Finite Group Databasebeta

← #14726891

Subgroups — #14726891

Order 2816.

1154 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 187 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#13082387C211yesmaximal, characteristic
2#13078647C212yesmaximal, complemented
3#13067652C214yesmaximal, complemented
4#13067584C214yesmaximal, complemented
5#13067175C212yesmaximal, complemented
6#13066940C211yesmaximal, characteristic, complemented
7C11×#2581C211yesmaximal, characteristic, complemented
8C2×#67040—21no—
9C2×C4×Q8×C11C2211yescharacteristic
10C2×C4×Q8×C11C2211yescharacteristic
11#10623108—22no—
12#10623107—24no—
13Q8×D44—22no—
14#10623041—21no—
15#10623041C2214yes—
16#10623008—22no—
17#10623008C2212yes—
18C11×#400C2212yes—
19C11×#395C2212yes—
20C11×#391—21no—
21C11×#389—21no—
22C11×#387—22no—
23C11×#382C2211yescharacteristic
24#10622840C2214yes—
25#10622640—22no—
26C4×#4325—24no—
27#10622633—22no—
28#10622581C2214yes—
29#10622538C2212yes—
30#10622166C2214yes—
31#10622089C2218yes—
32C22×Q8×C11D411yescharacteristic
33C22×Q8×C11C2311yescharacteristic
34#67040—44no—
35#67040—44no—
36C2×#4343—24no—
37C2×Q8×D11—24no—
38C2×#4339—24no—
39C2×#4339—22no—
40C4×Q8×C11—22no—
41C4×Q8×C11—22no—
42C4×Q8×C11—22no—
43C4×Q8×C11—22no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C11×C4⋊C4C2311yescharacteristic
49C2×C11×C4⋊C4C2312yes—
50C2×C42×C11—21no—
51C2×C42×C11D412yes—
52C2×C42×C11C2311yescharacteristic
53C2×#4325—24no—
54#66983—22no—
55#66983—24no—
56#66983C2314yes—
57#66950—24no—
58#66950—28no—
59#66948—24no—
60#66948—28no—
61#66928—24no—
62#66928—22no—
63#66927—22no—
64#66927D412yes—
65C4×D44—24no—
66C4×D44—24no—
67C4×D44—22no—
68C4×D44D414yes—
69#66922—22no—
70#66922D412yes—
71C11×#95—21no—
72C11×#95—22no—
73C11×#95—22no—
74C11×#95—22no—
75C11×#95C2312yes—
76#66899—24no—
77C22⋊(C11⋊C8)C2314yes—
78#66873—24no—
79#66872—24no—
80C4⋊(C11⋊C8)—22no—
81C4×C11⋊C8—22no—
82#18219—111nomaximal, Sylow
83C2×Q8×C11—22no—
84C2×Q8×C11—22no—
85C2×Q8×C11—22no—
86C2×Q8×C11—42no—
87C2×Q8×C11SD1614yescomplemented
88C22×C4×C11—21no—
89C22×C4×C11—22no—
90C22×C4×C11—21no—
91C22×C4×C11C2×D412yes—
92C22×C4×C11C2×D412yes—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2411yescharacteristic
96C2×C22⋊D11—24no—
97#4343—416no—
98Q8×D11—416no—
99#4339—48no—
100#4339—48no—
101#4339—44no—
102#4339—44no—
103C2×D44—24no—
104C2×D44—24no—
105C2×D44—22no—
106C2×D44—22no—
107C2×D44C2×D414yes—
108C2×C4×D11—28no—
109C2×C4×D11—24no—
110C2×Dic22—24no—
111C2×Dic22—22no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—24no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—44no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—42no—
119C42×C11—22no—
120C42×C11—22no—
121C42×C11—42no—
122C42×C11C2×D412yes—
123C42×C11C2×D412yes—
124#4325—48no—
125(C2×D11)⋊C4—28no—
126(C2×D11)⋊C4—24no—
127(C2×D11)⋊C4—24no—
128C4⋊Dic11—24no—
129C4⋊Dic11—22no—
130C4⋊Dic11C2×D414yes—
131C2×C11⋊C8—24no—
132#3497—111no—
133#3103—112no—
134#2581D1111yescharacteristic, complemented
135#1616—114no—
136#1604—114no—
137#1517—112no—
138#1461—111no—
139C23×C11C22×D411yescharacteristic
140C22×D11—24no—
141Q8×C11—28no—
142Q8×C11—24no—
143Q8×C11—42no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11—41no—
157C2×C4×C11—42no—
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12011yescharacteristic
160C2×C4×C11#12012yes—
161C2×C4×C11C2×SD1614yes—
162C2×C4×C11C2×SD1612yes—
163C2×C4×C11AGL(1,ℤ/8)12yes—
164C2×C4×C11C22×D412yes—
165C22⋊D11—44no—
166C22⋊D11—44no—
167C2×Dic11—24no—
168D44—44no—
169D44—44no—
170D44—48no—
171D44—44no—
172D44—84no—
173C4×D11—416no—
174C4×D11—48no—
175Dic22—48no—
176Dic22—44no—
177C11⋊C8—44no—
178C2×2−1+4—221no—
179#550—222no—
180D4×Q8—222no—
181#548—224no—
182#537—114no—
183#537—221no—
184#532—112no—
185#532—222no—
186C2×C4×Q8C2×D1111yescharacteristic
187C2×C4×Q8C2×D1111yescharacteristic
188#481—114no—
189#475—222no—
190#460—222no—
191#448—114no—
192C4×SD16—224no—
193#431—112no—
194#400C2×D1112yes—
195#395C2×D1112yes—
196#391—21no—
197#389—21no—
198#387—22no—
199#382C2×D1111yescharacteristic
200#327—118no—
201#324—114no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11C2×#12011yescharacteristic
205C22×C11C22×SD1611yescharacteristic
206C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
207C2×D11—44no—
208C2×D11—44no—
209C2×D11—44no—
210C4×C11—24no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—22no—
214C4×C11—42no—
215C4×C11—42no—
216C4×C11—82no—
217C4×C11—81no—
218C4×C11#45014yes—
219Dic11—44no—
2202−1+4—444no—
2212−1+4—444no—
222C2×#41—224no—
223C2×#41—222no—
224C2×#41—224no—
225C22×Q8—224no—
226C22×Q8C22⋊D1111yescharacteristic
227C22×Q8C22×D1111yescharacteristic
228C2×SD16—224no—
229C4⋊Q8—112no—
230C4⋊Q8—222no—
231#127—112no—
232#127—222no—
233#124—224no—
234#124—222no—
235C22⋊Q8—228no—
236C22⋊Q8—224no—
237#121—114no—
238#121—228no—
239#121—224no—
240#121—222no—
241#121—224no—
242C4×Q8—22no—
243C4×Q8—22no—
244C4×Q8—22no—
245C4×Q8—22no—
246C4×D4—114no—
247C4×D4—224no—
248C4×D4—224no—
249C4×D4—222no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4C22⋊D1111yescharacteristic
254C2×C4⋊C4C22×D1111yescharacteristic
255C2×C4⋊C4C22×D1112yes—
256C2×C42—21no—
257C2×C42C22⋊D1112yes—
258C2×C42C22×D1111yescharacteristic
259#106—224no—
260C4⋊C8—222no—
261#103—224no—
262#102—224no—
263C22⋊C8—114no—
264C4×C8—222no—
265#95—21no—
266#95—22no—
267#95—22no—
268#95—22no—
269#95C22×D1112yes—
270C2×C11—21no—
271C2×C11—21no—
272C2×C11C2×#45011yescharacteristic
273C2×C11#302011yescharacteristic
274C2×C11#302511yescharacteristic
275D11—84no—
276#41—448no—
277#41—4416no—
278#41—448no—
279#41—444no—
280#41—444no—
281C2×Q8—22no—
282C2×Q8—22no—
283C2×Q8—22no—
284C2×Q8—42no—
285C2×Q8—224no—
286C2×Q8—222no—
287C2×Q8—4416no—
288C2×Q8#432514yescomplemented
289C2×D4—114no—
290C2×D4—224no—
291C2×D4—224no—
292C2×D4—224no—
293C2×D4—222no—
294C2×D4—222no—
295C22×C4—21no—
296C22×C4—22no—
297C22×C4—21no—
298C22×C4—228no—
299C22×C4—224no—
300C22×C4C2×C22⋊D1112yes—
301C22×C4C2×C22⋊D1112yes—
302C22×C4C2×C22⋊D1111yescharacteristic
303C22×C4C2×C22⋊D1111yescharacteristic
304C22×C4C23×D1111yescharacteristic
305SD16—448no—
306C2×C8—224no—
307C4⋊C4—22no—
308C4⋊C4—24no—
309C4⋊C4—22no—
310C4⋊C4—44no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—42no—
314C4⋊C4—114no—
315C4⋊C4—224no—
316C4⋊C4—222no—
317C22⋊C4—228no—
318C22⋊C4—224no—
319C22⋊C4—224no—
320C42—22no—
321C42—22no—
322C42—42no—
323C42D4×D1112yes—
324C42D4×D1112yes—
325C11#1821911yescharacteristic, complemented, Sylow
326C23—224no—
327C23C22×C22⋊D1111yescharacteristic
328Q8—28no—
329Q8—24no—
330Q8—42no—
331Q8—448no—
332Q8—444no—
333D4—444no—
334D4—448no—
335D4—444no—
336D4—444no—
337D4—444no—
338D4—444no—
339D4—884no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—224no—
355C2×C4—4416no—
356C2×C4—448no—
357C2×C4#6699011yescharacteristic
358C2×C4#6699011yescharacteristic
359C2×C4#6699012yes—
360C2×C4C2×#432514yes—
361C2×C4C2×#432512yes—
362C2×C4#6700212yes—
363C2×C4C2×D4×D1112yes—
364C8—444no—
365C22—21no—
366C22—21no—
367C22—444no—
368C22—444no—
369C22—444no—
370C22C2×#6699011yescharacteristic
371C22C22×#432511yescharacteristic
372C22C2×#6700211yescharacteristic
373C4—24no—
374C4—21no—
375C4—21no—
376C4—22no—
377C4—42no—
378C4—42no—
379C4—82no—
380C4—81no—
381C4—444no—
382C4#1062265914yes—
383C2—21no—
384C2—21no—
385C2—884no—
386C2C2×#1062265911yescharacteristic
387C2#1307797911yescharacteristic
388C2#1307800711yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2581C2
socleC22×C11C2×#120
prime radical#13082387C2
hypercenter#2581D11
hypocenterC11#18219
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2581

Complements

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

NH ≅ G/Ntype
2. #13078647C2semidirect
3. #13067652C2semidirect
4. #13067584C2semidirect
5. #13067175C2semidirect
6. #13066940C2semidirect
7. C11×#2581C2semidirect
87. C2×Q8×C11SD16semidirect
134. #2581D11semidirect
288. C2×Q8#4325semidirect
325. C11#18219semidirect

Maximal subgroups

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

subgroupindex
#130823872
#130786472
#130676522
#130675842
#130671752
#130669402
C11×#25812
#1821911