Finite Group Databasebeta

← #14645486

Subgroups — #14645486

Order 2816.

1050 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 1050 conjugacy classes of subgroups — too many to draw. Only its 159 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#13068608C211yesmaximal, characteristic, complemented
2#13067284C212yesmaximal, complemented
3#13067045C212yesmaximal, complemented
4#13066937C211yesmaximal, characteristic, complemented
5C2×C11×#550C211yesmaximal, characteristic
6C22×C11×#41C412yes—
7C11×#550—24no—
8C11×#550—24no—
9C2×C11×#127—21no—
10C2×C11×#127C2211yescharacteristic
11C2×C11×#121—22no—
12C2×C11×#121C412yes—
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×D4×C11—21no—
15C2×C4×D4×C11C2211yescharacteristic
16C2×#66897—21no—
17#10622538C2212yes—
18#10622537C2212yes—
19#10622182—24no—
20Q8⋊(C11⋊C8)—24no—
21#10622168—21no—
22#10622163—22no—
23C2×C11×#41—24no—
24C2×C11×#41—24no—
25C2×C11×#41—48no—
26C22×Q8×C11C2×C411yescharacteristic
27C22×D4×C11—22no—
28C22×D4×C11—22no—
29C22×D4×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11C2×C412yes—
32C22×D4×C11D411yescharacteristic
33C23×C4×C11—22no—
34C23×C4×C11C2×C412yes—
35C11×#127—28no—
36C11×#127—22no—
37C11×#127D414yes—
38C11×#121—216no—
39C11×#121—24no—
40C11×#121—24no—
41C4×Q8×C11—22no—
42C4×Q8×C11D414yes—
43C4×D4×C11—28no—
44C4×D4×C11—22no—
45C4×D4×C11—22no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4C2×C411yescharacteristic
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C11×C22⋊C4—22no—
50C2×C11×C22⋊C4D412yes—
51C2×C42×C11—21no—
52C2×C42×C11C2311yescharacteristic
53C2×#4318—22no—
54#66897—42no—
55C22⋊(C11⋊C8)—22no—
56C4⋊(C11⋊C8)—22no—
57C4⋊(C11⋊C8)—22no—
58C4⋊(C11⋊C8)—22no—
59C4×C11⋊C8—22no—
60#8385—111nomaximal, Sylow
61C24×C11—22no—
62C24×C11C22⋊C412yes—
63C11×#41—416no—
64C11×#41—48no—
65C11×#41—48no—
66C2×Q8×C11—24no—
67C2×Q8×C11—21no—
68C2×Q8×C11C22⋊C412yes—
69C2×D4×C11—28no—
70C2×D4×C11—28no—
71C2×D4×C11—22no—
72C2×D4×C11—22no—
73C2×D4×C11—24no—
74C2×D4×C11—24no—
75C2×D4×C11—22no—
76C2×D4×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—48no—
79C2×D4×C11—44no—
80C2×D4×C11—42no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—82no—
84C2×D4×C11—84no—
85C2×D4×C11C22⋊C414yes—
86C22×C4×C11—21no—
87C22×C4×C11—28no—
88C22×C4×C11—21no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—48no—
92C22×C4×C11—44no—
93C22×C4×C11C22⋊C412yes—
94C22×C4×C11C22×C411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C11×C4⋊C4—21no—
98C11×C4⋊C4—24no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4C22⋊C412yes—
101C11×C22⋊C4—28no—
102C11×C22⋊C4—24no—
103C42×C11—24no—
104C42×C11C2×D412yes—
105C42×C11C2×D412yes—
106#4318—42no—
107#4318—42no—
108C2×C11⋊C8—42no—
109C2×C11⋊C8—42no—
110C2×#550D1111yescharacteristic
111#1800—111no—
112#1545—112no—
113#1487—112no—
114#1460—111no—
115C23×C11—22no—
116C23×C11—24no—
117C23×C11—22no—
118C23×C11—22no—
119C23×C11—44no—
120C23×C11—44no—
121C23×C11—42no—
122C23×C11—42no—
123C23×C11—42no—
124C23×C11—42no—
125C23×C11C2×C22⋊C411yescharacteristic
126Q8×C11—24no—
127Q8×C11—22no—
128Q8×C11#10014yescomplemented
129D4×C11—44no—
130D4×C11—416no—
131D4×C11—44no—
132D4×C11—42no—
133D4×C11—44no—
134D4×C11—42no—
135D4×C11—44no—
136D4×C11—84no—
137D4×C11—88no—
138C2×C4×C11—24no—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—41no—
144C2×C4×C11—416no—
145C2×C4×C11—44no—
146C2×C4×C11—42no—
147C2×C4×C11—44no—
148C2×C4×C11—42no—
149C2×C4×C11C2×C22⋊C411yescharacteristic
150C2×C4×C11C2×C22⋊C411yescharacteristic
151C2×C4×C11#12012yes—
152C2×C4×C11#12012yes—
153C2×C4×C11#13512yes—
154C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C11#13711yescharacteristic
156C11⋊C8—82no—
157C11⋊C8—82no—
158C22×#41Dic1112yes—
159#550—24no—
160#550—24no—
161C2×#127—21no—
162C2×#127C2×D1111yescharacteristic
163C2×#121—22no—
164C2×#121Dic1112yes—
165C2×C4×Q8C2×D1111yescharacteristic
166C2×C4×D4—21no—
167C2×C4×D4C2×D1111yescharacteristic
168#431—112no—
169#423—112no—
170C2×#100—221no—
171#343—221no—
172#331—224no—
173Q8⋊C8—224no—
174#323—222no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—42no—
178C22×C11—44no—
179C22×C11—42no—
180C22×C11—44no—
181C22×C11—42no—
182C22×C11—44no—
183C22×C11—82no—
184C22×C11—82no—
185C22×C11—84no—
186C22×C11—84no—
187C22×C11#37911yescharacteristic
188C22×C11#41611yescharacteristic
189C22×C11#41711yescharacteristic
190C4×C11—22no—
191C4×C11—24no—
192C4×C11—21no—
193C4×C11—42no—
194C4×C11—42no—
195C4×C11C2×#10012yes—
196C4×C11#44912yes—
197C4×C11#45212yes—
198C2×#41—24no—
199C2×#41—24no—
200C2×#41—48no—
201C22×Q8C2×Dic1111yescharacteristic
202C22×D4—22no—
203C22×D4—22no—
204C22×D4—21no—
205C22×D4—21no—
206C22×D4C2×Dic1112yes—
207C22×D4C22⋊D1111yescharacteristic
208C23×C4—22no—
209C23×C4C2×Dic1112yes—
210C2×M16—222no—
211#127—28no—
212#127—22no—
213#127C22⋊D1114yes—
214#121—216no—
215#121—24no—
216#121—24no—
217C4×Q8—22no—
218C4×Q8C22⋊D1114yes—
219C4×D4—28no—
220C4×D4—22no—
221C4×D4—22no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4C2×Dic1111yescharacteristic
224C2×C4⋊C4C22⋊D1111yescharacteristic
225C2×C22⋊C4—22no—
226C2×C22⋊C4C22⋊D1112yes—
227C2×C42—21no—
228C2×C42C22×D1111yescharacteristic
229C4⋊C8—222no—
230C4⋊C8—222no—
231C4⋊C8—222no—
232#100—442no—
233C22⋊C8—222no—
234C4×C8—222no—
235C2×C11—21no—
236C2×C11—21no—
237C2×C11—82no—
238C2×C11—84no—
239C2×C11#178311yescharacteristic
240C2×C11#178811yescharacteristic
241C2×C11#179511yescharacteristic
242C24—22no—
243C24C22⋊Dic1112yes—
244#41—416no—
245#41—48no—
246#41—48no—
247C2×Q8—24no—
248C2×Q8—21no—
249C2×Q8C22⋊Dic1112yes—
250C2×D4—28no—
251C2×D4—28no—
252C2×D4—21no—
253C2×D4—22no—
254C2×D4—21no—
255C2×D4—22no—
256C2×D4—22no—
257C2×D4—24no—
258C2×D4—24no—
259C2×D4—48no—
260C2×D4—44no—
261C2×D4—41no—
262C2×D4—42no—
263C2×D4—41no—
264C2×D4—82no—
265C2×D4—84no—
266C2×D4C22⋊Dic1114yes—
267C22×C4—21no—
268C22×C4—28no—
269C22×C4—21no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—48no—
273C22×C4—44no—
274C22×C4C22⋊Dic1112yes—
275C22×C4C22×Dic1111yescharacteristic
276C22×C4C2×C22⋊D1111yescharacteristic
277C22×C4C2×C22⋊D1111yescharacteristic
278M16—442no—
279M16—442no—
280C2×C8—442no—
281C2×C8—442no—
282C4⋊C4—21no—
283C4⋊C4—24no—
284C4⋊C4—22no—
285C4⋊C4C22⋊Dic1112yes—
286C22⋊C4—28no—
287C22⋊C4—24no—
288C42—24no—
289C42C2×C22⋊D1112yes—
290C42C2×C22⋊D1112yes—
291C11#838511yescharacteristic, complemented, Sylow
292C23—22no—
293C23—24no—
294C23—22no—
295C23—22no—
296C23—44no—
297C23—44no—
298C23—42no—
299C23—42no—
300C23—42no—
301C23—42no—
302C23C2×C22⋊Dic1111yescharacteristic
303Q8—24no—
304Q8—22no—
305Q8#6689714yescomplemented
306D4—44no—
307D4—416no—
308D4—44no—
309D4—42no—
310D4—44no—
311D4—42no—
312D4—44no—
313D4—84no—
314D4—88no—
315C2×C4—24no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—416no—
322C2×C4—44no—
323C2×C4—42no—
324C2×C4—44no—
325C2×C4—42no—
326C2×C4#6700211yescharacteristic
327C2×C4#6700312yes—
328C2×C4#6700411yescharacteristic
329C2×C4C2×C22⋊Dic1111yescharacteristic
330C2×C4C2×C22⋊Dic1111yescharacteristic
331C2×C4#6700612yes—
332C2×C4#6700612yes—
333C8—882no—
334C8—882no—
335C22—21no—
336C22—21no—
337C22—42no—
338C22—44no—
339C22—44no—
340C22—42no—
341C22—42no—
342C22—44no—
343C22—82no—
344C22—82no—
345C22—84no—
346C22—84no—
347C22#1062284511yescharacteristic
348C22#1062284611yescharacteristic
349C22#1062286011yescharacteristic
350C4—22no—
351C4—24no—
352C4—21no—
353C4—42no—
354C4—42no—
355C4C2×#6689712yes—
356C4#1062285112yes—
357C4#1062285212yes—
358C2—21no—
359C2—21no—
360C2—84no—
361C2—82no—
362C2#1306853711yescharacteristic
363C2#1306855611yescharacteristic
364C2#1306858611yescharacteristic
subgroupG/H
centerC22#10622860
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
Fitting, prime radicalC2×C11×#550C2
socleC22×C11#379
cosocleC2×C42×C11C23
hypercenterC2×#550D11
hypocenterC11#8385
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. #13068608C2semidirect
2. #13067284C2semidirect
3. #13067045C2semidirect
4. #13066937C2semidirect
128. Q8×C11#100semidirect
291. C11#8385semidirect
305. Q8#66897semidirect

Maximal subgroups

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

subgroupindex
#130686082
#130672842
#130670452
#130669372
C2×C11×#5502
#838511