Finite Group Databasebeta

← #14761648

Subgroups — #14761648

Order 2816.

898 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622637C211yesmaximal, characteristic, complemented
2C2×#10622625C211yesmaximal, characteristic
3#13069553C211yesmaximal, characteristic, complemented
4#13069411C211yesmaximal, characteristic
5#13069224C214yesmaximal, complemented
6#13068733C211yesmaximal, characteristic, complemented
7#13068400C214yesmaximal, complemented
8C42×C11⋊C8C211yesmaximal, characteristic, complemented
9C4×C11×#124C211yesmaximal, characteristic
10C2×C11×#124C411yescharacteristic
11C2×C4×Q8×C11C2211yescharacteristic
12C2×C4×D4×C11C2211yescharacteristic
13C22×#4318C2212yes—
14C11×#391C411yescharacteristic
15C11×#390C411yescharacteristic
16C11×#388C414yes—
17C11×#382C411yescharacteristic
18C4×C11×C22⋊C4C2214yes—
19C43×C11C2211yescharacteristic
20C2×C22⋊(C11⋊C8)C2212yes—
21C2×C22⋊(C11⋊C8)C2214yes—
22#10622637—24no—
23#10622625—24no—
24C2×C4⋊(C11⋊C8)C2211yescharacteristic
25C2×C4⋊(C11⋊C8)C2212yes—
26C2×C4⋊(C11⋊C8)C2211yescharacteristic
27C2×#66867C2212yes—
28C2×C4×C11⋊C8C2211yescharacteristic
29C2×C4×C11⋊C8C2212yes—
30C2×C4×C11⋊C8C2212yes—
31C2×C4×C11⋊C8C2211yescharacteristic
32#10622162C2214yes—
33#10622162C2214yes—
34C22×Q8×C11C2×C411yescharacteristic
35C22×D4×C11C2×C411yescharacteristic
36C23×C4×C11C2312yes—
37C11×#124—24no—
38C4×Q8×C11—22no—
39C4×Q8×C11—22no—
40C4×D4×C11—22no—
41C4×D4×C11—22no—
42C2×C11×C4⋊C4C2×C411yescharacteristic
43C2×C11×C4⋊C4C2×C411yescharacteristic
44C2×C11×C4⋊C4C2×C412yes—
45C2×C11×C22⋊C4C2×C414yes—
46C2×C11×C22⋊C4C2×C414yes—
47C2×C11×C22⋊C4C2×C412yes—
48C2×C42×C11C2×C412yes—
49C2×C42×C11C2×C411yescharacteristic
50C2×C42×C11C2×C411yescharacteristic
51C2×C42×C11C2312yes—
52C2×C42×C11C2312yes—
53C2×C42×C11C2311yescharacteristic
54C2×#4318—24no—
55C2×#4318—28no—
56C22×C11⋊C8C2312yes—
57C22×C11⋊C8C2312yes—
58C22×C11⋊C8C2311yescharacteristic
59C22×C11⋊C8C2312yes—
60C22×C11⋊C8C2311yescharacteristic
61C11×#95C2×C414yes—
62C11×#95C2×C414yes—
63C22⋊(C11⋊C8)—24no—
64C22⋊(C11⋊C8)—28no—
65C4⋊(C11⋊C8)—22no—
66C4⋊(C11⋊C8)—22no—
67C4⋊(C11⋊C8)—24no—
68#66867—24no—
69C4×C11⋊C8—22no—
70C4×C11⋊C8—24no—
71C4×C11⋊C8—24no—
72C4×C11⋊C8D414yes—
73#21631—111nomaximal, Sylow
74C24×C11C22×C412yes—
75C2×Q8×C11—22no—
76C2×Q8×C11—22no—
77C2×Q8×C11—22no—
78C2×D4×C11—22no—
79C2×D4×C11—22no—
80C2×D4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—24no—
83C22×C4×C11—24no—
84C22×C4×C11—22no—
85C22×C4×C11C22×C412yes—
86C22×C4×C11C22×C412yes—
87C22×C4×C11C22×C412yes—
88C22×C4×C11C22×C411yescharacteristic
89C22×C4×C11C22×C412yes—
90C22×C4×C11C22×C412yes—
91C22×C4×C11C22×C411yescharacteristic
92C22×C4×C11C2411yescharacteristic
93C11×C4⋊C4—22no—
94C11×C4⋊C4—22no—
95C11×C4⋊C4—24no—
96C11×C22⋊C4—24no—
97C11×C22⋊C4—28no—
98C11×C22⋊C4—28no—
99C42×C11—24no—
100C42×C11—22no—
101C42×C11—22no—
102C42×C11—22no—
103C42×C11—22no—
104C42×C11—22no—
105C42×C11M1614yescomplemented
106C42×C11C2×D412yes—
107C42×C11#4112yes—
108#4318—48no—
109C2×C11⋊C8—22no—
110C2×C11⋊C8—22no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—24no—
115C2×C11⋊C8—24no—
116C2×C11⋊C8C2×D412yes—
117C2×C11⋊C8C2×D412yes—
118C2×C11⋊C8#4114yes—
119C2×C11⋊C8#4114yes—
120C2×#446—111no—
121C2×#436—111no—
122C4×#124D1111yescharacteristic
123#1984—111no—
124#1954—111no—
125#1923—114no—
126#1831—111no—
127#1753—114no—
128C42×C8—111no—
129C23×C11—22no—
130C23×C11—24no—
131C23×C11—22no—
132C23×C11—24no—
133C23×C11—22no—
134C23×C11C23×C411yescharacteristic
135Q8×C11—44no—
136D4×C11—44no—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—24no—
146C2×C4×C11—22no—
147C2×C4×C11—24no—
148C2×C4×C11—22no—
149C2×C4×C11—42no—
150C2×C4×C11—44no—
151C2×C4×C11—42no—
152C2×C4×C11C4×D412yes—
153C2×C4×C11C4×D412yes—
154C2×C4×C11C2×M1614yes—
155C2×C4×C11C2×M1612yes—
156C2×C4×C11#13114yes—
157C2×C4×C11#13112yes—
158C2×C4×C11C22×D411yescharacteristic
159C2×C4×C11C2×#4111yescharacteristic
160C2×C4×C11C2×#4112yes—
161C2×C4×C11C2×#4112yes—
162C11⋊C8—24no—
163C11⋊C8—22no—
164C11⋊C8—42no—
165C11⋊C8—42no—
166C11⋊C8#12414yescomplemented
167C22×M16—112no—
168C2×#124Dic1111yescharacteristic
169C2×C4×Q8C2×D1111yescharacteristic
170C2×C4×D4C2×D1111yescharacteristic
171#446—224no—
172#436—224no—
173C2×C4⋊C8—111no—
174C2×C4⋊C8—111no—
175C2×C4⋊C8—112no—
176C2×C22⋊C8—112no—
177C2×C22⋊C8—114no—
178C2×#97—112no—
179C2×C4×C8—111no—
180C2×C4×C8—112no—
181C2×C4×C8—111no—
182C2×C4×C8—112no—
183#391Dic1111yescharacteristic
184#390Dic1111yescharacteristic
185#388Dic1114yes—
186#382Dic1111yescharacteristic
187C4×C22⋊C4C2×D1114yes—
188C43C2×D1111yescharacteristic
189#336—114no—
190#336—114no—
191C22×C11—42no—
192C22×C11—42no—
193C22×C11—44no—
194C22×C11—44no—
195C22×C11—42no—
196C22×C11C2×C4×D411yescharacteristic
197C22×C11C4×#4112yes—
198C22×C11C22×M1611yescharacteristic
199C22×C11C2×#13111yescharacteristic
200C22×C11C2×#13112yes—
201C4×C11—22no—
202C4×C11—24no—
203C4×C11—24no—
204C4×C11—42no—
205C4×C11—42no—
206C4×C11—42no—
207C4×C11#43614yes—
208C4×C11C2×#12411yescharacteristic
209C4×C11#52912yes—
210C4×C11#53211yescharacteristic
211C22×Q8C2×Dic1111yescharacteristic
212C22×D4C2×Dic1111yescharacteristic
213C23×C4C22×D1112yes—
214C2×M16—228no—
215C2×M16—224no—
216C22×C8—111no—
217C22×C8—112no—
218C22×C8—111no—
219C22×C8—112no—
220C22×C8—112no—
221#124—24no—
222C4×Q8—22no—
223C4×Q8—22no—
224C4×D4—22no—
225C4×D4—22no—
226C2×C4⋊C4C2×Dic1111yescharacteristic
227C2×C4⋊C4C2×Dic1111yescharacteristic
228C2×C4⋊C4C2×Dic1112yes—
229C2×C22⋊C4C2×Dic1112yes—
230C2×C22⋊C4C2×Dic1114yes—
231C2×C22⋊C4C2×Dic1114yes—
232C2×C42C2×Dic1112yes—
233C2×C42C2×Dic1111yescharacteristic
234C2×C42C2×Dic1111yescharacteristic
235C2×C42C22×D1112yes—
236C2×C42C22×D1112yes—
237C2×C42C22×D1111yescharacteristic
238C4⋊C8—224no—
239C4⋊C8—222no—
240C4⋊C8—222no—
241C22⋊C8—228no—
242C22⋊C8—224no—
243#97—224no—
244C4×C8—114no—
245C4×C8—224no—
246C4×C8—224no—
247C4×C8—222no—
248#95C2×Dic1114yes—
249#95C2×Dic1114yes—
250C2×C11—82no—
251C2×C11C4×#12411yescharacteristic
252C2×C11C2×#43611yescharacteristic
253C2×C11#293111yescharacteristic
254C2×C11#296512yes—
255C2×C11#296612yes—
256C24C22×Dic1112yes—
257C2×Q8—22no—
258C2×Q8—22no—
259C2×Q8—22no—
260C2×D4—22no—
261C2×D4—22no—
262C2×D4—22no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—24no—
266C22×C4—24no—
267C22×C4C22×Dic1112yes—
268C22×C4C22×Dic1112yes—
269C22×C4C22×Dic1112yes—
270C22×C4C22×Dic1112yes—
271C22×C4C22×Dic1111yescharacteristic
272C22×C4C22×Dic1112yes—
273C22×C4C22×Dic1111yescharacteristic
274C22×C4C23×D1111yescharacteristic
275M16—448no—
276C2×C8—112no—
277C2×C8—114no—
278C2×C8—112no—
279C2×C8—114no—
280C2×C8—222no—
281C2×C8—222no—
282C2×C8—222no—
283C2×C8—222no—
284C2×C8—222no—
285C2×C8—224no—
286C2×C8—224no—
287C4⋊C4—22no—
288C4⋊C4—22no—
289C4⋊C4—24no—
290C22⋊C4—28no—
291C22⋊C4—24no—
292C22⋊C4—28no—
293C42—24no—
294C42—22no—
295C42—22no—
296C42—22no—
297C42—22no—
298C42—22no—
299C42#431814yescomplemented
300C42D4×D1112yes—
301C42#434112yes—
302C11#2163111yescharacteristic, complemented, Sylow
303C23—22no—
304C23—22no—
305C23—24no—
306C23—22no—
307C23—24no—
308C23C23×Dic1111yescharacteristic
309Q8—44no—
310D4—44no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—24no—
321C2×C4—22no—
322C2×C4—24no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—44no—
326C2×C4C2×#431814yes—
327C2×C4C2×#431812yes—
328C2×C4D4×Dic1112yes—
329C2×C4D4×Dic1112yes—
330C2×C4#6700114yes—
331C2×C4#6700112yes—
332C2×C4C2×D4×D1111yescharacteristic
333C2×C4C2×#434111yescharacteristic
334C2×C4#41×D1112yes—
335C2×C4#41×D1112yes—
336C8—114no—
337C8—222no—
338C8—224no—
339C8—442no—
340C8—442no—
341C22—42no—
342C22—42no—
343C22—44no—
344C22—42no—
345C22—44no—
346C22C22×#431811yescharacteristic
347C22C2×D4×Dic1111yescharacteristic
348C22C2×#6700111yescharacteristic
349C22C2×#6700112yes—
350C22#41×Dic1112yes—
351C4—24no—
352C4—22no—
353C4—24no—
354C4—42no—
355C4—42no—
356C4—42no—
357C4#1062262514yes—
358C4#1062319911yescharacteristic
359C4D11×#12411yescharacteristic
360C4#1062321112yes—
361C2—82no—
362C2#124×Dic1111yescharacteristic
363C2C2×#1062262511yescharacteristic
364C2#1307732811yescharacteristic
365C2#1307758312yes—
366C2#1307759212yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC4×C11×#124C2
prime radicalC22×D4×C11C2×C4
cosocleC22×C4×C11C24
hypercenterC4×#124D11
hypocenterC11#21631
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#124

Complements

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

NH ≅ G/Ntype
1. C2×#10622637C2semidirect
3. #13069553C2semidirect
5. #13069224C2semidirect
6. #13068733C2semidirect
7. #13068400C2semidirect
8. C42×C11⋊C8C2semidirect
105. C42×C11M16semidirect
166. C11⋊C8#124semidirect
299. C42#4318semidirect
302. C11#21631semidirect

Maximal subgroups

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

subgroupindex
C2×#106226372
C2×#106226252
#130695532
#130694112
#130692242
#130687332
#130684002
C42×C11⋊C82
C4×C11×#1242
#2163111