Finite Group Databasebeta

← #14726188

Subgroups — #14726188

Order 2816.

1054 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 1054 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
1C2×#10623014C211yesmaximal, characteristic
2#13078564C212yesmaximal, complemented
3#13067640C214yesmaximal, complemented
4#13067606C214yesmaximal, complemented
5#13067148C212yesmaximal, complemented
6#13066943C211yesmaximal, characteristic
7C11×#2482C211yesmaximal, characteristic
8C2×C11×#117C2211yescharacteristic
9C22×C11×C22⋊C4C2211yescharacteristic
10C22×C22⋊Dic11—21no—
11C2×#66977—21no—
12C2×#66977C2212yes—
13#10623014—22no—
14#10623014—24no—
15#10623014C2214yes—
16C2×#66931—22no—
17C2×#66931—22no—
18C11×#399C2212yes—
19C11×#397C2212yes—
20C11×#388—22no—
21C11×#385—21no—
22C11×#381C2211yescharacteristic
23C11×#379—21no—
24#10622820C2212yes—
25#10622617—22no—
26#10622609—24no—
27#10622608—22no—
28#10622584C2214yescomplemented
29#10622583C2214yescomplemented
30#10622163C2214yes—
31#10622090C2218yescomplemented
32C25×C11D411yescharacteristic
33C23×C4×C11D411yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C23×Dic11—21no—
36C23×Dic11—21no—
37C22×Dic22—21no—
38C22×Dic22D412yes—
39C11×#117—22no—
40C11×#117—22no—
41C2×C11×C4⋊C4—22no—
42C2×C11×C4⋊C4C2311yescharacteristic
43C2×C11×C4⋊C4C2311yescharacteristic
44C2×C11×C22⋊C4—22no—
45C2×C11×C22⋊C4—22no—
46C2×C11×C22⋊C4—21no—
47C2×C11×C22⋊C4—21no—
48C2×C11×C22⋊C4—22no—
49C2×C11×C22⋊C4—22no—
50C2×C11×C22⋊C4D412yes—
51C2×C11×C22⋊C4C2312yes—
52C2×C42×C11—21no—
53C2×C22⋊Dic11—22no—
54C2×C22⋊Dic11—24no—
55C2×C22⋊Dic11—24no—
56C2×C22⋊Dic11—22no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11D412yes—
59#66977—24no—
60#66977—22no—
61#66977—22no—
62#66977—24no—
63#66977D414yes—
64#66977C2314yes—
65C2×Dic11⋊C4—22no—
66C2×Dic11⋊C4—22no—
67C2×#4318—22no—
68#66931—28no—
69#66931—28no—
70#66931—28no—
71#66931—28no—
72C11×#95—21no—
73C11×#95—22no—
74C11×#95C2312yes—
75C22⋊(C11⋊C8)—22no—
76C22⋊(C11⋊C8)C2314yes—
77#66874—24no—
78#66874—24no—
79#66872—24no—
80#66871—24no—
81#18138—111nomaximal, Sylow
82C24×C11—21no—
83C24×C11—21no—
84C24×C11—24no—
85C24×C11—42no—
86C24×C11—81no—
87C24×C11C2×D411yescharacteristic
88C24×C11C2×D412yes—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—22no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—42no—
95C22×C4×C11—81no—
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2411yescharacteristic
101C22×Dic11—24no—
102C22×Dic11—24no—
103C22×Dic11—22no—
104C22×Dic11—22no—
105C22×Dic11—82no—
106C22×Dic11—82no—
107C2×Dic22—24no—
108C2×Dic22—22no—
109C2×Dic22—44no—
110C2×Dic22—82no—
111C2×Dic22C2×D414yes—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—82no—
115C11×C22⋊C4—24no—
116C11×C22⋊C4—24no—
117C11×C22⋊C4—42no—
118C11×C22⋊C4—41no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—44no—
121C11×C22⋊C4—82no—
122C42×C11—42no—
123C22⋊Dic11—28no—
124C22⋊Dic11—24no—
125C22⋊Dic11—24no—
126C4⋊Dic11—24no—
127C4⋊Dic11—22no—
128C4⋊Dic11C2×D414yes—
129Dic11⋊C4—28no—
130Dic11⋊C4—24no—
131Dic11⋊C4—24no—
132#4318—44no—
133C2×C11⋊C8—24no—
134C2×#543—111no—
135#3095—112no—
136#2482D1111yescharacteristic
137#1614—114no—
138#1608—114no—
139#1511—112no—
140#1462—111no—
141C23×C11—24no—
142C23×C11—24no—
143C23×C11—22no—
144C23×C11—22no—
145C23×C11—22no—
146C23×C11—22no—
147C23×C11—41no—
148C23×C11—42no—
149C23×C11—42no—
150C23×C11—42no—
151C23×C11—42no—
152C23×C11—81no—
153C23×C11—81no—
154C23×C11—88no—
155C23×C11#12011yescharacteristic
156C23×C11#12011yescharacteristic
157C23×C11#13714yes—
158C23×C11C22×D411yescharacteristic
159C2×C4×C11—24no—
160C2×C4×C11—22no—
161C2×C4×C11—42no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—81no—
174C2×C4×C11#12012yes—
175C2×C4×C11C22×D412yes—
176C2×Dic11—24no—
177C2×Dic11—24no—
178C2×Dic11—44no—
179C2×Dic11—44no—
180C2×Dic11—84no—
181C2×Dic11—84no—
182Dic22—44no—
183Dic22—82no—
184Dic22—84no—
185C11⋊C8—44no—
186#543—114no—
187#543—224no—
188#543—222no—
189C2×C22⋊Q8—112no—
190C2×C22⋊Q8—222no—
191C2×C22⋊Q8—222no—
192C2×C22⋊Q8—221no—
193C2×#117C2×D1111yescharacteristic
194C22×C22⋊C4—221no—
195C22×C22⋊C4C2×D1111yescharacteristic
196#485—224no—
197#484—114no—
198#483—114no—
199#428—222no—
200#419—222no—
201#407—112no—
202#399C2×D1112yes—
203#397C2×D1112yes—
204#388—22no—
205#385—21no—
206#381C2×D1111yescharacteristic
207#379—21no—
208#328—118no—
209#323—114no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—24no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—44no—
219C22×C11—44no—
220C22×C11—48no—
221C22×C11—42no—
222C22×C11—42no—
223C22×C11—82no—
224C22×C11—84no—
225C22×C11#45812yes—
226C22×C11C2×#12011yescharacteristic
227C22×C11C2×#13712yes—
228C4×C11—22no—
229C4×C11—22no—
230C4×C11—42no—
231C4×C11—82no—
232C4×C11—81no—
233C4×C11—81no—
234Dic11—44no—
235Dic11—44no—
236C25C22⋊D1111yescharacteristic
237C22×Q8—112no—
238C22×Q8—221no—
239C23×C4—221no—
240C23×C4—221no—
241C23×C4C22⋊D1111yescharacteristic
242C23×C4C22×D1111yescharacteristic
243C2×M16—222no—
244C22⋊Q8—114no—
245C22⋊Q8—114no—
246C22⋊Q8—228no—
247C22⋊Q8—228no—
248C22⋊Q8—228no—
249C22⋊Q8—228no—
250C22⋊Q8—224no—
251C22⋊Q8—222no—
252C22⋊Q8—222no—
253C22⋊Q8—224no—
254#117—22no—
255#117—22no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—112no—
258C2×C4⋊C4—222no—
259C2×C4⋊C4—221no—
260C2×C4⋊C4—222no—
261C2×C4⋊C4C22×D1111yescharacteristic
262C2×C4⋊C4C22×D1111yescharacteristic
263C2×C22⋊C4—22no—
264C2×C22⋊C4—22no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—22no—
268C2×C22⋊C4—22no—
269C2×C22⋊C4—222no—
270C2×C22⋊C4—224no—
271C2×C22⋊C4—222no—
272C2×C22⋊C4—224no—
273C2×C22⋊C4C22⋊D1112yes—
274C2×C22⋊C4C22×D1112yes—
275C2×C42—21no—
276#107—224no—
277#106—224no—
278#103—224no—
279#103—224no—
280C22⋊C8—114no—
281C22⋊C8—222no—
282#95—21no—
283#95—22no—
284#95C22×D1112yes—
285C2×C11—22no—
286C2×C11—22no—
287C2×C11—41no—
288C2×C11—44no—
289C2×C11#300411yescharacteristic
290C2×C11#301911yescharacteristic
291C2×C11C2×#45811yescharacteristic
292C24—21no—
293C24—21no—
294C24—24no—
295C24—42no—
296C24—81no—
297C24C2×C22⋊D1111yescharacteristic
298C24C2×C22⋊D1112yes—
299C2×Q8—114no—
300C2×Q8—224no—
301C2×Q8—222no—
302C2×Q8—444no—
303C2×Q8—882no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—22no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—42no—
310C22×C4—81no—
311C22×C4—222no—
312C22×C4—222no—
313C22×C4—224no—
314C22×C4—224no—
315C22×C4—882no—
316C22×C4—882no—
317C22×C4D4×D1112yes—
318C22×C4D4×D1112yes—
319C22×C4C2×C22⋊D1112yes—
320C22×C4C2×C22⋊D1111yescharacteristic
321C22×C4C23×D1111yescharacteristic
322M16—444no—
323C2×C8—224no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—82no—
327C4⋊C4—114no—
328C4⋊C4—228no—
329C4⋊C4—224no—
330C4⋊C4—222no—
331C4⋊C4—224no—
332C4⋊C4—224no—
333C22⋊C4—24no—
334C22⋊C4—24no—
335C22⋊C4—42no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—44no—
339C22⋊C4—82no—
340C22⋊C4—228no—
341C22⋊C4—224no—
342C22⋊C4—224no—
343C42—42no—
344C11#1813811yescharacteristic, complemented, Sylow
345C23—24no—
346C23—24no—
347C23—22no—
348C23—22no—
349C23—22no—
350C23—22no—
351C23—41no—
352C23—42no—
353C23—42no—
354C23—42no—
355C23—42no—
356C23—81no—
357C23—81no—
358C23—88no—
359C23#6699011yescharacteristic
360C23#6699011yescharacteristic
361C23#6700414yes—
362C23C22×C22⋊D1111yescharacteristic
363Q8—444no—
364Q8—882no—
365Q8—884no—
366C2×C4—24no—
367C2×C4—22no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—81no—
381C2×C4—224no—
382C2×C4—224no—
383C2×C4—444no—
384C2×C4—444no—
385C2×C4—884no—
386C2×C4—884no—
387C2×C4#6699012yes—
388C2×C4C2×D4×D1112yes—
389C8—444no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—24no—
396C22—21no—
397C22—21no—
398C22—44no—
399C22—44no—
400C22—48no—
401C22—42no—
402C22—42no—
403C22—82no—
404C22—84no—
405C22#1062266612yes—
406C22C2×#6699011yescharacteristic
407C22C2×#6700412yes—
408C4—22no—
409C4—22no—
410C4—42no—
411C4—82no—
412C4—81no—
413C4—81no—
414C4—444no—
415C4—444no—
416C2—22no—
417C2—22no—
418C2—41no—
419C2—44no—
420C2#1307784911yescharacteristic
421C2#1307797211yescharacteristic
422C2C2×#1062266611yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2482C2
socleC22×C11C2×#120
prime radicalC25×C11D4
hypercenter#2482D11
hypocenterC11#18138
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2482

Complements

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

NH ≅ G/Ntype
2. #13078564C2semidirect
3. #13067640C2semidirect
4. #13067606C2semidirect
5. #13067148C2semidirect
28. #10622584C22semidirect
29. #10622583C22semidirect
31. #10622090C22semidirect
344. C11#18138semidirect

Maximal subgroups

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

subgroupindex
C2×#106230142
#130785642
#130676402
#130676062
#130671482
#130669432
C11×#24822
#1813811