Finite Group Databasebeta

← #14758998

Subgroups — #14758998

Order 2816.

1154 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623153C211yesmaximal, characteristic
2C22×#66879C211yesmaximal, characteristic
3#13071011C211yesmaximal, characteristic
4#13069587C212yesmaximal, complemented
5#13069434C212yesmaximal, complemented
6#13069040C211yesmaximal, characteristic
7#13069039C211yesmaximal, characteristic
8#13069037C211yesmaximal, characteristic
9#13068448C212yesmaximal, complemented
10#13068445C212yesmaximal, complemented
11C11×#1892C211yesmaximal, characteristic
12C23×C8×C11C2211yescharacteristic
13C2×C11×C22⋊Q8C2211yescharacteristic
14C2×Q8×Dic11C2211yescharacteristic
15C2×#66997C2211yescharacteristic
16C2×#66977C2211yescharacteristic
17C22×C4×Dic11C2211yescharacteristic
18C23×C11⋊C8C2211yescharacteristic
19#10623153—24no—
20#10623153C418yescomplemented
21C2×#66942—21no—
22C2×#66941C2211yescharacteristic
23C2×#66940—21no—
24C2×#66940C2211yescharacteristic
25C2×#66931—21no—
26C2×#66930—21no—
27C2×C11×#103C2212yes—
28C11×#380C2211yescharacteristic
29C2×#66899C2212yes—
30#10622825C2211yescharacteristic
31C2×#66880C2212yes—
32C2×#66879—24no—
33C2×#66879C2212yes—
34C2×#66879C2212yes—
35#10622590C2212yes—
36C4⋊C4×Dic11C2212yes—
37C2×#66874C2212yes—
38#10622556—21no—
39C22⋊C4×Dic11—21no—
40#10622264—21no—
41#10622261—21no—
42C11×#340C2212yes—
43#10622189C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46C22×Q8×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×Dic11D411yescharacteristic
49C23×Dic11D411yescharacteristic
50C22×Dic22—21no—
51C22×Dic22C2311yescharacteristic
52C22×C8×C11—22no—
53C22×C8×C11—24no—
54C22×C8×C11C2312yes—
55C11×C22⋊Q8—22no—
56C11×C22⋊Q8C2×C414yes—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C22⋊C4—21no—
61C2×C11×C22⋊C4—21no—
62C2×C22⋊Dic11—21no—
63C2×C22⋊Dic11—21no—
64Q8×Dic11—22no—
65Q8×Dic11C2×C414yes—
66#66997—22no—
67#66997C2×C414yes—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11C2312yes—
70C2×C4⋊Dic11C2311yescharacteristic
71#66977—22no—
72#66977C2×C414yes—
73C2×Dic11⋊C4—21no—
74C2×Dic11⋊C4—21no—
75C2×Dic11⋊C4—21no—
76C2×Dic11⋊C4—21no—
77C2×Dic11⋊C4—21no—
78C2×C4×Dic11—21no—
79C2×C4×Dic11—21no—
80C2×C4×Dic11—22no—
81C2×C4×Dic11C2×C414yes—
82C2×C4×Dic11D411yescharacteristic
83C2×C4×Dic11D411yescharacteristic
84C2×C4×Dic11D414yes—
85C2×C4×Dic11C2311yescharacteristic
86C2×C4×Dic11C2311yescharacteristic
87C22×C11⋊C8—22no—
88C22×C11⋊C8—24no—
89C22×C11⋊C8C2312yes—
90#66942—28no—
91#66941—22no—
92#66941C2×C414yes—
93#66940—28no—
94#66940—22no—
95#66940C2×C414yes—
96#66931—28no—
97#66930—28no—
98C11×#103—24no—
99C11×#95—21no—
100#66899—24no—
101C11⋊#95—21no—
102C11⋊#95—22no—
103C11⋊#95—22no—
104C11⋊#95—22no—
105#66880—24no—
106#66879—24no—
107#66879—24no—
108#66874—24no—
109#21407—111nomaximal, Sylow
110C24×C11C2×D411yescharacteristic
111C2×Q8×C11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11C22×C412yes—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11C22×C412yes—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2411yescharacteristic
124C22×Dic11—22no—
125C22×Dic11—22no—
126C22×Dic11—21no—
127C22×Dic11—21no—
128C22×Dic11—22no—
129C22×Dic11—42no—
130C22×Dic11C22⋊C414yes—
131C22×Dic11C22⋊C414yes—
132C22×Dic11C2×D411yescharacteristic
133C22×Dic11C2×D411yescharacteristic
134C22×Dic11C2×D411yescharacteristic
135C22×Dic11C2×D411yescharacteristic
136C2×Dic22—24no—
137C2×Dic22—21no—
138C2×Dic22—22no—
139C2×Dic22—22no—
140C2×Dic22—44no—
141C2×Dic22C22×C412yes—
142C2×C8×C11—28no—
143C2×C8×C11—22no—
144C2×C8×C11—22no—
145C2×C8×C11#4114yes—
146C11×C4⋊C4—24no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4C22×C412yes—
151C11×C22⋊C4—24no—
152C11×C22⋊C4—42no—
153C22⋊Dic11—24no—
154C22⋊Dic11—42no—
155C4⋊Dic11—24no—
156C4⋊Dic11—21no—
157C4⋊Dic11—22no—
158C4⋊Dic11—22no—
159C4⋊Dic11C22×C412yes—
160Dic11⋊C4—24no—
161Dic11⋊C4—24no—
162Dic11⋊C4—24no—
163Dic11⋊C4—24no—
164Dic11⋊C4—24no—
165C4×Dic11—24no—
166C4×Dic11—24no—
167C4×Dic11—44no—
168C4×Dic11C22⋊C414yes—
169C4×Dic11C22⋊C414yes—
170C4×Dic11C22×C412yes—
171C4×Dic11C22×C412yes—
172C4×Dic11C2×D412yes—
173C4×Dic11C2×D412yes—
174C2×C11⋊C8—28no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8#4114yes—
178C2×#533—111no—
179C22×#97—111no—
180#2283—111no—
181#1993—112no—
182#1960—112no—
183#1892—111no—
184#1892—111no—
185#1892—111no—
186#1892D1111yescharacteristic
187#1763—112no—
188#1763—112no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11C2×C22⋊C412yes—
192C23×C11#13712yes—
193C23×C11#13712yes—
194C23×C11C22×D411yescharacteristic
195Q8×C11—24no—
196Q8×C11—41no—
197Q8×C11—41no—
198C2×C4×C11—22no—
199C2×C4×C11—24no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11C2×C22⋊C412yes—
210C2×C4×C11C23×C411yescharacteristic
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11C2×#4112yes—
213C2×C4×C11C2×#4112yes—
214C2×Dic11—21no—
215C2×Dic11—21no—
216C2×Dic11—21no—
217C2×Dic11—21no—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—28no—
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—44no—
224C2×Dic11—42no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227C2×Dic11—42no—
228C2×Dic11—42no—
229C2×Dic11C2×C22⋊C412yes—
230C2×Dic11C2×C22⋊C412yes—
231C2×Dic11C2×C22⋊C412yes—
232C2×Dic11C2×C22⋊C412yes—
233Dic22—24no—
234Dic22—48no—
235Dic22—41no—
236Dic22—41no—
237C8×C11—24no—
238C11⋊C8—24no—
239C23×C8—111no—
240C23×C8C2×D1111yescharacteristic
241#533—118no—
242#533—224no—
243C2×C4⋊Q8—111no—
244C2×C4⋊Q8—111no—
245C2×#125—221no—
246C2×C22⋊Q8—111no—
247C2×C22⋊Q8—221no—
248C2×C22⋊Q8C2×D1111yescharacteristic
249C2×C4×Q8—111no—
250C2×C4×Q8—111no—
251C2×C4×Q8—221no—
252C2×#117—221no—
253C22×C42—111no—
254C2×#103—112no—
255C2×#103—112no—
256C2×#103—112no—
257C2×#103C2×D1112yes—
258C2×#97—112no—
259C2×#97—112no—
260C2×#97—224no—
261#383—221no—
262#382—112no—
263#381—221no—
264#380—111no—
265#380C2×D1111yescharacteristic
266C4×C4⋊C4—112no—
267C4×C22⋊C4—221no—
268#376—221no—
269#340—112no—
270#340—112no—
271#340—112no—
272#340C2×D1112yes—
273C22×C11—22no—
274C22×C11—24no—
275C22×C11—24no—
276C22×C11—22no—
277C22×C11#41914yes—
278C22×C11C22×C22⋊C411yescharacteristic
279C22×C11#53212yes—
280C22×C11C2×#13711yescharacteristic
281C22×C11C2×#13711yescharacteristic
282C22×C11#57512yes—
283C4×C11—22no—
284C4×C11—42no—
285C4×C11—42no—
286C4×C11—82no—
287C4×C11C4×#4112yes—
288C4×C11#52511yescharacteristic
289C4×C11#52511yescharacteristic
290Dic11—22no—
291Dic11—22no—
292Dic11—22no—
293Dic11—22no—
294Dic11—42no—
295Dic11—42no—
296Dic11—82no—
297C22×Q8—111no—
298C22×Q8—221no—
299C22×Q8C22×D1111yescharacteristic
300C23×C4—111no—
301C23×C4—111no—
302C23×C4C22×D1111yescharacteristic
303C22×C8—22no—
304C22×C8—24no—
305C22×C8—112no—
306C22×C8—224no—
307C22×C8—222no—
308C22×C8C22×D1112yes—
309C4⋊Q8—114no—
310C4⋊Q8—114no—
311C4⋊Q8—222no—
312C4⋊Q8—222no—
313#125—228no—
314C22⋊Q8—22no—
315C22⋊Q8—114no—
316C22⋊Q8—228no—
317C22⋊Q8—222no—
318C22⋊Q8C4×D1114yes—
319C4×Q8—114no—
320C4×Q8—114no—
321C4×Q8—222no—
322C4×Q8—228no—
323C4×Q8—222no—
324#117—228no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—111no—
327C2×C4⋊C4—112no—
328C2×C4⋊C4—221no—
329C2×C4⋊C4—221no—
330C2×C4⋊C4—221no—
331C2×C4⋊C4—221no—
332C2×C4⋊C4—221no—
333C2×C4⋊C4—221no—
334C2×C4⋊C4C22×D1112yes—
335C2×C4⋊C4C22×D1111yescharacteristic
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—221no—
339C2×C22⋊C4—221no—
340C2×C42—114no—
341C2×C42—111no—
342C2×C42—111no—
343C2×C42—114no—
344C2×C42—111no—
345C2×C42—111no—
346C2×C42—221no—
347C2×C42—221no—
348C2×C42—222no—
349#103—24no—
350#103—224no—
351#103—224no—
352#103—224no—
353#97—224no—
354#97—224no—
355#95—21no—
356#95—222no—
357#95—222no—
358#95—222no—
359#95—221no—
360C2×C11—24no—
361C2×C11#229711yescharacteristic
362C2×C11C2×#41911yescharacteristic
363C2×C11#289611yescharacteristic
364C2×C11#318112yes—
365C2×C11#318112yes—
366C24D4×D1111yescharacteristic
367C2×Q8—21no—
368C2×Q8—22no—
369C2×Q8—22no—
370C2×Q8—112no—
371C2×Q8—224no—
372C2×Q8—221no—
373C2×Q8—222no—
374C2×Q8—222no—
375C2×Q8—444no—
376C2×Q8C2×C4×D1112yes—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—22no—
382C22×C4—114no—
383C22×C4—111no—
384C22×C4—111no—
385C22×C4—111no—
386C22×C4—111no—
387C22×C4—114no—
388C22×C4—222no—
389C22×C4—222no—
390C22×C4—221no—
391C22×C4—221no—
392C22×C4—222no—
393C22×C4—442no—
394C22×C4C2×C4×D1112yes—
395C22×C4D4×D1111yescharacteristic
396C22×C4D4×D1112yes—
397C22×C4C23×D1111yescharacteristic
398C2×C8—28no—
399C2×C8—22no—
400C2×C8—22no—
401C2×C8—114no—
402C2×C8—228no—
403C2×C8—222no—
404C2×C8—222no—
405C2×C8#434114yes—
406C4⋊C4—24no—
407C4⋊C4—21no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—112no—
411C4⋊C4—224no—
412C4⋊C4—224no—
413C4⋊C4—224no—
414C4⋊C4—224no—
415C4⋊C4—224no—
416C4⋊C4—224no—
417C4⋊C4—221no—
418C4⋊C4—222no—
419C4⋊C4—222no—
420C4⋊C4C2×C4×D1112yes—
421C22⋊C4—24no—
422C22⋊C4—42no—
423C22⋊C4—224no—
424C22⋊C4—442no—
425C42—114no—
426C42—114no—
427C42—112no—
428C42—112no—
429C42—112no—
430C42—112no—
431C42—224no—
432C42—224no—
433C42—444no—
434C11#2140711yescharacteristic, complemented, Sylow
435C23—22no—
436C23—22no—
437C23C22⋊C4×D1112yes—
438C23#6696812yes—
439C23#6697112yes—
440C23C2×D4×D1111yescharacteristic
441Q8—24no—
442Q8—41no—
443Q8—41no—
444Q8—224no—
445Q8—448no—
446Q8—441no—
447Q8—441no—
448C2×C4—22no—
449C2×C4—24no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—112no—
460C2×C4—112no—
461C2×C4—112no—
462C2×C4—112no—
463C2×C4—221no—
464C2×C4—221no—
465C2×C4—221no—
466C2×C4—221no—
467C2×C4—222no—
468C2×C4—222no—
469C2×C4—228no—
470C2×C4—222no—
471C2×C4—222no—
472C2×C4—444no—
473C2×C4—442no—
474C2×C4—442no—
475C2×C4—442no—
476C2×C4—442no—
477C2×C4—442no—
478C2×C4C22⋊C4×D1112yes—
479C2×C4C22×C4×D1111yescharacteristic
480C2×C4C2×D4×D1111yescharacteristic
481C2×C4C2×#434112yes—
482C2×C4#41×D1112yes—
483C8—24no—
484C8—224no—
485C22—24no—
486C22—24no—
487C22—22no—
488C22—22no—
489C22#1062241514yes—
490C22C2×C22⋊C4×D1111yescharacteristic
491C22#1062312712yes—
492C22C2×#6696811yescharacteristic
493C22C2×#6697111yescharacteristic
494C22#1062329912yes—
495C4—22no—
496C4—42no—
497C4—42no—
498C4—82no—
499C4—222no—
500C4—222no—
501C4—222no—
502C4—222no—
503C4—442no—
504C4—442no—
505C4—882no—
506C4C4×#434112yes—
507C4#1062311711yescharacteristic
508C4#1062318711yescharacteristic
509C2—24no—
510C2#1307110111yescharacteristic
511C2C2×#1062241511yescharacteristic
512C2#1307713111yescharacteristic
513C2#1307931812yes—
514C2#1307932012yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1892C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1892D11
hypocenterC11#21407
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1892

Complements

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

NH ≅ G/Ntype
4. #13069587C2semidirect
5. #13069434C2semidirect
9. #13068448C2semidirect
10. #13068445C2semidirect
20. #10623153C4semidirect
434. C11#21407semidirect

Maximal subgroups

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

subgroupindex
C2×#106231532
C22×#668792
#130710112
#130695872
#130694342
#130690402
#130690392
#130690372
#130684482
#130684452
C11×#18922
#2140711