Finite Group Databasebeta

← #14670391

Subgroups — #14670391

Order 2816.

398 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622809C211yesmaximal, characteristic
2C2×#10622131C211yesmaximal, characteristic, complemented
3#13070323C211yesmaximal, characteristic
4#13069362C211yesmaximal, characteristic, complemented
5#13066712C211yesmaximal, characteristic, complemented
6#13066693C211yesmaximal, characteristic, complemented
7C2×C11×#359C211yesmaximal, characteristic
8C2×C11×#135C2211yescharacteristic
9C2×#67001—21no—
10C22×C11×C16C2211yescharacteristic
11C2×C11×#108C2211yescharacteristic
12C2×#66901—21no—
13#10622809—22no—
14#10622809—22no—
15#10622732—21no—
16C2×#66883C2211yescharacteristic
17#10622719C2211yescharacteristic
18C2×C8×Dic11C2211yescharacteristic
19C22×C11⋊C16C2211yescharacteristic
20C11×#359—22no—
21#10622202C411yescharacteristic, complemented
22#10622202C411yescharacteristic, complemented
23#10622200C411yescharacteristic, complemented
24#10622200C411yescharacteristic, complemented
25#10622193—21no—
26#10622131—22no—
27C2×C11×#41—21no—
28C11×#135—21no—
29C11×#135—21no—
30C11×#135D412yes—
31C11×#135Q812yes—
32C2×C11×Q16C2×C411yescharacteristic
33C2×C11×SD16—21no—
34C2×C11×D8C2×C411yescharacteristic
35C2×C11×M16—21no—
36C22×C8×C11C2311yescharacteristic
37#67001—24no—
38#67001—42no—
39#66979—21no—
40C2×C4×Dic11D411yescharacteristic
41C2×#4318—21no—
42C2×#4318—41no—
43C22×C11⋊C8—41no—
44C22×C11⋊C8D411yescharacteristic
45C2×C11×C16—21no—
46C2×C11×C16—21no—
47C2×C11×C16—21no—
48C11×#108—21no—
49C11×#108—21no—
50#66901—24no—
51#66883—21no—
52#66883D412yes—
53#66882C2×C411yescharacteristic
54#66882C2×C411yescharacteristic
55#66881—21no—
56Dic11⋊C8—41no—
57Dic11⋊C8—41no—
58C8×Dic11—21no—
59C8×Dic11—21no—
60C2×C11⋊C16—21no—
61C2×C11⋊C16—21no—
62C2×C11⋊C16C2×C411yescharacteristic
63C2×C11⋊C16C2×C411yescharacteristic
64#12939—111nomaximal, Sylow
65C11×#41—22no—
66C11×#41—22no—
67C11×#41—41no—
68C11×#41—41no—
69C2×Q8×C11—21no—
70C2×D4×C11—21no—
71C2×D4×C11—41no—
72C22×C4×C11—41no—
73C22×C4×C11C2×D411yescharacteristic
74C22×Dic11—21no—
75C11×Q16—21no—
76C11×Q16C4⋊C412yes—
77C11×SD16—22no—
78C11×SD16—22no—
79C11×D8—21no—
80C11×D8C4⋊C412yes—
81C11×M16—41no—
82C11×M16—41no—
83C2×C8×C11—41no—
84C2×C8×C11C22×C411yescharacteristic
85C2×C8×C11C2×D411yescharacteristic
86C2×C8×C11C2×D411yescharacteristic
87C2×C8×C11C2×Q811yescharacteristic
88C2×C8×C11#4111yescharacteristic
89C2×C8×C11#4111yescharacteristic
90C22⋊Dic11—41no—
91C4⋊Dic11—21no—
92C4⋊Dic11—21no—
93C4×Dic11—21no—
94C4×Dic11—21no—
95C4×Dic11—41no—
96#4318—22no—
97#4318—44no—
98#4318—41no—
99C2×C11⋊C8—21no—
100C2×C11⋊C8—21no—
101C2×C11⋊C8—44no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8D811yescharacteristic
104C2×C11⋊C8D811yescharacteristic
105C11×C16—41no—
106C11⋊C16—21no—
107C11⋊C16—21no—
108C2×#443—111no—
109C2×#368—111no—
110C2×#359D1111yescharacteristic
111#2138—111no—
112#1945—111no—
113#1382—111no—
114#1374—111no—
115C23×C11—41no—
116C23×C11#13511yescharacteristic
117Q8×C11—22no—
118Q8×C11—41no—
119D4×C11—22no—
120D4×C11—42no—
121D4×C11—42no—
122D4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11C4×D411yescharacteristic
127C2×C4×C11#12011yescharacteristic
128C2×C4×C11C22⋊Q811yescharacteristic
129C2×C4×C11C2×D811yescharacteristic
130C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C11#13711yescharacteristic
132C2×Dic11—22no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C8×C11—81no—
138C8×C11C2×C4⋊C411yescharacteristic
139C8×C11C4×D411yescharacteristic
140C8×C11C22⋊Q811yescharacteristic
141C8×C11#12311yescharacteristic
142C11⋊C8—21no—
143C11⋊C8—21no—
144C11⋊C8—42no—
145C2×#135C2×D1111yescharacteristic
146C2×#131—221no—
147C22×C16—111no—
148C22×C16C2×D1111yescharacteristic
149#443—222no—
150#443—222no—
151C2×#108—111no—
152C2×#108C2×D1111yescharacteristic
153#427—111no—
154#424—221no—
155C2×#104—221no—
156C2×C4×C8—111no—
157#368—222no—
158#359—22no—
159#358—111no—
160#358—111no—
161#357—111no—
162#357—111no—
163#339—221no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11—42no—
167C22×C11—81no—
168C22×C11—81no—
169C22×C11C4×D811yescharacteristic
170C22×C11#45211yescharacteristic
171C22×C11#47811yescharacteristic
172C4×C11—42no—
173C4×C11#38511yescharacteristic
174C4×C11#44011yescharacteristic
175C4×C11#44711yescharacteristic
176C4×C11#47411yescharacteristic
177Dic11—42no—
178Dic11—81no—
179Dic11—81no—
180C2×#41—21no—
181#135—21no—
182#135—21no—
183#135Dic2212yes—
184#135C22⋊D1112yes—
185C2×Q16C4×D1111yescharacteristic
186C2×SD16—21no—
187C2×D8C4×D1111yescharacteristic
188#131—224no—
189#131—442no—
190C2×M16—21no—
191C2×M16—221no—
192C2×M16—441no—
193C22×C8—111no—
194C22×C8—441no—
195C22×C8C22×D1111yescharacteristic
196#117—221no—
197C2×C42—111no—
198C2×C16—21no—
199C2×C16—21no—
200C2×C16—21no—
201C2×C16—111no—
202C2×C16—111no—
203C2×C16—221no—
204C2×C16—221no—
205#108—21no—
206#108—21no—
207#108—112no—
208#108—221no—
209#107—111no—
210#107—111no—
211#106—221no—
212C4⋊C8—441no—
213C4⋊C8—441no—
214#104—224no—
215C4×C8—221no—
216C4×C8—221no—
217C2×C11—21no—
218C2×C11—21no—
219C2×C11—82no—
220C2×C11#186211yescharacteristic
221C2×C11#217811yescharacteristic
222C2×C11#217911yescharacteristic
223#41—22no—
224#41—22no—
225#41—41no—
226#41—41no—
227C2×Q8—21no—
228C2×D4—21no—
229C2×D4—41no—
230C22×C4—41no—
231C22×C4—221no—
232C22×C4D4×D1111yescharacteristic
233Q16—21no—
234Q16Dic11⋊C412yes—
235SD16—22no—
236SD16—22no—
237D8—21no—
238D8Dic11⋊C412yes—
239M16—41no—
240M16—41no—
241M16—222no—
242M16—444no—
243M16—441no—
244C2×C8—41no—
245C2×C8—111no—
246C2×C8—111no—
247C2×C8—221no—
248C2×C8—221no—
249C2×C8—444no—
250C2×C8—441no—
251C2×C8C2×Dic2211yescharacteristic
252C2×C8C2×C4×D1111yescharacteristic
253C2×C8D4×D1111yescharacteristic
254C2×C8#434111yescharacteristic
255C2×C8#434111yescharacteristic
256C2×C8C2×C22⋊D1111yescharacteristic
257C4⋊C4—221no—
258C4⋊C4—221no—
259C22⋊C4—441no—
260C42—221no—
261C42—221no—
262C42—441no—
263C16—41no—
264C16—221no—
265C16—221no—
266C11#1293911yescharacteristic, complemented, Sylow
267C23—41no—
268C23#6696911yescharacteristic
269Q8—22no—
270Q8—41no—
271D4—22no—
272D4—42no—
273D4—42no—
274D4—41no—
275C2×C4—41no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—222no—
279C2×C4—441no—
280C2×C4—441no—
281C2×C4—441no—
282C2×C4—441no—
283C2×C4#6693111yescharacteristic
284C2×C4(C22⋊D11)⋊C411yescharacteristic
285C2×C4D8×D1111yescharacteristic
286C2×C4#6696411yescharacteristic
287C2×C4#6696811yescharacteristic
288C2×C4#6699011yescharacteristic
289C8—81no—
290C8—221no—
291C8—221no—
292C8—442no—
293C8#6693111yescharacteristic
294C8(C22⋊D11)⋊C411yescharacteristic
295C8C2×Dic11⋊C411yescharacteristic
296C8#6698811yescharacteristic
297C22—21no—
298C22—21no—
299C22—42no—
300C22—81no—
301C22—81no—
302C22#1062236911yescharacteristic
303C22#1062237611yescharacteristic
304C22#1062278611yescharacteristic
305C4—42no—
306C4—442no—
307C4—881no—
308C4—881no—
309C4#1062237011yescharacteristic
310C4#1062237211yescharacteristic
311C4#1062255911yescharacteristic
312C4#1062276911yescharacteristic
313C2—21no—
314C2—21no—
315C2—82no—
316C2#1306886111yescharacteristic
317C2#1307049411yescharacteristic
318C2#1307049911yescharacteristic
subgroupG/H
centerC2×C4D8×D11
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC2×C11×#359C2
socleC22×C11C4×D8
prime radicalC2×C11×#135C22
cosocleC22×C8×C11C23
hypercenterC2×#359D11
hypocenterC11#12939
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#359

Complements

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

NH ≅ G/Ntype
2. C2×#10622131C2semidirect
4. #13069362C2semidirect
5. #13066712C2semidirect
6. #13066693C2semidirect
21. #10622202C4semidirect
22. #10622202C4semidirect
23. #10622200C4semidirect
24. #10622200C4semidirect
266. C11#12939semidirect

Maximal subgroups

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

subgroupindex
C2×#106228092
C2×#106221312
#130703232
#130693622
#130667122
#130666932
C2×C11×#3592
#1293911