Finite Group Databasebeta

← #14649416

Subgroups — #14649416

Order 2816.

644 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊(C11⋊C8)C211yesmaximal, characteristic
2#13076968C211yesmaximal, characteristic
3C2×#10622120C212yesmaximal, complemented
4#13066500C212yesmaximal, complemented
5C11×#1797C211yesmaximal, characteristic
6C22×C42×C11C2211yescharacteristic
7C2×#66977—21no—
8C23×C11⋊C8—21no—
9C2×#66922C2211yescharacteristic
10C2×C11×C4⋊C8C2212yes—
11C2×C11×C22⋊C8—21no—
12#10622825—21no—
13#10622825C412yes—
14#10622548C2211yescharacteristic
15#10622542—21no—
16#10622541—21no—
17#10622541C412yes—
18C2×C4⋊(C11⋊C8)—21no—
19C2×C4⋊(C11⋊C8)—24no—
20C2×C4⋊(C11⋊C8)C2212yes—
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—24no—
44C22×C11⋊C8—22no—
45C22×C11⋊C8—42no—
46C22×C11⋊C8—42no—
47#66922—22no—
48#66922—22no—
49C11×C4⋊C8—22no—
50C11×C4⋊C8—22no—
51C11×C22⋊C8—42no—
52C11⋊#95—22no—
53C11⋊#95—22no—
54C4⋊(C11⋊C8)—24no—
55C4⋊(C11⋊C8)—22no—
56C4⋊(C11⋊C8)D414yes—
57#9129—111nomaximal, Sylow
58C24×C11C22⋊C411yescharacteristic
59C22×C4×C11—21no—
60C22×C4×C11—22no—
61C22×C4×C11—21no—
62C22×C4×C11—22no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—22no—
66C22×C4×C11—22no—
67C22×C4×C11—41no—
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11D812yes—
72C22×C4×C11SD1612yes—
73C22×C4×C11SD1612yes—
74C22×C4×C11Q1612yes—
75C22×C4×C11C22×C411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×Dic11—22no—
79C22×Dic11—22no—
80C2×Dic22—42no—
81C2×Dic22—41no—
82C2×Dic22—41no—
83C2×Dic22—42no—
84C2×C8×C11—42no—
85C2×C8×C11—42no—
86C2×C8×C11—42no—
87C42×C11—22no—
88C42×C11—21no—
89C42×C11—22no—
90C42×C11—21no—
91C42×C11C2×D412yes—
92C42×C11#4112yes—
93C22⋊Dic11—44no—
94C4⋊Dic11—24no—
95C4⋊Dic11—42no—
96C4⋊Dic11—41no—
97C4⋊Dic11—41no—
98C4⋊Dic11—41no—
99C4⋊Dic11—41no—
100C4⋊Dic11—41no—
101C4⋊Dic11—41no—
102Dic11⋊C4—44no—
103C2×C11⋊C8—24no—
104C2×C11⋊C8—48no—
105C2×C11⋊C8—42no—
106C2×C11⋊C8—42no—
107C22×C4⋊C8—111no—
108#2857—111no—
109#1797D1111yescharacteristic
110C2×#332—112no—
111#1296—112no—
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11#10112yes—
117C23×C11#10212yes—
118C23×C11#10312yes—
119C23×C11C2×C22⋊C411yescharacteristic
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—22no—
127C2×C4×C11—22no—
128C2×C4×C11—24no—
129C2×C4×C11—24no—
130C2×C4×C11—22no—
131C2×C4×C11—22no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—44no—
136C2×C4×C11#10212yes—
137C2×C4×C11#10312yes—
138C2×C4×C11C4×D412yes—
139C2×C4×C11#12011yescharacteristic
140C2×C4×C11#12112yes—
141C2×C4×C11#12311yescharacteristic
142C2×C4×C11C2×D811yescharacteristic
143C2×C4×C11C2×SD1611yescharacteristic
144C2×C4×C11C2×SD1611yescharacteristic
145C2×C4×C11C2×Q1611yescharacteristic
146C2×C4×C11#13512yes—
147C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C11#13711yescharacteristic
149C2×Dic11—42no—
150C2×Dic11—42no—
151C2×Dic11—42no—
152C2×Dic11—42no—
153C2×Dic11—42no—
154C2×Dic11—42no—
155Dic22—82no—
156Dic22—82no—
157C8×C11—82no—
158C11⋊C8—44no—
159C23×C8—221no—
160C2×C4⋊Q8—111no—
161C2×C22⋊Q8—221no—
162C22×C42C2×D1111yescharacteristic
163C2×C4⋊C8—112no—
164C2×C4⋊C8—224no—
165C2×C4⋊C8—221no—
166C2×C4⋊C8C2×D1112yes—
167C2×C22⋊C8—21no—
168#391—221no—
169#389—112no—
170#389—221no—
171#384—111no—
172#380—112no—
173#380—221no—
174#336—21no—
175#332—224no—
176C22×C11—22no—
177C22×C11—22no—
178C22×C11—22no—
179C22×C11—22no—
180C22×C11—22no—
181C22×C11—22no—
182C22×C11#33214yescomplemented
183C22×C11#38611yescharacteristic
184C22×C11C2×#10111yescharacteristic
185C22×C11#41311yescharacteristic
186C22×C11C2×#10211yescharacteristic
187C22×C11C2×#10311yescharacteristic
188C22×C11#41611yescharacteristic
189C22×C11#41711yescharacteristic
190C4×C11—22no—
191C4×C11—22no—
192C4×C11—22no—
193C4×C11—41no—
194C4×C11#45011yescharacteristic
195C4×C11#45111yescharacteristic
196C4×C11#46512yes—
197C4×C11#46612yes—
198C4×C11#48311yescharacteristic
199C4×C11#48411yescharacteristic
200Dic11—82no—
201Dic11—82no—
202C22×Q8—221no—
203C23×C4C4×D1111yescharacteristic
204C23×C4D4411yescharacteristic
205C23×C4C22⋊D1111yescharacteristic
206C22×C8—22no—
207C22×C8—224no—
208C22×C8—222no—
209C22×C8—442no—
210C22×C8—442no—
211C4⋊Q8—222no—
212C4⋊Q8—222no—
213C22⋊Q8—442no—
214C22⋊Q8—442no—
215C2×C4⋊C4—112no—
216C2×C4⋊C4—112no—
217C2×C4⋊C4—222no—
218C2×C4⋊C4—221no—
219C2×C4⋊C4—221no—
220C2×C4⋊C4—221no—
221C2×C22⋊C4—222no—
222C2×C42—22no—
223C2×C42—22no—
224C2×C42C4×D1111yescharacteristic
225C2×C42D4411yescharacteristic
226C2×C42C22⋊D1111yescharacteristic
227C2×C42C22×D1111yescharacteristic
228C4⋊C8—22no—
229C4⋊C8—22no—
230C4⋊C8—114no—
231C4⋊C8—224no—
232C4⋊C8—222no—
233C22⋊C8—42no—
234#95—222no—
235#95—222no—
236C2×C11—24no—
237C2×C11C2×#33211yescharacteristic
238C2×C11#154211yescharacteristic
239C2×C11#154711yescharacteristic
240C2×C11#155211yescharacteristic
241C2×C11#187211yescharacteristic
242C2×C11#189311yescharacteristic
243C2×C11#190111yescharacteristic
244C24(C2×D11)⋊C411yescharacteristic
245C2×Q8—441no—
246C2×Q8—442no—
247C2×Q8—441no—
248C2×Q8—442no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—41no—
258C22×C4—222no—
259C22×C4—222no—
260C22×C4#431412yes—
261C22×C4Dic4412yes—
262C22×C4(C2×D11)⋊C411yescharacteristic
263C22×C4(C2×D11)⋊C411yescharacteristic
264C22×C4(C2×D11)⋊C411yescharacteristic
265C22×C4#432312yes—
266C22×C4#432512yes—
267C22×C4C2×C4×D1111yescharacteristic
268C22×C4C2×D4411yescharacteristic
269C22×C4C2×C22⋊D1111yescharacteristic
270C2×C8—42no—
271C2×C8—42no—
272C2×C8—42no—
273C2×C8—224no—
274C2×C8—448no—
275C2×C8—442no—
276C2×C8—442no—
277C4⋊C4—224no—
278C4⋊C4—442no—
279C4⋊C4—444no—
280C4⋊C4—441no—
281C4⋊C4—441no—
282C4⋊C4—441no—
283C4⋊C4—441no—
284C4⋊C4—441no—
285C4⋊C4—441no—
286C22⋊C4—444no—
287C42—22no—
288C42—21no—
289C42—21no—
290C42—22no—
291C42D4×D1112yes—
292C42#434112yes—
293C11#912911yescharacteristic, complemented, Sylow
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23#6687312yes—
299C23#6688012yes—
300C23#6688812yes—
301C23C2×(C2×D11)⋊C411yescharacteristic
302Q8—882no—
303Q8—882no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—24no—
315C2×C4—24no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—44no—
320C2×C4—442no—
321C2×C4—442no—
322C2×C4—442no—
323C2×C4—442no—
324C2×C4—442no—
325C2×C4—442no—
326C2×C4#6687312yes—
327C2×C4#6688012yes—
328C2×C4(C22⋊D11)⋊C412yes—
329C2×C4#6693511yescharacteristic
330C2×C4#6693911yescharacteristic
331C2×C4C2×#431411yescharacteristic
332C2×C4C2×Dic4411yescharacteristic
333C2×C4#6696111yescharacteristic
334C2×C4#6696211yescharacteristic
335C2×C4C2×#432311yescharacteristic
336C2×C4#6699212yes—
337C2×C4C2×#432511yescharacteristic
338C2×C4#6700312yes—
339C8—82no—
340C8—444no—
341C22—22no—
342C22—22no—
343C22—22no—
344C22—22no—
345C22—22no—
346C22—22no—
347C22#1062212014yescomplemented
348C22#1062257111yescharacteristic
349C22C2×#6687311yescharacteristic
350C22#1062261511yescharacteristic
351C22C2×#6688011yescharacteristic
352C22#1062274511yescharacteristic
353C22#1062274611yescharacteristic
354C22C2×#6688811yescharacteristic
355C4—22no—
356C4—22no—
357C4—22no—
358C4—41no—
359C4—882no—
360C4—882no—
361C4#1062233411yescharacteristic
362C4#1062233511yescharacteristic
363C4#1062234411yescharacteristic
364C4#1062235211yescharacteristic
365C4#1062265112yes—
366C4#1062266112yes—
367C2—24no—
368C2C2×#1062212011yescharacteristic
369C2#1306727111yescharacteristic
370C2#1306729411yescharacteristic
371C2#1306731711yescharacteristic
372C2#1306892111yescharacteristic
373C2#1306904211yescharacteristic
374C2#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#9129
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
182. C22×C11#332semidirect
293. C11#9129semidirect
347. C22#10622120semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊(C11⋊C8)2
#130769682
C2×#106221202
#130665002
C11×#17972
#912911