Finite Group Databasebeta

← #14782676

Subgroups — #14782676

Order 2816.

906 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077133C212yesmaximal
2C2×#10622723C211yesmaximal, characteristic
3#13070062C214yesmaximal, complemented
4#13070057C214yesmaximal, complemented
5#13068355C212yesmaximal, complemented
6C2×#10622190C211yesmaximal, characteristic, complemented
7C2×C11×#427C211yesmaximal, characteristic, complemented
8C22×#4339C2211yescharacteristic
9C23×C8×C11C2211yescharacteristic
10C2×C11×#117C2212yes—
11C22×#4318C2212yes—
12C22×#4318C2211yescharacteristic
13C11×#427—22no—
14C11×#427—22no—
15C2×C11×#107C2212yescomplemented
16C2×C11×#106C2212yescomplemented
17#10622723—22no—
18#10622723C2212yes—
19#10622723C2212yes—
20C2×(C2×D11)⋊C8—22no—
21#10622617—22no—
22#10622615—24no—
23#10622614—22no—
24#10622579C2218yes—
25#10622190C2212yescomplemented
26#10622190C2212yescomplemented
27#10622168C2218yescomplemented
28C23×C4×C11C2311yescharacteristic
29C22×C22⋊D11—21no—
30C2×#4339—21no—
31C2×#4339—21no—
32C2×#4339—24no—
33C2×#4339—24no—
34C2×#4339D412yes—
35C2×#4339C2312yes—
36C22×D44D411yescharacteristic
37C22×C4×D11—21no—
38C22×Dic22D411yescharacteristic
39C22×C8×C11—24no—
40C22×C8×C11D412yes—
41C22×C8×C11D412yes—
42C22×C8×C11C2311yescharacteristic
43C22×C8×C11C2311yescharacteristic
44C11×#117—22no—
45C11×#117—22no—
46C11×#117—22no—
47C11×#117—22no—
48C2×C11×C4⋊C4C2314yes—
49C2×C11×C22⋊C4—22no—
50C2×C42×C11—22no—
51C2×#4318—21no—
52C2×#4318—22no—
53C2×#4318—24no—
54C2×#4318—24no—
55C2×#4318—24no—
56C2×#4318C2312yes—
57C2×#4318C2314yes—
58C22×C11⋊C8—21no—
59C22×C11⋊C8—22no—
60C11×#107—24no—
61C11×#106—24no—
62(C2×D11)⋊C8—24no—
63(C2×D11)⋊C8—24no—
64#66874—28no—
65#66873—28no—
66#23646—111nomaximal, Sylow
67C24×C11#4111yescharacteristic
68C23×D11—21no—
69C22×C4×C11—24no—
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11#4111yescharacteristic
75C22×C4×C11#4114yes—
76C22×C4×C11#4114yes—
77C22×C4×C11C2411yescharacteristic
78C2×C22⋊D11—22no—
79C2×C22⋊D11—22no—
80C2×C22⋊D11—44no—
81C22×Dic11—21no—
82#4339—28no—
83#4339—24no—
84#4339—24no—
85#4339—42no—
86#4339—42no—
87#4339—44no—
88C2×D44—21no—
89C2×D44—24no—
90C2×D44C2×D412yes—
91C2×C4×D11—22no—
92C2×C4×D11—22no—
93C2×C4×D11—42no—
94C2×C4×D11—42no—
95C2×Dic22—21no—
96C2×Dic22—24no—
97C2×Dic22C2×D412yes—
98C2×C8×C11—24no—
99C2×C8×C11—24no—
100C2×C8×C11—22no—
101C2×C8×C11—22no—
102C2×C8×C11C2×D412yes—
103C2×C8×C11C2×D412yes—
104C11×C4⋊C4—24no—
105C11×C4⋊C4—24no—
106C11×C22⋊C4—42no—
107C11×C22⋊C4—42no—
108C42×C11—42no—
109C42×C11—42no—
110#4318—24no—
111#4318—24no—
112#4318—24no—
113#4318—44no—
114#4318—42no—
115C2×C11⋊C8—24no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8—44no—
118C2×C11⋊C8—42no—
119C2×#427D1111yescharacteristic, complemented
120#2896—112no—
121C2×#408—111no—
122#2079—114no—
123#2078—114no—
124#1742—112no—
125C2×#341—111no—
126C23×C11—42no—
127C23×C11#12111yescharacteristic
128C23×C11#12111yescharacteristic
129C23×C11#12614yes—
130C23×C11C2×#4111yescharacteristic
131C22×D11—22no—
132C22×D11—44no—
133C22×D11—42no—
134C2×C4×C11—44no—
135C2×C4×C11—84no—
136C2×C4×C11#12111yescharacteristic
137C2×C4×C11#12111yescharacteristic
138C2×C4×C11#12314yes—
139C2×C4×C11#12314yes—
140C2×C4×C11#12312yes—
141C2×C4×C11#12312yes—
142C2×C4×C11#12412yes—
143C2×C4×C11#12412yes—
144C2×C4×C11#12614yes—
145C2×C4×C11C22×D411yescharacteristic
146C2×C4×C11C22×D411yescharacteristic
147C2×C4×C11C2×#4112yes—
148C2×C4×C11C2×#4112yes—
149C22⋊D11—44no—
150C22⋊D11—44no—
151C2×Dic11—22no—
152C2×Dic11—42no—
153D44—24no—
154D44—42no—
155C4×D11—42no—
156C4×D11—42no—
157C4×D11—44no—
158Dic22—24no—
159Dic22—42no—
160C8×C11—22no—
161C8×C11—22no—
162C11⋊C8—44no—
163C11⋊C8—42no—
164C22×#41—111no—
165C22×M16—111no—
166C22×M16—112no—
167C23×C8C2×D1111yescharacteristic
168C2×#117C2×D1112yes—
169#427—22no—
170#427—22no—
171C2×#107C2×D1112yescomplemented
172C2×#106C2×D1112yescomplemented
173#419—222no—
174#418—222no—
175#417—118no—
176#416—224no—
177#408—112no—
178#408—112no—
179#408—222no—
180C2×C22⋊C8—222no—
181#343—118no—
182#341—112no—
183#341—112no—
184C22×C11—22no—
185C22×C11—22no—
186C22×C11—22no—
187C22×C11—44no—
188C22×C11#39712yes—
189C22×C11#39712yes—
190C22×C11C2×#12111yescharacteristic
191C22×C11C2×#12612yes—
192C2×D11—42no—
193C2×D11—44no—
194C2×D11—84no—
195C4×C11—84no—
196C4×C11#39712yes—
197C4×C11#39712yes—
198C4×C11C2×#12312yes—
199C4×C11C2×#12311yescharacteristic
200C4×C11C2×#12411yescharacteristic
201Dic11—42no—
202C2×#41—112no—
203C2×#41—112no—
204C2×#41—221no—
205C2×#41—221no—
206C2×#41—224no—
207C2×#41—224no—
208C22×Q8—111no—
209C22×D4—111no—
210C22×D4—221no—
211C23×C4—221no—
212C23×C4C22×D1111yescharacteristic
213C2×M16—114no—
214C2×M16—112no—
215C2×M16—222no—
216C2×M16—221no—
217C2×M16—224no—
218C2×M16—224no—
219C2×M16—224no—
220C22×C8—24no—
221C22×C8—222no—
222C22×C8—221no—
223C22×C8C22⋊D1112yes—
224C22×C8C22⋊D1112yes—
225C22×C8C22×D1111yescharacteristic
226C22×C8C22×D1111yescharacteristic
227#117—22no—
228#117—22no—
229#117—22no—
230#117—22no—
231C2×C4⋊C4C22×D1114yes—
232C2×C22⋊C4—22no—
233C2×C42—22no—
234#107—24no—
235#106—24no—
236#103—228no—
237#102—228no—
238C22⋊C8—224no—
239C22⋊C8—224no—
240C2×C11—22no—
241C2×C11—22no—
242C2×C11—22no—
243C2×C11C2×#39711yescharacteristic
244C2×C11#306712yes—
245D11—82no—
246C24—221no—
247C24#434111yescharacteristic
248#41—228no—
249#41—224no—
250#41—224no—
251#41—444no—
252#41—442no—
253#41—442no—
254C2×Q8—112no—
255C2×Q8—221no—
256C2×Q8—224no—
257C2×D4—112no—
258C2×D4—222no—
259C2×D4—222no—
260C2×D4—224no—
261C2×D4—221no—
262C2×D4—444no—
263C22×C4—24no—
264C22×C4—221no—
265C22×C4—222no—
266C22×C4—222no—
267C22×C4—442no—
268C22×C4—442no—
269C22×C4#433914yes—
270C22×C4D4×D1111yescharacteristic
271C22×C4D4×D1111yescharacteristic
272C22×C4#434111yescharacteristic
273C22×C4#434314yes—
274C22×C4C2×C22⋊D1111yescharacteristic
275C22×C4C2×C22⋊D1111yescharacteristic
276C22×C4C23×D1111yescharacteristic
277M16—224no—
278M16—224no—
279M16—224no—
280M16—444no—
281M16—442no—
282C2×C8—24no—
283C2×C8—24no—
284C2×C8—22no—
285C2×C8—22no—
286C2×C8—224no—
287C2×C8—222no—
288C2×C8—444no—
289C2×C8—442no—
290C2×C8C2×C22⋊D1112yes—
291C2×C8C2×C22⋊D1112yes—
292C4⋊C4—24no—
293C4⋊C4—24no—
294C22⋊C4—42no—
295C22⋊C4—42no—
296C42—42no—
297C42—42no—
298C11#2364611yescharacteristic, complemented, Sylow
299C23—42no—
300C23—222no—
301C23—444no—
302C23—442no—
303C23#6695114yes—
304C23#6699111yescharacteristic
305C23#6699111yescharacteristic
306C23C2×#434111yescharacteristic
307Q8—224no—
308Q8—442no—
309D4—224no—
310D4—444no—
311D4—444no—
312D4—442no—
313C2×C4—44no—
314C2×C4—84no—
315C2×C4—222no—
316C2×C4—442no—
317C2×C4—442no—
318C2×C4—442no—
319C2×C4—444no—
320C2×C4#6694714yes—
321C2×C4#6694714yes—
322C2×C4#6695114yes—
323C2×C4#6698212yes—
324C2×C4#6698212yes—
325C2×C4#6699111yescharacteristic
326C2×C4#6699111yescharacteristic
327C2×C4#6700012yes—
328C2×C4#6700012yes—
329C2×C4C2×#433912yes—
330C2×C4C2×D4×D1111yescharacteristic
331C2×C4C2×#434312yes—
332C2×C4C22×C22⋊D1111yescharacteristic
333C8—22no—
334C8—22no—
335C8—444no—
336C8—442no—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—44no—
341C22—444no—
342C22—442no—
343C22—884no—
344C22#1062260612yes—
345C22#1062260612yes—
346C22C2×#6695112yes—
347C22C2×#6699111yescharacteristic
348C4—84no—
349C4—442no—
350C4#1062260612yes—
351C4#1062260612yes—
352C4C2×#6694712yes—
353C4C2×#6698211yescharacteristic
354C4C2×#6700011yescharacteristic
355C2—22no—
356C2—22no—
357C2—22no—
358C2—882no—
359C2C2×#1062260611yescharacteristic
360C2#1307833212yes—
subgroupG/H
centerC2×C4#66991
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#427C2
socleC22×C11C2×#121
prime radicalC22×#4339C22
hypercenterC2×#427D11
hypocenterC11#23646
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#427

Complements

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

NH ≅ G/Ntype
3. #13070062C2semidirect
4. #13070057C2semidirect
5. #13068355C2semidirect
6. C2×#10622190C2semidirect
7. C2×C11×#427C2semidirect
15. C2×C11×#107C22semidirect
16. C2×C11×#106C22semidirect
25. #10622190C22semidirect
26. #10622190C22semidirect
27. #10622168C22semidirect
119. C2×#427D11semidirect
171. C2×#107C2×D11semidirect
172. C2×#106C2×D11semidirect
298. C11#23646semidirect

Maximal subgroups

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

subgroupindex
#130771332
C2×#106227232
#130700622
#130700572
#130683552
C2×#106221902
C2×C11×#4272
#2364611