Finite Group Databasebeta

← #14642965

Subgroups — #14642965

Order 2816.

380 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 79 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#13076598C211yesmaximal, characteristic
2#13070175C211yesmaximal, characteristic, complemented
3#13070024C211yesmaximal, characteristic, complemented
4#13070021C211yesmaximal, characteristic
5#13066440C211yesmaximal, characteristic, complemented
6#13066436C211yesmaximal, characteristic
7C11×#1272C211yesmaximal, characteristic, complemented
8C11×#391C2211yescharacteristic
9#10622844—21no—
10C2×#66899—21no—
11C2×#66885—21no—
12#10622603—21no—
13#10622552C2211yescharacteristic
14#10622548C2211yescharacteristic
15#10622541C2211yescharacteristic
16#10622287—21no—
17#10622285—21no—
18#10622283—21no—
19#10622268—21no—
20C11×#336C2211yescharacteristic
21C11×#336C2211yescharacteristic
22#10622189—21no—
23#10622189—21no—
24#10622189—21no—
25#10622167—21no—
26#10622162C2211yescharacteristic
27C22×Q8×C11D411yescharacteristic
28C22×D44D411yescharacteristic
29C22×C8×C11—21no—
30C22×C8×C11—21no—
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C42×C11C2311yescharacteristic
33C2×(C2×D11)⋊C4—21no—
34C2×(C2×D11)⋊C4—21no—
35C2×(C2×D11)⋊C4—21no—
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11D411yescharacteristic
43C2×C4⋊Dic11D411yescharacteristic
44C2×C4⋊Dic11D411yescharacteristic
45C2×Dic11⋊C4—21no—
46C2×C4×Dic11—21no—
47C22×C11⋊C8—21no—
48C11×#95—21no—
49C11×#95—21no—
50#66899—42no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55#66885—42no—
56#7811—111nomaximal, Sylow
57C23×D11—21no—
58C2×Q8×C11—21no—
59C2×Q8×C11—21no—
60C2×Q8×C11—41no—
61C2×Q8×C11—41no—
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—21no—
73C2×D44—41no—
74C2×D44—41no—
75C2×C8×C11—41no—
76C2×C8×C11—41no—
77C2×C8×C11—41no—
78C2×C8×C11—41no—
79C2×C8×C11—41no—
80C2×C8×C11—41no—
81C11×C4⋊C4—41no—
82C42×C11—41no—
83(C2×D11)⋊C4—41no—
84(C2×D11)⋊C4—41no—
85(C2×D11)⋊C4—41no—
86(C2×D11)⋊C4—41no—
87(C2×D11)⋊C4—81no—
88(C2×D11)⋊C4—81no—
89(C2×D11)⋊C4—81no—
90(C2×D11)⋊C4—81no—
91C4⋊Dic11—21no—
92C4⋊Dic11—21no—
93C4⋊Dic11—41no—
94C4⋊Dic11—41no—
95C4⋊Dic11—42no—
96C4⋊Dic11—41no—
97C4⋊Dic11—41no—
98C4⋊Dic11—41no—
99C4⋊Dic11—41no—
100Dic11⋊C4—41no—
101Dic11⋊C4—41no—
102C4×Dic11—81no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—41no—
105C2×C11⋊C8—41no—
106#2808—111no—
107#2099—111no—
108#2072—111no—
109#2071—111no—
110#1272D1111yescharacteristic, complemented
111#1271—111no—
112#1270—111no—
113C23×C11#12011yescharacteristic
114C22×D11—41no—
115C22×D11—41no—
116C22×D11—41no—
117C22×D11—41no—
118C22×D11—41no—
119C22×D11—41no—
120C22×D11—41no—
121Q8×C11—42no—
122Q8×C11—81no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11#13511yescharacteristic
136C2×C4×C11#13511yescharacteristic
137C2×C4×C11#13511yescharacteristic
138C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C11#13711yescharacteristic
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—81no—
151C2×Dic11—81no—
152C2×Dic11—81no—
153D44—42no—
154D44—81no—
155C8×C11—81no—
156C8×C11—81no—
157C11⋊C8—81no—
158C2×#103—221no—
159C2×#102—221no—
160#397—221no—
161#394—221no—
162#393—221no—
163#391C2×D1111yescharacteristic
164#390—111no—
165#389—111no—
166#388—221no—
167#388—221no—
168#387—221no—
169#384—111no—
170#340—221no—
171#340—221no—
172#340—221no—
173#340—221no—
174#336—111no—
175#336C2×D1111yescharacteristic
176#336C2×D1111yescharacteristic
177C22×C11#44911yescharacteristic
178C22×C11#44911yescharacteristic
179C22×C11#45211yescharacteristic
180C22×C11#45411yescharacteristic
181C22×C11#45511yescharacteristic
182C22×C11#45511yescharacteristic
183C22×C11#45811yescharacteristic
184C2×D11—81no—
185C2×D11—81no—
186C2×D11—81no—
187C2×D11—81no—
188C2×D11—81no—
189C2×D11—81no—
190C2×D11—81no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—81no—
198C4×C11—81no—
199Dic11—81no—
200Dic11—81no—
201Dic11—81no—
202Dic11—161no—
203C22×Q8D4411yescharacteristic
204C22×D4—111no—
205C22×C8—21no—
206C22×C8—21no—
207C22×C8—221no—
208C2×C4⋊C4—111no—
209C2×C4⋊C4—111no—
210C2×C4⋊C4—111no—
211C2×C4⋊C4—221no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4—221no—
215C2×C4⋊C4D4411yescharacteristic
216C2×C22⋊C4—221no—
217C2×C22⋊C4—221no—
218C2×C22⋊C4—221no—
219C2×C22⋊C4—221no—
220C2×C22⋊C4—221no—
221C2×C22⋊C4—221no—
222C2×C42—221no—
223C2×C42C22×D1111yescharacteristic
224#103—442no—
225#102—442no—
226#95—21no—
227#95—21no—
228#95—221no—
229#95—221no—
230#95—221no—
231#95—221no—
232C2×C11#161211yescharacteristic
233C2×C11#161211yescharacteristic
234C2×C11#161511yescharacteristic
235C2×C11#162811yescharacteristic
236C2×C11#164011yescharacteristic
237C2×C11#164611yescharacteristic
238C2×C11#166211yescharacteristic
239D11—161no—
240C24—221no—
241C2×Q8—21no—
242C2×Q8—21no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×D4—221no—
246C2×D4—221no—
247C2×D4—441no—
248C2×D4—441no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—221no—
252C22×C4—221no—
253C22×C4—221no—
254C22×C4—441no—
255C22×C4C2×D4411yescharacteristic
256C22×C4D4×D1111yescharacteristic
257C22×C4D4×D1111yescharacteristic
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—441no—
265C2×C8—441no—
266C2×C8—441no—
267C4⋊C4—41no—
268C4⋊C4—221no—
269C4⋊C4—221no—
270C4⋊C4—441no—
271C4⋊C4—441no—
272C4⋊C4—442no—
273C4⋊C4—441no—
274C4⋊C4—441no—
275C4⋊C4—441no—
276C4⋊C4—441no—
277C4⋊C4—441no—
278C4⋊C4—441no—
279C22⋊C4—441no—
280C22⋊C4—441no—
281C22⋊C4—441no—
282C22⋊C4—441no—
283C22⋊C4—881no—
284C22⋊C4—881no—
285C22⋊C4—881no—
286C22⋊C4—881no—
287C42—41no—
288C42—881no—
289C11#781111yescharacteristic, complemented, Sylow
290C23—441no—
291C23—441no—
292C23—441no—
293C23—441no—
294C23—441no—
295C23—441no—
296C23—441no—
297C23#6693511yescharacteristic
298Q8—42no—
299Q8—81no—
300D4—442no—
301D4—881no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—881no—
324C2×C4—881no—
325C2×C4—881no—
326C2×C4#6695711yescharacteristic
327C2×C4#6696111yescharacteristic
328C2×C4#6696711yescharacteristic
329C2×C4#6696911yescharacteristic
330C2×C4#6697111yescharacteristic
331C2×C4#6697211yescharacteristic
332C8—81no—
333C8—81no—
334C8—881no—
335C22—881no—
336C22—881no—
337C22—881no—
338C22—881no—
339C22—881no—
340C22—881no—
341C22—881no—
342C22#1062234711yescharacteristic
343C22#1062235511yescharacteristic
344C22#1062235911yescharacteristic
345C22#1062242311yescharacteristic
346C22#1062242411yescharacteristic
347C22#1062243811yescharacteristic
348C22#1062244011yescharacteristic
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—81no—
356C4—81no—
357C4—881no—
358C4—881no—
359C4—881no—
360C4—1761no—
361C2—1761no—
362C2#1306763211yescharacteristic
363C2#1306763311yescharacteristic
364C2#1306765011yescharacteristic
365C2#1306772911yescharacteristic
366C2#1306780411yescharacteristic
367C2#1306784511yescharacteristic
368C2#1306794111yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1272C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenter#1272D11
hypocenterC11#7811
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
2. #13070175C2semidirect
3. #13070024C2semidirect
5. #13066440C2semidirect
7. C11×#1272C2semidirect
110. #1272D11semidirect
289. C11#7811semidirect

Maximal subgroups

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

subgroupindex
#130765982
#130701752
#130700242
#130700212
#130664402
#130664362
C11×#12722
#781111