Finite Group Databasebeta

← #14755419

Subgroups — #14755419

Order 2816.

1742 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081819C211yesmaximal, characteristic
2C2×#10622853C211yesmaximal, characteristic
3#13071202C212yesmaximal, complemented
4#13069030C218yesmaximal, complemented
5#13068348C212yesmaximal, complemented
6C2×C11×#536C211yesmaximal, characteristic
7C22×C11×#41C2211yescharacteristic
8C23×Q8×C11C2211yescharacteristic
9C11×#536—24no—
10C11×#536C418yescomplemented
11C2×C11×C4⋊Q8—21no—
12C2×C11×#124—21no—
13C2×C11×#123C2214yes—
14C2×C11×C22⋊Q8—22no—
15C2×C11×#117C2211yescharacteristic
16#10623358—24no—
17#41×Dic11—24no—
18#10623343—21no—
19#10623329—21no—
20#10623329C2214yes—
21C2×#66979—22no—
22C2×#66979C2212yes—
23C2×#66979C2212yes—
24#10622853—24no—
25#10622843—24no—
26#10622843—24no—
27C2×#66898C2214yes—
28#10622824C2218yes—
29#10622165C2218yes—
30C2×C11×#41—22no—
31C2×C11×#41—22no—
32C2×C11×#41—24no—
33C2×C11×#41C2×C414yes—
34C2×C11×#41D414yes—
35C22×Q8×C11—22no—
36C22×Q8×C11—22no—
37C22×Q8×C11—21no—
38C22×Q8×C11—21no—
39C22×Q8×C11—22no—
40C22×Q8×C11—24no—
41C22×Q8×C11C2×C414yescomplemented
42C22×Q8×C11D411yescharacteristic
43C22×D4×C11D411yescharacteristic
44C22×D4×C11C2312yes—
45C23×C4×C11D412yes—
46C23×C4×C11C2312yes—
47C23×C4×C11C2311yescharacteristic
48C11×C4⋊Q8—28no—
49C11×#124—28no—
50C11×#123—28no—
51C11×#123C2×C4116yescomplemented
52C11×C22⋊Q8—216no—
53C11×#117—22no—
54C11×#117C2×C414yescomplemented
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—24no—
57C2×C11×C22⋊C4—24no—
58C2×C11×C22⋊C4C2312yes—
59C2×C42×C11—21no—
60C2×C22⋊Dic11—24no—
61C2×C22⋊Dic11C2314yes—
62C2×C22⋊Dic11C2314yes—
63Q8×Dic11—28no—
64D4×Dic11—28no—
65D4×Dic11—216no—
66#66979—24no—
67#66979—24no—
68#66979—22no—
69#66979—24no—
70#66979—22no—
71#66979—22no—
72#66979—22no—
73#66979—24no—
74#66979—24no—
75C2×C4⋊Dic11—24no—
76C2×C4⋊Dic11—22no—
77C2×C4⋊Dic11D414yes—
78C2×C4×Dic11—24no—
79C2×C4×Dic11—22no—
80C2×C4×Dic11D414yes—
81#66898—28no—
82C11⋊#95—216no—
83#20962—111nomaximal, Sylow
84C24×C11C2×D412yes—
85C24×C11C2411yescharacteristic
86C11×#41—28no—
87C11×#41—28no—
88C11×#41—28no—
89C11×#41—28no—
90C2×Q8×C11—24no—
91C2×Q8×C11—24no—
92C2×Q8×C11—28no—
93C2×Q8×C11—28no—
94C2×Q8×C11—22no—
95C2×Q8×C11—22no—
96C2×Q8×C11—41no—
97C2×Q8×C11—42no—
98C2×Q8×C11—41no—
99C2×Q8×C11—44no—
100C2×Q8×C11—44no—
101C2×Q8×C11—42no—
102C2×Q8×C11—42no—
103C2×Q8×C11C22⋊C414yes—
104C2×D4×C11—24no—
105C2×D4×C11—24no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11C22⋊C414yes—
109C2×D4×C11C22×C414yes—
110C2×D4×C11C2×D414yes—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—24no—
114C22×C4×C11—24no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—24no—
119C22×C4×C11C22⋊C418yes—
120C22×C4×C11C22×C414yes—
121C22×C4×C11C22×C412yes—
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11#4114yes—
129C22×Dic11—28no—
130C22×Dic11—24no—
131C22×Dic11C2×D418yes—
132C11×C4⋊C4—24no—
133C11×C4⋊C4—216no—
134C11×C22⋊C4—216no—
135C11×C22⋊C4—22no—
136C11×C22⋊C4C22×C414yes—
137C42×C11—24no—
138C22⋊Dic11—28no—
139C22⋊Dic11—24no—
140C22⋊Dic11—24no—
141C22⋊Dic11—24no—
142C22⋊Dic11—24no—
143C4⋊Dic11—28no—
144C4⋊Dic11—24no—
145C4⋊Dic11—24no—
146C4⋊Dic11—44no—
147C4×Dic11—28no—
148C4×Dic11—24no—
149C4×Dic11—24no—
150C4×Dic11—44no—
151C2×#536D1111yescharacteristic
152#3428—111no—
153C2×#410—111no—
154#2310—112no—
155#1890—118no—
156#1740—112no—
157C23×C11—22no—
158C23×C11—22no—
159C23×C11—42no—
160C23×C11—44no—
161C23×C11C2×C22⋊C414yes—
162C23×C11C23×C411yescharacteristic
163C23×C11C22×D412yes—
164C23×C11C22×D411yescharacteristic
165C23×C11C22×D411yescharacteristic
166C23×C11C2×#4112yes—
167Q8×C11—28no—
168Q8×C11—44no—
169Q8×C11—44no—
170Q8×C11—48no—
171D4×C11—28no—
172D4×C11—28no—
173D4×C11—28no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—28no—
177C2×C4×C11—28no—
178C2×C4×C11—24no—
179C2×C4×C11—24no—
180C2×C4×C11—28no—
181C2×C4×C11—44no—
182C2×C4×C11—42no—
183C2×C4×C11—44no—
184C2×C4×C11—42no—
185C2×C4×C11C2×C22⋊C414yes—
186C2×C4×C11C2×C22⋊C412yes—
187C2×C4×C11C2×C22⋊C412yes—
188C2×C4×C11C4×D414yes—
189C2×C4×C11C4×D414yes—
190C2×C4×C11#12011yescharacteristic
191C2×C4×C11#12012yes—
192C2×C4×C11#12011yescharacteristic
193C2×C4×C11#12114yes—
194C2×C4×C11#12114yes—
195C2×C4×C11#12312yes—
196C2×C4×C11#12312yes—
197C2×Dic11—28no—
198C2×Dic11—48no—
199C2×Dic11—48no—
200C2×Dic11—44no—
201C2×Dic11—88no—
202C22×#41C2×D1111yescharacteristic
203C23×Q8C2×D1111yescharacteristic
204#536—24no—
205#536Dic1118yescomplemented
206C2×C4⋊Q8—21no—
207C2×#124—21no—
208C2×#123C2×D1114yes—
209C2×C22⋊Q8—22no—
210#520—224no—
211#519—221no—
212#518—114no—
213#518—221no—
214C4×#41—224no—
215C2×#117—112no—
216C2×#117—112no—
217C2×#117—222no—
218C2×#117C2×D1111yescharacteristic
219#410—224no—
220C2×#99—114no—
221#391—224no—
222#391—224no—
223#381—118no—
224#342—118no—
225C22×C11—22no—
226C22×C11—24no—
227C22×C11—24no—
228C22×C11—41no—
229C22×C11—41no—
230C22×C11—42no—
231C22×C11—44no—
232C22×C11—44no—
233C22×C11—82no—
234C22×C11C22×C22⋊C411yescharacteristic
235C22×C11C2×C4×D412yes—
236C22×C11C2×#12011yescharacteristic
237C22×C11C2×#12112yes—
238C22×C11C2×#12311yescharacteristic
239C4×C11—24no—
240C4×C11—44no—
241C4×C11—44no—
242C4×C11#38612yes—
243C4×C11#38612yes—
244C4×C11#38614yes—
245Dic11—48no—
246Dic11—84no—
247C2×#41—22no—
248C2×#41—22no—
249C2×#41—24no—
250C2×#41C2×Dic1114yes—
251C2×#41C22⋊D1114yes—
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8—24no—
255C22×Q8—21no—
256C22×Q8—21no—
257C22×Q8—22no—
258C22×Q8C2×Dic1114yescomplemented
259C22×Q8C22⋊D1111yescharacteristic
260C22×D4C22⋊D1111yescharacteristic
261C22×D4C22×D1112yes—
262C23×C4C22⋊D1112yes—
263C23×C4C22×D1112yes—
264C23×C4C22×D1111yescharacteristic
265C4⋊Q8—28no—
266#124—28no—
267#123—28no—
268#123C2×Dic11116yescomplemented
269C22⋊Q8—216no—
270C4×Q8—228no—
271C4×D4—2216no—
272C4×D4—228no—
273#117—22no—
274#117—224no—
275#117—224no—
276#117—222no—
277#117—222no—
278#117—222no—
279#117—222no—
280#117—224no—
281#117—224no—
282#117—224no—
283#117C2×Dic1114yescomplemented
284C2×C4⋊C4—21no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—114no—
287C2×C4⋊C4—224no—
288C2×C4⋊C4—222no—
289C2×C22⋊C4—24no—
290C2×C22⋊C4—114no—
291C2×C22⋊C4—114no—
292C2×C22⋊C4—224no—
293C2×C22⋊C4C22×D1112yes—
294C2×C42—21no—
295C2×C42—114no—
296C2×C42—224no—
297C2×C42—222no—
298#99—228no—
299#95—2216no—
300C2×C11—22no—
301C2×C11—21no—
302C2×C11—21no—
303C2×C11—22no—
304C2×C11—44no—
305C2×C11C2×#38611yescharacteristic
306C2×C11#302812yes—
307C24C2×C22⋊D1112yes—
308C24C23×D1111yescharacteristic
309#41—28no—
310#41—28no—
311#41—28no—
312#41—28no—
313C2×Q8—28no—
314C2×Q8—28no—
315C2×Q8—22no—
316C2×Q8—22no—
317C2×Q8—24no—
318C2×Q8—24no—
319C2×Q8—42no—
320C2×Q8—42no—
321C2×Q8—41no—
322C2×Q8—42no—
323C2×Q8—41no—
324C2×Q8—44no—
325C2×Q8—44no—
326C2×Q8C22⋊Dic1114yes—
327C2×D4—24no—
328C2×D4—24no—
329C2×D4—22no—
330C2×D4—22no—
331C2×D4C22⋊Dic1114yes—
332C2×D4C22×Dic1114yes—
333C2×D4C2×C22⋊D1114yes—
334C22×C4—24no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—24no—
338C22×C4—24no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—118no—
343C22×C4—228no—
344C22×C4—224no—
345C22×C4C22⋊Dic1118yes—
346C22×C4D4×D1112yes—
347C22×C4D4×D1112yes—
348C22×C4#434114yes—
349C22×C4C22×Dic1114yes—
350C22×C4C22×Dic1112yes—
351C22×C4C2×C22⋊D1112yes—
352C22×C4C2×C22⋊D1111yescharacteristic
353C22×C4C2×C22⋊D1111yescharacteristic
354C22×C4C2×C22⋊D1112yes—
355C4⋊C4—24no—
356C4⋊C4—216no—
357C4⋊C4—228no—
358C4⋊C4—224no—
359C4⋊C4—224no—
360C4⋊C4—444no—
361C22⋊C4—216no—
362C22⋊C4—22no—
363C22⋊C4—228no—
364C22⋊C4—224no—
365C22⋊C4—224no—
366C22⋊C4—224no—
367C22⋊C4—224no—
368C22⋊C4C22×Dic1114yes—
369C42—24no—
370C42—228no—
371C42—224no—
372C42—224no—
373C42—444no—
374C11#2096211yescharacteristic, complemented, Sylow
375C23—22no—
376C23—22no—
377C23—42no—
378C23—44no—
379C23C2×C22⋊Dic1114yes—
380C23C2×D4×D1112yes—
381C23C2×#434112yes—
382C23C23×Dic1111yescharacteristic
383C23C22×C22⋊D1111yescharacteristic
384C23C22×C22⋊D1111yescharacteristic
385Q8—28no—
386Q8—44no—
387Q8—44no—
388Q8—48no—
389D4—28no—
390D4—28no—
391D4—28no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—28no—
395C2×C4—28no—
396C2×C4—28no—
397C2×C4—24no—
398C2×C4—24no—
399C2×C4—44no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—44no—
403C2×C4—228no—
404C2×C4—448no—
405C2×C4—448no—
406C2×C4—444no—
407C2×C4—888no—
408C2×C4D4×Dic1114yes—
409C2×C4D4×Dic1114yes—
410C2×C4#6698812yes—
411C2×C4#6698812yes—
412C2×C4#6699011yescharacteristic
413C2×C4#6699012yes—
414C2×C4#6699011yescharacteristic
415C2×C4#6699214yes—
416C2×C4#6699214yes—
417C2×C4C2×C22⋊Dic1114yes—
418C2×C4C2×C22⋊Dic1112yes—
419C2×C4C2×C22⋊Dic1112yes—
420C22—22no—
421C22—24no—
422C22—24no—
423C22—42no—
424C22—41no—
425C22—41no—
426C22—44no—
427C22—44no—
428C22—82no—
429C22C2×D4×Dic1112yes—
430C22C2×#6698811yescharacteristic
431C22C2×#6699011yescharacteristic
432C22C2×#6699212yes—
433C22C22×C22⋊Dic1111yescharacteristic
434C4—24no—
435C4—44no—
436C4—44no—
437C4—448no—
438C4—884no—
439C4#1062283312yes—
440C4#1062283312yes—
441C4#1062283314yes—
442C2—21no—
443C2—22no—
444C2—21no—
445C2—22no—
446C2—44no—
447C2C2×#1062283311yescharacteristic
448C2#1307802112yes—
subgroupG/H
centerC22C2×#66990
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC2×C11×#536C2
socleC22×C11C2×#120
prime radicalC22×C11×#41C22
cosocleC24×C11C24
hypercenterC2×#536D11
hypocenterC11#20962
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
3. #13071202C2semidirect
4. #13069030C2semidirect
5. #13068348C2semidirect
10. C11×#536C4semidirect
41. C22×Q8×C11C2×C4semidirect
51. C11×#123C2×C4semidirect
54. C11×#117C2×C4semidirect
205. #536Dic11semidirect
258. C22×Q8C2×Dic11semidirect
268. #123C2×Dic11semidirect
283. #117C2×Dic11semidirect
374. C11#20962semidirect

Maximal subgroups

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

subgroupindex
#130818192
C2×#106228532
#130712022
#130690302
#130683482
C2×C11×#5362
#2096211