Finite Group Databasebeta

← #14719696

Subgroups — #14719696

Order 2816.

1206 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623054C211yesmaximal, characteristic
2#13077656C212yesmaximal, complemented
3#13066951C214yesmaximal, complemented
4#13066944C214yesmaximal, complemented
5#13066939C212yesmaximal, complemented
6#13066930C211yesmaximal, characteristic, complemented
7C11×#1458C211yesmaximal, characteristic, complemented
8C22×#4339C411yescharacteristic
9C2×C11×#117C2211yescharacteristic
10C22×C4⋊Dic11C411yescharacteristic
11#10623054—24no—
12#10623054—24no—
13C2×#66945C412yes—
14C2×C4⋊C4×D11C2212yes—
15C2×(C22⋊D11)⋊C4C412yes—
16C2×(C22⋊D11)⋊C4C2212yes—
17C2×C4×D44C411yescharacteristic
18C2×C4×D44C2211yescharacteristic
19C2×C4×Dic22C411yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C11×#431C2212yes—
22#10622538C2212yes—
23#10622451—24no—
24#10622339C2218yes—
25#10622301—24no—
26C11×#324C2212yes—
27C11×#323C2212yes—
28#10622166C2212yes—
29#10622163C2212yes—
30#10622107C2218yes—
31C23×C4×C11C2×C411yescharacteristic
32C22×C22⋊D11C2×C412yes—
33C23×Dic11C2×C412yes—
34C2×#4339—24no—
35C2×#4339—22no—
36C2×#4339—22no—
37C2×#4339—24no—
38C22×D44C2×C411yescharacteristic
39C22×C4×D11C2×C412yes—
40C22×C4×D11C2×C412yes—
41C22×C4×D11C2312yes—
42C22×Dic22C2×C411yescharacteristic
43C11×#117—22no—
44C11×#117—22no—
45C2×C11×C4⋊C4C2×C411yescharacteristic
46C2×C11×C4⋊C4C2311yescharacteristic
47C2×C11×C22⋊C4C2×C411yescharacteristic
48C2×C11×C22⋊C4C2311yescharacteristic
49C2×C42×C11C2×C411yescharacteristic
50C2×C42×C11C2311yescharacteristic
51C2×(C2×D11)⋊C4C2×C412yes—
52C2×(C2×D11)⋊C4C2×C412yes—
53C2×C4⋊Dic11—22no—
54C2×C4⋊Dic11—22no—
55C2×C4⋊Dic11C2×C411yescharacteristic
56C2×C4⋊Dic11C2×C412yes—
57C2×C4⋊Dic11C2×C411yescharacteristic
58C2×Dic11⋊C4C2×C412yes—
59C2×Dic11⋊C4C2312yes—
60C2×C4×Dic11C2×C412yes—
61C2×C4×Dic11C2×C412yes—
62C2×#4313—28no—
63#66945—28no—
64C4⋊C4×D11—28no—
65(C22⋊D11)⋊C4—28no—
66(C22⋊D11)⋊C4—28no—
67C4×D44—22no—
68C4×D44—22no—
69C4×D44D414yes—
70C4×D44D414yes—
71C4×Dic22—22no—
72C4×Dic22—22no—
73C4×Dic22—22no—
74C4×Dic22—22no—
75C11×C4⋊C8—22no—
76C11×C22⋊C8C2314yes—
77C4×C8×C11—22no—
78C22⋊(C11⋊C8)C2314yes—
79(C2×D11)⋊C8—28no—
80C4⋊(C11⋊C8)—22no—
81C4×C11⋊C8—22no—
82#17370—111nomaximal, Sylow
83C24×C11C22×C411yescharacteristic
84C23×D11C22×C412yes—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—22no—
88C22×C4×C11M1614yescomplemented
89C22×C4×C11C22×C411yescharacteristic
90C22×C4×C11C22×C411yescharacteristic
91C22×C4×C11C22×C411yescharacteristic
92C22×C4×C11C22×C411yescharacteristic
93C22×C4×C11C22×C411yescharacteristic
94C22×C4×C11C2411yescharacteristic
95C2×C22⋊D11—24no—
96C2×C22⋊D11—24no—
97C2×C22⋊D11—24no—
98C22×Dic11—24no—
99C22×Dic11—82no—
100C22×Dic11C22×C412yes—
101C22×Dic11C22×C412yes—
102C22×Dic11C22×C412yes—
103#4339—216no—
104#4339—216no—
105C2×D44—22no—
106C2×D44—22no—
107C2×D44C22⋊C412yes—
108C2×D44C22⋊C412yes—
109C2×C4×D11—24no—
110C2×C4×D11—24no—
111C2×C4×D11—24no—
112C2×C4×D11—24no—
113C2×C4×D11—82no—
114C2×C4×D11—82no—
115C2×C4×D11C2×D418yes—
116C2×Dic22—21no—
117C2×Dic22—21no—
118C2×Dic22—22no—
119C2×Dic22M1614yescomplemented
120C2×C8×C11—24no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C22⋊C4—22no—
124C11×C22⋊C4—22no—
125C42×C11—21no—
126C42×C11—21no—
127C42×C11C2×D412yes—
128C42×C11C2×D412yes—
129(C2×D11)⋊C4—24no—
130(C2×D11)⋊C4C22⋊C418yes—
131C4⋊Dic11—24no—
132C4⋊Dic11—21no—
133C4⋊Dic11—21no—
134C4⋊Dic11C22⋊C412yes—
135C4⋊Dic11C22⋊C412yes—
136Dic11⋊C4—24no—
137Dic11⋊C4—24no—
138C4×Dic11—24no—
139C4×Dic11—24no—
140C2×C11⋊C8—24no—
141#4313—88no—
142C2×#520—111no—
143#2975—112no—
144#1465—114no—
145#1463—114no—
146#1461—112no—
147#1458—111no—
148#1458D1111yescharacteristic, complemented
149C23×C11—21no—
150C23×C11—21no—
151C23×C11—41no—
152C23×C11—41no—
153C23×C11C2×M1612yes—
154C23×C11C23×C411yescharacteristic
155C22×D11—22no—
156C22×D11—22no—
157C22×D11—42no—
158C22×D11—42no—
159C22×D11C2×C22⋊C414yes—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—24no—
163C2×C4×C11—24no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11C2×C22⋊C412yes—
171C2×C4×C11C2×C22⋊C411yescharacteristic
172C2×C4×C11C2×C22⋊C411yescharacteristic
173C2×C4×C11C2×M1612yes—
174C2×C4×C11C2×M1612yes—
175C2×C4×C11C2×M1612yes—
176C2×C4×C11C22×D412yes—
177C22⋊D11—216no—
178C2×Dic11—22no—
179C2×Dic11—22no—
180C2×Dic11—22no—
181C2×Dic11—42no—
182C2×Dic11—42no—
183C2×Dic11—84no—
184C2×Dic11C2×C22⋊C414yes—
185C2×Dic11C2×M1614yes—
186D44—24no—
187D44—24no—
188C4×D11—216no—
189C4×D11—48no—
190C4×D11—84no—
191Dic22—24no—
192Dic22—24no—
193C8×C11—44no—
194C11⋊C8—44no—
195C22×#41—111no—
196#520—224no—
197#520—224no—
198C2×C4×Q8—111no—
199C2×C4×Q8—111no—
200C2×C4×D4—112no—
201C2×C4×D4—112no—
202C2×C4×D4—111no—
203C2×C4×D4—111no—
204C2×#117—112no—
205C2×#117C2×D1111yescharacteristic
206C22×C4⋊C4—111no—
207C22×C4⋊C4—112no—
208#436—224no—
209#436—224no—
210#431—112no—
211#431C2×D1112yes—
212#407—118no—
213#324—112no—
214#324—118no—
215#324C2×D1112yes—
216#323—112no—
217#323C2×D1112yes—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—22no—
221C22×C11—42no—
222C22×C11—42no—
223C22×C11—41no—
224C22×C11—41no—
225C22×C11C22×C22⋊C411yescharacteristic
226C22×C11C22×M1611yescharacteristic
227C22×C11C22×M1611yescharacteristic
228C2×D11—24no—
229C2×D11—24no—
230C2×D11—24no—
231C2×D11—44no—
232C2×D11—44no—
233C4×C11—22no—
234C4×C11—22no—
235C4×C11—22no—
236C4×C11—41no—
237C4×C11—41no—
238C4×C11#40712yes—
239C4×C11#40712yes—
240Dic11—24no—
241Dic11—24no—
242Dic11—42no—
243C2×#41—222no—
244C2×#41—222no—
245C2×#41—224no—
246C2×#41—224no—
247C22×Q8—111no—
248C22×D4—112no—
249C22×D4—111no—
250C23×C4—112no—
251C23×C4—112no—
252C23×C4—112no—
253C23×C4—112no—
254C23×C4C4×D1111yescharacteristic
255C2×M16—228no—
256C4×Q8—222no—
257C4×Q8—222no—
258C4×Q8—222no—
259C4×Q8—222no—
260C4×D4—114no—
261C4×D4—114no—
262C4×D4—222no—
263C4×D4—222no—
264C4×D4—228no—
265C4×D4—228no—
266#117—22no—
267#117—22no—
268#117—228no—
269C2×C4⋊C4—111no—
270C2×C4⋊C4—112no—
271C2×C4⋊C4—112no—
272C2×C4⋊C4—111no—
273C2×C4⋊C4—112no—
274C2×C4⋊C4—228no—
275C2×C4⋊C4—222no—
276C2×C4⋊C4—222no—
277C2×C4⋊C4C4×D1111yescharacteristic
278C2×C4⋊C4C22×D1111yescharacteristic
279C2×C22⋊C4—112no—
280C2×C22⋊C4—112no—
281C2×C22⋊C4C4×D1111yescharacteristic
282C2×C22⋊C4C22×D1111yescharacteristic
283C2×C42—112no—
284C2×C42—112no—
285C2×C42C4×D1111yescharacteristic
286C2×C42C22×D1111yescharacteristic
287C4⋊C8—22no—
288C4⋊C8—222no—
289C22⋊C8—114no—
290C22⋊C8—228no—
291C22⋊C8C22×D1114yes—
292C4×C8—22no—
293C4×C8—222no—
294C2×C11—21no—
295C2×C11—21no—
296C2×C11—42no—
297C2×C11C2×#40711yescharacteristic
298C2×C11#288311yescharacteristic
299C2×C11#288911yescharacteristic
300D11—44no—
301C24—112no—
302C24C2×C4×D1111yescharacteristic
303#41—2216no—
304#41—2216no—
305C2×Q8—114no—
306C2×Q8—221no—
307C2×Q8—221no—
308C2×Q8—222no—
309C2×D4—112no—
310C2×D4—112no—
311C2×D4—224no—
312C2×D4—224no—
313C2×D4—224no—
314C2×D4—222no—
315C2×D4—222no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—22no—
319C22×C4—112no—
320C22×C4—112no—
321C22×C4—118no—
322C22×C4—112no—
323C22×C4—224no—
324C22×C4—224no—
325C22×C4—224no—
326C22×C4—224no—
327C22×C4—224no—
328C22×C4—882no—
329C22×C4—882no—
330C22×C4—882no—
331C22×C4#431314yescomplemented
332C22×C4C2×C4×D1111yescharacteristic
333C22×C4C2×C4×D1111yescharacteristic
334C22×C4C2×C4×D1111yescharacteristic
335C22×C4C2×C4×D1111yescharacteristic
336C22×C4C2×C4×D1111yescharacteristic
337C22×C4C23×D1111yescharacteristic
338M16—888no—
339C2×C8—24no—
340C2×C8—224no—
341C4⋊C4—22no—
342C4⋊C4—22no—
343C4⋊C4—112no—
344C4⋊C4—112no—
345C4⋊C4—224no—
346C4⋊C4—224no—
347C4⋊C4—221no—
348C4⋊C4—221no—
349C4⋊C4—224no—
350C22⋊C4—22no—
351C22⋊C4—22no—
352C22⋊C4—118no—
353C22⋊C4—224no—
354C42—21no—
355C42—21no—
356C42—224no—
357C42—224no—
358C42D4×D1112yes—
359C42D4×D1112yes—
360C11#1737011yescharacteristic, complemented, Sylow
361C23—21no—
362C23—21no—
363C23—41no—
364C23—41no—
365C23—114no—
366C23—222no—
367C23—222no—
368C23—442no—
369C23—442no—
370C23C2×#431312yes—
371C23C22×C4×D1111yescharacteristic
372Q8—224no—
373Q8—224no—
374D4—2216no—
375D4—224no—
376D4—224no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—24no—
380C2×C4—24no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—114no—
388C2×C4—114no—
389C2×C4—2216no—
390C2×C4—222no—
391C2×C4—222no—
392C2×C4—222no—
393C2×C4—448no—
394C2×C4—442no—
395C2×C4—442no—
396C2×C4—884no—
397C2×C4—884no—
398C2×C4C22⋊C4×D1112yes—
399C2×C4C22⋊C4×D1111yescharacteristic
400C2×C4C22⋊C4×D1111yescharacteristic
401C2×C4C2×#431312yes—
402C2×C4C2×#431312yes—
403C2×C4M16×D1112yes—
404C2×C4C2×D4×D1112yes—
405C8—44no—
406C8—444no—
407C22—21no—
408C22—21no—
409C22—22no—
410C22—42no—
411C22—42no—
412C22—41no—
413C22—41no—
414C22—224no—
415C22—224no—
416C22—224no—
417C22—444no—
418C22—444no—
419C22C2×C22⋊C4×D1111yescharacteristic
420C22C22×#431311yescharacteristic
421C22C2×M16×D1111yescharacteristic
422C4—22no—
423C4—22no—
424C4—22no—
425C4—41no—
426C4—41no—
427C4—224no—
428C4—224no—
429C4—442no—
430C4#1062233912yes—
431C4#1062233912yes—
432C2—21no—
433C2—21no—
434C2—42no—
435C2—444no—
436C2C2×#1062233911yescharacteristic
437C2#1307707511yescharacteristic
438C2#1307709711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1458C2
socleC22×C11C22×C22⋊C4
prime radicalC22×#4339C4
cosocleC22×C4×C11C24
hypercenter#1458D11
hypocenterC11#17370
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1458

Complements

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

NH ≅ G/Ntype
2. #13077656C2semidirect
3. #13066951C2semidirect
4. #13066944C2semidirect
5. #13066939C2semidirect
6. #13066930C2semidirect
7. C11×#1458C2semidirect
88. C22×C4×C11M16semidirect
119. C2×Dic22M16semidirect
148. #1458D11semidirect
331. C22×C4#4313semidirect
360. C11#17370semidirect

Maximal subgroups

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

subgroupindex
C2×#106230542
#130776562
#130669512
#130669442
#130669392
#130669302
C11×#14582
#1737011