Finite Group Databasebeta

← #14655546

Subgroups — #14655546

Order 2816.

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

normal subgroups only

This group has 630 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#13079737C211yesmaximal, characteristic, complemented
2#13079066C211yesmaximal, characteristic
3#13069461C211yesmaximal, characteristic, complemented
4#13067284C211yesmaximal, characteristic, complemented
5#13067068C211yesmaximal, characteristic, complemented
6#13066453C211yesmaximal, characteristic, complemented
7C2×C11×#486C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×#127C2211yescharacteristic
10C2×#66985—22no—
11#10623008C2211yescharacteristic
12C11×#486—22no—
13C11×#486—22no—
14C2×C11×#102—22no—
15C2×C4×C8×C11C2211yescharacteristic
16C2×#66900—22no—
17#10622701—21no—
18#10622700—22no—
19#10622691—21no—
20#10622689—21no—
21#10622687—22no—
22#10622686—21no—
23#10622580—22no—
24#10622538C2211yescharacteristic
25#10622537C2211yescharacteristic
26C4×#4318C2211yescharacteristic
27#10622182—22no—
28#10622097—22no—
29C22×Q8×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C2×#4339—21no—
34C22×C8×C11—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×#127—21no—
40C11×#127—21no—
41C11×#127—21no—
42C11×#127D412yes—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4D412yes—
45C2×C42×C11C2311yescharacteristic
46C2×#4324—24no—
47#66985—44no—
48#66985—44no—
49C2×#4323—24no—
50#66983—21no—
51#66983—21no—
52C2×#4318—21no—
53C2×#4318D412yes—
54#66928—21no—
55#66927D411yescharacteristic
56C4×D44—21no—
57C4×D44—21no—
58#66922D411yescharacteristic
59C11×#102—28no—
60C4×C8×C11—21no—
61C4×C8×C11D412yes—
62#66900—44no—
63C22⋊(C11⋊C8)—21no—
64#66873—24no—
65#66871—24no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)D412yes—
69#66867—21no—
70C4×C11⋊C8—21no—
71C4×C11⋊C8—21no—
72#10150—111nomaximal, Sylow
73C24×C11—41no—
74C2×Q8×C11—41no—
75C2×Q8×C11—41no—
76C2×Q8×C11—42no—
77C2×Q8×C11—42no—
78C2×D4×C11—22no—
79C2×D4×C11—22no—
80C2×D4×C11—22no—
81C2×D4×C11—44no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—42no—
86C2×D4×C11—42no—
87C2×D4×C11—82no—
88C22×C4×C11—22no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C2×C22⋊D11—41no—
93#4339—42no—
94#4339—42no—
95C2×D44—21no—
96C2×D44—21no—
97C2×D44—21no—
98C2×C4×D11—41no—
99C2×Dic22—21no—
100C2×C8×C11—22no—
101C2×C8×C11—42no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110#4324—48no—
111#4323—48no—
112(C2×D11)⋊C4—41no—
113(C2×D11)⋊C4—41no—
114C4⋊Dic11—21no—
115C4⋊Dic11—21no—
116#4318—22no—
117#4318—42no—
118#4318D814yes—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—41no—
122#3226—111no—
123#3151—111no—
124C2×#486D1111yescharacteristic, complemented
125#1966—111no—
126#1545—111no—
127#1492—111no—
128#1278—111no—
129C23×C11—42no—
130C23×C11—82no—
131C23×C11—82no—
132C23×C11—82no—
133C23×C11#12111yescharacteristic
134C22×D11—41no—
135Q8×C11—82no—
136Q8×C11—81no—
137Q8×C11—81no—
138D4×C11—44no—
139D4×C11—44no—
140D4×C11—82no—
141D4×C11—82no—
142D4×C11—82no—
143D4×C11—81no—
144D4×C11—81no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—42no—
148C2×C4×C11—44no—
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12711yescharacteristic
155C2×C4×C11C2×D812yes—
156C2×C4×C11AGL(1,ℤ/8)12yes—
157C22⋊D11—82no—
158C2×Dic11—41no—
159D44—42no—
160D44—42no—
161D44—42no—
162C4×D11—81no—
163C4×D11—81no—
164Dic22—42no—
165C8×C11—42no—
166C11⋊C8—24no—
167C11⋊C8—42no—
168C11⋊C8—81no—
169C2×AGL(1,ℤ/8)—222no—
170#532—111no—
171C2×C4⋊Q8C2×D1111yescharacteristic
172C2×#127C2×D1111yescharacteristic
173#500—221no—
174#496—222no—
175#493—221no—
176#492—221no—
177#486—22no—
178#486—22no—
179#486—221no—
180#480—222no—
181#474—222no—
182#431—111no—
183#423—111no—
184C2×#102—22no—
185C2×#101—222no—
186C4×M16—111no—
187C2×C4×C8C2×D1111yescharacteristic
188#331—222no—
189D4⋊C8—222no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—82no—
193C22×C11—82no—
194C22×C11—82no—
195C22×C11—164no—
196C22×C11#39211yescharacteristic
197C22×C11#45912yes—
198C2×D11—81no—
199C2×D11—81no—
200C2×D11—81no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—82no—
204C4×C11#44712yes—
205C4×C11#45412yes—
206C4×C11#47112yes—
207C4×C11#49311yescharacteristic
208C4×C11#49611yescharacteristic
209Dic11—81no—
210C2×#41—221no—
211C22×Q8—21no—
212C22×D4—21no—
213C22×D4—21no—
214C22×D4—21no—
215AGL(1,ℤ/8)—444no—
216AGL(1,ℤ/8)—444no—
217C2×SD16—224no—
218C2×D8—224no—
219C2×M16—112no—
220C2×M16—221no—
221C22×C8—21no—
222C4⋊Q8—21no—
223C4⋊Q8—21no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—111no—
227#127—21no—
228#127—21no—
229#127—21no—
230#127—111no—
231#127C22⋊D1112yes—
232#124—221no—
233#121—221no—
234#121—221no—
235C4×D4—221no—
236C4×D4—221no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4C22⋊D1112yes—
239C2×C42C22×D1111yescharacteristic
240#107—224no—
241C4⋊C8—112no—
242C4⋊C8—221no—
243C4⋊C8—221no—
244#102—28no—
245#102—224no—
246#101—444no—
247C22⋊C8—221no—
248#97—221no—
249C4×C8—21no—
250C4×C8—221no—
251C4×C8—221no—
252C4×C8C22⋊D1112yes—
253C2×C11—22no—
254C2×C11—162no—
255C2×C11#200311yescharacteristic
256C2×C11#201111yescharacteristic
257C2×C11#201911yescharacteristic
258D11—161no—
259C24—41no—
260#41—442no—
261#41—442no—
262C2×Q8—42no—
263C2×Q8—42no—
264C2×Q8—41no—
265C2×Q8—41no—
266C2×Q8—221no—
267C2×D4—22no—
268C2×D4—22no—
269C2×D4—22no—
270C2×D4—44no—
271C2×D4—42no—
272C2×D4—42no—
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—441no—
283C22×C4D4×D1111yescharacteristic
284C22×C4#434111yescharacteristic
285C22×C4C2×C22⋊D1111yescharacteristic
286SD16—448no—
287D8—448no—
288M16—114no—
289M16—222no—
290M16—442no—
291C2×C8—22no—
292C2×C8—42no—
293C2×C8—222no—
294C2×C8—222no—
295C2×C8—441no—
296C4⋊C4—22no—
297C4⋊C4—22no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—221no—
301C4⋊C4—221no—
302C22⋊C4—441no—
303C22⋊C4—441no—
304C42D4×D1111yescharacteristic
305C42D4×D1111yescharacteristic
306C42C2×C22⋊D1111yescharacteristic
307C42C2×C22⋊D1111yescharacteristic
308C11#1015011yescharacteristic, complemented, Sylow
309C23—42no—
310C23—82no—
311C23—82no—
312C23—82no—
313C23—441no—
314C23#6699211yescharacteristic
315Q8—81no—
316Q8—81no—
317Q8—82no—
318Q8—442no—
319D4—44no—
320D4—44no—
321D4—82no—
322D4—81no—
323D4—81no—
324D4—82no—
325D4—82no—
326D4—442no—
327D4—442no—
328D4—442no—
329D4—882no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—44no—
333C2×C4—42no—
334C2×C4—441no—
335C2×C4—881no—
336C2×C4—881no—
337C2×C4D8×D1112yes—
338C2×C4#6696412yes—
339C2×C4#6699011yescharacteristic
340C2×C4#6699011yescharacteristic
341C2×C4#6699111yescharacteristic
342C2×C4#6699211yescharacteristic
343C2×C4#6699311yescharacteristic
344C2×C4#6700611yescharacteristic
345C8—42no—
346C8—224no—
347C8—442no—
348C8—881no—
349C22—21no—
350C22—21no—
351C22—82no—
352C22—82no—
353C22—82no—
354C22—164no—
355C22—881no—
356C22—881no—
357C22—881no—
358C22#1062276312yes—
359C22#1062283611yescharacteristic
360C4—21no—
361C4—21no—
362C4—82no—
363C4—881no—
364C4#1062267512yes—
365C4#1062276411yescharacteristic
366C4#1062276711yescharacteristic
367C4#1062276912yes—
368C4#1062279012yes—
369C2—22no—
370C2—162no—
371C2—1761no—
372C2#1306963811yescharacteristic
373C2#1306968511yescharacteristic
374C2#1306972811yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#486C2
socleC22×C11#392
prime radical#13079066C2
hypercenterC2×#486D11
hypocenterC11#10150
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#486

Complements

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

NH ≅ G/Ntype
1. #13079737C2semidirect
3. #13069461C2semidirect
4. #13067284C2semidirect
5. #13067068C2semidirect
6. #13066453C2semidirect
7. C2×C11×#486C2semidirect
124. C2×#486D11semidirect
308. C11#10150semidirect

Maximal subgroups

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

subgroupindex
#130797372
#130790662
#130694612
#130672842
#130670682
#130664532
C2×C11×#4862
#1015011