Finite Group Databasebeta

← #14853534

Subgroups — #14853534

Order 2816.

754 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074591C211yesmaximal, characteristic, complemented
2#13070183C212yesmaximal, complemented
3#13069847C212yesmaximal
4#13069316C212yesmaximal, complemented
5#13069302C212yesmaximal, complemented
6#13068626C212yesmaximal, complemented
7#13068616C212yesmaximal, complemented
8#13068473C211yesmaximal, characteristic, complemented
9C11×#2328C211yesmaximal, characteristic
10C2×C11×#127C2211yescharacteristic
11C2×C4×D4×C11C2212yes—
12C11×#390C2212yes—
13C11×#386—22no—
14C11×#386—22no—
15C11×#382C2211yescharacteristic
16C11×#376C2211yescharacteristic
17C2×#66896C2212yes—
18C2×#66896C2212yes—
19C2×#66896C2212yes—
20C2×#66896C2212yes—
21#10622549C2211yescharacteristic
22#10622548C2211yescharacteristic
23#10622541C2212yes—
24#10622541C2212yes—
25C2×C4⋊(C11⋊C8)C2212yes—
26C2×#66867C2211yescharacteristic
27C2×C4×C11⋊C8C2211yescharacteristic
28#10622273—22no—
29#10622270—22no—
30#10622167C2212yes—
31#10622167C2212yes—
32#10622167C2212yes—
33#10622167C2212yes—
34#10622162C2212yes—
35C22×D4×C11—21no—
36C22×D4×C11—21no—
37C22×D4×C11C2312yes—
38C23×C4×C11—22no—
39C11×#127—24no—
40C4×D4×C11—24no—
41C4×D4×C11—24no—
42C2×C11×C4⋊C4C2312yes—
43C2×C11×C22⋊C4—22no—
44C2×C11×C22⋊C4—22no—
45C2×C11×C22⋊C4—22no—
46C2×C42×C11C2311yescharacteristic
47C2×C42×C11C2311yescharacteristic
48C2×C42×C11C2311yescharacteristic
49C2×C4⋊Dic11—22no—
50C2×C4⋊Dic11C2312yes—
51C2×C4⋊Dic11C2312yes—
52C2×Dic11⋊C4—22no—
53C2×Dic11⋊C4—22no—
54C22×C11⋊C8C2312yes—
55C22×C11⋊C8C2312yes—
56C11×#95—21no—
57C11×#95—21no—
58C11×#95D412yes—
59C11×#95D412yes—
60#66896—24no—
61#66896—24no—
62#66896—42no—
63#66896—42no—
64C11⋊#95—22no—
65C11⋊#95—22no—
66C11⋊#95—22no—
67C4⋊(C11⋊C8)—24no—
68#66867—41no—
69C4×C11⋊C8—41no—
70#29133—111nomaximal, Sylow
71C24×C11—22no—
72C2×D4×C11—24no—
73C2×D4×C11—24no—
74C2×D4×C11—22no—
75C2×D4×C11—22no—
76C2×D4×C11—22no—
77C2×D4×C11—22no—
78C2×D4×C11—22no—
79C2×D4×C11—82no—
80C2×D4×C11—82no—
81C2×D4×C11#4114yes—
82C22×C4×C11—22no—
83C22×C4×C11—44no—
84C22×C4×C11—82no—
85C22×C4×C11—82no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D412yes—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D412yes—
90C22×C4×C11C2411yescharacteristic
91C22×Dic11—22no—
92C22×Dic11—22no—
93C11×C4⋊C4—22no—
94C11×C4⋊C4—22no—
95C11×C22⋊C4—44no—
96C11×C22⋊C4—82no—
97C11×C22⋊C4—82no—
98C42×C11—22no—
99C42×C11—21no—
100C42×C11—21no—
101C42×C11#4114yes—
102C4⋊Dic11—22no—
103C4⋊Dic11—22no—
104C4⋊Dic11—22no—
105C4⋊Dic11—22no—
106C4⋊Dic11—82no—
107Dic11⋊C4—82no—
108Dic11⋊C4—82no—
109C2×C11⋊C8—22no—
110C2×C11⋊C8—22no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—22no—
115#2647—111no—
116#2328D1111yescharacteristic
117#2101—112no—
118#2041—112no—
119#1936—112no—
120#1934—112no—
121#1804—112no—
122#1802—112no—
123#1768—111no—
124C23×C11—24no—
125C23×C11—42no—
126C23×C11—42no—
127C23×C11—42no—
128C23×C11—42no—
129C23×C11—42no—
130C23×C11—42no—
131C23×C11C22×D411yescharacteristic
132D4×C11—24no—
133D4×C11—24no—
134D4×C11—42no—
135D4×C11—42no—
136D4×C11—84no—
137D4×C11—84no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—88no—
151C2×C4×C11#12414yes—
152C2×C4×C11C2×#4112yes—
153C2×C4×C11C2×#4112yes—
154C2×C4×C11H(5,𝔽2)11yescharacteristic
155C2×C4×C112−1+411yescharacteristic
156C2×Dic11—42no—
157C2×Dic11—42no—
158C2×Dic11—42no—
159C2×Dic11—42no—
160C2×Dic11—42no—
161C2×Dic11—42no—
162C11⋊C8—42no—
163C11⋊C8—42no—
164C2×#127C2×D1111yescharacteristic
165C2×C4×D4C2×D1112yes—
166C2×C4⋊C8—112no—
167C2×#102—112no—
168C2×#102—112no—
169C2×#102—112no—
170C2×#102—112no—
171C2×#97—111no—
172C2×C4×C8—111no—
173#400—222no—
174#398—222no—
175#390C2×D1112yes—
176#389—112no—
177#389—112no—
178#386—22no—
179#386—22no—
180#384—111no—
181#382—111no—
182#382C2×D1111yescharacteristic
183#376C2×D1111yescharacteristic
184#340—112no—
185#340—112no—
186#340—112no—
187#340—112no—
188#336—112no—
189C22×C11—44no—
190C22×C11—44no—
191C22×C11—44no—
192C22×C11—82no—
193C22×C11—82no—
194C22×C11—82no—
195C22×C11—82no—
196C22×C11#52511yescharacteristic
197C22×C11C2×#12411yescharacteristic
198C22×C11#53711yescharacteristic
199C22×C11#57612yes—
200C22×C11#57712yes—
201C4×C11—24no—
202C4×C11—41no—
203C4×C11—41no—
204C4×C11—42no—
205C4×C11—82no—
206C4×C11#55212yes—
207C4×C11#55312yes—
208Dic11—82no—
209Dic11—82no—
210C22×D4—21no—
211C22×D4—21no—
212C22×D4C22×D1112yes—
213C23×C4—22no—
214C22×C8—112no—
215C22×C8—112no—
216#127—24no—
217C4×D4—24no—
218C4×D4—24no—
219C2×C4⋊C4—112no—
220C2×C4⋊C4—112no—
221C2×C4⋊C4—222no—
222C2×C4⋊C4—222no—
223C2×C4⋊C4—222no—
224C2×C4⋊C4C22×D1112yes—
225C2×C22⋊C4—22no—
226C2×C22⋊C4—22no—
227C2×C22⋊C4—22no—
228C2×C42C22×D1111yescharacteristic
229C2×C42C22×D1111yescharacteristic
230C2×C42C22×D1111yescharacteristic
231C4⋊C8—224no—
232#102—224no—
233#102—224no—
234#102—442no—
235#102—442no—
236#97—441no—
237C4×C8—441no—
238#95—21no—
239#95—21no—
240#95—222no—
241#95—222no—
242#95—222no—
243#95C22⋊D1112yes—
244#95C22⋊D1112yes—
245C2×C11—84no—
246C2×C11#256211yescharacteristic
247C2×C11#312211yescharacteristic
248C2×C11#312311yescharacteristic
249C2×C11#313612yes—
250C2×C11#325712yes—
251C24—22no—
252C2×D4—24no—
253C2×D4—24no—
254C2×D4—22no—
255C2×D4—22no—
256C2×D4—22no—
257C2×D4—22no—
258C2×D4—22no—
259C2×D4—82no—
260C2×D4—82no—
261C2×D4#433914yes—
262C22×C4—22no—
263C22×C4—44no—
264C22×C4—82no—
265C22×C4—82no—
266C22×C4—222no—
267C22×C4—222no—
268C22×C4C2×C22⋊D1111yescharacteristic
269C22×C4C2×C22⋊D1111yescharacteristic
270C22×C4C2×C22⋊D1112yes—
271C22×C4C2×C22⋊D1112yes—
272C22×C4C23×D1111yescharacteristic
273C2×C8—222no—
274C2×C8—222no—
275C2×C8—222no—
276C2×C8—222no—
277C2×C8—222no—
278C2×C8—222no—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—222no—
282C4⋊C4—222no—
283C4⋊C4—222no—
284C4⋊C4—222no—
285C4⋊C4—882no—
286C4⋊C4—882no—
287C4⋊C4—882no—
288C22⋊C4—44no—
289C22⋊C4—82no—
290C22⋊C4—82no—
291C42—22no—
292C42—21no—
293C42—21no—
294C42#434114yes—
295C11#2913311yescharacteristic, complemented, Sylow
296C23—24no—
297C23—42no—
298C23—42no—
299C23—42no—
300C23—42no—
301C23—42no—
302C23—42no—
303C23C22×C22⋊D1111yescharacteristic
304D4—24no—
305D4—24no—
306D4—42no—
307D4—42no—
308D4—84no—
309D4—84no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—88no—
323C2×C4—442no—
324C2×C4—442no—
325C2×C4—442no—
326C2×C4—442no—
327C2×C4—442no—
328C2×C4—442no—
329C2×C4#6698914yes—
330C2×C4C2×#433912yes—
331C2×C4C2×#434112yes—
332C2×C4#6704211yescharacteristic
333C2×C4#6704311yescharacteristic
334C8—442no—
335C8—442no—
336C22—44no—
337C22—44no—
338C22—44no—
339C22—82no—
340C22—82no—
341C22—82no—
342C22—82no—
343C22#1062332211yescharacteristic
344C22C2×#6698911yescharacteristic
345C22#1062336411yescharacteristic
346C22#1062336612yes—
347C22#1062336712yes—
348C4—24no—
349C4—41no—
350C4—41no—
351C4—42no—
352C4—82no—
353C4—882no—
354C4—882no—
355C4#1062307212yes—
356C4#1062309612yes—
357C2—84no—
358C2#1307378211yescharacteristic
359C2#1307885911yescharacteristic
360C2#1307886811yescharacteristic
361C2#1307897012yes—
362C2#1308002112yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2328C2
socleC23×C11C22×D4
prime radicalC2×C11×#127C22
hypercenter#2328D11
hypocenterC11#29133
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ #376 ◁ #2328

Complements

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

NH ≅ G/Ntype
1. #13074591C2semidirect
2. #13070183C2semidirect
4. #13069316C2semidirect
5. #13069302C2semidirect
6. #13068626C2semidirect
7. #13068616C2semidirect
8. #13068473C2semidirect
295. C11#29133semidirect

Maximal subgroups

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

subgroupindex
#130745912
#130701832
#130698472
#130693162
#130693022
#130686262
#130686162
#130684732
C11×#23282
#2913311