Finite Group Databasebeta

← #11864070

Subgroups — #11864070

Order 1152.

1665 conjugacy classes of subgroups.

The subgroup lattice has 645 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#237C211yesmaximal, characteristic, complemented
2C2×#64141C211yesmaximal, characteristic, complemented
3#10595023C211yesmaximal, characteristic, complemented
4C2×#63833C211yesmaximal, characteristic, complemented
5C3×#5215C211yesmaximal, characteristic, complemented
6#10591463C214yesmaximal, complemented
7#10591452C214yesmaximal, complemented
8#10591099C211yesmaximal, characteristic, complemented
9#10591069C211yesmaximal, characteristic, complemented
10#84081—31nomaximal
11#78927—31nomaximal
12C22×C32×D4C2211yescharacteristic
13C2×#3828C2211yescharacteristic
14C22×C3×#67—21no—
15C23×C3×Dic3—21no—
16C2×C3×#237—24no—
17C2×C3×#237—22no—
18C2×C3×#237—24no—
19C2×C3×#237C2214yes—
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic
22C2×#3754C2212yescomplemented
23#64141—24no—
24C2×#3753C2212yescomplemented
25C2×#3748C2211yescharacteristic
26C3×#926C2211yescharacteristic
27C2×C3×#208C2211yescharacteristic
28#63977—21no—
29#63966—21no—
30#63909C2212yescomplemented
31C4×#626—22no—
32#63857C2212yescomplemented
33C2×#3719C2212yescomplemented
34#63833—24no—
35C2×#3717C2212yescomplemented
36C3×#832C2214yescomplemented
37#63565C2214yescomplemented
38(C2×D3)⋊(C3⋊C8)C2214yescomplemented
39C22×C3×#41—31no—
40C22×#237D311yescharacteristic, complemented
41C2×#942—31no—
42C2×#932—31no—
43C2×#932—31no—
44C2×#932—61no—
45#5791—31no—
46C2×#909—31no—
47#5524—31no—
48C3×#418—31no—
49#5239—34no—
50#5238—34no—
51#5225—31no—
52#5215D311yescharacteristic, complemented
53#5207—31no—
54#5126—31no—
55#5004—31no—
56#4783—34no—
57#4781—34no—
58C24×C32—21no—
59C23×C3×D3D411yescharacteristic
60C2×C32×D4—21no—
61C2×C32×D4—22no—
62C2×C32×D4D414yescomplemented
63C2×C32×D4C2312yes—
64C22×C32×C4C2311yescharacteristic
65C2×#638—21no—
66#3828—22no—
67#3828—22no—
68C2×C4⋊(C3⋊D3)C2311yescharacteristic
69C2×C4×C3⋊D3—21no—
70C2×#634C2311yescharacteristic
71C2×C3×#67—28no—
72C2×C3×#67—24no—
73C22×C3×Dic3—28no—
74C22×C3×Dic3—21no—
75C22×C3×Dic3—24no—
76C22×C3×Dic3D411yescharacteristic
77C3×#237—216no—
78C3×#237—28no—
79C3×#237—28no—
80C2×C3×C4×D3—22no—
81C2×C3×C4×D3—22no—
82C2×C3×C4×D3D412yes—
83C2×C3×C4×D3C2312yes—
84C2×C3×Dic6—21no—
85C2×C3×Dic6—22no—
86C2×C3×Dic6D414yescomplemented
87C2×C3×Dic6C2312yes—
88C2×#626—22no—
89#3754—24no—
90#3753—24no—
91#3748—22no—
92C2×C3⋊(C3⋊C8)C2312yes—
93C3×#217—21no—
94C3×C4⋊Dic3C2312yes—
95C3×C4×Dic3—21no—
96C3×#208—22no—
97C2×C3×C3⋊C8C2312yes—
98Dic3⋊Dic3—22no—
99#3722—22no—
100(C2×D3)⋊Dic3—22no—
101#3719—24no—
102#3717—24no—
103#3005—91noSylow
104C2×C3×#41—34no—
105C2×C3×#41—62no—
106C2×C3×#41—64no—
107C2×C3×#41—64no—
108C22×C3×Q8—31no—
109C22×C3×D4—21no—
110C22×C3×D4—61no—
111C22×C3×D4C2×D311yescharacteristic
112C22×C3×D4C2×D311yescharacteristic
113C23×C3×C4—31no—
114C23×C3×C4—61no—
115C22×#67—21no—
116C23×Dic3—21no—
117C2×#237—24no—
118C2×#237—22no—
119C2×#237—24no—
120C2×#237C2×D314yes—
121C2×#235—31no—
122C2×#235—31no—
123C2×#235—61no—
124C22×C4×D3C2×D311yescharacteristic
125C22×Dic6C2×D311yescharacteristic
126C2×C3×M16—31no—
127C3×#117—31no—
128#953—61no—
129C2×#216—32no—
130#942—64no—
131C2×#215—32no—
132C2×#214—32no—
133C2×#214—32no—
134C2×#214—62no—
135#932—68no—
136#932—64no—
137#932—64no—
138C2×#213—32no—
139C2×#213—32no—
140C2×#213—62no—
141#930—32no—
142#929—61no—
143C4×#67—62no—
144#926C2×D311yescharacteristic
145#924—32no—
146C2×#208—31no—
147C2×#208—31no—
148C2×#208—61no—
149C2×#208C2×D311yescharacteristic
150#909—64no—
151C2×Dic12—32no—
152C2×#204—32no—
153#897—32no—
154#895—32no—
155#886—61no—
156#882—61no—
157C4×D12—62no—
158C3×#102—34no—
159#835—34no—
160#832C2×D314yescomplemented
161#830—34no—
162(C2×D3)⋊C8—34no—
163#810—34no—
164C23×C32—24no—
165C23×C32—22no—
166C23×C32—44no—
167C23×C32C2×D411yescharacteristic
168C22×C3⋊D3—21no—
169C22×C3×D3—22no—
170C22×C3×D3—42no—
171C22×C3×D3C2×D412yes—
172C32×D4—24no—
173C32×D4—22no—
174C32×D4C2×D414yes—
175C2×C32×C4C2×D412yes—
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2×D412yes—
178C2×C32×C4C2411yescharacteristic
179#638—42no—
180C2×C3⋊Dic3—21no—
181C4⋊(C3⋊D3)—21no—
182C4⋊(C3⋊D3)—21no—
183C4×C3⋊D3—42no—
184#634—21no—
185#634—21no—
186C3×#67—216no—
187C2×C3×Dic3—216no—
188C2×C3×Dic3—24no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3C2×D412yes—
193C3×C4×D3—24no—
194C3×C4×D3—22no—
195C3×C4×D3—22no—
196C3×Dic6—24no—
197C3×Dic6—22no—
198C3×Dic6C2×D414yes—
199#626—44no—
200C3⋊(C3⋊C8)—22no—
201C3×C3⋊C8—22no—
202C22×#41—31no—
203C2×#137—91no—
204C2×AGL(1,ℤ/8)—91no—
205#525—91no—
206#452—94no—
207#449—94no—
208#419—91no—
209#418—31no—
210#407—91no—
211C24×C3—21no—
212C24×C3—21no—
213C24×C3—31no—
214C24×C3—41no—
215C23×D3#6711yescharacteristic
216C3×#41—68no—
217C3×#41—616no—
218C3×#41—68no—
219C2×C3×Q8—34no—
220C2×C3×Q8—32no—
221C2×C3×Q8—62no—
222C2×C3×Q8—61no—
223C2×C3×D4—21no—
224C2×C3×D4—22no—
225C2×C3×D4—21no—
226C2×C3×D4—22no—
227C2×C3×D4—24no—
228C2×C3×D4—22no—
229C2×C3×D4—41no—
230C2×C3×D4—42no—
231C2×C3×D4—64no—
232C2×C3×D4—68no—
233C2×C3×D4D1214yescomplemented
234C2×C3×D4#6714yescomplemented
235C2×C3×D4C22×D312yes—
236C2×C3×D4C22×D312yes—
237C22×C3×C4—21no—
238C22×C3×C4—31no—
239C22×C3×C4—32no—
240C22×C3×C4—32no—
241C22×C3×C4—64no—
242C22×C3×C4—68no—
243C22×C3×C4—61no—
244C22×C3×C4—62no—
245C22×C3×C4—62no—
246C22×C3×C4C22×D311yescharacteristic
247C22×C3×C4C22×D311yescharacteristic
248C2×#67—28no—
249C2×#67—24no—
250C2×#67—62no—
251C2×#67—61no—
252C2×#67—61no—
253C2×#67—121no—
254C22×Dic3—28no—
255C22×Dic3—21no—
256C22×Dic3—24no—
257C22×Dic3#6711yescharacteristic
258#237—216no—
259#237—28no—
260#237—28no—
261#235—64no—
262#235—62no—
263#235—62no—
264#235—62no—
265#235—62no—
266#235—122no—
267C2×D12—31no—
268C2×D12—31no—
269C2×D12—61no—
270C2×D12—62no—
271C2×C4×D3—22no—
272C2×C4×D3—22no—
273C2×C4×D3—61no—
274C2×C4×D3—61no—
275C2×C4×D3—121no—
276C2×C4×D3#6712yes—
277C2×C4×D3C22×D312yes—
278C2×Dic6—22no—
279C2×Dic6—21no—
280C2×Dic6—31no—
281C2×Dic6—31no—
282C2×Dic6—61no—
283C2×Dic6#6714yescomplemented
284C2×Dic6C22×D312yes—
285C3×M16—62no—
286C2×C3×C8—32no—
287C3×C4⋊C4—32no—
288C3×C22⋊C4—61no—
289C3×C42—61no—
290#217—21no—
291#217—62no—
292#216—64no—
293#215—64no—
294#214—68no—
295#214—64no—
296#214—64no—
297#213—68no—
298#213—64no—
299#213—64no—
300(C2×D3)⋊C4—62no—
301(C2×D3)⋊C4—62no—
302(C2×D3)⋊C4—62no—
303C4⋊Dic3—62no—
304C4⋊Dic3C22×D312yes—
305Dic3⋊C4—62no—
306C4×Dic3—21no—
307#208—22no—
308#208—64no—
309#208—62no—
310#208—62no—
311C2×C3⋊C8—32no—
312C2×C3⋊C8—32no—
313C2×C3⋊C8—62no—
314C2×C3⋊C8C22×D312yes—
315Dic12—64no—
316#204—64no—
317C22×C32—22no—
318C22×C32—24no—
319C22×C32—48no—
320C22×C32—44no—
321C22×C32#12012yes—
322C22×C32C22×D411yescharacteristic
323C2×C3⋊D3—41no—
324C2×C3⋊D3—42no—
325C2×C3×D3—22no—
326C2×C3×D3—22no—
327C2×C3×D3—22no—
328C2×C3×D3—44no—
329C32×C4#12012yes—
330C32×C4C22×D411yescharacteristic
331C32×C4C22×D411yescharacteristic
332C3⋊Dic3—41no—
333C3×Dic3—24no—
334C3×Dic3—22no—
335C3×Dic3—42no—
336C2×#41—34no—
337C2×#41—62no—
338C2×#41—64no—
339C2×#41—64no—
340C2×#41—91no—
341C22×Q8—31no—
342C22×D4—61no—
343C22×D4D3211yescharacteristic
344C23×C4—31no—
345C23×C4—61no—
346#137—184no—
347AGL(1,ℤ/8)—184no—
348C2×Q16—92no—
349C2×SD16—92no—
350C2×SD16—92no—
351C2×D8—92no—
352C2×M16—31no—
353C2×M16—91no—
354#123—181no—
355C22⋊Q8—92no—
356#121—92no—
357#120—181no—
358C4×D4—182no—
359#117—31no—
360#103—94no—
361#102—34no—
362C22⋊C8—94no—
363C23×C3—24no—
364C23×C3—24no—
365C23×C3—22no—
366C23×C3—22no—
367C23×C3—21no—
368C23×C3—32no—
369C23×C3—42no—
370C23×C3—44no—
371C23×C3—44no—
372C23×C3—44no—
373C23×C3—62no—
374C23×C3—84no—
375C23×C3—122no—
376C23×C3D3×D411yescharacteristic
377C23×C3C2×#6711yescharacteristic
378C22×D3—22no—
379C22×D3—42no—
380C22×D3—61no—
381C22×D3—61no—
382C22×D3—121no—
383C22×D3C2×#6712yes—
384C3×Q8—34no—
385C3×Q8—64no—
386C3×Q8—62no—
387C3×D4—24no—
388C3×D4—24no—
389C3×D4—22no—
390C3×D4—22no—
391C3×D4—24no—
392C3×D4—42no—
393C3×D4—44no—
394C3×D4—616no—
395C3×D4C2×D1214yes—
396C3×D4C2×#6714yes—
397C2×C3×C4—21no—
398C2×C3×C4—22no—
399C2×C3×C4—21no—
400C2×C3×C4—22no—
401C2×C3×C4—32no—
402C2×C3×C4—616no—
403C2×C3×C4—62no—
404C2×C3×C4—64no—
405C2×C3×C4—62no—
406C2×C3×C4—64no—
407C2×C3×C4—62no—
408C2×C3×C4—62no—
409C2×C3×C4—62no—
410C2×C3×C4C2×D1212yes—
411C2×C3×C4D3×D411yescharacteristic
412C2×C3×C4D3×D412yes—
413C2×C3×C4C2×#6712yes—
414C2×C3×C4C2×#6711yescharacteristic
415C2×C3×C4C2×#6712yes—
416C2×C3×C4C23×D311yescharacteristic
417C2×C3×C4C23×D311yescharacteristic
418#67—216no—
419#67—124no—
420#67—124no—
421#67—122no—
422#67—122no—
423C2×Dic3—216no—
424C2×Dic3—24no—
425C2×Dic3—22no—
426C2×Dic3—22no—
427C2×Dic3—22no—
428C2×Dic3—61no—
429C2×Dic3—61no—
430C2×Dic3—121no—
431C2×Dic3C2×#6712yes—
432D12—62no—
433D12—61no—
434D12—61no—
435D12—61no—
436D12—61no—
437D12—121no—
438D12—124no—
439C4×D3—24no—
440C4×D3—22no—
441C4×D3—22no—
442C4×D3—124no—
443C4×D3—122no—
444C4×D3—122no—
445Dic6—24no—
446Dic6—22no—
447Dic6—62no—
448Dic6—61no—
449Dic6—61no—
450Dic6—61no—
451Dic6—61no—
452Dic6—121no—
453Dic6C2×#6714yes—
454C3×C8—62no—
455C3⋊C8—22no—
456C3⋊C8—64no—
457C3⋊C8—62no—
458C3⋊C8—62no—
459C2×C32—22no—
460C2×C32—44no—
461C2×C32C2×#12011yescharacteristic
462C2×C32#57512yes—
463C3⋊D3—81no—
464C3×D3—42no—
465C24—21no—
466C24—31no—
467#41—68no—
468#41—616no—
469#41—68no—
470#41—182no—
471#41—182no—
472C2×Q8—32no—
473C2×Q8—34no—
474C2×Q8—62no—
475C2×Q8—61no—
476C2×Q8—91no—
477C2×D4—22no—
478C2×D4—21no—
479C2×D4—64no—
480C2×D4—68no—
481C2×D4—91no—
482C2×D4—182no—
483C2×D4—181no—
484C2×D4#62614yescomplemented
485C2×D4C2×D3212yes—
486C22×C4—31no—
487C22×C4—32no—
488C22×C4—32no—
489C22×C4—64no—
490C22×C4—68no—
491C22×C4—61no—
492C22×C4—62no—
493C22×C4—62no—
494C22×C4—181no—
495C22×C4C2×D3211yescharacteristic
496Q16—184no—
497SD16—184no—
498SD16—184no—
499D8—184no—
500M16—62no—
501M16—182no—
502C2×C8—32no—
503C2×C8—92no—
504C4⋊C4—32no—
505C4⋊C4—182no—
506C22⋊C4—61no—
507C22⋊C4—182no—
508C22⋊C4—182no—
509C42—61no—
510C22×C3—22no—
511C22×C3—22no—
512C22×C3—24no—
513C22×C3—24no—
514C22×C3—21no—
515C22×C3—22no—
516C22×C3—42no—
517C22×C3—44no—
518C22×C3—48no—
519C22×C3—48no—
520C22×C3—44no—
521C22×C3—44no—
522C22×C3—62no—
523C22×C3—62no—
524C22×C3—62no—
525C22×C3—84no—
526C22×C3—88no—
527C22×C3—124no—
528C22×C3#88212yes—
529C22×C3#95312yes—
530C22×C3C2×D3×D411yescharacteristic
531C22×C3C22×#6711yescharacteristic
532C2×D3—22no—
533C2×D3—22no—
534C2×D3—22no—
535C2×D3—44no—
536C2×D3—122no—
537C2×D3—121no—
538C2×D3—122no—
539C2×D3—122no—
540C2×D3—121no—
541C2×D3—242no—
542C3×C4—21no—
543C3×C4—21no—
544C3×C4—22no—
545C3×C4—62no—
546C3×C4—64no—
547C3×C4—122no—
548C3×C4#88212yes—
549C3×C4#95312yes—
550C3×C4C22×D1211yescharacteristic
551C3×C4C2×D3×D411yescharacteristic
552C3×C4C22×#6711yescharacteristic
553C3×C4C22×#6711yescharacteristic
554Dic3—24no—
555Dic3—22no—
556Dic3—42no—
557Dic3—122no—
558Dic3—121no—
559Dic3—121no—
560C32#300511yescharacteristic, complemented, Sylow
561C23—22no—
562C23—24no—
563C23—32no—
564C23—44no—
565C23—62no—
566C23—122no—
567C23—181no—
568C23D3×#6711yescharacteristic
569Q8—34no—
570Q8—62no—
571Q8—64no—
572Q8—181no—
573Q8—181no—
574D4—22no—
575D4—24no—
576D4—616no—
577D4—181no—
578D4—181no—
579D4—364no—
580D4—362no—
581D4C2×#62614yes—
582C2×C4—32no—
583C2×C4—616no—
584C2×C4—62no—
585C2×C4—62no—
586C2×C4—64no—
587C2×C4—62no—
588C2×C4—62no—
589C2×C4—64no—
590C2×C4—62no—
591C2×C4—181no—
592C2×C4—362no—
593C2×C4C2×#62612yes—
594C2×C4D3×#6712yes—
595C2×C4D3×#6711yescharacteristic
596C2×C4C22×D3211yescharacteristic
597C8—62no—
598C8—182no—
599C2×C3—22no—
600C2×C3—22no—
601C2×C3—22no—
602C2×C3—21no—
603C2×C3—42no—
604C2×C3—44no—
605C2×C3—44no—
606C2×C3—84no—
607C2×C3—122no—
608C2×C3C2×#88211yescharacteristic
609C2×C3#577312yes—
610C2×C3#582212yes—
611C2×C3C2×#95311yescharacteristic
612D3—42no—
613D3—242no—
614D3—241no—
615D3—241no—
616C22—22no—
617C22—24no—
618C22—48no—
619C22—44no—
620C22—62no—
621C22—62no—
622C22—62no—
623C22—124no—
624C22—362no—
625C22—361no—
626C22#6397712yes—
627C22C2×D3×#6711yescharacteristic
628C4—62no—
629C4—64no—
630C4—122no—
631C4—361no—
632C4#6397712yes—
633C4C22×#62611yescharacteristic
634C4C2×D3×#6711yescharacteristic
635C3—21no—
636C3#7892711yescharacteristic, complemented
637C3#8408111yescharacteristic, complemented
638C2—22no—
639C2—44no—
640C2—122no—
641C2—721no—
642C2#1059509512yes—
643C2C2×#6397711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32#3005
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#237C2semidirect
2. C2×#64141C2semidirect
3. #10595023C2semidirect
4. C2×#63833C2semidirect
5. C3×#5215C2semidirect
6. #10591463C2semidirect
7. #10591452C2semidirect
8. #10591099C2semidirect
9. #10591069C2semidirect
22. C2×#3754C22semidirect
24. C2×#3753C22semidirect
30. #63909C22semidirect
32. #63857C22semidirect
33. C2×#3719C22semidirect
35. C2×#3717C22semidirect
36. C3×#832C22semidirect
37. #63565C22semidirect
38. (C2×D3)⋊(C3⋊C8)C22semidirect
40. C22×#237D3semidirect
52. #5215D3semidirect
62. C2×C32×D4D4semidirect
86. C2×C3×Dic6D4semidirect
160. #832C2×D3semidirect
233. C2×C3×D4D12semidirect
234. C2×C3×D4#67semidirect
283. C2×Dic6#67semidirect
484. C2×D4#626semidirect
560. C32#3005semidirect
636. C3#78927semidirect
637. C3#84081semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2372
C2×#641412
#105950232
C2×#638332
C3×#52152
#105914632
#105914522
#105910992
#105910692
#840813
#789273