Finite Group Databasebeta

← #14726837

Subgroups — #14726837

Order 2816.

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

normal subgroups only

This group has 974 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
2#13078655C212yesmaximal, complemented
3#13067640C214yesmaximal, complemented
4#13067572C214yesmaximal, complemented
5#13067179C212yesmaximal, complemented
6#13066937C211yesmaximal, characteristic
7C11×#2580C211yesmaximal, characteristic
8C2×C4×Q8×C11C2211yescharacteristic
9C2×C4×D4×C11C2211yescharacteristic
10#10623329—21no—
11C2×#66977—22no—
12#10623074—22no—
13#10623070—24no—
14D4×Dic22—22no—
15#10623031—21no—
16#10623014C2214yes—
17#10623001C2212yes—
18C11×#399C2212yes—
19C11×#393C2212yes—
20C11×#390—21no—
21C11×#389—21no—
22C11×#385—22no—
23C11×#382C2211yescharacteristic
24#10622841C2214yes—
25#10622644—22no—
26C4×#4326—24no—
27#10622634—22no—
28#10622583C2214yes—
29#10622538C2212yes—
30#10622163C2214yes—
31#10622090C2218yes—
32C22×Q8×C11C2311yescharacteristic
33C22×D4×C11D411yescharacteristic
34C23×C4×C11D412yes—
35C22×Dic22—22no—
36C4×Q8×C11—22no—
37C4×Q8×C11—22no—
38C4×D4×C11—22no—
39C4×D4×C11—22no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4D411yescharacteristic
44C2×C11×C4⋊C4C2311yescharacteristic
45C2×C11×C22⋊C4—22no—
46C2×C11×C22⋊C4—22no—
47C2×C11×C22⋊C4C2312yes—
48C2×C42×C11—21no—
49C2×C42×C11C2311yescharacteristic
50C2×C22⋊Dic11—24no—
51C2×#4326—24no—
52D4×Dic11—24no—
53D4×Dic11—24no—
54#66979—22no—
55C2×C4⋊Dic11—22no—
56#66977—24no—
57#66977—24no—
58#66977—22no—
59#66977—24no—
60#66977C2314yes—
61C2×Dic11⋊C4—24no—
62#66943—24no—
63#66941—24no—
64#66931—28no—
65#66931—28no—
66#66923—22no—
67#66922D412yes—
68#66922D412yes—
69C4×Dic22—22no—
70C4×Dic22D414yes—
71C11×#95—21no—
72C11×#95—22no—
73C11×#95C2312yes—
74#66899—24no—
75C22⋊(C11⋊C8)C2314yes—
76#66874—24no—
77#66871—24no—
78C4⋊(C11⋊C8)—22no—
79C4×C11⋊C8—22no—
80#18213—111nomaximal, Sylow
81C24×C11C2×D412yes—
82C2×Q8×C11—22no—
83C2×Q8×C11—42no—
84C2×D4×C11—22no—
85C2×D4×C11—22no—
86C2×D4×C11Q1614yescomplemented
87C22×C4×C11—21no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—21no—
92C22×C4×C11—82no—
93C22×C4×C11C2×D412yes—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2411yescharacteristic
97C22×Dic11—24no—
98C22×Dic11—24no—
99C2×Dic22—24no—
100C2×Dic22—22no—
101C2×Dic22—84no—
102C2×Dic22C2×D414yes—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—42no—
108C11×C4⋊C4—82no—
109C11×C22⋊C4—24no—
110C11×C22⋊C4—44no—
111C11×C22⋊C4—82no—
112C42×C11—42no—
113C42×C11C2×D412yes—
114C42×C11C2×D412yes—
115C22⋊Dic11—28no—
116C22⋊Dic11—24no—
117#4326—48no—
118C4⋊Dic11—24no—
119C4⋊Dic11—22no—
120C4⋊Dic11—22no—
121C4⋊Dic11—22no—
122C4⋊Dic11C2×D414yes—
123Dic11⋊C4—28no—
124Dic11⋊C4—24no—
125Dic11⋊C4—24no—
126C4×Dic11—24no—
127C2×C11⋊C8—24no—
128#3501—111no—
129#3104—112no—
130#2580D1111yescharacteristic
131#1614—114no—
132#1602—114no—
133#1518—112no—
134#1460—111no—
135C23×C11—22no—
136C23×C11—22no—
137C23×C11—42no—
138C23×C11—42no—
139C23×C11C2×Q1614yes—
140C23×C11C22×D411yescharacteristic
141Q8×C11—24no—
142Q8×C11—42no—
143D4×C11—28no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—44no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—41no—
154C2×C4×C11—42no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—42no—
158C2×C4×C11—82no—
159C2×C4×C11#12011yescharacteristic
160C2×C4×C11#12011yescharacteristic
161C2×C4×C11#12012yes—
162C2×C4×C11C2×Q1612yes—
163C2×C4×C11#13712yes—
164C2×C4×C11C22×D412yes—
165C2×Dic11—24no—
166C2×Dic11—24no—
167C2×Dic11—84no—
168C2×Dic11—84no—
169Dic22—44no—
170Dic22—44no—
171Dic22—84no—
172C11⋊C8—44no—
173#554—224no—
174#554—222no—
175D4×Q8—222no—
176#544—221no—
177#543—114no—
178#533—112no—
179C2×C22⋊Q8—222no—
180#518—221no—
181C2×C4×Q8C2×D1111yescharacteristic
182C2×C4×D4C2×D1111yescharacteristic
183#484—114no—
184#477—222no—
185#462—222no—
186#451—114no—
187C4×Q16—224no—
188#431—112no—
189#399C2×D1112yes—
190#393C2×D1112yes—
191#390—21no—
192#389—21no—
193#385—22no—
194#382C2×D1111yescharacteristic
195#328—118no—
196#323—114no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—24no—
200C22×C11—44no—
201C22×C11—42no—
202C22×C11—42no—
203C22×C11—82no—
204C22×C11C2×#12011yescharacteristic
205C22×C11C22×Q1611yescharacteristic
206C22×C11C2×#13711yescharacteristic
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—22no—
210C4×C11—42no—
211C4×C11—42no—
212C4×C11—82no—
213C4×C11—81no—
214C4×C11#45114yes—
215Dic11—44no—
216Dic11—44no—
217C22×Q8—222no—
218C22×Q8C22×D1111yescharacteristic
219C22×D4C22⋊D1111yescharacteristic
220C23×C4C22⋊D1112yes—
221C2×Q16—224no—
222C4⋊Q8—112no—
223C4⋊Q8—112no—
224C4⋊Q8—224no—
225#125—224no—
226#125—222no—
227C22⋊Q8—114no—
228C22⋊Q8—228no—
229C22⋊Q8—228no—
230C22⋊Q8—224no—
231C22⋊Q8—224no—
232C22⋊Q8—222no—
233C22⋊Q8—224no—
234C4×Q8—22no—
235C4×Q8—22no—
236C4×Q8—114no—
237C4×Q8—222no—
238C4×D4—22no—
239C4×D4—22no—
240C4×D4—224no—
241C4×D4—224no—
242#117—222no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—224no—
247C2×C4⋊C4—222no—
248C2×C4⋊C4C22⋊D1111yescharacteristic
249C2×C4⋊C4C22×D1111yescharacteristic
250C2×C22⋊C4—22no—
251C2×C22⋊C4—22no—
252C2×C22⋊C4—224no—
253C2×C22⋊C4C22×D1112yes—
254C2×C42—21no—
255C2×C42C22×D1111yescharacteristic
256#107—224no—
257C4⋊C8—222no—
258#103—224no—
259#103—224no—
260C22⋊C8—114no—
261C4×C8—222no—
262#95—21no—
263#95—22no—
264#95C22×D1112yes—
265C2×C11—21no—
266C2×C11—21no—
267C2×C11—44no—
268C2×C11C2×#45111yescharacteristic
269C2×C11#301911yescharacteristic
270C2×C11#302511yescharacteristic
271C24C2×C22⋊D1112yes—
272C2×Q8—22no—
273C2×Q8—42no—
274C2×Q8—114no—
275C2×Q8—224no—
276C2×Q8—222no—
277C2×Q8—884no—
278C2×D4—22no—
279C2×D4—22no—
280C2×D4#432614yescomplemented
281C22×C4—21no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—21no—
286C22×C4—82no—
287C22×C4—224no—
288C22×C4—224no—
289C22×C4C2×C22⋊D1112yes—
290C22×C4C2×C22⋊D1111yescharacteristic
291C22×C4C2×C22⋊D1111yescharacteristic
292C22×C4C23×D1111yescharacteristic
293Q16—448no—
294C2×C8—224no—
295C4⋊C4—22no—
296C4⋊C4—22no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—42no—
300C4⋊C4—82no—
301C4⋊C4—114no—
302C4⋊C4—224no—
303C4⋊C4—228no—
304C4⋊C4—224no—
305C4⋊C4—222no—
306C4⋊C4—222no—
307C4⋊C4—222no—
308C4⋊C4—224no—
309C22⋊C4—24no—
310C22⋊C4—44no—
311C22⋊C4—82no—
312C22⋊C4—228no—
313C22⋊C4—224no—
314C42—42no—
315C42—224no—
316C42D4×D1112yes—
317C42D4×D1112yes—
318C11#1821311yescharacteristic, complemented, Sylow
319C23—22no—
320C23—22no—
321C23—42no—
322C23—42no—
323C23C2×#432614yes—
324C23C22×C22⋊D1111yescharacteristic
325Q8—24no—
326Q8—42no—
327Q8—444no—
328Q8—444no—
329Q8—884no—
330D4—28no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—44no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—82no—
346C2×C4—224no—
347C2×C4—224no—
348C2×C4—884no—
349C2×C4—884no—
350C2×C4#6699011yescharacteristic
351C2×C4#6699011yescharacteristic
352C2×C4#6699012yes—
353C2×C4C2×#432612yes—
354C2×C4#6700412yes—
355C2×C4C2×D4×D1112yes—
356C8—444no—
357C22—21no—
358C22—21no—
359C22—24no—
360C22—44no—
361C22—42no—
362C22—42no—
363C22—82no—
364C22C2×#6699011yescharacteristic
365C22C22×#432611yescharacteristic
366C22C2×#6700411yescharacteristic
367C4—21no—
368C4—21no—
369C4—22no—
370C4—42no—
371C4—42no—
372C4—82no—
373C4—81no—
374C4—444no—
375C4—444no—
376C4#1062266314yes—
377C2—21no—
378C2—21no—
379C2—44no—
380C2C2×#1062266311yescharacteristic
381C2#1307797211yescharacteristic
382C2#1307800711yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2580C2
socleC22×C11C2×#120
prime radicalC22×D4×C11D4
hypercenter#2580D11
hypocenterC11#18213
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2580

Complements

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

NH ≅ G/Ntype
2. #13078655C2semidirect
3. #13067640C2semidirect
4. #13067572C2semidirect
5. #13067179C2semidirect
86. C2×D4×C11Q16semidirect
280. C2×D4#4326semidirect
318. C11#18213semidirect

Maximal subgroups

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

subgroupindex
#130824192
#130786552
#130676402
#130675722
#130671792
#130669372
C11×#25802
#1821311