Finite Group Databasebeta

← #14655532

Subgroups — #14655532

Order 2816.

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

normal subgroups only

This group has 614 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#13079744C211yesmaximal, characteristic, complemented
2#13079066C211yesmaximal, characteristic
3#13069606C211yesmaximal, 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
16#10622701—21no—
17#10622697—22no—
18#10622692—21no—
19#10622689—21no—
20#10622687—22no—
21#10622686—21no—
22#10622581—22no—
23#10622538C2211yescharacteristic
24#10622537C2211yescharacteristic
25C4×#4318C2211yescharacteristic
26#10622182—22no—
27#10622168—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—
62C22⋊(C11⋊C8)—21no—
63#66873—24no—
64#66872—24no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)D412yes—
68#66867—21no—
69C4×C11⋊C8—21no—
70C4×C11⋊C8—21no—
71#10148—111nomaximal, Sylow
72C24×C11—41no—
73C2×Q8×C11—41no—
74C2×Q8×C11—41no—
75C2×Q8×C11—82no—
76C2×D4×C11—22no—
77C2×D4×C11—22no—
78C2×D4×C11—22no—
79C2×D4×C11—44no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—42no—
84C2×D4×C11—42no—
85C2×D4×C11—82no—
86C22×C4×C11—22no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C2×C22⋊D11—41no—
91#4339—42no—
92#4339—42no—
93C2×D44—21no—
94C2×D44—21no—
95C2×D44—21no—
96C2×C4×D11—41no—
97C2×Dic22—21no—
98C2×C8×C11—22no—
99C2×C8×C11—42no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108#4324—48no—
109#4323—48no—
110(C2×D11)⋊C4—41no—
111(C2×D11)⋊C4—41no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114#4318—22no—
115#4318—42no—
116#4318SD1614yes—
117C2×C11⋊C8—22no—
118C2×C11⋊C8—22no—
119C2×C11⋊C8—41no—
120#3227—111no—
121#3151—111no—
122C2×#486D1111yescharacteristic, complemented
123#1997—111no—
124#1545—111no—
125#1492—111no—
126#1278—111no—
127C23×C11—42no—
128C23×C11—82no—
129C23×C11—82no—
130C23×C11—82no—
131C23×C11#12111yescharacteristic
132C22×D11—41no—
133Q8×C11—82no—
134Q8×C11—82no—
135D4×C11—44no—
136D4×C11—44no—
137D4×C11—82no—
138D4×C11—82no—
139D4×C11—82no—
140D4×C11—81no—
141D4×C11—81no—
142C2×C4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11—42no—
145C2×C4×C11—82no—
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12711yescharacteristic
152C2×C4×C11C2×SD1612yes—
153C2×C4×C11AGL(1,ℤ/8)12yes—
154C22⋊D11—82no—
155C2×Dic11—41no—
156D44—42no—
157D44—42no—
158D44—42no—
159C4×D11—81no—
160C4×D11—81no—
161Dic22—42no—
162C8×C11—42no—
163C11⋊C8—24no—
164C11⋊C8—42no—
165C11⋊C8—81no—
166C2×AGL(1,ℤ/8)—222no—
167#532—111no—
168C2×C4⋊Q8C2×D1111yescharacteristic
169C2×#127C2×D1111yescharacteristic
170#498—221no—
171#496—222no—
172#493—221no—
173#492—221no—
174#486—22no—
175#486—22no—
176#486—221no—
177#481—222no—
178#476—222no—
179#431—111no—
180#423—111no—
181C2×#102—22no—
182C4×M16—111no—
183C2×C4×C8C2×D1111yescharacteristic
184#343—222no—
185#331—222no—
186D4⋊C8—222no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—82no—
190C22×C11—82no—
191C22×C11—82no—
192C22×C11—164no—
193C22×C11#39211yescharacteristic
194C22×C11#46012yes—
195C2×D11—81no—
196C2×D11—81no—
197C2×D11—81no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—82no—
201C4×C11#45012yes—
202C4×C11#45412yes—
203C4×C11#47212yes—
204C4×C11#49211yescharacteristic
205C4×C11#49611yescharacteristic
206Dic11—81no—
207C2×#41—221no—
208C22×Q8—21no—
209C22×D4—21no—
210C22×D4—21no—
211C22×D4—21no—
212AGL(1,ℤ/8)—444no—
213AGL(1,ℤ/8)—444no—
214C2×SD16—224no—
215C2×D8—224no—
216C2×M16—112no—
217C2×M16—221no—
218C22×C8—21no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8—111no—
224#127—21no—
225#127—21no—
226#127—21no—
227#127—111no—
228#127C22⋊D1112yes—
229#124—221no—
230#121—221no—
231#121—221no—
232C4×D4—221no—
233C4×D4—221no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4C22⋊D1112yes—
236C2×C42C22×D1111yescharacteristic
237#106—224no—
238C4⋊C8—112no—
239C4⋊C8—221no—
240C4⋊C8—221no—
241#102—28no—
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—162no—
251C2×C11#200311yescharacteristic
252C2×C11#201411yescharacteristic
253C2×C11#201811yescharacteristic
254D11—161no—
255C24—41no—
256#41—442no—
257#41—442no—
258C2×Q8—41no—
259C2×Q8—41no—
260C2×Q8—82no—
261C2×Q8—221no—
262C2×D4—22no—
263C2×D4—22no—
264C2×D4—22no—
265C2×D4—44no—
266C2×D4—42no—
267C2×D4—42no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—82no—
272C2×D4—221no—
273C2×D4—221no—
274C2×D4—221no—
275C2×D4—441no—
276C22×C4—22no—
277C22×C4—441no—
278C22×C4D4×D1111yescharacteristic
279C22×C4#434111yescharacteristic
280C22×C4C2×C22⋊D1111yescharacteristic
281SD16—448no—
282D8—448no—
283M16—114no—
284M16—222no—
285M16—442no—
286C2×C8—22no—
287C2×C8—42no—
288C2×C8—222no—
289C2×C8—222no—
290C2×C8—441no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—221no—
296C4⋊C4—221no—
297C22⋊C4—441no—
298C22⋊C4—441no—
299C42D4×D1111yescharacteristic
300C42D4×D1111yescharacteristic
301C42C2×C22⋊D1111yescharacteristic
302C42C2×C22⋊D1111yescharacteristic
303C11#1014811yescharacteristic, complemented, Sylow
304C23—42no—
305C23—82no—
306C23—82no—
307C23—82no—
308C23—441no—
309C23#6699211yescharacteristic
310Q8—82no—
311Q8—82no—
312Q8—442no—
313D4—44no—
314D4—44no—
315D4—82no—
316D4—82no—
317D4—81no—
318D4—81no—
319D4—82no—
320D4—442no—
321D4—442no—
322D4—442no—
323D4—882no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—42no—
327C2×C4—82no—
328C2×C4—441no—
329C2×C4—881no—
330C2×C4—881no—
331C2×C4SD16×D1112yes—
332C2×C4#6696712yes—
333C2×C4#6699011yescharacteristic
334C2×C4#6699011yescharacteristic
335C2×C4#6699111yescharacteristic
336C2×C4#6699211yescharacteristic
337C2×C4#6699311yescharacteristic
338C2×C4#6700611yescharacteristic
339C8—42no—
340C8—224no—
341C8—442no—
342C8—881no—
343C22—21no—
344C22—21no—
345C22—82no—
346C22—82no—
347C22—82no—
348C22—164no—
349C22—881no—
350C22—881no—
351C22—881no—
352C22#1062277612yes—
353C22#1062283611yescharacteristic
354C4—21no—
355C4—21no—
356C4—82no—
357C4—881no—
358C4#1062267512yes—
359C4#1062277312yes—
360C4#1062278212yes—
361C4#1062278811yescharacteristic
362C4#1062278911yescharacteristic
363C2—22no—
364C2—162no—
365C2—1761no—
366C2#1306963811yescharacteristic
367C2#1306970211yescharacteristic
368C2#1306972311yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#486C2
socleC22×C11#392
prime radical#13079066C2
hypercenterC2×#486D11
hypocenterC11#10148
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. #13079744C2semidirect
3. #13069606C2semidirect
4. #13067284C2semidirect
5. #13067068C2semidirect
6. #13066453C2semidirect
7. C2×C11×#486C2semidirect
122. C2×#486D11semidirect
303. C11#10148semidirect

Maximal subgroups

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

subgroupindex
#130797442
#130790662
#130696062
#130672842
#130670682
#130664532
C2×C11×#4862
#1014811