Finite Group Databasebeta

← #14719668

Subgroups — #14719668

Order 2816.

1246 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4341C211yesmaximal, characteristic
2#13077244C212yesmaximal, complemented
3#13066951C214yesmaximal, complemented
4#13066947C214yesmaximal, complemented
5#13066939C212yesmaximal, complemented
6#13066937C211yesmaximal, characteristic, complemented
7C11×#1460C211yesmaximal, characteristic, complemented
8C22×#4341C411yescharacteristic
9C2×C4×D4×C11C2211yescharacteristic
10C2×D4×Dic11C411yescharacteristic
11C2×C4×C22⋊D11C412yes—
12C22×C4×Dic11C412yes—
13C4×#4341—22no—
14C4×#4341—22no—
15C4×#4341—22no—
16C4×#4341—22no—
17C2×#66945C411yescharacteristic
18C2×#66940C411yescharacteristic
19C2×(C22⋊D11)⋊C4C2212yes—
20C2×#66930C2212yes—
21C2×C42×D11C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C11×#431C2212yes—
24#10622538C2212yes—
25#10622450—22no—
26#10622448—22no—
27#10622339C2214yes—
28#10622332C2214yes—
29C4×#4313—22no—
30#10622298—22no—
31C11×#323C2214yes—
32#10622163C2214yes—
33#10622107C2218yes—
34C22×D4×C11C2×C411yescharacteristic
35C23×C4×C11C2×C412yes—
36C22×C22⋊D11C2×C412yes—
37C23×Dic11C2×C412yes—
38C23×Dic11C2×C412yes—
39C2×#4341—24no—
40C2×#4341—22no—
41C2×#4341—22no—
42C2×#4341—24no—
43C22×C4×D11C2×C411yescharacteristic
44C22×C4×D11C2×C411yescharacteristic
45C22×C4×D11C2311yescharacteristic
46C22×Dic22C2×C411yescharacteristic
47C4×D4×C11—22no—
48C4×D4×C11—22no—
49C2×C11×C4⋊C4C2×C411yescharacteristic
50C2×C11×C22⋊C4C2312yes—
51C2×C42×C11C2311yescharacteristic
52C2×C22⋊Dic11C2×C412yes—
53D4×Dic11—22no—
54D4×Dic11—22no—
55C4×C22⋊D11—24no—
56C4×C22⋊D11—24no—
57C2×(C2×D11)⋊C4C2×C412yes—
58C2×C4⋊Dic11C2×C411yescharacteristic
59C2×Dic11⋊C4C2×C412yes—
60C2×Dic11⋊C4C2312yes—
61C2×C4×Dic11—22no—
62C2×C4×Dic11—22no—
63C2×C4×Dic11—22no—
64C2×C4×Dic11—22no—
65C2×C4×Dic11C2×C412yes—
66C2×C4×Dic11C2×C412yes—
67C2×C4×Dic11C2×C412yes—
68C2×C4×Dic11C2×C411yescharacteristic
69C2×C4×Dic11C2×C411yescharacteristic
70C2×C4×Dic11C2311yescharacteristic
71C2×#4313—24no—
72#66945—22no—
73#66945—22no—
74#66940—22no—
75#66940—22no—
76(C22⋊D11)⋊C4—24no—
77(C22⋊D11)⋊C4—24no—
78#66930—24no—
79#66930—24no—
80C42×D11D412yes—
81C42×D11D412yes—
82C42×D11D412yes—
83C42×D11D412yes—
84C4×Dic22—22no—
85C4×Dic22—22no—
86C11×C4⋊C8—22no—
87C11×C22⋊C8C2314yes—
88C4×C8×C11—22no—
89C22⋊(C11⋊C8)C2314yes—
90(C2×D11)⋊C8—24no—
91#66879—24no—
92Dic11⋊C8—24no—
93C4⋊(C11⋊C8)—22no—
94C4×C11⋊C8—22no—
95#17366—111nomaximal, Sylow
96C24×C11C22×C412yes—
97C23×D11C22×C411yescharacteristic
98C2×D4×C11—22no—
99C2×D4×C11—22no—
100C2×D4×C11M1614yescomplemented
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—44no—
104C22×C4×C11C22×C411yescharacteristic
105C22×C4×C11C22×C412yes—
106C22×C4×C11C22×C411yescharacteristic
107C22×C4×C11C2411yescharacteristic
108C2×C22⋊D11—24no—
109C2×C22⋊D11—24no—
110C2×C22⋊D11—24no—
111C22×Dic11—22no—
112C22×Dic11—22no—
113C22×Dic11—24no—
114C22×Dic11—22no—
115C22×Dic11—22no—
116C22×Dic11—24no—
117C22×Dic11—44no—
118C22×Dic11C22×C411yescharacteristic
119C22×Dic11C22×C411yescharacteristic
120C22×Dic11C22×C412yes—
121C22×Dic11C22×C412yes—
122C22×Dic11C22×C411yescharacteristic
123#4341—216no—
124#4341—216no—
125C2×C4×D11—22no—
126C2×C4×D11—22no—
127C2×C4×D11—42no—
128C2×C4×D11—42no—
129C2×C4×D11C22⋊C412yes—
130C2×C4×D11C22⋊C412yes—
131C2×C4×D11C22⋊C412yes—
132C2×C4×D11C22⋊C412yes—
133C2×C4×D11C2×D412yes—
134C2×C4×D11C2×D412yes—
135C2×Dic22—22no—
136C2×Dic22—22no—
137C2×Dic22M1614yescomplemented
138C2×C8×C11—24no—
139C11×C4⋊C4—22no—
140C11×C22⋊C4—24no—
141C42×C11C2×D412yes—
142C42×C11C2×D412yes—
143C22⋊Dic11—24no—
144(C2×D11)⋊C4—24no—
145C4⋊Dic11—22no—
146Dic11⋊C4—24no—
147Dic11⋊C4—24no—
148C4×Dic11—22no—
149C4×Dic11—22no—
150C4×Dic11—22no—
151C4×Dic11—22no—
152C4×Dic11—22no—
153C4×Dic11—22no—
154C4×Dic11C22⋊C412yes—
155C4×Dic11C22⋊C412yes—
156C4×Dic11C22⋊C411yescharacteristic
157C4×Dic11C22⋊C411yescharacteristic
158C4×Dic11C22⋊C411yescharacteristic
159C4×Dic11C22⋊C411yescharacteristic
160C4×Dic11C2×D412yes—
161C4×Dic11C2×D412yes—
162C2×C11⋊C8—24no—
163#4313—48no—
164C2×C4×#41—111no—
165#2920—112no—
166#1465—114no—
167#1464—114no—
168#1461—112no—
169#1460—111no—
170#1460D1111yescharacteristic, complemented
171C23×C11—22no—
172C23×C11—22no—
173C23×C11—42no—
174C23×C11—42no—
175C23×C11C2×M1614yes—
176C23×C11C23×C411yescharacteristic
177C22×D11—21no—
178C22×D11—21no—
179C22×D11—41no—
180C22×D11—41no—
181C22×D11C2×C22⋊C412yes—
182D4×C11—28no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—41no—
186C2×C4×C11—44no—
187C2×C4×C11—44no—
188C2×C4×C11—42no—
189C2×C4×C11C2×C22⋊C411yescharacteristic
190C2×C4×C11C2×C22⋊C412yes—
191C2×C4×C11C2×C22⋊C411yescharacteristic
192C2×C4×C11C2×M1612yes—
193C2×C4×C11C2×M1612yes—
194C2×C4×C11C22×D412yes—
195C22⋊D11—216no—
196C2×Dic11—28no—
197C2×Dic11—28no—
198C2×Dic11—22no—
199C2×Dic11—22no—
200C2×Dic11—21no—
201C2×Dic11—21no—
202C2×Dic11—22no—
203C2×Dic11—22no—
204C2×Dic11—41no—
205C2×Dic11—44no—
206C2×Dic11—44no—
207C2×Dic11—42no—
208C2×Dic11C2×C22⋊C411yescharacteristic
209C2×Dic11C2×C22⋊C411yescharacteristic
210C2×Dic11C2×C22⋊C411yescharacteristic
211C2×Dic11C2×C22⋊C412yes—
212C2×Dic11C2×C22⋊C411yescharacteristic
213C2×Dic11C2×M1614yes—
214C4×D11—24no—
215C4×D11—24no—
216C4×D11—24no—
217C4×D11—24no—
218C4×D11—42no—
219C4×D11—42no—
220Dic22—28no—
221C8×C11—44no—
222C11⋊C8—44no—
223C22×#41—111no—
224C4×#41—222no—
225C4×#41—222no—
226C4×#41—222no—
227C4×#41—222no—
228C2×C4×Q8—111no—
229C2×C4×Q8—111no—
230C2×C4×D4—111no—
231C2×C4×D4—112no—
232C2×C4×D4—112no—
233C2×C4×D4C2×D1111yescharacteristic
234C2×#117—111no—
235C2×#117—112no—
236C22×C42—111no—
237C22×C42—112no—
238#432—114no—
239#432—222no—
240#431—112no—
241#431—222no—
242#431C2×D1112yes—
243#423—222no—
244#407—114no—
245C4×M16—222no—
246#324—118no—
247#323—114no—
248#323C2×D1114yes—
249C22×C11—21no—
250C22×C11—21no—
251C22×C11—24no—
252C22×C11—44no—
253C22×C11—44no—
254C22×C11—42no—
255C22×C11—42no—
256C22×C11C22×C22⋊C411yescharacteristic
257C22×C11C22×M1611yescharacteristic
258C22×C11C22×M1611yescharacteristic
259C2×D11—22no—
260C2×D11—22no—
261C2×D11—22no—
262C2×D11—42no—
263C2×D11—42no—
264C4×C11—22no—
265C4×C11—21no—
266C4×C11—42no—
267C4×C11#40714yes—
268C4×C11#41312yes—
269Dic11—24no—
270Dic11—21no—
271Dic11—21no—
272Dic11—21no—
273Dic11—22no—
274Dic11—42no—
275Dic11#41012yes—
276C2×#41—222no—
277C2×#41—222no—
278C2×#41—224no—
279C2×#41—224no—
280C22×Q8—111no—
281C22×D4—112no—
282C22×D4C4×D1111yescharacteristic
283C23×C4—111no—
284C23×C4—111no—
285C23×C4—111no—
286C23×C4—112no—
287C23×C4—112no—
288C23×C4C4×D1112yes—
289C2×M16—224no—
290C4×Q8—222no—
291C4×Q8—222no—
292C4×Q8—222no—
293C4×Q8—222no—
294C4×D4—22no—
295C4×D4—22no—
296C4×D4—222no—
297C4×D4—222no—
298C4×D4—224no—
299C4×D4—224no—
300C4×D4—224no—
301C4×D4—224no—
302#117—224no—
303#117—224no—
304#117—222no—
305#117—222no—
306C2×C4⋊C4—112no—
307C2×C4⋊C4—111no—
308C2×C4⋊C4—112no—
309C2×C4⋊C4C4×D1111yescharacteristic
310C2×C22⋊C4—112no—
311C2×C22⋊C4—112no—
312C2×C22⋊C4C22×D1112yes—
313C2×C42—111no—
314C2×C42—111no—
315C2×C42—111no—
316C2×C42—112no—
317C2×C42—112no—
318C2×C42—112no—
319C2×C42—112no—
320C2×C42—112no—
321C2×C42—112no—
322C2×C42—112no—
323C2×C42—222no—
324C2×C42—222no—
325C2×C42—222no—
326C2×C42—222no—
327C2×C42C22×D1111yescharacteristic
328C4⋊C8—22no—
329C4⋊C8—224no—
330C4⋊C8—222no—
331C22⋊C8—114no—
332C22⋊C8—224no—
333C22⋊C8C22×D1114yes—
334#97—224no—
335C4×C8—22no—
336C4×C8—222no—
337C2×C11—21no—
338C2×C11—21no—
339C2×C11—44no—
340C2×C11C2×#40711yescharacteristic
341C2×C11C2×#41011yescharacteristic
342C2×C11C2×#41311yescharacteristic
343D11—42no—
344C24—111no—
345C24C2×C4×D1112yes—
346#41—2216no—
347#41—2216no—
348C2×Q8—114no—
349C2×Q8—222no—
350C2×Q8—222no—
351C2×D4—22no—
352C2×D4—22no—
353C2×D4—224no—
354C2×D4—224no—
355C2×D4—224no—
356C2×D4#431314yescomplemented
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—44no—
360C22×C4—111no—
361C22×C4—111no—
362C22×C4—112no—
363C22×C4—111no—
364C22×C4—112no—
365C22×C4—112no—
366C22×C4—112no—
367C22×C4—112no—
368C22×C4—112no—
369C22×C4—112no—
370C22×C4—112no—
371C22×C4—222no—
372C22×C4—222no—
373C22×C4—224no—
374C22×C4—222no—
375C22×C4—222no—
376C22×C4—224no—
377C22×C4—222no—
378C22×C4—222no—
379C22×C4—442no—
380C22×C4—442no—
381C22×C4—444no—
382C22×C4C2×C4×D1111yescharacteristic
383C22×C4C2×C4×D1112yes—
384C22×C4C2×C4×D1111yescharacteristic
385C22×C4C23×D1111yescharacteristic
386M16—448no—
387C2×C8—24no—
388C2×C8—224no—
389C4⋊C4—22no—
390C4⋊C4—224no—
391C4⋊C4—222no—
392C4⋊C4—224no—
393C22⋊C4—24no—
394C22⋊C4—224no—
395C22⋊C4—224no—
396C42—111no—
397C42—111no—
398C42—112no—
399C42—112no—
400C42—111no—
401C42—111no—
402C42—112no—
403C42—112no—
404C42—222no—
405C42—222no—
406C42—222no—
407C42—222no—
408C42—222no—
409C42—222no—
410C42D4×D1112yes—
411C42D4×D1112yes—
412C11#1736611yescharacteristic, complemented, Sylow
413C23—22no—
414C23—22no—
415C23—42no—
416C23—42no—
417C23—112no—
418C23—221no—
419C23—221no—
420C23—441no—
421C23—441no—
422C23C2×#431314yes—
423C23C22×C4×D1111yescharacteristic
424Q8—228no—
425D4—28no—
426D4—2216no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—41no—
430C2×C4—44no—
431C2×C4—44no—
432C2×C4—42no—
433C2×C4—111no—
434C2×C4—111no—
435C2×C4—111no—
436C2×C4—111no—
437C2×C4—112no—
438C2×C4—114no—
439C2×C4—224no—
440C2×C4—222no—
441C2×C4—228no—
442C2×C4—228no—
443C2×C4—221no—
444C2×C4—222no—
445C2×C4—222no—
446C2×C4—221no—
447C2×C4—224no—
448C2×C4—224no—
449C2×C4—224no—
450C2×C4—222no—
451C2×C4—442no—
452C2×C4—442no—
453C2×C4—444no—
454C2×C4—441no—
455C2×C4—444no—
456C2×C4—442no—
457C2×C4C22⋊C4×D1111yescharacteristic
458C2×C4C22⋊C4×D1112yes—
459C2×C4C22⋊C4×D1111yescharacteristic
460C2×C4C2×#431312yes—
461C2×C4M16×D1112yes—
462C2×C4C2×D4×D1112yes—
463C8—44no—
464C8—444no—
465C22—21no—
466C22—21no—
467C22—24no—
468C22—44no—
469C22—44no—
470C22—42no—
471C22—42no—
472C22—222no—
473C22—222no—
474C22—222no—
475C22—442no—
476C22—442no—
477C22C2×C22⋊C4×D1111yescharacteristic
478C22C22×#431311yescharacteristic
479C22C2×M16×D1111yescharacteristic
480C4—22no—
481C4—21no—
482C4—42no—
483C4—112no—
484C4—221no—
485C4—221no—
486C4—224no—
487C4—221no—
488C4—222no—
489C4—442no—
490C4#1062233914yes—
491C4#1062235812yes—
492C2—21no—
493C2—21no—
494C2—44no—
495C2—442no—
496C2C2×#1062233911yescharacteristic
497C2D11×#41011yescharacteristic
498C2C2×#1062235811yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1460C2
socleC22×C11C22×C22⋊C4
prime radicalC22×#4341C4
cosocleC22×C4×C11C24
hypercenter#1460D11
hypocenterC11#17366
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1460

Complements

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

NH ≅ G/Ntype
2. #13077244C2semidirect
3. #13066951C2semidirect
4. #13066947C2semidirect
5. #13066939C2semidirect
6. #13066937C2semidirect
7. C11×#1460C2semidirect
100. C2×D4×C11M16semidirect
137. C2×Dic22M16semidirect
170. #1460D11semidirect
356. C2×D4#4313semidirect
412. C11#17366semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43412
#130772442
#130669512
#130669472
#130669392
#130669372
C11×#14602
#1736611