Finite Group Databasebeta

← #14644665

Subgroups — #14644665

Order 2816.

628 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#66977C211yesmaximal, characteristic
2C2×#10622105C212yesmaximal
3#13066843C211yesmaximal, characteristic
4#13066496C212yesmaximal
5C11×#1749C211yesmaximal, characteristic
6C22×C42×C11C2211yescharacteristic
7C2×#66977C2211yescharacteristic
8C2×C4×Dic22C411yescharacteristic, complemented
9C2×C11×C22⋊C8C2212yes—
10C2×C11×#97—21no—
11#10622825C2211yescharacteristic
12#10622823—21no—
13C4×C22⋊Dic11—21no—
14C2×C11⋊#95—21no—
15C2×C11⋊#95—21no—
16C2×C11⋊#95C2212yes—
17C4×C4⋊Dic11C411yescharacteristic, complemented
18#10622546—21no—
19C4×Dic11⋊C4—21no—
20#10622542C411yescharacteristic, complemented
21#10622541C411yescharacteristic, complemented
22C11×#336—21no—
23#10622105C418yescomplemented
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C23×C4×C11C2311yescharacteristic
27C23×Dic11—22no—
28C22×Dic22C2×C411yescharacteristic
29C22×C8×C11—22no—
30C2×C42×C11—42no—
31C2×C42×C11C2×C411yescharacteristic
32C2×C42×C11C2×C411yescharacteristic
33C2×C42×C11D411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37C2×C4⋊Dic11C2×C411yescharacteristic
38C2×C4⋊Dic11C2×C411yescharacteristic
39C2×C4⋊Dic11C2×C411yescharacteristic
40#66977—22no—
41#66977C2×C414yes—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×C4×Dic11—21no—
46C2×C4×Dic11—21no—
47C4×Dic22—42no—
48C11×C22⋊C8—22no—
49C11×C22⋊C8C2×C414yes—
50C11×#97—42no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—22no—
57C11⋊#95—42no—
58C11⋊#95—42no—
59C11⋊#95C2×C414yes—
60#8217—111nomaximal, Sylow
61C24×C11C2×D411yescharacteristic
62C22×C4×C11—21no—
63C22×C4×C11—22no—
64C22×C4×C11—21no—
65C22×C4×C11—22no—
66C22×C4×C11—41no—
67C22×C4×C11—41no—
68C22×C4×C11—41no—
69C22×C4×C11—41no—
70C22×C4×C11—41no—
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22×C411yescharacteristic
76C22×C4×C11C22×C412yes—
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11#4112yes—
79C22×Dic11—21no—
80C22×Dic11—21no—
81C22×Dic11—21no—
82C22×Dic11—21no—
83C22×Dic11—24no—
84C22×Dic11—42no—
85C22×Dic11—42no—
86C22×Dic11—42no—
87C22×Dic11—42no—
88C22×Dic11—42no—
89C22×Dic11—42no—
90C2×Dic22—21no—
91C2×Dic22—41no—
92C2×Dic22—41no—
93C2×Dic22C4212yes—
94C2×C8×C11—24no—
95C2×C8×C11—42no—
96C2×C8×C11—42no—
97C42×C11—22no—
98C42×C11—22no—
99C42×C11—41no—
100C42×C11—41no—
101C22⋊Dic11—24no—
102C22⋊Dic11—41no—
103C22⋊Dic11—41no—
104C4⋊Dic11—21no—
105C4⋊Dic11—41no—
106C4⋊Dic11—41no—
107C4⋊Dic11C4212yes—
108Dic11⋊C4—24no—
109Dic11⋊C4—42no—
110Dic11⋊C4—42no—
111C4×Dic11—42no—
112C4×Dic11—42no—
113C4×C22⋊Q8—111no—
114#1749D1111yescharacteristic
115C2×#328—112no—
116#1434—111no—
117#1294—112no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11C2×C22⋊C411yescharacteristic
123C23×C11C4×D412yes—
124C23×C11AGL(1,ℤ/8)11yescharacteristic
125C23×C11#13711yescharacteristic
126C23×C11#13712yes—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—44no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11#9912yes—
148C2×C4×C11C2×C4211yescharacteristic
149C2×C4×C11#11711yescharacteristic
150C2×C4×C11C4×D412yes—
151C2×Dic11—22no—
152C2×Dic11—22no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—44no—
158C2×Dic11—44no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—44no—
166C2×Dic11—82no—
167C2×Dic11—82no—
168C2×Dic11—82no—
169C2×Dic11—82no—
170Dic22—42no—
171Dic22—42no—
172C8×C11—44no—
173C2×C22⋊Q8—111no—
174C2×C4×Q8—111no—
175C22×C42C2×D1111yescharacteristic
176C2×C22⋊C8C2×D1112yes—
177C2×#97—21no—
178#391—111no—
179#389—111no—
180#387—221no—
181#385—221no—
182#380—111no—
183C4×C4⋊C4—111no—
184C4×C4⋊C4—221no—
185C4×C22⋊C4—221no—
186C2×#95—112no—
187C2×#95—221no—
188C2×#95—221no—
189#336—21no—
190#328—118no—
191C22×C11—22no—
192C22×C11—22no—
193C22×C11—22no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11—22no—
199C22×C11C4×C22⋊C411yescharacteristic
200C22×C11C2×#9911yescharacteristic
201C22×C11#41011yescharacteristic
202C22×C11#41711yescharacteristic
203C22×C11#41911yescharacteristic
204C22×C11#42111yescharacteristic
205C22×C11#42111yescharacteristic
206C22×C11#44012yes—
207C22×C11#44112yes—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—22no—
211C4×C11—22no—
212C4×C11—41no—
213C4×C11—41no—
214C4×C11—41no—
215Dic11—42no—
216Dic11—42no—
217Dic11—84no—
218Dic11—81no—
219Dic11—81no—
220C22×Q8—111no—
221C23×C4—222no—
222C23×C4D4411yescharacteristic
223C23×C4D4411yescharacteristic
224C23×C4C22×D1111yescharacteristic
225C22×C8—22no—
226C22⋊Q8—114no—
227C22⋊Q8—222no—
228C4×Q8—442no—
229C2×C4⋊C4—111no—
230C2×C4⋊C4—111no—
231C2×C4⋊C4—111no—
232C2×C4⋊C4—221no—
233C2×C4⋊C4—221no—
234C2×C4⋊C4—221no—
235C2×C22⋊C4—221no—
236C2×C22⋊C4—221no—
237C2×C42—42no—
238C2×C42—221no—
239C2×C42—221no—
240C2×C42C4×D1111yescharacteristic
241C2×C42C4×D1111yescharacteristic
242C2×C42C22⋊D1111yescharacteristic
243C2×C42C22⋊D1111yescharacteristic
244C22⋊C8—22no—
245C22⋊C8C4×D1114yes—
246#97—42no—
247#95—114no—
248#95—221no—
249#95—221no—
250#95—221no—
251#95—221no—
252#95—222no—
253#95—221no—
254#95—442no—
255#95—442no—
256C2×C11—22no—
257C2×C11—22no—
258C2×C11#151111yescharacteristic
259C2×C11#151211yescharacteristic
260C2×C11#151311yescharacteristic
261C2×C11#151511yescharacteristic
262C2×C11C4×#9911yescharacteristic
263C2×C11#175911yescharacteristic
264C2×C11#176311yescharacteristic
265C24C2×D4411yescharacteristic
266C2×Q8—112no—
267C2×Q8—221no—
268C2×Q8—441no—
269C2×Q8—441no—
270C22×C4—21no—
271C22×C4—22no—
272C22×C4—21no—
273C22×C4—22no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—221no—
280C22×C4—221no—
281C22×C4—224no—
282C22×C4—221no—
283C22×C4—221no—
284C22×C4—442no—
285C22×C4—442no—
286C22×C4—442no—
287C22×C4—442no—
288C22×C4—442no—
289C22×C4—442no—
290C22×C4(C2×D11)⋊C411yescharacteristic
291C22×C4(C2×D11)⋊C411yescharacteristic
292C22×C4(C2×D11)⋊C411yescharacteristic
293C22×C4(C2×D11)⋊C411yescharacteristic
294C22×C4C2×C4×D1111yescharacteristic
295C22×C4C2×C4×D1112yes—
296C22×C4#433912yes—
297C22×C4C2×C22⋊D1111yescharacteristic
298C2×C8—24no—
299C2×C8—42no—
300C2×C8—42no—
301C4⋊C4—112no—
302C4⋊C4—221no—
303C4⋊C4—224no—
304C4⋊C4—441no—
305C4⋊C4—441no—
306C4⋊C4—442no—
307C4⋊C4—442no—
308C22⋊C4—224no—
309C22⋊C4—441no—
310C22⋊C4—441no—
311C42—22no—
312C42—22no—
313C42—41no—
314C42—41no—
315C42—442no—
316C42—442no—
317C11#821711yescharacteristic, complemented, Sylow
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23C4×D4412yes—
323C23#6696111yescharacteristic
324C23#6696212yes—
325C23#6696211yescharacteristic
326C23C2×(C2×D11)⋊C411yescharacteristic
327Q8—442no—
328Q8—442no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—44no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—222no—
350C2×C4—222no—
351C2×C4—441no—
352C2×C4—441no—
353C2×C4—441no—
354C2×C4—441no—
355C2×C4—444no—
356C2×C4—444no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4—441no—
360C2×C4—441no—
361C2×C4—441no—
362C2×C4—444no—
363C2×C4—441no—
364C2×C4—882no—
365C2×C4—882no—
366C2×C4—882no—
367C2×C4—882no—
368C2×C4#6687012yes—
369C2×C4C42×D1111yescharacteristic
370C2×C4#6692511yescharacteristic
371C2×C4C4×C22⋊D1112yes—
372C8—44no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—22no—
381C22#1062232312yes—
382C22#1062232912yes—
383C22C4×(C2×D11)⋊C411yescharacteristic
384C22C2×#6687011yescharacteristic
385C22#1062261911yescharacteristic
386C22#1062273311yescharacteristic
387C22#1062274611yescharacteristic
388C22#1062275211yescharacteristic
389C22#1062275211yescharacteristic
390C4—22no—
391C4—21no—
392C4—21no—
393C4—22no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—442no—
398C4—442no—
399C4—884no—
400C4—881no—
401C4—881no—
402C2—22no—
403C2—22no—
404C2#1306715011yescharacteristic
405C2#1306715511yescharacteristic
406C2#1306716011yescharacteristic
407C2#1306716811yescharacteristic
408C2C4×#6687011yescharacteristic
409C2#1306842911yescharacteristic
410C2#1306844711yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC2×C4×C11C2×C42
FrattiniC23×C4C22×D11
FittingC11×#1749C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#1749D11
hypocenterC11#8217
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1749

Complements

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

NH ≅ G/Ntype
8. C2×C4×Dic22C4semidirect
17. C4×C4⋊Dic11C4semidirect
20. #10622542C4semidirect
21. #10622541C4semidirect
23. #10622105C4semidirect
317. C11#8217semidirect

Maximal subgroups

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

subgroupindex
C4×#669772
C2×#106221052
#130668432
#130664962
C11×#17492
#821711