Finite Group Databasebeta

← #14655537

Subgroups — #14655537

Order 2816.

614 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 614 conjugacy classes of subgroups — too many to draw. Only its 107 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#13079741C211yesmaximal, characteristic, complemented
2#13079069C211yesmaximal, characteristic
3C2×#10622307C211yesmaximal, characteristic, complemented
4#13069604C211yesmaximal, characteristic, complemented
5#13067285C211yesmaximal, characteristic, complemented
6#13066453C211yesmaximal, characteristic, complemented
7C11×#1492C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×#67002—22no—
10C2×#66927C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C2×C4×C8×C11C2211yescharacteristic
14C2×#66885—22no—
15#10622698—21no—
16#10622692—21no—
17#10622686—21no—
18#10622683—21no—
19#10622671—22no—
20#10622647—22no—
21#10622621—22no—
22#10622538C2211yescharacteristic
23C4×#4318C2211yescharacteristic
24#10622307—22no—
25#10622307—22no—
26C11×D4⋊C8—22no—
27#10622192—22no—
28#10622123—22no—
29C2×C11×#41—21no—
30C22×D44—21no—
31C22×D44—21no—
32C22×D44—21no—
33C22×Dic22—21no—
34C2×C11×M16—21no—
35C22×C8×C11—21no—
36C11×C4⋊Q8D411yescharacteristic
37C11×#127D411yescharacteristic
38C11×#124—21no—
39C11×#121—21no—
40C11×#121—21no—
41C4×D4×C11—21no—
42C4×D4×C11—21no—
43C2×C42×C11C2311yescharacteristic
44#67002—44no—
45#67002—44no—
46C2×#4325—24no—
47C2×#4323—24no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11D412yes—
50C2×#4318D412yes—
51#66927—21no—
52#66927—21no—
53#66927—21no—
54#66927D412yes—
55#66922—21no—
56#66922—21no—
57#66922—21no—
58#66922—21no—
59C11×C4⋊C8—21no—
60C11×C4⋊C8—21no—
61C4×C8×C11—21no—
62C4×C8×C11D412yes—
63#66896—24no—
64C22⋊(C11⋊C8)—21no—
65#66885—28no—
66#66872—24no—
67C4⋊(C11⋊C8)D412yes—
68#66867—21no—
69C4×C11⋊C8—21no—
70C4×C11⋊C8—21no—
71#10148—111nomaximal, Sylow
72C23×D11—41no—
73C11×#41—42no—
74C11×#41—42no—
75C2×Q8×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11—41no—
80C22×C4×C11—41no—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11#4111yescharacteristic
84C22×Dic11—22no—
85C2×D44—22no—
86C2×D44—22no—
87C2×D44—22no—
88C2×D44—44no—
89C2×D44—41no—
90C2×D44—41no—
91C2×D44—41no—
92C2×D44—42no—
93C2×D44—42no—
94C2×D44—82no—
95C2×Dic22—41no—
96C2×Dic22—41no—
97C2×Dic22—82no—
98C11×M16—42no—
99C2×C8×C11—22no—
100C2×C8×C11—42no—
101C2×C8×C11—41no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110#4325—48no—
111#4323—48no—
112C4⋊Dic11—22no—
113C4⋊Dic11—22no—
114C4⋊Dic11—41no—
115C4⋊Dic11—41no—
116#4318—22no—
117#4318SD1614yes—
118C2×C11⋊C8—22no—
119C2×C11⋊C8—22no—
120#3227—111no—
121#3151—111no—
122C2×#486—111no—
123#1997—111no—
124#1545—111no—
125#1492D1111yescharacteristic, complemented
126#1278—111no—
127C23×C11—41no—
128C23×C11#12111yescharacteristic
129C22×D11—42no—
130C22×D11—82no—
131C22×D11—82no—
132C22×D11—82no—
133Q8×C11—42no—
134D4×C11—42no—
135D4×C11—42no—
136D4×C11—42no—
137D4×C11—82no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—41no—
141C2×C4×C11—81no—
142C2×C4×C11—81no—
143C2×C4×C11#12011yescharacteristic
144C2×C4×C11#12011yescharacteristic
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12711yescharacteristic
149C2×C4×C11C2×SD1612yes—
150C2×C4×C11AGL(1,ℤ/8)12yes—
151C2×Dic11—42no—
152C2×Dic11—82no—
153D44—44no—
154D44—44no—
155D44—82no—
156D44—82no—
157D44—82no—
158D44—81no—
159D44—81no—
160Dic22—82no—
161Dic22—82no—
162C8×C11—42no—
163C8×C11—81no—
164C11⋊C8—24no—
165C11⋊C8—42no—
166C2×AGL(1,ℤ/8)—222no—
167#532C2×D1111yescharacteristic
168C2×C4⋊Q8—111no—
169C2×#127—111no—
170#498—221no—
171#496—222no—
172#493—221no—
173#492—221no—
174#486—222no—
175#486—221no—
176#486—222no—
177#481—222no—
178#476—222no—
179#431—111no—
180#423C2×D1111yescharacteristic
181C2×#102—222no—
182C4×M16—111no—
183C2×C4×C8C2×D1111yescharacteristic
184#343—222no—
185#331—222no—
186D4⋊C8—22no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—81no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11#39211yescharacteristic
193C22×C11#46012yes—
194C2×D11—82no—
195C2×D11—82no—
196C2×D11—82no—
197C2×D11—164no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—81no—
201C4×C11#45012yes—
202C4×C11#45412yes—
203C4×C11#47212yes—
204C4×C11#49211yescharacteristic
205C4×C11#49611yescharacteristic
206Dic11—82no—
207C2×#41—21no—
208C22×Q8—221no—
209C22×D4—221no—
210C22×D4—221no—
211C22×D4—221no—
212AGL(1,ℤ/8)—444no—
213AGL(1,ℤ/8)—444no—
214C2×SD16—224no—
215C2×D8—224no—
216C2×M16—21no—
217C2×M16—112no—
218C22×C8—21no—
219C4⋊Q8—221no—
220C4⋊Q8—221no—
221C4⋊Q8—221no—
222C4⋊Q8—221no—
223C4⋊Q8D4411yescharacteristic
224#127—112no—
225#127—221no—
226#127—221no—
227#127—221no—
228#127D4411yescharacteristic
229#124—21no—
230#121—21no—
231#121—21no—
232C4×D4—21no—
233C4×D4—21no—
234C2×C4⋊C4—112no—
235C2×C4⋊C4—221no—
236C2×C42C22×D1111yescharacteristic
237#106—224no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8—112no—
241#102—228no—
242#102—224no—
243C22⋊C8—221no—
244#97—221no—
245C4×C8—21no—
246C4×C8—221no—
247C4×C8—221no—
248C4×C8C22⋊D1112yes—
249C2×C11—22no—
250C2×C11—161no—
251C2×C11#200311yescharacteristic
252C2×C11#201411yescharacteristic
253C2×C11#201811yescharacteristic
254D11—162no—
255C24—441no—
256#41—42no—
257#41—42no—
258C2×Q8—21no—
259C2×Q8—441no—
260C2×Q8—441no—
261C2×Q8—882no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—41no—
266C2×D4—222no—
267C2×D4—222no—
268C2×D4—222no—
269C2×D4—444no—
270C2×D4—441no—
271C2×D4—442no—
272C2×D4—442no—
273C2×D4—441no—
274C2×D4—441no—
275C2×D4—882no—
276C22×C4—41no—
277C22×C4—222no—
278C22×C4#433911yescharacteristic
279C22×C4D4×D1111yescharacteristic
280C22×C4D4×D1111yescharacteristic
281SD16—448no—
282D8—448no—
283M16—42no—
284M16—114no—
285M16—222no—
286C2×C8—22no—
287C2×C8—42no—
288C2×C8—41no—
289C2×C8—222no—
290C2×C8—222no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—222no—
294C4⋊C4—222no—
295C4⋊C4—441no—
296C4⋊C4—441no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C42C2×D4411yescharacteristic
300C42D4×D1111yescharacteristic
301C42D4×D1111yescharacteristic
302C42C2×C22⋊D1111yescharacteristic
303C11#1014811yescharacteristic, complemented, Sylow
304C23—41no—
305C23—442no—
306C23—882no—
307C23—882no—
308C23—882no—
309C23#6693711yescharacteristic
310Q8—42no—
311Q8—882no—
312Q8—882no—
313D4—42no—
314D4—42no—
315D4—42no—
316D4—82no—
317D4—444no—
318D4—444no—
319D4—882no—
320D4—882no—
321D4—881no—
322D4—881no—
323D4—882no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—41no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—442no—
330C2×C4—882no—
331C2×C4#6693511yescharacteristic
332C2×C4#6693511yescharacteristic
333C2×C4#6693711yescharacteristic
334C2×C4#6696412yes—
335C2×C4SD16×D1112yes—
336C2×C4#6698311yescharacteristic
337C2×C4#6699011yescharacteristic
338C2×C4#6699311yescharacteristic
339C8—42no—
340C8—81no—
341C8—224no—
342C8—442no—
343C22—21no—
344C22—21no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22—882no—
349C22—882no—
350C22—882no—
351C22—1764no—
352C22#1062237512yes—
353C22#1062257311yescharacteristic
354C4—21no—
355C4—21no—
356C4—81no—
357C4—882no—
358C4#1062238912yes—
359C4#1062244012yes—
360C4#1062275512yes—
361C4#1062276711yescharacteristic
362C4#1062278811yescharacteristic
363C2—22no—
364C2—161no—
365C2—1762no—
366C2#1306963711yescharacteristic
367C2#1306970511yescharacteristic
368C2#1306972511yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1492C2
socleC22×C11#392
prime radical#13079069C2
hypercenter#1492D11
hypocenterC11#10148
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1492

Complements

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

NH ≅ G/Ntype
1. #13079741C2semidirect
3. C2×#10622307C2semidirect
4. #13069604C2semidirect
5. #13067285C2semidirect
6. #13066453C2semidirect
7. C11×#1492C2semidirect
125. #1492D11semidirect
303. C11#10148semidirect

Maximal subgroups

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

subgroupindex
#130797412
#130790692
C2×#106223072
#130696042
#130672852
#130664532
C11×#14922
#1014811