Finite Group Databasebeta

← #14657544

Subgroups — #14657544

Order 2816.

398 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 93 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#13078415C211yesmaximal, characteristic
2#13068627C211yesmaximal, characteristic
3#13067274C211yesmaximal, characteristic, complemented
4#13067181C211yesmaximal, characteristic, complemented
5#13066936C211yesmaximal, characteristic
6#13066476C211yesmaximal, characteristic, complemented
7C11×#1571C211yesmaximal, characteristic, complemented
8C2×C4×D44C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13#10622744—21no—
14#10622734—21no—
15C2×#66885—21no—
16#10622549C2211yescharacteristic
17#10622538C2211yescharacteristic
18#10622460—22no—
19#10622459—21no—
20#10622455—21no—
21C11×#335—22no—
22#10622189—21no—
23#10622124—21no—
24#10622119—21no—
25#10622106—22no—
26#10622105—22no—
27C22×D44D411yescharacteristic
28C22×C4×D11—21no—
29C2×C11×M16—21no—
30C22×C8×C11—21no—
31C2×C42×C11C2311yescharacteristic
32C2×(C2×D11)⋊C4—21no—
33#66979—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11D411yescharacteristic
36#66977—21no—
37#66977—21no—
38C4×D44—21no—
39C4×D44—21no—
40C4×D44—21no—
41C4×D44—21no—
42#66923—21no—
43#66922D411yescharacteristic
44#66922D411yescharacteristic
45C4×Dic22—21no—
46C4×Dic22—21no—
47C11×C4⋊C8—21no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8—21no—
51C11×C4⋊C8D412yes—
52C11×C22⋊C8D412yes—
53C4×C8×C11—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C22⋊(C11⋊C8)—21no—
57#66885—22no—
58#66885—22no—
59#66885—42no—
60#66882—22no—
61#66881—22no—
62C4⋊(C11⋊C8)—21no—
63C4×C11⋊C8—21no—
64#10469—111nomaximal, Sylow
65C23×D11—21no—
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11#4111yescharacteristic
69C22×Dic11—21no—
70C22×Dic11—41no—
71C2×D44—21no—
72C2×D44—21no—
73C2×D44—21no—
74C2×D44—21no—
75C2×D44—21no—
76C2×D44Q1612yes—
77C2×C4×D11—41no—
78C2×C4×D11—41no—
79C2×C4×D11—82no—
80C2×Dic22—21no—
81C2×Dic22—21no—
82C11×M16—41no—
83C11×M16—41no—
84C2×C8×C11—22no—
85C2×C8×C11—22no—
86C2×C8×C11—41no—
87C2×C8×C11—41no—
88C2×C8×C11—41no—
89C42×C11C2×D411yescharacteristic
90C42×C11C2×D411yescharacteristic
91C42×C11#4111yescharacteristic
92C42×C11#4111yescharacteristic
93C22⋊Dic11—41no—
94(C2×D11)⋊C4—41no—
95(C2×D11)⋊C4—41no—
96C4⋊Dic11—21no—
97C4⋊Dic11—21no—
98C4⋊Dic11—21no—
99C4⋊Dic11—21no—
100C4⋊Dic11—21no—
101C4⋊Dic11—21no—
102C4⋊Dic11—41no—
103C4⋊Dic11—41no—
104Dic11⋊C4—41no—
105Dic11⋊C4—41no—
106C4×Dic11—41no—
107C2×C11⋊C8—41no—
108#3077—111no—
109#1804—111no—
110#1571D1111yescharacteristic, complemented
111#1542—111no—
112#1518—111no—
113#1460—111no—
114#1286—111no—
115C23×C11#12111yescharacteristic
116C22×D11—22no—
117C22×D11—41no—
118C22×D11—41no—
119C22×D11—81no—
120C22×D11—81no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11#12011yescharacteristic
124C2×C4×C11#12111yescharacteristic
125C2×C4×C11#12111yescharacteristic
126C2×C4×C11#12311yescharacteristic
127C2×C4×C11#12311yescharacteristic
128C2×C4×C11#12411yescharacteristic
129C2×C4×C11C2×Q1611yescharacteristic
130C2×C4×C11#13511yescharacteristic
131C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C11#13711yescharacteristic
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—81no—
137C2×Dic11—81no—
138C2×Dic11—81no—
139C2×Dic11—81no—
140D44—22no—
141D44—22no—
142D44—41no—
143D44—41no—
144C4×D11—82no—
145C4×D11—82no—
146Dic22—81no—
147Dic22—81no—
148C8×C11—42no—
149C8×C11—42no—
150C8×C11—81no—
151C11⋊C8—81no—
152#533—111no—
153C2×C4×D4—111no—
154#478—222no—
155#476—221no—
156#474—221no—
157#431—111no—
158#431C2×D1111yescharacteristic
159#428—221no—
160#423C2×D1111yescharacteristic
161C2×C4⋊C8C2×D1111yescharacteristic
162#418—221no—
163C2×#102—221no—
164#382—111no—
165#340—221no—
166#335—22no—
167#333—221no—
168#332—221no—
169#328—222no—
170#323—222no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11#39411yescharacteristic
174C22×C11#46711yescharacteristic
175C22×C11#46811yescharacteristic
176C2×D11—42no—
177C2×D11—82no—
178C2×D11—81no—
179C2×D11—81no—
180C2×D11—82no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11#44911yescharacteristic
186C4×C11#45111yescharacteristic
187C4×C11#48411yescharacteristic
188C4×C11#48511yescharacteristic
189Dic11—81no—
190Dic11—81no—
191Dic11—81no—
192Dic11—161no—
193C22×D4—111no—
194C23×C4—221no—
195C2×M16—21no—
196C22×C8—21no—
197C4⋊Q8—111no—
198C4⋊Q8—111no—
199#125—221no—
200C22⋊Q8—221no—
201C22⋊Q8—221no—
202C4×Q8—221no—
203C4×Q8—221no—
204C4×D4—221no—
205C4×D4—221no—
206C4×D4—221no—
207C4×D4—221no—
208#117—221no—
209C2×C4⋊C4—111no—
210C2×C4⋊C4—221no—
211C2×C22⋊C4—221no—
212C2×C42C22×D1111yescharacteristic
213#107—222no—
214#106—222no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—221no—
220C4⋊C8C22⋊D1112yes—
221#102—222no—
222#102—222no—
223#102—442no—
224C22⋊C8—221no—
225C22⋊C8D4412yes—
226C4×C8—21no—
227C4×C8—221no—
228#95—221no—
229#95—221no—
230C2×C11—21no—
231C2×C11—21no—
232C2×C11#203611yescharacteristic
233C2×C11#204811yescharacteristic
234C2×C11#205311yescharacteristic
235D11—82no—
236C24—221no—
237C2×Q8—221no—
238C2×Q8—221no—
239C2×D4—112no—
240C2×D4—221no—
241C2×D4—221no—
242C2×D4—221no—
243C2×D4—221no—
244C2×D4—221no—
245C22×C4—221no—
246C22×C4—441no—
247C22×C4—441no—
248C22×C4—441no—
249C22×C4—882no—
250C22×C4C2×D4411yescharacteristic
251C22×C4D4×D1111yescharacteristic
252C22×C4#434311yescharacteristic
253M16—41no—
254M16—41no—
255C2×C8—22no—
256C2×C8—22no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—441no—
261C4⋊C4—221no—
262C4⋊C4—221no—
263C4⋊C4—221no—
264C4⋊C4—221no—
265C4⋊C4—221no—
266C4⋊C4—221no—
267C4⋊C4—441no—
268C4⋊C4—441no—
269C4⋊C4—441no—
270C4⋊C4—441no—
271C22⋊C4—441no—
272C22⋊C4—441no—
273C22⋊C4—441no—
274C42—441no—
275C42#433911yescharacteristic
276C42D4×D1111yescharacteristic
277C42#434311yescharacteristic
278C42C2×C22⋊D1111yescharacteristic
279C11#1046911yescharacteristic, complemented, Sylow
280C23—222no—
281C23—441no—
282C23—441no—
283C23—881no—
284C23—881no—
285C23#6694811yescharacteristic
286Q8—881no—
287Q8—881no—
288D4—222no—
289D4—222no—
290D4—441no—
291D4—441no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—441no—
295C2×C4—441no—
296C2×C4—441no—
297C2×C4—882no—
298C2×C4—882no—
299C2×C4—881no—
300C2×C4—881no—
301C2×C4—881no—
302C2×C4—881no—
303C2×C4#6694711yescharacteristic
304C2×C4#6694711yescharacteristic
305C2×C4#6694811yescharacteristic
306C2×C4#6696411yescharacteristic
307C2×C4#6696511yescharacteristic
308C2×C4Q16×D1111yescharacteristic
309C2×C4#6697111yescharacteristic
310C2×C4#6698311yescharacteristic
311C2×C4#6699011yescharacteristic
312C2×C4#6700011yescharacteristic
313C8—42no—
314C8—42no—
315C8—81no—
316C8—881no—
317C22—21no—
318C22—21no—
319C22—442no—
320C22—882no—
321C22—882no—
322C22—881no—
323C22—881no—
324C22#1062249911yescharacteristic
325C22#1062250011yescharacteristic
326C22#1062260411yescharacteristic
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—881no—
332C4—881no—
333C4—881no—
334C4—1761no—
335C4#1062249711yescharacteristic
336C4#1062250111yescharacteristic
337C4#1062277111yescharacteristic
338C4#1062279911yescharacteristic
339C2—21no—
340C2—21no—
341C2—882no—
342C2#1306982111yescharacteristic
343C2#1306989111yescharacteristic
344C2#1306992211yescharacteristic
subgroupG/H
centerC22#10622604
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1571C2
socleC22×C11#394
prime radicalC22×D44D4
hypercenter#1571D11
hypocenterC11#10469
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1571

Complements

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

NH ≅ G/Ntype
3. #13067274C2semidirect
4. #13067181C2semidirect
6. #13066476C2semidirect
7. C11×#1571C2semidirect
110. #1571D11semidirect
279. C11#10469semidirect

Maximal subgroups

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

subgroupindex
#130784152
#130686272
#130672742
#130671812
#130669362
#130664762
C11×#15712
#1046911