Finite Group Databasebeta

← #14908650

Subgroups — #14908650

Order 2816.

568 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078286C211yesmaximal, characteristic
2#13077216C211yesmaximal, characteristic, complemented
3#13070825C212yesmaximal, complemented
4#13070814C212yesmaximal, complemented
5#13070808C212yesmaximal, complemented
6#13070802C212yesmaximal, complemented
7#13070404C211yesmaximal, characteristic, complemented
8C2×#10622143C211yesmaximal, characteristic, complemented
9#13070329C211yesmaximal, characteristic, complemented
10#13070324C211yesmaximal, characteristic, complemented
11C11×#2113C211yesmaximal, characteristic, complemented
12C2×C11×#131C2211yescharacteristic
13#10623364—21no—
14#10623358—21no—
15C2×#66957C2211yescharacteristic
16C2×C11×M32C2211yescharacteristic
17C22×C11×C16C2211yescharacteristic
18#10622747—22no—
19#10622746—21no—
20#10622734—21no—
21#10622734—22no—
22#10622729C2212yes—
23#10622728C2212yes—
24#10622719C2211yescharacteristic
25#10622719C2212yes—
26C2×#66882C2211yescharacteristic
27C2×#66882C2211yescharacteristic
28C2×#66882C2212yes—
29C11×C22⋊C16C2212yes—
30C11×C22⋊C16C2212yes—
31#10622147C2211yescharacteristic
32#10622147C2212yes—
33#10622147C2211yescharacteristic
34#10622143C2212yes—
35#10622143C2212yes—
36#10622143C2212yes—
37#10622142C2212yes—
38#10622141C2211yescharacteristic
39#10622141C2212yes—
40#10622141C2211yescharacteristic
41C2×C11×#41D411yescharacteristic
42C2×#4339—21no—
43C11×#131—22no—
44C11×#131—22no—
45C2×C11×M16D411yescharacteristic
46C2×C11×M16D412yes—
47C22×C8×C11C2312yes—
48C22×C8×C11C2311yescharacteristic
49#66999—41no—
50Q8×Dic11—41no—
51#66992—42no—
52#66991—41no—
53D4×Dic11—41no—
54D4×Dic11—42no—
55#66983—22no—
56#66979—22no—
57#66979—21no—
58C2×C4⋊Dic11—22no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11—21no—
61#66977—22no—
62C2×Dic44C2311yescharacteristic
63#66957—22no—
64#66957—22no—
65C2×D88C2311yescharacteristic
66C2×#4314—21no—
67C11×M32—22no—
68C2×C11×C16—22no—
69C2×C11×C16C2311yescharacteristic
70C2×C11×C16C2311yescharacteristic
71C2×C11×C16C2312yes—
72#66885—22no—
73#66882—22no—
74#66882—21no—
75#66882—21no—
76#66882C2312yes—
77#66882C2311yescharacteristic
78#66882C2311yescharacteristic
79#66882C2312yes—
80#66881—22no—
81#66881—21no—
82#66880—22no—
83#33653—111nomaximal, Sylow
84C11×#41—22no—
85C11×#41—22no—
86C2×Q8×C11D811yescharacteristic
87C2×D4×C11D811yescharacteristic
88C2×D4×C11D812yes—
89C22×C4×C11C2×D412yes—
90C22×C4×C11C2×D411yescharacteristic
91C2×C22⋊D11—41no—
92C2×C22⋊D11—42no—
93C22×Dic11—42no—
94C22×Dic11—41no—
95C22×Dic11—41no—
96#4339—42no—
97#4339—42no—
98C2×D44—21no—
99C2×C4×D11—41no—
100C2×Dic22—21no—
101C11×M16—24no—
102C11×M16—22no—
103C2×C8×C11—22no—
104C2×C8×C11—22no—
105C2×C8×C11C2×D412yes—
106C2×C8×C11C2×D411yescharacteristic
107C2×C8×C11#4112yes—
108C2×C8×C11#4112yes—
109C2×C8×C11C2411yescharacteristic
110C22⋊Dic11—42no—
111C22⋊Dic11—42no—
112C22⋊Dic11—41no—
113(C2×D11)⋊C4—42no—
114C4⋊Dic11—22no—
115C4⋊Dic11—21no—
116C4⋊Dic11—22no—
117C4⋊Dic11—21no—
118C4⋊Dic11—42no—
119C4⋊Dic11—41no—
120C4⋊Dic11—41no—
121Dic11⋊C4—42no—
122C4×Dic11—42no—
123C4×Dic11—41no—
124Dic44—21no—
125Dic44—21no—
126D88—21no—
127D88—21no—
128#4314—42no—
129C11×C16—21no—
130C11×C16—21no—
131C11×C16—22no—
132#3061—111no—
133#2913—111no—
134#2237—112no—
135#2235—112no—
136#2234—112no—
137#2233—112no—
138#2159—111no—
139C2×#367—111no—
140#2139—111no—
141#2138—111no—
142#2113D1111yescharacteristic, complemented
143C23×C11C2×D812yes—
144C23×C11C2×D811yescharacteristic
145C22×D11—41no—
146Q8×C11—22no—
147D4×C11—24no—
148D4×C11—22no—
149C2×C4×C11—22no—
150C2×C4×C11—22no—
151C2×C4×C11#12312yes—
152C2×C4×C11C2×D812yes—
153C2×C4×C11C2×D811yescharacteristic
154C2×C4×C11#13712yes—
155C2×C4×C11C22×D411yescharacteristic
156C22⋊D11—82no—
157C22⋊D11—162no—
158C2×Dic11—41no—
159C2×Dic11—42no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—42no—
163C2×Dic11—161no—
164C2×Dic11—162no—
165C2×Dic11—161no—
166D44—41no—
167D44—41no—
168C4×D11—82no—
169Dic22—41no—
170Dic22—41no—
171C8×C11—22no—
172C8×C11#12312yes—
173C8×C11C2×#4111yescharacteristic
174C8×C11C2×#4111yescharacteristic
175C2×#135—111no—
176C2×#131C2×D1111yescharacteristic
177#537—221no—
178#520—221no—
179C2×M32C2×D1111yescharacteristic
180C22×C16C2×D1111yescharacteristic
181#468—222no—
182#467—112no—
183#466—112no—
184#428—221no—
185#428—222no—
186#427—111no—
187#427—112no—
188C2×#107—111no—
189C2×#107—112no—
190C2×#107—111no—
191#417—221no—
192#367—112no—
193#367—112no—
194#367—112no—
195#366—112no—
196#358—111no—
197#358—111no—
198#358—112no—
199#357—111no—
200#357—111no—
201#357—112no—
202C22⋊C16C2×D1112yes—
203C22⋊C16C2×D1112yes—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—22no—
207C22×C11—22no—
208C22×C11—22no—
209C22×C11#48012yes—
210C22×C11C22×D811yescharacteristic
211C2×D11—81no—
212C2×D11—81no—
213C2×D11—81no—
214C4×C11—22no—
215C4×C11#48012yes—
216C4×C11C2×#12311yescharacteristic
217C4×C11C2×#13711yescharacteristic
218Dic11—81no—
219Dic11—81no—
220Dic11—82no—
221Dic11—81no—
222Dic11—82no—
223C2×#41—221no—
224C2×#41D4411yescharacteristic
225#135—222no—
226#135—222no—
227C2×Q16—111no—
228C2×SD16—221no—
229C2×D8—111no—
230#131—22no—
231#131—22no—
232C2×M16D4411yescharacteristic
233C2×M16D4412yes—
234C22×C8C22×D1112yes—
235C22×C8C22×D1111yescharacteristic
236C22⋊Q8—222no—
237C22⋊Q8—441no—
238#121—222no—
239#121—441no—
240#121—442no—
241C4×Q8—441no—
242C4×D4—442no—
243C4×D4—441no—
244#117—222no—
245#117—221no—
246C2×C4⋊C4—222no—
247C2×C4⋊C4—221no—
248C2×C4⋊C4—221no—
249M32—22no—
250C2×C16—22no—
251C2×C16C22×D1112yes—
252C2×C16C22×D1111yescharacteristic
253C2×C16C22×D1111yescharacteristic
254#107—111no—
255#107—111no—
256#107—112no—
257#107—112no—
258#107—222no—
259#107—221no—
260#107—221no—
261#106—222no—
262#106—221no—
263#103—222no—
264#102—222no—
265C2×C11—22no—
266C2×C11—42no—
267C2×C11C2×#48011yescharacteristic
268C2×C11#341611yescharacteristic
269C2×C11#341611yescharacteristic
270D11—161no—
271#41—22no—
272#41—22no—
273#41—442no—
274#41—442no—
275C2×Q8—221no—
276C2×Q8D8811yescharacteristic
277C2×D4—221no—
278C2×D4—441no—
279C2×D4—442no—
280C2×D4D8812yes—
281C2×D4D8811yescharacteristic
282C22×C4—442no—
283C22×C4—441no—
284C22×C4—441no—
285C22×C4—441no—
286C22×C4C2×D4412yes—
287C22×C4C2×D4411yescharacteristic
288Q16—221no—
289Q16—221no—
290SD16—442no—
291D8—221no—
292D8—221no—
293M16—22no—
294M16—24no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8C2×D4412yes—
298C2×C8C2×D4411yescharacteristic
299C2×C8#434112yes—
300C2×C8#434112yes—
301C2×C8C23×D1111yescharacteristic
302C4⋊C4—222no—
303C4⋊C4—221no—
304C4⋊C4—222no—
305C4⋊C4—221no—
306C4⋊C4—442no—
307C4⋊C4—441no—
308C4⋊C4—441no—
309C4⋊C4—442no—
310C22⋊C4—442no—
311C22⋊C4—441no—
312C22⋊C4—442no—
313C22⋊C4—442no—
314C42—442no—
315C42—441no—
316C16—21no—
317C16—21no—
318C16—22no—
319C11#3365311yescharacteristic, complemented, Sylow
320C23—441no—
321C23C2×D8812yes—
322C23C2×D8811yescharacteristic
323Q8—22no—
324Q8—441no—
325Q8—441no—
326D4—24no—
327D4—22no—
328D4—441no—
329D4—441no—
330D4—882no—
331D4—1762no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—441no—
335C2×C4—442no—
336C2×C4—441no—
337C2×C4—442no—
338C2×C4—441no—
339C2×C4—882no—
340C2×C4—1761no—
341C2×C4—1762no—
342C2×C4—1761no—
343C2×C4#6693912yes—
344C2×C4C2×D8812yes—
345C2×C4C2×D8811yescharacteristic
346C2×C4#6696212yes—
347C2×C4C22×D4411yescharacteristic
348C8—22no—
349C8#6693912yes—
350C8C2×#434111yescharacteristic
351C8C2×#434111yescharacteristic
352C22—21no—
353C22—21no—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—881no—
358C22—881no—
359C22—881no—
360C22#1062234912yes—
361C22C22×D8811yescharacteristic
362C4—22no—
363C4—882no—
364C4—881no—
365C4—882no—
366C4—881no—
367C4—881no—
368C4#1062234912yes—
369C4C2×#6693911yescharacteristic
370C4C2×#6696211yescharacteristic
371C2—22no—
372C2—42no—
373C2—1761no—
374C2C2×#1062234911yescharacteristic
375C2#1308176411yescharacteristic
376C2#1308176411yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2113C2
socleC22×C11C22×D8
prime radical#13078286C2
hypercenter#2113D11
hypocenterC11#33653
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131 ◁ #2113

Complements

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

NH ≅ G/Ntype
2. #13077216C2semidirect
3. #13070825C2semidirect
4. #13070814C2semidirect
5. #13070808C2semidirect
6. #13070802C2semidirect
7. #13070404C2semidirect
8. C2×#10622143C2semidirect
9. #13070329C2semidirect
10. #13070324C2semidirect
11. C11×#2113C2semidirect
142. #2113D11semidirect
319. C11#33653semidirect

Maximal subgroups

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

subgroupindex
#130782862
#130772162
#130708252
#130708142
#130708082
#130708022
#130704042
C2×#106221432
#130703292
#130703242
C11×#21132
#3365311