Finite Group Databasebeta

← #14771458

Subgroups — #14771458

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×#10622719C211yesmaximal, characteristic
2#13071507C211yesmaximal, characteristic
3#13071499C211yesmaximal, characteristic
4#13069359C212yesmaximal, complemented
5#13069209C212yesmaximal, complemented
6#13069188C212yesmaximal, complemented
7#13068712C211yesmaximal, characteristic
8#13068712C211yesmaximal, characteristic
9#13068645C211yesmaximal, characteristic
10#13068513C212yesmaximal, complemented
11C11×#1752C211yesmaximal, characteristic
12C23×C8×C11C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C2×C11×C22⋊C8C2211yescharacteristic
16C2×C11×#97C2212yes—
17C4×C11×C22⋊C4C2211yescharacteristic
18#10622825C2211yescharacteristic
19#10622825C2211yescharacteristic
20#10622719C418yescomplemented
21C2×#66882C2212yes—
22C2×#66882C2211yescharacteristic
23C2×#66882C2211yescharacteristic
24C2×#66881C2211yescharacteristic
25C2×#66881C2211yescharacteristic
26#10622558—22no—
27#10622557—22no—
28C4×C4⋊Dic11C2212yes—
29C4×C4⋊Dic11C2212yes—
30#10622541C2212yes—
31#10622541C2212yes—
32#10622264—21no—
33#10622263—21no—
34#10622262—21no—
35#10622261—21no—
36C11×#336C2212yes—
37#10622189C2212yes—
38#10622189C2212yes—
39#10622189C2212yes—
40#10622189C2212yes—
41#10622189C2212yes—
42C23×C4×C11C2311yescharacteristic
43C22×C8×C11—24no—
44C22×C8×C11C2×C414yes—
45C22×C8×C11C2312yes—
46C22×C8×C11C2311yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C2×C11×C22⋊C4D412yes—
49C2×C42×C11C2312yes—
50C2×C22⋊Dic11—21no—
51C2×C22⋊Dic11—21no—
52C2×C22⋊Dic11—21no—
53C2×C22⋊Dic11—21no—
54#66979—22no—
55#66979—22no—
56#66979C2×C414yes—
57#66979C2×C414yes—
58C2×C4⋊Dic11C2312yes—
59C2×C4⋊Dic11C2312yes—
60C2×C4⋊Dic11C2311yescharacteristic
61C2×C4⋊Dic11C2311yescharacteristic
62C2×C4⋊Dic11C2311yescharacteristic
63C2×C4⋊Dic11C2311yescharacteristic
64C2×Dic11⋊C4—22no—
65C2×Dic11⋊C4—22no—
66C2×C4×Dic11—21no—
67C2×C4×Dic11—21no—
68C2×C4×Dic11—22no—
69C2×C4×Dic11—22no—
70C11×C22⋊C8—22no—
71C11×#97—24no—
72C11×#95D411yescharacteristic
73C11×#95D411yescharacteristic
74C11⋊#95—21no—
75C11⋊#95—22no—
76C11⋊#95—21no—
77C11⋊#95—22no—
78C11⋊#95—22no—
79C11⋊#95—22no—
80#66882—24no—
81#66882C2×C414yes—
82#66882C2×C414yes—
83#66881C2×C414yes—
84#66881C2×C414yes—
85#22616—111nomaximal, Sylow
86C24×C11C2×D411yescharacteristic
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11C22×C412yes—
90C22×C4×C11C2×D412yes—
91C22×C4×C11C2×D412yes—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11#4112yes—
94C22×C4×C11C2411yescharacteristic
95C22×Dic11—21no—
96C22×Dic11—21no—
97C22×Dic11—21no—
98C22×Dic11—21no—
99C22×Dic11—22no—
100C22×Dic11—22no—
101C2×C8×C11—28no—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C2×C8×C11—22no—
105C2×C8×C11—22no—
106C2×C8×C11C22×C412yes—
107C2×C8×C11C22×C412yes—
108C2×C8×C11#4114yes—
109C11×C22⋊C4—42no—
110C42×C11—22no—
111C42×C11—22no—
112C22⋊Dic11—24no—
113C22⋊Dic11—24no—
114C22⋊Dic11—81no—
115C22⋊Dic11—81no—
116C4⋊Dic11—21no—
117C4⋊Dic11—21no—
118C4⋊Dic11—21no—
119C4⋊Dic11—21no—
120C4⋊Dic11—22no—
121C4⋊Dic11—22no—
122C4⋊Dic11—22no—
123C4⋊Dic11—22no—
124C4⋊Dic11C22×C412yes—
125C4⋊Dic11C22×C412yes—
126C4⋊Dic11C22×C412yes—
127C4⋊Dic11C22×C412yes—
128Dic11⋊C4—44no—
129Dic11⋊C4—82no—
130C4×Dic11—24no—
131C4×Dic11—24no—
132C4×Dic11—44no—
133C4×Dic11—82no—
134C2×#427—111no—
135#2347—111no—
136#2346—111no—
137#1944—112no—
138#1921—112no—
139#1918—112no—
140#1825—111no—
141#1825—111no—
142#1808—111no—
143#1776—112no—
144#1752D1111yescharacteristic
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×C11C4×D412yes—
162C2×C4×C11C23×C411yescharacteristic
163C2×C4×C11C2×#4111yescharacteristic
164C2×C4×C11C2×#4112yes—
165C2×C4×C112−1+412yes—
166C2×Dic11—22no—
167C2×Dic11—22no—
168C2×Dic11—22no—
169C2×Dic11—22no—
170C2×Dic11—42no—
171C2×Dic11—42no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—42no—
177C2×Dic11—42no—
178C2×Dic11—42no—
179C2×Dic11—42no—
180C2×Dic11—42no—
181C2×Dic11—42no—
182C8×C11—22no—
183C8×C11—42no—
184C8×C11#11714yes—
185C23×C8C2×D1111yescharacteristic
186C2×#117—111no—
187C2×#117—111no—
188#427—118no—
189C2×#107—111no—
190C2×#107—111no—
191C2×#107—112no—
192C2×#106—111no—
193C2×#106—111no—
194C2×C22⋊C8C2×D1111yescharacteristic
195C2×#97C2×D1112yes—
196#389—112no—
197#389—112no—
198#388—222no—
199#388—222no—
200#383—221no—
201#382—221no—
202#380—111no—
203#380—111no—
204C4×C4⋊C4—112no—
205C4×C4⋊C4—112no—
206C4×C4⋊C4—221no—
207C4×C22⋊C4C2×D1111yescharacteristic
208#376—221no—
209#340—112no—
210#340—112no—
211#340—112no—
212#340—112no—
213#340—112no—
214#336C2×D1112yes—
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#57611yescharacteristic
224C22×C11#57811yescharacteristic
225C4×C11—22no—
226C4×C11—42no—
227C4×C11—42no—
228C4×C11C2×#11711yescharacteristic
229C4×C11#51911yescharacteristic
230C4×C11#55212yes—
231Dic11—42no—
232Dic11—42no—
233Dic11—42no—
234Dic11—42no—
235Dic11—82no—
236Dic11—82no—
237C23×C4C22×D1111yescharacteristic
238C22×C8—24no—
239C22×C8C4×D1114yes—
240C22×C8C22×D1112yes—
241C22×C8C22×D1111yescharacteristic
242C22×C8C22×D1111yescharacteristic
243#117—114no—
244#117—114no—
245#117—222no—
246#117—222no—
247C2×C4⋊C4—111no—
248C2×C4⋊C4—111no—
249C2×C4⋊C4—111no—
250C2×C4⋊C4—111no—
251C2×C4⋊C4—112no—
252C2×C4⋊C4—112no—
253C2×C4⋊C4—222no—
254C2×C4⋊C4—222no—
255C2×C22⋊C4—221no—
256C2×C22⋊C4—221no—
257C2×C22⋊C4—221no—
258C2×C22⋊C4—221no—
259C2×C22⋊C4D4412yes—
260C2×C42—221no—
261C2×C42—221no—
262C2×C42—222no—
263C2×C42—222no—
264C2×C42C22×D1112yes—
265#107—114no—
266#107—114no—
267#107—224no—
268#106—114no—
269#106—114no—
270C22⋊C8—22no—
271#97—24no—
272#95—221no—
273#95—222no—
274#95—222no—
275#95—222no—
276#95—221no—
277#95—222no—
278#95D4411yescharacteristic
279#95D4411yescharacteristic
280C2×C11—42no—
281C2×C11#234411yescharacteristic
282C2×C11#294311yescharacteristic
283C2×C11#295111yescharacteristic
284C2×C11#334712yes—
285C2×C11#334912yes—
286C24C2×D4411yescharacteristic
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—221no—
290C22×C4—221no—
291C22×C4—221no—
292C22×C4—221no—
293C22×C4—222no—
294C22×C4—222no—
295C22×C4C2×C4×D1112yes—
296C22×C4C2×D4412yes—
297C22×C4C2×D4412yes—
298C22×C4C2×D4411yescharacteristic
299C22×C4#433912yes—
300C22×C4C23×D1111yescharacteristic
301C2×C8—22no—
302C2×C8—28no—
303C2×C8—22no—
304C2×C8—22no—
305C2×C8—22no—
306C2×C8C2×C4×D1112yes—
307C2×C8C2×C4×D1112yes—
308C2×C8#434114yes—
309C4⋊C4—112no—
310C4⋊C4—112no—
311C4⋊C4—112no—
312C4⋊C4—112no—
313C4⋊C4—221no—
314C4⋊C4—221no—
315C4⋊C4—221no—
316C4⋊C4—221no—
317C4⋊C4—222no—
318C4⋊C4—222no—
319C4⋊C4—222no—
320C4⋊C4—222no—
321C4⋊C4—444no—
322C4⋊C4—882no—
323C22⋊C4—42no—
324C22⋊C4—224no—
325C22⋊C4—224no—
326C22⋊C4—881no—
327C22⋊C4—881no—
328C42—22no—
329C42—22no—
330C42—224no—
331C42—224no—
332C42—444no—
333C42—882no—
334C11#2261611yescharacteristic, complemented, Sylow
335C23—22no—
336C23—21no—
337C23—21no—
338C23—22no—
339C23C4×D4412yes—
340C23C22×D4411yescharacteristic
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—222no—
352C2×C4—222no—
353C2×C4—222no—
354C2×C4—222no—
355C2×C4—442no—
356C2×C4—442no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4—441no—
360C2×C4—441no—
361C2×C4—442no—
362C2×C4—442no—
363C2×C4—442no—
364C2×C4—442no—
365C2×C4—442no—
366C2×C4—442no—
367C2×C4C4×D4412yes—
368C2×C4C22×C4×D1111yescharacteristic
369C2×C4C2×#433911yescharacteristic
370C2×C4C2×#434112yes—
371C2×C4#6704312yes—
372C8—22no—
373C8—42no—
374C8#6693014yes—
375C22—22no—
376C22—22no—
377C22—22no—
378C22—42no—
379C22—42no—
380C22C2×C4×D4411yescharacteristic
381C22#1062308612yes—
382C22#1062327912yes—
383C22#1062328311yescharacteristic
384C22#1062328411yescharacteristic
385C4—22no—
386C4—42no—
387C4—42no—
388C4—442no—
389C4—442no—
390C4—442no—
391C4—442no—
392C4—882no—
393C4—882no—
394C4C2×#6693011yescharacteristic
395C4#1062304711yescharacteristic
396C4#1062307212yes—
397C2—42no—
398C2#1307148311yescharacteristic
399C2#1307741811yescharacteristic
400C2#1307749311yescharacteristic
401C2#1308111812yes—
402C2#1308114812yes—
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1752C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1752D11
hypocenterC11#22616
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1752

Complements

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

NH ≅ G/Ntype
4. #13069359C2semidirect
5. #13069209C2semidirect
6. #13069188C2semidirect
10. #13068513C2semidirect
20. #10622719C4semidirect
334. C11#22616semidirect

Maximal subgroups

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

subgroupindex
C2×#106227192
#130715072
#130714992
#130693592
#130692092
#130691882
#130687122
#130686452
#130685132
C11×#17522
#2261611