Finite Group Databasebeta

← #14655122

Subgroups — #14655122

Order 2816.

628 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 85 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#13079806C211yesmaximal, characteristic, complemented
2#13079066C211yesmaximal, characteristic
3#13067330C211yesmaximal, characteristic, complemented
4#13067218C211yesmaximal, characteristic, complemented
5#13067123C211yesmaximal, characteristic, complemented
6#13066509C211yesmaximal, characteristic, complemented
7C11×#2641C211yesmaximal, characteristic, complemented
8C2×C11×#127C2211yescharacteristic
9C2×C11×#125C2211yescharacteristic
10C2×#66985—22no—
11#10623008C2211yescharacteristic
12C11×#394—22no—
13C11×#394—22no—
14C11×#390—21no—
15C11×#390—21no—
16C11×#376C2211yescharacteristic
17#10622689—21no—
18#10622687—22no—
19#10622686—21no—
20#10622680—21no—
21#10622679—22no—
22#10622678—21no—
23#10622581—21no—
24#10622580—21no—
25#10622539C2211yescharacteristic
26#10622539C2211yescharacteristic
27C4×#4318C2211yescharacteristic
28#10622182—22no—
29#10622181—22no—
30#10622089—22no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11D412yes—
34C2×#4339—21no—
35C11×#127—21no—
36C11×#127—21no—
37C11×#127—21no—
38C11×#127—21no—
39C11×#125—21no—
40C11×#125—21no—
41C11×#125—21no—
42C11×#125—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4D411yescharacteristic
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C11×C22⋊C4—24no—
48C2×C11×C22⋊C4—24no—
49C2×C42×C11—21no—
50C2×C42×C11C2311yescharacteristic
51C2×#4324—24no—
52#66985—48no—
53C2×#4323—24no—
54#66983—21no—
55#66983—21no—
56C2×#4318—21no—
57#66928—21no—
58#66927D411yescharacteristic
59C4×D44—21no—
60C4×D44—21no—
61#66922D411yescharacteristic
62C11×#95—21no—
63C11×#95D412yes—
64C22⋊(C11⋊C8)—21no—
65C22⋊(C11⋊C8)—21no—
66#66873—22no—
67#66873—22no—
68#66872—22no—
69#66871—22no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)D412yes—
72#66867—21no—
73#66867—21no—
74#66867D412yes—
75C4×C11⋊C8—21no—
76#10089—111nomaximal, Sylow
77C24×C11—22no—
78C2×D4×C11—22no—
79C2×D4×C11—22no—
80C2×D4×C11—44no—
81C2×D4×C11—44no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—82no—
87C22×C4×C11—22no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C2×C22⋊D11—41no—
94#4339—44no—
95C2×D44—21no—
96C2×D44—21no—
97C2×D44—21no—
98C2×C4×D11—41no—
99C2×Dic22—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C22⋊C4—84no—
109C11×C22⋊C4—84no—
110C42×C11—42no—
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11#4111yescharacteristic
115#4324—48no—
116#4323—48no—
117(C2×D11)⋊C4—41no—
118(C2×D11)⋊C4—41no—
119C4⋊Dic11—21no—
120C4⋊Dic11—21no—
121#4318—24no—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—41no—
125#3234—111no—
126#3151—111no—
127#2641D1111yescharacteristic, complemented
128#1555—111no—
129#1528—111no—
130#1505—111no—
131#1300—111no—
132C23×C11—44no—
133C23×C11—44no—
134C23×C11—42no—
135C23×C11—44no—
136C23×C11#12011yescharacteristic
137C22×D11—41no—
138D4×C11—44no—
139D4×C11—82no—
140D4×C11—82no—
141D4×C11—82no—
142D4×C11—82no—
143D4×C11—82no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—41no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11#12011yescharacteristic
155C2×C4×C11#12011yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11#12711yescharacteristic
160C22⋊D11—82no—
161C2×Dic11—41no—
162D44—42no—
163D44—42no—
164D44—81no—
165C4×D11—82no—
166Dic22—42no—
167C11⋊C8—24no—
168C11⋊C8—42no—
169C11⋊C8—81no—
170C2×AGL(1,ℤ/8)—222no—
171#532—111no—
172C2×#127C2×D1111yescharacteristic
173C2×#125C2×D1111yescharacteristic
174#501—221no—
175#496—222no—
176#493—221no—
177#492—221no—
178#490—221no—
179#481—221no—
180#480—221no—
181#478—222no—
182#432—111no—
183#432—111no—
184C4×M16—111no—
185#394—22no—
186#394—22no—
187#390—21no—
188#390—21no—
189#376C2×D1111yescharacteristic
190#331—222no—
191#330—222no—
192#327—222no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—88no—
196C22×C11—82no—
197C22×C11—82no—
198C22×C11—82no—
199C22×C11#39211yescharacteristic
200C22×C11#45312yes—
201C2×D11—81no—
202C2×D11—81no—
203C2×D11—81no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—82no—
210C4×C11—81no—
211C4×C11—81no—
212C4×C11#45412yes—
213Dic11—81no—
214C2×#41—221no—
215C22×D4—21no—
216C22×D4—21no—
217C22×D4C22⋊D1112yes—
218AGL(1,ℤ/8)—448no—
219C2×SD16—224no—
220C2×D8—224no—
221C2×M16—221no—
222C4⋊Q8—111no—
223#127—21no—
224#127—21no—
225#127—21no—
226#127—21no—
227#127—111no—
228#125—21no—
229#125—21no—
230#125—21no—
231#125—21no—
232#124—221no—
233#121—221no—
234#121—221no—
235C4×D4—221no—
236C4×D4—221no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4C22⋊D1111yescharacteristic
240C2×C4⋊C4C22⋊D1111yescharacteristic
241C2×C22⋊C4—24no—
242C2×C22⋊C4—24no—
243C2×C42—21no—
244C2×C42C22×D1111yescharacteristic
245#107—222no—
246#106—222no—
247C4⋊C8—112no—
248C4⋊C8—221no—
249#102—222no—
250#102—222no—
251C22⋊C8—221no—
252C22⋊C8—221no—
253#97—112no—
254#97—221no—
255#97—221no—
256C4×C8—221no—
257#95—21no—
258#95C22⋊D1112yes—
259C2×C11—22no—
260C2×C11—162no—
261C2×C11#200211yescharacteristic
262C2×C11#200311yescharacteristic
263C2×C11#200811yescharacteristic
264D11—161no—
265C24—22no—
266#41—444no—
267C2×Q8—221no—
268C2×D4—22no—
269C2×D4—22no—
270C2×D4—44no—
271C2×D4—44no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—82no—
277C2×D4—221no—
278C2×D4—221no—
279C2×D4—221no—
280C2×D4—441no—
281C22×C4—22no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—441no—
285C22×C4C2×C22⋊D1111yescharacteristic
286C22×C4C2×C22⋊D1111yescharacteristic
287C22×C4C2×C22⋊D1111yescharacteristic
288SD16—448no—
289D8—448no—
290M16—224no—
291C2×C8—222no—
292C2×C8—222no—
293C2×C8—441no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—221no—
303C4⋊C4—221no—
304C22⋊C4—84no—
305C22⋊C4—84no—
306C22⋊C4—441no—
307C22⋊C4—441no—
308C42—42no—
309C42D4×D1111yescharacteristic
310C42D4×D1111yescharacteristic
311C42D4×D1111yescharacteristic
312C42#434111yescharacteristic
313C11#1008911yescharacteristic, complemented, Sylow
314C23—44no—
315C23—44no—
316C23—42no—
317C23—44no—
318C23—441no—
319C23#6700611yescharacteristic
320Q8—442no—
321D4—44no—
322D4—82no—
323D4—82no—
324D4—82no—
325D4—82no—
326D4—82no—
327D4—442no—
328D4—442no—
329D4—881no—
330D4—882no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—441no—
342C2×C4—882no—
343C2×C4#6699011yescharacteristic
344C2×C4#6699011yescharacteristic
345C2×C4#6699111yescharacteristic
346C2×C4#6699211yescharacteristic
347C2×C4#6699211yescharacteristic
348C2×C4#6699311yescharacteristic
349C8—224no—
350C8—442no—
351C8—881no—
352C22—21no—
353C22—21no—
354C22—88no—
355C22—82no—
356C22—82no—
357C22—82no—
358C22—881no—
359C22—881no—
360C22—881no—
361C22#1062283611yescharacteristic
362C22#1062285412yes—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—82no—
369C4—81no—
370C4—81no—
371C4—881no—
372C4#1062267512yes—
373C2—22no—
374C2—162no—
375C2—1761no—
376C2#1306962911yescharacteristic
377C2#1306963811yescharacteristic
378C2#1306966911yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2641C2
socleC22×C11#392
prime radical#13079066C2
hypercenter#2641D11
hypocenterC11#10089
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2641

Complements

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

NH ≅ G/Ntype
1. #13079806C2semidirect
3. #13067330C2semidirect
4. #13067218C2semidirect
5. #13067123C2semidirect
6. #13066509C2semidirect
7. C11×#2641C2semidirect
127. #2641D11semidirect
313. C11#10089semidirect

Maximal subgroups

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

subgroupindex
#130798062
#130790662
#130673302
#130672182
#130671232
#130665092
C11×#26412
#1008911