Finite Group Databasebeta

← #14738339

Subgroups — #14738339

Order 2816.

680 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079994C212yesmaximal, complemented
2#13079195C211yesmaximal, characteristic, complemented
3#13068149C214yesmaximal, complemented
4#13068015C212yesmaximal, complemented
5#13067971C212yesmaximal, complemented
6#13067375C211yesmaximal, characteristic, complemented
7#13067349C212yesmaximal, complemented
8C11×#2931C211yesmaximal, characteristic, complemented
9C2×C11×#131—21no—
10C11×#532C2211yescharacteristic
11#10623008C2212yes—
12C11×#436—21no—
13C11×#436C2212yes—
14C8×D4×C11—21no—
15C8×D4×C11C2212yes—
16C11×#423C2211yescharacteristic
17C11×#408—21no—
18C2×C4×C8×C11C2211yescharacteristic
19#10622728—21no—
20#10622728—21no—
21#10622697—22no—
22#10622685—22no—
23#10622652—24no—
24#10622628C2214yes—
25#10622621C2214yes—
26#10622537C2212yes—
27#10622308C2211yescharacteristic
28#10622307C2212yes—
29C4×D88—21no—
30C4×D88—21no—
31#10622295C2211yescharacteristic
32#10622123C2214yes—
33#10622119C2214yes—
34#10622096C2212yes—
35#10622096C2212yes—
36C2×C11×#41—21no—
37C2×#4339—22no—
38C11×#131—44no—
39C2×C11×M16—21no—
40C2×C11×M16—22no—
41C22×C8×C11—22no—
42C22×C8×C11D411yescharacteristic
43C22×C8×C11D411yescharacteristic
44C11×C4⋊Q8D411yescharacteristic
45C11×#127D411yescharacteristic
46C11×#124—21no—
47C11×#121—21no—
48C11×#121D412yes—
49C4×D4×C11—21no—
50C4×D4×C11C2312yes—
51C2×C42×C11C2311yescharacteristic
52C2×#4323—24no—
53#66983—22no—
54#66983—22no—
55C2×#4318—22no—
56C2×D88—21no—
57C2×D88—21no—
58#66928—22no—
59#66927C2312yes—
60C4×D44—22no—
61C4×D44—22no—
62#66922C2312yes—
63C11×C4⋊C8—21no—
64C11×C4⋊C8C2312yes—
65C11×C22⋊C8—22no—
66C11×C22⋊C8—22no—
67C4×C8×C11D411yescharacteristic
68C4×C8×C11D411yescharacteristic
69C4×C8×C11C2311yescharacteristic
70C4×C8×C11C2311yescharacteristic
71#66896—24no—
72#66885—22no—
73#66885—22no—
74#66882—21no—
75#66882—21no—
76#66873—24no—
77#66872—24no—
78C4⋊(C11⋊C8)—22no—
79C4⋊(C11⋊C8)C2314yes—
80#19332—111nomaximal, Sylow
81C11×#41—42no—
82C11×#41—42no—
83C2×Q8×C11—21no—
84C2×D4×C11—22no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11C2×D412yes—
88C22×C4×C11—22no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C2×C22⋊D11—42no—
93#4339—84no—
94C2×D44—22no—
95C2×D44—22no—
96C2×D44—22no—
97C2×C4×D11—42no—
98C2×Dic22—22no—
99C11×M16—42no—
100C11×M16—44no—
101C2×C8×C11—22no—
102C2×C8×C11—22no—
103C2×C8×C11—41no—
104C2×C8×C11—44no—
105C2×C8×C11C2×D411yescharacteristic
106C2×C8×C11C2×D411yescharacteristic
107C2×C8×C11C2×D411yescharacteristic
108C2×C8×C11C2×D411yescharacteristic
109C11×C4⋊C4—21no—
110C11×C4⋊C4C2×D412yes—
111C11×C22⋊C4—22no—
112C11×C22⋊C4—22no—
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11#4111yescharacteristic
116C42×C11C2411yescharacteristic
117#4323—84no—
118(C2×D11)⋊C4—42no—
119(C2×D11)⋊C4—42no—
120C4⋊Dic11—22no—
121C4⋊Dic11—22no—
122#4318—82no—
123C2×C11⋊C8—24no—
124D88—42no—
125D88—42no—
126#3253—112no—
127#3169—111no—
128#2931D1111yescharacteristic, complemented
129#1697—114no—
130#1675—112no—
131#1667—112no—
132#1567—111no—
133#1560—112no—
134C23×C11—22no—
135C23×C11#12111yescharacteristic
136C22×D11—42no—
137Q8×C11—42no—
138D4×C11—22no—
139D4×C11—22no—
140D4×C11—42no—
141D4×C11—44no—
142D4×C11—42no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—22no—
148C2×C4×C11—22no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11C22×D411yescharacteristic
155C2×C4×C11C22×D411yescharacteristic
156C2×C4×C11C2×#4111yescharacteristic
157C22⋊D11—84no—
158C2×Dic11—42no—
159D44—42no—
160D44—42no—
161D44—42no—
162D44—42no—
163D44—82no—
164C4×D11—84no—
165Dic22—82no—
166C8×C11—21no—
167C8×C11—21no—
168C8×C11—21no—
169C8×C11—42no—
170C8×C11AGL(1,ℤ/8)12yes—
171C11⋊C8—44no—
172C2×#131—21no—
173#532—112no—
174#532C2×D1111yescharacteristic
175#500—111no—
176#493—111no—
177#486—112no—
178#476—114no—
179#476—222no—
180#469—224no—
181#466—221no—
182#466—221no—
183#459—114no—
184#459—222no—
185C4×D8—221no—
186C4×D8—221no—
187#436—21no—
188#436C2×D1112yes—
189C8×D4—21no—
190C8×D4C2×D1112yes—
191#423—112no—
192#423C2×D1111yescharacteristic
193#408—21no—
194C2×C4×C8C2×D1111yescharacteristic
195#335—112no—
196#335—112no—
197#333—114no—
198#331—114no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11—42no—
203C22×C11—42no—
204C22×C11—42no—
205C22×C11C2×#12111yescharacteristic
206C2×D11—82no—
207C2×D11—82no—
208C2×D11—82no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—42no—
213C4×C11#47212yes—
214C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
215C4×C11#57511yescharacteristic
216C4×C11#57611yescharacteristic
217C4×C11#57811yescharacteristic
218Dic11—82no—
219C2×#41—21no—
220C2×#41—222no—
221C2×D8—224no—
222C2×D8—221no—
223C2×D8—221no—
224#131—44no—
225C2×M16—21no—
226C2×M16—22no—
227C2×M16—222no—
228C22×C8—22no—
229C22×C8C22⋊D1111yescharacteristic
230C22×C8C22⋊D1111yescharacteristic
231C4⋊Q8—112no—
232C4⋊Q8D4411yescharacteristic
233#127—112no—
234#127D4411yescharacteristic
235#124—21no—
236#124—222no—
237#121—21no—
238#121—222no—
239#121—222no—
240#121D4412yes—
241C4×D4—21no—
242C4×D4—222no—
243C4×D4—222no—
244C4×D4C22×D1112yes—
245C2×C42C22×D1111yescharacteristic
246#107—221no—
247#107—221no—
248#106—224no—
249C4⋊C8—21no—
250C4⋊C8—114no—
251C4⋊C8—222no—
252C4⋊C8C22×D1112yes—
253#102—224no—
254#102—222no—
255#102—222no—
256#102—224no—
257C22⋊C8—22no—
258C22⋊C8—22no—
259C4×C8C22⋊D1111yescharacteristic
260C4×C8C22⋊D1111yescharacteristic
261C4×C8C22×D1111yescharacteristic
262C4×C8C22×D1111yescharacteristic
263C2×C11—41no—
264C2×C11—82no—
265C2×C11#303611yescharacteristic
266C2×C11#306111yescharacteristic
267C2×C11C2×#47211yescharacteristic
268D11—162no—
269#41—42no—
270#41—42no—
271#41—884no—
272C2×Q8—21no—
273C2×Q8—222no—
274C2×D4—22no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—222no—
278C2×D4—222no—
279C2×D4—222no—
280C2×D4—442no—
281C2×D4C2×D4412yes—
282C22×C4—22no—
283C22×C4—442no—
284C22×C4C2×D4411yescharacteristic
285C22×C4#433911yescharacteristic
286C22×C4C2×C22⋊D1111yescharacteristic
287D8—442no—
288D8—442no—
289D8—884no—
290M16—44no—
291M16—42no—
292M16—882no—
293C2×C8—22no—
294C2×C8—22no—
295C2×C8—41no—
296C2×C8—44no—
297C2×C8—224no—
298C2×C8C2×C22⋊D1111yescharacteristic
299C2×C8C2×C22⋊D1111yescharacteristic
300C2×C8C2×C22⋊D1111yescharacteristic
301C2×C8C2×C22⋊D1111yescharacteristic
302C4⋊C4—21no—
303C4⋊C4—222no—
304C4⋊C4—222no—
305C4⋊C4C2×D4412yes—
306C22⋊C4—22no—
307C22⋊C4—22no—
308C22⋊C4—442no—
309C22⋊C4—442no—
310C42C2×D4411yescharacteristic
311C42#433911yescharacteristic
312C42C2×C22⋊D1111yescharacteristic
313C42C23×D1111yescharacteristic
314C11#1933211yescharacteristic, complemented, Sylow
315C23—22no—
316C23—442no—
317C23#6698311yescharacteristic
318Q8—42no—
319Q8—882no—
320D4—22no—
321D4—22no—
322D4—42no—
323D4—44no—
324D4—42no—
325D4—442no—
326D4—442no—
327D4—442no—
328D4—442no—
329D4—882no—
330D4—884no—
331C2×C4—22no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—22no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—442no—
340C2×C4—884no—
341C2×C4#6698311yescharacteristic
342C2×C4#6698311yescharacteristic
343C2×C4#6698311yescharacteristic
344C2×C4C22×D4411yescharacteristic
345C2×C4C2×#433911yescharacteristic
346C2×C4C22×C22⋊D1111yescharacteristic
347C8—21no—
348C8—21no—
349C8—21no—
350C8—42no—
351C8—444no—
352C8#6698512yes—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—42no—
357C22—42no—
358C22—42no—
359C22—882no—
360C22—882no—
361C22—882no—
362C22C2×#6698311yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—42no—
367C4—882no—
368C4#1062275512yes—
369C4#1062328311yescharacteristic
370C4#1062328411yescharacteristic
371C4C2×#6698511yescharacteristic
372C4#1062335311yescharacteristic
373C2—41no—
374C2—82no—
375C2—1762no—
376C2#1307808011yescharacteristic
377C2#1307828611yescharacteristic
378C2C2×#1062275511yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2931C2
socleC22×C11C2×#121
hypercenter#2931D11
hypocenterC11#19332
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2931

Complements

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

NH ≅ G/Ntype
1. #13079994C2semidirect
2. #13079195C2semidirect
3. #13068149C2semidirect
4. #13068015C2semidirect
5. #13067971C2semidirect
6. #13067375C2semidirect
7. #13067349C2semidirect
8. C11×#2931C2semidirect
128. #2931D11semidirect
314. C11#19332semidirect

Maximal subgroups

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

subgroupindex
#130799942
#130791952
#130681492
#130680152
#130679712
#130673752
#130673492
C11×#29312
#1933211