Finite Group Databasebeta

← #14782585

Subgroups — #14782585

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622746C211yesmaximal, characteristic
2C2×#10622726C211yesmaximal, characteristic
3#13071239C211yesmaximal, characteristic, complemented
4#13071204C211yesmaximal, characteristic
5#13070036C212yesmaximal, complemented
6#13070031C212yesmaximal, complemented
7#13070026C212yesmaximal, complemented
8#13070021C212yesmaximal, complemented
9#13068336C211yesmaximal, characteristic, complemented
10C2×#10622189C211yesmaximal, characteristic, complemented
11C11×#1729C211yesmaximal, characteristic, complemented
12C22×#4339C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C23×C8×C11C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C2×#66979C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19#10622746—24no—
20#10622726—24no—
21C2×#66885C2211yescharacteristic
22C2×#66885C2211yescharacteristic
23C2×#66885C2212yes—
24C2×#66880C2211yescharacteristic
25C2×#66880C2211yescharacteristic
26C2×#66880C2212yes—
27#10622600—21no—
28#10622600—21no—
29#10622598—21no—
30#10622598—21no—
31#10622571—22no—
32#10622563—22no—
33#10622552C2212yes—
34#10622549C2212yes—
35#10622548C2212yes—
36#10622542C2212yes—
37C11×#336C2212yes—
38C11×#336C2212yes—
39#10622189C2212yes—
40#10622189C2212yes—
41#10622189C2212yes—
42#10622189C2212yes—
43C23×C4×C11C2311yescharacteristic
44C22×C22⋊D11—21no—
45C23×Dic11—21no—
46C23×Dic11—21no—
47C2×#4339—22no—
48C2×#4339—22no—
49C2×#4339—22no—
50C2×#4339—22no—
51C2×#4339—22no—
52C2×#4339D414yes—
53C22×D44C2311yescharacteristic
54C22×C4×D11—21no—
55C22×Dic22C2311yescharacteristic
56C2×C11×M16—22no—
57C2×C11×M16—22no—
58C2×C11×M16—22no—
59C22×C8×C11—22no—
60C22×C8×C11—22no—
61C22×C8×C11—22no—
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2312yes—
65C11×#117—22no—
66C11×#117—22no—
67C2×C11×C4⋊C4D411yescharacteristic
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C11×C22⋊C4D412yes—
70C2×C42×C11C2312yes—
71C2×C22⋊Dic11—21no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4—22no—
74#66979—22no—
75#66979—22no—
76C2×C4⋊Dic11—22no—
77C2×C4⋊Dic11—22no—
78C2×C4⋊Dic11—22no—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—22no—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2312yes—
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2312yes—
88C2×C4×Dic11—21no—
89C11⋊#95—22no—
90C11⋊#95—22no—
91C11⋊#95—22no—
92C11⋊#95—22no—
93#66885—22no—
94#66885—22no—
95#66885—24no—
96#66880—22no—
97#66880—22no—
98#66880—24no—
99#23634—111nomaximal, Sylow
100C24×C11C2×D411yescharacteristic
101C23×D11—21no—
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2×D412yes—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D412yes—
106C22×C4×C11#4112yes—
107C22×C4×C11#4112yes—
108C22×C4×C11#4112yes—
109C22×C4×C11#4112yes—
110C22×C4×C11#4112yes—
111C22×C4×C11C2411yescharacteristic
112C2×C22⋊D11—24no—
113C2×C22⋊D11—42no—
114C2×C22⋊D11—42no—
115C22×Dic11—21no—
116C22×Dic11—21no—
117C22×Dic11—22no—
118C22×Dic11—22no—
119C22×Dic11—21no—
120C22×Dic11—42no—
121C22×Dic11—42no—
122C22×Dic11—81no—
123C22×Dic11—81no—
124C22×Dic11—81no—
125C22×Dic11—81no—
126#4339—28no—
127#4339—28no—
128#4339—44no—
129#4339—44no—
130C2×D44—21no—
131C2×D44—21no—
132C2×D44—21no—
133C2×D44—21no—
134C2×D44—21no—
135C2×D44C2×D412yes—
136C2×C4×D11—24no—
137C2×C4×D11—42no—
138C2×C4×D11—42no—
139C2×Dic22—21no—
140C2×Dic22—21no—
141C2×Dic22—21no—
142C2×Dic22—21no—
143C2×Dic22—21no—
144C2×Dic22C2×D412yes—
145C11×M16—44no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—22no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C2×C8×C11—44no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C22⋊C4—24no—
159C42×C11—22no—
160C42×C11—22no—
161C22⋊Dic11—42no—
162(C2×D11)⋊C4—82no—
163(C2×D11)⋊C4—82no—
164C4⋊Dic11—22no—
165C4⋊Dic11—21no—
166C4⋊Dic11—21no—
167C4⋊Dic11—22no—
168C4⋊Dic11—22no—
169C4⋊Dic11—22no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—42no—
173C4⋊Dic11—42no—
174C4⋊Dic11—82no—
175C4⋊Dic11—82no—
176C4×Dic11—42no—
177C2×#417—111no—
178C2×#416—111no—
179#2317—111no—
180#2311—111no—
181#2074—112no—
182#2073—112no—
183#2072—112no—
184#2071—112no—
185#1736—111no—
186C2×#340—111no—
187#1729D1111yescharacteristic, complemented
188C23×C11—21no—
189C23×C11—21no—
190C23×C11—21no—
191C23×C11—21no—
192C23×C11#12112yes—
193C23×C11#12312yes—
194C23×C11#12412yes—
195C23×C11C22×D411yescharacteristic
196C22×D11—22no—
197C22×D11—41no—
198C22×D11—41no—
199C22×D11—41no—
200C22×D11—41no—
201C22×D11—41no—
202C22×D11—41no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11#12112yes—
210C2×C4×C11#12314yes—
211C2×C4×C11#12314yes—
212C2×C4×C11#12312yes—
213C2×C4×C11#12412yes—
214C2×C4×C11#12614yes—
215C2×C4×C11#12614yes—
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C2×#4111yescharacteristic
218C2×C4×C11C2×#4111yescharacteristic
219C2×C4×C11C2×#4111yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C2×C4×C11C2×#4111yescharacteristic
222C22⋊D11—48no—
223C2×Dic11—22no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—42no—
229C2×Dic11—42no—
230C2×Dic11—41no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—41no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11—41no—
237C2×Dic11—41no—
238C2×Dic11—84no—
239C2×Dic11—84no—
240D44—22no—
241D44—22no—
242D44—41no—
243D44—41no—
244C4×D11—48no—
245Dic22—22no—
246Dic22—22no—
247Dic22—41no—
248Dic22—41no—
249C8×C11—41no—
250C8×C11—41no—
251C8×C11—42no—
252C22×#41—111no—
253C22×M16C2×D1111yescharacteristic
254C23×C8C2×D1111yescharacteristic
255C2×#117—111no—
256C2×#117C2×D1111yescharacteristic
257C22×C4⋊C4—111no—
258C22×C4⋊C4—111no—
259#417—224no—
260#416—224no—
261C2×#103—111no—
262C2×#103—112no—
263C2×#103—111no—
264C2×#102—111no—
265C2×#102—112no—
266C2×#102—111no—
267#391—112no—
268#390—112no—
269#389—221no—
270#389—221no—
271#386—222no—
272#385—222no—
273#384—112no—
274#382—112no—
275#380—221no—
276#380—221no—
277#340—112no—
278#340—112no—
279#340—112no—
280#340—112no—
281#336C2×D1112yes—
282#336C2×D1112yes—
283C22×C11—22no—
284C22×C11—22no—
285C22×C11—22no—
286C22×C11—22no—
287C22×C11—22no—
288C22×C11—22no—
289C22×C11#39714yes—
290C22×C11C2×#12111yescharacteristic
291C22×C11C2×#12311yescharacteristic
292C22×C11C2×#12411yescharacteristic
293C22×C11#57611yescharacteristic
294C22×C11#57711yescharacteristic
295C22×C11#57711yescharacteristic
296C22×C11#57811yescharacteristic
297C2×D11—42no—
298C2×D11—42no—
299C2×D11—42no—
300C2×D11—81no—
301C2×D11—81no—
302C2×D11—81no—
303C2×D11—81no—
304C4×C11—42no—
305C4×C11—42no—
306C4×C11#39714yes—
307C4×C11C2×#12311yescharacteristic
308C4×C11C2×#12311yescharacteristic
309C4×C11C2×#12611yescharacteristic
310C4×C11C2×#12611yescharacteristic
311Dic11—42no—
312Dic11—82no—
313Dic11—81no—
314Dic11—82no—
315Dic11—81no—
316C2×#41—114no—
317C2×#41—222no—
318C2×#41—222no—
319C2×#41—222no—
320C2×#41—222no—
321C2×#41—222no—
322C22×Q8—111no—
323C22×D4—111no—
324C22×D4—221no—
325C23×C4—221no—
326C23×C4—221no—
327C23×C4—221no—
328C23×C4C22×D1111yescharacteristic
329C2×M16—22no—
330C2×M16—22no—
331C2×M16—22no—
332C22×C8—22no—
333C22×C8—22no—
334C22×C8—22no—
335C22×C8C22×D1111yescharacteristic
336C22×C8C22×D1111yescharacteristic
337C22×C8C22×D1112yes—
338#117—22no—
339#117—22no—
340#117—222no—
341#117—222no—
342C2×C4⋊C4—112no—
343C2×C4⋊C4—112no—
344C2×C4⋊C4—111no—
345C2×C4⋊C4—111no—
346C2×C4⋊C4—222no—
347C2×C4⋊C4—222no—
348C2×C4⋊C4—222no—
349C2×C4⋊C4—222no—
350C2×C4⋊C4—221no—
351C2×C4⋊C4—221no—
352C2×C4⋊C4—222no—
353C2×C4⋊C4—222no—
354C2×C4⋊C4D4411yescharacteristic
355C2×C4⋊C4D4411yescharacteristic
356C2×C22⋊C4—221no—
357C2×C22⋊C4—222no—
358C2×C22⋊C4—222no—
359C2×C22⋊C4D4412yes—
360C2×C42—221no—
361C2×C42C22×D1112yes—
362#103—222no—
363#103—222no—
364#103—224no—
365#102—222no—
366#102—222no—
367#102—224no—
368#95—222no—
369#95—222no—
370#95—222no—
371#95—222no—
372C2×C11—24no—
373C2×C11C2×#39711yescharacteristic
374C2×C11#304511yescharacteristic
375C2×C11#304611yescharacteristic
376C2×C11#309811yescharacteristic
377C2×C11#309911yescharacteristic
378C2×C11#313611yescharacteristic
379C2×C11#313711yescharacteristic
380D11—82no—
381C24—221no—
382C24C2×D4411yescharacteristic
383#41—228no—
384#41—228no—
385#41—444no—
386#41—444no—
387C2×Q8—112no—
388C2×Q8—221no—
389C2×Q8—221no—
390C2×Q8—221no—
391C2×Q8—221no—
392C2×Q8—221no—
393C2×D4—112no—
394C2×D4—224no—
395C2×D4—221no—
396C2×D4—221no—
397C2×D4—221no—
398C2×D4—221no—
399C2×D4—221no—
400C2×D4—442no—
401C2×D4—442no—
402C22×C4—221no—
403C22×C4—224no—
404C22×C4—221no—
405C22×C4—222no—
406C22×C4—222no—
407C22×C4—221no—
408C22×C4—442no—
409C22×C4—442no—
410C22×C4—442no—
411C22×C4—442no—
412C22×C4—881no—
413C22×C4—881no—
414C22×C4—881no—
415C22×C4—881no—
416C22×C4C2×D4412yes—
417C22×C4C2×D4412yes—
418C22×C4C2×D4411yescharacteristic
419C22×C4#433912yes—
420C22×C4#433912yes—
421C22×C4D4×D1112yes—
422C22×C4#434112yes—
423C22×C4#434112yes—
424C22×C4#434312yes—
425C22×C4C23×D1111yescharacteristic
426M16—44no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—22no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—22no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—22no—
436C2×C8—44no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—222no—
440C4⋊C4—222no—
441C4⋊C4—222no—
442C4⋊C4—221no—
443C4⋊C4—221no—
444C4⋊C4—222no—
445C4⋊C4—221no—
446C4⋊C4—221no—
447C4⋊C4—442no—
448C4⋊C4—442no—
449C4⋊C4—882no—
450C4⋊C4—882no—
451C22⋊C4—24no—
452C22⋊C4—442no—
453C22⋊C4—882no—
454C22⋊C4—882no—
455C42—22no—
456C42—22no—
457C42—442no—
458C11#2363411yescharacteristic, complemented, Sylow
459C23—21no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—222no—
464C23—441no—
465C23—441no—
466C23—441no—
467C23—441no—
468C23—441no—
469C23—441no—
470C23#6692812yes—
471C23#6693912yes—
472C23#6694812yes—
473C23C22×D4411yescharacteristic
474Q8—222no—
475Q8—222no—
476Q8—441no—
477Q8—441no—
478D4—222no—
479D4—222no—
480D4—448no—
481D4—441no—
482D4—441no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—222no—
490C2×C4—441no—
491C2×C4—441no—
492C2×C4—448no—
493C2×C4—442no—
494C2×C4—442no—
495C2×C4—441no—
496C2×C4—442no—
497C2×C4—441no—
498C2×C4—442no—
499C2×C4—441no—
500C2×C4—442no—
501C2×C4—441no—
502C2×C4—441no—
503C2×C4—441no—
504C2×C4—442no—
505C2×C4—884no—
506C2×C4—884no—
507C2×C4#6692812yes—
508C2×C4#6693614yes—
509C2×C4#6693614yes—
510C2×C4#6693912yes—
511C2×C4#6694812yes—
512C2×C4#6695114yes—
513C2×C4#6695114yes—
514C2×C4C2×#433911yescharacteristic
515C2×C4C2×#433911yescharacteristic
516C2×C4C2×D4×D1111yescharacteristic
517C2×C4C2×#434111yescharacteristic
518C2×C4C2×#434111yescharacteristic
519C2×C4C2×#434311yescharacteristic
520C8—41no—
521C8—41no—
522C8—42no—
523C22—22no—
524C22—22no—
525C22—22no—
526C22—22no—
527C22—22no—
528C22—22no—
529C22—442no—
530C22—442no—
531C22—442no—
532C22—881no—
533C22—881no—
534C22—881no—
535C22—881no—
536C22#1062228714yes—
537C22C2×#6692811yescharacteristic
538C22C2×#6693911yescharacteristic
539C22C2×#6694811yescharacteristic
540C22#1062328211yescharacteristic
541C22#1062328211yescharacteristic
542C22#1062328311yescharacteristic
543C22#1062328411yescharacteristic
544C4—42no—
545C4—42no—
546C4—442no—
547C4—882no—
548C4—881no—
549C4—881no—
550C4—882no—
551C4#1062228714yes—
552C4C2×#6693611yescharacteristic
553C4C2×#6693611yescharacteristic
554C4C2×#6695111yescharacteristic
555C4C2×#6695111yescharacteristic
556C2—24no—
557C2—882no—
558C2C2×#1062228711yescharacteristic
559C2#1307815711yescharacteristic
560C2#1307816811yescharacteristic
561C2#1307859611yescharacteristic
562C2#1307860711yescharacteristic
563C2#1307897211yescharacteristic
564C2#1307898311yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1729C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
hypercenter#1729D11
hypocenterC11#23634
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #1729

Complements

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

NH ≅ G/Ntype
3. #13071239C2semidirect
5. #13070036C2semidirect
6. #13070031C2semidirect
7. #13070026C2semidirect
8. #13070021C2semidirect
9. #13068336C2semidirect
10. C2×#10622189C2semidirect
11. C11×#1729C2semidirect
187. #1729D11semidirect
458. C11#23634semidirect

Maximal subgroups

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

subgroupindex
C2×#106227462
C2×#106227262
#130712392
#130712042
#130700362
#130700312
#130700262
#130700212
#130683362
C2×#106221892
C11×#17292
#2363411