Finite Group Databasebeta

← #14758666

Subgroups — #14758666

Order 2816.

982 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071023C211yesmaximal, characteristic
2C2×C4×C4⋊Dic11C211yesmaximal, characteristic
3#13069380C212yesmaximal, complemented
4#13069375C212yesmaximal, complemented
5#13068811C212yesmaximal
6#13068806C212yesmaximal
7#13068513C214yesmaximal, complemented
8C2×C11×#432C211yesmaximal, characteristic
9C22×C42×C11C2211yescharacteristic
10C2×#66979—21no—
11C22×C4⋊Dic11C2211yescharacteristic
12C22×C4⋊Dic11C2211yescharacteristic
13C22×C4×Dic11—21no—
14C11×#432C418yescomplemented
15C2×C11×C4⋊C8C2212yes—
16C2×C11×C22⋊C8C2212yes—
17C2×C11×#97C2212yes—
18#10622825—21no—
19#10622825C2212yes—
20C2×C11⋊#95—21no—
21C2×#66882C2214yes—
22C2×#66881C2214yes—
23#10622549—21no—
24#10622548C2211yescharacteristic
25#10622548C2211yescharacteristic
26C4×C4⋊Dic11—21no—
27C4×C4⋊Dic11—21no—
28C4×C4⋊Dic11—21no—
29C4×C4⋊Dic11C2212yes—
30C4×C4⋊Dic11C2212yes—
31C4×C4⋊Dic11C2212yes—
32#10622189C2214yes—
33#10622189C2214yes—
34C23×C4×C11D411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C23×Dic11—21no—
38C23×Dic11—21no—
39C22×C8×C11C2314yes—
40C2×C42×C11C2×C414yes—
41C2×C42×C11D411yescharacteristic
42C2×C42×C11D411yescharacteristic
43C2×C42×C11Q814yes—
44C2×C42×C11C2311yescharacteristic
45C2×C42×C11C2311yescharacteristic
46C2×C22⋊Dic11—22no—
47#66979—44no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—24no—
51C2×C4⋊Dic11—24no—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11—21no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11C2312yes—
57C2×C4⋊Dic11C2312yes—
58C2×C4⋊Dic11C2312yes—
59C2×C4⋊Dic11C2312yes—
60C2×C4×Dic11—22no—
61C2×C4×Dic11—22no—
62C2×C4×Dic11—22no—
63C2×C4×Dic11—44no—
64C11×C4⋊C8C2×C418yescomplemented
65C11×C22⋊C8C2×C418yes—
66C11×#97C2×C418yescomplemented
67C11⋊#95—22no—
68C11⋊#95—22no—
69C11⋊#95—22no—
70C11⋊#95—22no—
71#66882—28no—
72#66881—28no—
73#21365—111nomaximal, Sylow
74C24×C11C2×D411yescharacteristic
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11—22no—
81C22×C4×C11C4⋊C414yes—
82C22×C4×C11C4⋊C414yes—
83C22×C4×C11C22×C412yes—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×Q812yes—
90C22×C4×C11C2411yescharacteristic
91C22×Dic11—24no—
92C22×Dic11—24no—
93C22×Dic11—22no—
94C22×Dic11—22no—
95C22×Dic11—22no—
96C22×Dic11—22no—
97C22×Dic11—42no—
98C22×Dic11—42no—
99C22×Dic11—42no—
100C22×Dic11—42no—
101C2×C8×C11—24no—
102C2×C8×C11—24no—
103C2×C8×C11C22×C418yes—
104C42×C11C4⋊C414yes—
105C42×C11C4⋊C414yes—
106C42×C11C22×C412yes—
107C42×C11C22×C412yes—
108C42×C11C2×Q812yes—
109C42×C11C2×Q812yes—
110C22⋊Dic11—44no—
111C4⋊Dic11—24no—
112C4⋊Dic11—24no—
113C4⋊Dic11—22no—
114C4⋊Dic11—22no—
115C4⋊Dic11—24no—
116C4⋊Dic11—24no—
117C4⋊Dic11—42no—
118C4⋊Dic11—42no—
119C4⋊Dic11—42no—
120C4⋊Dic11—42no—
121C4⋊Dic11#4114yes—
122C4⋊Dic11#4114yes—
123C4×Dic11—44no—
124C4×Dic11—44no—
125C4×Dic11—44no—
126C2×#432D1111yescharacteristic
127#2285—111no—
128C2×C4×C4⋊C4—111no—
129#1948—112no—
130#1947—112no—
131#1853—112no—
132#1852—112no—
133#1776—114no—
134C23×C11—21no—
135C23×C11—21no—
136C23×C11—21no—
137C23×C11—21no—
138C23×C11C2×C4⋊C412yes—
139C23×C11AGL(1,ℤ/8)12yes—
140C23×C11#13712yes—
141C23×C11C22×D411yescharacteristic
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—28no—
151C2×C4×C11—24no—
152C2×C4×C11—24no—
153C2×C4×C11—28no—
154C2×C4×C11C2×C4⋊C412yes—
155C2×C4×C11C2×C4⋊C412yes—
156C2×C4×C11C2×C4⋊C412yes—
157C2×C4×C11C2×C4⋊C412yes—
158C2×C4×C11C2×C4⋊C412yes—
159C2×C4×C11AGL(1,ℤ/8)12yes—
160C2×C4×C11#13712yes—
161C2×C4×C11C23×C411yescharacteristic
162C2×C4×C11C22×Q811yescharacteristic
163C2×C4×C11C2×#4112yes—
164C2×C4×C11C2×#4112yes—
165C2×Dic11—24no—
166C2×Dic11—24no—
167C2×Dic11—48no—
168C2×Dic11—48no—
169C2×Dic11—42no—
170C2×Dic11—42no—
171C2×Dic11—42no—
172C2×Dic11—42no—
173C2×Dic11—42no—
174C2×Dic11—42no—
175C2×Dic11—42no—
176C2×Dic11—42no—
177C2×Dic11—42no—
178C2×Dic11—42no—
179C8×C11—28no—
180C2×#117—221no—
181C22×C4⋊C4—111no—
182C22×C4⋊C4—111no—
183C22×C42—221no—
184C22×C42C2×D1111yescharacteristic
185#432Dic1118yescomplemented
186C2×#107—114no—
187C2×#106—114no—
188C2×C4⋊C8C2×D1112yes—
189C2×C22⋊C8C2×D1112yes—
190C2×#97C2×D1112yes—
191#384—111no—
192#384—111no—
193#382—221no—
194#380—112no—
195#380—221no—
196C4×C4⋊C4—112no—
197C4×C4⋊C4—112no—
198C4×C4⋊C4—112no—
199C4×C4⋊C4—221no—
200C4×C4⋊C4—221no—
201C4×C4⋊C4—221no—
202C2×#95—221no—
203#340—114no—
204#340—114no—
205C22×C11—22no—
206C22×C11—22no—
207C22×C11—22no—
208C22×C11—22no—
209C22×C11—22no—
210C22×C11—22no—
211C22×C11#42814yes—
212C22×C11C22×C4⋊C411yescharacteristic
213C22×C11#52511yescharacteristic
214C22×C11#52511yescharacteristic
215C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
216C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
217C22×C11C2×#13711yescharacteristic
218C22×C11C2×#13711yescharacteristic
219C4×C11—22no—
220C4×C11—22no—
221C4×C11—22no—
222C4×C11—22no—
223C4×C11#42814yes—
224C4×C11C4×#4112yes—
225C4×C11#53312yes—
226Dic11—44no—
227Dic11—44no—
228Dic11—82no—
229Dic11—82no—
230C23×C4—221no—
231C23×C4—221no—
232C23×C4D4411yescharacteristic
233C23×C4D4411yescharacteristic
234C23×C4C22×D1111yescharacteristic
235C22×C8C22×D1114yes—
236#117—444no—
237C2×C4⋊C4—112no—
238C2×C4⋊C4—112no—
239C2×C4⋊C4—112no—
240C2×C4⋊C4—112no—
241C2×C4⋊C4—224no—
242C2×C4⋊C4—224no—
243C2×C4⋊C4—221no—
244C2×C4⋊C4—221no—
245C2×C4⋊C4—221no—
246C2×C4⋊C4—221no—
247C2×C4⋊C4—221no—
248C2×C4⋊C4—221no—
249C2×C22⋊C4—222no—
250C2×C42—222no—
251C2×C42—222no—
252C2×C42—222no—
253C2×C42—444no—
254C2×C42Dic2214yes—
255C2×C42D4411yescharacteristic
256C2×C42D4411yescharacteristic
257C2×C42C2×Dic1114yes—
258C2×C42C22×D1111yescharacteristic
259C2×C42C22×D1111yescharacteristic
260#107—228no—
261#106—228no—
262C4⋊C8C2×Dic1118yescomplemented
263C22⋊C8C2×Dic1118yes—
264#97C2×Dic1118yescomplemented
265#95—222no—
266#95—222no—
267#95—222no—
268#95—222no—
269C2×C11—24no—
270C2×C11#229611yescharacteristic
271C2×C11C2×#42811yescharacteristic
272C2×C11C2×#42811yescharacteristic
273C2×C11#310911yescharacteristic
274C2×C11#311011yescharacteristic
275C2×C11#311211yescharacteristic
276C2×C11#311311yescharacteristic
277C24C2×D4411yescharacteristic
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—224no—
285C22×C4—224no—
286C22×C4—222no—
287C22×C4—222no—
288C22×C4—222no—
289C22×C4—222no—
290C22×C4—442no—
291C22×C4—442no—
292C22×C4—442no—
293C22×C4—442no—
294C22×C4C4⋊Dic1114yes—
295C22×C4C4⋊Dic1114yes—
296C22×C4C2×Dic2212yes—
297C22×C4C2×D4411yescharacteristic
298C22×C4C2×D4411yescharacteristic
299C22×C4C2×D4411yescharacteristic
300C22×C4C2×D4411yescharacteristic
301C22×C4C2×D4411yescharacteristic
302C22×C4C22×Dic1112yes—
303C22×C4C23×D1111yescharacteristic
304C2×C8—24no—
305C2×C8—24no—
306C2×C8C22×Dic1118yes—
307C4⋊C4—114no—
308C4⋊C4—114no—
309C4⋊C4—224no—
310C4⋊C4—224no—
311C4⋊C4—222no—
312C4⋊C4—222no—
313C4⋊C4—224no—
314C4⋊C4—224no—
315C4⋊C4—442no—
316C4⋊C4—442no—
317C4⋊C4—442no—
318C4⋊C4—442no—
319C22⋊C4—444no—
320C42—444no—
321C42—444no—
322C42—444no—
323C42C4⋊Dic1114yes—
324C42C4⋊Dic1114yes—
325C42C2×Dic2212yes—
326C42C2×Dic2212yes—
327C42C22×Dic1112yes—
328C42C22×Dic1112yes—
329C11#2136511yescharacteristic, complemented, Sylow
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23#6696112yes—
335C23#6696212yes—
336C23C2×C4⋊Dic1112yes—
337C23C22×D4411yescharacteristic
338C2×C4—28no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—28no—
348C2×C4—24no—
349C2×C4—24no—
350C2×C4—224no—
351C2×C4—224no—
352C2×C4—448no—
353C2×C4—448no—
354C2×C4—442no—
355C2×C4—442no—
356C2×C4—442no—
357C2×C4—442no—
358C2×C4—442no—
359C2×C4—442no—
360C2×C4—442no—
361C2×C4—442no—
362C2×C4—442no—
363C2×C4—442no—
364C2×C4#6696112yes—
365C2×C4#6696212yes—
366C2×C4C2×C4⋊Dic1112yes—
367C2×C4C2×C4⋊Dic1112yes—
368C2×C4C2×C4⋊Dic1112yes—
369C2×C4C2×C4⋊Dic1112yes—
370C2×C4C2×C4⋊Dic1112yes—
371C2×C4C22×Dic2211yescharacteristic
372C2×C4#41×D1112yes—
373C2×C4#41×D1112yes—
374C2×C4C23×Dic1111yescharacteristic
375C8—28no—
376C22—22no—
377C22—22no—
378C22—22no—
379C22—22no—
380C22—22no—
381C22—22no—
382C22#1062273414yes—
383C22#1062305511yescharacteristic
384C22#1062305511yescharacteristic
385C22C2×#6696111yescharacteristic
386C22C2×#6696111yescharacteristic
387C22C2×#6696211yescharacteristic
388C22C2×#6696211yescharacteristic
389C22C22×C4⋊Dic1111yescharacteristic
390C4—22no—
391C4—22no—
392C4—22no—
393C4—22no—
394C4—444no—
395C4—444no—
396C4—882no—
397C4—882no—
398C4#1062273414yes—
399C4#1062304812yes—
400C4#41×Dic1112yes—
401C2—24no—
402C2#1307110011yescharacteristic
403C2C2×#1062273411yescharacteristic
404C2C2×#1062273411yescharacteristic
405C2#1307870811yescharacteristic
406C2#1307871611yescharacteristic
407C2#1307873911yescharacteristic
408C2#1307874711yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#432C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC2×#432D11
hypocenterC11#21365
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#432

Complements

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

NH ≅ G/Ntype
3. #13069380C2semidirect
4. #13069375C2semidirect
7. #13068513C2semidirect
14. C11×#432C4semidirect
64. C11×C4⋊C8C2×C4semidirect
66. C11×#97C2×C4semidirect
185. #432Dic11semidirect
262. C4⋊C8C2×Dic11semidirect
264. #97C2×Dic11semidirect
329. C11#21365semidirect

Maximal subgroups

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

subgroupindex
#130710232
C2×C4×C4⋊Dic112
#130693802
#130693752
#130688112
#130688062
#130685132
C2×C11×#4322
#2136511