Finite Group Databasebeta

← #14642018

Subgroups — #14642018

Order 2816.

590 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 590 conjugacy classes of subgroups — too many to draw. Only its 105 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#13071097C211yesmaximal, characteristic
2#13068308C211yesmaximal, characteristic
3#13068308C211yesmaximal, characteristic
4#13066440C211yesmaximal, characteristic, complemented
5#13066439C211yesmaximal, characteristic, complemented
6#13066438C211yesmaximal, characteristic, complemented
7C11×#1271C211yesmaximal, characteristic, complemented
8C22×#4313—21no—
9C22×#4313—21no—
10C2×#66945C411yescharacteristic
11C2×#66945C411yescharacteristic
12C2×C42×D11C2211yescharacteristic
13C11×#389C2211yescharacteristic
14#10622602—21no—
15#10622598C411yescharacteristic
16C4⋊C4×Dic11—21no—
17#10622586C411yescharacteristic
18#10622541C2211yescharacteristic
19#10622281—21no—
20#10622262—21no—
21C11×#336C2211yescharacteristic
22C11×#336C2211yescharacteristic
23#10622188—21no—
24#10622188—21no—
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×C4×D11C2×C411yescharacteristic
28C22×C4×D11D411yescharacteristic
29C22×C4×D11D411yescharacteristic
30C22×C8×C11—21no—
31C22×C8×C11—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C42×C11C2311yescharacteristic
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×C4⋊Dic11C2×C411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×C4×Dic11—21no—
44C2×C4×Dic11—21no—
45C2×C4×Dic11C2×C411yescharacteristic
46C2×C4×Dic11D411yescharacteristic
47C2×C4×Dic11D411yescharacteristic
48C22×C11⋊C8—21no—
49C22×C11⋊C8—21no—
50C2×#4313—24no—
51C2×#4313—24no—
52C2×#4313—42no—
53C2×#4313—42no—
54C2×#4313—42no—
55C2×#4313—42no—
56#66945—22no—
57#66945—22no—
58#66945—42no—
59C42×D11—42no—
60C11×#95—21no—
61C11⋊#95—21no—
62C11⋊#95—21no—
63C11⋊#95—21no—
64#7632—111nomaximal, Sylow
65C23×D11C22⋊C411yescharacteristic
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×Dic11—21no—
72C22×Dic11—21no—
73C22×Dic11C22⋊C411yescharacteristic
74C22×Dic11C22⋊C411yescharacteristic
75C22×Dic11C22⋊C411yescharacteristic
76C2×C4×D11—22no—
77C2×C4×D11—22no—
78C2×C4×D11—22no—
79C2×C4×D11—22no—
80C2×C4×D11—22no—
81C2×C4×D11—22no—
82C2×C4×D11—21no—
83C2×C4×D11—21no—
84C2×C4×D11—21no—
85C2×C4×D11—21no—
86C2×C4×D11—21no—
87C2×C4×D11—21no—
88C2×C8×C11—22no—
89C2×C8×C11—22no—
90C2×C8×C11—41no—
91C2×C8×C11—41no—
92C2×C8×C11—41no—
93C2×C8×C11—41no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4M1612yescomplemented
99C42×C11—41no—
100(C2×D11)⋊C4—24no—
101(C2×D11)⋊C4—42no—
102C4⋊Dic11—21no—
103C4⋊Dic11—41no—
104C4⋊Dic11—42no—
105C4⋊Dic11M1612yescomplemented
106Dic11⋊C4—42no—
107Dic11⋊C4—41no—
108Dic11⋊C4—41no—
109C4×Dic11—24no—
110C4×Dic11—41no—
111C4×Dic11—41no—
112C4×Dic11—41no—
113C4×Dic11—42no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—41no—
117C2×C11⋊C8—41no—
118C2×C11⋊C8—41no—
119C2×C11⋊C8—41no—
120#4313—48no—
121#4313—48no—
122#2296—111no—
123#1728—111no—
124#1728—111no—
125#1271—111no—
126#1271—111no—
127#1271—111no—
128#1271D1111yescharacteristic, complemented
129C23×C11C2×C22⋊C411yescharacteristic
130C22×D11—21no—
131C22×D11—21no—
132C22×D11—21no—
133C22×D11—21no—
134C22×D11—21no—
135C22×D11—21no—
136C22×D11#9912yes—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—22no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11C2×M1611yescharacteristic
150C2×C4×C11C2×M1611yescharacteristic
151C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C11#13711yescharacteristic
154C2×C4×C11#13711yescharacteristic
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—21no—
158C2×Dic11—21no—
159C2×Dic11—21no—
160C2×Dic11—21no—
161C2×Dic11—22no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11#10112yes—
168C2×Dic11#10412yes—
169C2×Dic11#10412yes—
170C4×D11—24no—
171C4×D11—24no—
172C4×D11—24no—
173C4×D11—24no—
174C4×D11—24no—
175C4×D11—24no—
176C8×C11—42no—
177C8×C11—42no—
178C11⋊C8—42no—
179C11⋊C8—42no—
180C22×M16—221no—
181C22×M16—221no—
182C2×#117—111no—
183C2×#117—111no—
184C22×C42—111no—
185#389—111no—
186#389—111no—
187#389—111no—
188#389C2×D1111yescharacteristic
189#385—221no—
190#385—221no—
191C4×C4⋊C4—221no—
192C4×C4⋊C4—221no—
193#336—111no—
194#336—111no—
195#336—221no—
196#336—221no—
197#336C2×D1111yescharacteristic
198#336C2×D1111yescharacteristic
199C22×C11#40711yescharacteristic
200C22×C11C2×#9911yescharacteristic
201C22×C11C2×#10111yescharacteristic
202C22×C11#41711yescharacteristic
203C22×C11#41711yescharacteristic
204C22×C11C2×#10411yescharacteristic
205C22×C11C2×#10411yescharacteristic
206C2×D11—22no—
207C2×D11—22no—
208C2×D11—22no—
209C2×D11—41no—
210C2×D11—41no—
211C2×D11—41no—
212C2×D11—41no—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—21no—
219C4×C11—42no—
220C4×C11—81no—
221Dic11—22no—
222Dic11—22no—
223Dic11—22no—
224Dic11—42no—
225Dic11—81no—
226C23×C4—111no—
227C23×C4—111no—
228C23×C4—111no—
229C2×M16—224no—
230C2×M16—224no—
231C2×M16—442no—
232C2×M16—442no—
233C2×M16—442no—
234C2×M16—442no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—221no—
238C22×C8—221no—
239#117—222no—
240#117—222no—
241#117—442no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—111no—
244C2×C4⋊C4—111no—
245C2×C4⋊C4—221no—
246C2×C4⋊C4—221no—
247C2×C4⋊C4—221no—
248C2×C4⋊C4C4×D1111yescharacteristic
249C2×C4⋊C4C4×D1111yescharacteristic
250C2×C22⋊C4—221no—
251C2×C22⋊C4—221no—
252C2×C42—111no—
253C2×C42—111no—
254C2×C42—111no—
255C2×C42—221no—
256C2×C42—221no—
257C2×C42—442no—
258C2×C42C22×D1111yescharacteristic
259#95—21no—
260#95—221no—
261#95—221no—
262#95—221no—
263C2×C11#146311yescharacteristic
264C2×C11#148911yescharacteristic
265C2×C11#148911yescharacteristic
266C2×C11#150411yescharacteristic
267C2×C11#150411yescharacteristic
268C2×C11#152611yescharacteristic
269C2×C11#156111yescharacteristic
270D11—42no—
271C24—111no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—111no—
275C22×C4—111no—
276C22×C4—111no—
277C22×C4—222no—
278C22×C4—222no—
279C22×C4—222no—
280C22×C4—222no—
281C22×C4—222no—
282C22×C4—222no—
283C22×C4—221no—
284C22×C4—221no—
285C22×C4—221no—
286C22×C4—221no—
287C22×C4—221no—
288C22×C4—221no—
289C22×C4—221no—
290C22×C4—221no—
291C22×C4C2×C4×D1111yescharacteristic
292C22×C4D4×D1111yescharacteristic
293C22×C4D4×D1111yescharacteristic
294M16—448no—
295M16—448no—
296C2×C8—22no—
297C2×C8—22no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—222no—
303C2×C8—222no—
304C2×C8—441no—
305C2×C8—441no—
306C2×C8—441no—
307C2×C8—441no—
308C4⋊C4—21no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—112no—
313C4⋊C4—221no—
314C4⋊C4—441no—
315C4⋊C4—442no—
316C4⋊C4—442no—
317C4⋊C4—441no—
318C4⋊C4—441no—
319C4⋊C4#431312yescomplemented
320C22⋊C4—224no—
321C22⋊C4—442no—
322C42—41no—
323C42—224no—
324C42—441no—
325C42—441no—
326C42—441no—
327C42—442no—
328C11#763211yescharacteristic, complemented, Sylow
329C23—112no—
330C23—221no—
331C23—221no—
332C23—221no—
333C23—221no—
334C23—221no—
335C23—221no—
336C23C22⋊C4×D1111yescharacteristic
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—22no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—112no—
350C2×C4—112no—
351C2×C4—112no—
352C2×C4—224no—
353C2×C4—224no—
354C2×C4—224no—
355C2×C4—224no—
356C2×C4—224no—
357C2×C4—224no—
358C2×C4—221no—
359C2×C4—221no—
360C2×C4—221no—
361C2×C4—221no—
362C2×C4—221no—
363C2×C4—221no—
364C2×C4—222no—
365C2×C4—441no—
366C2×C4—441no—
367C2×C4—441no—
368C2×C4—441no—
369C2×C4—441no—
370C2×C4C2×#431311yescharacteristic
371C2×C4M16×D1111yescharacteristic
372C2×C4#6696411yescharacteristic
373C2×C4#6696711yescharacteristic
374C2×C4#6696811yescharacteristic
375C2×C4#6697111yescharacteristic
376C8—42no—
377C8—42no—
378C8—442no—
379C8—442no—
380C22—222no—
381C22—222no—
382C22—222no—
383C22—441no—
384C22—441no—
385C22—441no—
386C22—441no—
387C22#1062233911yescharacteristic
388C22D11×#9911yescharacteristic
389C22D11×#10111yescharacteristic
390C22#1062238411yescharacteristic
391C22#1062241611yescharacteristic
392C22D11×#10411yescharacteristic
393C22D11×#10411yescharacteristic
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—42no—
401C4—81no—
402C4—222no—
403C4—222no—
404C4—222no—
405C4—442no—
406C4—881no—
407C2—442no—
408C2#1306694411yescharacteristic
409C2#1306705211yescharacteristic
410C2#1306705411yescharacteristic
411C2#1306711711yescharacteristic
412C2#1306711911yescharacteristic
413C2#1306720911yescharacteristic
414C2#1306735211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1271C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1271D11
hypocenterC11#7632
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
4. #13066440C2semidirect
5. #13066439C2semidirect
6. #13066438C2semidirect
7. C11×#1271C2semidirect
98. C11×C4⋊C4M16semidirect
105. C4⋊Dic11M16semidirect
128. #1271D11semidirect
319. C4⋊C4#4313semidirect
328. C11#7632semidirect

Maximal subgroups

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

subgroupindex
#130710972
#130683082
#130664402
#130664392
#130664382
C11×#12712
#763211