Finite Group Databasebeta

← #14649421

Subgroups — #14649421

Order 2816.

588 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
1C2×#10622538C211yesmaximal, characteristic
2#13076968C211yesmaximal, characteristic
3C2×#10622120C212yesmaximal, complemented
4#13066500C212yesmaximal, complemented
5C11×#1797C211yesmaximal, characteristic
6C22×C42×C11C2211yescharacteristic
7C2×#66977—21no—
8C2×#66922C2211yescharacteristic
9C2×C11×C4⋊C8C2212yes—
10C2×C11×C22⋊C8—21no—
11#10622825—21no—
12#10622825C412yes—
13C2×C22⋊(C11⋊C8)—21no—
14#10622548C2211yescharacteristic
15#10622542—21no—
16#10622541—21no—
17#10622541C412yes—
18#10622538—24no—
19C2×C4⋊(C11⋊C8)C2212yes—
20C2×C4×C11⋊C8—21no—
21C11×#336—21no—
22#10622120—24no—
23C23×C4×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×Dic22—21no—
27C22×C8×C11—22no—
28C2×C42×C11—22no—
29C2×C42×C11—22no—
30C2×C42×C11C2×C411yescharacteristic
31C2×C42×C11D411yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×C42×C11C2311yescharacteristic
34C2×C22⋊Dic11—22no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11C2×C412yes—
39C2×C4⋊Dic11C2×C412yes—
40#66977—42no—
41#66977—42no—
42C2×Dic11⋊C4—22no—
43C22×C11⋊C8—22no—
44#66922—22no—
45#66922—22no—
46C11×C4⋊C8—22no—
47C11×C4⋊C8—22no—
48C11×C22⋊C8—42no—
49C11⋊#95—22no—
50C11⋊#95—22no—
51C22⋊(C11⋊C8)—24no—
52C4⋊(C11⋊C8)—22no—
53C4⋊(C11⋊C8)D414yes—
54C4×C11⋊C8—24no—
55#9130—111nomaximal, Sylow
56C24×C11C22⋊C411yescharacteristic
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11—22no—
60C22×C4×C11—22no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—22no—
64C22×C4×C11—22no—
65C22×C4×C11—41no—
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11D812yes—
70C22×C4×C11SD1612yes—
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×Dic11—22no—
75C22×Dic11—22no—
76C2×Dic22—42no—
77C2×Dic22—41no—
78C2×Dic22—41no—
79C2×Dic22—42no—
80C2×C8×C11—42no—
81C2×C8×C11—42no—
82C2×C8×C11—42no—
83C42×C11—22no—
84C42×C11—21no—
85C42×C11—22no—
86C42×C11—21no—
87C42×C11C2×D412yes—
88C42×C11#4112yes—
89C22⋊Dic11—44no—
90C4⋊Dic11—24no—
91C4⋊Dic11—42no—
92C4⋊Dic11—41no—
93C4⋊Dic11—41no—
94C4⋊Dic11—41no—
95C4⋊Dic11—41no—
96C4⋊Dic11—42no—
97Dic11⋊C4—44no—
98C2×C11⋊C8—24no—
99C2×C11⋊C8—42no—
100C2×C11⋊C8—42no—
101C2×#431—111no—
102#2857—111no—
103#1797D1111yescharacteristic
104C2×#332—112no—
105#1296—112no—
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—21no—
112C23×C11#10212yes—
113C23×C11C2×C22⋊C411yescharacteristic
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—24no—
121C2×C4×C11—24no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—44no—
126C2×C4×C11—42no—
127C2×C4×C11—42no—
128C2×C4×C11#10112yes—
129C2×C4×C11#10212yes—
130C2×C4×C11C4×D412yes—
131C2×C4×C11#12011yescharacteristic
132C2×C4×C11#12112yes—
133C2×C4×C11#12311yescharacteristic
134C2×C4×C11C2×D811yescharacteristic
135C2×C4×C11C2×SD1611yescharacteristic
136C2×C4×C11#13512yes—
137C2×C4×C11#13512yes—
138C2×C4×C11#13712yes—
139C2×Dic11—42no—
140C2×Dic11—42no—
141C2×Dic11—42no—
142C2×Dic11—42no—
143C2×Dic11—42no—
144C2×Dic11—42no—
145Dic22—82no—
146Dic22—82no—
147C8×C11—82no—
148C11⋊C8—44no—
149C2×C4⋊Q8—111no—
150C2×C22⋊Q8—221no—
151C22×C42C2×D1111yescharacteristic
152#431—224no—
153C2×C4⋊C8—112no—
154C2×C4⋊C8C2×D1112yes—
155C2×C22⋊C8—21no—
156C2×C22⋊C8—221no—
157C2×C4×C8—221no—
158#391—221no—
159#389—112no—
160#389—221no—
161#384—111no—
162#380—112no—
163#380—221no—
164#336—21no—
165#332—224no—
166C22×C11—22no—
167C22×C11—22no—
168C22×C11—22no—
169C22×C11—41no—
170C22×C11—41no—
171C22×C11—41no—
172C22×C11—41no—
173C22×C11#38611yescharacteristic
174C22×C11C2×#10111yescharacteristic
175C22×C11#41311yescharacteristic
176C22×C11C2×#10211yescharacteristic
177C22×C11#41611yescharacteristic
178C22×C11#41611yescharacteristic
179C22×C11#41911yescharacteristic
180C4×C11—22no—
181C4×C11—22no—
182C4×C11—22no—
183C4×C11—41no—
184C4×C11#45212yes—
185C4×C11#46512yes—
186C4×C11#46612yes—
187C4×C11#48512yes—
188Dic11—82no—
189Dic11—82no—
190C22×Q8—221no—
191C23×C4C4×D1111yescharacteristic
192C23×C4D4411yescharacteristic
193C23×C4C22⋊D1111yescharacteristic
194C22×C8—22no—
195C22×C8—222no—
196C4⋊Q8—222no—
197C4⋊Q8—222no—
198C22⋊Q8—442no—
199C22⋊Q8—442no—
200C2×C4⋊C4—112no—
201C2×C4⋊C4—112no—
202C2×C4⋊C4—222no—
203C2×C4⋊C4—221no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4—221no—
206C2×C22⋊C4—222no—
207C2×C42—22no—
208C2×C42—22no—
209C2×C42C4×D1111yescharacteristic
210C2×C42D4411yescharacteristic
211C2×C42C22⋊D1111yescharacteristic
212C2×C42C22×D1111yescharacteristic
213C4⋊C8—22no—
214C4⋊C8—22no—
215C4⋊C8—114no—
216C4⋊C8—222no—
217C22⋊C8—42no—
218C22⋊C8—224no—
219C4×C8—224no—
220#95—222no—
221#95—222no—
222C2×C11—42no—
223C2×C11#154011yescharacteristic
224C2×C11#154411yescharacteristic
225C2×C11#154611yescharacteristic
226C2×C11#155411yescharacteristic
227C2×C11#187311yescharacteristic
228C2×C11#189311yescharacteristic
229C2×C11#190111yescharacteristic
230C24(C2×D11)⋊C411yescharacteristic
231C2×Q8—441no—
232C2×Q8—442no—
233C2×Q8—441no—
234C2×Q8—442no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—41no—
244C22×C4—222no—
245C22×C4—222no—
246C22×C4(C2×D11)⋊C411yescharacteristic
247C22×C4(C2×D11)⋊C411yescharacteristic
248C22×C4(C2×D11)⋊C411yescharacteristic
249C22×C4#432312yes—
250C22×C4#432512yes—
251C22×C4C2×C4×D1111yescharacteristic
252C22×C4C2×D4411yescharacteristic
253C22×C4C2×C22⋊D1111yescharacteristic
254C2×C8—42no—
255C2×C8—42no—
256C2×C8—42no—
257C2×C8—224no—
258C2×C8—442no—
259C2×C8—442no—
260C4⋊C4—224no—
261C4⋊C4—442no—
262C4⋊C4—444no—
263C4⋊C4—441no—
264C4⋊C4—441no—
265C4⋊C4—442no—
266C4⋊C4—441no—
267C4⋊C4—441no—
268C22⋊C4—444no—
269C42—22no—
270C42—21no—
271C42—21no—
272C42—22no—
273C42D4×D1112yes—
274C42#434112yes—
275C11#913011yescharacteristic, complemented, Sylow
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23#6687312yes—
283C23C2×(C2×D11)⋊C411yescharacteristic
284Q8—882no—
285Q8—882no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—24no—
293C2×C4—24no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—44no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—442no—
301C2×C4—442no—
302C2×C4—442no—
303C2×C4—442no—
304C2×C4—442no—
305C2×C4—442no—
306C2×C4#6687312yes—
307C2×C4#6688812yes—
308C2×C4(C22⋊D11)⋊C412yes—
309C2×C4#6693511yescharacteristic
310C2×C4#6693911yescharacteristic
311C2×C4#6695712yes—
312C2×C4#6696212yes—
313C2×C4C2×#432311yescharacteristic
314C2×C4#6699212yes—
315C2×C4C2×#432511yescharacteristic
316C2×C4#6700312yes—
317C8—82no—
318C8—444no—
319C22—22no—
320C22—22no—
321C22—22no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22#1062257111yescharacteristic
327C22C2×#6687311yescharacteristic
328C22#1062261511yescharacteristic
329C22#1062272611yescharacteristic
330C22#1062273311yescharacteristic
331C22#1062274511yescharacteristic
332C22C2×#6688811yescharacteristic
333C4—22no—
334C4—22no—
335C4—22no—
336C4—41no—
337C4—882no—
338C4—882no—
339C4#1062233612yes—
340C4#1062234612yes—
341C4#1062265112yes—
342C4#1062266112yes—
343C2—42no—
344C2#1306726611yescharacteristic
345C2#1306728011yescharacteristic
346C2#1306728911yescharacteristic
347C2#1306732711yescharacteristic
348C2#1306892611yescharacteristic
349C2#1306904211yescharacteristic
350C2#1306908211yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1797C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1797D11
hypocenterC11#9130
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
3. C2×#10622120C2semidirect
4. #13066500C2semidirect
275. C11#9130semidirect

Maximal subgroups

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

subgroupindex
C2×#106225382
#130769682
C2×#106221202
#130665002
C11×#17972
#913011