Finite Group Databasebeta

← #14784657

Subgroups — #14784657

Order 2816.

616 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077546C211yesmaximal, characteristic, complemented
2#13077519C211yesmaximal, characteristic
3#13070197C211yesmaximal, characteristic, complemented
4#13070191C211yesmaximal, characteristic, complemented
5#13070069C212yesmaximal, complemented
6#13069919C211yesmaximal, characteristic
7#13069788C212yesmaximal, complemented
8#13068454C212yesmaximal, complemented
9#13068419C212yesmaximal, complemented
10#13068372C211yesmaximal, characteristic, complemented
11C11×#2050C211yesmaximal, characteristic
12C11×#575C2211yescharacteristic
13C2×#67001C2212yes—
14#10623001C2211yescharacteristic
15C11×#423C2211yescharacteristic
16C2×C11×#104C2212yes—
17C11×#413C2212yes—
18#10622853C2212yes—
19#10622849C2212yes—
20#10622846C2212yes—
21#10622810—22no—
22#10622809—22no—
23#10622738C2211yescharacteristic
24#10622735C2211yescharacteristic
25#10622735C2212yes—
26#10622735C2211yescharacteristic
27#10622732C2211yescharacteristic
28#10622732C2211yescharacteristic
29C2×C4×C11⋊C8C2211yescharacteristic
30#10622444—22no—
31#10622443—22no—
32C11×#338C2211yescharacteristic
33#10622197C2212yes—
34#10622197C2212yes—
35#10622196C2212yes—
36#10622195C2211yescharacteristic
37#10622195C2212yes—
38#10622161C2212yes—
39C2×C11×#41C2312yes—
40C11×#137—22no—
41C11×AGL(1,ℤ/8)—22no—
42C11×#135—22no—
43C2×C11×M16C2311yescharacteristic
44C2×C11×M16C2312yes—
45C2×C11×M16C2311yescharacteristic
46C2×C42×C11C2311yescharacteristic
47#67001—22no—
48#67001—22no—
49#67001—22no—
50#67001—22no—
51#66979C2312yes—
52#66979C2311yescharacteristic
53#66979C2311yescharacteristic
54#66977—22no—
55C2×#4318—22no—
56C2×#4318C2312yes—
57C22×C11⋊C8—22no—
58C22×C11⋊C8C2311yescharacteristic
59C22×C11⋊C8C2311yescharacteristic
60#66923—21no—
61#66922—21no—
62C4×Dic22—22no—
63C11×C4⋊C8—22no—
64C11×#104—22no—
65C11×#104—22no—
66C11×#101—22no—
67C11×#100—22no—
68#66901—24no—
69#66899—22no—
70#66898—24no—
71#66896—22no—
72#66883—22no—
73#66879—21no—
74#66879—22no—
75#66879D412yes—
76Dic11⋊C8—22no—
77Dic11⋊C8—22no—
78C8×Dic11—21no—
79C8×Dic11—22no—
80C8×Dic11D412yes—
81C4×C11⋊C8—21no—
82C4×C11⋊C8—21no—
83#23833—111nomaximal, Sylow
84C11×#41—22no—
85C11×#41—22no—
86C11×#41—22no—
87C11×#41—22no—
88C2×Q8×C11#4112yes—
89C2×D4×C11—22no—
90C2×D4×C11#4112yes—
91C22×C4×C11—21no—
92C22×C4×C11—22no—
93C22×C4×C11C2411yescharacteristic
94C2×Dic22—22no—
95C11×Q16—22no—
96C11×SD16—24no—
97C11×D8—22no—
98C11×M16—22no—
99C11×M16—22no—
100C11×M16—22no—
101C11×M16—22no—
102C2×C8×C11—21no—
103C2×C8×C11—22no—
104C2×C8×C11C2×D412yes—
105C42×C11—21no—
106C42×C11#4111yescharacteristic
107C42×C11#4111yescharacteristic
108C22⋊Dic11—21no—
109C22⋊Dic11—22no—
110C22⋊Dic11#4112yes—
111C4⋊Dic11—22no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114C4⋊Dic11—22no—
115Dic11⋊C4—24no—
116C4×Dic11—21no—
117C4×Dic11—22no—
118C4×Dic11C2×D412yes—
119#4318—22no—
120#4318—22no—
121#4318—42no—
122#4318—42no—
123C2×C11⋊C8—21no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—42no—
127C2×C11⋊C8—42no—
128C2×C11⋊C8C2×D411yescharacteristic
129C2×C11⋊C8C2×D411yescharacteristic
130C2×C11⋊C8#4112yes—
131C2×C11⋊C8#4112yes—
132#2960—111no—
133#2955—111no—
134#2103—111no—
135#2102—111no—
136#2080—112no—
137#2053—111no—
138#2050D1111yescharacteristic
139#2031—112no—
140#1764—112no—
141#1757—112no—
142#1747—111no—
143C23×C11—22no—
144C23×C11C2×#4111yescharacteristic
145Q8×C11—22no—
146Q8×C11—22no—
147D4×C11—22no—
148D4×C11—22no—
149D4×C11—42no—
150D4×C11—42no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—22no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11—42no—
157C2×C4×C11C22×D411yescharacteristic
158C2×C4×C11C2×#4112yes—
159C2×C4×C11C2×#4111yescharacteristic
160C2×C4×C11C2×#4112yes—
161C2×Dic11—22no—
162C2×Dic11—22no—
163C2×Dic11—42no—
164Dic22—44no—
165C8×C11—22no—
166C8×C11—41no—
167C8×C11—42no—
168C11⋊C8—41no—
169C11⋊C8—42no—
170C11⋊C8#12411yescharacteristic
171C11⋊C8#12412yes—
172C11⋊C8#12411yescharacteristic
173#575C2×D1111yescharacteristic
174C2×#131—112no—
175#533—111no—
176#446—222no—
177C8×Q8—222no—
178#444—222no—
179#443—222no—
180#430—111no—
181#424—111no—
182#424—111no—
183#423C2×D1111yescharacteristic
184#421—112no—
185C2×#104C2×D1112yes—
186#416—112no—
187#413C2×D1112yes—
188#410—112no—
189#405—111no—
190#405—111no—
191#405—112no—
192C2×C4×C8—111no—
193#344—112no—
194#344—112no—
195#341—112no—
196#339—112no—
197#338C2×D1111yescharacteristic
198H(3,ℤ/4)—111no—
199H(3,ℤ/4)—112no—
200C22×C11—41no—
201C22×C11—42no—
202C22×C11—82no—
203C22×C11#52511yescharacteristic
204C22×C11#52912yes—
205C4×C11—22no—
206C4×C11—41no—
207C4×C11—42no—
208C4×C11#52511yescharacteristic
209C4×C11C2×#12411yescharacteristic
210C4×C11#52912yes—
211Dic11—42no—
212Dic11—42no—
213Dic11—82no—
214C2×#41C22×D1112yes—
215#137—22no—
216AGL(1,ℤ/8)—22no—
217#135—22no—
218#131—222no—
219#131—222no—
220#131—222no—
221#131—222no—
222C2×M16—112no—
223C2×M16—222no—
224C2×M16C22×D1112yes—
225C2×M16C22×D1111yescharacteristic
226C2×M16C22×D1111yescharacteristic
227C22×C8—111no—
228C22×C8—111no—
229C22×C8—222no—
230C4⋊Q8—221no—
231#125—221no—
232C22⋊Q8—222no—
233C4×Q8—222no—
234#117—111no—
235#117—111no—
236#117—112no—
237C2×C42C22×D1111yescharacteristic
238#108—222no—
239C4⋊C8—22no—
240C4⋊C8—222no—
241C4⋊C8—222no—
242#104—22no—
243#104—22no—
244#104—224no—
245#103—222no—
246#102—222no—
247#101—22no—
248#100—22no—
249#99—224no—
250#97—112no—
251#97—222no—
252#97—221no—
253C4×C8—112no—
254C4×C8—221no—
255C4×C8—221no—
256C4×C8—222no—
257C4×C8—221no—
258C2×C11—21no—
259C2×C11—22no—
260C2×C11—82no—
261C2×C11#239811yescharacteristic
262#41—22no—
263#41—22no—
264#41—22no—
265#41—22no—
266C2×Q8—222no—
267C2×Q8#434112yes—
268C2×D4—22no—
269C2×D4#434112yes—
270C22×C4—21no—
271C22×C4—22no—
272C22×C4C23×D1111yescharacteristic
273Q16—22no—
274SD16—24no—
275D8—22no—
276M16—22no—
277M16—22no—
278M16—22no—
279M16—22no—
280M16—222no—
281M16—222no—
282M16—442no—
283M16—442no—
284C2×C8—21no—
285C2×C8—22no—
286C2×C8—111no—
287C2×C8—111no—
288C2×C8—112no—
289C2×C8—112no—
290C2×C8—221no—
291C2×C8—222no—
292C2×C8—222no—
293C2×C8—442no—
294C2×C8—442no—
295C2×C8D4×D1112yes—
296C4⋊C4—224no—
297C4⋊C4—222no—
298C4⋊C4—221no—
299C4⋊C4—221no—
300C4⋊C4—222no—
301C22⋊C4—112no—
302C22⋊C4—221no—
303C22⋊C4—222no—
304C42—21no—
305C42—112no—
306C42—221no—
307C42—222no—
308C42#434111yescharacteristic
309C42#434111yescharacteristic
310C11#2383311yescharacteristic, complemented, Sylow
311C23—22no—
312C23#41×D1111yescharacteristic
313Q8—22no—
314Q8—22no—
315Q8—444no—
316D4—22no—
317D4—22no—
318D4—42no—
319D4—42no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—22no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—222no—
327C2×C4—222no—
328C2×C4—442no—
329C2×C4C2×D4×D1111yescharacteristic
330C2×C4C2×#434112yes—
331C2×C4C2×#434111yescharacteristic
332C2×C4#41×D1112yes—
333C8—22no—
334C8—41no—
335C8—42no—
336C8—111no—
337C8—112no—
338C8—111no—
339C8—441no—
340C8—442no—
341C22—41no—
342C22—42no—
343C22—82no—
344C22#1062313711yescharacteristic
345C22#1062318012yes—
346C4—22no—
347C4—41no—
348C4—42no—
349C4—442no—
350C4—442no—
351C4—882no—
352C4#1062311711yescharacteristic
353C4#1062313112yes—
354C4D11×#12411yescharacteristic
355C2—21no—
356C2—22no—
357C2—82no—
358C2#1307190411yescharacteristic
subgroupG/H
centerC4D11×#124
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2050C2
socleC2×C11#2398
prime radicalC11×#575C22
hypercenter#2050D11
hypocenterC11#23833
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ #2050

Complements

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

NH ≅ G/Ntype
1. #13077546C2semidirect
3. #13070197C2semidirect
4. #13070191C2semidirect
5. #13070069C2semidirect
7. #13069788C2semidirect
8. #13068454C2semidirect
9. #13068419C2semidirect
10. #13068372C2semidirect
310. C11#23833semidirect

Maximal subgroups

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

subgroupindex
#130775462
#130775192
#130701972
#130701912
#130700692
#130699192
#130697882
#130684542
#130684192
#130683722
C11×#20502
#2383311