Finite Group Databasebeta

← #14657513

Subgroups — #14657513

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#13078076C211yesmaximal, characteristic
2#13068623C211yesmaximal, characteristic, complemented
3#13067387C211yesmaximal, characteristic, complemented
4#13067265C211yesmaximal, characteristic, complemented
5#13066936C211yesmaximal, characteristic, complemented
6#13066474C211yesmaximal, characteristic, complemented
7C11×#1517C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×#67002—21no—
10C2×C4×D44C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#382C2211yescharacteristic
13#10622845—21no—
14#10622696—21no—
15#10622685—21no—
16#10622670—22no—
17C2×#66873—21no—
18#10622538C2211yescharacteristic
19#10622537C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21C11×#327—22no—
22#10622185—21no—
23#10622182—21no—
24#10622167—21no—
25#10622106—22no—
26#10622095—22no—
27C2×C11×#41—21no—
28C22×D44D411yescharacteristic
29C22×C4×D11—21no—
30C11×C4⋊Q8D411yescharacteristic
31C11×#127D411yescharacteristic
32C11×#124—21no—
33C11×#121—21no—
34C11×#121—21no—
35C4×D4×C11—21no—
36C4×D4×C11—21no—
37C2×C11×C4⋊C4—21no—
38C2×C42×C11C2311yescharacteristic
39#67002—42no—
40#67002—42no—
41C2×#4325—22no—
42C2×#4323—22no—
43C2×(C2×D11)⋊C4—21no—
44C2×C4⋊Dic11D411yescharacteristic
45C2×#4318—21no—
46C22×C11⋊C8—21no—
47C4×D44—21no—
48C4×D44—21no—
49C4×D44—21no—
50C4×D44—21no—
51C11×C4⋊C8—21no—
52C11×C22⋊C8D412yes—
53C4×C8×C11—21no—
54C11×#95—21no—
55C11×#95—21no—
56#66899—22no—
57#66896—22no—
58C22⋊(C11⋊C8)—21no—
59#66873—42no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)D412yes—
65C4×C11⋊C8—21no—
66#10465—111nomaximal, Sylow
67C23×D11—21no—
68C11×#41—41no—
69C11×#41—41no—
70C11×#41—41no—
71C11×#41—41no—
72C2×Q8×C11—21no—
73C2×D4×C11—21no—
74C2×D4×C11—21no—
75C2×D4×C11—21no—
76C2×D4×C11—41no—
77C22×C4×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11#4111yescharacteristic
82C22×Dic11—21no—
83C2×D44—21no—
84C2×D44—21no—
85C2×D44—21no—
86C2×D44—21no—
87C2×D44—21no—
88C2×D44SD1612yes—
89C2×C4×D11—41no—
90C2×C4×D11—41no—
91C2×C4×D11—82no—
92C2×C8×C11—22no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—41no—
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11#4111yescharacteristic
102C42×C11#4111yescharacteristic
103#4325—44no—
104#4323—44no—
105(C2×D11)⋊C4—41no—
106(C2×D11)⋊C4—41no—
107C4⋊Dic11—21no—
108C4⋊Dic11—21no—
109#4318—41no—
110#4318—41no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8—41no—
115C2×C11⋊C8—41no—
116#3036—111no—
117#1804—111no—
118#1570—111no—
119#1540—111no—
120#1517D1111yescharacteristic, complemented
121#1460—111no—
122#1286—111no—
123C23×C11—41no—
124C23×C11#12111yescharacteristic
125C22×D11—22no—
126C22×D11—41no—
127C22×D11—41no—
128C22×D11—81no—
129C22×D11—81no—
130Q8×C11—41no—
131Q8×C11—41no—
132D4×C11—41no—
133D4×C11—41no—
134D4×C11—81no—
135D4×C11—81no—
136D4×C11—81no—
137D4×C11—81no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—81no—
142C2×C4×C11—81no—
143C2×C4×C11—81no—
144C2×C4×C11—81no—
145C2×C4×C11—81no—
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12311yescharacteristic
150C2×C4×C11#12311yescharacteristic
151C2×C4×C11#12411yescharacteristic
152C2×C4×C11C2×SD1611yescharacteristic
153C2×C4×C11#13511yescharacteristic
154C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
156C2×Dic11—41no—
157C2×Dic11—81no—
158D44—22no—
159D44—22no—
160D44—41no—
161D44—41no—
162C4×D11—82no—
163C4×D11—82no—
164C8×C11—42no—
165C11⋊C8—42no—
166C11⋊C8—81no—
167C11⋊C8—81no—
168C2×AGL(1,ℤ/8)—221no—
169#532C2×D1111yescharacteristic
170C2×C4×D4—111no—
171#463—222no—
172#461—221no—
173#459—221no—
174#431—111no—
175#431C2×D1111yescharacteristic
176#423—111no—
177C2×C4⋊C8—111no—
178#417—221no—
179C2×#102—221no—
180#382C2×D1111yescharacteristic
181#340—221no—
182#334—222no—
183#332—221no—
184#331—221no—
185#327—22no—
186#323—222no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—81no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11#39411yescharacteristic
193C22×C11#46511yescharacteristic
194C22×C11#46911yescharacteristic
195C2×D11—42no—
196C2×D11—82no—
197C2×D11—81no—
198C2×D11—81no—
199C2×D11—82no—
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—21no—
212C22×D4—111no—
213C23×C4—221no—
214AGL(1,ℤ/8)—442no—
215AGL(1,ℤ/8)—442no—
216C2×SD16—222no—
217C2×D8—222no—
218C2×M16—221no—
219C22×C8—221no—
220C4⋊Q8D4411yescharacteristic
221#127D4411yescharacteristic
222#124—21no—
223#121—21no—
224#121—21no—
225C4×D4—21no—
226C4×D4—21no—
227C4×D4—221no—
228C4×D4—221no—
229C4×D4—221no—
230C4×D4—221no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—111no—
233C2×C22⋊C4—221no—
234C2×C42C22×D1111yescharacteristic
235C4⋊C8—21no—
236C4⋊C8—112no—
237C4⋊C8—221no—
238C4⋊C8—221no—
239C4⋊C8—221no—
240C4⋊C8—221no—
241#103—222no—
242#102—222no—
243#102—442no—
244C22⋊C8—221no—
245C22⋊C8C22⋊D1112yes—
246C4×C8—21no—
247C4×C8—221no—
248#95—21no—
249#95—21no—
250C2×C11—21no—
251C2×C11—21no—
252C2×C11—161no—
253C2×C11#203411yescharacteristic
254C2×C11#204811yescharacteristic
255C2×C11#205311yescharacteristic
256D11—82no—
257C24—221no—
258#41—41no—
259#41—41no—
260#41—41no—
261#41—41no—
262C2×Q8—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—41no—
267C2×D4—112no—
268C2×D4—221no—
269C2×D4—221no—
270C2×D4—221no—
271C2×D4—221no—
272C2×D4—221no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—221no—
276C22×C4—441no—
277C22×C4—441no—
278C22×C4—882no—
279C22×C4D4×D1111yescharacteristic
280C22×C4#434111yescharacteristic
281C22×C4C2×C22⋊D1111yescharacteristic
282SD16—444no—
283D8—444no—
284M16—441no—
285M16—441no—
286C2×C8—22no—
287C2×C8—222no—
288C2×C8—441no—
289C2×C8—441no—
290C2×C8—441no—
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—
302C42C2×D4411yescharacteristic
303C42#433911yescharacteristic
304C42D4×D1111yescharacteristic
305C42#434111yescharacteristic
306C11#1046511yescharacteristic, complemented, Sylow
307C23—41no—
308C23—222no—
309C23—441no—
310C23—441no—
311C23—881no—
312C23—881no—
313C23#6699111yescharacteristic
314Q8—41no—
315Q8—41no—
316D4—41no—
317D4—41no—
318D4—81no—
319D4—81no—
320D4—81no—
321D4—81no—
322D4—222no—
323D4—222no—
324D4—441no—
325D4—441no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—441no—
335C2×C4—882no—
336C2×C4—882no—
337C2×C4—881no—
338C2×C4#6693511yescharacteristic
339C2×C4#6693611yescharacteristic
340C2×C4#6693811yescharacteristic
341C2×C4#6693911yescharacteristic
342C2×C4#6696411yescharacteristic
343C2×C4#6696411yescharacteristic
344C2×C4SD16×D1111yescharacteristic
345C2×C4#6696911yescharacteristic
346C2×C4#6698311yescharacteristic
347C2×C4#6699211yescharacteristic
348C8—42no—
349C8—442no—
350C8—881no—
351C8—881no—
352C22—21no—
353C22—21no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22—442no—
358C22—882no—
359C22—882no—
360C22—881no—
361C22—881no—
362C22#1062257411yescharacteristic
363C22#1062277211yescharacteristic
364C22#1062278411yescharacteristic
365C4—21no—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—81no—
370C4—161no—
371C4—881no—
372C4#1062238911yescharacteristic
373C4#1062239011yescharacteristic
374C4#1062239211yescharacteristic
375C4#1062239411yescharacteristic
376C2—21no—
377C2—21no—
378C2—161no—
379C2—882no—
380C2#1306980411yescharacteristic
381C2#1306989011yescharacteristic
382C2#1306992111yescharacteristic
subgroupG/H
centerC22#10622574
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1517C2
socleC22×C11#394
prime radical#13078076C2
hypercenter#1517D11
hypocenterC11#10465
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1517

Complements

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

NH ≅ G/Ntype
2. #13068623C2semidirect
3. #13067387C2semidirect
4. #13067265C2semidirect
5. #13066936C2semidirect
6. #13066474C2semidirect
7. C11×#1517C2semidirect
120. #1517D11semidirect
306. C11#10465semidirect

Maximal subgroups

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

subgroupindex
#130780762
#130686232
#130673872
#130672652
#130669362
#130664742
C11×#15172
#1046511