Finite Group Databasebeta

← #14655518

Subgroups — #14655518

Order 2816.

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

normal subgroups only

This group has 690 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#13079541C211yesmaximal, characteristic, complemented
2#13079066C211yesmaximal, characteristic
3#13069606C211yesmaximal, characteristic, complemented
4#13067284C211yesmaximal, characteristic, complemented
5#13067068C211yesmaximal, characteristic, complemented
6#13066453C211yesmaximal, characteristic, complemented
7C2×C11×#492C211yesmaximal, characteristic, complemented
8C22×C11×SD16—22no—
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×#127C2211yescharacteristic
11C2×#66985—22no—
12#10623008C2211yescharacteristic
13C11×#492—22no—
14C11×#492—22no—
15C2×C4×C8×C11C2211yescharacteristic
16#10622840—22no—
17#10622698—21no—
18#10622696—22no—
19#10622694—21no—
20#10622689—21no—
21#10622687—22no—
22#10622686—21no—
23#10622538C2211yescharacteristic
24#10622537C2211yescharacteristic
25C4×#4318C2211yescharacteristic
26#10622182—22no—
27#10622168—22no—
28#10622097—22no—
29C22×Q8×C11D412yes—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C2×#4339—21no—
34C2×C11×SD16—28no—
35C2×C11×SD16—48no—
36C22×C8×C11—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×#127—21no—
42C11×#127—21no—
43C11×#127—21no—
44C11×#127D412yes—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C42×C11C2311yescharacteristic
48C2×#4325—24no—
49C2×#4324—24no—
50#66985—44no—
51#66985—44no—
52C2×#4323—24no—
53#66983—21no—
54#66983—21no—
55C2×#4318—21no—
56C2×#4318D412yes—
57#66928—21no—
58#66927D411yescharacteristic
59C4×D44—21no—
60C4×D44—21no—
61#66922D411yescharacteristic
62C4×C8×C11—21no—
63C4×C8×C11D412yes—
64#66899—24no—
65C22⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)D412yes—
69#66867—21no—
70C4×C11⋊C8—21no—
71C4×C11⋊C8—21no—
72#10146—111nomaximal, Sylow
73C24×C11—41no—
74C2×Q8×C11—22no—
75C2×Q8×C11—22no—
76C2×Q8×C11—44no—
77C2×D4×C11—22no—
78C2×D4×C11—22no—
79C2×D4×C11—22no—
80C2×D4×C11—44no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—42no—
85C2×D4×C11—42no—
86C2×D4×C11—82no—
87C22×C4×C11—22no—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11#4111yescharacteristic
91C2×C22⋊D11—41no—
92#4339—42no—
93#4339—42no—
94C2×D44—21no—
95C2×D44—21no—
96C2×D44—21no—
97C2×C4×D11—41no—
98C2×Dic22—21no—
99C11×SD16—416no—
100C2×C8×C11—24no—
101C2×C8×C11—22no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110#4325—84no—
111#4324—48no—
112#4323—48no—
113(C2×D11)⋊C4—41no—
114(C2×D11)⋊C4—41no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117#4318—22no—
118#4318—42no—
119#4318SD1614yescomplemented
120C2×C11⋊C8—22no—
121C2×C11⋊C8—22no—
122C2×C11⋊C8—41no—
123#3206—111no—
124#3151—111no—
125C2×#492D1111yescharacteristic, complemented
126#1997—111no—
127#1545—111no—
128#1492—111no—
129#1278—111no—
130C23×C11—42no—
131C23×C11—82no—
132C23×C11—82no—
133C23×C11—82no—
134C23×C11#12111yescharacteristic
135C22×D11—41no—
136Q8×C11—44no—
137Q8×C11—44no—
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—82no—
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×SD1612yes—
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—24no—
166C11⋊C8—24no—
167C11⋊C8—42no—
168C11⋊C8—81no—
169C2×AGL(1,ℤ/8)—222no—
170C22×SD16—22no—
171#532—111no—
172C2×C4⋊Q8C2×D1111yescharacteristic
173C2×#127C2×D1111yescharacteristic
174#496—222no—
175#493—221no—
176#492—22no—
177#492—22no—
178#492—221no—
179#492—221no—
180#487—221no—
181#461—222no—
182#448—222no—
183#431—111no—
184#423—111no—
185C4×M16—111no—
186C2×C4×C8C2×D1111yescharacteristic
187#343—222no—
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#46012yes—
198C2×D11—81no—
199C2×D11—81no—
200C2×D11—81no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—82no—
204C4×C11#45012yes—
205C4×C11#45312yes—
206C4×C11#47112yes—
207C4×C11#49211yescharacteristic
208C4×C11#49611yescharacteristic
209Dic11—81no—
210C2×#41—221no—
211C22×Q8C22⋊D1112yes—
212C22×D4—21no—
213C22×D4—21no—
214C22×D4—21no—
215AGL(1,ℤ/8)—444no—
216AGL(1,ℤ/8)—444no—
217C2×SD16—28no—
218C2×SD16—48no—
219C2×SD16—224no—
220C2×SD16—224no—
221C2×D8—224no—
222C2×M16—112no—
223C2×M16—221no—
224C22×C8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—111no—
230#127—21no—
231#127—21no—
232#127—21no—
233#127—111no—
234#127C22⋊D1112yes—
235#124—221no—
236#121—221no—
237#121—221no—
238C4×D4—221no—
239C4×D4—221no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C42C22×D1111yescharacteristic
243C4⋊C8—112no—
244C4⋊C8—221no—
245C4⋊C8—221no—
246#103—224no—
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#200211yescharacteristic
256C2×C11#201411yescharacteristic
257C2×C11#201911yescharacteristic
258D11—161no—
259C24—41no—
260#41—442no—
261#41—442no—
262C2×Q8—22no—
263C2×Q8—22no—
264C2×Q8—44no—
265C2×Q8—221no—
266C2×D4—22no—
267C2×D4—22no—
268C2×D4—22no—
269C2×D4—44no—
270C2×D4—42no—
271C2×D4—42no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—82no—
276C2×D4—221no—
277C2×D4—221no—
278C2×D4—221no—
279C2×D4—441no—
280C22×C4—22no—
281C22×C4—441no—
282C22×C4D4×D1111yescharacteristic
283C22×C4#434111yescharacteristic
284C22×C4C2×C22⋊D1111yescharacteristic
285SD16—416no—
286SD16—448no—
287SD16—884no—
288D8—448no—
289M16—114no—
290M16—222no—
291M16—442no—
292C2×C8—24no—
293C2×C8—22no—
294C2×C8—222no—
295C2×C8—222no—
296C2×C8—441no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—221no—
302C4⋊C4—221no—
303C22⋊C4—441no—
304C22⋊C4—441no—
305C42D4×D1111yescharacteristic
306C42D4×D1111yescharacteristic
307C42C2×C22⋊D1111yescharacteristic
308C42C2×C22⋊D1111yescharacteristic
309C11#1014611yescharacteristic, complemented, Sylow
310C23—42no—
311C23—82no—
312C23—82no—
313C23—82no—
314C23—441no—
315C23#6699211yescharacteristic
316Q8—44no—
317Q8—44no—
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—42no—
333C2×C4—82no—
334C2×C4—441no—
335C2×C4—881no—
336C2×C4—881no—
337C2×C4SD16×D1112yes—
338C2×C4#6696712yes—
339C2×C4#6699011yescharacteristic
340C2×C4#6699011yescharacteristic
341C2×C4#6699111yescharacteristic
342C2×C4#6699211yescharacteristic
343C2×C4#6699311yescharacteristic
344C2×C4#6700611yescharacteristic
345C8—24no—
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#1062277612yes—
359C22#1062283611yescharacteristic
360C4—21no—
361C4—21no—
362C4—82no—
363C4—881no—
364C4#1062269012yes—
365C4#1062278212yes—
366C4#1062278811yescharacteristic
367C4#1062278911yescharacteristic
368C4#1062279012yes—
369C2—22no—
370C2—162no—
371C2—1761no—
372C2#1306963111yescharacteristic
373C2#1306970211yescharacteristic
374C2#1306972811yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#492C2
socleC22×C11#392
prime radical#13079066C2
hypercenterC2×#492D11
hypocenterC11#10146
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#492

Complements

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

NH ≅ G/Ntype
1. #13079541C2semidirect
3. #13069606C2semidirect
4. #13067284C2semidirect
5. #13067068C2semidirect
6. #13066453C2semidirect
7. C2×C11×#492C2semidirect
119. #4318SD16semidirect
125. C2×#492D11semidirect
309. C11#10146semidirect

Maximal subgroups

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

subgroupindex
#130795412
#130790662
#130696062
#130672842
#130670682
#130664532
C2×C11×#4922
#1014611