Finite Group Databasebeta

← #11864086

Subgroups — #11864086

Order 1152.

1611 conjugacy classes of subgroups.

The subgroup lattice has 631 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3796C211yesmaximal, characteristic, complemented
2C2×C3×#909C211yesmaximal, characteristic, complemented
3#10595034C211yesmaximal, characteristic, complemented
4C2×#63823C211yesmaximal, characteristic, complemented
5#10592825C211yesmaximal, characteristic, complemented
6C3×#5131C211yesmaximal, characteristic, complemented
7#10591099C211yesmaximal, characteristic, complemented
8#10590965C214yesmaximal, complemented
9#10590964C214yesmaximal, complemented
10#83980—31nomaximal
11#78927—31nomaximal
12C22×C4×C3⋊D3C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C22×#626—21no—
17C22×D3×Dic3—21no—
18C2×#3796—22no—
19C2×#3796—24no—
20C2×#3796—24no—
21C2×#3796C2214yes—
22C2×C32×M16C2211yescharacteristic
23C2×#3748C2211yescharacteristic
24C3×#926C2211yescharacteristic
25C3×#909—24no—
26C2×C3×Dic12C2212yescomplemented
27C2×C3×#204C2212yescomplemented
28#63981—21no—
29#63962—21no—
30#63916C2212yescomplemented
31C4×#626—22no—
32#63871C2212yescomplemented
33C2×#3715C2212yescomplemented
34#63823—24no—
35C2×#3713C2212yescomplemented
36#63647C2214yescomplemented
37C3×#821C2214yescomplemented
38#63565C2214yescomplemented
39C22×#239—31no—
40C22×#237—31no—
41C2×C3×#137—31no—
42#5828—31no—
43C2×#949—31no—
44C2×#932—31no—
45C2×#909D311yescharacteristic, complemented
46#5524—31no—
47C3×#418—31no—
48#5225—31no—
49#5187—34no—
50#5172—34no—
51#5131D311yescharacteristic, complemented
52#5126—31no—
53#5126—31no—
54#5126—61no—
55#5004—31no—
56#4783—34no—
57#4781—34no—
58C23×C3⋊D3D411yescharacteristic
59C23×C3×D3—21no—
60C22×C32×C4C2311yescharacteristic
61C22×C3⋊Dic3D411yescharacteristic
62C2×C4×C3⋊D3—22no—
63C2×C4×C3⋊D3—22no—
64C2×C4×C3⋊D3D412yes—
65C2×C4×C3⋊D3C2312yes—
66C2×C3×#67—21no—
67C22×C3×Dic3—21no—
68C3×#235—22no—
69C3×#235—22no—
70C2×C3×D12—21no—
71C2×C3×D12—22no—
72C2×C3×D12D414yescomplemented
73C2×C3×D12C2311yescharacteristic
74C2×C3×D12C2312yes—
75C2×C3×C4×D3—21no—
76C2×C3×Dic6—21no—
77C2×C3×Dic6—22no—
78C2×C3×Dic6D414yescomplemented
79C2×C3×Dic6C2311yescharacteristic
80C2×C3×Dic6C2312yes—
81C2×#626—28no—
82C2×#626—24no—
83C2×#626—22no—
84C2×D3×Dic3—28no—
85C2×D3×Dic3—24no—
86#3796—216no—
87#3796—28no—
88#3796—28no—
89C32×M16—22no—
90C2×C32×C8C2312yes—
91#3748—22no—
92C2×C3⋊(C3⋊C8)C2312yes—
93C3×#217—21no—
94C3×C4⋊Dic3C2312yes—
95C3×C4×Dic3—21no—
96C3×Dic12—24no—
97C3×#204—24no—
98Dic3⋊Dic3—22no—
99#3722—22no—
100(C2×D3)⋊Dic3—22no—
101#3715—24no—
102#3713—24no—
103#3005—91noSylow
104C2×C3×#41—31no—
105C22×C3×Q8—31no—
106C22×C3×D4—31no—
107C22×#67—61no—
108C23×Dic3—61no—
109C2×#239—34no—
110C2×#239—62no—
111C2×#239—64no—
112C2×#239—64no—
113C2×#237—34no—
114C2×#237—62no—
115C2×#237—64no—
116C2×#237—64no—
117C2×#235C2×D311yescharacteristic
118C22×D12—61no—
119C22×D12C2×D311yescharacteristic
120C22×C4×D3—31no—
121C22×C4×D3—31no—
122C22×C4×D3—61no—
123C22×C4×D3—61no—
124C22×Dic6C2×D311yescharacteristic
125C3×#137—64no—
126C2×C3×Q16—32no—
127C2×C3×SD16—32no—
128C2×C3×M16—21no—
129C2×C3×M16C2×D311yescharacteristic
130C2×C3×M16C2×D311yescharacteristic
131C3×#117—31no—
132#949—64no—
133#946—32no—
134C2×#215—32no—
135#938—32no—
136#937—61no—
137#935—61no—
138C2×#214—32no—
139#932—64no—
140C2×#213—32no—
141C2×#213—32no—
142C4×#67—62no—
143#926C2×D311yescharacteristic
144C2×#208—31no—
145C2×#208—31no—
146C2×#208—61no—
147#909—24no—
148C2×Dic12C2×D312yescomplemented
149C2×#204C2×D312yescomplemented
150#897—32no—
151#895—32no—
152#886—61no—
153#882—61no—
154C4×D12—62no—
155C3×#102—34no—
156#835—34no—
157#821C2×D314yescomplemented
158(C2×D3)⋊C8—34no—
159(C2×D3)⋊C8—34no—
160(C2×D3)⋊C8—64no—
161#810—34no—
162C23×C32C2×D411yescharacteristic
163C22×C3⋊D3—22no—
164C22×C3⋊D3—42no—
165C22×C3⋊D3C2×D412yes—
166C22×C3×D3—24no—
167C22×C3×D3—22no—
168C22×C3×D3—21no—
169C22×C3×D3—44no—
170C2×C32×C4C2×D412yes—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D412yes—
173C2×C32×C4C2411yescharacteristic
174C2×C3⋊Dic3—22no—
175C2×C3⋊Dic3C2×D412yes—
176C4×C3⋊D3—24no—
177C4×C3⋊D3—22no—
178C4×C3⋊D3—22no—
179C3×#67—42no—
180C2×C3×Dic3—24no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—21no—
184C3×D12—24no—
185C3×D12—22no—
186C3×D12—21no—
187C3×D12—21no—
188C3×D12C2×D414yes—
189C3×C4×D3—42no—
190C3×Dic6—24no—
191C3×Dic6—22no—
192C3×Dic6—21no—
193C3×Dic6—21no—
194C3×Dic6C2×D414yes—
195#626—216no—
196#626—44no—
197D3×Dic3—216no—
198C32×C8—22no—
199C3⋊(C3⋊C8)—22no—
200C22×#41—91no—
201C2×#137—31no—
202C2×AGL(1,ℤ/8)—91no—
203#525—91no—
204#452—94no—
205#449—94no—
206#419—91no—
207#418—31no—
208#407—91no—
209C24×C3—61no—
210C23×D3—21no—
211C23×D3—31no—
212C23×D3—31no—
213C23×D3—61no—
214C3×#41—62no—
215C3×#41—62no—
216C2×C3×Q8—34no—
217C2×C3×Q8—32no—
218C2×C3×Q8—31no—
219C2×C3×Q8—62no—
220C2×C3×Q8—61no—
221C2×C3×D4—34no—
222C2×C3×D4—32no—
223C2×C3×D4—31no—
224C2×C3×D4—61no—
225C2×C3×D4—61no—
226C2×C3×D4—62no—
227C22×C3×C4—21no—
228C22×C3×C4—61no—
229C22×C3×C4—61no—
230C22×C3×C4C22×D311yescharacteristic
231C22×C3×C4C22×D311yescharacteristic
232C2×#67—21no—
233C2×#67—64no—
234C2×#67—68no—
235C2×#67—62no—
236C22×Dic3—21no—
237C22×Dic3—31no—
238C22×Dic3—31no—
239C22×Dic3—61no—
240C22×Dic3—64no—
241C22×Dic3—68no—
242#239—68no—
243#239—616no—
244#239—68no—
245#237—68no—
246#237—616no—
247#237—68no—
248#235—22no—
249#235—22no—
250C2×D12—21no—
251C2×D12—22no—
252C2×D12—64no—
253C2×D12—68no—
254C2×D12—62no—
255C2×D12D1214yescomplemented
256C2×D12C22×D311yescharacteristic
257C2×D12C22×D312yes—
258C2×C4×D3—21no—
259C2×C4×D3—32no—
260C2×C4×D3—32no—
261C2×C4×D3—32no—
262C2×C4×D3—32no—
263C2×C4×D3—62no—
264C2×C4×D3—62no—
265C2×C4×D3—64no—
266C2×C4×D3—68no—
267C2×C4×D3—62no—
268C2×C4×D3—62no—
269C2×C4×D3—62no—
270C2×C4×D3—62no—
271C2×C4×D3—122no—
272C2×C4×D3—122no—
273C2×Dic6—22no—
274C2×Dic6—21no—
275C2×Dic6#6714yescomplemented
276C2×Dic6C22×D311yescharacteristic
277C2×Dic6C22×D312yes—
278C3×Q16—64no—
279C3×SD16—64no—
280C3×M16—22no—
281C3×M16—22no—
282C3×M16—42no—
283C2×C3×C8—22no—
284C2×C3×C8C22×D312yes—
285C2×C3×C8C22×D312yes—
286C3×C4⋊C4—32no—
287C3×C22⋊C4—61no—
288C3×C42—61no—
289#217—21no—
290#217—62no—
291#215—64no—
292#214—64no—
293#213—64no—
294#213—64no—
295(C2×D3)⋊C4—62no—
296(C2×D3)⋊C4—62no—
297(C2×D3)⋊C4—62no—
298C4⋊Dic3—62no—
299C4⋊Dic3C22×D312yes—
300Dic3⋊C4—62no—
301C4×Dic3—21no—
302#208—62no—
303#208—62no—
304#208—122no—
305C2×C3⋊C8—32no—
306C2×C3⋊C8—32no—
307C2×C3⋊C8—62no—
308Dic12—24no—
309#204—24no—
310C22×C32—22no—
311C22×C32#12012yes—
312C22×C32C22×D411yescharacteristic
313C2×C3⋊D3—22no—
314C2×C3⋊D3—22no—
315C2×C3⋊D3—22no—
316C2×C3⋊D3—44no—
317C2×C3×D3—24no—
318C2×C3×D3—48no—
319C2×C3×D3—44no—
320C2×C3×D3—41no—
321C2×C3×D3—42no—
322C32×C4#12012yes—
323C32×C4C22×D411yescharacteristic
324C32×C4C22×D411yescharacteristic
325C3⋊Dic3—22no—
326C3×Dic3—24no—
327C3×Dic3—41no—
328C3×Dic3—42no—
329C2×#41—31no—
330C2×#41—94no—
331C2×#41—182no—
332C2×#41—184no—
333C2×#41—184no—
334C22×Q8—31no—
335C22×D4—31no—
336C22×D4—181no—
337C23×C4—91no—
338C23×C4—181no—
339#137—64no—
340AGL(1,ℤ/8)—184no—
341C2×Q16—32no—
342C2×SD16—32no—
343C2×SD16—92no—
344C2×D8—92no—
345C2×M16—91no—
346C2×M16D3211yescharacteristic
347#123—181no—
348C22⋊Q8—92no—
349#121—92no—
350#120—181no—
351C4×D4—182no—
352#117—31no—
353#103—94no—
354#102—34no—
355C22⋊C8—94no—
356C23×C3—21no—
357C23×C3—64no—
358C23×C3—62no—
359C23×C3—61no—
360C23×C3—124no—
361C23×C3D3×D411yescharacteristic
362C23×C3D3×D411yescharacteristic
363C22×D3—24no—
364C22×D3—22no—
365C22×D3—21no—
366C22×D3—32no—
367C22×D3—32no—
368C22×D3—44no—
369C22×D3—62no—
370C22×D3—62no—
371C22×D3—62no—
372C22×D3—122no—
373C22×D3—122no—
374C22×D3—122no—
375C22×D3—124no—
376C3×Q8—34no—
377C3×Q8—64no—
378C3×Q8—62no—
379C3×Q8—61no—
380C3×Q8—61no—
381C3×D4—34no—
382C3×D4—64no—
383C3×D4—61no—
384C3×D4—61no—
385C3×D4—62no—
386C3×D4—122no—
387C2×C3×C4—21no—
388C2×C3×C4—22no—
389C2×C3×C4—21no—
390C2×C3×C4—22no—
391C2×C3×C4—64no—
392C2×C3×C4—62no—
393C2×C3×C4—61no—
394C2×C3×C4—62no—
395C2×C3×C4—122no—
396C2×C3×C4C2×D1212yes—
397C2×C3×C4D3×D412yes—
398C2×C3×C4D3×D411yescharacteristic
399C2×C3×C4D3×D411yescharacteristic
400C2×C3×C4D3×D412yes—
401C2×C3×C4C2×#6712yes—
402C2×C3×C4C23×D311yescharacteristic
403C2×C3×C4C23×D311yescharacteristic
404#67—42no—
405#67—616no—
406#67—124no—
407C2×Dic3—24no—
408C2×Dic3—22no—
409C2×Dic3—22no—
410C2×Dic3—21no—
411C2×Dic3—32no—
412C2×Dic3—32no—
413C2×Dic3—62no—
414C2×Dic3—616no—
415C2×Dic3—62no—
416C2×Dic3—62no—
417C2×Dic3—122no—
418D12—24no—
419D12—22no—
420D12—21no—
421D12—21no—
422D12—616no—
423D12—124no—
424D12C2×D1214yes—
425C4×D3—42no—
426C4×D3—616no—
427C4×D3—64no—
428C4×D3—64no—
429C4×D3—62no—
430C4×D3—62no—
431C4×D3—62no—
432C4×D3—62no—
433C4×D3—122no—
434C4×D3—122no—
435C4×D3—124no—
436Dic6—24no—
437Dic6—22no—
438Dic6—21no—
439Dic6—21no—
440Dic6C2×#6714yes—
441C3×C8—22no—
442C3×C8—22no—
443C3×C8—42no—
444C3⋊C8—62no—
445C3⋊C8—62no—
446C3⋊C8—122no—
447C2×C32—22no—
448C2×C32C2×#12011yescharacteristic
449C2×C32#57512yes—
450C3⋊D3—42no—
451C3×D3—44no—
452C3×D3—81no—
453C24—61no—
454C24—91no—
455#41—62no—
456#41—62no—
457#41—188no—
458#41—188no—
459#41—1816no—
460C2×Q8—32no—
461C2×Q8—31no—
462C2×Q8—34no—
463C2×Q8—62no—
464C2×Q8—61no—
465C2×D4—32no—
466C2×D4—31no—
467C2×D4—34no—
468C2×D4—61no—
469C2×D4—61no—
470C2×D4—62no—
471C2×D4—184no—
472C2×D4—188no—
473C2×D4—182no—
474C22×C4—61no—
475C22×C4—61no—
476C22×C4—91no—
477C22×C4—92no—
478C22×C4—92no—
479C22×C4—184no—
480C22×C4—188no—
481C22×C4—182no—
482C22×C4—182no—
483C22×C4C2×D3211yescharacteristic
484Q16—64no—
485SD16—64no—
486SD16—184no—
487D8—184no—
488M16—22no—
489M16—182no—
490C2×C8—92no—
491C2×C8C2×D3212yes—
492C4⋊C4—32no—
493C4⋊C4—182no—
494C22⋊C4—61no—
495C22⋊C4—182no—
496C22⋊C4—182no—
497C42—61no—
498C22×C3—22no—
499C22×C3—22no—
500C22×C3—21no—
501C22×C3—22no—
502C22×C3—42no—
503C22×C3—64no—
504C22×C3—128no—
505C22×C3—124no—
506C22×C3—121no—
507C22×C3—122no—
508C22×C3#88212yes—
509C22×C3#93712yes—
510C22×C3C2×D3×D411yescharacteristic
511C22×C3C2×D3×D411yescharacteristic
512C2×D3—24no—
513C2×D3—48no—
514C2×D3—44no—
515C2×D3—42no—
516C2×D3—41no—
517C2×D3—64no—
518C2×D3—62no—
519C2×D3—62no—
520C2×D3—62no—
521C2×D3—62no—
522C2×D3—62no—
523C2×D3—62no—
524C2×D3—122no—
525C2×D3—122no—
526C2×D3—124no—
527C2×D3—124no—
528C2×D3—128no—
529C3×C4—21no—
530C3×C4—21no—
531C3×C4—22no—
532C3×C4—64no—
533C3×C4—121no—
534C3×C4—122no—
535C3×C4#88212yes—
536C3×C4#93712yes—
537C3×C4C22×D1211yescharacteristic
538C3×C4C2×D3×D411yescharacteristic
539C3×C4C2×D3×D411yescharacteristic
540C3×C4C22×#6711yescharacteristic
541Dic3—24no—
542Dic3—42no—
543Dic3—41no—
544Dic3—62no—
545Dic3—62no—
546Dic3—122no—
547C32#300511yescharacteristic, complemented, Sylow
548C23—62no—
549C23—64no—
550C23—61no—
551C23—92no—
552C23—124no—
553C23—182no—
554C23—362no—
555C23#380211yescharacteristic
556Q8—34no—
557Q8—62no—
558Q8—64no—
559Q8—61no—
560Q8—61no—
561D4—34no—
562D4—61no—
563D4—62no—
564D4—61no—
565D4—64no—
566D4—122no—
567D4—1816no—
568D4—364no—
569C2×C4—62no—
570C2×C4—64no—
571C2×C4—62no—
572C2×C4—61no—
573C2×C4—92no—
574C2×C4—122no—
575C2×C4—1816no—
576C2×C4—182no—
577C2×C4—182no—
578C2×C4—182no—
579C2×C4—184no—
580C2×C4D3×D1212yes—
581C2×C4#380211yescharacteristic
582C2×C4D3×#6712yes—
583C2×C4C22×D3211yescharacteristic
584C8—22no—
585C8—182no—
586C2×C3—22no—
587C2×C3—22no—
588C2×C3—22no—
589C2×C3—21no—
590C2×C3—42no—
591C2×C3—124no—
592C2×C3—241no—
593C2×C3C2×#88211yescharacteristic
594C2×C3#577312yes—
595C2×C3#577712yes—
596C2×C3C2×#93711yescharacteristic
597D3—44no—
598D3—81no—
599D3—124no—
600D3—122no—
601D3—122no—
602C22—22no—
603C22—64no—
604C22—128no—
605C22—124no—
606C22—122no—
607C22—121no—
608C22—182no—
609C22—182no—
610C22—182no—
611C22—364no—
612C22#6392212yes—
613C22C2×#380211yescharacteristic
614C4—64no—
615C4—122no—
616C4—121no—
617C4—182no—
618C4#6392212yes—
619C4C2×D3×D1211yescharacteristic
620C4C2×D3×#6711yescharacteristic
621C3—21no—
622C3#7892711yescharacteristic, complemented
623C3#8398011yescharacteristic, complemented
624C2—22no—
625C2—124no—
626C2—241no—
627C2—362no—
628C2#1059471812yes—
629C2C2×#6392211yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
hypercenterC2×M16D32
hypocenterC32#3005
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C22×#3796C2semidirect
2. C2×C3×#909C2semidirect
3. #10595034C2semidirect
4. C2×#63823C2semidirect
5. #10592825C2semidirect
6. C3×#5131C2semidirect
7. #10591099C2semidirect
8. #10590965C2semidirect
9. #10590964C2semidirect
26. C2×C3×Dic12C22semidirect
27. C2×C3×#204C22semidirect
30. #63916C22semidirect
32. #63871C22semidirect
33. C2×#3715C22semidirect
35. C2×#3713C22semidirect
36. #63647C22semidirect
37. C3×#821C22semidirect
38. #63565C22semidirect
45. C2×#909D3semidirect
51. #5131D3semidirect
72. C2×C3×D12D4semidirect
78. C2×C3×Dic6D4semidirect
148. C2×Dic12C2×D3semidirect
149. C2×#204C2×D3semidirect
157. #821C2×D3semidirect
255. C2×D12D12semidirect
275. C2×Dic6#67semidirect
547. C32#3005semidirect
622. C3#78927semidirect
623. C3#83980semidirect

Maximal subgroups

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

subgroupindex
C22×#37962
C2×C3×#9092
#105950342
C2×#638232
#105928252
C3×#51312
#105910992
#105909652
#105909642
#839803
#789273