Finite Group Databasebeta

← #14655932

Subgroups — #14655932

Order 2816.

512 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 101 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#13079737C211yesmaximal, characteristic
3#13069569C211yesmaximal, characteristic, complemented
4#13069535C211yesmaximal, characteristic
5#13067115C211yesmaximal, characteristic, complemented
6#13066467C211yesmaximal, characteristic, complemented
7C11×#3139C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10#10623008C2211yescharacteristic
11C11×#491—22no—
12C11×#487—21no—
13C11×#487—21no—
14C11×#419—22no—
15C4×C11×M16C2211yescharacteristic
16C2×#66889—22no—
17#10622701—21no—
18#10622700—22no—
19#10622697—21no—
20#10622696—21no—
21#10622691—21no—
22#10622661—22no—
23#10622640—21no—
24#10622633—21no—
25#10622580—22no—
26C4×C4⋊Dic11C2211yescharacteristic
27#10622538C2211yescharacteristic
28C2×C4⋊(C11⋊C8)C2211yescharacteristic
29#10622176—22no—
30#10622167—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⋊Q8D412yes—
38C11×C4⋊Q8D411yescharacteristic
39C11×C4⋊Q8D411yescharacteristic
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×#103—24no—
61C11×#103—24no—
62C11×#97—21no—
63C4×C8×C11—21no—
64#66899—22no—
65C11⋊#95—21no—
66C22⋊(C11⋊C8)D412yes—
67#66889—44no—
68#66873—24no—
69#66873—22no—
70#66872—22no—
71#66871—24no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
75C4×C11⋊C8—21no—
76#10205—111nomaximal, Sylow
77C2×Q8×C11—21no—
78C2×Q8×C11—22no—
79C2×Q8×C11—21no—
80C2×Q8×C11—41no—
81C2×Q8×C11—42no—
82C2×Q8×C11—42no—
83C22×C4×C11—41no—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C2×C22⋊D11—41no—
88C22×Dic11—41no—
89#4339—42no—
90#4339—42no—
91C2×D44—21no—
92C2×D44—21no—
93C2×D44—21no—
94C2×C4×D11—41no—
95C2×Dic22—21no—
96C11×M16—22no—
97C11×M16—22no—
98C2×C8×C11—22no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C22⋊C4—41no—
110C42×C11—41no—
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11#4111yescharacteristic
115#4325—82no—
116(C2×D11)⋊C4—41no—
117(C2×D11)⋊C4—41no—
118C4⋊Dic11—22no—
119C4⋊Dic11—21no—
120C4⋊Dic11—21no—
121C4⋊Dic11—41no—
122C4×Dic11—42no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—42no—
126#3246—111no—
127#3226—111no—
128#3139D1111yescharacteristic, complemented
129#1988—111no—
130#1980—111no—
131#1503—111no—
132#1283—111no—
133C23×C11#12711yescharacteristic
134C22×D11—41no—
135Q8×C11—44no—
136Q8×C11—41no—
137Q8×C11—41no—
138Q8×C11—81no—
139Q8×C11—82no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—42no—
146C2×C4×C11—81no—
147C2×C4×C11—81no—
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#13512yes—
155C2×C4×C11AGL(1,ℤ/8)12yes—
156C22⋊D11—81no—
157C22⋊D11—81no—
158C2×Dic11—42no—
159C2×Dic11—41no—
160C2×Dic11—81no—
161C2×Dic11—81no—
162D44—42no—
163D44—41no—
164D44—41no—
165D44—42no—
166C4×D11—82no—
167Dic22—42no—
168C8×C11—42no—
169C11⋊C8—42no—
170C11⋊C8—42no—
171#533C2×D1111yescharacteristic
172#532—111no—
173C2×C4⋊Q8C2×D1111yescharacteristic
174#500—221no—
175#491—22no—
176#487—21no—
177#487—21no—
178#486—221no—
179#480—222no—
180#476—221no—
181#475—221no—
182#474—222no—
183#465—222no—
184#461—221no—
185#460—221no—
186#431—111no—
187C2×C4⋊C8—111no—
188C2×#104—222no—
189#419—22no—
190C4×M16C2×D1111yescharacteristic
191C4×C4⋊C4—111no—
192#340—222no—
193#328—222no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11#39211yescharacteristic
197C22×C11#49511yescharacteristic
198C22×C11#49611yescharacteristic
199C2×D11—81no—
200C2×D11—81no—
201C2×D11—81no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—81no—
206C4×C11—81no—
207C4×C11—82no—
208C4×C11#44912yes—
209C4×C11#45511yescharacteristic
210C4×C11#45611yescharacteristic
211C4×C11#46312yes—
212Dic11—82no—
213Dic11—81no—
214C2×#41—221no—
215C22×Q8—21no—
216C2×SD16—222no—
217C2×M16C22⋊D1112yes—
218C22×C8—112no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—111no—
223C4⋊Q8C22⋊D1112yes—
224C4⋊Q8C22⋊D1111yescharacteristic
225C4⋊Q8C22⋊D1111yescharacteristic
226#127—111no—
227#125—21no—
228#124—221no—
229C22⋊Q8—21no—
230C22⋊Q8—21no—
231#121—221no—
232#121—221no—
233C4×Q8—21no—
234C4×Q8—21no—
235C4×D4—221no—
236C4×D4—221no—
237#117—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—221no—
241C2×C42—221no—
242C2×C42C22×D1111yescharacteristic
243#107—224no—
244#106—222no—
245C4⋊C8—221no—
246C4⋊C8—221no—
247C4⋊C8—221no—
248#104—444no—
249#103—24no—
250#103—24no—
251#103—222no—
252#102—222no—
253#102—224no—
254C22⋊C8—112no—
255#97—21no—
256C4×C8—21no—
257C4×C8—221no—
258#95—221no—
259C2×C11—21no—
260C2×C11—21no—
261C2×C11#200711yescharacteristic
262C2×C11#200911yescharacteristic
263C2×C11#201211yescharacteristic
264D11—161no—
265#41—442no—
266#41—442no—
267C2×Q8—21no—
268C2×Q8—21no—
269C2×Q8—22no—
270C2×Q8—41no—
271C2×Q8—42no—
272C2×Q8—42no—
273C2×Q8—221no—
274C2×D4—221no—
275C2×D4—221no—
276C2×D4—221no—
277C2×D4—441no—
278C22×C4—41no—
279C22×C4—441no—
280C22×C4—441no—
281C22×C4D4×D1111yescharacteristic
282C22×C4D4×D1111yescharacteristic
283C22×C4C2×C22⋊D1111yescharacteristic
284SD16—882no—
285M16—22no—
286M16—22no—
287C2×C8—22no—
288C2×C8—222no—
289C2×C8—222no—
290C2×C8—442no—
291C4⋊C4—21no—
292C4⋊C4—22no—
293C4⋊C4—22no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—222no—
302C4⋊C4—221no—
303C4⋊C4—221no—
304C4⋊C4—441no—
305C22⋊C4—41no—
306C22⋊C4—441no—
307C22⋊C4—441no—
308C42—41no—
309C42—442no—
310C42D4×D1111yescharacteristic
311C42#434111yescharacteristic
312C42C2×C22⋊D1111yescharacteristic
313C42C2×C22⋊D1111yescharacteristic
314C11#1020511yescharacteristic, complemented, Sylow
315C23—441no—
316C23#6699311yescharacteristic
317Q8—41no—
318Q8—41no—
319Q8—44no—
320Q8—81no—
321Q8—82no—
322Q8—442no—
323D4—442no—
324D4—441no—
325D4—441no—
326D4—442no—
327D4—881no—
328D4—881no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—442no—
338C2×C4—441no—
339C2×C4—881no—
340C2×C4—881no—
341C2×C4—882no—
342C2×C4#6699011yescharacteristic
343C2×C4#6699011yescharacteristic
344C2×C4#6699111yescharacteristic
345C2×C4#6699211yescharacteristic
346C2×C4#6699211yescharacteristic
347C2×C4#6700212yes—
348C2×C4#6700312yes—
349C2×C4#6700611yescharacteristic
350C8—42no—
351C8—442no—
352C8—442no—
353C22—21no—
354C22—21no—
355C22—881no—
356C22—881no—
357C22—881no—
358C22#1062267111yescharacteristic
359C22#1062267211yescharacteristic
360C22#1062283611yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—81no—
365C4—81no—
366C4—82no—
367C4—882no—
368C4—881no—
369C4#1062267012yes—
370C4#1062281511yescharacteristic
371C4#1062281811yescharacteristic
372C4#1062285112yes—
373C2—21no—
374C2—21no—
375C2—1761no—
376C2#1306966111yescharacteristic
377C2#1306967411yescharacteristic
378C2#1306969311yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3139C2
socleC22×C11#392
prime radical#10623008C22
hypercenter#3139D11
hypocenterC11#10205
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3139

Complements

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

NH ≅ G/Ntype
3. #13069569C2semidirect
5. #13067115C2semidirect
6. #13066467C2semidirect
7. C11×#3139C2semidirect
128. #3139D11semidirect
314. C11#10205semidirect

Maximal subgroups

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

subgroupindex
#130799282
#130797372
#130695692
#130695352
#130671152
#130664672
C11×#31392
#1020511