Finite Group Databasebeta

← #14666446

Subgroups — #14666446

Order 2816.

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

normal subgroups only

This group has 434 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#13074106C211yesmaximal, characteristic, complemented
2#13069658C211yesmaximal, characteristic
3#13067653C211yesmaximal, characteristic, complemented
4#13066644C211yesmaximal, characteristic, complemented
5#13066622C211yesmaximal, characteristic, complemented
6#13066547C211yesmaximal, characteristic, complemented
7C11×#1610C211yesmaximal, characteristic, complemented
8C11×#537C2211yescharacteristic
9C2×#67002—21no—
10C11×#480—21no—
11C11×#398C2211yescharacteristic
12C2×#66901—21no—
13#10622647—21no—
14#10622604—21no—
15#10622603—21no—
16#10622601C2211yescharacteristic
17#10622599C2211yescharacteristic
18C4⋊C4×Dic11—21no—
19#10622283—21no—
20#10622283—21no—
21#10622283—21no—
22C11×#327—21no—
23C11×#324C2211yescharacteristic
24#10622175—21no—
25#10622168C2211yescharacteristic
26#10622166C2211yescharacteristic
27C2×C11×#41—21no—
28C22×D44D411yescharacteristic
29C11×C22⋊Q8—41no—
30C11×#121—21no—
31C11×#121—21no—
32C11×#121—41no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C4⋊C4C2311yescharacteristic
36#67002—42no—
37#67002—42no—
38C2×#4325—41no—
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⋊Dic11—21no—
47C2×C4⋊Dic11D411yescharacteristic
48C2×C4×Dic11—21no—
49C2×C4×Dic11—21no—
50C2×C4×Dic11D411yescharacteristic
51C2×#4318—21no—
52C11×#107—41no—
53C11×#102—41no—
54C11×C22⋊C8—21no—
55C11×#95—21no—
56C11×#95D411yescharacteristic
57#66901—42no—
58#66896—41no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95D411yescharacteristic
63C22⋊(C11⋊C8)—21no—
64#66872—41no—
65#12196—111nomaximal, Sylow
66C23×D11—21no—
67C11×#41—41no—
68C11×#41—41no—
69C11×#41—41no—
70C11×#41—41no—
71C2×Q8×C11—21no—
72C2×D4×C11—21no—
73C2×D4×C11—21no—
74C2×D4×C11—21no—
75C2×D4×C11—41no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—41no—
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—21no—
85C2×D44—21no—
86C2×D44—21no—
87C2×D44—41no—
88C2×D44—41no—
89C2×C8×C11—41no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—41no—
98#4325—44no—
99#4323—44no—
100(C2×D11)⋊C4—42no—
101(C2×D11)⋊C4—42no—
102(C2×D11)⋊C4—42no—
103(C2×D11)⋊C4—42no—
104(C2×D11)⋊C4—81no—
105(C2×D11)⋊C4—81no—
106C4⋊Dic11—41no—
107C4⋊Dic11—42no—
108C4×Dic11—41no—
109C4×Dic11—42no—
110C4×Dic11—81no—
111#4318—22no—
112#4318—41no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8—41no—
115#2593—111no—
116#2006—111no—
117#1616—111no—
118#1610D1111yescharacteristic, complemented
119#1353—111no—
120#1346—111no—
121#1318—111no—
122C23×C11—41no—
123C23×C11#12011yescharacteristic
124C22×D11—41no—
125C22×D11—41no—
126C22×D11—41no—
127C22×D11—41no—
128C22×D11—41no—
129C22×D11—41no—
130C22×D11—41no—
131Q8×C11—41no—
132Q8×C11—41no—
133D4×C11—41no—
134D4×C11—41no—
135D4×C11—81no—
136D4×C11—81no—
137D4×C11—81no—
138D4×C11—81no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—22no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
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—81no—
153C2×C4×C11—81no—
154C2×C4×C11#13511yescharacteristic
155C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
156C2×Dic11—22no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165D44—42no—
166D44—81no—
167C8×C11—81no—
168C11⋊C8—42no—
169C11⋊C8—81no—
170C2×AGL(1,ℤ/8)—221no—
171#537C2×D1111yescharacteristic
172#481—221no—
173#480—21no—
174C2×#104—221no—
175#400—111no—
176#398C2×D1111yescharacteristic
177#394—221no—
178#390—111no—
179#388—221no—
180#388—221no—
181#388—221no—
182#388—221no—
183C4×C4⋊C4—221no—
184#343—111no—
185#327—21no—
186#327—221no—
187#324—111no—
188#324C2×D1111yescharacteristic
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—81no—
192C22×C11—81no—
193C22×C11—81no—
194C22×C11#44911yescharacteristic
195C22×C11#45311yescharacteristic
196C22×C11B(4,𝔽2)11yescharacteristic
197C2×D11—81no—
198C2×D11—81no—
199C2×D11—81no—
200C2×D11—81no—
201C2×D11—81no—
202C2×D11—81no—
203C2×D11—81no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—42no—
207C4×C11—41no—
208C4×C11—41no—
209C4×C11—81no—
210C4×C11—81no—
211Dic11—42no—
212Dic11—81no—
213Dic11—81no—
214C2×#41—21no—
215C22×D4—111no—
216AGL(1,ℤ/8)—442no—
217AGL(1,ℤ/8)—442no—
218C2×SD16—441no—
219C2×D8—441no—
220C2×M16—221no—
221C22⋊Q8—41no—
222#121—21no—
223#121—21no—
224#121—41no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—111no—
227C2×C4⋊C4—221no—
228C2×C4⋊C4C22⋊D1111yescharacteristic
229C2×C4⋊C4C22×D1111yescharacteristic
230C2×C22⋊C4—221no—
231C2×C22⋊C4—221no—
232C2×C22⋊C4—221no—
233C2×C22⋊C4—221no—
234C2×C22⋊C4—221no—
235C2×C22⋊C4—221no—
236C2×C42—111no—
237C2×C42—221no—
238C2×C42—221no—
239#107—41no—
240#106—441no—
241#104—442no—
242#102—41no—
243#102—441no—
244C22⋊C8—21no—
245C22⋊C8—221no—
246#95—21no—
247#95—111no—
248#95—221no—
249#95—221no—
250#95—221no—
251#95C22⋊D1111yescharacteristic
252C2×C11—21no—
253C2×C11—21no—
254C2×C11—161no—
255C2×C11#160011yescharacteristic
256C2×C11#219811yescharacteristic
257C2×C11#220411yescharacteristic
258D11—161no—
259C24—221no—
260#41—41no—
261#41—41no—
262#41—41no—
263#41—41no—
264C2×Q8—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—41no—
269C2×D4—221no—
270C2×D4—221no—
271C2×D4—441no—
272C2×D4—441no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—41no—
276C22×C4—221no—
277C22×C4—221no—
278C22×C4—221no—
279C22×C4D4×D1111yescharacteristic
280C22×C4D4×D1111yescharacteristic
281C22×C4C2×C22⋊D1111yescharacteristic
282SD16—444no—
283D8—444no—
284M16—222no—
285M16—441no—
286C2×C8—41no—
287C2×C8—441no—
288C2×C8—441no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—441no—
296C4⋊C4—442no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—442no—
300C22⋊C4—442no—
301C22⋊C4—442no—
302C22⋊C4—442no—
303C22⋊C4—881no—
304C22⋊C4—881no—
305C42—441no—
306C42—442no—
307C42—881no—
308C11#1219611yescharacteristic, complemented, Sylow
309C23—41no—
310C23—441no—
311C23—441no—
312C23—441no—
313C23—441no—
314C23—441no—
315C23—441no—
316C23—441no—
317C23#6699011yescharacteristic
318Q8—41no—
319Q8—41no—
320D4—41no—
321D4—41no—
322D4—81no—
323D4—81no—
324D4—81no—
325D4—81no—
326D4—442no—
327D4—881no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—22no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—222no—
344C2×C4—441no—
345C2×C4—441no—
346C2×C4—441no—
347C2×C4—441no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4#6696411yescharacteristic
353C2×C4#6696511yescharacteristic
354C8—81no—
355C8—442no—
356C8—881no—
357C22—21no—
358C22—21no—
359C22—81no—
360C22—81no—
361C22—81no—
362C22—881no—
363C22—881no—
364C22—881no—
365C22—881no—
366C22—881no—
367C22—881no—
368C22—881no—
369C22#1062264511yescharacteristic
370C22#1062277111yescharacteristic
371C22#1062281111yescharacteristic
372C4—21no—
373C4—21no—
374C4—42no—
375C4—41no—
376C4—41no—
377C4—81no—
378C4—81no—
379C4—442no—
380C4—881no—
381C4—881no—
382C2—21no—
383C2—21no—
384C2—161no—
385C2—1761no—
386C2#1306755911yescharacteristic
387C2#1307061011yescharacteristic
388C2#1307064111yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1610C2
socleC22×C11B(4,𝔽2)
prime radical#13069658C2
hypercenter#1610D11
hypocenterC11#12196
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1610

Complements

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

NH ≅ G/Ntype
1. #13074106C2semidirect
3. #13067653C2semidirect
4. #13066644C2semidirect
5. #13066622C2semidirect
6. #13066547C2semidirect
7. C11×#1610C2semidirect
118. #1610D11semidirect
308. C11#12196semidirect

Maximal subgroups

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

subgroupindex
#130741062
#130696582
#130676532
#130666442
#130666222
#130665472
C11×#16102
#1219611