Finite Group Databasebeta

← #14764346

Subgroups — #14764346

Order 2816.

830 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622539C211yesmaximal, characteristic
2#13071023C211yesmaximal, characteristic
3#13069377C212yesmaximal, complemented
4#13069372C212yesmaximal, complemented
5#13068815C214yesmaximal
6#13068785C212yesmaximal, complemented
7#13068749C212yesmaximal, complemented
8C11×#2285C211yesmaximal, characteristic
9C2×C11×#117C2212yes—
10C22×C42×C11C2211yescharacteristic
11C2×#66979—21no—
12C11×#384C2211yescharacteristic
13C11×#384C2211yescharacteristic
14C11×#382C2212yes—
15C11×#380—21no—
16C11×#380—21no—
17C4×C11×C4⋊C4—21no—
18C4×C11×C4⋊C4—21no—
19#10622825—21no—
20#10622825C2212yes—
21C2×C22⋊(C11⋊C8)C2212yes—
22C2×#66872C2214yes—
23C2×#66871C2214yes—
24#10622549—21no—
25#10622548C2211yescharacteristic
26#10622548C2211yescharacteristic
27C4×C4⋊Dic11—21no—
28C4×C4⋊Dic11C2212yes—
29#10622539C418yescomplemented
30C2×C4⋊(C11⋊C8)C2212yes—
31C2×#66867C2212yes—
32#10622167C2214yes—
33#10622167C2214yes—
34C23×C4×C11D411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C11×#117—44no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4C2312yes—
43C2×C11×C4⋊C4C2312yes—
44C2×C11×C22⋊C4—22no—
45C2×C42×C11—22no—
46C2×C42×C11C2×C414yes—
47C2×C42×C11D411yescharacteristic
48C2×C42×C11D411yescharacteristic
49C2×C42×C11Q814yes—
50C2×C42×C11C2311yescharacteristic
51C2×C42×C11C2311yescharacteristic
52C2×C22⋊Dic11—22no—
53#66979—44no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11C2312yes—
59C2×C4⋊Dic11C2312yes—
60C2×C4×Dic11—22no—
61C22×C11⋊C8C2314yes—
62C11×#95—22no—
63C11×#95—22no—
64C11⋊#95—22no—
65C11⋊#95—22no—
66C22⋊(C11⋊C8)C2×C418yes—
67#66872—44no—
68#66871—44no—
69C4⋊(C11⋊C8)C2×C418yes—
70#66867C2×C418yes—
71#21988—111nomaximal, Sylow
72C24×C11C2×D411yescharacteristic
73C22×C4×C11—22no—
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—41no—
80C22×C4×C11—41no—
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—22no—
92C22×Dic11—22no—
93C11×C4⋊C4—24no—
94C11×C4⋊C4—24no—
95C11×C4⋊C4—42no—
96C11×C4⋊C4—42no—
97C11×C4⋊C4—42no—
98C11×C4⋊C4—42no—
99C11×C22⋊C4—44no—
100C42×C11—44no—
101C42×C11C4⋊C414yes—
102C42×C11C4⋊C414yes—
103C42×C11C22×C412yes—
104C42×C11C22×C412yes—
105C42×C11C2×Q812yes—
106C42×C11C2×Q812yes—
107C22⋊Dic11—44no—
108C4⋊Dic11—22no—
109C4⋊Dic11—22no—
110C4⋊Dic11—24no—
111C4⋊Dic11—42no—
112C4⋊Dic11—42no—
113C4⋊Dic11—42no—
114C4⋊Dic11—42no—
115C4×Dic11—44no—
116C2×C11⋊C8—24no—
117C2×C11⋊C8—24no—
118C2×C11⋊C8C22×C418yes—
119C2×#432—111no—
120#2285—111no—
121#2285D1111yescharacteristic
122#1948—112no—
123#1947—112no—
124#1854—114no—
125#1847—112no—
126#1836—112no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11C2×C4⋊C412yes—
134C23×C11C22×D411yescharacteristic
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—24no—
144C2×C4×C11—24no—
145C2×C4×C11—28no—
146C2×C4×C11—44no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11C2×C4⋊C412yes—
154C2×C4×C11C2×C4⋊C412yes—
155C2×C4×C11C2×C4⋊C412yes—
156C2×C4×C11C2×C4⋊C412yes—
157C2×C4×C11C2×C4⋊C412yes—
158C2×C4×C11AGL(1,ℤ/8)12yes—
159C2×C4×C11#13712yes—
160C2×C4×C11C23×C411yescharacteristic
161C2×C4×C11C22×Q811yescharacteristic
162C2×C4×C11H(5,𝔽2)12yes—
163C2×C4×C112−1+412yes—
164C2×Dic11—42no—
165C2×Dic11—42no—
166C2×Dic11—42no—
167C2×Dic11—42no—
168C2×Dic11—42no—
169C2×Dic11—42no—
170C11⋊C8—28no—
171C2×#117—221no—
172C2×#117C2×D1112yes—
173C22×C42C2×D1111yescharacteristic
174#432—118no—
175C2×#107—114no—
176C2×#106—114no—
177C2×C4⋊C8—112no—
178C2×C22⋊C8—112no—
179C2×#97—112no—
180#384—111no—
181#384—111no—
182#384C2×D1111yescharacteristic
183#384C2×D1111yescharacteristic
184#382—221no—
185#382C2×D1112yes—
186#380—21no—
187#380—21no—
188#380—112no—
189#380—221no—
190C4×C4⋊C4—21no—
191C4×C4⋊C4—21no—
192C4×C4⋊C4—112no—
193C4×C4⋊C4—221no—
194#340—114no—
195#340—114no—
196C22×C11—22no—
197C22×C11—22no—
198C22×C11—22no—
199C22×C11—41no—
200C22×C11—41no—
201C22×C11—41no—
202C22×C11—41no—
203C22×C11C22×C4⋊C411yescharacteristic
204C22×C11#53511yescharacteristic
205C22×C11#53611yescharacteristic
206C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
207C22×C11C2×#13711yescharacteristic
208C22×C11#57511yescharacteristic
209C22×C11#57511yescharacteristic
210C4×C11—22no—
211C4×C11—22no—
212C4×C11—22no—
213C4×C11—22no—
214C4×C11—82no—
215C4×C11—82no—
216C4×C11#42814yes—
217C4×C11#52012yes—
218C4×C11#54412yes—
219Dic11—82no—
220Dic11—82no—
221C23×C4C22⋊D1111yescharacteristic
222C23×C4C22⋊D1111yescharacteristic
223C23×C4C22×D1111yescharacteristic
224C22×C8—114no—
225#117—44no—
226#117—444no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—112no—
232C2×C4⋊C4—112no—
233C2×C4⋊C4—221no—
234C2×C4⋊C4—221no—
235C2×C4⋊C4—221no—
236C2×C4⋊C4—221no—
237C2×C4⋊C4C22×D1112yes—
238C2×C4⋊C4C22×D1112yes—
239C2×C22⋊C4—22no—
240C2×C22⋊C4—222no—
241C2×C42—22no—
242C2×C42—222no—
243C2×C42Dic2214yes—
244C2×C42C4×D1114yes—
245C2×C42C22⋊D1111yescharacteristic
246C2×C42C22⋊D1111yescharacteristic
247C2×C42C22×D1111yescharacteristic
248C2×C42C22×D1111yescharacteristic
249#107—444no—
250#106—444no—
251C4⋊C8—118no—
252C22⋊C8—118no—
253#97—118no—
254#95—22no—
255#95—22no—
256#95—222no—
257#95—222no—
258C2×C11—42no—
259C2×C11#231711yescharacteristic
260C2×C11C2×#42811yescharacteristic
261C2×C11#291111yescharacteristic
262C2×C11#321411yescharacteristic
263C2×C11#321611yescharacteristic
264C2×C11#323511yescharacteristic
265C2×C11#323711yescharacteristic
266C24C2×C22⋊D1111yescharacteristic
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—222no—
276C22×C4—222no—
277C22×C4Dic11⋊C414yes—
278C22×C4Dic11⋊C414yes—
279C22×C4C2×Dic2212yes—
280C22×C4C2×C4×D1112yes—
281C22×C4C2×C22⋊D1111yescharacteristic
282C22×C4C2×C22⋊D1111yescharacteristic
283C22×C4C2×C22⋊D1111yescharacteristic
284C22×C4C2×C22⋊D1111yescharacteristic
285C22×C4C2×C22⋊D1111yescharacteristic
286C22×C4C23×D1111yescharacteristic
287C2×C8—118no—
288C2×C8—224no—
289C2×C8—224no—
290C4⋊C4—24no—
291C4⋊C4—24no—
292C4⋊C4—42no—
293C4⋊C4—42no—
294C4⋊C4—42no—
295C4⋊C4—42no—
296C4⋊C4—222no—
297C4⋊C4—222no—
298C4⋊C4—224no—
299C4⋊C4—442no—
300C4⋊C4—442no—
301C4⋊C4—442no—
302C4⋊C4—442no—
303C22⋊C4—44no—
304C22⋊C4—444no—
305C42—44no—
306C42—444no—
307C42Dic11⋊C414yes—
308C42Dic11⋊C414yes—
309C42C2×Dic2212yes—
310C42C2×Dic2212yes—
311C42C2×C4×D1112yes—
312C42C2×C4×D1112yes—
313C11#2198811yescharacteristic, complemented, Sylow
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23C2×Dic11⋊C412yes—
321C23C22×C22⋊D1111yescharacteristic
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—24no—
331C2×C4—24no—
332C2×C4—28no—
333C2×C4—44no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—442no—
341C2×C4—442no—
342C2×C4—442no—
343C2×C4—442no—
344C2×C4—442no—
345C2×C4—442no—
346C2×C4C2×Dic11⋊C412yes—
347C2×C4C2×Dic11⋊C412yes—
348C2×C4C2×Dic11⋊C412yes—
349C2×C4C2×Dic11⋊C412yes—
350C2×C4C2×Dic11⋊C412yes—
351C2×C4#6700212yes—
352C2×C4#6700412yes—
353C2×C4C22×Dic2211yescharacteristic
354C2×C4C22×C4×D1111yescharacteristic
355C2×C4#6703712yes—
356C2×C4#6704012yes—
357C8—228no—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22C22×Dic11⋊C411yescharacteristic
366C22#1062333611yescharacteristic
367C22#1062334711yescharacteristic
368C22C2×#6700211yescharacteristic
369C22#1062335311yescharacteristic
370C22#1062335311yescharacteristic
371C22C2×#6700411yescharacteristic
372C4—22no—
373C4—22no—
374C4—22no—
375C4—22no—
376C4—82no—
377C4—82no—
378C4—882no—
379C4—882no—
380C4#1062260814yes—
381C4#1062303112yes—
382C4#1062303512yes—
383C2—42no—
384C2#1307124011yescharacteristic
385C2C2×#1062260811yescharacteristic
386C2#1307720511yescharacteristic
387C2#1307961111yescharacteristic
388C2#1307962711yescharacteristic
389C2#1307981411yescharacteristic
390C2#1307983011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2285C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#2285D11
hypocenterC11#21988
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2285

Complements

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

NH ≅ G/Ntype
3. #13069377C2semidirect
4. #13069372C2semidirect
6. #13068785C2semidirect
7. #13068749C2semidirect
29. #10622539C4semidirect
313. C11#21988semidirect

Maximal subgroups

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

subgroupindex
C2×#106225392
#130710232
#130693772
#130693722
#130688152
#130687852
#130687492
C11×#22852
#2198811