Finite Group Databasebeta

← #14644672

Subgroups — #14644672

Order 2816.

720 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068378C211yesmaximal, characteristic
2C2×#10622176C212yesmaximal
3C4×C11⋊#95C211yesmaximal, characteristic
4#13066494C212yesmaximal
5C4×C11×C22⋊Q8C211yesmaximal, characteristic
6C2×C11×C22⋊Q8C2211yescharacteristic
7C2×C4×Q8×C11C411yescharacteristic, complemented
8C22×C42×C11C2211yescharacteristic
9C22×C4×Dic11—21no—
10C11×#391C411yescharacteristic, complemented
11C11×#389C411yescharacteristic, complemented
12C11×#387—21no—
13C11×#385—21no—
14C11×#380C2211yescharacteristic
15C4×C11×C4⋊C4—21no—
16C4×C11×C4⋊C4C411yescharacteristic, complemented
17C4×C11×C22⋊C4—21no—
18C2×C11⋊#95—21no—
19C2×C11⋊#95C2212yes—
20C2×C22⋊(C11⋊C8)C2212yes—
21C2×#66867—21no—
22#10622176C418yescomplemented
23#10622162—21no—
24C22×Q8×C11C2×C411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11C2311yescharacteristic
28C23×Dic11—22no—
29C11×C22⋊Q8—22no—
30C11×C22⋊Q8C2×C414yes—
31C4×Q8×C11—42no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4C2×C411yescharacteristic
36C2×C11×C4⋊C4C2×C411yescharacteristic
37C2×C11×C4⋊C4C2×C411yescharacteristic
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C42×C11—21no—
41C2×C42×C11—21no—
42C2×C42×C11—42no—
43C2×C42×C11C2×C411yescharacteristic
44C2×C42×C11C2×C411yescharacteristic
45C2×C42×C11D411yescharacteristic
46C2×C42×C11D411yescharacteristic
47C2×C4×Dic11—24no—
48C2×C4×Dic11—42no—
49C2×C4×Dic11—42no—
50C22×C11⋊C8—22no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11⋊#95—24no—
57C11⋊#95—22no—
58C11⋊#95C2×C414yes—
59C22⋊(C11⋊C8)—22no—
60C22⋊(C11⋊C8)C2×C414yes—
61#66867—42no—
62#8219—111nomaximal, Sylow
63C24×C11C2×D411yescharacteristic
64C2×Q8×C11—21no—
65C2×Q8×C11—41no—
66C2×Q8×C11—41no—
67C2×Q8×C11C4212yescomplemented
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—22no—
71C22×C4×C11—22no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—41no—
79C22×C4×C11—41no—
80C22×C4×C11—41no—
81C22×C4×C11C22⋊C411yescharacteristic
82C22×C4×C11C22⋊C411yescharacteristic
83C22×C4×C11C22⋊C411yescharacteristic
84C22×C4×C11C22⋊C411yescharacteristic
85C22×C4×C11C22×C411yescharacteristic
86C22×C4×C11C22×C412yes—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11#4112yes—
89C22×Dic11—24no—
90C22×Dic11—24no—
91C22×Dic11—24no—
92C22×Dic11—42no—
93C22×Dic11—42no—
94C22×Dic11—42no—
95C22×Dic11—42no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—24no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—42no—
101C11×C4⋊C4—42no—
102C11×C4⋊C4C4212yescomplemented
103C11×C22⋊C4—24no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C42×C11—22no—
107C42×C11—22no—
108C42×C11—41no—
109C42×C11—41no—
110C42×C11—42no—
111C42×C11—42no—
112C4×Dic11—48no—
113C2×C11⋊C8—24no—
114C2×C11⋊C8—42no—
115C2×C11⋊C8—42no—
116C4×C22⋊Q8D1111yescharacteristic
117#1749—111no—
118C2×#328—112no—
119C4×#95—111no—
120#1294—112no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11C2×C22⋊C411yescharacteristic
126C23×C11C4×D412yes—
127C23×C11AGL(1,ℤ/8)11yescharacteristic
128C23×C11#13712yes—
129C23×C11#13711yescharacteristic
130Q8×C11—42no—
131Q8×C11—42no—
132C2×C4×C11—24no—
133C2×C4×C11—24no—
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—21no—
143C2×C4×C11—21no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—44no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11#9912yes—
163C2×C4×C11#10412yes—
164C2×C4×C11#10412yes—
165C2×C4×C11C2×C4211yescharacteristic
166C2×C4×C11#11711yescharacteristic
167C2×C4×C11C4×D412yes—
168C2×Dic11—28no—
169C2×Dic11—44no—
170C2×Dic11—44no—
171C2×Dic11—44no—
172C2×Dic11—44no—
173C2×Dic11—44no—
174C2×Dic11—44no—
175C11⋊C8—44no—
176C2×C22⋊Q8C2×D1111yescharacteristic
177C2×C4×Q8Dic1111yescharacteristic, complemented
178C22×C42—221no—
179C22×C42C2×D1111yescharacteristic
180C2×C22⋊C8—112no—
181C2×#97—221no—
182#391Dic1111yescharacteristic, complemented
183#389Dic1111yescharacteristic, complemented
184#387—21no—
185#385—21no—
186#380C2×D1111yescharacteristic
187C4×C4⋊C4—21no—
188C4×C4⋊C4Dic1111yescharacteristic, complemented
189C4×C22⋊C4—21no—
190C2×#95—112no—
191C2×#95—221no—
192#336—221no—
193#328—118no—
194C22×C11—22no—
195C22×C11—22no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11—22no—
199C22×C11—22no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11C4×C22⋊C411yescharacteristic
203C22×C11C2×#9911yescharacteristic
204C22×C11#41011yescharacteristic
205C22×C11#41711yescharacteristic
206C22×C11#41911yescharacteristic
207C22×C11C2×#10411yescharacteristic
208C22×C11C2×#10411yescharacteristic
209C22×C11#44012yes—
210C22×C11#44112yes—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—22no—
214C4×C11—22no—
215C4×C11—22no—
216C4×C11—22no—
217C4×C11—42no—
218C4×C11—42no—
219C4×C11—41no—
220C4×C11—81no—
221C4×C11—81no—
222Dic11—48no—
223C22×Q8C2×Dic1111yescharacteristic
224C23×C4—222no—
225C23×C4C22⋊D1111yescharacteristic
226C23×C4C22⋊D1111yescharacteristic
227C23×C4C22×D1111yescharacteristic
228C22×C8—222no—
229C22⋊Q8—22no—
230C22⋊Q8C4×D1114yes—
231C4×Q8—42no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4C2×Dic1111yescharacteristic
236C2×C4⋊C4C2×Dic1111yescharacteristic
237C2×C4⋊C4C2×Dic1111yescharacteristic
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C42—21no—
241C2×C42—21no—
242C2×C42—42no—
243C2×C42—224no—
244C2×C42—442no—
245C2×C42—442no—
246C2×C42C2×Dic1111yescharacteristic
247C2×C42C2×Dic1111yescharacteristic
248C2×C42C22⋊D1111yescharacteristic
249C2×C42C22⋊D1111yescharacteristic
250C22⋊C8—114no—
251C22⋊C8—222no—
252#97—442no—
253#95—21no—
254#95—21no—
255#95—21no—
256#95—21no—
257#95—21no—
258#95—114no—
259#95—224no—
260#95—222no—
261C2×C11—22no—
262C2×C11—22no—
263C2×C11#150411yescharacteristic
264C2×C11#150611yescharacteristic
265C2×C11#150811yescharacteristic
266C2×C11#150911yescharacteristic
267C2×C11C4×#9911yescharacteristic
268C2×C11C4×#10411yescharacteristic
269C2×C11#176311yescharacteristic
270C24C2×C22⋊D1111yescharacteristic
271C2×Q8—21no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8C4×Dic1112yescomplemented
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—22no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—224no—
289C22×C4—224no—
290C22×C4—224no—
291C22×C4—442no—
292C22×C4—442no—
293C22×C4—442no—
294C22×C4—442no—
295C22×C4C22⋊Dic1111yescharacteristic
296C22×C4C22⋊Dic1111yescharacteristic
297C22×C4C22⋊Dic1111yescharacteristic
298C22×C4C22⋊Dic1111yescharacteristic
299C22×C4C2×C4×D1112yes—
300C22×C4#433912yes—
301C22×C4C22×Dic1111yescharacteristic
302C22×C4C2×C22⋊D1111yescharacteristic
303C2×C8—224no—
304C2×C8—442no—
305C2×C8—442no—
306C4⋊C4—21no—
307C4⋊C4—24no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—42no—
311C4⋊C4—42no—
312C4⋊C4C4×Dic1112yescomplemented
313C22⋊C4—24no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C42—22no—
317C42—22no—
318C42—41no—
319C42—41no—
320C42—42no—
321C42—42no—
322C42—448no—
323C11#821911yescharacteristic, complemented, Sylow
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23C4×C22⋊D1112yes—
329C23#6699512yes—
330C23#6700211yescharacteristic
331C23#6700411yescharacteristic
332C23C2×C22⋊Dic1111yescharacteristic
333Q8—42no—
334Q8—42no—
335C2×C4—24no—
336C2×C4—24no—
337C2×C4—21no—
338C2×C4—21no—
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—22no—
348C2×C4—22no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—44no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—228no—
366C2×C4—444no—
367C2×C4—444no—
368C2×C4—444no—
369C2×C4—444no—
370C2×C4—444no—
371C2×C4—444no—
372C2×C4#6689812yes—
373C2×C4#6690112yes—
374C2×C4#6690112yes—
375C2×C4C2×C4×Dic1111yescharacteristic
376C2×C4#6697911yescharacteristic
377C2×C4C4×C22⋊D1112yes—
378C8—444no—
379C22—21no—
380C22—21no—
381C22—22no—
382C22—22no—
383C22—22no—
384C22—21no—
385C22—21no—
386C22—22no—
387C22#1062263912yes—
388C22#1062264312yes—
389C22C4×C22⋊Dic1111yescharacteristic
390C22C2×#6689811yescharacteristic
391C22#1062283811yescharacteristic
392C22#1062284511yescharacteristic
393C22C2×#6690111yescharacteristic
394C22C2×#6690111yescharacteristic
395C22#1062285311yescharacteristic
396C4—22no—
397C4—22no—
398C4—22no—
399C4—21no—
400C4—21no—
401C4—22no—
402C4—42no—
403C4—41no—
404C4—42no—
405C4—81no—
406C4—81no—
407C4—448no—
408C2—22no—
409C2—22no—
410C2#1306712011yescharacteristic
411C2#1306712811yescharacteristic
412C2#1306713611yescharacteristic
413C2#1306714111yescharacteristic
414C2C4×#6689811yescharacteristic
415C2C4×#6690111yescharacteristic
416C2#1306844611yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC2×C4×C11C2×C42
FrattiniC23×C4C22×D11
FittingC4×C11×C22⋊Q8C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenterC4×C22⋊Q8D11
hypocenterC11#8219
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
7. C2×C4×Q8×C11C4semidirect
10. C11×#391C4semidirect
11. C11×#389C4semidirect
16. C4×C11×C4⋊C4C4semidirect
22. #10622176C4semidirect
67. C2×Q8×C11C42semidirect
102. C11×C4⋊C4C42semidirect
177. C2×C4×Q8Dic11semidirect
182. #391Dic11semidirect
183. #389Dic11semidirect
188. C4×C4⋊C4Dic11semidirect
274. C2×Q8C4×Dic11semidirect
312. C4⋊C4C4×Dic11semidirect
323. C11#8219semidirect

Maximal subgroups

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

subgroupindex
#130683782
C2×#106221762
C4×C11⋊#952
#130664942
C4×C11×C22⋊Q82
#821911