Finite Group Databasebeta

← #14657514

Subgroups — #14657514

Order 2816.

452 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 93 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#13078080C211yesmaximal, characteristic
2#13067386C211yesmaximal, characteristic, complemented
3#13067266C211yesmaximal, characteristic, complemented
4#13067175C211yesmaximal, characteristic, complemented
5#13066937C211yesmaximal, characteristic, complemented
6#13066474C211yesmaximal, characteristic, complemented
7C11×#1804C211yesmaximal, characteristic, complemented
8C2×C4×D4×C11C2211yescharacteristic
9C2×#66985—21no—
10#10623008C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×#102—21no—
13C11×#382C2211yescharacteristic
14#10622632—21no—
15#10622629—22no—
16#10622628—21no—
17#10622579—21no—
18#10622538C2211yescharacteristic
19#10622538C2211yescharacteristic
20#10622537C2211yescharacteristic
21C11×#340—21no—
22#10622163—22no—
23#10622123—21no—
24#10622120—21no—
25#10622118—22no—
26#10622089—22no—
27C22×D4×C11D411yescharacteristic
28C23×C4×C11—21no—
29C2×#4339—21no—
30C22×C8×C11—21no—
31C4×D4×C11—21no—
32C4×D4×C11—21no—
33C4×D4×C11—21no—
34C4×D4×C11—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C11×C22⋊C4—21no—
38C2×C42×C11C2311yescharacteristic
39C2×#4324—22no—
40#66985—42no—
41#66985—42no—
42C2×#4323—22no—
43#66983—21no—
44#66983—21no—
45C2×#4318—21no—
46#66928—21no—
47#66927D411yescharacteristic
48C4×D44—21no—
49C4×D44—21no—
50#66922D411yescharacteristic
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×#102—42no—
54C11×#95—21no—
55C11×#95—21no—
56C22⋊(C11⋊C8)—21no—
57C22⋊(C11⋊C8)D412yes—
58#66874—22no—
59#66873—22no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)D412yes—
64C4×C11⋊C8—21no—
65C4×C11⋊C8—21no—
66#10465—111nomaximal, Sylow
67C24×C11—21no—
68C2×D4×C11—21no—
69C2×D4×C11—21no—
70C2×D4×C11—21no—
71C2×D4×C11—21no—
72C2×D4×C11—21no—
73C2×D4×C11SD1612yes—
74C22×C4×C11—21no—
75C22×C4×C11—41no—
76C22×C4×C11—41no—
77C22×C4×C11—41no—
78C22×C4×C11—82no—
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11#4111yescharacteristic
82C2×C22⋊D11—41no—
83#4339—41no—
84#4339—41no—
85#4339—41no—
86#4339—41no—
87C2×D44—21no—
88C2×D44—21no—
89C2×D44—21no—
90C2×C4×D11—41no—
91C2×Dic22—21no—
92C2×C8×C11—41no—
93C2×C8×C11—41no—
94C2×C8×C11—41no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—41no—
101C42×C11C2×D411yescharacteristic
102C42×C11C2×D411yescharacteristic
103C42×C11#4111yescharacteristic
104C42×C11#4111yescharacteristic
105#4324—44no—
106#4323—44no—
107(C2×D11)⋊C4—41no—
108(C2×D11)⋊C4—41no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111#4318—41no—
112#4318—41no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—41no—
116#3036—111no—
117#1804D1111yescharacteristic, complemented
118#1570—111no—
119#1540—111no—
120#1517—111no—
121#1460—111no—
122#1286—111no—
123C23×C11—22no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—81no—
127C23×C11—81no—
128C23×C11#12111yescharacteristic
129C22×D11—41no—
130D4×C11—22no—
131D4×C11—22no—
132D4×C11—41no—
133D4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—82no—
138C2×C4×C11—82no—
139C2×C4×C11—81no—
140C2×C4×C11—81no—
141C2×C4×C11—81no—
142C2×C4×C11—81no—
143C2×C4×C11#12011yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12311yescharacteristic
147C2×C4×C11#12311yescharacteristic
148C2×C4×C11#12411yescharacteristic
149C2×C4×C11C2×SD1611yescharacteristic
150C2×C4×C11#13511yescharacteristic
151C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
153C22⋊D11—81no—
154C22⋊D11—81no—
155C2×Dic11—41no—
156D44—41no—
157D44—41no—
158D44—81no—
159D44—81no—
160C4×D11—81no—
161C4×D11—81no—
162Dic22—41no—
163Dic22—41no—
164C8×C11—81no—
165C11⋊C8—42no—
166C11⋊C8—42no—
167C11⋊C8—81no—
168C2×AGL(1,ℤ/8)—221no—
169#532—111no—
170C2×C4×D4C2×D1111yescharacteristic
171#463—222no—
172#461—221no—
173#459—221no—
174#431—111no—
175#431—111no—
176#423—111no—
177C2×C4⋊C8C2×D1111yescharacteristic
178#417—221no—
179C2×#102—21no—
180#382C2×D1111yescharacteristic
181#340—21no—
182#334—222no—
183#332—221no—
184#331—221no—
185#327—222no—
186#323—222no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—42no—
190C22×C11—82no—
191C22×C11—82no—
192C22×C11—81no—
193C22×C11—81no—
194C22×C11#39411yescharacteristic
195C22×C11#46511yescharacteristic
196C22×C11#46911yescharacteristic
197C2×D11—81no—
198C2×D11—81no—
199C2×D11—81no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—81no—
205C4×C11—161no—
206C4×C11#44911yescharacteristic
207C4×C11#45011yescharacteristic
208C4×C11#48111yescharacteristic
209C4×C11#48211yescharacteristic
210Dic11—81no—
211C2×#41—221no—
212C22×D4C22⋊D1111yescharacteristic
213C23×C4—21no—
214AGL(1,ℤ/8)—442no—
215AGL(1,ℤ/8)—442no—
216C2×SD16—222no—
217C2×D8—222no—
218C2×M16—221no—
219C22×C8—21no—
220C4⋊Q8—111no—
221#127—111no—
222#124—221no—
223#121—221no—
224#121—221no—
225C4×D4—21no—
226C4×D4—21no—
227C4×D4—21no—
228C4×D4—21no—
229C4×D4—221no—
230C4×D4—221no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4C22⋊D1111yescharacteristic
233C2×C22⋊C4—21no—
234C2×C42C22×D1111yescharacteristic
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8—112no—
238C4⋊C8—221no—
239C4⋊C8—221no—
240C4⋊C8—221no—
241#103—222no—
242#102—42no—
243#102—222no—
244C22⋊C8—112no—
245C22⋊C8—221no—
246C4×C8—221no—
247C4×C8—221no—
248#95—21no—
249#95—21no—
250C2×C11—21no—
251C2×C11—21no—
252C2×C11—82no—
253C2×C11#203411yescharacteristic
254C2×C11#204811yescharacteristic
255C2×C11#205311yescharacteristic
256D11—161no—
257C24—21no—
258#41—441no—
259#41—441no—
260#41—441no—
261#41—441no—
262C2×Q8—221no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—221no—
269C2×D4—221no—
270C2×D4—221no—
271C2×D4—441no—
272C2×D4#432512yes—
273C22×C4—21no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—82no—
278C22×C4—441no—
279C22×C4D4×D1111yescharacteristic
280C22×C4#434111yescharacteristic
281C22×C4C2×C22⋊D1111yescharacteristic
282SD16—444no—
283D8—444no—
284M16—441no—
285M16—441no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—222no—
290C2×C8—222no—
291C2×C8—441no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—221no—
297C4⋊C4—221no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—441no—
301C22⋊C4—441no—
302C42#433911yescharacteristic
303C42#433911yescharacteristic
304C42D4×D1111yescharacteristic
305C42D4×D1111yescharacteristic
306C11#1046511yescharacteristic, complemented, Sylow
307C23—22no—
308C23—41no—
309C23—41no—
310C23—81no—
311C23—81no—
312C23—441no—
313C23#6699211yescharacteristic
314Q8—441no—
315Q8—441no—
316D4—22no—
317D4—22no—
318D4—41no—
319D4—41no—
320D4—441no—
321D4—441no—
322D4—881no—
323D4—881no—
324D4—881no—
325D4—881no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—82no—
330C2×C4—82no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—441no—
336C2×C4—881no—
337C2×C4—881no—
338C2×C4#6693611yescharacteristic
339C2×C4#6693711yescharacteristic
340C2×C4#6693711yescharacteristic
341C2×C4#6693811yescharacteristic
342C2×C4#6698211yescharacteristic
343C2×C4#6698511yescharacteristic
344C2×C4#6699011yescharacteristic
345C2×C4C2×#432511yescharacteristic
346C2×C4#6700211yescharacteristic
347C2×C4#6700311yescharacteristic
348C8—81no—
349C8—442no—
350C8—442no—
351C8—881no—
352C22—21no—
353C22—21no—
354C22—42no—
355C22—82no—
356C22—82no—
357C22—81no—
358C22—81no—
359C22—881no—
360C22—881no—
361C22—881no—
362C22#1062257211yescharacteristic
363C22#1062265211yescharacteristic
364C22#1062266111yescharacteristic
365C4—21no—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—81no—
370C4—161no—
371C4—881no—
372C4#1062258111yescharacteristic
373C4#1062261611yescharacteristic
374C4#1062265011yescharacteristic
375C4#1062265911yescharacteristic
376C2—21no—
377C2—21no—
378C2—82no—
379C2—1761no—
380C2#1306980511yescharacteristic
381C2#1306988711yescharacteristic
382C2#1306992011yescharacteristic
subgroupG/H
centerC22#10622572
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1804C2
socleC22×C11#394
prime radical#13078080C2
hypercenter#1804D11
hypocenterC11#10465
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
2. #13067386C2semidirect
3. #13067266C2semidirect
4. #13067175C2semidirect
5. #13066937C2semidirect
6. #13066474C2semidirect
7. C11×#1804C2semidirect
117. #1804D11semidirect
306. C11#10465semidirect

Maximal subgroups

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

subgroupindex
#130780802
#130673862
#130672662
#130671752
#130669372
#130664742
C11×#18042
#1046511