Finite Group Databasebeta

← #14908644

Subgroups — #14908644

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#13077216C211yesmaximal, characteristic, complemented
2#13070821C212yesmaximal, complemented
3#13070811C212yesmaximal, complemented
4#13070804C212yesmaximal, complemented
5#13070799C212yesmaximal, complemented
6#13070402C211yesmaximal, characteristic, complemented
7C2×#10622128C211yesmaximal, characteristic, complemented
8#13070328C211yesmaximal, characteristic, complemented
9#13070323C211yesmaximal, characteristic, complemented
10#13070230C211yesmaximal, characteristic, complemented
11C11×#3061C211yesmaximal, characteristic
12C2×C11×#135C2211yescharacteristic
13C2×C11×#131C2211yescharacteristic
14C11×#537—21no—
15#10623358—21no—
16C11×#468—22no—
17C11×#467C2212yes—
18C11×#466C2212yes—
19C2×C11×#107C2211yescharacteristic
20C11×#417—21no—
21#10622734—21no—
22#10622734—22no—
23#10622719C2211yescharacteristic
24#10622719C2212yes—
25C2×#66882C2211yescharacteristic
26C2×#66882C2212yes—
27C2×#66876C2211yescharacteristic
28C22×C11⋊C16C2211yescharacteristic
29#10622202C2211yescharacteristic
30#10622202C2212yes—
31#10622202C2211yescharacteristic
32#10622200C2211yescharacteristic
33#10622200C2212yes—
34#10622200C2211yescharacteristic
35C22⋊(C11⋊C16)C2212yes—
36C22⋊(C11⋊C16)C2212yes—
37#10622128C2212yes—
38#10622128C2212yes—
39#10622128C2212yes—
40#10622127C2212yes—
41C2×C11×#41—21no—
42C2×C11×#41D411yescharacteristic
43C11×#135—22no—
44C11×#135—22no—
45C2×C11×Q16C2311yescharacteristic
46C2×C11×SD16—21no—
47C2×C11×D8C2311yescharacteristic
48C11×#131—22no—
49C11×#131—22no—
50C2×C11×M16D411yescharacteristic
51C2×C11×M16D412yes—
52C22×C8×C11C2312yes—
53C22×C8×C11C2311yescharacteristic
54C11×C22⋊Q8—22no—
55C11×C22⋊Q8—41no—
56C11×#121—22no—
57C11×#121—41no—
58C11×#121—42no—
59C2×C11×C4⋊C4—21no—
60Q8×Dic11—41no—
61D4×Dic11—42no—
62D4×Dic11—41no—
63#66979—22no—
64#66979—21no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11—21no—
67C11×#107—21no—
68C11×#107C2312yes—
69C11×#103—22no—
70C11×#102—22no—
71#66882—22no—
72#66882—21no—
73#66882C2311yescharacteristic
74#66882C2312yes—
75#66882C2311yescharacteristic
76#66881—22no—
77#66881—21no—
78#66876—22no—
79C2×C11⋊C16—22no—
80C2×C11⋊C16C2312yes—
81C2×C11⋊C16C2311yescharacteristic
82C2×C11⋊C16C2311yescharacteristic
83#33653—111nomaximal, Sylow
84C11×#41—22no—
85C11×#41—22no—
86C11×#41—42no—
87C11×#41—42no—
88C2×Q8×C11—21no—
89C2×Q8×C11D811yescharacteristic
90C2×D4×C11—21no—
91C2×D4×C11—41no—
92C2×D4×C11—42no—
93C2×D4×C11D812yes—
94C2×D4×C11D811yescharacteristic
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D411yescharacteristic
99C22×Dic11—42no—
100C22×Dic11—41no—
101C11×Q16—21no—
102C11×Q16—21no—
103C11×SD16—42no—
104C11×D8—21no—
105C11×D8—21no—
106C11×M16—24no—
107C11×M16—22no—
108C2×C8×C11—22no—
109C2×C8×C11—22no—
110C2×C8×C11C2×D412yes—
111C2×C8×C11C2×D411yescharacteristic
112C2×C8×C11#4112yes—
113C2×C8×C11#4112yes—
114C2×C8×C11C2411yescharacteristic
115C11×C4⋊C4—22no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—42no—
118C11×C22⋊C4—42no—
119C11×C22⋊C4—42no—
120C22⋊Dic11—42no—
121C22⋊Dic11—41no—
122C4⋊Dic11—21no—
123C4⋊Dic11—22no—
124C4⋊Dic11—21no—
125C4⋊Dic11—42no—
126C4⋊Dic11—41no—
127C4×Dic11—42no—
128C4×Dic11—41no—
129C11⋊C16—21no—
130C11⋊C16—21no—
131C11⋊C16—22no—
132#3061D1111yescharacteristic
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#2113—111no—
143C23×C11—41no—
144C23×C11C2×D812yes—
145C23×C11C2×D811yescharacteristic
146Q8×C11—22no—
147Q8×C11—41no—
148Q8×C11—41no—
149D4×C11—24no—
150D4×C11—22no—
151D4×C11—41no—
152D4×C11—41no—
153D4×C11—82no—
154D4×C11—162no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—42no—
158C2×C4×C11—41no—
159C2×C4×C11—82no—
160C2×C4×C11—161no—
161C2×C4×C11#12312yes—
162C2×C4×C11C2×D812yes—
163C2×C4×C11C2×D811yescharacteristic
164C2×C4×C11#13712yes—
165C2×C4×C11C22×D411yescharacteristic
166C2×Dic11—41no—
167C2×Dic11—42no—
168C2×Dic11—41no—
169C2×Dic11—161no—
170C2×Dic11—162no—
171C8×C11—22no—
172C8×C11#12312yes—
173C8×C11C2×#4111yescharacteristic
174C8×C11C2×#4111yescharacteristic
175C2×#135C2×D1111yescharacteristic
176C2×#131C2×D1111yescharacteristic
177#537—21no—
178#520—221no—
179C2×M32—111no—
180C22×C16—111no—
181#468—22no—
182#467C2×D1112yes—
183#466C2×D1112yes—
184#428—221no—
185#428—222no—
186#427—111no—
187#427—112no—
188C2×#107—111no—
189C2×#107—112no—
190C2×#107C2×D1111yescharacteristic
191#417—21no—
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⋊C16—112no—
203C22⋊C16—112no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—22no—
207C22×C11—22no—
208C22×C11—22no—
209C22×C11—81no—
210C22×C11—81no—
211C22×C11—81no—
212C22×C11#48012yes—
213C22×C11C22×D811yescharacteristic
214C4×C11—22no—
215C4×C11—81no—
216C4×C11—82no—
217C4×C11#48012yes—
218C4×C11C2×#12311yescharacteristic
219C4×C11C2×#13711yescharacteristic
220Dic11—81no—
221Dic11—82no—
222Dic11—81no—
223C2×#41—21no—
224C2×#41C22⋊D1111yescharacteristic
225#135—22no—
226#135—22no—
227C2×Q16C22×D1111yescharacteristic
228C2×SD16—21no—
229C2×D8C22×D1111yescharacteristic
230#131—22no—
231#131—22no—
232C2×M16C22⋊D1111yescharacteristic
233C2×M16C22⋊D1112yes—
234C22×C8C22×D1112yes—
235C22×C8C22×D1111yescharacteristic
236C22⋊Q8—22no—
237C22⋊Q8—41no—
238#121—22no—
239#121—41no—
240#121—42no—
241C4×Q8—441no—
242C4×D4—442no—
243C4×D4—441no—
244#117—222no—
245#117—221no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—222no—
248C2×C4⋊C4—221no—
249M32—222no—
250C2×C16—112no—
251C2×C16—111no—
252C2×C16—111no—
253C2×C16—222no—
254#107—21no—
255#107—111no—
256#107—111no—
257#107—112no—
258#107—222no—
259#107—221no—
260#107C22×D1112yes—
261#106—222no—
262#106—221no—
263#103—22no—
264#102—22no—
265C2×C11—22no—
266C2×C11—42no—
267C2×C11—161no—
268C2×C11C2×#48011yescharacteristic
269C2×C11#341611yescharacteristic
270C2×C11#341611yescharacteristic
271#41—22no—
272#41—22no—
273#41—42no—
274#41—42no—
275C2×Q8—21no—
276C2×Q8#432311yescharacteristic
277C2×D4—21no—
278C2×D4—41no—
279C2×D4—42no—
280C2×D4#432312yes—
281C2×D4#432311yescharacteristic
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—442no—
285C22×C4—441no—
286C22×C4C2×C22⋊D1112yes—
287C22×C4C2×C22⋊D1111yescharacteristic
288Q16—21no—
289Q16—21no—
290SD16—42no—
291D8—21no—
292D8—21no—
293M16—22no—
294M16—24no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8#434112yes—
298C2×C8#434112yes—
299C2×C8C2×C22⋊D1112yes—
300C2×C8C2×C22⋊D1111yescharacteristic
301C2×C8C23×D1111yescharacteristic
302C4⋊C4—22no—
303C4⋊C4—41no—
304C4⋊C4—42no—
305C4⋊C4—221no—
306C4⋊C4—222no—
307C4⋊C4—221no—
308C4⋊C4—442no—
309C4⋊C4—441no—
310C22⋊C4—42no—
311C22⋊C4—42no—
312C22⋊C4—442no—
313C22⋊C4—441no—
314C42—442no—
315C42—441no—
316C16—221no—
317C16—221no—
318C16—222no—
319C11#3365311yescharacteristic, complemented, Sylow
320C23—41no—
321C23C2×#432312yes—
322C23C2×#432311yescharacteristic
323Q8—22no—
324Q8—41no—
325Q8—41no—
326D4—24no—
327D4—22no—
328D4—41no—
329D4—41no—
330D4—82no—
331D4—162no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—82no—
337C2×C4—161no—
338C2×C4—441no—
339C2×C4—442no—
340C2×C4—441no—
341C2×C4—1761no—
342C2×C4—1762no—
343C2×C4C2×#432312yes—
344C2×C4C2×#432311yescharacteristic
345C2×C4#6698812yes—
346C2×C4#6700412yes—
347C2×C4C22×C22⋊D1111yescharacteristic
348C8—22no—
349C8#6698812yes—
350C8C2×#434111yescharacteristic
351C8C2×#434111yescharacteristic
352C22—21no—
353C22—21no—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22#1062264612yes—
361C22C22×#432311yescharacteristic
362C4—22no—
363C4—82no—
364C4—81no—
365C4—882no—
366C4—881no—
367C4—881no—
368C4#1062264612yes—
369C4C2×#6698811yescharacteristic
370C4C2×#6700411yescharacteristic
371C2—22no—
372C2—42no—
373C2—161no—
374C2C2×#1062264611yescharacteristic
375C2#1308176011yescharacteristic
376C2#1308176311yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
Fitting, prime radicalC11×#3061C2
socleC22×C11C22×D8
hypercenter#3061D11
hypocenterC11#33653
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131 ◁ #3061

Complements

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

NH ≅ G/Ntype
1. #13077216C2semidirect
2. #13070821C2semidirect
3. #13070811C2semidirect
4. #13070804C2semidirect
5. #13070799C2semidirect
6. #13070402C2semidirect
7. C2×#10622128C2semidirect
8. #13070328C2semidirect
9. #13070323C2semidirect
10. #13070230C2semidirect
319. C11#33653semidirect

Maximal subgroups

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

subgroupindex
#130772162
#130708212
#130708112
#130708042
#130707992
#130704022
C2×#106221282
#130703282
#130703232
#130702302
C11×#30612
#3365311