Finite Group Databasebeta

← #14670993

Subgroups — #14670993

Order 2816.

456 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 117 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#13077533C211yesmaximal, characteristic
2C2×#10622203C211yesmaximal, characteristic, complemented
3#13070344C211yesmaximal, characteristic
4#13069532C211yesmaximal, characteristic, complemented
5#13066720C211yesmaximal, characteristic, complemented
6#13066701C211yesmaximal, characteristic, complemented
7C2×C11×#510C211yesmaximal, characteristic
8C2×C11×#135C2211yescharacteristic
9C22×C11×Q16C2211yescharacteristic
10#10623350—21no—
11C11×#510—22no—
12C11×#510—22no—
13C2×C11×Q32C412yescomplemented
14C2×C11×SD32C412yescomplemented
15C2×C11×M32C2211yescharacteristic
16#10622849—21no—
17C2×#66900—21no—
18#10622838—21no—
19#10622810—22no—
20#10622809—22no—
21C2×#66883C2211yescharacteristic
22C2×#66883C2211yescharacteristic
23#10622714C2211yescharacteristic
24C2×#66876C2211yescharacteristic
25#10622205—22no—
26#10622203—22no—
27C2×C11×#41—21no—
28C22×Q8×C11—21no—
29C11×#135—21no—
30C11×#135—21no—
31C11×#135D412yes—
32C11×#135D412yes—
33C2×C11×Q16—21no—
34C2×C11×Q16—21no—
35C2×C11×Q16—21no—
36C2×C11×Q16—21no—
37C2×C11×Q16—21no—
38C2×C11×Q16C2×C412yes—
39C2×C11×Q16C2×C411yescharacteristic
40C2×C11×SD16—21no—
41C2×C11×D8C2×C411yescharacteristic
42C22×C8×C11C2311yescharacteristic
43#67001—24no—
44#67001—42no—
45#66979D411yescharacteristic
46C2×#4318—21no—
47C2×#4318—21no—
48C2×#4318—42no—
49C2×#4318D411yescharacteristic
50C11×Q32—24no—
51C11×SD32—24no—
52C11×M32—21no—
53C11×M32—21no—
54C2×C11×C16C2×C412yes—
55#66901—24no—
56#66900—42no—
57#66899—42no—
58#66883—21no—
59#66883—21no—
60#66883—21no—
61#66883D412yes—
62#66879—21no—
63C8×Dic11—21no—
64#66876—21no—
65#66876—21no—
66C2×C11⋊C16—21no—
67#13035—111nomaximal, Sylow
68C11×#41—22no—
69C11×#41—22no—
70C11×#41—41no—
71C11×#41—41no—
72C2×Q8×C11—21no—
73C2×Q8×C11—22no—
74C2×Q8×C11—41no—
75C2×Q8×C11—41no—
76C2×Q8×C11—41no—
77C2×Q8×C11—41no—
78C2×Q8×C11—41no—
79C2×D4×C11—21no—
80C2×D4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11C2×D411yescharacteristic
84C11×Q16—21no—
85C11×Q16—22no—
86C11×Q16—22no—
87C11×Q16—41no—
88C11×Q16—41no—
89C11×Q16C22⋊C412yes—
90C11×SD16—22no—
91C11×SD16—22no—
92C11×D8—21no—
93C11×D8C22⋊C412yes—
94C2×C8×C11C22×C411yescharacteristic
95C2×C8×C11C2×D411yescharacteristic
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11C2×D411yescharacteristic
98C2×C8×C11#4111yescharacteristic
99C2×C8×C11#4111yescharacteristic
100C22⋊Dic11—21no—
101C4⋊Dic11—21no—
102C4×Dic11—21no—
103#4318—22no—
104#4318—21no—
105#4318—44no—
106#4318—41no—
107#4318—41no—
108#4318—41no—
109#4318D812yes—
110C2×C11⋊C8—21no—
111C2×C11⋊C8—44no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114C11×C16—22no—
115C11⋊C16—41no—
116C2×#510D1111yescharacteristic
117#2957—111no—
118C2×#362—111no—
119#2143—111no—
120#1979—111no—
121#1385—111no—
122#1378—111no—
123C23×C11—41no—
124C23×C11#13511yescharacteristic
125Q8×C11—22no—
126Q8×C11—41no—
127Q8×C11—42no—
128Q8×C11—42no—
129Q8×C11—81no—
130Q8×C11—81no—
131D4×C11—22no—
132D4×C11—42no—
133D4×C11—42no—
134D4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11—81no—
140C2×C4×C11—81no—
141C2×C4×C11C4×D411yescharacteristic
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11C2×D811yescharacteristic
145C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
147C2×Dic11—41no—
148C8×C11C2×C22⋊C411yescharacteristic
149C8×C11C4×D411yescharacteristic
150C8×C11#12111yescharacteristic
151C8×C11#12311yescharacteristic
152C11⋊C8—22no—
153C11⋊C8—42no—
154C11⋊C8—81no—
155C2×#135C2×D1111yescharacteristic
156C22×Q16C2×D1111yescharacteristic
157#568—221no—
158#510—22no—
159#510—22no—
160C2×Q32Dic1112yescomplemented
161C2×SD32Dic1112yescomplemented
162C2×M32—111no—
163C2×M32C2×D1111yescharacteristic
164#444—222no—
165#443—222no—
166C2×#108—111no—
167C2×#108—111no—
168#421—221no—
169#419—221no—
170C2×#101—221no—
171#405—111no—
172#362—222no—
173#359—222no—
174C22×C11—41no—
175C22×C11—42no—
176C22×C11—161no—
177C22×C11C4×D811yescharacteristic
178C22×C11#44911yescharacteristic
179C22×C11#46311yescharacteristic
180C4×C11—42no—
181C4×C11—82no—
182C4×C11#38611yescharacteristic
183C4×C11#44211yescharacteristic
184C4×C11#44711yescharacteristic
185C4×C11#45911yescharacteristic
186Dic11—81no—
187C2×#41—21no—
188C22×Q8—21no—
189#135—21no—
190#135—21no—
191#135C22⋊D1112yes—
192#135C22⋊D1112yes—
193C2×Q16—21no—
194C2×Q16—21no—
195C2×Q16—21no—
196C2×Q16—21no—
197C2×Q16—21no—
198C2×Q16C2×Dic1112yes—
199C2×Q16C2×Dic1111yescharacteristic
200C2×SD16—21no—
201C2×D8C2×Dic1111yescharacteristic
202#131—224no—
203#131—442no—
204C2×M16—111no—
205C2×M16—221no—
206C2×M16—221no—
207C2×M16—442no—
208C22×C8C22×D1111yescharacteristic
209#117—111no—
210Q32—24no—
211SD32—24no—
212M32—21no—
213M32—21no—
214M32—221no—
215M32—221no—
216C2×C16—221no—
217C2×C16C2×Dic1112yes—
218#108—112no—
219#108—221no—
220#108—221no—
221#108—221no—
222#104—224no—
223#103—442no—
224#101—442no—
225#97—221no—
226C4×C8—221no—
227C2×C11—21no—
228C2×C11—21no—
229C2×C11—21no—
230C2×C11—82no—
231C2×C11#187911yescharacteristic
232#41—22no—
233#41—22no—
234#41—41no—
235#41—41no—
236C2×Q8—21no—
237C2×Q8—22no—
238C2×Q8—41no—
239C2×Q8—41no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8—41no—
243C2×D4—21no—
244C2×D4—41no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4D4×D1111yescharacteristic
248Q16—21no—
249Q16—22no—
250Q16—22no—
251Q16—41no—
252Q16—41no—
253Q16C22⋊Dic1112yes—
254SD16—22no—
255SD16—22no—
256D8—21no—
257D8C22⋊Dic1112yes—
258M16—112no—
259M16—221no—
260M16—222no—
261M16—444no—
262M16—441no—
263M16—441no—
264M16—441no—
265C2×C8—221no—
266C2×C8—444no—
267C2×C8—441no—
268C2×C8—441no—
269C2×C8D4×D1111yescharacteristic
270C2×C8#434111yescharacteristic
271C2×C8#434111yescharacteristic
272C2×C8C22×Dic1111yescharacteristic
273C2×C8C2×C22⋊D1111yescharacteristic
274C2×C8C2×C22⋊D1111yescharacteristic
275C4⋊C4—221no—
276C22⋊C4—221no—
277C42—221no—
278C16—22no—
279C16—441no—
280C11#1303511yescharacteristic, complemented, Sylow
281C23—41no—
282C23#6696511yescharacteristic
283Q8—22no—
284Q8—41no—
285Q8—42no—
286Q8—42no—
287Q8—81no—
288Q8—81no—
289D4—22no—
290D4—42no—
291D4—42no—
292D4—41no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—441no—
300C2×C4D8×D1111yescharacteristic
301C2×C4#6696411yescharacteristic
302C2×C4#6696411yescharacteristic
303C2×C4D4×Dic1111yescharacteristic
304C2×C4#6699011yescharacteristic
305C2×C4#6699211yescharacteristic
306C8—222no—
307C8—442no—
308C8—881no—
309C8D4×Dic1111yescharacteristic
310C8#6698811yescharacteristic
311C8#6699211yescharacteristic
312C8C2×C22⋊Dic1111yescharacteristic
313C22—41no—
314C22—42no—
315C22—161no—
316C22D8×Dic1111yescharacteristic
317C22#1062276611yescharacteristic
318C22#1062277111yescharacteristic
319C4—42no—
320C4—82no—
321C4—881no—
322C4#1062276311yescharacteristic
323C4#1062276511yescharacteristic
324C4#1062276911yescharacteristic
325C4#1062283311yescharacteristic
326C2—21no—
327C2—21no—
328C2—21no—
329C2—82no—
330C2#1306896611yescharacteristic
subgroupG/H
centerC2#13068966
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC2×C11×#510C2
socleC2×C11#1879
prime radicalC2×C11×#135C22
cosocleC22×C8×C11C23
hypercenterC2×#510D11
hypocenterC11#13035
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ C2×#510

Complements

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

NH ≅ G/Ntype
2. C2×#10622203C2semidirect
4. #13069532C2semidirect
5. #13066720C2semidirect
6. #13066701C2semidirect
13. C2×C11×Q32C4semidirect
14. C2×C11×SD32C4semidirect
160. C2×Q32Dic11semidirect
161. C2×SD32Dic11semidirect
280. C11#13035semidirect

Maximal subgroups

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

subgroupindex
#130775332
C2×#106222032
#130703442
#130695322
#130667202
#130667012
C2×C11×#5102
#1303511