Finite Group Databasebeta

← #14666123

Subgroups — #14666123

Order 2816.

398 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076445C211yesmaximal, characteristic, complemented
2#13067653C211yesmaximal, characteristic, complemented
3#13067551C211yesmaximal, characteristic
4#13066642C211yesmaximal, characteristic, complemented
5#13066618C211yesmaximal, characteristic, complemented
6#13066562C211yesmaximal, characteristic, complemented
7C11×#2039C211yesmaximal, characteristic, complemented
8C11×#537C2211yescharacteristic
9C2×C11×#104—21no—
10C11×#417—21no—
11C11×#384C2211yescharacteristic
12#10622649—21no—
13#10622647—21no—
14#10622607—21no—
15#10622604—21no—
16#10622604C2211yescharacteristic
17#10622603—21no—
18#10622603—21no—
19#10622599C2211yescharacteristic
20#10622591—21no—
21#10622553—21no—
22C11×#343C2211yescharacteristic
23#10622175—21no—
24#10622175—21no—
25#10622166C2211yescharacteristic
26#10622166C2211yescharacteristic
27C2×C11×#41—21no—
28C22×D44D411yescharacteristic
29C2×C11×M16—21no—
30C11×C22⋊Q8—41no—
31C11×#121—21no—
32C11×#121—21no—
33C11×#121—41no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C11×C4⋊C4C2311yescharacteristic
38C2×C42×C11D411yescharacteristic
39C2×#4323—41no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×C4⋊Dic11D411yescharacteristic
47C2×Dic11⋊C4—21no—
48C2×C4×Dic11—21no—
49C11×#104—42no—
50C11×#103—41no—
51C11×#102—41no—
52#66896—41no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95D411yescharacteristic
58C11⋊#95D411yescharacteristic
59C22⋊(C11⋊C8)—21no—
60C22⋊(C11⋊C8)—21no—
61#66873—41no—
62#66872—41no—
63#12144—111nomaximal, Sylow
64C23×D11—21no—
65C11×#41—41no—
66C11×#41—41no—
67C11×#41—41no—
68C11×#41—41no—
69C2×Q8×C11—21no—
70C2×D4×C11—21no—
71C2×D4×C11—21no—
72C2×D4×C11—21no—
73C2×D4×C11—41no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—41no—
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×Dic11—21no—
81C22×Dic11—21no—
82C22×Dic11—21no—
83C2×D44—41no—
84C2×D44—81no—
85C11×M16—41no—
86C11×M16—41no—
87C2×C8×C11—41no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—81no—
93C11×C4⋊C4—81no—
94C11×C22⋊C4—41no—
95C11×C22⋊C4—41no—
96C42×C11—21no—
97C42×C11—21no—
98#4323—82no—
99(C2×D11)⋊C4—42no—
100(C2×D11)⋊C4—42no—
101(C2×D11)⋊C4—41no—
102(C2×D11)⋊C4—41no—
103(C2×D11)⋊C4—81no—
104(C2×D11)⋊C4—81no—
105(C2×D11)⋊C4—81no—
106C4⋊Dic11—41no—
107Dic11⋊C4—42no—
108C4×Dic11—81no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111#2795—111no—
112#2039D1111yescharacteristic, complemented
113#1616—111no—
114#1598—111no—
115#1353—111no—
116#1345—111no—
117#1325—111no—
118C23×C11—41no—
119C23×C11#12011yescharacteristic
120C22×D11—41no—
121C22×D11—41no—
122C22×D11—41no—
123C22×D11—41no—
124C22×D11—41no—
125C22×D11—41no—
126C22×D11—41no—
127Q8×C11—41no—
128Q8×C11—41no—
129D4×C11—41no—
130D4×C11—41no—
131D4×C11—81no—
132D4×C11—81no—
133D4×C11—81no—
134D4×C11—81no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—22no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—81no—
149C2×C4×C11—81no—
150C2×C4×C11#13511yescharacteristic
151C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161D44—42no—
162D44—81no—
163C8×C11—81no—
164C11⋊C8—81no—
165C11⋊C8—81no—
166#537C2×D1111yescharacteristic
167#481—221no—
168#447—221no—
169C2×#104—21no—
170#417—21no—
171#400—111no—
172#396—221no—
173#394—111no—
174#394—221no—
175#388—221no—
176#388—221no—
177#388—221no—
178#387—221no—
179#384C2×D1111yescharacteristic
180#343C2×D1111yescharacteristic
181#327—221no—
182#327—221no—
183#324—111no—
184#324—111no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—81no—
188C22×C11—81no—
189C22×C11—81no—
190C22×C11#44911yescharacteristic
191C22×C11#45411yescharacteristic
192C22×C11B(4,𝔽2)11yescharacteristic
193C2×D11—81no—
194C2×D11—81no—
195C2×D11—81no—
196C2×D11—81no—
197C2×D11—81no—
198C2×D11—81no—
199C2×D11—81no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—42no—
203C4×C11—41no—
204C4×C11—41no—
205C4×C11—81no—
206C4×C11—81no—
207Dic11—81no—
208Dic11—81no—
209Dic11—81no—
210C2×#41—21no—
211C22×D4—111no—
212C2×D8—441no—
213C2×M16—21no—
214C22⋊Q8—41no—
215#121—21no—
216#121—21no—
217#121—41no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—111no—
221C2×C4⋊C4—221no—
222C2×C4⋊C4C22⋊D1111yescharacteristic
223C2×C4⋊C4C22×D1111yescharacteristic
224C2×C22⋊C4—221no—
225C2×C22⋊C4—221no—
226C2×C22⋊C4—221no—
227C2×C22⋊C4—221no—
228C2×C22⋊C4—221no—
229C2×C22⋊C4—221no—
230C2×C42—221no—
231C2×C42C22⋊D1111yescharacteristic
232#106—441no—
233#104—42no—
234#103—41no—
235#102—41no—
236#102—441no—
237#102—441no—
238C22⋊C8—221no—
239C22⋊C8—221no—
240#95—111no—
241#95—111no—
242#95—221no—
243#95—221no—
244#95—221no—
245#95—221no—
246C2×C11—21no—
247C2×C11—21no—
248C2×C11—161no—
249C2×C11#159711yescharacteristic
250C2×C11#220011yescharacteristic
251C2×C11#220411yescharacteristic
252D11—161no—
253C24—221no—
254#41—41no—
255#41—41no—
256#41—41no—
257#41—41no—
258C2×Q8—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—41no—
263C2×D4—441no—
264C2×D4—881no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—41no—
268C22×C4—221no—
269C22×C4—221no—
270C22×C4—221no—
271C22×C4D4×D1111yescharacteristic
272C22×C4D4×D1111yescharacteristic
273C22×C4C2×C22⋊D1111yescharacteristic
274D8—882no—
275M16—41no—
276M16—41no—
277C2×C8—41no—
278C2×C8—441no—
279C2×C8—441no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—81no—
285C4⋊C4—81no—
286C4⋊C4—441no—
287C4⋊C4—442no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—442no—
291C22⋊C4—442no—
292C22⋊C4—441no—
293C22⋊C4—441no—
294C22⋊C4—881no—
295C22⋊C4—881no—
296C22⋊C4—881no—
297C42—21no—
298C42—21no—
299C42—881no—
300C11#1214411yescharacteristic, complemented, Sylow
301C23—41no—
302C23—441no—
303C23—441no—
304C23—441no—
305C23—441no—
306C23—441no—
307C23—441no—
308C23—441no—
309C23#6699011yescharacteristic
310Q8—41no—
311Q8—41no—
312D4—41no—
313D4—41no—
314D4—81no—
315D4—81no—
316D4—81no—
317D4—81no—
318D4—442no—
319D4—881no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—22no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—441no—
344C2×C4#6698511yescharacteristic
345C2×C4#6700311yescharacteristic
346C8—81no—
347C8—881no—
348C8—881no—
349C22—21no—
350C22—21no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—881no—
355C22—881no—
356C22—881no—
357C22—881no—
358C22—881no—
359C22—881no—
360C22—881no—
361C22#1062264511yescharacteristic
362C22#1062265011yescharacteristic
363C22#1062267511yescharacteristic
364C4—21no—
365C4—21no—
366C4—42no—
367C4—41no—
368C4—41no—
369C4—81no—
370C4—81no—
371C4—881no—
372C4—881no—
373C4—881no—
374C2—21no—
375C2—21no—
376C2—161no—
377C2—1761no—
378C2#1306754311yescharacteristic
379C2#1307062211yescharacteristic
380C2#1307064111yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2039C2
socleC22×C11B(4,𝔽2)
prime radical#13067551C2
hypercenter#2039D11
hypocenterC11#12144
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2039

Complements

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

NH ≅ G/Ntype
1. #13076445C2semidirect
2. #13067653C2semidirect
4. #13066642C2semidirect
5. #13066618C2semidirect
6. #13066562C2semidirect
7. C11×#2039C2semidirect
112. #2039D11semidirect
300. C11#12144semidirect

Maximal subgroups

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

subgroupindex
#130764452
#130676532
#130675512
#130666422
#130666182
#130665622
C11×#20392
#1214411