Finite Group Databasebeta

← #14643016

Subgroups — #14643016

Order 2816.

434 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 81 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#13075545C211yesmaximal, characteristic
2#13070143C211yesmaximal, characteristic
3#13070094C211yesmaximal, characteristic, complemented
4#13070092C211yesmaximal, characteristic, complemented
5#13066440C211yesmaximal, characteristic, complemented
6#13066436C211yesmaximal, characteristic
7C11×#1271C211yesmaximal, characteristic, complemented
8C2×#66947—21no—
9C11×#389C2211yescharacteristic
10C2×#66885—21no—
11C2×#66882—21no—
12C2×#66881—21no—
13#10622606—21no—
14#10622602—21no—
15#10622597—21no—
16C2×#66872—21no—
17#10622552C2211yescharacteristic
18#10622548C2211yescharacteristic
19#10622541C2211yescharacteristic
20#10622287—21no—
21#10622281—21no—
22C11×#336C2211yescharacteristic
23C11×#336C2211yescharacteristic
24#10622189—21no—
25#10622167—21no—
26#10622162C2211yescharacteristic
27C22×D44D411yescharacteristic
28C22×C4×D11—21no—
29C22×C8×C11—21no—
30C22×C8×C11—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C42×C11C2311yescharacteristic
35C2×(C2×D11)⋊C4—21no—
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11D411yescharacteristic
44C2×C4⋊Dic11D411yescharacteristic
45C2×C4⋊Dic11D411yescharacteristic
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C22×C11⋊C8—21no—
49#66947—42no—
50#66947—42no—
51C11×#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56#66885—42no—
57#66882—42no—
58#66881—42no—
59#66872—42no—
60#7819—111nomaximal, Sylow
61C23×D11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×Dic11—21no—
68C22×Dic11—21no—
69C22×Dic11—21no—
70C22×Dic11—41no—
71C2×D44—21no—
72C2×D44—41no—
73C2×D44—41no—
74C2×D44SD1612yes—
75C2×C4×D11—42no—
76C2×C4×D11—81no—
77C2×C4×D11—81no—
78C2×C8×C11—22no—
79C2×C8×C11—22no—
80C2×C8×C11—41no—
81C2×C8×C11—41no—
82C2×C8×C11—41no—
83C2×C8×C11—41no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C42×C11—41no—
90(C2×D11)⋊C4—42no—
91(C2×D11)⋊C4—42no—
92(C2×D11)⋊C4—42no—
93(C2×D11)⋊C4—41no—
94(C2×D11)⋊C4—41no—
95(C2×D11)⋊C4—41no—
96(C2×D11)⋊C4—41no—
97C4⋊Dic11—21no—
98C4⋊Dic11—21no—
99C4⋊Dic11—41no—
100C4⋊Dic11—41no—
101C4⋊Dic11—41no—
102C4⋊Dic11—41no—
103C4⋊Dic11—41no—
104C4⋊Dic11—41no—
105C4⋊Dic11—41no—
106C4⋊Dic11—41no—
107Dic11⋊C4—41no—
108Dic11⋊C4—41no—
109Dic11⋊C4—81no—
110C2×C11⋊C8—22no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113#2724—111no—
114#2093—111no—
115#2084—111no—
116#2084—111no—
117#1271—111no—
118#1271D1111yescharacteristic, complemented
119#1270—111no—
120C23×C11#12011yescharacteristic
121C22×D11—22no—
122C22×D11—41no—
123C22×D11—41no—
124C22×D11—41no—
125C22×D11—41no—
126C22×D11—41no—
127C22×D11—41no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11C2×SD1611yescharacteristic
141C2×C4×C11#13511yescharacteristic
142C2×C4×C11#13511yescharacteristic
143C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—81no—
156C2×Dic11—81no—
157C2×Dic11—81no—
158D44—42no—
159D44—81no—
160C4×D11—84no—
161C8×C11—42no—
162C8×C11—42no—
163C11⋊C8—42no—
164C2×#123—221no—
165C2×#107—221no—
166C2×#106—221no—
167C2×#106—221no—
168C2×#102—221no—
169#398—221no—
170#397—221no—
171#397—221no—
172#390—111no—
173#389—111no—
174#389C2×D1111yescharacteristic
175#385—221no—
176#385—221no—
177#384—111no—
178#340—221no—
179#340—221no—
180#336—111no—
181#336C2×D1111yescharacteristic
182#336C2×D1111yescharacteristic
183C22×C11#44911yescharacteristic
184C22×C11#44911yescharacteristic
185C22×C11#45011yescharacteristic
186C22×C11#45311yescharacteristic
187C22×C11#45611yescharacteristic
188C22×C11#45611yescharacteristic
189C22×C11#45811yescharacteristic
190C2×D11—42no—
191C2×D11—42no—
192C2×D11—42no—
193C2×D11—81no—
194C2×D11—81no—
195C2×D11—81no—
196C2×D11—81no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—81no—
204C4×C11—81no—
205Dic11—81no—
206Dic11—81no—
207Dic11—81no—
208Dic11—161no—
209C22×D4—111no—
210C23×C4—221no—
211C22×C8—21no—
212C22×C8—21no—
213C22×C8—221no—
214#123—442no—
215#123—442no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—111no—
218C2×C4⋊C4—111no—
219C2×C4⋊C4—111no—
220C2×C4⋊C4—221no—
221C2×C4⋊C4—221no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4—221no—
224C2×C4⋊C4—221no—
225C2×C4⋊C4D4411yescharacteristic
226C2×C4⋊C4D4411yescharacteristic
227C2×C22⋊C4—221no—
228C2×C22⋊C4—221no—
229C2×C22⋊C4—221no—
230C2×C22⋊C4—221no—
231C2×C22⋊C4—221no—
232C2×C42C22×D1111yescharacteristic
233#107—442no—
234#106—442no—
235#106—442no—
236#102—442no—
237#95—21no—
238#95—221no—
239#95—221no—
240#95—221no—
241#95—221no—
242C2×C11#160911yescharacteristic
243C2×C11#160911yescharacteristic
244C2×C11#161311yescharacteristic
245C2×C11#162011yescharacteristic
246C2×C11#165411yescharacteristic
247C2×C11#165411yescharacteristic
248C2×C11#166011yescharacteristic
249D11—82no—
250C24—221no—
251C2×D4—112no—
252C2×D4—221no—
253C2×D4—441no—
254C2×D4—441no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—221no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4—442no—
261C22×C4—441no—
262C22×C4—881no—
263C22×C4—881no—
264C22×C4C2×D4411yescharacteristic
265C22×C4D4×D1111yescharacteristic
266C22×C4D4×D1111yescharacteristic
267C2×C8—22no—
268C2×C8—22no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—222no—
274C2×C8—441no—
275C2×C8—441no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—221no—
282C4⋊C4—221no—
283C4⋊C4—441no—
284C4⋊C4—441no—
285C4⋊C4—441no—
286C4⋊C4—441no—
287C4⋊C4—441no—
288C4⋊C4—441no—
289C4⋊C4—441no—
290C4⋊C4—441no—
291C4⋊C4—441no—
292C4⋊C4—441no—
293C4⋊C4—881no—
294C22⋊C4—442no—
295C22⋊C4—442no—
296C22⋊C4—442no—
297C22⋊C4—441no—
298C22⋊C4—441no—
299C22⋊C4—441no—
300C22⋊C4—441no—
301C42—41no—
302C11#781911yescharacteristic, complemented, Sylow
303C23—222no—
304C23—441no—
305C23—441no—
306C23—441no—
307C23—441no—
308C23—441no—
309C23—441no—
310C23#6693511yescharacteristic
311D4—442no—
312D4—881no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—441no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4—441no—
329C2×C4—441no—
330C2×C4—441no—
331C2×C4—441no—
332C2×C4—441no—
333C2×C4—441no—
334C2×C4—884no—
335C2×C4—881no—
336C2×C4—881no—
337C2×C4—881no—
338C2×C4#6695711yescharacteristic
339C2×C4#6696111yescharacteristic
340C2×C4#6696411yescharacteristic
341C2×C4SD16×D1111yescharacteristic
342C2×C4#6696711yescharacteristic
343C2×C4#6697211yescharacteristic
344C8—42no—
345C8—42no—
346C8—442no—
347C22—442no—
348C22—442no—
349C22—442no—
350C22—881no—
351C22—881no—
352C22—881no—
353C22—881no—
354C22#1062234711yescharacteristic
355C22#1062235511yescharacteristic
356C22#1062236511yescharacteristic
357C22#1062238911yescharacteristic
358C22#1062242411yescharacteristic
359C22#1062243511yescharacteristic
360C22#1062243911yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—81no—
368C4—81no—
369C4—881no—
370C4—881no—
371C4—881no—
372C4—1761no—
373C2—882no—
374C2#1306761511yescharacteristic
375C2#1306761611yescharacteristic
376C2#1306763711yescharacteristic
377C2#1306767711yescharacteristic
378C2#1306790111yescharacteristic
379C2#1306790211yescharacteristic
380C2#1306792911yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1271C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenter#1271D11
hypocenterC11#7819
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
3. #13070094C2semidirect
4. #13070092C2semidirect
5. #13066440C2semidirect
7. C11×#1271C2semidirect
118. #1271D11semidirect
302. C11#7819semidirect

Maximal subgroups

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

subgroupindex
#130755452
#130701432
#130700942
#130700922
#130664402
#130664362
C11×#12712
#781911