Finite Group Databasebeta

← #14764328

Subgroups — #14764328

Order 2816.

858 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071023C211yesmaximal, characteristic
2C2×#10622549C211yesmaximal, characteristic
3#13069386C214yesmaximal, complemented
4#13068811C212yesmaximal
5#13068806C212yesmaximal
6#13068784C212yesmaximal, complemented
7#13068750C212yesmaximal, complemented
8C2×C11×#432C211yesmaximal, characteristic
9C22×C42×C11C2211yescharacteristic
10C2×#66979—21no—
11C22×C4⋊Dic11C2211yescharacteristic
12C22×C4⋊Dic11C2211yescharacteristic
13C11×#432C418yescomplemented
14C2×C11×C4⋊C8C2212yes—
15C2×C11×C22⋊C8C2212yes—
16C2×C11×#97C2212yes—
17#10622825—21no—
18#10622825C2212yes—
19C2×C11⋊#95—21no—
20C2×C11⋊#95—21no—
21C2×#66882C2214yes—
22C2×#66881C2214yes—
23#10622549—21no—
24#10622549—21no—
25#10622549—21no—
26#10622549C2212yes—
27#10622549C2212yes—
28#10622548C2211yescharacteristic
29#10622548C2211yescharacteristic
30C4×C4⋊Dic11—21no—
31C4×C4⋊Dic11C2212yes—
32#10622189C2214yes—
33#10622189C2214yes—
34C23×C4×C11D411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C23×Dic11—21no—
38C23×Dic11—21no—
39C22×C8×C11C2314yes—
40C2×C42×C11C2×C414yes—
41C2×C42×C11D411yescharacteristic
42C2×C42×C11D411yescharacteristic
43C2×C42×C11Q814yes—
44C2×C42×C11C2311yescharacteristic
45C2×C42×C11C2311yescharacteristic
46C2×C22⋊Dic11—22no—
47#66979—44no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11—21no—
54C2×C4⋊Dic11—42no—
55C2×C4⋊Dic11—42no—
56C2×C4⋊Dic11C2312yes—
57C2×C4⋊Dic11C2312yes—
58C2×C4⋊Dic11C2312yes—
59C2×C4⋊Dic11C2312yes—
60C2×C4×Dic11—22no—
61C11×C4⋊C8C2×C418yescomplemented
62C11×C22⋊C8C2×C418yes—
63C11×#97C2×C418yescomplemented
64C11⋊#95—22no—
65C11⋊#95—22no—
66C11⋊#95—22no—
67C11⋊#95—22no—
68C11⋊#95—22no—
69C11⋊#95—22no—
70#66882—44no—
71#66881—44no—
72#21986—111nomaximal, Sylow
73C24×C11C2×D411yescharacteristic
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—41no—
79C22×C4×C11—41no—
80C22×C4×C11C4⋊C414yes—
81C22×C4×C11C4⋊C414yes—
82C22×C4×C11C22×C412yes—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×Q812yes—
89C22×C4×C11C2411yescharacteristic
90C22×Dic11—22no—
91C22×Dic11—22no—
92C22×Dic11—22no—
93C22×Dic11—22no—
94C22×Dic11—42no—
95C22×Dic11—42no—
96C22×Dic11—42no—
97C22×Dic11—42no—
98C22×Dic11—42no—
99C22×Dic11—42no—
100C2×C8×C11—24no—
101C2×C8×C11—24no—
102C2×C8×C11C22×C418yes—
103C42×C11C4⋊C414yes—
104C42×C11C4⋊C414yes—
105C42×C11C22×C412yes—
106C42×C11C22×C412yes—
107C42×C11C2×Q812yes—
108C42×C11C2×Q812yes—
109C22⋊Dic11—44no—
110C4⋊Dic11—24no—
111C4⋊Dic11—24no—
112C4⋊Dic11—24no—
113C4⋊Dic11—24no—
114C4⋊Dic11—42no—
115C4⋊Dic11—42no—
116C4⋊Dic11—42no—
117C4⋊Dic11—42no—
118C4⋊Dic11—42no—
119C4⋊Dic11—42no—
120C4×Dic11—44no—
121C2×#432D1111yescharacteristic
122#2285—111no—
123C2×#382—111no—
124#1949—114no—
125#1853—112no—
126#1852—112no—
127#1847—112no—
128#1836—112no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11C2×C4⋊C412yes—
134C23×C11AGL(1,ℤ/8)12yes—
135C23×C11#13712yes—
136C23×C11C22×D411yescharacteristic
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—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—28no—
148C2×C4×C11—24no—
149C2×C4×C11—24no—
150C2×C4×C11—44no—
151C2×C4×C11C2×C4⋊C412yes—
152C2×C4×C11C2×C4⋊C412yes—
153C2×C4×C11C2×C4⋊C412yes—
154C2×C4×C11C2×C4⋊C412yes—
155C2×C4×C11C2×C4⋊C412yes—
156C2×C4×C11C23×C411yescharacteristic
157C2×C4×C11C22×Q811yescharacteristic
158C2×C4×C11H(5,𝔽2)12yes—
159C2×C4×C112−1+412yes—
160C2×Dic11—42no—
161C2×Dic11—42no—
162C2×Dic11—42no—
163C2×Dic11—42no—
164C2×Dic11—42no—
165C2×Dic11—42no—
166C2×Dic11—42no—
167C2×Dic11—42no—
168C2×Dic11—42no—
169C2×Dic11—42no—
170C2×Dic11—42no—
171C2×Dic11—42no—
172C2×Dic11—84no—
173C2×Dic11—84no—
174C8×C11—28no—
175C2×#117—221no—
176C22×C4⋊C4—111no—
177C22×C4⋊C4—111no—
178C22×C42C2×D1111yescharacteristic
179#432Dic1118yescomplemented
180C2×#107—114no—
181C2×#106—114no—
182C2×C4⋊C8C2×D1112yes—
183C2×C22⋊C8C2×D1112yes—
184C2×#97C2×D1112yes—
185#384—111no—
186#384—111no—
187#382—112no—
188#382—112no—
189#382—221no—
190#382—221no—
191#382—221no—
192#380—112no—
193#380—221no—
194C4×C4⋊C4—112no—
195C4×C4⋊C4—221no—
196C2×#95—221no—
197C2×#95—221no—
198#340—114no—
199#340—114no—
200C22×C11—22no—
201C22×C11—22no—
202C22×C11—22no—
203C22×C11—22no—
204C22×C11—22no—
205C22×C11—22no—
206C22×C11#42814yes—
207C22×C11C22×C4⋊C411yescharacteristic
208C22×C11#53511yescharacteristic
209C22×C11#53611yescharacteristic
210C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
211C22×C11C2×#13711yescharacteristic
212C22×C11#57511yescharacteristic
213C22×C11#57511yescharacteristic
214C4×C11—22no—
215C4×C11—22no—
216C4×C11—22no—
217C4×C11—22no—
218C4×C11—22no—
219C4×C11#52012yes—
220C4×C11#54412yes—
221Dic11—82no—
222Dic11—82no—
223Dic11—82no—
224Dic11—82no—
225C23×C4—221no—
226C23×C4—221no—
227C23×C4D4411yescharacteristic
228C23×C4D4411yescharacteristic
229C23×C4C22×D1111yescharacteristic
230C22×C8C22×D1114yes—
231#117—444no—
232C2×C4⋊C4—112no—
233C2×C4⋊C4—112no—
234C2×C4⋊C4—112no—
235C2×C4⋊C4—112no—
236C2×C4⋊C4—221no—
237C2×C4⋊C4—221no—
238C2×C4⋊C4—221no—
239C2×C4⋊C4—221no—
240C2×C4⋊C4—221no—
241C2×C4⋊C4—221no—
242C2×C4⋊C4—442no—
243C2×C4⋊C4—442no—
244C2×C22⋊C4—222no—
245C2×C42—222no—
246C2×C42Dic2214yes—
247C2×C42D4411yescharacteristic
248C2×C42D4411yescharacteristic
249C2×C42C2×Dic1114yes—
250C2×C42C22×D1111yescharacteristic
251C2×C42C22×D1111yescharacteristic
252#107—444no—
253#106—444no—
254C4⋊C8C2×Dic1118yescomplemented
255C22⋊C8C2×Dic1118yes—
256#97C2×Dic1118yescomplemented
257#95—222no—
258#95—222no—
259#95—222no—
260#95—222no—
261#95—222no—
262#95—222no—
263C2×C11—24no—
264C2×C11#231711yescharacteristic
265C2×C11C2×#42811yescharacteristic
266C2×C11#291111yescharacteristic
267C2×C11#321311yescharacteristic
268C2×C11#321511yescharacteristic
269C2×C11#323411yescharacteristic
270C2×C11#323611yescharacteristic
271C24C2×D4411yescharacteristic
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—222no—
279C22×C4—222no—
280C22×C4—222no—
281C22×C4—222no—
282C22×C4—442no—
283C22×C4—442no—
284C22×C4—442no—
285C22×C4—442no—
286C22×C4—442no—
287C22×C4—442no—
288C22×C4C4⋊Dic1114yes—
289C22×C4C4⋊Dic1114yes—
290C22×C4C2×Dic2212yes—
291C22×C4C2×D4411yescharacteristic
292C22×C4C2×D4411yescharacteristic
293C22×C4C2×D4411yescharacteristic
294C22×C4C2×D4411yescharacteristic
295C22×C4C2×D4411yescharacteristic
296C22×C4C22×Dic1112yes—
297C22×C4C23×D1111yescharacteristic
298C2×C8—24no—
299C2×C8—24no—
300C2×C8C22×Dic1118yes—
301C4⋊C4—224no—
302C4⋊C4—224no—
303C4⋊C4—224no—
304C4⋊C4—224no—
305C4⋊C4—442no—
306C4⋊C4—442no—
307C4⋊C4—442no—
308C4⋊C4—442no—
309C4⋊C4—442no—
310C4⋊C4—442no—
311C22⋊C4—444no—
312C42—444no—
313C42C4⋊Dic1114yes—
314C42C4⋊Dic1114yes—
315C42C2×Dic2212yes—
316C42C2×Dic2212yes—
317C42C22×Dic1112yes—
318C42C22×Dic1112yes—
319C11#2198611yescharacteristic, complemented, Sylow
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23#6696112yes—
325C23#6696212yes—
326C23C2×C4⋊Dic1112yes—
327C23C22×D4411yescharacteristic
328C2×C4—28no—
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—24no—
340C2×C4—24no—
341C2×C4—44no—
342C2×C4—442no—
343C2×C4—442no—
344C2×C4—442no—
345C2×C4—442no—
346C2×C4—442no—
347C2×C4—442no—
348C2×C4—442no—
349C2×C4—442no—
350C2×C4—442no—
351C2×C4—442no—
352C2×C4—442no—
353C2×C4—442no—
354C2×C4—884no—
355C2×C4—884no—
356C2×C4C2×C4⋊Dic1112yes—
357C2×C4C2×C4⋊Dic1112yes—
358C2×C4C2×C4⋊Dic1112yes—
359C2×C4C2×C4⋊Dic1112yes—
360C2×C4C2×C4⋊Dic1112yes—
361C2×C4C22×Dic2211yescharacteristic
362C2×C4#6704212yes—
363C2×C4#6704312yes—
364C2×C4C23×Dic1111yescharacteristic
365C8—28no—
366C22—22no—
367C22—22no—
368C22—22no—
369C22—22no—
370C22—22no—
371C22—22no—
372C22#1062273414yes—
373C22#1062305611yescharacteristic
374C22#1062305711yescharacteristic
375C22C2×#6696111yescharacteristic
376C22C2×#6696211yescharacteristic
377C22#1062327911yescharacteristic
378C22#1062327911yescharacteristic
379C22C22×C4⋊Dic1111yescharacteristic
380C4—22no—
381C4—22no—
382C4—22no—
383C4—22no—
384C4—22no—
385C4—882no—
386C4—882no—
387C4—882no—
388C4—882no—
389C4#1062305012yes—
390C4#1062335812yes—
391C2—24no—
392C2#1307123911yescharacteristic
393C2C2×#1062273411yescharacteristic
394C2#1307720611yescharacteristic
395C2#1307960511yescharacteristic
396C2#1307962111yescharacteristic
397C2#1307980811yescharacteristic
398C2#1307982411yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#432C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC2×#432D11
hypocenterC11#21986
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#432

Complements

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

NH ≅ G/Ntype
3. #13069386C2semidirect
6. #13068784C2semidirect
7. #13068750C2semidirect
13. C11×#432C4semidirect
61. C11×C4⋊C8C2×C4semidirect
63. C11×#97C2×C4semidirect
179. #432Dic11semidirect
254. C4⋊C8C2×Dic11semidirect
256. #97C2×Dic11semidirect
319. C11#21986semidirect

Maximal subgroups

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

subgroupindex
#130710232
C2×#106225492
#130693862
#130688112
#130688062
#130687842
#130687502
C2×C11×#4322
#2198611