Finite Group Databasebeta

← #14726830

Subgroups — #14726830

Order 2816.

1058 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 1058 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#13082419C211yesmaximal, characteristic, complemented
2#13078624C212yesmaximal, complemented
3#13067606C214yesmaximal, complemented
4#13067538C214yesmaximal, complemented
5#13067179C212yesmaximal, complemented
6#13066937C211yesmaximal, characteristic, complemented
7C11×#2535C211yesmaximal, characteristic
8C2×C11×#121—21no—
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×#397C2212yes—
20C11×#392C2212yes—
21C11×#386—22no—
22C11×#382C2211yescharacteristic
23C11×#380—21no—
24#10622831C2214yes—
25#10622632—22no—
26C4×#4324—24no—
27#10622621—22no—
28#10622584C2214yes—
29#10622538C2212yes—
30#10622163C2214yes—
31#10622090C2218yes—
32C22×D4×C11—22no—
33C22×D4×C11D411yescharacteristic
34C22×D4×C11C2311yescharacteristic
35C23×C4×C11—21no—
36C23×C4×C11D412yes—
37C22×Dic22—22no—
38C11×#121—44no—
39C4×D4×C11—22no—
40C4×D4×C11—22no—
41C4×D4×C11—22no—
42C4×D4×C11—22no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4D411yescharacteristic
45C2×C11×C4⋊C4C2311yescharacteristic
46C2×C11×C22⋊C4—22no—
47C2×C11×C22⋊C4—21no—
48C2×C11×C22⋊C4—22no—
49C2×C11×C22⋊C4C2312yes—
50C2×C42×C11C2311yescharacteristic
51C2×C22⋊Dic11—24no—
52D4×Dic11—24no—
53D4×Dic11—24no—
54C2×#4324—24no—
55#66979—22no—
56C2×C4⋊Dic11—22no—
57#66977—24no—
58#66977—24no—
59#66977—22no—
60#66977—24no—
61#66977C2314yes—
62C2×Dic11⋊C4—24no—
63#66943—24no—
64#66941—24no—
65#66931—28no—
66#66931—28no—
67#66923—22no—
68#66922D412yescomplemented
69#66922D412yescomplemented
70C4×Dic22—22no—
71C4×Dic22D414yescomplemented
72C11×#95—22no—
73C11×#95—21no—
74C11×#95C2312yes—
75#66896—24no—
76C22⋊(C11⋊C8)C2314yes—
77#66874—24no—
78#66872—24no—
79C4⋊(C11⋊C8)—22no—
80C4×C11⋊C8—22no—
81#18212—111nomaximal, Sylow
82C24×C11—21no—
83C24×C11C2×D412yes—
84C2×D4×C11—22no—
85C2×D4×C11—22no—
86C2×D4×C11—22no—
87C2×D4×C11—42no—
88C2×D4×C11—44no—
89C2×D4×C11—44no—
90C2×D4×C11—82no—
91C2×D4×C11SD1614yescomplemented
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—21no—
96C22×C4×C11—42no—
97C22×C4×C11—42no—
98C22×C4×C11—42no—
99C22×C4×C11—82no—
100C22×C4×C11C2×D412yes—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2411yescharacteristic
104C22×Dic11—24no—
105C22×Dic11—24no—
106C2×Dic22—24no—
107C2×Dic22—22no—
108C2×Dic22—84no—
109C2×Dic22C2×D414yes—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—42no—
113C11×C22⋊C4—24no—
114C11×C22⋊C4—44no—
115C11×C22⋊C4—41no—
116C11×C22⋊C4—41no—
117C11×C22⋊C4—82no—
118C42×C11C2×D412yes—
119C42×C11C2×D412yes—
120C22⋊Dic11—28no—
121C22⋊Dic11—24no—
122#4324—48no—
123C4⋊Dic11—24no—
124C4⋊Dic11—22no—
125C4⋊Dic11—22no—
126C4⋊Dic11—22no—
127C4⋊Dic11C2×D414yes—
128Dic11⋊C4—28no—
129Dic11⋊C4—24no—
130Dic11⋊C4—24no—
131C4×Dic11—24no—
132C2×C11⋊C8—24no—
133#3501—111no—
134#3101—112no—
135#2535D1111yescharacteristic
136#1608—114no—
137#1596—114no—
138#1518—112no—
139#1460—111no—
140C23×C11—22no—
141C23×C11—22no—
142C23×C11—22no—
143C23×C11—42no—
144C23×C11—42no—
145C23×C11—41no—
146C23×C11—41no—
147C23×C11—41no—
148C23×C11—41no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11C2×SD1614yes—
152C23×C11C22×D411yescharacteristic
153D4×C11—24no—
154D4×C11—28no—
155D4×C11—42no—
156D4×C11—88no—
157C2×C4×C11—22no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—44no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—42no—
167C2×C4×C11—41no—
168C2×C4×C11—82no—
169C2×C4×C11—84no—
170C2×C4×C11#12011yescharacteristic
171C2×C4×C11#12011yescharacteristic
172C2×C4×C11#12012yes—
173C2×C4×C11C2×SD1612yes—
174C2×C4×C11#13712yes—
175C2×C4×C11C22×D412yes—
176C2×Dic11—24no—
177C2×Dic11—24no—
178C2×Dic11—84no—
179C2×Dic11—84no—
180Dic22—44no—
181Dic22—44no—
182Dic22—84no—
183C11⋊C8—44no—
184#554—224no—
185#554—222no—
186D4×Q8—222no—
187#544—221no—
188#543—114no—
189#533—112no—
190C2×C22⋊Q8—222no—
191C2×#121—21no—
192#518—221no—
193C2×C4×D4C2×D1111yescharacteristic
194C2×C4×D4C2×D1111yescharacteristic
195#483—114no—
196#476—222no—
197#461—222no—
198#450—114no—
199C4×SD16—224no—
200#431—112no—
201#397C2×D1112yes—
202#392C2×D1112yes—
203#386—22no—
204#382C2×D1111yescharacteristic
205#380—21no—
206#328—118no—
207#323—114no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—24no—
211C22×C11—44no—
212C22×C11—42no—
213C22×C11—42no—
214C22×C11—42no—
215C22×C11—42no—
216C22×C11—42no—
217C22×C11—82no—
218C22×C11—81no—
219C22×C11—81no—
220C22×C11—81no—
221C22×C11—81no—
222C22×C11C2×#12011yescharacteristic
223C22×C11C22×SD1611yescharacteristic
224C22×C11C2×#13711yescharacteristic
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—22no—
228C4×C11—42no—
229C4×C11—82no—
230C4×C11—81no—
231C4×C11#44814yes—
232Dic11—44no—
233Dic11—44no—
234C22×Q8—222no—
235C22×D4—22no—
236C22×D4C22⋊D1111yescharacteristic
237C22×D4C22×D1111yescharacteristic
238C23×C4—21no—
239C23×C4C22⋊D1112yes—
240C2×SD16—224no—
241C4⋊Q8—112no—
242C4⋊Q8—112no—
243C4⋊Q8—224no—
244#125—224no—
245#125—222no—
246C22⋊Q8—114no—
247C22⋊Q8—228no—
248C22⋊Q8—228no—
249C22⋊Q8—224no—
250C22⋊Q8—224no—
251C22⋊Q8—222no—
252C22⋊Q8—224no—
253#121—44no—
254C4×Q8—114no—
255C4×Q8—222no—
256C4×D4—22no—
257C4×D4—22no—
258C4×D4—22no—
259C4×D4—22no—
260C4×D4—224no—
261C4×D4—224no—
262#117—222no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—224no—
265C2×C4⋊C4—222no—
266C2×C4⋊C4C22⋊D1111yescharacteristic
267C2×C4⋊C4C22×D1111yescharacteristic
268C2×C22⋊C4—22no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—22no—
271C2×C22⋊C4—224no—
272C2×C22⋊C4C22×D1112yes—
273C2×C42C22×D1111yescharacteristic
274#106—224no—
275C4⋊C8—222no—
276#103—224no—
277#102—224no—
278C22⋊C8—114no—
279C4×C8—222no—
280#95—22no—
281#95—21no—
282#95C22×D1112yes—
283C2×C11—21no—
284C2×C11—21no—
285C2×C11—44no—
286C2×C11—82no—
287C2×C11C2×#44811yescharacteristic
288C2×C11#301911yescharacteristic
289C2×C11#302511yescharacteristic
290C24—21no—
291C24C2×C22⋊D1112yes—
292C2×Q8—114no—
293C2×Q8—224no—
294C2×Q8—222no—
295C2×Q8—884no—
296C2×D4—22no—
297C2×D4—22no—
298C2×D4—22no—
299C2×D4—42no—
300C2×D4—44no—
301C2×D4—44no—
302C2×D4—82no—
303C2×D4#432414yescomplemented
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—21no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—82no—
312C22×C4—224no—
313C22×C4—224no—
314C22×C4C2×C22⋊D1112yes—
315C22×C4C2×C22⋊D1111yescharacteristic
316C22×C4C2×C22⋊D1111yescharacteristic
317C22×C4C23×D1111yescharacteristic
318SD16—448no—
319C2×C8—224no—
320C4⋊C4—22no—
321C4⋊C4—22no—
322C4⋊C4—42no—
323C4⋊C4—114no—
324C4⋊C4—224no—
325C4⋊C4—228no—
326C4⋊C4—224no—
327C4⋊C4—222no—
328C4⋊C4—222no—
329C4⋊C4—222no—
330C4⋊C4—224no—
331C22⋊C4—24no—
332C22⋊C4—44no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—82no—
336C22⋊C4—228no—
337C22⋊C4—224no—
338C42—224no—
339C42D4×D1112yes—
340C42D4×D1112yes—
341C11#1821211yescharacteristic, complemented, Sylow
342C23—22no—
343C23—22no—
344C23—22no—
345C23—42no—
346C23—42no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23C2×#432414yes—
354C23C22×C22⋊D1111yescharacteristic
355Q8—444no—
356Q8—444no—
357Q8—884no—
358D4—24no—
359D4—28no—
360D4—42no—
361D4—88no—
362C2×C4—22no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—44no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—82no—
374C2×C4—84no—
375C2×C4—224no—
376C2×C4—224no—
377C2×C4—884no—
378C2×C4—884no—
379C2×C4C2×#432412yes—
380C2×C4#6699011yescharacteristic
381C2×C4#6699011yescharacteristic
382C2×C4#6699012yes—
383C2×C4#6700412yes—
384C2×C4C2×D4×D1112yes—
385C8—444no—
386C22—21no—
387C22—21no—
388C22—24no—
389C22—44no—
390C22—42no—
391C22—42no—
392C22—42no—
393C22—42no—
394C22—42no—
395C22—82no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22—81no—
400C22C22×#432411yescharacteristic
401C22C2×#6699011yescharacteristic
402C22C2×#6700411yescharacteristic
403C4—21no—
404C4—21no—
405C4—22no—
406C4—42no—
407C4—82no—
408C4—81no—
409C4—444no—
410C4—444no—
411C4#1062265314yes—
412C2—21no—
413C2—21no—
414C2—44no—
415C2—82no—
416C2C2×#1062265311yescharacteristic
417C2#1307797211yescharacteristic
418C2#1307800711yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#2535C2
socleC22×C11C2×#120
hypercenter#2535D11
hypocenterC11#18212
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2535

Complements

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

NH ≅ G/Ntype
1. #13082419C2semidirect
2. #13078624C2semidirect
3. #13067606C2semidirect
4. #13067538C2semidirect
5. #13067179C2semidirect
6. #13066937C2semidirect
68. #66922D4semidirect
69. #66922D4semidirect
71. C4×Dic22D4semidirect
91. C2×D4×C11SD16semidirect
303. C2×D4#4324semidirect
341. C11#18212semidirect

Maximal subgroups

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

subgroupindex
#130824192
#130786242
#130676062
#130675382
#130671792
#130669372
C11×#25352
#1821211