Finite Group Databasebeta

← #14666442

Subgroups — #14666442

Order 2816.

458 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 59 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#13069662C211yesmaximal, characteristic, complemented
2#13067652C211yesmaximal, characteristic, complemented
3#13067550C211yesmaximal, characteristic
4#13066643C211yesmaximal, characteristic, complemented
5#13066619C211yesmaximal, characteristic, complemented
6#13066550C211yesmaximal, characteristic, complemented
7C11×#2572C211yesmaximal, characteristic, complemented
8C2×#66995—21no—
9#10623041C2211yescharacteristic
10C11×#400C2211yescharacteristic
11C11×#394C2211yescharacteristic
12C11×#393—21no—
13C11×#391C2211yescharacteristic
14C11×#388—21no—
15C11×#386—21no—
16C11×#383—21no—
17C11×#381—21no—
18C4×C11×C22⋊C4—21no—
19#10622830—21no—
20#10622581—21no—
21C2×#66869—21no—
22#10622168C2211yescharacteristic
23#10622166C2211yescharacteristic
24#10622166C2211yescharacteristic
25#10622089—21no—
26#10622089—21no—
27C22×Q8×C11D411yescharacteristic
28C22×D4×C11D411yescharacteristic
29C23×C4×C11—21no—
30C2×#4339—21no—
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C11×C4⋊C4C2311yescharacteristic
33C2×C11×C22⋊C4—21no—
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C42×C11—21no—
39C2×C42×C11D411yescharacteristic
40C2×#4326—41no—
41#66995—42no—
42#66995—42no—
43C2×#4325—41no—
44C2×#4323—41no—
45#66983—21no—
46#66983—21no—
47C2×#4318—21no—
48#66950—41no—
49#66948—41no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95—21no—
57C11×#95D411yescharacteristic
58C11×#95D411yescharacteristic
59#66896—41no—
60C22⋊(C11⋊C8)—21no—
61C22⋊(C11⋊C8)—21no—
62#66873—41no—
63#66872—41no—
64#66869—42no—
65#12195—111nomaximal, Sylow
66C24×C11—21no—
67C2×Q8×C11—21no—
68C2×Q8×C11—21no—
69C2×Q8×C11—41no—
70C2×Q8×C11—41no—
71C2×D4×C11—41no—
72C2×D4×C11—42no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—42no—
79C22×C4×C11—42no—
80C22×C4×C11—81no—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C2×C22⋊D11—41no—
85#4339—41no—
86#4339—41no—
87#4339—41no—
88#4339—41no—
89C2×D44—21no—
90C2×D44—21no—
91C2×D44—21no—
92C2×C4×D11—41no—
93C2×Dic22—21no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C22⋊C4—42no—
97C11×C22⋊C4—42no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—81no—
101C11×C22⋊C4—81no—
102C42×C11—42no—
103C42×C11—41no—
104#4326—44no—
105#4325—44no—
106#4323—82no—
107(C2×D11)⋊C4—41no—
108(C2×D11)⋊C4—41no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111#4318—22no—
112#4318—41no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8—41no—
115C2×C11⋊C8—41no—
116#2572D1111yescharacteristic, complemented
117#2007—111no—
118#1616—111no—
119#1598—111no—
120#1353—111no—
121#1345—111no—
122#1319—111no—
123C23×C11—22no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11#12011yescharacteristic
131C22×D11—41no—
132Q8×C11—42no—
133Q8×C11—81no—
134D4×C11—42no—
135D4×C11—81no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—22no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
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—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—84no—
158C2×C4×C11#13511yescharacteristic
159C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
160C22⋊D11—81no—
161C22⋊D11—81no—
162C2×Dic11—41no—
163D44—41no—
164D44—41no—
165D44—81no—
166D44—81no—
167C4×D11—81no—
168C4×D11—81no—
169Dic22—41no—
170Dic22—41no—
171C11⋊C8—42no—
172C11⋊C8—81no—
173C11⋊C8—81no—
174C2×#137—221no—
175#537—111no—
176#481—221no—
177#447—221no—
178C2×#104—221no—
179#400C2×D1111yescharacteristic
180#394C2×D1111yescharacteristic
181#393—21no—
182#391C2×D1111yescharacteristic
183#388—21no—
184#386—21no—
185#383—21no—
186#381—21no—
187C4×C22⋊C4—21no—
188#343—111no—
189#327—221no—
190#327—221no—
191#324—111no—
192#324—111no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—42no—
196C22×C11—42no—
197C22×C11—42no—
198C22×C11—81no—
199C22×C11—81no—
200C22×C11—81no—
201C22×C11—81no—
202C22×C11#44911yescharacteristic
203C22×C11#45311yescharacteristic
204C22×C11B(4,𝔽2)11yescharacteristic
205C2×D11—81no—
206C2×D11—81no—
207C2×D11—81no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—42no—
211C4×C11—41no—
212C4×C11—41no—
213C4×C11—81no—
214C4×C11—81no—
215C4×C11—81no—
216C4×C11—81no—
217Dic11—81no—
218C2×#41—221no—
219C22×Q8C22⋊D1111yescharacteristic
220C22×D4C22⋊D1111yescharacteristic
221C23×C4—21no—
222#137—442no—
223#137—442no—
224C2×Q16—441no—
225C2×SD16—441no—
226C2×D8—441no—
227C2×M16—221no—
228C22⋊Q8—441no—
229#121—221no—
230#121—221no—
231#121—441no—
232C2×C4⋊C4C22⋊D1111yescharacteristic
233C2×C4⋊C4C22×D1111yescharacteristic
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C42—21no—
240C2×C42C22⋊D1111yescharacteristic
241#106—441no—
242#104—442no—
243#102—441no—
244#102—441no—
245C22⋊C8—221no—
246C22⋊C8—221no—
247#95—21no—
248#95—21no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95—21no—
254#95C22⋊D1111yescharacteristic
255#95C22⋊D1111yescharacteristic
256C2×C11—21no—
257C2×C11—21no—
258C2×C11—82no—
259C2×C11#160011yescharacteristic
260C2×C11#219711yescharacteristic
261C2×C11#220411yescharacteristic
262D11—161no—
263C24—21no—
264#41—441no—
265#41—441no—
266#41—441no—
267#41—441no—
268C2×Q8—21no—
269C2×Q8—21no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×Q8—221no—
273C2×D4—41no—
274C2×D4—42no—
275C2×D4—221no—
276C2×D4—221no—
277C2×D4—221no—
278C2×D4—441no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—81no—
287C22×C4—441no—
288C22×C4C2×C22⋊D1111yescharacteristic
289C22×C4C2×C22⋊D1111yescharacteristic
290C22×C4C2×C22⋊D1111yescharacteristic
291Q16—444no—
292SD16—444no—
293D8—882no—
294M16—222no—
295M16—441no—
296C2×C8—441no—
297C2×C8—441no—
298C2×C8—441no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—221no—
302C4⋊C4—221no—
303C22⋊C4—42no—
304C22⋊C4—42no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—81no—
308C22⋊C4—81no—
309C22⋊C4—441no—
310C22⋊C4—441no—
311C42—41no—
312C42—42no—
313C11#1219511yescharacteristic, complemented, Sylow
314C23—22no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—441no—
322C23#6700611yescharacteristic
323Q8—42no—
324Q8—81no—
325Q8—441no—
326Q8—441no—
327D4—42no—
328D4—81no—
329D4—441no—
330D4—441no—
331D4—881no—
332D4—881no—
333D4—881no—
334D4—881no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—22no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—84no—
357C2×C4—441no—
358C2×C4—881no—
359C2×C4—881no—
360C2×C4#6700211yescharacteristic
361C2×C4#6700311yescharacteristic
362C8—442no—
363C8—881no—
364C8—881no—
365C22—21no—
366C22—21no—
367C22—42no—
368C22—42no—
369C22—42no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22—881no—
375C22—881no—
376C22—881no—
377C22#1062285111yescharacteristic
378C22#1062285411yescharacteristic
379C22#1062285711yescharacteristic
380C4—21no—
381C4—21no—
382C4—42no—
383C4—41no—
384C4—41no—
385C4—81no—
386C4—81no—
387C4—81no—
388C4—81no—
389C4—881no—
390C2—21no—
391C2—21no—
392C2—82no—
393C2—1761no—
394C2#1306756211yescharacteristic
395C2#1307060611yescharacteristic
396C2#1307064211yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2572C2
socleC22×C11B(4,𝔽2)
prime radical#13067550C2
hypercenter#2572D11
hypocenterC11#12195
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2572

Complements

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

NH ≅ G/Ntype
1. #13069662C2semidirect
2. #13067652C2semidirect
4. #13066643C2semidirect
5. #13066619C2semidirect
6. #13066550C2semidirect
7. C11×#2572C2semidirect
116. #2572D11semidirect
313. C11#12195semidirect

Maximal subgroups

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

subgroupindex
#130696622
#130676522
#130675502
#130666432
#130666192
#130665502
C11×#25722
#1219511