Finite Group Databasebeta

← #14649429

Subgroups — #14649429

Order 2816.

644 conjugacy classes of subgroups.

The subgroup lattice has 380 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×#10622185C212yesmaximal, complemented
4#13066499C212yesmaximal, complemented
5C11×#2857C211yesmaximal, characteristic
6C2×C11×C4⋊Q8C2211yescharacteristic
7C2×C11×C22⋊Q8—21no—
8C22×C42×C11C2211yescharacteristic
9C23×C11⋊C8—21no—
10C11×#391—21no—
11C11×#389—21no—
12C11×#389C412yes—
13C11×#384C2211yescharacteristic
14C11×#380—21no—
15C11×#380C412yes—
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#10622185—24no—
22#10622162—21no—
23C22×Q8×C11—21no—
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C11×C4⋊Q8—22no—
28C11×C4⋊Q8—22no—
29C11×C22⋊Q8—42no—
30C11×C22⋊Q8—42no—
31C2×C11×C4⋊C4—22no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4C2×C412yes—
36C2×C11×C4⋊C4C2×C412yes—
37C2×C11×C22⋊C4—22no—
38C2×C42×C11—22no—
39C2×C42×C11—22no—
40C2×C42×C11C2×C411yescharacteristic
41C2×C42×C11D411yescharacteristic
42C2×C42×C11D411yescharacteristic
43C2×C42×C11C2311yescharacteristic
44C22×C11⋊C8—24no—
45C22×C11⋊C8—22no—
46C22×C11⋊C8—22no—
47C22×C11⋊C8—42no—
48C22×C11⋊C8—42no—
49C11×#95—22no—
50C11×#95—22no—
51C22⋊(C11⋊C8)—42no—
52C4⋊(C11⋊C8)—24no—
53C4⋊(C11⋊C8)—22no—
54C4⋊(C11⋊C8)—22no—
55C4⋊(C11⋊C8)—22no—
56C4⋊(C11⋊C8)D414yes—
57#9131—111nomaximal, Sylow
58C24×C11C22⋊C411yescharacteristic
59C2×Q8×C11—41no—
60C2×Q8×C11—41no—
61C2×Q8×C11—41no—
62C2×Q8×C11—41no—
63C2×Q8×C11—41no—
64C2×Q8×C11—41no—
65C22×C4×C11—21no—
66C22×C4×C11—22no—
67C22×C4×C11—21no—
68C22×C4×C11—22no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—22no—
72C22×C4×C11—22no—
73C22×C4×C11—22no—
74C22×C4×C11—22no—
75C22×C4×C11—41no—
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11C22⋊C411yescharacteristic
78C22×C4×C11C22⋊C411yescharacteristic
79C22×C4×C11D812yes—
80C22×C4×C11SD1612yes—
81C22×C4×C11SD1612yes—
82C22×C4×C11Q1612yes—
83C22×C4×C11C22×C411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C11×C4⋊C4—24no—
87C11×C4⋊C4—42no—
88C11×C4⋊C4—44no—
89C11×C4⋊C4—42no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—42no—
93C11×C22⋊C4—44no—
94C42×C11—22no—
95C42×C11—21no—
96C42×C11—22no—
97C42×C11—21no—
98C42×C11C2×D412yes—
99C42×C11#4112yes—
100C2×C11⋊C8—24no—
101C2×C11⋊C8—48no—
102C2×C11⋊C8—42no—
103C2×C11⋊C8—42no—
104C2×C11⋊C8—42no—
105C2×C11⋊C8—42no—
106C2×C11⋊C8—42no—
107C22×C4⋊C8—111no—
108#2857D1111yescharacteristic
109#1797—111no—
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
120Q8×C11—81no—
121Q8×C11—81no—
122Q8×C11—81no—
123Q8×C11—81no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—22no—
131C2×C4×C11—22no—
132C2×C4×C11—24no—
133C2×C4×C11—24no—
134C2×C4×C11—22no—
135C2×C4×C11—22no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—44no—
140C2×C4×C11—42no—
141C2×C4×C11—42no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11#10212yes—
147C2×C4×C11#10312yes—
148C2×C4×C11C4×D412yes—
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12112yes—
151C2×C4×C11#12311yescharacteristic
152C2×C4×C11C2×D811yescharacteristic
153C2×C4×C11C2×SD1611yescharacteristic
154C2×C4×C11C2×SD1611yescharacteristic
155C2×C4×C11C2×Q1611yescharacteristic
156C2×C4×C11#13512yes—
157C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C11#13711yescharacteristic
159C11⋊C8—44no—
160C11⋊C8—82no—
161C23×C8—221no—
162C2×C4⋊Q8C2×D1111yescharacteristic
163C2×C22⋊Q8—21no—
164C22×C42C2×D1111yescharacteristic
165C2×C4⋊C8—112no—
166C2×C4⋊C8—112no—
167C2×C4⋊C8—224no—
168C2×C4⋊C8—221no—
169C2×C22⋊C8—221no—
170#391—21no—
171#389—21no—
172#389Dic1112yes—
173#384C2×D1111yescharacteristic
174#380—21no—
175#380Dic1112yes—
176#336—221no—
177#332—224no—
178C22×C11—22no—
179C22×C11—22no—
180C22×C11—22no—
181C22×C11—22no—
182C22×C11—22no—
183C22×C11—22no—
184C22×C11#33214yescomplemented
185C22×C11#38611yescharacteristic
186C22×C11C2×#10111yescharacteristic
187C22×C11#41311yescharacteristic
188C22×C11C2×#10211yescharacteristic
189C22×C11C2×#10311yescharacteristic
190C22×C11#41611yescharacteristic
191C22×C11#41711yescharacteristic
192C4×C11—22no—
193C4×C11—22no—
194C4×C11—22no—
195C4×C11—41no—
196C4×C11—82no—
197C4×C11—82no—
198C4×C11#44711yescharacteristic
199C4×C11#44811yescharacteristic
200C4×C11#46512yes—
201C4×C11#46712yes—
202C4×C11#48011yescharacteristic
203C4×C11#48111yescharacteristic
204C22×Q8—21no—
205C23×C4C2×Dic1111yescharacteristic
206C23×C4C22⋊D1111yescharacteristic
207C23×C4C22⋊D1111yescharacteristic
208C22×C8—224no—
209C22×C8—222no—
210C22×C8—222no—
211C22×C8—442no—
212C22×C8—442no—
213C4⋊Q8—22no—
214C4⋊Q8—22no—
215C22⋊Q8—42no—
216C22⋊Q8—42no—
217C2×C4⋊C4—22no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4C2×Dic1112yes—
222C2×C4⋊C4C2×Dic1112yes—
223C2×C22⋊C4—22no—
224C2×C42—22no—
225C2×C42—22no—
226C2×C42C2×Dic1111yescharacteristic
227C2×C42C22⋊D1111yescharacteristic
228C2×C42C22⋊D1111yescharacteristic
229C2×C42C22×D1111yescharacteristic
230C4⋊C8—114no—
231C4⋊C8—224no—
232C4⋊C8—222no—
233C4⋊C8—222no—
234C4⋊C8—222no—
235C22⋊C8—442no—
236#95—22no—
237#95—22no—
238C2×C11—24no—
239C2×C11C2×#33211yescharacteristic
240C2×C11#154011yescharacteristic
241C2×C11#155011yescharacteristic
242C2×C11#155211yescharacteristic
243C2×C11#187411yescharacteristic
244C2×C11#189211yescharacteristic
245C2×C11#190111yescharacteristic
246C24C22⋊Dic1111yescharacteristic
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8—41no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—22no—
256C22×C4—21no—
257C22×C4—22no—
258C22×C4—21no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—41no—
264C22×C4#432312yes—
265C22×C4#432412yes—
266C22×C4#432512yes—
267C22×C4#432612yes—
268C22×C4C22⋊Dic1111yescharacteristic
269C22×C4C22⋊Dic1111yescharacteristic
270C22×C4C22⋊Dic1111yescharacteristic
271C22×C4C22×Dic1111yescharacteristic
272C22×C4C2×C22⋊D1111yescharacteristic
273C22×C4C2×C22⋊D1111yescharacteristic
274C2×C8—224no—
275C2×C8—448no—
276C2×C8—442no—
277C2×C8—442no—
278C2×C8—442no—
279C2×C8—442no—
280C2×C8—442no—
281C4⋊C4—24no—
282C4⋊C4—42no—
283C4⋊C4—44no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—42no—
287C4⋊C4—42no—
288C22⋊C4—44no—
289C42—22no—
290C42—21no—
291C42—21no—
292C42—22no—
293C42D4×D1112yes—
294C42#434112yes—
295C11#913111yescharacteristic, complemented, Sylow
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23#6689612yes—
301C23#6689912yes—
302C23#6690012yes—
303C23C2×C22⋊Dic1111yescharacteristic
304Q8—81no—
305Q8—81no—
306Q8—81no—
307Q8—81no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—24no—
319C2×C4—24no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—44no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4#6689612yes—
331C2×C4#6689912yes—
332C2×C4C2×#432311yescharacteristic
333C2×C4C2×#432411yescharacteristic
334C2×C4D4×Dic1112yes—
335C2×C4#6698811yescharacteristic
336C2×C4#6699011yescharacteristic
337C2×C4#6699212yes—
338C2×C4C2×#432511yescharacteristic
339C2×C4C2×#432611yescharacteristic
340C2×C4#6700211yescharacteristic
341C2×C4#6700312yes—
342C2×C4#6700411yescharacteristic
343C8—444no—
344C8—882no—
345C22—22no—
346C22—22no—
347C22—22no—
348C22—22no—
349C22—22no—
350C22—22no—
351C22#1062218514yescomplemented
352C22C2×#6689611yescharacteristic
353C22#1062283311yescharacteristic
354C22C2×#6689911yescharacteristic
355C22C2×#6690011yescharacteristic
356C22#1062284511yescharacteristic
357C22#1062284611yescharacteristic
358C22#1062285011yescharacteristic
359C4—22no—
360C4—22no—
361C4—22no—
362C4—41no—
363C4—82no—
364C4—82no—
365C4#1062264611yescharacteristic
366C4#1062264711yescharacteristic
367C4#1062264911yescharacteristic
368C4#1062265311yescharacteristic
369C4#1062266112yes—
370C4#1062266412yes—
371C2—24no—
372C2C2×#1062218511yescharacteristic
373C2#1306726511yescharacteristic
374C2#1306730611yescharacteristic
375C2#1306731611yescharacteristic
376C2#1306893411yescharacteristic
377C2#1306904011yescharacteristic
378C2#1306908511yescharacteristic
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#9131
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×#10622185C2semidirect
4. #13066499C2semidirect
184. C22×C11#332semidirect
295. C11#9131semidirect
351. C22#10622185semidirect

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×#106221852
#130664992
C11×#28572
#913111