Finite Group Databasebeta

← #14853507

Subgroups — #14853507

Order 2816.

878 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076979C211yesmaximal, characteristic, complemented
2#13070178C212yesmaximal, complemented
3#13069847C212yesmaximal
4#13069316C214yesmaximal, complemented
5#13068616C212yesmaximal, complemented
6#13068616C212yesmaximal, complemented
7#13068469C211yesmaximal, characteristic, complemented
8C4×C11×#127C211yesmaximal, characteristic
9C2×C11×#127C2211yescharacteristic
10C2×C4×D4×C11—21no—
11C2×C4×D4×C11—21no—
12C2×C4×D4×C11C2212yes—
13C2×#66923—21no—
14C11×#390—21no—
15C11×#390—21no—
16C11×#390C2212yes—
17C11×#384C2211yescharacteristic
18C43×C11C2211yescharacteristic
19C2×#66896C2214yes—
20C2×#66896C2214yes—
21#10622549—21no—
22#10622548C2211yescharacteristic
23#10622548C2211yescharacteristic
24#10622541—21no—
25#10622541—21no—
26#10622541C2212yes—
27#10622541C2212yes—
28C2×C4⋊(C11⋊C8)C2212yes—
29C2×#66867C2212yes—
30#10622167C2214yes—
31#10622167C2214yes—
32#10622162C2212yes—
33C22×D4×C11—21no—
34C22×D4×C11—21no—
35C22×D4×C11C2312yes—
36C23×C4×C11—22no—
37C11×#127—24no—
38C4×D4×C11—24no—
39C4×D4×C11—24no—
40C4×D4×C11—44no—
41C4×D4×C11—44no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4C2312yes—
45C2×C11×C22⋊C4—22no—
46C2×C11×C22⋊C4—22no—
47C2×C11×C22⋊C4—22no—
48C2×C42×C11D411yescharacteristic
49C2×C42×C11D411yescharacteristic
50C2×C42×C11D411yescharacteristic
51C2×C42×C11D411yescharacteristic
52C2×C42×C11C2311yescharacteristic
53C2×C42×C11C2311yescharacteristic
54C2×C42×C11C2311yescharacteristic
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11C2312yes—
60C2×C4⋊Dic11C2312yes—
61C2×Dic11⋊C4—22no—
62C2×Dic11⋊C4—22no—
63C22×C11⋊C8C2314yes—
64#66923—44no—
65#66896—28no—
66#66896—44no—
67C11⋊#95—22no—
68C11⋊#95—22no—
69C4⋊(C11⋊C8)—24no—
70#66867—42no—
71#29130—111nomaximal, Sylow
72C24×C11—22no—
73C2×D4×C11—24no—
74C2×D4×C11—24no—
75C2×D4×C11—22no—
76C2×D4×C11—22no—
77C2×D4×C11—22no—
78C2×D4×C11—22no—
79C2×D4×C11—22no—
80C2×D4×C11—42no—
81C2×D4×C11—42no—
82C2×D4×C11—42no—
83C2×D4×C11—42no—
84C2×D4×C11#4114yes—
85C22×C4×C11—22no—
86C22×C4×C11—44no—
87C22×C4×C11—44no—
88C22×C4×C11—44no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2411yescharacteristic
96C22×Dic11—22no—
97C22×Dic11—22no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—42no—
101C11×C4⋊C4—42no—
102C11×C22⋊C4—44no—
103C11×C22⋊C4—44no—
104C11×C22⋊C4—44no—
105C42×C11—22no—
106C42×C11—22no—
107C42×C11—22no—
108C42×C11—22no—
109C42×C11—22no—
110C42×C11—21no—
111C42×C11—21no—
112C42×C11#4114yes—
113C4⋊Dic11—24no—
114C4⋊Dic11—22no—
115C4⋊Dic11—22no—
116C4⋊Dic11—42no—
117C4⋊Dic11—42no—
118C4⋊Dic11—42no—
119C4⋊Dic11—42no—
120Dic11⋊C4—44no—
121Dic11⋊C4—44no—
122C2×C11⋊C8—24no—
123C2×C11⋊C8—24no—
124C2×C11⋊C8—24no—
125#2859—111no—
126C4×#127D1111yescharacteristic
127#2100—112no—
128#2041—112no—
129#1936—114no—
130#1802—112no—
131#1802—112no—
132#1767—111no—
133C23×C11—24no—
134C23×C11—42no—
135C23×C11—42no—
136C23×C11—42no—
137C23×C11—42no—
138C23×C11—42no—
139C23×C11—42no—
140C23×C11C22×D411yescharacteristic
141D4×C11—24no—
142D4×C11—24no—
143D4×C11—48no—
144D4×C11—48no—
145D4×C11—42no—
146D4×C11—42no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—88no—
163C2×C4×C11#12412yes—
164C2×C4×C11#12412yes—
165C2×C4×C11AGL(1,ℤ/8)12yes—
166C2×C4×C11AGL(1,ℤ/8)12yes—
167C2×C4×C11AGL(1,ℤ/8)12yes—
168C2×C4×C11#13712yes—
169C2×C4×C11C2×#4112yes—
170C2×C4×C11C2×#4112yes—
171C2×C4×C11H(5,𝔽2)11yescharacteristic
172C2×C4×C112−1+411yescharacteristic
173C2×Dic11—42no—
174C2×Dic11—42no—
175C2×Dic11—42no—
176C2×Dic11—42no—
177C2×Dic11—42no—
178C2×Dic11—42no—
179C11⋊C8—44no—
180C2×#127C2×D1111yescharacteristic
181C2×#125—221no—
182C2×C4×D4—21no—
183C2×C4×D4—21no—
184C2×C4×D4C2×D1112yes—
185C2×C4⋊C8—112no—
186C2×#102—114no—
187C2×#102—114no—
188C2×#97—112no—
189#390—21no—
190#390—21no—
191#390C2×D1112yes—
192#389—112no—
193#389—112no—
194#389—221no—
195#389—221no—
196#384—111no—
197#384—111no—
198#384C2×D1111yescharacteristic
199#382—221no—
200C43C2×D1111yescharacteristic
201#340—114no—
202#340—114no—
203#336—112no—
204C22×C11—44no—
205C22×C11—44no—
206C22×C11—44no—
207C22×C11—82no—
208C22×C11—82no—
209C22×C11—82no—
210C22×C11—82no—
211C22×C11#52511yescharacteristic
212C22×C11C2×#12411yescharacteristic
213C22×C11#53711yescharacteristic
214C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
215C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
216C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
217C22×C11C2×#13711yescharacteristic
218C4×C11—22no—
219C4×C11—22no—
220C4×C11—22no—
221C4×C11—41no—
222C4×C11—41no—
223C4×C11—82no—
224C4×C11#49014yes—
225C4×C11#55212yes—
226C4×C11#55312yes—
227Dic11—82no—
228Dic11—82no—
229C22×D4—21no—
230C22×D4—21no—
231C22×D4C22×D1112yes—
232C23×C4—22no—
233C22×C8—114no—
234#127—24no—
235#125—444no—
236C4×D4—24no—
237C4×D4—24no—
238C4×D4—44no—
239C4×D4—44no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—112no—
243C2×C4⋊C4—112no—
244C2×C4⋊C4—221no—
245C2×C4⋊C4—221no—
246C2×C4⋊C4—222no—
247C2×C4⋊C4—222no—
248C2×C4⋊C4—221no—
249C2×C4⋊C4—221no—
250C2×C4⋊C4C22×D1112yes—
251C2×C22⋊C4—22no—
252C2×C22⋊C4—22no—
253C2×C22⋊C4—22no—
254C2×C42C22⋊D1111yescharacteristic
255C2×C42C22⋊D1111yescharacteristic
256C2×C42C22⋊D1111yescharacteristic
257C2×C42C22⋊D1111yescharacteristic
258C2×C42C22×D1111yescharacteristic
259C2×C42C22×D1111yescharacteristic
260C2×C42C22×D1111yescharacteristic
261C4⋊C8—224no—
262#102—228no—
263#102—444no—
264#97—442no—
265#95—222no—
266#95—222no—
267C2×C11—84no—
268C2×C11#256211yescharacteristic
269C2×C11#310911yescharacteristic
270C2×C11#311011yescharacteristic
271C2×C11C2×#49011yescharacteristic
272C2×C11#314111yescharacteristic
273C2×C11#325311yescharacteristic
274C2×C11#325411yescharacteristic
275C24—22no—
276C2×D4—24no—
277C2×D4—24no—
278C2×D4—22no—
279C2×D4—22no—
280C2×D4—22no—
281C2×D4—22no—
282C2×D4—22no—
283C2×D4—42no—
284C2×D4—42no—
285C2×D4—42no—
286C2×D4—42no—
287C2×D4#433914yes—
288C22×C4—22no—
289C22×C4—44no—
290C22×C4—44no—
291C22×C4—44no—
292C22×C4—222no—
293C22×C4—222no—
294C22×C4C2×C22⋊D1111yescharacteristic
295C22×C4C2×C22⋊D1111yescharacteristic
296C22×C4C2×C22⋊D1111yescharacteristic
297C22×C4C2×C22⋊D1111yescharacteristic
298C22×C4C2×C22⋊D1111yescharacteristic
299C22×C4C2×C22⋊D1111yescharacteristic
300C22×C4C23×D1111yescharacteristic
301C2×C8—224no—
302C2×C8—224no—
303C2×C8—224no—
304C4⋊C4—22no—
305C4⋊C4—22no—
306C4⋊C4—42no—
307C4⋊C4—42no—
308C4⋊C4—224no—
309C4⋊C4—222no—
310C4⋊C4—222no—
311C4⋊C4—444no—
312C4⋊C4—442no—
313C4⋊C4—442no—
314C4⋊C4—442no—
315C4⋊C4—442no—
316C4⋊C4—444no—
317C22⋊C4—44no—
318C22⋊C4—44no—
319C22⋊C4—44no—
320C42—22no—
321C42—22no—
322C42—22no—
323C42—22no—
324C42—22no—
325C42—21no—
326C42—21no—
327C42#434114yes—
328C11#2913011yescharacteristic, complemented, Sylow
329C23—24no—
330C23—42no—
331C23—42no—
332C23—42no—
333C23—42no—
334C23—42no—
335C23—42no—
336C23C22×C22⋊D1111yescharacteristic
337D4—24no—
338D4—24no—
339D4—48no—
340D4—48no—
341D4—42no—
342D4—42no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—88no—
359C2×C4—442no—
360C2×C4—442no—
361C2×C4—442no—
362C2×C4—442no—
363C2×C4—442no—
364C2×C4—442no—
365C2×C4#6698512yes—
366C2×C4#6698512yes—
367C2×C4#6698912yes—
368C2×C4#6698912yes—
369C2×C4#6700212yes—
370C2×C4#6700412yes—
371C2×C4C2×#433912yes—
372C2×C4C2×#434112yes—
373C2×C4#6704211yescharacteristic
374C2×C4#6704311yescharacteristic
375C8—444no—
376C22—44no—
377C22—44no—
378C22—44no—
379C22—82no—
380C22—82no—
381C22—82no—
382C22—82no—
383C22#1062332211yescharacteristic
384C22C2×#6698511yescharacteristic
385C22C2×#6698511yescharacteristic
386C22C2×#6698911yescharacteristic
387C22C2×#6700211yescharacteristic
388C22C2×#6700411yescharacteristic
389C22#1062336411yescharacteristic
390C4—22no—
391C4—22no—
392C4—22no—
393C4—41no—
394C4—41no—
395C4—82no—
396C4—882no—
397C4—882no—
398C4#1062268414yes—
399C4#1062307212yes—
400C4#1062309612yes—
401C2—84no—
402C2#1307378211yescharacteristic
403C2#1307870711yescharacteristic
404C2#1307871511yescharacteristic
405C2C2×#1062268411yescharacteristic
406C2#1307900911yescharacteristic
407C2#1307999411yescharacteristic
408C2#1308000311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#127C2
socleC23×C11C22×D4
prime radicalC2×C11×#127C22
hypercenterC4×#127D11
hypocenterC11#29130
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ C4×#127

Complements

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

NH ≅ G/Ntype
1. #13076979C2semidirect
2. #13070178C2semidirect
4. #13069316C2semidirect
5. #13068616C2semidirect
6. #13068616C2semidirect
7. #13068469C2semidirect
328. C11#29130semidirect

Maximal subgroups

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

subgroupindex
#130769792
#130701782
#130698472
#130693162
#130686162
#130684692
C4×C11×#1272
#2913011