Finite Group Databasebeta

← #14655129

Subgroups — #14655129

Order 2816.

598 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 85 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#13079603C211yesmaximal, characteristic
2#13079073C211yesmaximal, characteristic, complemented
3#13067342C211yesmaximal, characteristic, complemented
4#13067214C211yesmaximal, characteristic, complemented
5#13067123C211yesmaximal, characteristic, complemented
6#13066509C211yesmaximal, characteristic, complemented
7C11×#2640C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×#124C2211yescharacteristic
10C2×#66995—22no—
11#10623008C2211yescharacteristic
12C11×#397—22no—
13C11×#393—22no—
14C11×#391—21no—
15C11×#390—21no—
16C11×#376C2211yescharacteristic
17#10622840—21no—
18#10622830—21no—
19#10622705—21no—
20#10622699—22no—
21#10622698—21no—
22#10622671—21no—
23#10622670—22no—
24#10622668—21no—
25#10622539C2211yescharacteristic
26#10622539C2211yescharacteristic
27C4×#4318C2211yescharacteristic
28#10622184—22no—
29#10622178—22no—
30#10622089—22no—
31C22×Q8×C11D412yes—
32C22×Q8×C11D411yescharacteristic
33C22×D4×C11D411yescharacteristic
34C2×#4339—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×#124—21no—
40C11×#124—21no—
41C11×#124—21no—
42C11×#124—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4—21no—
47C2×C11×C22⋊C4—24no—
48C2×C42×C11—21no—
49C2×C42×C11C2311yescharacteristic
50C2×#4326—24no—
51#66995—48no—
52C2×#4325—24no—
53C2×#4325—22no—
54C2×#4323—22no—
55#66983—21no—
56#66983—21no—
57C2×#4318—21no—
58#66928—21no—
59#66927D411yescharacteristic
60C4×D44—21no—
61C4×D44—21no—
62#66922D411yescharacteristic
63C11×#95—24no—
64C11×#95—21no—
65C11×#95D412yes—
66#66899—22no—
67#66896—22no—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)D412yes—
72#66867—21no—
73#66867—21no—
74#66867D412yes—
75C4×C11⋊C8—21no—
76#10090—111nomaximal, Sylow
77C24×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—22no—
80C2×Q8×C11—21no—
81C2×Q8×C11—22no—
82C2×Q8×C11—42no—
83C2×Q8×C11—44no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—42no—
87C22×C4×C11—21no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C2×C22⋊D11—41no—
94#4339—44no—
95C2×D44—21no—
96C2×D44—21no—
97C2×D44—21no—
98C2×C4×D11—41no—
99C2×Dic22—21no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—41no—
108C11×C22⋊C4—84no—
109C42×C11—42no—
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11#4111yescharacteristic
114#4326—48no—
115#4325—48no—
116#4325—82no—
117#4323—82no—
118(C2×D11)⋊C4—41no—
119(C2×D11)⋊C4—41no—
120C4⋊Dic11—21no—
121C4⋊Dic11—21no—
122#4318—24no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—41no—
126#3213—111no—
127#3152—111no—
128#2640D1111yescharacteristic, complemented
129#1558—111no—
130#1527—111no—
131#1505—111no—
132#1300—111no—
133C23×C11—42no—
134C23×C11—42no—
135C23×C11—41no—
136C23×C11—42no—
137C23×C11#12011yescharacteristic
138C22×D11—41no—
139Q8×C11—44no—
140Q8×C11—42no—
141Q8×C11—82no—
142Q8×C11—81no—
143D4×C11—42no—
144D4×C11—81no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—41no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—41no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—44no—
155C2×C4×C11#12011yescharacteristic
156C2×C4×C11#12011yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12711yescharacteristic
161C22⋊D11—82no—
162C2×Dic11—41no—
163D44—42no—
164D44—42no—
165D44—81no—
166C4×D11—82no—
167Dic22—42no—
168C11⋊C8—24no—
169C11⋊C8—42no—
170C11⋊C8—81no—
171C2×#137—222no—
172#532—111no—
173C2×C4⋊Q8C2×D1111yescharacteristic
174C2×#124C2×D1111yescharacteristic
175#497—222no—
176#496—221no—
177#494—221no—
178#492—221no—
179#489—221no—
180#463—222no—
181#448—221no—
182#447—221no—
183#432—111no—
184#432—111no—
185C4×M16—111no—
186#397—22no—
187#393—22no—
188#391—21no—
189#390—21no—
190#376C2×D1111yescharacteristic
191#333—222no—
192#329—222no—
193#327—222no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—84no—
197C22×C11—81no—
198C22×C11—81no—
199C22×C11—81no—
200C22×C11#39211yescharacteristic
201C22×C11#45312yes—
202C2×D11—81no—
203C2×D11—81no—
204C2×D11—81no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—82no—
211C4×C11—82no—
212C4×C11—81no—
213C4×C11#45512yes—
214Dic11—81no—
215C2×#41—221no—
216C22×Q8C22⋊D1111yescharacteristic
217C22×Q8C22⋊D1112yes—
218C22×D4C22⋊D1111yescharacteristic
219#137—448no—
220C2×Q16—224no—
221C2×SD16—224no—
222C2×SD16—222no—
223C2×D8—222no—
224C2×M16—221no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—111no—
230#127—111no—
231#124—21no—
232#124—21no—
233#124—21no—
234#124—21no—
235#124—221no—
236#121—221no—
237#121—221no—
238C4×D4—221no—
239C4×D4—221no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—24no—
245C2×C42—21no—
246C2×C42C22×D1111yescharacteristic
247C4⋊C8—112no—
248C4⋊C8—221no—
249#103—222no—
250#102—222no—
251C22⋊C8—221no—
252C22⋊C8—221no—
253#97—112no—
254#97—221no—
255#97—221no—
256C4×C8—221no—
257#95—24no—
258#95—21no—
259#95C22⋊D1112yes—
260C2×C11—22no—
261C2×C11—161no—
262C2×C11#200211yescharacteristic
263C2×C11#200411yescharacteristic
264C2×C11#200911yescharacteristic
265D11—161no—
266C24—21no—
267#41—444no—
268C2×Q8—21no—
269C2×Q8—22no—
270C2×Q8—21no—
271C2×Q8—22no—
272C2×Q8—42no—
273C2×Q8—44no—
274C2×Q8—221no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—42no—
278C2×D4—221no—
279C2×D4—221no—
280C2×D4—221no—
281C2×D4—441no—
282C22×C4—21no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—441no—
286C22×C4C2×C22⋊D1111yescharacteristic
287C22×C4C2×C22⋊D1111yescharacteristic
288C22×C4C2×C22⋊D1111yescharacteristic
289Q16—448no—
290SD16—448no—
291SD16—882no—
292D8—882no—
293M16—224no—
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—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—84no—
308C22⋊C4—441no—
309C22⋊C4—441no—
310C42—42no—
311C42D4×D1111yescharacteristic
312C42D4×D1111yescharacteristic
313C42D4×D1111yescharacteristic
314C42#434111yescharacteristic
315C11#1009011yescharacteristic, complemented, Sylow
316C23—42no—
317C23—42no—
318C23—41no—
319C23—42no—
320C23—441no—
321C23#6700611yescharacteristic
322Q8—44no—
323Q8—42no—
324Q8—82no—
325Q8—81no—
326Q8—442no—
327D4—42no—
328D4—81no—
329D4—442no—
330D4—442no—
331D4—881no—
332D4—882no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—44no—
343C2×C4—441no—
344C2×C4—882no—
345C2×C4#6699011yescharacteristic
346C2×C4#6699011yescharacteristic
347C2×C4#6699111yescharacteristic
348C2×C4#6699211yescharacteristic
349C2×C4#6699211yescharacteristic
350C2×C4#6699311yescharacteristic
351C8—224no—
352C8—442no—
353C8—881no—
354C22—21no—
355C22—21no—
356C22—84no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22—881no—
361C22—881no—
362C22—881no—
363C22#1062283611yescharacteristic
364C22#1062285412yes—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—82no—
371C4—82no—
372C4—81no—
373C4—881no—
374C4#1062267412yes—
375C2—22no—
376C2—161no—
377C2—1761no—
378C2#1306962911yescharacteristic
379C2#1306964511yescharacteristic
380C2#1306967611yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2640C2
socleC22×C11#392
prime radical#13079603C2
hypercenter#2640D11
hypocenterC11#10090
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2640

Complements

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

NH ≅ G/Ntype
2. #13079073C2semidirect
3. #13067342C2semidirect
4. #13067214C2semidirect
5. #13067123C2semidirect
6. #13066509C2semidirect
7. C11×#2640C2semidirect
128. #2640D11semidirect
315. C11#10090semidirect

Maximal subgroups

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

subgroupindex
#130796032
#130790732
#130673422
#130672142
#130671232
#130665092
C11×#26402
#1009011