Finite Group Databasebeta

← #14655672

Subgroups — #14655672

Order 2816.

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

normal subgroups only

This group has 642 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#13079534C211yesmaximal, characteristic
2#13079073C211yesmaximal, characteristic, complemented
3#13069457C211yesmaximal, characteristic, complemented
4#13067288C211yesmaximal, characteristic, complemented
5#13067068C211yesmaximal, characteristic, complemented
6#13066453C211yesmaximal, characteristic, complemented
7C2×C11×#486C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×#127C2211yescharacteristic
10C2×#66995—22no—
11#10623008C2211yescharacteristic
12C11×#486—22no—
13C11×#486—22no—
14C2×C11×#102—22no—
15C2×C4×C8×C11C2211yescharacteristic
16#10622830—22no—
17C2×#66897—22no—
18#10622705—21no—
19#10622699—22no—
20#10622698—21no—
21#10622686—21no—
22#10622685—22no—
23#10622683—21no—
24#10622538C2211yescharacteristic
25#10622537C2211yescharacteristic
26C4×#4318C2211yescharacteristic
27#10622185—22no—
28#10622097—22no—
29C22×Q8×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11D412yes—
33C2×#4339—21no—
34C22×C8×C11—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8D412yes—
39C11×#127—21no—
40C11×#127—21no—
41C11×#127—21no—
42C11×#127—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C42×C11C2311yescharacteristic
46C2×#4326—24no—
47#66995—44no—
48#66995—44no—
49C2×#4325—24no—
50C2×#4323—24no—
51#66983—21no—
52#66983—21no—
53C2×#4318—21no—
54C2×#4318D412yes—
55#66928—21no—
56#66927D411yescharacteristic
57C4×D44—21no—
58C4×D44—21no—
59#66922D411yescharacteristic
60C11×#102—28no—
61C4×C8×C11—21no—
62C4×C8×C11D412yes—
63#66897—44no—
64#66896—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#10168—111nomaximal, Sylow
73C24×C11—22no—
74C2×Q8×C11—22no—
75C2×Q8×C11—41no—
76C2×Q8×C11—42no—
77C2×Q8×C11—42no—
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—41no—
85C2×D4×C11—42no—
86C2×D4×C11—42no—
87C2×D4×C11—82no—
88C22×C4×C11—41no—
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#4326—48no—
111#4325—48no—
112#4323—84no—
113(C2×D11)⋊C4—41no—
114(C2×D11)⋊C4—41no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117#4318—22no—
118#4318—42no—
119#4318D814yescomplemented
120C2×C11⋊C8—22no—
121C2×C11⋊C8—22no—
122C2×C11⋊C8—41no—
123#3205—111no—
124#3152—111no—
125C2×#486D1111yescharacteristic, complemented
126#1965—111no—
127#1546—111no—
128#1492—111no—
129#1278—111no—
130C23×C11—42no—
131C23×C11—44no—
132C23×C11—82no—
133C23×C11—82no—
134C23×C11#12111yescharacteristic
135C22×D11—41no—
136Q8×C11—44no—
137Q8×C11—81no—
138Q8×C11—81no—
139D4×C11—44no—
140D4×C11—44no—
141D4×C11—82no—
142D4×C11—82no—
143D4×C11—82no—
144D4×C11—81no—
145D4×C11—81no—
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11—42no—
149C2×C4×C11—82no—
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11#12011yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#12711yescharacteristic
156C2×C4×C11C2×D812yes—
157C2×C4×C11AGL(1,ℤ/8)12yes—
158C22⋊D11—82no—
159C2×Dic11—41no—
160D44—42no—
161D44—42no—
162D44—42no—
163C4×D11—81no—
164C4×D11—81no—
165Dic22—42no—
166C8×C11—42no—
167C11⋊C8—24no—
168C11⋊C8—42no—
169C11⋊C8—81no—
170C2×#137—222no—
171#532—111no—
172C2×C4⋊Q8C2×D1111yescharacteristic
173C2×#127C2×D1111yescharacteristic
174#497—222no—
175#494—221no—
176#493—221no—
177#492—221no—
178#486—22no—
179#486—22no—
180#486—221no—
181#459—222no—
182#447—222no—
183#431—111no—
184#423—111no—
185C2×#102—22no—
186C2×#100—222no—
187C4×M16—111no—
188C2×C4×C8C2×D1111yescharacteristic
189#332—222no—
190D4⋊C8—222no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—82no—
194C22×C11—82no—
195C22×C11—82no—
196C22×C11—164no—
197C22×C11#39211yescharacteristic
198C22×C11#45912yes—
199C2×D11—81no—
200C2×D11—81no—
201C2×D11—81no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—82no—
205C4×C11#44712yes—
206C4×C11#45512yes—
207C4×C11#47112yes—
208C4×C11#49311yescharacteristic
209C4×C11#49611yescharacteristic
210Dic11—81no—
211C2×#41—221no—
212C22×Q8—21no—
213C22×D4—21no—
214C22×D4—21no—
215C22×D4C22⋊D1112yes—
216#137—444no—
217#137—444no—
218C2×Q16—224no—
219C2×SD16—224no—
220C2×D8—224no—
221C2×M16—112no—
222C2×M16—221no—
223C22×C8—21no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—111no—
228C4⋊Q8C22⋊D1112yes—
229#127—21no—
230#127—21no—
231#127—21no—
232#127—21no—
233#127—111no—
234#124—221no—
235#121—221no—
236#121—221no—
237C4×D4—221no—
238C4×D4—221no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C42C22×D1111yescharacteristic
242C4⋊C8—112no—
243C4⋊C8—221no—
244C4⋊C8—221no—
245#102—28no—
246#102—224no—
247#100—444no—
248C22⋊C8—221no—
249#97—221no—
250C4×C8—21no—
251C4×C8—221no—
252C4×C8—221no—
253C4×C8C22⋊D1112yes—
254C2×C11—22no—
255C2×C11—162no—
256C2×C11#200411yescharacteristic
257C2×C11#201111yescharacteristic
258C2×C11#201911yescharacteristic
259D11—161no—
260C24—22no—
261#41—442no—
262#41—442no—
263C2×Q8—22no—
264C2×Q8—41no—
265C2×Q8—42no—
266C2×Q8—42no—
267C2×Q8—221no—
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—41no—
277C2×D4—82no—
278C2×D4—221no—
279C2×D4—221no—
280C2×D4—221no—
281C2×D4—441no—
282C22×C4—41no—
283C22×C4—441no—
284C22×C4D4×D1111yescharacteristic
285C22×C4#434111yescharacteristic
286C22×C4C2×C22⋊D1111yescharacteristic
287Q16—448no—
288SD16—448no—
289D8—884no—
290M16—114no—
291M16—222no—
292M16—442no—
293C2×C8—22no—
294C2×C8—42no—
295C2×C8—222no—
296C2×C8—222no—
297C2×C8—441no—
298C4⋊C4—22no—
299C4⋊C4—22no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—221no—
303C4⋊C4—221no—
304C22⋊C4—441no—
305C22⋊C4—441no—
306C42D4×D1111yescharacteristic
307C42D4×D1111yescharacteristic
308C42C2×C22⋊D1111yescharacteristic
309C42C2×C22⋊D1111yescharacteristic
310C11#1016811yescharacteristic, complemented, Sylow
311C23—42no—
312C23—44no—
313C23—82no—
314C23—82no—
315C23—441no—
316C23#6699211yescharacteristic
317Q8—44no—
318Q8—81no—
319Q8—81no—
320Q8—442no—
321D4—44no—
322D4—44no—
323D4—82no—
324D4—81no—
325D4—81no—
326D4—82no—
327D4—82no—
328D4—442no—
329D4—442no—
330D4—442no—
331D4—882no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—42no—
335C2×C4—82no—
336C2×C4—441no—
337C2×C4—881no—
338C2×C4—881no—
339C2×C4D8×D1112yes—
340C2×C4#6696412yes—
341C2×C4#6699011yescharacteristic
342C2×C4#6699011yescharacteristic
343C2×C4#6699111yescharacteristic
344C2×C4#6699211yescharacteristic
345C2×C4#6699311yescharacteristic
346C2×C4#6700611yescharacteristic
347C8—42no—
348C8—224no—
349C8—442no—
350C8—881no—
351C22—21no—
352C22—21no—
353C22—82no—
354C22—82no—
355C22—82no—
356C22—164no—
357C22—881no—
358C22—881no—
359C22—881no—
360C22#1062276312yes—
361C22#1062283611yescharacteristic
362C4—21no—
363C4—21no—
364C4—82no—
365C4—881no—
366C4#1062267412yes—
367C4#1062276411yescharacteristic
368C4#1062276711yescharacteristic
369C4#1062276912yes—
370C4#1062279012yes—
371C2—22no—
372C2—162no—
373C2—1761no—
374C2#1306964511yescharacteristic
375C2#1306968511yescharacteristic
376C2#1306972811yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#486C2
socleC22×C11#392
prime radical#13079534C2
hypercenterC2×#486D11
hypocenterC11#10168
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
2. #13079073C2semidirect
3. #13069457C2semidirect
4. #13067288C2semidirect
5. #13067068C2semidirect
6. #13066453C2semidirect
7. C2×C11×#486C2semidirect
119. #4318D8semidirect
125. C2×#486D11semidirect
310. C11#10168semidirect

Maximal subgroups

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

subgroupindex
#130795342
#130790732
#130694572
#130672882
#130670682
#130664532
C2×C11×#4862
#1016811