Finite Group Databasebeta

← #14757252

Subgroups — #14757252

Order 2816.

1110 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622608C212yesmaximal
2C2×#10622537C211yesmaximal, characteristic
3C2×#10622548C211yesmaximal, characteristic
4#13069379C214yesmaximal, complemented
5#13069374C214yesmaximal, complemented
6#13068337C212yesmaximal
7C4×C11×#117C211yesmaximal, characteristic
8C2×C11×#117C2211yescharacteristic
9C2×C11×#117C2211yescharacteristic
10C22×C42×C11C2211yescharacteristic
11C22×C4⋊Dic11—22no—
12C22×C4⋊Dic11C2212yes—
13C22×#4318C2212yes—
14C4×C11×C4⋊C4C2212yes—
15C4×C11×C4⋊C4C2212yes—
16C4×C11×C22⋊C4—22no—
17C11×#376—21no—
18C43×C11—21no—
19#10622608—28no—
20C2×#66872C2214yes—
21C2×#66871C2214yes—
22#10622548—21no—
23#10622548—21no—
24#10622548C2214yes—
25#10622537C418yescomplemented
26C2×C4⋊(C11⋊C8)C2214yes—
27#10622167C2218yes—
28C23×C4×C11D412yes—
29C23×C4×C11C2311yescharacteristic
30C23×Dic11—22no—
31C11×#117—22no—
32C11×#117—22no—
33C11×#117D414yes—
34C11×#117Q814yes—
35C2×C11×C4⋊C4C2311yescharacteristic
36C2×C11×C4⋊C4C2311yescharacteristic
37C2×C11×C4⋊C4C2312yes—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C42×C11—21no—
41C2×C42×C11—21no—
42C2×C42×C11—22no—
43C2×C42×C11—22no—
44C2×C42×C11C2×C414yes—
45C2×C42×C11D411yescharacteristic
46C2×C42×C11D411yescharacteristic
47C2×C42×C11Q814yes—
48C2×C42×C11C2312yes—
49C2×C4⋊Dic11—24no—
50C2×C4⋊Dic11—24no—
51C2×C4⋊Dic11—22no—
52C2×C4⋊Dic11—24no—
53C2×C4⋊Dic11—24no—
54C2×C4⋊Dic11—48no—
55C2×C4⋊Dic11C2314yes—
56C2×#4318—24no—
57C2×#4318—24no—
58C2×#4318C2×C418yes—
59C22×C11⋊C8C2314yes—
60C11×#95—22no—
61C11×#95—22no—
62#66872—28no—
63#66871—28no—
64C4⋊(C11⋊C8)C2×C4116yescomplemented
65#21171—111nomaximal, Sylow
66C24×C11C2×D411yescharacteristic
67C22×C4×C11—24no—
68C22×C4×C11—24no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—22no—
72C22×C4×C11C4⋊C418yes—
73C22×C4×C11C22×C412yes—
74C22×C4×C11C2×D412yes—
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D412yes—
77C22×C4×C11C2×D412yes—
78C22×C4×C11C2×Q812yes—
79C22×C4×C11C2×Q812yes—
80C22×C4×C11#4112yes—
81C22×C4×C11#4112yes—
82C22×C4×C11C2411yescharacteristic
83C22×Dic11—24no—
84C22×Dic11—48no—
85C22×Dic11—44no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—22no—
89C11×C4⋊C4C2×D412yes—
90C11×C4⋊C4C2×D412yes—
91C11×C4⋊C4C2×Q814yes—
92C11×C22⋊C4—24no—
93C11×C22⋊C4—24no—
94C42×C11—24no—
95C42×C11—24no—
96C42×C11—44no—
97C42×C11—44no—
98C42×C11C4⋊C414yes—
99C42×C11C4⋊C414yes—
100C42×C11C22×C414yes—
101C42×C11C2×Q814yes—
102C4⋊Dic11—24no—
103C4⋊Dic11—24no—
104C4⋊Dic11—48no—
105C4⋊Dic11—44no—
106C4⋊Dic11—48no—
107#4318—216no—
108C2×C11⋊C8—24no—
109C2×C11⋊C8—24no—
110C2×C11⋊C8C22×C418yes—
111C2×#428—112no—
112C2×#423—111no—
113C2×#384—111no—
114C4×#117D1111yescharacteristic
115#1948—114no—
116#1947—114no—
117#1736—112no—
118C23×C11—22no—
119C23×C11—22no—
120C23×C11C2×C4⋊C412yes—
121C23×C11#12112yes—
122C23×C11C22⋊Q812yes—
123C23×C11C22×D411yescharacteristic
124C2×C4×C11—22no—
125C2×C4×C11—22no—
126C2×C4×C11—216no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—24no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11C2×C4⋊C414yes—
135C2×C4×C11C2×C4⋊C412yes—
136C2×C4×C11C2×C4⋊C414yes—
137C2×C4×C11C4×D414yes—
138C2×C4×C11C4×Q814yes—
139C2×C4×C11#12112yes—
140C2×C4×C11C22⋊Q812yes—
141C2×C4×C11#12514yes—
142C2×C4×C11C4⋊Q814yes—
143C2×C4×C11AGL(1,ℤ/8)14yes—
144C2×C4×C11#13714yes—
145C2×C4×C11C23×C411yescharacteristic
146C2×C4×C11C22×D411yescharacteristic
147C2×C4×C11C22×Q811yescharacteristic
148C2×C4×C11C22×Q811yescharacteristic
149C2×C4×C11C2×#4111yescharacteristic
150C2×C4×C11C2×#4111yescharacteristic
151C2×Dic11—44no—
152C2×Dic11—48no—
153C2×Dic11—88no—
154C11⋊C8—28no—
155C22×M16—112no—
156C2×#117C2×D1111yescharacteristic
157C2×#117C2×D1111yescharacteristic
158C22×C4⋊C4—112no—
159C22×C4⋊C4—222no—
160C22×C42C2×D1111yescharacteristic
161#428—228no—
162C2×#107—114no—
163C2×#106—114no—
164#423—118no—
165C2×C4⋊C8—114no—
166#384—114no—
167#384—221no—
168#384—221no—
169C4×C4⋊C4C2×D1112yes—
170C4×C4⋊C4C2×D1112yes—
171C4×C22⋊C4—22no—
172#376—21no—
173C43—21no—
174#340—118no—
175C22×C11—24no—
176C22×C11—24no—
177C22×C11—22no—
178C22×C11—22no—
179C22×C11#38914yes—
180C22×C11C22×C4⋊C411yescharacteristic
181C22×C11C2×#12111yescharacteristic
182C22×C11C2×C22⋊Q811yescharacteristic
183C22×C11C2×AGL(1,ℤ/8)12yes—
184C22×C11C2×#13712yes—
185C4×C11—24no—
186C4×C11—44no—
187C4×C11—42no—
188C4×C11—42no—
189C4×C11#38914yes—
190C4×C11#42818yescomplemented
191C4×C11C2×C4×D411yescharacteristic
192C4×C11C2×C4×Q811yescharacteristic
193C4×C11C2×#12511yescharacteristic
194C4×C11C2×C4⋊Q811yescharacteristic
195Dic11—84no—
196C23×C4—222no—
197C23×C4C22⋊D1112yes—
198C23×C4C22×D1111yescharacteristic
199C2×M16—118no—
200C2×M16—224no—
201C2×M16—224no—
202C22×C8—114no—
203#117—22no—
204#117—22no—
205#117Dic2214yes—
206#117D4414yes—
207C2×C4⋊C4—114no—
208C2×C4⋊C4—224no—
209C2×C4⋊C4—224no—
210C2×C4⋊C4—222no—
211C2×C4⋊C4—224no—
212C2×C4⋊C4—224no—
213C2×C4⋊C4—448no—
214C2×C4⋊C4C22×D1112yes—
215C2×C4⋊C4C22×D1111yescharacteristic
216C2×C4⋊C4C22×D1111yescharacteristic
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C42—21no—
220C2×C42—21no—
221C2×C42—22no—
222C2×C42—22no—
223C2×C42Dic2214yes—
224C2×C42C4×D1114yes—
225C2×C42C22⋊D1111yescharacteristic
226C2×C42C22⋊D1111yescharacteristic
227C2×C42C22×D1112yes—
228#107—228no—
229#106—228no—
230C4⋊C8—1116no—
231#95—22no—
232#95—22no—
233C2×C11—24no—
234C2×C11C2×#38911yescharacteristic
235C2×C11C2×#42812yes—
236C2×C11#303811yescharacteristic
237C2×C11#303911yescharacteristic
238C2×C11#307912yes—
239C24C2×C22⋊D1111yescharacteristic
240C22×C4—24no—
241C22×C4—24no—
242C22×C4—22no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—224no—
246C22×C4—448no—
247C22×C4—444no—
248C22×C4Dic11⋊C418yes—
249C22×C4C2×Dic2212yes—
250C22×C4C2×Dic2212yes—
251C22×C4C2×C4×D1112yes—
252C22×C4C2×D4412yes—
253C22×C4#433912yes—
254C22×C4#433912yes—
255C22×C4C2×C22⋊D1112yes—
256C22×C4C2×C22⋊D1111yescharacteristic
257C22×C4C2×C22⋊D1112yes—
258C22×C4C23×D1111yescharacteristic
259M16—2216no—
260C2×C8—118no—
261C2×C8—224no—
262C2×C8—224no—
263C4⋊C4—22no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—224no—
267C4⋊C4—224no—
268C4⋊C4—448no—
269C4⋊C4—444no—
270C4⋊C4—448no—
271C4⋊C4C2×Dic2214yes—
272C4⋊C4C2×D4412yes—
273C4⋊C4C2×D4412yes—
274C22⋊C4—24no—
275C22⋊C4—24no—
276C42—24no—
277C42—24no—
278C42—44no—
279C42—44no—
280C42Dic11⋊C414yes—
281C42Dic11⋊C414yes—
282C42C2×Dic2214yes—
283C42C2×C4×D1114yes—
284C11#2117111yescharacteristic, complemented, Sylow
285C23—22no—
286C23—22no—
287C23C2×Dic11⋊C412yes—
288C23#6697712yes—
289C23#6698312yes—
290C23C22×C22⋊D1111yescharacteristic
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—216no—
294C2×C4—24no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—444no—
302C2×C4—448no—
303C2×C4—888no—
304C2×C4C4×Dic2214yes—
305C2×C4#6692214yes—
306C2×C4#6692314yes—
307C2×C4C4×D4414yes—
308C2×C4C2×Dic11⋊C414yes—
309C2×C4C2×Dic11⋊C412yes—
310C2×C4C2×Dic11⋊C414yes—
311C2×C4#6697712yes—
312C2×C4#6698312yes—
313C2×C4#6700214yes—
314C2×C4#6700414yes—
315C2×C4C22×Dic2211yescharacteristic
316C2×C4C22×Dic2211yescharacteristic
317C2×C4C22×C4×D1111yescharacteristic
318C2×C4C22×D4411yescharacteristic
319C2×C4C2×#433911yescharacteristic
320C2×C4C2×#433911yescharacteristic
321C8—228no—
322C22—22no—
323C22—22no—
324C22—24no—
325C22—24no—
326C22#1062254114yes—
327C22C22×Dic11⋊C411yescharacteristic
328C22C2×#6697711yescharacteristic
329C22C2×#6698311yescharacteristic
330C22C2×#6700212yes—
331C22C2×#6700412yes—
332C4—24no—
333C4—42no—
334C4—42no—
335C4—44no—
336C4—884no—
337C4#1062254114yes—
338C4#1062260818yescomplemented
339C4C2×C4×Dic2211yescharacteristic
340C4C2×#6692211yescharacteristic
341C4C2×#6692311yescharacteristic
342C4C2×C4×D4411yescharacteristic
343C2—24no—
344C2C2×#1062254111yescharacteristic
345C2C2×#1062260812yes—
346C2#1307809611yescharacteristic
347C2#1307810311yescharacteristic
348C2#1307843112yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#117C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC4×#117D11
hypocenterC11#21171
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#117

Complements

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

NH ≅ G/Ntype
4. #13069379C2semidirect
5. #13069374C2semidirect
25. #10622537C4semidirect
64. C4⋊(C11⋊C8)C2×C4semidirect
190. C4×C11#428semidirect
284. C11#21171semidirect
338. C4#10622608semidirect

Maximal subgroups

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

subgroupindex
C2×#106226082
C2×#106225372
C2×#106225482
#130693792
#130693742
#130683372
C4×C11×#1172
#2117111