Finite Group Databasebeta

← #14673155

Subgroups — #14673155

Order 2816.

456 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C2×#10622203C211yesmaximal, characteristic, complemented
2C2×#10622201C211yesmaximal, characteristic
3#13070336C211yesmaximal, characteristic, complemented
4#13070332C211yesmaximal, characteristic
5#13069364C211yesmaximal, characteristic, complemented
6#13066698C211yesmaximal, characteristic, complemented
7C2×C11×#495C211yesmaximal, characteristic
8C22×C11×Q16C2211yescharacteristic
9C22×C11×SD16—21no—
10C22×C11×D8C2211yescharacteristic
11C2×C11×#124—21no—
12C11×#495—22no—
13C11×#495—22no—
14C2×C4×C8×C11C2211yescharacteristic
15C2×#66883C2211yescharacteristic
16#10622719C2211yescharacteristic
17#10622715—21no—
18C2×#66876C2211yescharacteristic
19C2×#66876C2211yescharacteristic
20#10622203—22no—
21#10622202—22no—
22#10622201—22no—
23#10622200—22no—
24#10622161—21no—
25C22×Q8×C11—21no—
26C22×D4×C11—21no—
27C2×C11×Q16—21no—
28C2×C11×Q16—21no—
29C2×C11×Q16—21no—
30C2×C11×Q16—21no—
31C2×C11×Q16—21no—
32C2×C11×Q16D412yes—
33C2×C11×SD16—24no—
34C2×C11×SD16—42no—
35C2×C11×SD16—42no—
36C2×C11×D8—21no—
37C2×C11×D8—21no—
38C2×C11×D8—21no—
39C2×C11×D8—21no—
40C2×C11×D8—21no—
41C2×C11×D8D412yes—
42C22×C8×C11D411yescharacteristic
43C22×C8×C11C2311yescharacteristic
44C11×#124—24no—
45C11×#124—42no—
46C2×C11×C22⋊C4—42no—
47C2×C42×C11D411yescharacteristic
48#66979—21no—
49C2×#4318—21no—
50C4×C8×C11—21no—
51C4×C8×C11—21no—
52#66883—21no—
53#66883—21no—
54#66882D412yes—
55#66881—21no—
56Dic11⋊C8—42no—
57#66876—21no—
58#66876—21no—
59#66876—21no—
60#66876—21no—
61C2×C11⋊C16—21no—
62C2×C11⋊C16—21no—
63#13414—111nomaximal, Sylow
64C24×C11—41no—
65C2×Q8×C11—22no—
66C2×Q8×C11—41no—
67C2×Q8×C11—41no—
68C2×Q8×C11—41no—
69C2×Q8×C11—41no—
70C2×Q8×C11—41no—
71C2×D4×C11—22no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C2×D4×C11—41no—
75C2×D4×C11—41no—
76C2×D4×C11—41no—
77C22×C4×C11—21no—
78C22×C4×C11—41no—
79C22×C4×C11C2×D411yescharacteristic
80C11×Q16—22no—
81C11×Q16—22no—
82C11×Q16—41no—
83C11×Q16—41no—
84C11×SD16—48no—
85C11×D8—22no—
86C11×D8—22no—
87C11×D8—41no—
88C11×D8—41no—
89C2×C8×C11—21no—
90C2×C8×C11—21no—
91C2×C8×C11D812yes—
92C2×C8×C11C2×D411yescharacteristic
93C2×C8×C11C2×D411yescharacteristic
94C2×C8×C11C2×D411yescharacteristic
95C2×C8×C11#4111yescharacteristic
96C2×C8×C11#4111yescharacteristic
97C2×C8×C11#4111yescharacteristic
98C11×C22⋊C4—48no—
99C42×C11—21no—
100C42×C11SD1612yes—
101C22⋊Dic11—41no—
102C4⋊Dic11—22no—
103C4×Dic11—41no—
104#4318—41no—
105#4318—41no—
106C2×C11⋊C8—41no—
107C11⋊C16—41no—
108C11⋊C16—41no—
109C2×#495D1111yescharacteristic
110C2×#362—111no—
111C2×#361—111no—
112#2141—111no—
113#2140—111no—
114#1945—111no—
115#1376—111no—
116C23×C11—42no—
117C23×C11—84no—
118C23×C11—81no—
119C23×C11—81no—
120C23×C11AGL(1,ℤ/8)11yescharacteristic
121Q8×C11—42no—
122Q8×C11—42no—
123Q8×C11—81no—
124Q8×C11—81no—
125D4×C11—42no—
126D4×C11—42no—
127D4×C11—81no—
128D4×C11—81no—
129C2×C4×C11—22no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11—81no—
133C2×C4×C11—81no—
134C2×C4×C11#12011yescharacteristic
135C2×C4×C11#12111yescharacteristic
136C2×C4×C11#12411yescharacteristic
137C2×C4×C11C2×D811yescharacteristic
138C2×C4×C11C2×SD1611yescharacteristic
139C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
140C2×Dic11—42no—
141C8×C11—22no—
142C8×C11#12111yescharacteristic
143C8×C11#12111yescharacteristic
144C8×C11#12311yescharacteristic
145C8×C11#12311yescharacteristic
146C11⋊C8—81no—
147C22×Q16C2×D1111yescharacteristic
148C22×SD16—21no—
149C22×D8C2×D1111yescharacteristic
150C2×#124—21no—
151C2×M32—111no—
152C2×M32—111no—
153#495—22no—
154#495—22no—
155C2×#108—111no—
156#427—111no—
157#424—221no—
158C2×C4×C8C2×D1111yescharacteristic
159#362—222no—
160#361—222no—
161#358—222no—
162#357—222no—
163#339—221no—
164C22×C11—22no—
165C22×C11—84no—
166C22×C11—82no—
167C22×C11—162no—
168C22×C11—162no—
169C22×C11#45011yescharacteristic
170C22×C11#45911yescharacteristic
171C22×C11#49011yescharacteristic
172C4×C11—42no—
173C4×C11—82no—
174C4×C11#39411yescharacteristic
175C4×C11#44711yescharacteristic
176C4×C11#46011yescharacteristic
177C4×C11#48611yescharacteristic
178Dic11—82no—
179C22×Q8—21no—
180C22×D4—21no—
181C2×Q16—21no—
182C2×Q16—21no—
183C2×Q16—21no—
184C2×Q16—21no—
185C2×Q16—21no—
186C2×Q16C22⋊D1112yes—
187C2×SD16—24no—
188C2×SD16—42no—
189C2×SD16—42no—
190C2×D8—21no—
191C2×D8—21no—
192C2×D8—21no—
193C2×D8—21no—
194C2×D8—21no—
195C2×D8C22⋊D1112yes—
196C2×M16—221no—
197C22×C8C22⋊D1111yescharacteristic
198C22×C8C22×D1111yescharacteristic
199#124—24no—
200#124—42no—
201#117—221no—
202C2×C22⋊C4—42no—
203C2×C42C22⋊D1111yescharacteristic
204M32—221no—
205M32—221no—
206M32—221no—
207M32—221no—
208C2×C16—221no—
209C2×C16—221no—
210#108—221no—
211#108—221no—
212#107—112no—
213#106—221no—
214C4⋊C8—442no—
215C4×C8—21no—
216C4×C8—21no—
217C2×C11—21no—
218C2×C11—21no—
219C2×C11—162no—
220C2×C11#204111yescharacteristic
221C2×C11#221212yes—
222C24—41no—
223C2×Q8—22no—
224C2×Q8—41no—
225C2×Q8—41no—
226C2×Q8—41no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×D4—22no—
230C2×D4—41no—
231C2×D4—41no—
232C2×D4—41no—
233C2×D4—41no—
234C2×D4—41no—
235C22×C4—21no—
236C22×C4—41no—
237C22×C4C2×C22⋊D1111yescharacteristic
238Q16—22no—
239Q16—22no—
240Q16—41no—
241Q16—41no—
242SD16—48no—
243D8—22no—
244D8—22no—
245D8—41no—
246D8—41no—
247M16—441no—
248M16—441no—
249C2×C8—21no—
250C2×C8—21no—
251C2×C8—441no—
252C2×C8#432312yes—
253C2×C8D4×D1111yescharacteristic
254C2×C8#434111yescharacteristic
255C2×C8#434111yescharacteristic
256C2×C8#434111yescharacteristic
257C2×C8C2×C22⋊D1111yescharacteristic
258C2×C8C2×C22⋊D1111yescharacteristic
259C4⋊C4—222no—
260C22⋊C4—48no—
261C22⋊C4—441no—
262C42—21no—
263C42—441no—
264C42#432412yes—
265C16—441no—
266C16—441no—
267C11#1341411yescharacteristic, complemented, Sylow
268C23—42no—
269C23—84no—
270C23—81no—
271C23—81no—
272C23#6698511yescharacteristic
273Q8—42no—
274Q8—42no—
275Q8—81no—
276Q8—81no—
277D4—42no—
278D4—42no—
279D4—81no—
280D4—81no—
281C2×C4—22no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—442no—
287C2×C4C2×#432311yescharacteristic
288C2×C4#6698511yescharacteristic
289C2×C4C2×#432411yescharacteristic
290C2×C4#6698911yescharacteristic
291C2×C4#6699111yescharacteristic
292C2×C4#6700611yescharacteristic
293C8—22no—
294C8—881no—
295C8#6698811yescharacteristic
296C8#6698811yescharacteristic
297C8#6699211yescharacteristic
298C8#6699211yescharacteristic
299C22—22no—
300C22—84no—
301C22—82no—
302C22—162no—
303C22—162no—
304C22#1062268411yescharacteristic
305C22#1062268511yescharacteristic
306C22#1062283111yescharacteristic
307C4—42no—
308C4—82no—
309C4—882no—
310C4#1062268311yescharacteristic
311C4#1062268811yescharacteristic
312C4#1062283011yescharacteristic
313C4#1062283511yescharacteristic
314C2—21no—
315C2—21no—
316C2—162no—
317C2#1306984711yescharacteristic
318C2#1307068212yes—
subgroupG/H
centerC22#10622685
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC2×C11×#495C2
socleC22×C11#459
prime radicalC22×C11×D8C22
hypercenterC2×#495D11
hypocenterC11#13414
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#495

Complements

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

NH ≅ G/Ntype
1. C2×#10622203C2semidirect
3. #13070336C2semidirect
5. #13069364C2semidirect
6. #13066698C2semidirect
267. C11#13414semidirect

Maximal subgroups

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

subgroupindex
C2×#106222032
C2×#106222012
#130703362
#130703322
#130693642
#130666982
C2×C11×#4952
#1341411