Finite Group Databasebeta

← #14642249

Subgroups — #14642249

Order 2816.

464 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076983C211yesmaximal, characteristic
2#13068469C211yesmaximal, characteristic, complemented
3#13066438C212yesmaximal, complemented
4#13066436C212yesmaximal
5C4×C11×C4⋊C8C211yesmaximal, characteristic, complemented
6C2×#66929—21no—
7C2×C11×C4⋊C8—21no—
8C2×C4×C8×C11—21no—
9C43×C11C2211yescharacteristic
10#10622553—21no—
11#10622553—21no—
12#10622553—21no—
13#10622552C411yescharacteristic
14#10622552C411yescharacteristic
15#10622552C2211yescharacteristic
16#10622541C411yescharacteristic
17#10622541C411yescharacteristic
18#10622541C2211yescharacteristic
19C2×C4⋊(C11⋊C8)—21no—
20C2×#66867—21no—
21C11×#336C2212yes—
22#10622162C2212yes—
23C22×D44C2×C411yescharacteristic
24C22×C8×C11—22no—
25C2×C42×C11C2×C411yescharacteristic
26C2×C42×C11C2×C411yescharacteristic
27C2×C42×C11D411yescharacteristic
28C2×C42×C11D411yescharacteristic
29C2×C42×C11D411yescharacteristic
30C2×C42×C11D411yescharacteristic
31C2×C42×C11C2311yescharacteristic
32C2×(C2×D11)⋊C4—21no—
33C2×(C2×D11)⋊C4—21no—
34C2×(C2×D11)⋊C4—21no—
35C2×(C2×D11)⋊C4—21no—
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×C4⋊Dic11C2×C411yescharacteristic
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×C4⋊Dic11C2×C411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C22×C11⋊C8—22no—
45#66929—42no—
46#66929—42no—
47C11×C4⋊C8—24no—
48C4×C8×C11—42no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C4⋊(C11⋊C8)—24no—
53#66867—42no—
54#7686—111nomaximal, Sylow
55C23×D11—21no—
56C22×C4×C11C22⋊C411yescharacteristic
57C22×C4×C11C22⋊C411yescharacteristic
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22×C411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×Dic11—21no—
64C22×Dic11—21no—
65C22×Dic11—21no—
66C2×D44—22no—
67C2×D44—41no—
68C2×D44—41no—
69C2×C8×C11—24no—
70C2×C8×C11—42no—
71C2×C8×C11—42no—
72C42×C11—22no—
73C42×C11—22no—
74C42×C11—22no—
75C42×C11—21no—
76C42×C11—21no—
77C42×C11—41no—
78C42×C11—41no—
79C42×C11D812yes—
80C42×C11SD1612yes—
81(C2×D11)⋊C4—42no—
82(C2×D11)⋊C4—42no—
83(C2×D11)⋊C4—42no—
84(C2×D11)⋊C4—42no—
85(C2×D11)⋊C4—41no—
86(C2×D11)⋊C4—41no—
87(C2×D11)⋊C4—41no—
88(C2×D11)⋊C4—41no—
89C4⋊Dic11—22no—
90C4⋊Dic11—41no—
91C4⋊Dic11—41no—
92Dic11⋊C4—42no—
93Dic11⋊C4—42no—
94Dic11⋊C4—41no—
95Dic11⋊C4—41no—
96C2×C11⋊C8—24no—
97C2×C11⋊C8—42no—
98C2×C11⋊C8—42no—
99#2860—111no—
100#1767—111no—
101C4×C4⋊C8D1111yescharacteristic, complemented
102#1271—112no—
103#1270—112no—
104C23×C11C2×C22⋊C411yescharacteristic
105C22×D11—41no—
106C22×D11—41no—
107C22×D11—41no—
108C22×D11—41no—
109C22×D11—41no—
110C22×D11—41no—
111C22×D11—41no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11#10212yes—
127C2×C4×C11#10212yes—
128C2×C4×C11#10412yes—
129C2×C4×C11#10412yes—
130C2×C4×C11#13112yes—
131C2×C4×C11C2×D811yescharacteristic
132C2×C4×C11C2×SD1611yescharacteristic
133C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C11#13711yescharacteristic
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144D44—82no—
145C8×C11—44no—
146C11⋊C8—44no—
147C2×#126—221no—
148C2×C4⋊C8—21no—
149C2×C4⋊C8—221no—
150C2×#97—221no—
151C2×C4×C8—21no—
152#390—111no—
153#390—111no—
154#390—111no—
155#389—111no—
156#389—111no—
157#389—111no—
158#388—221no—
159#388—221no—
160#388—221no—
161C43C2×D1111yescharacteristic
162#336—112no—
163#336C2×D1112yes—
164C22×C11#40811yescharacteristic
165C22×C11#41011yescharacteristic
166C22×C11#41311yescharacteristic
167C22×C11C2×#10211yescharacteristic
168C22×C11#41711yescharacteristic
169C22×C11C2×#10411yescharacteristic
170C22×C11C2×#10411yescharacteristic
171C2×D11—81no—
172C2×D11—81no—
173C2×D11—81no—
174C2×D11—81no—
175C2×D11—81no—
176C2×D11—81no—
177C2×D11—81no—
178C4×C11—22no—
179C4×C11—22no—
180C4×C11—22no—
181C4×C11—22no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—22no—
187Dic11—81no—
188Dic11—81no—
189Dic11—81no—
190C22×D4—111no—
191C22×C8—22no—
192C22×C8—222no—
193#126—442no—
194#126—442no—
195C2×C4⋊C4—111no—
196C2×C4⋊C4—111no—
197C2×C4⋊C4—111no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4—221no—
200C2×C4⋊C4—221no—
201C2×C22⋊C4—221no—
202C2×C22⋊C4—221no—
203C2×C22⋊C4—221no—
204C2×C22⋊C4—221no—
205C2×C22⋊C4—221no—
206C2×C22⋊C4—221no—
207C2×C42C4×D1111yescharacteristic
208C2×C42C4×D1111yescharacteristic
209C2×C42D4411yescharacteristic
210C2×C42D4411yescharacteristic
211C2×C42C22⋊D1111yescharacteristic
212C2×C42C22⋊D1111yescharacteristic
213C2×C42C22×D1111yescharacteristic
214C4⋊C8—24no—
215C4⋊C8—224no—
216#97—442no—
217C4×C8—42no—
218#95—221no—
219#95—221no—
220#95—221no—
221C2×C11#147311yescharacteristic
222C2×C11#148311yescharacteristic
223C2×C11#149211yescharacteristic
224C2×C11#150211yescharacteristic
225C2×C11#150911yescharacteristic
226C2×C11#152411yescharacteristic
227C2×C11#154711yescharacteristic
228D11—161no—
229C24—221no—
230C2×D4—222no—
231C2×D4—441no—
232C2×D4—441no—
233C22×C4—221no—
234C22×C4—221no—
235C22×C4—221no—
236C22×C4(C2×D11)⋊C411yescharacteristic
237C22×C4(C2×D11)⋊C411yescharacteristic
238C22×C4(C2×D11)⋊C411yescharacteristic
239C22×C4(C2×D11)⋊C411yescharacteristic
240C22×C4C2×C4×D1111yescharacteristic
241C22×C4C2×D4411yescharacteristic
242C22×C4C2×C22⋊D1111yescharacteristic
243C2×C8—24no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—224no—
247C2×C8—442no—
248C2×C8—442no—
249C4⋊C4—222no—
250C4⋊C4—441no—
251C4⋊C4—441no—
252C4⋊C4—442no—
253C4⋊C4—442no—
254C4⋊C4—441no—
255C4⋊C4—441no—
256C22⋊C4—442no—
257C22⋊C4—442no—
258C22⋊C4—442no—
259C22⋊C4—442no—
260C22⋊C4—441no—
261C22⋊C4—441no—
262C22⋊C4—441no—
263C22⋊C4—441no—
264C42—22no—
265C42—22no—
266C42—22no—
267C42—21no—
268C42—21no—
269C42—41no—
270C42—41no—
271C42#431412yes—
272C42D8812yes—
273C11#768611yescharacteristic, complemented, Sylow
274C23—441no—
275C23—441no—
276C23—441no—
277C23—441no—
278C23—441no—
279C23—441no—
280C23—441no—
281C23C2×(C2×D11)⋊C411yescharacteristic
282D4—882no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—441no—
298C2×C4—441no—
299C2×C4—441no—
300C2×C4—441no—
301C2×C4—441no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4—441no—
305C2×C4—441no—
306C2×C4#6686912yes—
307C2×C4#6688512yes—
308C2×C4#6688512yes—
309C2×C4#6688912yes—
310C2×C4#6695412yes—
311C2×C4C2×#431411yescharacteristic
312C2×C4C2×D8811yescharacteristic
313C2×C4#6698511yescharacteristic
314C2×C4#6699511yescharacteristic
315C8—44no—
316C8—444no—
317C22—881no—
318C22—881no—
319C22—881no—
320C22—881no—
321C22—881no—
322C22—881no—
323C22—881no—
324C22C2×#6686911yescharacteristic
325C22#1062257911yescharacteristic
326C22#1062261911yescharacteristic
327C22#1062272311yescharacteristic
328C22C2×#6688511yescharacteristic
329C22#1062274511yescharacteristic
330C22C2×#6688911yescharacteristic
331C4—22no—
332C4—22no—
333C4—22no—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—22no—
339C4—22no—
340C4—881no—
341C4—881no—
342C4—881no—
343C2—1761no—
344C2#1306698311yescharacteristic
345C2#1306702711yescharacteristic
346C2#1306706811yescharacteristic
347C2#1306711211yescharacteristic
348C2#1306713911yescharacteristic
349C2#1306720511yescharacteristic
350C2#1306729111yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC4×C11×C4⋊C8C2
socleC23×C11C2×C22⋊C4
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenterC4×C4⋊C8D11
hypocenterC11#7686
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ C4×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #13068469C2semidirect
3. #13066438C2semidirect
5. C4×C11×C4⋊C8C2semidirect
101. C4×C4⋊C8D11semidirect
273. C11#7686semidirect

Maximal subgroups

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

subgroupindex
#130769832
#130684692
#130664382
#130664362
C4×C11×C4⋊C82
#768611