Finite Group Databasebeta

← #14726558

Subgroups — #14726558

Order 2816.

1106 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 1106 conjugacy classes of subgroups — too many to draw. Only its 167 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#13082419C211yesmaximal, characteristic, complemented
2#13078715C212yesmaximal, complemented
3#13067640C214yesmaximal, complemented
4#13067538C214yesmaximal, complemented
5#13067127C212yesmaximal, complemented
6#13066957C211yesmaximal, characteristic, complemented
7C11×#2397C211yesmaximal, characteristic
8C2×C4×D4×C11—22no—
9C2×C4×D4×C11C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11#10623329—21no—
12C2×#66977—22no—
13#10623074—22no—
14#10623070—24no—
15D4×Dic22—22no—
16#10623031—21no—
17#10623014C2214yes—
18#10623001C2212yes—
19C11×#399—21no—
20C11×#399C2212yes—
21C11×#392—21no—
22C11×#392C2212yes—
23C11×#376C2211yescharacteristic
24#10622831C2214yes—
25#10622632—22no—
26#10622631—24no—
27#10622620—22no—
28#10622583C2214yes—
29#10622539C2212yes—
30#10622163C2214yes—
31#10622090C2218yes—
32C22×D4×C11—22no—
33C22×D4×C11D411yescharacteristic
34C22×D4×C11C2311yescharacteristic
35C23×C4×C11—21no—
36C23×C4×C11D412yes—
37C22×Dic22—22no—
38C4×D4×C11—22no—
39C4×D4×C11—22no—
40C4×D4×C11—22no—
41C4×D4×C11—22no—
42C4×D4×C11—48no—
43C2×C11×C4⋊C4—22no—
44C2×C11×C4⋊C4D411yescharacteristic
45C2×C11×C4⋊C4C2311yescharacteristic
46C2×C11×C22⋊C4—22no—
47C2×C11×C22⋊C4—22no—
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4C2312yes—
50C2×C42×C11—21no—
51C2×C42×C11C2311yescharacteristic
52C2×C22⋊Dic11—24no—
53D4×Dic11—24no—
54D4×Dic11—24no—
55C2×#4324—24no—
56#66979—22no—
57C2×C4⋊Dic11—22no—
58#66977—24no—
59#66977—24no—
60#66977—22no—
61#66977—24no—
62#66977C2314yes—
63C2×Dic11⋊C4—24no—
64#66943—24no—
65#66941—24no—
66#66931—28no—
67#66931—28no—
68#66923—22no—
69#66922D412yescomplemented
70#66922D412yescomplemented
71C4×Dic22—22no—
72C4×Dic22D414yescomplemented
73C11×#95—21no—
74C11×#95C2312yes—
75#66896—24no—
76C22⋊(C11⋊C8)C2314yes—
77#66874—24no—
78#66871—24no—
79C4⋊(C11⋊C8)—22no—
80#66867—22no—
81#18180—111nomaximal, Sylow
82C24×C11—21no—
83C24×C11C2×D412yes—
84C2×D4×C11—24no—
85C2×D4×C11—22no—
86C2×D4×C11—22no—
87C2×D4×C11—44no—
88C2×D4×C11—42no—
89C2×D4×C11—44no—
90C2×D4×C11—44no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—21no—
95C22×C4×C11—44no—
96C22×C4×C11—44no—
97C22×C4×C11—41no—
98C22×C4×C11—41no—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2411yescharacteristic
103C22×Dic11—24no—
104C22×Dic11—24no—
105C2×Dic22—24no—
106C2×Dic22—22no—
107C2×Dic22—84no—
108C2×Dic22C2×D414yes—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—44no—
112C11×C22⋊C4—24no—
113C11×C22⋊C4—44no—
114C11×C22⋊C4—44no—
115C11×C22⋊C4—42no—
116C42×C11—24no—
117C42×C11C2×D412yes—
118C42×C11C2×D412yes—
119C22⋊Dic11—28no—
120C22⋊Dic11—24no—
121#4324—48no—
122C4⋊Dic11—24no—
123C4⋊Dic11—22no—
124C4⋊Dic11—22no—
125C4⋊Dic11—22no—
126C4⋊Dic11C2×D414yes—
127Dic11⋊C4—28no—
128Dic11⋊C4—24no—
129Dic11⋊C4—24no—
130C4×Dic11—24no—
131C2×C11⋊C8—24no—
132#3501—111no—
133#3110—112no—
134#2397D1111yescharacteristic
135#1614—114no—
136#1596—114no—
137#1506—112no—
138#1466—111no—
139C23×C11—22no—
140C23×C11—22no—
141C23×C11—22no—
142C23×C11—42no—
143C23×C11—42no—
144C23×C11—42no—
145C23×C11—41no—
146C23×C11—41no—
147C23×C11—42no—
148C23×C11#13714yes—
149C23×C11C22×D411yescharacteristic
150D4×C11—28no—
151D4×C11—24no—
152D4×C11—42no—
153D4×C11—416no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—24no—
157C2×C4×C11—22no—
158C2×C4×C11—41no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11—44no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—41no—
165C2×C4×C11—82no—
166C2×C4×C11—82no—
167C2×C4×C11—82no—
168C2×C4×C11#12012yes—
169C2×C4×C11#12011yescharacteristic
170C2×C4×C11#12011yescharacteristic
171C2×C4×C11C22×D412yes—
172C2×Dic11—24no—
173C2×Dic11—24no—
174C2×Dic11—84no—
175C2×Dic11—84no—
176Dic22—44no—
177Dic22—44no—
178Dic22—84no—
179C11⋊C8—44no—
180#554—224no—
181#554—222no—
182D4×Q8—222no—
183#544—221no—
184#543—114no—
185#533—112no—
186C2×C22⋊Q8—222no—
187#518—221no—
188C2×C4×D4—22no—
189C2×C4×D4C2×D1111yescharacteristic
190C2×C4×D4C2×D1111yescharacteristic
191#484—114no—
192#474—222no—
193#461—222no—
194#450—114no—
195#440—224no—
196#432—112no—
197#399—21no—
198#399C2×D1112yes—
199#392—21no—
200#392C2×D1112yes—
201#376C2×D1111yescharacteristic
202#328—118no—
203#323—114no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—24no—
207C22×C11—44no—
208C22×C11—44no—
209C22×C11—42no—
210C22×C11—42no—
211C22×C11—42no—
212C22×C11—82no—
213C22×C11—82no—
214C22×C11—81no—
215C22×C11—81no—
216C22×C11C2×#12011yescharacteristic
217C22×C11C2×#13712yes—
218C4×C11—22no—
219C4×C11—21no—
220C4×C11—22no—
221C4×C11—44no—
222C4×C11—42no—
223C4×C11—81no—
224C4×C11#45312yes—
225Dic11—44no—
226Dic11—44no—
227C22×Q8—222no—
228C22×D4—22no—
229C22×D4C22⋊D1111yescharacteristic
230C22×D4C22×D1111yescharacteristic
231C23×C4—21no—
232C23×C4C22⋊D1112yes—
233C2×SD16—224no—
234C4⋊Q8—112no—
235C4⋊Q8—112no—
236C4⋊Q8—224no—
237#125—224no—
238#125—222no—
239C22⋊Q8—114no—
240C22⋊Q8—228no—
241C22⋊Q8—228no—
242C22⋊Q8—224no—
243C22⋊Q8—224no—
244C22⋊Q8—222no—
245C22⋊Q8—224no—
246C4×Q8—114no—
247C4×Q8—222no—
248C4×D4—22no—
249C4×D4—22no—
250C4×D4—22no—
251C4×D4—22no—
252C4×D4—48no—
253C4×D4—224no—
254C4×D4—224no—
255#117—222no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—224no—
258C2×C4⋊C4—222no—
259C2×C4⋊C4C22⋊D1111yescharacteristic
260C2×C4⋊C4C22×D1111yescharacteristic
261C2×C22⋊C4—22no—
262C2×C22⋊C4—22no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—224no—
265C2×C22⋊C4C22×D1112yes—
266C2×C42—21no—
267C2×C42C22×D1111yescharacteristic
268#107—224no—
269C4⋊C8—222no—
270#103—224no—
271#102—224no—
272C22⋊C8—114no—
273#97—222no—
274#95—21no—
275#95C22×D1112yes—
276C2×C11—22no—
277C2×C11—44no—
278C2×C11—82no—
279C2×C11#300411yescharacteristic
280C2×C11C2×#45311yescharacteristic
281C2×C11#302511yescharacteristic
282C24—21no—
283C24C2×C22⋊D1112yes—
284C2×Q8—114no—
285C2×Q8—224no—
286C2×Q8—222no—
287C2×Q8—884no—
288C2×D4—24no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—44no—
292C2×D4—42no—
293C2×D4—44no—
294C2×D4—44no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—21no—
299C22×C4—44no—
300C22×C4—44no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—224no—
304C22×C4—224no—
305C22×C4C2×C22⋊D1111yescharacteristic
306C22×C4C2×C22⋊D1111yescharacteristic
307C22×C4C2×C22⋊D1112yes—
308C22×C4C23×D1111yescharacteristic
309SD16—448no—
310C2×C8—224no—
311C4⋊C4—22no—
312C4⋊C4—22no—
313C4⋊C4—44no—
314C4⋊C4—114no—
315C4⋊C4—224no—
316C4⋊C4—228no—
317C4⋊C4—224no—
318C4⋊C4—222no—
319C4⋊C4—222no—
320C4⋊C4—222no—
321C4⋊C4—224no—
322C22⋊C4—24no—
323C22⋊C4—44no—
324C22⋊C4—44no—
325C22⋊C4—42no—
326C22⋊C4—228no—
327C22⋊C4—224no—
328C42—24no—
329C42—224no—
330C42D4×D1112yes—
331C42D4×D1112yes—
332C11#1818011yescharacteristic, complemented, Sylow
333C23—22no—
334C23—22no—
335C23—22no—
336C23—42no—
337C23—42no—
338C23—42no—
339C23—41no—
340C23—41no—
341C23—42no—
342C23#6700414yes—
343C23C22×C22⋊D1111yescharacteristic
344Q8—444no—
345Q8—444no—
346Q8—884no—
347D4—28no—
348D4—24no—
349D4—42no—
350D4—416no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—24no—
354C2×C4—22no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—44no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—82no—
363C2×C4—82no—
364C2×C4—82no—
365C2×C4—224no—
366C2×C4—224no—
367C2×C4—884no—
368C2×C4—884no—
369C2×C4#6699012yes—
370C2×C4#6699011yescharacteristic
371C2×C4#6699011yescharacteristic
372C2×C4C2×D4×D1112yes—
373C8—444no—
374C22—21no—
375C22—21no—
376C22—24no—
377C22—44no—
378C22—44no—
379C22—42no—
380C22—42no—
381C22—42no—
382C22—82no—
383C22—82no—
384C22—81no—
385C22—81no—
386C22C2×#6699011yescharacteristic
387C22C2×#6700412yes—
388C4—22no—
389C4—21no—
390C4—22no—
391C4—44no—
392C4—42no—
393C4—81no—
394C4—444no—
395C4—444no—
396C4#1062269012yes—
397C2—22no—
398C2—44no—
399C2—82no—
400C2#1307784911yescharacteristic
401C2C2×#1062269011yescharacteristic
402C2#1307800711yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#2397C2
socleC22×C11C2×#120
hypercenter#2397D11
hypocenterC11#18180
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2397

Complements

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

NH ≅ G/Ntype
1. #13082419C2semidirect
2. #13078715C2semidirect
3. #13067640C2semidirect
4. #13067538C2semidirect
5. #13067127C2semidirect
6. #13066957C2semidirect
69. #66922D4semidirect
70. #66922D4semidirect
72. C4×Dic22D4semidirect
332. C11#18180semidirect

Maximal subgroups

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

subgroupindex
#130824192
#130787152
#130676402
#130675382
#130671272
#130669572
C11×#23972
#1818011