Finite Group Databasebeta

← #14771496

Subgroups — #14771496

Order 2816.

766 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622611C211yesmaximal, characteristic
2#13071507C211yesmaximal, characteristic
3#13069351C212yesmaximal, complemented
4#13069201C212yesmaximal, complemented
5#13069198C212yesmaximal, complemented
6#13068711C211yesmaximal, characteristic
7#13068708C211yesmaximal, characteristic
8#13068639C211yesmaximal, characteristic
9#13068514C212yesmaximal, complemented
10#13068394C211yesmaximal, characteristic
11C11×#2347C211yesmaximal, characteristic
12C2×C11×#117C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C23×C11⋊C8C2211yescharacteristic
15C11×#389C2212yes—
16C11×#388—22no—
17C11×#383—21no—
18C11×#380C2211yescharacteristic
19C4×C11×C4⋊C4—21no—
20C4×C11×C4⋊C4C2212yes—
21C4×C11×C22⋊C4C2211yescharacteristic
22#10622825C2211yescharacteristic
23C2×C22⋊(C11⋊C8)C2211yescharacteristic
24#10622611C418yescomplemented
25C2×#66872C2212yes—
26C2×#66872C2211yescharacteristic
27C2×#66872C2211yescharacteristic
28C2×#66871C2211yescharacteristic
29C2×#66871C2211yescharacteristic
30#10622558—22no—
31C4×C4⋊Dic11C2212yes—
32#10622541C2212yes—
33C2×#66867C2212yes—
34#10622264—21no—
35#10622262—21no—
36#10622167C2212yes—
37#10622167C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622162C2212yes—
42C23×C4×C11C2311yescharacteristic
43C11×#117—22no—
44C11×#117C2×C414yes—
45C2×C11×C4⋊C4—22no—
46C2×C11×C4⋊C4C2312yes—
47C2×C11×C4⋊C4C2311yescharacteristic
48C2×C11×C4⋊C4C2311yescharacteristic
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4—21no—
51C2×C11×C22⋊C4D412yes—
52C2×C42×C11—21no—
53C2×C42×C11—22no—
54C2×C42×C11C2312yes—
55C2×C22⋊Dic11—21no—
56C2×C22⋊Dic11—21no—
57#66979—22no—
58#66979C2×C414yes—
59C2×C4⋊Dic11C2312yes—
60C2×C4⋊Dic11C2311yescharacteristic
61C2×C4⋊Dic11C2311yescharacteristic
62C2×Dic11⋊C4—22no—
63C2×C4×Dic11—21no—
64C2×C4×Dic11—22no—
65C22×C11⋊C8—24no—
66C22×C11⋊C8C2×C414yes—
67C22×C11⋊C8C2312yes—
68C22×C11⋊C8C2311yescharacteristic
69C22×C11⋊C8C2311yescharacteristic
70C11×#95—21no—
71C11×#95—22no—
72C11×#95—22no—
73C11×#95D411yescharacteristic
74C11×#95D411yescharacteristic
75C11⋊#95—21no—
76C11⋊#95—22no—
77C11⋊#95—22no—
78C22⋊(C11⋊C8)—22no—
79#66872—24no—
80#66872C2×C414yes—
81#66872C2×C414yes—
82#66871C2×C414yes—
83#66871C2×C414yes—
84#66867—24no—
85#22620—111nomaximal, Sylow
86C24×C11C2×D411yescharacteristic
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—22no—
92C22×C4×C11C22×C412yes—
93C22×C4×C11C2×D412yes—
94C22×C4×C11C2×D412yes—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11#4112yes—
97C22×C4×C11C2411yescharacteristic
98C22×Dic11—21no—
99C22×Dic11—21no—
100C22×Dic11—22no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—44no—
106C11×C4⋊C4C22×C412yes—
107C11×C4⋊C4C22×C412yes—
108C11×C22⋊C4—24no—
109C11×C22⋊C4—42no—
110C11×C22⋊C4—81no—
111C42×C11—24no—
112C42×C11—22no—
113C42×C11—22no—
114C42×C11—82no—
115C22⋊Dic11—24no—
116C22⋊Dic11—81no—
117C4⋊Dic11—21no—
118C4⋊Dic11—21no—
119C4⋊Dic11—22no—
120C4⋊Dic11—22no—
121C4⋊Dic11C22×C412yes—
122C4⋊Dic11C22×C412yes—
123Dic11⋊C4—44no—
124C4×Dic11—24no—
125C4×Dic11—82no—
126C2×C11⋊C8—28no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8C22×C412yes—
132C2×C11⋊C8C22×C412yes—
133C2×C11⋊C8#4114yes—
134C2×#427—111no—
135#2347—111no—
136#2347D1111yescharacteristic
137#1943—112no—
138#1920—112no—
139#1920—112no—
140#1825—111no—
141#1825—111no—
142#1807—111no—
143#1776—112no—
144#1752—111no—
145C23×C11—22no—
146C23×C11—22no—
147C23×C11—21no—
148C23×C11—21no—
149C23×C11C4×D412yes—
150C23×C11C22×D411yescharacteristic
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11—24no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—42no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11C4×D412yes—
170C2×C4×C11C23×C411yescharacteristic
171C2×C4×C11C2×#4111yescharacteristic
172C2×C4×C11C2×#4112yes—
173C2×C4×C112−1+412yes—
174C2×Dic11—22no—
175C2×Dic11—22no—
176C2×Dic11—42no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—42no—
180C2×Dic11—42no—
181C2×Dic11—42no—
182C11⋊C8—22no—
183C11⋊C8—42no—
184C11⋊C8#11714yes—
185C23×C8—111no—
186C2×#117—111no—
187C2×#117C2×D1111yescharacteristic
188#427—118no—
189C2×#107—111no—
190C2×#107—111no—
191C2×#106—111no—
192C2×#106—111no—
193C2×#106—112no—
194C2×C22⋊C8—111no—
195C2×#97—112no—
196#389—112no—
197#389C2×D1112yes—
198#388—22no—
199#388—222no—
200#383—21no—
201#383—221no—
202#380—111no—
203#380C2×D1111yescharacteristic
204C4×C4⋊C4—21no—
205C4×C4⋊C4—112no—
206C4×C4⋊C4—221no—
207C4×C4⋊C4C2×D1112yes—
208C4×C22⋊C4C2×D1111yescharacteristic
209#340—112no—
210#340—112no—
211#340—112no—
212#340—112no—
213#340—112no—
214#336—112no—
215C22×C11—22no—
216C22×C11—22no—
217C22×C11—22no—
218C22×C11—42no—
219C22×C11—42no—
220C22×C11C2×C4×D411yescharacteristic
221C22×C11#54712yes—
222C22×C11#57512yes—
223C22×C11#57711yescharacteristic
224C22×C11#57711yescharacteristic
225C4×C11—22no—
226C4×C11—42no—
227C4×C11—42no—
228C4×C11—42no—
229C4×C11—42no—
230C4×C11—82no—
231C4×C11C2×#11711yescharacteristic
232C4×C11#51911yescharacteristic
233C4×C11#55212yes—
234Dic11—42no—
235Dic11—42no—
236Dic11—82no—
237C23×C4C22×D1111yescharacteristic
238C22×C8—111no—
239C22×C8—114no—
240C22×C8—111no—
241C22×C8—112no—
242C22×C8—224no—
243#117—22no—
244#117—114no—
245#117—222no—
246#117C4×D1114yes—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—111no—
249C2×C4⋊C4—111no—
250C2×C4⋊C4—112no—
251C2×C4⋊C4—222no—
252C2×C4⋊C4C22×D1112yes—
253C2×C4⋊C4C22×D1111yescharacteristic
254C2×C4⋊C4C22×D1111yescharacteristic
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—221no—
258C2×C22⋊C4—221no—
259C2×C22⋊C4C22⋊D1112yes—
260C2×C42—21no—
261C2×C42—22no—
262C2×C42—221no—
263C2×C42—222no—
264C2×C42C22×D1112yes—
265#107—114no—
266#107—114no—
267#106—114no—
268#106—114no—
269#106—224no—
270C22⋊C8—222no—
271#97—224no—
272#95—21no—
273#95—22no—
274#95—22no—
275#95—222no—
276#95—221no—
277#95—222no—
278#95C22⋊D1111yescharacteristic
279#95C22⋊D1111yescharacteristic
280C2×C11—42no—
281C2×C11#234411yescharacteristic
282C2×C11#294311yescharacteristic
283C2×C11#295211yescharacteristic
284C2×C11#335012yes—
285C2×C11#335012yes—
286C24C2×C22⋊D1111yescharacteristic
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—22no—
292C22×C4—221no—
293C22×C4—221no—
294C22×C4—222no—
295C22×C4C2×C4×D1112yes—
296C22×C4#433912yes—
297C22×C4C2×C22⋊D1112yes—
298C22×C4C2×C22⋊D1112yes—
299C22×C4C2×C22⋊D1111yescharacteristic
300C22×C4C23×D1111yescharacteristic
301C2×C8—112no—
302C2×C8—114no—
303C2×C8—112no—
304C2×C8—228no—
305C2×C8—222no—
306C2×C8—222no—
307C2×C8—222no—
308C2×C8—222no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—22no—
312C4⋊C4—22no—
313C4⋊C4—44no—
314C4⋊C4—112no—
315C4⋊C4—112no—
316C4⋊C4—221no—
317C4⋊C4—221no—
318C4⋊C4—222no—
319C4⋊C4—222no—
320C4⋊C4—444no—
321C4⋊C4C2×C4×D1112yes—
322C4⋊C4C2×C4×D1112yes—
323C22⋊C4—24no—
324C22⋊C4—42no—
325C22⋊C4—81no—
326C22⋊C4—224no—
327C22⋊C4—881no—
328C42—24no—
329C42—22no—
330C42—22no—
331C42—82no—
332C42—224no—
333C42—882no—
334C11#2262011yescharacteristic, complemented, Sylow
335C23—22no—
336C23—22no—
337C23—21no—
338C23—21no—
339C23C4×C22⋊D1112yes—
340C23C22×C22⋊D1111yescharacteristic
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—24no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—42no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—222no—
360C2×C4—222no—
361C2×C4—442no—
362C2×C4—441no—
363C2×C4—441no—
364C2×C4—442no—
365C2×C4—442no—
366C2×C4—442no—
367C2×C4C4×C22⋊D1112yes—
368C2×C4C22×C4×D1111yescharacteristic
369C2×C4C2×#433911yescharacteristic
370C2×C4#41×D1112yes—
371C2×C4#6704312yes—
372C8—114no—
373C8—222no—
374C8—442no—
375C22—22no—
376C22—22no—
377C22—22no—
378C22—42no—
379C22—42no—
380C22C2×C4×C22⋊D1111yescharacteristic
381C22#1062335312yes—
382C22#1062335512yes—
383C22#1062336711yescharacteristic
384C22#1062336811yescharacteristic
385C4—22no—
386C4—42no—
387C4—42no—
388C4—42no—
389C4—42no—
390C4—82no—
391C4—442no—
392C4—442no—
393C4—882no—
394C4#1062304711yescharacteristic
395C4D11×#11711yescharacteristic
396C4#1062306212yes—
397C2—42no—
398C2#1307148611yescharacteristic
399C2#1307741411yescharacteristic
400C2#1307749711yescharacteristic
401C2#1308115512yes—
402C2#1308116112yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2347C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#2347D11
hypocenterC11#22620
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2347

Complements

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

NH ≅ G/Ntype
3. #13069351C2semidirect
4. #13069201C2semidirect
5. #13069198C2semidirect
9. #13068514C2semidirect
24. #10622611C4semidirect
334. C11#22620semidirect

Maximal subgroups

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

subgroupindex
C2×#106226112
#130715072
#130693512
#130692012
#130691982
#130687112
#130687082
#130686392
#130685142
#130683942
C11×#23472
#2262011