Finite Group Databasebeta

← #14666477

Subgroups — #14666477

Order 2816.

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

normal subgroups only

This group has 424 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#13069657C211yesmaximal, characteristic
2#13067618C211yesmaximal, characteristic, complemented
3#13067584C211yesmaximal, characteristic, complemented
4#13066646C211yesmaximal, characteristic, complemented
5#13066622C211yesmaximal, characteristic, complemented
6#13066548C211yesmaximal, characteristic, complemented
7C11×#2830C211yesmaximal, characteristic, complemented
8C2×#66985—21no—
9#10623041C2211yescharacteristic
10C11×#398C2211yescharacteristic
11C11×#397—21no—
12C11×#397—21no—
13C11×#396—21no—
14C11×#395C2211yescharacteristic
15C11×#394—21no—
16C11×#393—21no—
17C11×#390C2211yescharacteristic
18C11×#387—21no—
19#10622840—21no—
20#10622580—21no—
21C2×#66869—21no—
22#10622168C2211yescharacteristic
23#10622166C2211yescharacteristic
24#10622166C2211yescharacteristic
25#10622089—21no—
26#10622089—21no—
27C22×Q8×C11D411yescharacteristic
28C22×D4×C11D411yescharacteristic
29C2×#4339—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C4⋊C4C2311yescharacteristic
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C42×C11D411yescharacteristic
42C2×#4325—41no—
43C2×#4324—41no—
44#66985—42no—
45#66985—42no—
46C2×#4323—41no—
47#66983—21no—
48#66983—21no—
49C2×#4318—21no—
50#66950—41no—
51#66948—41no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95—21no—
57C11×#95D411yescharacteristic
58C11×#95D411yescharacteristic
59#66899—41no—
60C22⋊(C11⋊C8)—21no—
61C22⋊(C11⋊C8)—21no—
62#66873—41no—
63#66871—41no—
64#66869—42no—
65#12200—111nomaximal, Sylow
66C24×C11—21no—
67C2×Q8×C11—41no—
68C2×Q8×C11—81no—
69C2×D4×C11—21no—
70C2×D4×C11—21no—
71C2×D4×C11—41no—
72C2×D4×C11—41no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C2×C22⋊D11—41no—
82#4339—41no—
83#4339—41no—
84#4339—41no—
85#4339—41no—
86C2×D44—21no—
87C2×D44—21no—
88C2×D44—21no—
89C2×C4×D11—41no—
90C2×Dic22—21no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—81no—
96C11×C4⋊C4—81no—
97C11×C22⋊C4—81no—
98C11×C22⋊C4—81no—
99C11×C22⋊C4—81no—
100C11×C22⋊C4—81no—
101C11×C22⋊C4—81no—
102C11×C22⋊C4—81no—
103C42×C11—41no—
104#4325—82no—
105#4324—44no—
106#4323—44no—
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#2830D1111yescharacteristic, complemented
117#2006—111no—
118#1610—111no—
119#1604—111no—
120#1354—111no—
121#1346—111no—
122#1318—111no—
123C23×C11—41no—
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—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—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#13511yescharacteristic
158C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
159C22⋊D11—81no—
160C22⋊D11—81no—
161C2×Dic11—41no—
162D44—41no—
163D44—41no—
164D44—81no—
165D44—81no—
166C4×D11—81no—
167C4×D11—81no—
168Dic22—41no—
169Dic22—41no—
170C11⋊C8—42no—
171C11⋊C8—81no—
172C11⋊C8—81no—
173C2×AGL(1,ℤ/8)—221no—
174#537—111no—
175#480—221no—
176#448—221no—
177C2×#104—221no—
178#398C2×D1111yescharacteristic
179#397—21no—
180#397—21no—
181#396—21no—
182#395C2×D1111yescharacteristic
183#394—21no—
184#393—21no—
185#390C2×D1111yescharacteristic
186#387—21no—
187#343—111no—
188#327—221no—
189#327—221no—
190#324—111no—
191#324—111no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—81no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11—81no—
198C22×C11—81no—
199C22×C11—81no—
200C22×C11—81no—
201C22×C11#44911yescharacteristic
202C22×C11#45311yescharacteristic
203C22×C11B(4,𝔽2)11yescharacteristic
204C2×D11—81no—
205C2×D11—81no—
206C2×D11—81no—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—41no—
210C4×C11—41no—
211C4×C11—81no—
212C4×C11—81no—
213C4×C11—81no—
214C4×C11—81no—
215C4×C11—81no—
216Dic11—81no—
217C2×#41—221no—
218C22×Q8C22⋊D1111yescharacteristic
219C22×D4C22⋊D1111yescharacteristic
220AGL(1,ℤ/8)—442no—
221AGL(1,ℤ/8)—442no—
222C2×SD16—441no—
223C2×SD16—441no—
224C2×D8—441no—
225C2×M16—221no—
226C22⋊Q8—441no—
227#121—221no—
228#121—221no—
229#121—441no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4C22⋊D1111yescharacteristic
234C2×C4⋊C4C22×D1111yescharacteristic
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C42C22⋊D1111yescharacteristic
242#107—441no—
243#104—442no—
244#103—441no—
245#102—441no—
246C22⋊C8—221no—
247C22⋊C8—221no—
248#95—21no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95C22⋊D1111yescharacteristic
254#95C22⋊D1111yescharacteristic
255C2×C11—21no—
256C2×C11—21no—
257C2×C11—161no—
258C2×C11#160011yescharacteristic
259C2×C11#220011yescharacteristic
260C2×C11#220311yescharacteristic
261D11—161no—
262C24—21no—
263#41—441no—
264#41—441no—
265#41—441no—
266#41—441no—
267C2×Q8—41no—
268C2×Q8—81no—
269C2×Q8—221no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—221no—
275C2×D4—221no—
276C2×D4—221no—
277C2×D4—441no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—441no—
284C22×C4C2×C22⋊D1111yescharacteristic
285C22×C4C2×C22⋊D1111yescharacteristic
286C22×C4C2×C22⋊D1111yescharacteristic
287SD16—444no—
288SD16—882no—
289D8—444no—
290M16—222no—
291M16—441no—
292C2×C8—441no—
293C2×C8—441no—
294C2×C8—441no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—81no—
300C4⋊C4—81no—
301C4⋊C4—221no—
302C4⋊C4—221no—
303C22⋊C4—81no—
304C22⋊C4—81no—
305C22⋊C4—81no—
306C22⋊C4—81no—
307C22⋊C4—81no—
308C22⋊C4—81no—
309C22⋊C4—441no—
310C22⋊C4—441no—
311C42—41no—
312C11#1220011yescharacteristic, complemented, Sylow
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—441no—
321C23#6700611yescharacteristic
322Q8—42no—
323Q8—81no—
324Q8—441no—
325Q8—441no—
326D4—42no—
327D4—81no—
328D4—441no—
329D4—441no—
330D4—881no—
331D4—881no—
332D4—881no—
333D4—881no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—41no—
339C2×C4—41no—
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—441no—
356C2×C4—881no—
357C2×C4—881no—
358C2×C4#6700211yescharacteristic
359C2×C4#6700311yescharacteristic
360C8—442no—
361C8—881no—
362C8—881no—
363C22—21no—
364C22—21no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22—81no—
372C22—881no—
373C22—881no—
374C22—881no—
375C22#1062285111yescharacteristic
376C22#1062285411yescharacteristic
377C22#1062285711yescharacteristic
378C4—21no—
379C4—21no—
380C4—41no—
381C4—41no—
382C4—81no—
383C4—81no—
384C4—81no—
385C4—81no—
386C4—81no—
387C4—881no—
388C2—21no—
389C2—21no—
390C2—161no—
391C2—1761no—
392C2#1306756211yescharacteristic
393C2#1307062311yescharacteristic
394C2#1307063711yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2830C2
socleC22×C11B(4,𝔽2)
prime radical#13069657C2
hypercenter#2830D11
hypocenterC11#12200
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2830

Complements

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

NH ≅ G/Ntype
2. #13067618C2semidirect
3. #13067584C2semidirect
4. #13066646C2semidirect
5. #13066622C2semidirect
6. #13066548C2semidirect
7. C11×#2830C2semidirect
116. #2830D11semidirect
312. C11#12200semidirect

Maximal subgroups

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

subgroupindex
#130696572
#130676182
#130675842
#130666462
#130666222
#130665482
C11×#28302
#1220011