Finite Group Databasebeta

← #14658406

Subgroups — #14658406

Order 2816.

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

normal subgroups only

This group has 322 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#13069459C211yesmaximal, characteristic
2#13069392C211yesmaximal, characteristic
3#13067369C211yesmaximal, characteristic
4#13067287C211yesmaximal, characteristic
5C2×#10622120C211yesmaximal, characteristic
6#13066490C211yesmaximal, characteristic
7C11×#1571C211yesmaximal, characteristic
8C2×#66922C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×#66888—21no—
13C2×#66888—21no—
14C2×#66883—21no—
15#10622537C2211yescharacteristic
16C2×C4⋊(C11⋊C8)C2211yescharacteristic
17C4×#4318C2211yescharacteristic
18C11×#335—22no—
19#10622190—21no—
20#10622124—21no—
21#10622124—21no—
22#10622120—22no—
23#10622118—21no—
24#10622117—21no—
25C22×Dic22—21no—
26C2×C11×M16—21no—
27C22×C8×C11—21no—
28C2×C42×C11C2311yescharacteristic
29C2×C4⋊Dic11—21no—
30C2×C4⋊Dic11Q812yes—
31C2×#4318—21no—
32C2×#4318D411yescharacteristic
33C2×#4318D411yescharacteristic
34C22×C11⋊C8—21no—
35#66922—21no—
36#66922—21no—
37#66922—21no—
38#66922—21no—
39C11×C4⋊C8—21no—
40C11×C4⋊C8—21no—
41C11×C4⋊C8—21no—
42C11×C4⋊C8D411yescharacteristic
43C11×C4⋊C8D411yescharacteristic
44C11×C4⋊C8D412yes—
45C11×C22⋊C8—21no—
46C4×C8×C11—21no—
47#66888—42no—
48#66888—42no—
49#66883—42no—
50C4⋊(C11⋊C8)—21no—
51C4⋊(C11⋊C8)—21no—
52C4⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)—21no—
54#66867—21no—
55C4×C11⋊C8—21no—
56#10604—111nomaximal, Sylow
57C22×C4×C11C2×D411yescharacteristic
58C22×C4×C11C2×Q811yescharacteristic
59C22×C4×C11#4111yescharacteristic
60C22×Dic11—22no—
61C2×Dic22—41no—
62C2×Dic22—41no—
63C2×Dic22—41no—
64C2×Dic22—41no—
65C2×Dic22—41no—
66C2×Dic22—41no—
67C11×M16—41no—
68C11×M16—41no—
69C2×C8×C11—21no—
70C2×C8×C11—21no—
71C2×C8×C11—22no—
72C2×C8×C11—41no—
73C2×C8×C11—41no—
74C2×C8×C11—41no—
75C42×C11C2×D411yescharacteristic
76C42×C11C2×D411yescharacteristic
77C42×C11#4111yescharacteristic
78C42×C11#4111yescharacteristic
79C4⋊Dic11—22no—
80C4⋊Dic11—22no—
81C4⋊Dic11—41no—
82C4⋊Dic11—41no—
83#4318—21no—
84#4318—21no—
85#4318—21no—
86#4318—41no—
87#4318—41no—
88#4318D812yes—
89C2×C11⋊C8—21no—
90C2×C11⋊C8—21no—
91C2×C11⋊C8—41no—
92C2×C11⋊C8—41no—
93C2×C11⋊C8—81no—
94#1966—111no—
95#1950—111no—
96#1571D1111yescharacteristic
97#1565—111no—
98#1546—111no—
99C2×#332—111no—
100#1292—111no—
101C23×C11C22⋊Q811yescharacteristic
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—41no—
105C2×C4×C11#12111yescharacteristic
106C2×C4×C11#12111yescharacteristic
107C2×C4×C11#12111yescharacteristic
108C2×C4×C11C22⋊Q811yescharacteristic
109C2×C4×C11C22⋊Q811yescharacteristic
110C2×C4×C11#12611yescharacteristic
111C2×C4×C11C2×D811yescharacteristic
112C2×C4×C11#13511yescharacteristic
113C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
114C2×C4×C11#13711yescharacteristic
115C2×Dic11—42no—
116C2×Dic11—42no—
117C2×Dic11—42no—
118Dic22—81no—
119Dic22—81no—
120Dic22—81no—
121Dic22—81no—
122C8×C11—42no—
123C8×C11—41no—
124C8×C11—41no—
125C8×C11—81no—
126C11⋊C8—22no—
127C11⋊C8—41no—
128C11⋊C8—81no—
129C11⋊C8—81no—
130C2×C4⋊Q8—111no—
131#431C2×D1111yescharacteristic
132C2×#108—221no—
133#423—111no—
134#423C2×D1111yescharacteristic
135C2×C4⋊C8—111no—
136C2×C4⋊C8C2×D1111yescharacteristic
137C2×#101—221no—
138C2×#101—221no—
139C4×M16—111no—
140#341—221no—
141#335—22no—
142#335—221no—
143#334—221no—
144#332—221no—
145#332—221no—
146#332—222no—
147C22×C11—21no—
148C22×C11—21no—
149C22×C11#39611yescharacteristic
150C22×C11#47411yescharacteristic
151C22×C11#47811yescharacteristic
152C4×C11—21no—
153C4×C11—21no—
154C4×C11—21no—
155C4×C11#45911yescharacteristic
156C4×C11#46411yescharacteristic
157C4×C11#46611yescharacteristic
158C4×C11#46811yescharacteristic
159C4×C11#47111yescharacteristic
160C4×C11#47311yescharacteristic
161Dic11—82no—
162C22×Q8—221no—
163C2×M16—21no—
164C2×M16—111no—
165C2×M16—111no—
166C2×M16—221no—
167C22×C8—21no—
168C22×C8—221no—
169C4⋊Q8—221no—
170C4⋊Q8—221no—
171C4⋊Q8—221no—
172C4⋊Q8—221no—
173C2×C4⋊C4—112no—
174C2×C4⋊C4—221no—
175C2×C42C22×D1111yescharacteristic
176#108—442no—
177C4⋊C8—21no—
178C4⋊C8—21no—
179C4⋊C8—21no—
180C4⋊C8—221no—
181C4⋊C8—221no—
182C4⋊C8—221no—
183C4⋊C8—221no—
184C4⋊C8D4411yescharacteristic
185C4⋊C8D4411yescharacteristic
186C4⋊C8C22⋊D1112yes—
187#101—442no—
188#101—442no—
189C22⋊C8—21no—
190#97—221no—
191C4×C8—21no—
192C4×C8—221no—
193C2×C11—21no—
194C2×C11—21no—
195C2×C11#206411yescharacteristic
196C2×C11#206711yescharacteristic
197C2×C11#207011yescharacteristic
198C2×Q8—441no—
199C2×Q8—441no—
200C2×Q8—441no—
201C2×Q8—441no—
202C2×Q8—441no—
203C2×Q8—441no—
204C22×C4—222no—
205C22×C4#433911yescharacteristic
206C22×C4D4×D1111yescharacteristic
207C22×C4Q8×D1111yescharacteristic
208M16—41no—
209M16—41no—
210M16—112no—
211M16—221no—
212M16—221no—
213M16—221no—
214M16—441no—
215M16—441no—
216C2×C8—21no—
217C2×C8—21no—
218C2×C8—22no—
219C2×C8—41no—
220C2×C8—41no—
221C2×C8—41no—
222C2×C8—221no—
223C2×C8—221no—
224C2×C8—441no—
225C2×C8—441no—
226C2×C8—881no—
227C4⋊C4—222no—
228C4⋊C4—222no—
229C4⋊C4—441no—
230C4⋊C4—441no—
231C42C2×D4411yescharacteristic
232C42#434111yescharacteristic
233C42#434311yescharacteristic
234C42C2×C22⋊D1111yescharacteristic
235C11#1060411yescharacteristic, complemented, Sylow
236C23#6694911yescharacteristic
237Q8—881no—
238Q8—881no—
239Q8—881no—
240Q8—881no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—442no—
245C2×C4—442no—
246C2×C4—442no—
247C2×C4#6694811yescharacteristic
248C2×C4#6695011yescharacteristic
249C2×C4#6695111yescharacteristic
250C2×C4D8×D1111yescharacteristic
251C2×C4#6696411yescharacteristic
252C2×C4#6697111yescharacteristic
253C2×C4#6697211yescharacteristic
254C2×C4#6698311yescharacteristic
255C2×C4#6699211yescharacteristic
256C2×C4#6699911yescharacteristic
257C8—41no—
258C8—41no—
259C8—42no—
260C8—81no—
261C8—222no—
262C8—441no—
263C8—881no—
264C8—881no—
265C22—21no—
266C22—21no—
267C22#1062250311yescharacteristic
268C22#1062250411yescharacteristic
269C22#1062260711yescharacteristic
270C4—21no—
271C4—21no—
272C4—21no—
273C4—882no—
274C4#1062249611yescharacteristic
275C4#1062249911yescharacteristic
276C4#1062275411yescharacteristic
277C4#1062275611yescharacteristic
278C4#1062276311yescharacteristic
279C4#1062279811yescharacteristic
280C2—21no—
281C2—21no—
282C2#1306998211yescharacteristic
283C2#1306999911yescharacteristic
284C2#1307001611yescharacteristic
subgroupG/H
centerC22#10622607
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1571C2
socleC22×C11#396
prime radicalC23×C11C22⋊Q8
hypercenter#1571D11
hypocenterC11#10604
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1571

Complements

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

NH ≅ G/Ntype
235. C11#10604semidirect

Maximal subgroups

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

subgroupindex
#130694592
#130693922
#130673692
#130672872
C2×#106221202
#130664902
C11×#15712
#1060411