescharacteristic
38C2×#4318C2×C411yescharacteristic
39C2×#4318D412yes—
40C22×C11⋊C8—21no—
41C22×C11⋊C8C2×C411yescharacteristic
42C22×C11⋊C8C2×C411yescharacteristic
43C22×C11⋊C8D412yes—
44C11×#99—22no—
45C11×#99—22no—
46#66898—22no—
47#66898—22no—
48C22⋊(C11⋊C8)—22no—
49C22⋊(C11⋊C8)—22no—
50#66872—42no—
51#66871—42no—
52C4⋊(C11⋊C8)—22no—
53#66867—21no—
54#66867—21no—
55#12808—111nomaximal, Sylow
56C11×#41—41no—
57C11×#41—41no—
58C11×#41—41no—
59C11×#41—41no—
60C2×Q8×C11C4⋊C411yescharacteristic
61C2×Q8×C11C2×Q811yescharacteristic
62C2×D4×C11—21no—
63C2×D4×C11—22no—
64C2×D4×C11C4⋊C411yescharacteristic
65C2×D4×C11C2×D411yescharacteristic
66C2×D4×C11#4112yes—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D412yes—
71C11×C4⋊C4—22no—
72C11×C4⋊C4—42no—
73C11×C22⋊C4—22no—
74C11×C22⋊C4—22no—
75C11×C22⋊C4—42no—
76C42×C11—21no—
77C42×C11—42no—
78C42×C11C4⋊C411yescharacteristic
79C42×C11C4⋊C411yescharacteristic
80C22⋊Dic11—42no—
81C4⋊Dic11—42no—
82C4×Dic11—42no—
83#4318—41no—
84#4318—42no—
85#4318—41no—
86#4318—42no—
87C2×C11⋊C8—22no—
88C2×C11⋊C8—22no—
89C2×C11⋊C8—22no—
90C2×C11⋊C8—21no—
91C2×C11⋊C8—21no—
92C2×C11⋊C8—41no—
93C2×C11⋊C8—42no—
94C2×C11⋊C8C22⋊C411yescharacteristic
95C2×C11⋊C8C22⋊C412yes—
96C2×C11⋊C8C22⋊C411yescharacteristic
97#2932—111no—
98#2126—111no—
99#2126D1111yescharacteristic
100#1812—112no—
101#1391—112no—
102C23×C11—21no—
103C23×C11#11711yescharacteristic
104C23×C11#12112yes—
105Q8×C11—41no—
106Q8×C11—41no—
107D4×C11—41no—
108D4×C11—42no—
109D4×C11—41no—
110D4×C11—42no—
111D4×C11—82no—
112C2×C4×C11—21no—
113C2×C4×C11—22no—
114C2×C4×C11—21no—
115C2×C4×C11—22no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—81no—
122C2×C4×C11—82no—
123C2×C4×C11C2×C22⋊C411yescharacteristic
124C2×C4×C11C2×C4⋊C411yescharacteristic
125C2×C4×C11C22⋊Q812yes—
126C2×Dic11—82no—
127C11⋊C8—21no—
128C11⋊C8—22no—
129C11⋊C8—41no—
130C11⋊C8—41no—
131C11⋊C8#9912yes—
132C2×#131—111no—
133C2×#131—111no—
134#532C2×D1111yescharacteristic
135#435—222no—
136#435—222no—
137#427—222no—
138#423—111no—
139#410—112no—
140#410C2×D1112yes—
141#408—111no—
142#408—111no—
143C2×#97—111no—
144#354—21no—
145#354—221no—
146#353—21no—
147#353—221no—
148H(3,ℤ/4)—222no—
149C22×C11—22no—
150C22×C11—21no—
151C22×C11—41no—
152C22×C11—42no—
153C22×C11—42no—
154C22×C11—41no—
155C22×C11#38011yescharacteristic
156C4×C11—21no—
157C4×C11—22no—
158C4×C11—41no—
159C4×C11—41no—
160C4×C11—41no—
161C4×C11—162no—
162C4×C11C2×#9911yescharacteristic
163C4×C11#41011yescharacteristic
164Dic11—162no—
165C2×#41C4×D1111yescharacteristic
166C2×#41C22×D1111yescharacteristic
167#131—442no—
168#131—442no—
169C2×M16—111no—
170C2×M16—112no—
171C2×M16—111no—
172C2×M16—221no—
173C22×C8—111no—
174C22×C8—112no—
175C22×C8—111no—
176C22×C8—221no—
177C4⋊Q8Dic2211yescharacteristic
178#127C22⋊D1111yescharacteristic
179#124Dic2211yescharacteristic
180#124C22⋊D1111yescharacteristic
181#121—22no—
182C4×D4—22no—
183#117—22no—
184#117—222no—
185C2×C42C4×D1111yescharacteristic
186#107—442no—
187#106—442no—
188C4⋊C8—222no—
189#99—22no—
190#99—22no—
191#99—222no—
192#99—222no—
193C22⋊C8—222no—
194C22⋊C8—222no—
195#97—221no—
196#97—221no—
197C2×C11—21no—
198C2×C11—42no—
199C2×C11—41no—
200C2×C11—81no—
201C2×C11#179911yescharacteristic
202#41—41no—
203#41—41no—
204#41—41no—
205#41—41no—
206C2×Q8Dic11⋊C411yescharacteristic
207C2×Q8C2×Dic2211yescharacteristic
208C2×D4—21no—
209C2×D4—22no—
210C2×D4Dic11⋊C411yescharacteristic
211C2×D4#434112yes—
212C2×D4C2×C22⋊D1111yescharacteristic
213C22×C4—21no—
214C22×C4—21no—
215C22×C4C2×C4×D1111yescharacteristic
216C22×C4D4×D1112yes—
217M16—442no—
218M16—442no—
219M16—441no—
220M16—441no—
221C2×C8—111no—
222C2×C8—111no—
223C2×C8—112no—
224C2×C8—222no—
225C2×C8—222no—
226C2×C8—222no—
227C2×C8—221no—
228C2×C8—221no—
229C2×C8—442no—
230C2×C8—441no—
231C4⋊C4—22no—
232C4⋊C4—42no—
233C4⋊C4—442no—
234C22⋊C4—22no—
235C22⋊C4—22no—
236C22⋊C4—42no—
237C22⋊C4—442no—
238C42—21no—
239C42—42no—
240C42—442no—
241C42Dic11⋊C411yescharacteristic
242C42Dic11⋊C411yescharacteristic
243C11#1280811yescharacteristic, complemented, Sylow
244C23—21no—
245C23#6693011yescharacteristic
246C23#6699212yes—
247Q8—41no—
248Q8—41no—
249D4—42no—
250D4—41no—
251D4—41no—
252D4—42no—
253D4—82no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—81no—
264C2×C4—82no—
265C2×C4—882no—
266C2×C4#6693112yes—
267C2×C4C22⋊C4×D1111yescharacteristic
268C2×C4C2×Dic11⋊C411yescharacteristic
269C8—112no—
270C8—221no—
271C8—222no—
272C8—441no—
273C8—441no—
274C22—22no—
275C22—21no—
276C22—41no—
277C22—42no—
278C22—42no—
279C22—41no—
280C22#1062255511yescharacteristic
281C4—22no—
282C4—21no—
283C4—41no—
284C4—41no—
285C4—41no—
286C4—162no—
287C4—1762no—
288C4#1062235311yescharacteristic
289C4D11×#9911yescharacteristic
290C2—21no—
291C2—42no—
292C2—41no—
293C2—81no—
294C2#1306860211yescharacteristic
subgroupG/H
centerC4#10622353
commutatorC22×C4×C11C22×C4
FrattiniC2×#41C22×D11
FittingC11×#2126C2
socleC2×C11#1799
prime radicalC11×#532C22
cosocleC2×C11×#41C23
hypercenter#2126D11
hypocenterC11#12808
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #2126

Complements

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

NH ≅ G/Ntype
3. #13068660C2semidirect
4. #13066736C2semidirect
7. C2×#67001C4semidirect
11. #10622847C4semidirect
16. #10622537C4semidirect
17. C2×#66867C4semidirect
243. C11#12808semidirect

Maximal subgroups

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

subgroupindex
#130773342
#130702812
#130686602
#130667362
C11×#21262
#1280811