Finite Group Databasebeta

← #14649409

Subgroups — #14649409

Order 2816.

644 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊(C11⋊C8)C211yesmaximal, characteristic
2#13068596C211yesmaximal, characteristic
3C2×#10622184C212yesmaximal, complemented
4#13066499C212yesmaximal, complemented
5C11×#2857C211yesmaximal, characteristic
6C2×C11×C4⋊Q8C2211yescharacteristic
7C2×C11×C22⋊Q8C412yes—
8C22×C42×C11C2211yescharacteristic
9C23×C11⋊C8—21no—
10C11×#391C412yes—
11C11×#389—21no—
12C11×#389—21no—
13C11×#384C2211yescharacteristic
14C11×#380—21no—
15C11×#380—21no—
16C2×C22⋊(C11⋊C8)—21no—
17C2×C4⋊(C11⋊C8)—21no—
18C2×C4⋊(C11⋊C8)—24no—
19C2×C4⋊(C11⋊C8)C2212yes—
20C2×C4⋊(C11⋊C8)C2212yes—
21#10622184—24no—
22#10622162—21no—
23C22×Q8×C11C2×C412yes—
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C11×C4⋊Q8—22no—
28C11×C4⋊Q8—22no—
29C11×C22⋊Q8—44no—
30C2×C11×C4⋊C4—22no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4C2×C412yes—
36C2×C11×C22⋊C4—22no—
37C2×C42×C11—22no—
38C2×C42×C11—22no—
39C2×C42×C11C2×C411yescharacteristic
40C2×C42×C11D411yescharacteristic
41C2×C42×C11D411yescharacteristic
42C2×C42×C11C2311yescharacteristic
43C22×C11⋊C8—24no—
44C22×C11⋊C8—22no—
45C22×C11⋊C8—22no—
46C22×C11⋊C8—42no—
47C22×C11⋊C8—42no—
48C11×#95—22no—
49C11×#95—22no—
50C22⋊(C11⋊C8)—42no—
51C4⋊(C11⋊C8)—24no—
52C4⋊(C11⋊C8)—22no—
53C4⋊(C11⋊C8)—22no—
54C4⋊(C11⋊C8)—22no—
55C4⋊(C11⋊C8)D414yes—
56#9127—111nomaximal, Sylow
57C24×C11C22⋊C411yescharacteristic
58C2×Q8×C11—24no—
59C2×Q8×C11—42no—
60C2×Q8×C11—42no—
61C22×C4×C11—21no—
62C22×C4×C11—22no—
63C22×C4×C11—21no—
64C22×C4×C11—22no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—22no—
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11—22no—
71C22×C4×C11—41no—
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11SD1612yes—
76C22×C4×C11SD1612yes—
77C22×C4×C11Q1612yes—
78C22×C4×C11Q1612yes—
79C22×C4×C11C22×C411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C11×C4⋊C4—44no—
83C11×C4⋊C4—42no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—42no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—42no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C22⋊C4—44no—
91C42×C11—22no—
92C42×C11—21no—
93C42×C11—22no—
94C42×C11—21no—
95C42×C11C2×D412yes—
96C42×C11#4112yes—
97C2×C11⋊C8—24no—
98C2×C11⋊C8—48no—
99C2×C11⋊C8—42no—
100C2×C11⋊C8—42no—
101C2×C11⋊C8—42no—
102C2×C11⋊C8—42no—
103C2×C11⋊C8—42no—
104C22×C4⋊C8—111no—
105#2857D1111yescharacteristic
106#1797—111no—
107C2×#333—112no—
108#1296—112no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—21no—
112C23×C11—21no—
113C23×C11#10012yes—
114C23×C11#10312yes—
115C23×C11#10312yes—
116C23×C11C2×C22⋊C411yescharacteristic
117Q8×C11—84no—
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—22no—
125C2×C4×C11—22no—
126C2×C4×C11—24no—
127C2×C4×C11—24no—
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—44no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11#10312yes—
141C2×C4×C11#10312yes—
142C2×C4×C11C4×D412yes—
143C2×C4×C11#12011yescharacteristic
144C2×C4×C11#12112yes—
145C2×C4×C11#12311yescharacteristic
146C2×C4×C11C2×SD1611yescharacteristic
147C2×C4×C11C2×SD1611yescharacteristic
148C2×C4×C11C2×Q1611yescharacteristic
149C2×C4×C11C2×Q1611yescharacteristic
150C2×C4×C11#13512yes—
151C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C11#13711yescharacteristic
153C11⋊C8—44no—
154C11⋊C8—82no—
155C23×C8—221no—
156C2×C4⋊Q8C2×D1111yescharacteristic
157C2×C22⋊Q8Dic1112yes—
158C22×C42C2×D1111yescharacteristic
159C2×C4⋊C8—112no—
160C2×C4⋊C8—112no—
161C2×C4⋊C8—224no—
162C2×C4⋊C8—221no—
163C2×C22⋊C8—221no—
164#391Dic1112yes—
165#389—21no—
166#389—21no—
167#384C2×D1111yescharacteristic
168#380—21no—
169#380—21no—
170#336—221no—
171#333—224no—
172C22×C11—22no—
173C22×C11—22no—
174C22×C11—22no—
175C22×C11—22no—
176C22×C11—22no—
177C22×C11—22no—
178C22×C11#33314yescomplemented
179C22×C11#38611yescharacteristic
180C22×C11C2×#10011yescharacteristic
181C22×C11#41311yescharacteristic
182C22×C11C2×#10311yescharacteristic
183C22×C11C2×#10311yescharacteristic
184C22×C11#41611yescharacteristic
185C22×C11#41711yescharacteristic
186C4×C11—22no—
187C4×C11—22no—
188C4×C11—22no—
189C4×C11—41no—
190C4×C11—82no—
191C4×C11—82no—
192C4×C11#45011yescharacteristic
193C4×C11#45111yescharacteristic
194C4×C11#46512yes—
195C4×C11#46712yes—
196C4×C11#48311yescharacteristic
197C4×C11#48411yescharacteristic
198C22×Q8C2×Dic1112yes—
199C23×C4C2×Dic1111yescharacteristic
200C23×C4C22⋊D1111yescharacteristic
201C23×C4C22⋊D1111yescharacteristic
202C22×C8—224no—
203C22×C8—222no—
204C22×C8—222no—
205C22×C8—442no—
206C22×C8—442no—
207C4⋊Q8—22no—
208C4⋊Q8—22no—
209C22⋊Q8—44no—
210C2×C4⋊C4—22no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4C2×Dic1112yes—
216C2×C22⋊C4—22no—
217C2×C42—22no—
218C2×C42—22no—
219C2×C42C2×Dic1111yescharacteristic
220C2×C42C22⋊D1111yescharacteristic
221C2×C42C22⋊D1111yescharacteristic
222C2×C42C22×D1111yescharacteristic
223C4⋊C8—114no—
224C4⋊C8—224no—
225C4⋊C8—222no—
226C4⋊C8—222no—
227C4⋊C8—222no—
228C22⋊C8—442no—
229#95—22no—
230#95—22no—
231C2×C11—24no—
232C2×C11C2×#33311yescharacteristic
233C2×C11#154211yescharacteristic
234C2×C11#155011yescharacteristic
235C2×C11#155111yescharacteristic
236C2×C11#187211yescharacteristic
237C2×C11#189211yescharacteristic
238C2×C11#190011yescharacteristic
239C24C22⋊Dic1111yescharacteristic
240C2×Q8—24no—
241C2×Q8—42no—
242C2×Q8—42no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—22no—
246C22×C4—21no—
247C22×C4—22no—
248C22×C4—21no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—41no—
254C22×C4#432512yes—
255C22×C4#432512yes—
256C22×C4#432612yes—
257C22×C4#432612yes—
258C22×C4C22⋊Dic1111yescharacteristic
259C22×C4C22⋊Dic1111yescharacteristic
260C22×C4C22⋊Dic1111yescharacteristic
261C22×C4C22×Dic1111yescharacteristic
262C22×C4C2×C22⋊D1111yescharacteristic
263C22×C4C2×C22⋊D1111yescharacteristic
264C2×C8—224no—
265C2×C8—448no—
266C2×C8—442no—
267C2×C8—442no—
268C2×C8—442no—
269C2×C8—442no—
270C2×C8—442no—
271C4⋊C4—42no—
272C4⋊C4—44no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—42no—
276C4⋊C4—41no—
277C4⋊C4—42no—
278C4⋊C4—41no—
279C22⋊C4—44no—
280C42—22no—
281C42—21no—
282C42—21no—
283C42—22no—
284C42D4×D1112yes—
285C42#434112yes—
286C11#912711yescharacteristic, complemented, Sylow
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23#6689712yes—
292C23#6689912yes—
293C23#6689912yes—
294C23C2×C22⋊Dic1111yescharacteristic
295Q8—84no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—24no—
306C2×C4—22no—
307C2×C4—24no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—44no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4#6689912yes—
319C2×C4#6689912yes—
320C2×C4D4×Dic1112yes—
321C2×C4#6698811yescharacteristic
322C2×C4#6699011yescharacteristic
323C2×C4#6699212yes—
324C2×C4C2×#432511yescharacteristic
325C2×C4C2×#432511yescharacteristic
326C2×C4C2×#432611yescharacteristic
327C2×C4C2×#432611yescharacteristic
328C2×C4#6700211yescharacteristic
329C2×C4#6700312yes—
330C2×C4#6700411yescharacteristic
331C8—444no—
332C8—882no—
333C22—22no—
334C22—22no—
335C22—22no—
336C22—22no—
337C22—22no—
338C22—22no—
339C22#1062218414yescomplemented
340C22C2×#6689711yescharacteristic
341C22#1062283311yescharacteristic
342C22C2×#6689911yescharacteristic
343C22C2×#6689911yescharacteristic
344C22#1062284511yescharacteristic
345C22#1062284611yescharacteristic
346C22#1062285011yescharacteristic
347C4—22no—
348C4—22no—
349C4—22no—
350C4—41no—
351C4—82no—
352C4—82no—
353C4#1062265611yescharacteristic
354C4#1062265711yescharacteristic
355C4#1062265911yescharacteristic
356C4#1062266112yes—
357C4#1062266311yescharacteristic
358C4#1062266412yes—
359C2—24no—
360C2C2×#1062218411yescharacteristic
361C2#1306727311yescharacteristic
362C2#1306730611yescharacteristic
363C2#1306731111yescharacteristic
364C2#1306892411yescharacteristic
365C2#1306904011yescharacteristic
366C2#1306908011yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2857C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#2857D11
hypocenterC11#9127
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2857

Complements

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

NH ≅ G/Ntype
3. C2×#10622184C2semidirect
4. #13066499C2semidirect
178. C22×C11#333semidirect
286. C11#9127semidirect
339. C22#10622184semidirect

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
#130685962
C2×#106221842
#130664992
C11×#28572
#912711