Finite Group Databasebeta

← #14655904

Subgroups — #14655904

Order 2816.

528 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 109 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#13079928C211yesmaximal, characteristic
2#13079744C211yesmaximal, characteristic
3#13069540C211yesmaximal, characteristic, complemented
4#13069535C211yesmaximal, characteristic
5#13067115C211yesmaximal, characteristic, complemented
6#13066467C211yesmaximal, characteristic, complemented
7C11×#3165C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10#10623008C2211yescharacteristic
11C11×#501—22no—
12C11×#500—21no—
13C11×#498—21no—
14C11×#428—22no—
15C4×C11×M16C2211yescharacteristic
16C2×#66899—22no—
17C2×#66889—22no—
18#10622701—21no—
19#10622697—21no—
20#10622697—22no—
21#10622696—21no—
22#10622692—21no—
23#10622661—22no—
24#10622640—21no—
25#10622633—21no—
26#10622581—22no—
27C4×C4⋊Dic11C2211yescharacteristic
28#10622538C2211yescharacteristic
29C2×C4⋊(C11⋊C8)C2211yescharacteristic
30#10622176—22no—
31C22×Q8×C11—21no—
32C2×#4339—21no—
33C2×C11×M16D412yes—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8D411yescharacteristic
38C11×C4⋊Q8D411yescharacteristic
39C11×C4⋊Q8D412yes—
40C11×#125—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C11×#117—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C42×C11C2311yescharacteristic
49C2×#4325—22no—
50#66983—21no—
51#66983—21no—
52C2×C4⋊Dic11—21no—
53C2×C4×Dic11—21no—
54C22×C11⋊C8D412yes—
55#66928—21no—
56#66927D411yescharacteristic
57C4×D44—21no—
58C4×D44—21no—
59#66922D411yescharacteristic
60C11×#107—24no—
61C11×#106—24no—
62C11×#97—21no—
63C4×C8×C11—21no—
64#66899—22no—
65#66899—44no—
66C11⋊#95—21no—
67C22⋊(C11⋊C8)D412yes—
68#66889—44no—
69#66873—24no—
70#66873—22no—
71#66872—24no—
72#66872—22no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)—21no—
76C4×C11⋊C8—21no—
77#10201—111nomaximal, Sylow
78C2×Q8×C11—21no—
79C2×Q8×C11—22no—
80C2×Q8×C11—21no—
81C2×Q8×C11—42no—
82C2×Q8×C11—42no—
83C2×Q8×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C2×C22⋊D11—41no—
89C22×Dic11—41no—
90#4339—42no—
91#4339—42no—
92C2×D44—21no—
93C2×D44—21no—
94C2×D44—21no—
95C2×C4×D11—41no—
96C2×Dic22—21no—
97C11×M16—22no—
98C11×M16SD1614yescomplemented
99C2×C8×C11—22no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C22⋊C4—41no—
111C42×C11—41no—
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11#4111yescharacteristic
116#4325—82no—
117(C2×D11)⋊C4—41no—
118(C2×D11)⋊C4—41no—
119C4⋊Dic11—22no—
120C4⋊Dic11—21no—
121C4⋊Dic11—21no—
122C4⋊Dic11—41no—
123C4×Dic11—42no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—42no—
127#3246—111no—
128#3227—111no—
129#3165D1111yescharacteristic, complemented
130#1981—111no—
131#1980—111no—
132#1503—111no—
133#1283—111no—
134C23×C11#12711yescharacteristic
135C22×D11—41no—
136Q8×C11—44no—
137Q8×C11—41no—
138Q8×C11—41no—
139Q8×C11—81no—
140Q8×C11—81no—
141Q8×C11—81no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—42no—
148C2×C4×C11—82no—
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11C2×SD1612yes—
156C2×C4×C11#13712yes—
157C22⋊D11—81no—
158C22⋊D11—81no—
159C2×Dic11—42no—
160C2×Dic11—41no—
161C2×Dic11—81no—
162C2×Dic11—81no—
163D44—42no—
164D44—41no—
165D44—41no—
166D44—42no—
167C4×D11—82no—
168Dic22—42no—
169C8×C11—24no—
170C11⋊C8—42no—
171C11⋊C8—42no—
172#533C2×D1111yescharacteristic
173#532—111no—
174C2×C4⋊Q8C2×D1111yescharacteristic
175#501—22no—
176#500—21no—
177#498—21no—
178#498—221no—
179#486—221no—
180#481—222no—
181#476—222no—
182#476—221no—
183#475—221no—
184#465—222no—
185#461—221no—
186#460—221no—
187#431—111no—
188#428—22no—
189C2×C4⋊C8—111no—
190C2×#104—222no—
191C2×#103—222no—
192C4×M16C2×D1111yescharacteristic
193C4×C4⋊C4—111no—
194#328—222no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11#39211yescharacteristic
198C22×C11#49211yescharacteristic
199C22×C11#49711yescharacteristic
200C2×D11—81no—
201C2×D11—81no—
202C2×D11—81no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—82no—
207C4×C11—81no—
208C4×C11—81no—
209C4×C11#44812yes—
210C4×C11#45311yescharacteristic
211C4×C11#45411yescharacteristic
212C4×C11#46112yes—
213Dic11—82no—
214Dic11—81no—
215C2×#41—221no—
216C22×Q8—21no—
217C2×SD16—222no—
218C2×M16C22⋊D1112yes—
219C22×C8—112no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8—111no—
224C4⋊Q8C22⋊D1112yes—
225C4⋊Q8C22⋊D1111yescharacteristic
226C4⋊Q8C22⋊D1111yescharacteristic
227#127—111no—
228#125—21no—
229#124—221no—
230C22⋊Q8—21no—
231C22⋊Q8—21no—
232#121—221no—
233#121—221no—
234C4×Q8—21no—
235C4×Q8—21no—
236C4×D4—221no—
237C4×D4—221no—
238#117—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—221no—
242C2×C42—221no—
243C2×C42C22×D1111yescharacteristic
244#107—24no—
245#106—24no—
246#106—222no—
247#106—224no—
248C4⋊C8—221no—
249C4⋊C8—221no—
250C4⋊C8—221no—
251#104—444no—
252#103—222no—
253#103—444no—
254#102—222no—
255#102—224no—
256C22⋊C8—112no—
257#97—21no—
258C4×C8—21no—
259C4×C8—221no—
260#95—221no—
261C2×C11—21no—
262C2×C11—21no—
263C2×C11#200611yescharacteristic
264C2×C11#200911yescharacteristic
265C2×C11#201311yescharacteristic
266D11—161no—
267#41—442no—
268#41—442no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—21no—
272C2×Q8—42no—
273C2×Q8—42no—
274C2×Q8—41no—
275C2×Q8—221no—
276C2×D4—221no—
277C2×D4—221no—
278C2×D4—221no—
279C2×D4—441no—
280C22×C4—41no—
281C22×C4—441no—
282C22×C4—441no—
283C22×C4D4×D1111yescharacteristic
284C22×C4D4×D1111yescharacteristic
285C22×C4C2×C22⋊D1111yescharacteristic
286SD16—882no—
287M16—22no—
288M16#432514yescomplemented
289C2×C8—22no—
290C2×C8—222no—
291C2×C8—222no—
292C2×C8—442no—
293C4⋊C4—22no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—22no—
298C4⋊C4—21no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—222no—
304C4⋊C4—221no—
305C4⋊C4—221no—
306C4⋊C4—441no—
307C22⋊C4—41no—
308C22⋊C4—441no—
309C22⋊C4—441no—
310C42—41no—
311C42—442no—
312C42D4×D1111yescharacteristic
313C42#434111yescharacteristic
314C42C2×C22⋊D1111yescharacteristic
315C42C2×C22⋊D1111yescharacteristic
316C11#1020111yescharacteristic, complemented, Sylow
317C23—441no—
318C23#6699311yescharacteristic
319Q8—44no—
320Q8—41no—
321Q8—41no—
322Q8—81no—
323Q8—81no—
324Q8—81no—
325Q8—442no—
326D4—442no—
327D4—441no—
328D4—441no—
329D4—442no—
330D4—881no—
331D4—881no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—82no—
339C2×C4—442no—
340C2×C4—441no—
341C2×C4—881no—
342C2×C4—881no—
343C2×C4—882no—
344C2×C4#6699011yescharacteristic
345C2×C4#6699011yescharacteristic
346C2×C4#6699111yescharacteristic
347C2×C4#6699211yescharacteristic
348C2×C4#6699211yescharacteristic
349C2×C4C2×#432512yes—
350C2×C4#6699512yes—
351C2×C4#6700611yescharacteristic
352C8—24no—
353C8—442no—
354C8—442no—
355C22—21no—
356C22—21no—
357C22—881no—
358C22—881no—
359C22—881no—
360C22#1062269811yescharacteristic
361C22#1062269911yescharacteristic
362C22#1062283611yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—82no—
367C4—81no—
368C4—81no—
369C4—882no—
370C4—881no—
371C4#1062269612yes—
372C4#1062281111yescharacteristic
373C4#1062281411yescharacteristic
374C4#1062284012yes—
375C2—21no—
376C2—21no—
377C2—1761no—
378C2#1306965611yescharacteristic
379C2#1306967411yescharacteristic
380C2#1306969911yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3165C2
socleC22×C11#392
prime radical#10623008C22
hypercenter#3165D11
hypocenterC11#10201
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3165

Complements

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

NH ≅ G/Ntype
3. #13069540C2semidirect
5. #13067115C2semidirect
6. #13066467C2semidirect
7. C11×#3165C2semidirect
98. C11×M16SD16semidirect
129. #3165D11semidirect
288. M16#4325semidirect
316. C11#10201semidirect

Maximal subgroups

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

subgroupindex
#130799282
#130797442
#130695402
#130695352
#130671152
#130664672
C11×#31652
#1020111