Finite Group Databasebeta

← #14853529

Subgroups — #14853529

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#13071341C211yesmaximal, characteristic
3#13070185C212yesmaximal, complemented
4#13069851C212yesmaximal
5#13069313C212yesmaximal, complemented
6#13069299C212yesmaximal, complemented
7#13068627C212yesmaximal, complemented
8#13068617C212yesmaximal, complemented
9C11×#1768C211yesmaximal, characteristic, complemented
10C2×#66927C2211yescharacteristic
11C2×C4×D44C2212yes—
12C2×C11×C4⋊C8C2212yes—
13C2×C11×#97C2211yescharacteristic
14C2×C4×C8×C11C2211yescharacteristic
15C11×#376C2211yescharacteristic
16C2×#66885C2212yes—
17C2×#66885C2212yes—
18C2×#66885C2212yes—
19C2×#66885C2212yes—
20#10622552C2212yes—
21#10622549C2211yescharacteristic
22#10622549C2211yescharacteristic
23#10622548C2211yescharacteristic
24#10622541C2212yes—
25#10622541C2212yes—
26#10622278—22no—
27#10622278—22no—
28#10622273—22no—
29#10622270—22no—
30C11×#336C2212yes—
31#10622189C2212yes—
32#10622189C2212yes—
33#10622189C2212yes—
34#10622189C2212yes—
35C22×D44—21no—
36C22×D44—21no—
37C22×D44C2312yes—
38C22×C4×D11—22no—
39C22×C8×C11C2312yes—
40C22×C8×C11C2312yes—
41C2×C42×C11C2311yescharacteristic
42C2×C42×C11C2311yescharacteristic
43C2×C42×C11C2311yescharacteristic
44C2×(C2×D11)⋊C4—22no—
45C2×(C2×D11)⋊C4—22no—
46C2×(C2×D11)⋊C4—22no—
47C2×C4⋊Dic11—22no—
48C2×C4⋊Dic11C2312yes—
49C2×C4⋊Dic11C2312yes—
50C2×C4⋊Dic11C2312yes—
51C2×Dic11⋊C4—22no—
52C2×Dic11⋊C4—22no—
53#66927—24no—
54C4×D44—24no—
55C4×D44—24no—
56C11×C4⋊C8—24no—
57C11×#97—41no—
58C4×C8×C11—41no—
59C11×#95D412yes—
60C11×#95D412yes—
61C11⋊#95—22no—
62C11⋊#95—22no—
63C11⋊#95—22no—
64C11⋊#95—21no—
65C11⋊#95—21no—
66#66885—24no—
67#66885—24no—
68#66885—42no—
69#66885—42no—
70#29133—111nomaximal, Sylow
71C23×D11—22no—
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D412yes—
75C22×C4×C11C2×D412yes—
76C22×C4×C11C2411yescharacteristic
77C22×Dic11—22no—
78C22×Dic11—22no—
79C22×Dic11—22no—
80C2×D44—24no—
81C2×D44—24no—
82C2×D44—22no—
83C2×D44—22no—
84C2×D44—22no—
85C2×D44—22no—
86C2×D44—22no—
87C2×D44—82no—
88C2×D44—82no—
89C2×D44#4114yes—
90C2×C4×D11—44no—
91C2×C4×D11—82no—
92C2×C4×D11—82no—
93C2×C8×C11—22no—
94C2×C8×C11—22no—
95C2×C8×C11—22no—
96C2×C8×C11—22no—
97C2×C8×C11—22no—
98C2×C8×C11—22no—
99C42×C11—22no—
100C42×C11—21no—
101C42×C11—21no—
102C42×C11#4114yes—
103(C2×D11)⋊C4—44no—
104(C2×D11)⋊C4—82no—
105(C2×D11)⋊C4—82no—
106C4⋊Dic11—22no—
107C4⋊Dic11—22no—
108C4⋊Dic11—22no—
109C4⋊Dic11—22no—
110C4⋊Dic11—22no—
111C4⋊Dic11—22no—
112C4⋊Dic11—82no—
113Dic11⋊C4—82no—
114Dic11⋊C4—82no—
115#2647—111no—
116#2328—111no—
117#2101—112no—
118#2041—112no—
119#1936—112no—
120#1934—112no—
121#1804—112no—
122#1802—112no—
123#1768D1111yescharacteristic, complemented
124C23×C11C22×D411yescharacteristic
125C22×D11—24no—
126C22×D11—42no—
127C22×D11—42no—
128C22×D11—42no—
129C22×D11—42no—
130C22×D11—42no—
131C22×D11—42no—
132C2×C4×C11—22no—
133C2×C4×C11—22no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11#12414yes—
142C2×C4×C11C2×#4112yes—
143C2×C4×C11C2×#4112yes—
144C2×C4×C11H(5,𝔽2)11yescharacteristic
145C2×C4×C112−1+411yescharacteristic
146C2×Dic11—42no—
147C2×Dic11—42no—
148C2×Dic11—42no—
149C2×Dic11—42no—
150C2×Dic11—42no—
151C2×Dic11—42no—
152C2×Dic11—42no—
153C2×Dic11—42no—
154C2×Dic11—42no—
155D44—24no—
156D44—24no—
157D44—42no—
158D44—42no—
159D44—84no—
160D44—84no—
161C4×D11—88no—
162C8×C11—42no—
163C8×C11—42no—
164C2×#127—111no—
165C2×C4×D4—112no—
166C2×C4⋊C8C2×D1112yes—
167C2×#102—112no—
168C2×#102—112no—
169C2×#102—112no—
170C2×#102—112no—
171C2×#97C2×D1111yescharacteristic
172C2×C4×C8C2×D1111yescharacteristic
173#400—222no—
174#398—222no—
175#390—112no—
176#389—112no—
177#389—112no—
178#386—222no—
179#386—222no—
180#384—111no—
181#382—111no—
182#382—111no—
183#376C2×D1111yescharacteristic
184#340—112no—
185#340—112no—
186#340—112no—
187#340—112no—
188#336C2×D1112yes—
189C22×C11#52511yescharacteristic
190C22×C11C2×#12411yescharacteristic
191C22×C11#53711yescharacteristic
192C22×C11#57612yes—
193C22×C11#57712yes—
194C2×D11—44no—
195C2×D11—44no—
196C2×D11—44no—
197C2×D11—82no—
198C2×D11—82no—
199C2×D11—82no—
200C2×D11—82no—
201C4×C11—24no—
202C4×C11—41no—
203C4×C11—41no—
204C4×C11—42no—
205C4×C11#55212yes—
206C4×C11#55312yes—
207Dic11—82no—
208Dic11—82no—
209Dic11—82no—
210C22×D4—112no—
211C22×D4—221no—
212C22×D4—221no—
213C23×C4—222no—
214C22×C8C22×D1112yes—
215C22×C8C22×D1112yes—
216#127—224no—
217C4×D4—224no—
218C4×D4—224no—
219C2×C4⋊C4—112no—
220C2×C4⋊C4—112no—
221C2×C4⋊C4—112no—
222C2×C4⋊C4—222no—
223C2×C4⋊C4—222no—
224C2×C4⋊C4—222no—
225C2×C22⋊C4—222no—
226C2×C22⋊C4—222no—
227C2×C22⋊C4—222no—
228C2×C42C22×D1111yescharacteristic
229C2×C42C22×D1111yescharacteristic
230C2×C42C22×D1111yescharacteristic
231C4⋊C8—24no—
232#102—224no—
233#102—224no—
234#102—442no—
235#102—442no—
236#97—41no—
237C4×C8—41no—
238#95—221no—
239#95—221no—
240#95—222no—
241#95—222no—
242#95—222no—
243#95D4412yes—
244#95D4412yes—
245C2×C11#256211yescharacteristic
246C2×C11#312211yescharacteristic
247C2×C11#312311yescharacteristic
248C2×C11#313612yes—
249C2×C11#325712yes—
250D11—84no—
251C24—222no—
252C2×D4—114no—
253C2×D4—224no—
254C2×D4—224no—
255C2×D4—222no—
256C2×D4—222no—
257C2×D4—222no—
258C2×D4—222no—
259C2×D4—222no—
260C2×D4—882no—
261C2×D4—882no—
262C22×C4—222no—
263C22×C4—222no—
264C22×C4—222no—
265C22×C4—444no—
266C22×C4—882no—
267C22×C4—882no—
268C22×C4C2×D4411yescharacteristic
269C22×C4C2×D4412yes—
270C22×C4C2×D4411yescharacteristic
271C22×C4C2×D4412yes—
272C22×C4C23×D1111yescharacteristic
273C2×C8—22no—
274C2×C8—22no—
275C2×C8—22no—
276C2×C8—22no—
277C2×C8—22no—
278C2×C8—22no—
279C4⋊C4—222no—
280C4⋊C4—222no—
281C4⋊C4—222no—
282C4⋊C4—222no—
283C4⋊C4—222no—
284C4⋊C4—222no—
285C4⋊C4—882no—
286C4⋊C4—882no—
287C4⋊C4—882no—
288C22⋊C4—444no—
289C22⋊C4—882no—
290C22⋊C4—882no—
291C42—21no—
292C42—21no—
293C42—22no—
294C42#433914yes—
295C11#2913311yescharacteristic, complemented, Sylow
296C23—224no—
297C23—442no—
298C23—442no—
299C23—442no—
300C23—442no—
301C23—442no—
302C23—442no—
303C23C22×D4411yescharacteristic
304D4—224no—
305D4—224no—
306D4—442no—
307D4—442no—
308D4—884no—
309D4—884no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—442no—
320C2×C4—442no—
321C2×C4—442no—
322C2×C4—442no—
323C2×C4—442no—
324C2×C4—442no—
325C2×C4—442no—
326C2×C4—442no—
327C2×C4—442no—
328C2×C4—888no—
329C2×C4#6692814yes—
330C2×C4C2×#433912yes—
331C2×C4#6703711yescharacteristic
332C2×C4#6704011yescharacteristic
333C2×C4#41×D1112yes—
334C8—42no—
335C8—42no—
336C22—444no—
337C22—444no—
338C22—444no—
339C22—882no—
340C22—882no—
341C22—882no—
342C22—882no—
343C22C2×#6692811yescharacteristic
344C22#1062304111yescharacteristic
345C22#1062305511yescharacteristic
346C22#1062328212yes—
347C22#1062328312yes—
348C4—24no—
349C4—41no—
350C4—41no—
351C4—42no—
352C4—882no—
353C4—882no—
354C4—882no—
355C4#1062308912yes—
356C4#1062311212yes—
357C2—884no—
358C2#1307377711yescharacteristic
359C2#1307886011yescharacteristic
360C2#1307886911yescharacteristic
361C2#1307897212yes—
362C2#1308002912yes—
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1768C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
hypercenter#1768D11
hypocenterC11#29133
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ #376 ◁ #1768

Complements

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

NH ≅ G/Ntype
1. #13074591C2semidirect
3. #13070185C2semidirect
5. #13069313C2semidirect
6. #13069299C2semidirect
7. #13068627C2semidirect
8. #13068617C2semidirect
9. C11×#1768C2semidirect
123. #1768D11semidirect
295. C11#29133semidirect

Maximal subgroups

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

subgroupindex
#130745912
#130713412
#130701852
#130698512
#130693132
#130692992
#130686272
#130686172
C11×#17682
#2913311