Finite Group Databasebeta

← #14652071

Subgroups — #14652071

Order 2816.

394 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069552C211yesmaximal, characteristic
2C4×#66874C211yesmaximal, characteristic
3C2×#10622122C211yesmaximal, characteristic
4C2×#10622092C211yesmaximal, characteristic
5#13066457C211yesmaximal, characteristic
6#13066450C211yesmaximal, characteristic
7C11×#1939C211yesmaximal, characteristic
8C2×C4×Dic22C2211yescharacteristic
9C2×C11×C4⋊C8—21no—
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×C4×C8×C11C2211yescharacteristic
12C4×C11×C4⋊C4C2211yescharacteristic
13C2×#66874C411yescharacteristic
14C2×#66874C411yescharacteristic
15C2×C4⋊(C11⋊C8)C2211yescharacteristic
16C2×C4×C11⋊C8C2211yescharacteristic
17C2×C4×C11⋊C8C2211yescharacteristic
18C11×#336—21no—
19#10622188—21no—
20#10622188—21no—
21#10622167C411yescharacteristic
22#10622167C411yescharacteristic
23#10622122—22no—
24#10622092—22no—
25C22×Dic22C2×C411yescharacteristic
26C22×C8×C11—21no—
27C22×C8×C11D411yescharacteristic
28C22×C8×C11D411yescharacteristic
29C2×C11×C4⋊C4C2×C411yescharacteristic
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C42×C11—21no—
32C2×C42×C11C2311yescharacteristic
33C2×C4⋊Dic11C2×C411yescharacteristic
34C2×Dic11⋊C4—21no—
35C2×C4×Dic11—21no—
36C22×C11⋊C8—21no—
37C22×C11⋊C8—21no—
38C22×C11⋊C8C2×C411yescharacteristic
39C22×C11⋊C8C2×C411yescharacteristic
40C4×Dic22—21no—
41C4×Dic22—21no—
42C4×Dic22—21no—
43C4×Dic22—21no—
44C11×C4⋊C8—21no—
45C11×C4⋊C8—21no—
46C11×C4⋊C8—42no—
47C4×C8×C11—21no—
48C4×C8×C11—21no—
49C11×#95—21no—
50#66874—22no—
51#66874—22no—
52C4⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)—21no—
54C4×C11⋊C8—21no—
55C4×C11⋊C8—21no—
56C4×C11⋊C8—21no—
57C4×C11⋊C8D412yes—
58#9559—111nomaximal, Sylow
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11C22×C411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11#4111yescharacteristic
64C22×Dic11—21no—
65C22×Dic11—21no—
66C2×Dic22—21no—
67C2×Dic22—21no—
68C2×Dic22—21no—
69C2×Dic22—21no—
70C2×Dic22—21no—
71C2×Dic22M1612yes—
72C2×C8×C11—21no—
73C2×C8×C11—21no—
74C2×C8×C11—21no—
75C2×C8×C11—21no—
76C2×C8×C11—21no—
77C2×C8×C11—21no—
78C2×C8×C11—41no—
79C2×C8×C11—41no—
80C2×C8×C11—41no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4M1612yes—
85C42×C11—41no—
86C42×C11—41no—
87C42×C11C2×D411yescharacteristic
88C42×C11#4111yescharacteristic
89C42×C11#4111yescharacteristic
90C42×C11#4111yescharacteristic
91C4⋊Dic11—21no—
92C4⋊Dic11—21no—
93Dic11⋊C4—41no—
94Dic11⋊C4—41no—
95C4×Dic11—41no—
96C4×Dic11—41no—
97C2×C11⋊C8—22no—
98C2×C11⋊C8—22no—
99C2×C11⋊C8—21no—
100C2×C11⋊C8—21no—
101C2×C11⋊C8—22no—
102C2×C11⋊C8—21no—
103C2×C11⋊C8—21no—
104C2×C11⋊C8—21no—
105C2×C11⋊C8—21no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8—41no—
109#1984—111no—
110#1939D1111yescharacteristic
111C4×#103—111no—
112C2×Q8⋊C8—111no—
113C2×#322—111no—
114#1279—111no—
115#1277—111no—
116C23×C11C4×D411yescharacteristic
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—22no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11#11711yescharacteristic
126C2×C4×C11C4×D411yescharacteristic
127C2×C4×C11#12111yescharacteristic
128C2×C4×C11#12311yescharacteristic
129C2×C4×C11#12411yescharacteristic
130C2×C4×C11#12611yescharacteristic
131C2×C4×C11C2×M1611yescharacteristic
132C2×C4×C11C2×M1611yescharacteristic
133C2×C4×C11#13111yescharacteristic
134C2×C4×C11#13111yescharacteristic
135C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C11#13711yescharacteristic
137C2×C4×C11#13711yescharacteristic
138C2×C4×C11#13711yescharacteristic
139C2×Dic11—22no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145Dic22—22no—
146Dic22—22no—
147Dic22—41no—
148Dic22—41no—
149C8×C11—41no—
150C8×C11—41no—
151C8×C11—81no—
152C11⋊C8—24no—
153C11⋊C8—41no—
154C11⋊C8—41no—
155C11⋊C8—81no—
156C2×C4×Q8—111no—
157C2×C4⋊C8—21no—
158C2×C4⋊C8—111no—
159C2×C4⋊C8C2×D1111yescharacteristic
160C2×#103—111no—
161C2×#103—111no—
162C2×C4×C8—111no—
163C2×C4×C8—111no—
164C2×C4×C8C2×D1111yescharacteristic
165C4×C4⋊C4C2×D1111yescharacteristic
166#340—111no—
167#340—111no—
168#336—21no—
169#336—221no—
170#336—221no—
171Q8⋊C8—222no—
172#322—222no—
173C22×C11#38811yescharacteristic
174C22×C11#43511yescharacteristic
175C22×C11#43511yescharacteristic
176C22×C11#44011yescharacteristic
177C22×C11#44111yescharacteristic
178C22×C11#44311yescharacteristic
179C22×C11#44311yescharacteristic
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—42no—
183C4×C11—81no—
184C4×C11#43211yescharacteristic
185C4×C11#43311yescharacteristic
186C4×C11#43511yescharacteristic
187C4×C11#43611yescharacteristic
188C4×C11#46811yescharacteristic
189C4×C11#47011yescharacteristic
190C4×C11#48911yescharacteristic
191C4×C11#49111yescharacteristic
192Dic11—42no—
193Dic11—81no—
194C22×Q8—111no—
195C22×C8—21no—
196C22×C8—111no—
197C22×C8—111no—
198C22×C8—221no—
199C22×C8—221no—
200C22×C8C22⋊D1111yescharacteristic
201C22×C8C22⋊D1111yescharacteristic
202C4×Q8—221no—
203C4×Q8—221no—
204C4×Q8—221no—
205C4×Q8—221no—
206C2×C4⋊C4—111no—
207C2×C4⋊C4—221no—
208C2×C4⋊C4C4×D1111yescharacteristic
209C2×C4⋊C4C4×D1111yescharacteristic
210C2×C42—21no—
211C2×C42—221no—
212C2×C42C22×D1111yescharacteristic
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8—42no—
216C4⋊C8—221no—
217C4⋊C8—221no—
218#103—222no—
219#103—222no—
220C4×C8—21no—
221C4×C8—21no—
222C4×C8—112no—
223C4×C8—221no—
224C4×C8—221no—
225C4×C8—221no—
226#95—21no—
227C2×C11#158511yescharacteristic
228C2×C11#158711yescharacteristic
229C2×C11#158711yescharacteristic
230C2×C11#158811yescharacteristic
231C2×C11#192411yescharacteristic
232C2×C11#193511yescharacteristic
233C2×C11#193711yescharacteristic
234C2×Q8—112no—
235C2×Q8—221no—
236C2×Q8—221no—
237C2×Q8—221no—
238C2×Q8—221no—
239C2×Q8—221no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—221no—
243C22×C4—221no—
244C22×C4C2×C4×D1111yescharacteristic
245C22×C4#433911yescharacteristic
246C22×C4C2×C22⋊D1111yescharacteristic
247C2×C8—21no—
248C2×C8—21no—
249C2×C8—21no—
250C2×C8—21no—
251C2×C8—21no—
252C2×C8—21no—
253C2×C8—41no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—222no—
257C2×C8—222no—
258C2×C8—222no—
259C2×C8—221no—
260C2×C8—221no—
261C2×C8—221no—
262C2×C8—221no—
263C2×C8—221no—
264C2×C8—221no—
265C2×C8—441no—
266C2×C8—441no—
267C2×C8—441no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—221no—
272C4⋊C4—221no—
273C4⋊C4—441no—
274C4⋊C4—441no—
275C4⋊C4#431312yes—
276C42—41no—
277C42—41no—
278C42—441no—
279C42—441no—
280C42D4×D1111yescharacteristic
281C42#434111yescharacteristic
282C42#434311yescharacteristic
283C42#434311yescharacteristic
284C11#955911yescharacteristic, complemented, Sylow
285C23C4×C22⋊D1111yescharacteristic
286Q8—222no—
287Q8—222no—
288Q8—441no—
289Q8—441no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—222no—
299C2×C4—441no—
300C2×C4—441no—
301C2×C4—441no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4#6694511yescharacteristic
305C2×C4#6694611yescharacteristic
306C2×C4#6694711yescharacteristic
307C2×C4#6695111yescharacteristic
308C2×C4C2×#431311yescharacteristic
309C2×C4#6695411yescharacteristic
310C2×C4M16×D1111yescharacteristic
311C2×C4#6696011yescharacteristic
312C2×C4#6698511yescharacteristic
313C2×C4#6699211yescharacteristic
314C2×C4#6699511yescharacteristic
315C2×C4#6700011yescharacteristic
316C2×C4#6700411yescharacteristic
317C2×C4#6700411yescharacteristic
318C8—41no—
319C8—41no—
320C8—81no—
321C8—224no—
322C8—441no—
323C8—441no—
324C8—881no—
325C22#1062260311yescharacteristic
326C22#1062263111yescharacteristic
327C22#1062264311yescharacteristic
328C22#1062272411yescharacteristic
329C22#1062274011yescharacteristic
330C22#1062275711yescharacteristic
331C22#1062275711yescharacteristic
332C4—21no—
333C4—21no—
334C4—42no—
335C4—81no—
336C4—442no—
337C4—881no—
338C4#1062244811yescharacteristic
339C4#1062244911yescharacteristic
340C4#1062245111yescharacteristic
341C4#1062245311yescharacteristic
342C4#1062265511yescharacteristic
343C4#1062266511yescharacteristic
344C4#1062268211yescharacteristic
345C4#1062270211yescharacteristic
346C2#1306747311yescharacteristic
347C2#1306748511yescharacteristic
348C2#1306748711yescharacteristic
349C2#1306749211yescharacteristic
350C2#1306922811yescharacteristic
351C2#1306930511yescharacteristic
352C2#1306931911yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1939C2
socle, prime radicalC23×C11C4×D4
cosocleC2×C42×C11C23
hypercenter#1939D11
hypocenterC11#9559
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ #1939

Complements

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

NH ≅ G/Ntype
284. C11#9559semidirect

Maximal subgroups

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

subgroupindex
#130695522
C4×#668742
C2×#106221222
C2×#106220922
#130664572
#130664502
C11×#19392
#955911