Finite Group Databasebeta

← #11861227

Subgroups — #11861227

Order 1152.

981 conjugacy classes of subgroups.

The subgroup lattice has 621 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#950C211yesmaximal, characteristic
2C3×#5819C211yesmaximal, characteristic, complemented
3#10594776C211yesmaximal, characteristic, complemented
4#10592935C211yesmaximal, characteristic, complemented
5#10591674C214yesmaximal, complemented
6#10591673C214yesmaximal, complemented
7C2×#63577C211yesmaximal, characteristic, complemented
8#10591110C211yesmaximal, characteristic, complemented
9#10591059C211yesmaximal, characteristic, complemented
10#83910—31nomaximal
11#83812—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14#64135C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C3×#950C412yescomplemented
17C3×#950C412yescomplemented
18C3×#950C2212yes—
19C3×#950C2212yes—
20C3×#948—22no—
21C3×#948C2214yescomplemented
22C2×C3×#216C411yescharacteristic, complemented
23C2×C3×#215C411yescharacteristic, complemented
24C2×C3×#214C411yescharacteristic, complemented
25C2×C3×#213C411yescharacteristic, complemented
26C2×C3×#208—22no—
27C2×C3×#208C2211yescharacteristic
28C2×C3×#208C2211yescharacteristic
29C22×C3×C3⋊C8C2211yescharacteristic
30#63815—22no—
31#63814C2214yescomplemented
32D3×#208—22no—
33#63664C2214yescomplemented
34#63577C2212yescomplemented
35#63577C2212yescomplemented
36#63568C2214yescomplemented
37#63555C2212yescomplemented
38#63553C2212yescomplemented
39C2×C3×#135—31no—
40C3×#568—31no—
41C2×#950D311yescharacteristic
42#5819—31no—
43#5819D311yescharacteristic, complemented
44#5745—31no—
45#5236—31no—
46#5236—31no—
47#5236—31no—
48#5236—61no—
49#5197—34no—
50#5196—34no—
51#5145—34no—
52#5144—34no—
53#5139—31no—
54C2×#822—31no—
55#5122—31no—
56C2×#819—31no—
57#5101—31no—
58C32×#41—21no—
59C32×#41—21no—
60C32×#41C2×C412yes—
61C32×#41C2312yes—
62C2×C32×Q8C2×C411yescharacteristic
63C2×C32×D4—21no—
64C2×C32×D4C2×C411yescharacteristic
65C22×C32×C4—21no—
66C22×C32×C4C2311yescharacteristic
67C2×C3×#67—21no—
68C3×#235—21no—
69C3×#235—21no—
70C3×#235C2×C412yes—
71C3×#235C2312yes—
72C2×C3×D12C2×C411yescharacteristic
73C2×C3×C4×D3—21no—
74C2×C3×Dic6C2×C411yescharacteristic
75#3757—21no—
76C4⋊(C3⋊Dic3)—21no—
77C4×C3⋊Dic3C2312yes—
78#3748—21no—
79#3748C2312yes—
80C2×C3⋊(C3⋊C8)—21no—
81C3×#216C2×C412yes—
82C3×#216C2×C412yes—
83C3×#215C2×C412yes—
84C3×#215C2×C412yes—
85C3×#214C2×C412yes—
86C3×#214C2×C412yes—
87C3×#213C2×C412yes—
88C3×#213C2×C412yes—
89C3×#208—21no—
90C3×#208—24no—
91C3×#208D412yes—
92C3×#208D412yes—
93C3×#208C2312yes—
94C2×C3×C3⋊C8—21no—
95C2×C3×C3⋊C8—24no—
96C2×C3×C3⋊C8C2×C411yescharacteristic
97C2×C3×C3⋊C8C2×C411yescharacteristic
98C2×C3×C3⋊C8C2×C411yescharacteristic
99C2×C3×C3⋊C8C2×C411yescharacteristic
100C2×C3×C3⋊C8C2311yescharacteristic
101C2×C3×C3⋊C8C2311yescharacteristic
102C2×C3×C3⋊C8C2312yes—
103#3711—24no—
104D3×C3⋊C8—24no—
105#2957—91noSylow
106C2×C3×#41—21no—
107C2×C3×#41—31no—
108C2×C3×#41C2×D311yescharacteristic
109C2×C3×#41C2×D311yescharacteristic
110C2×#235C2×D311yescharacteristic
111C3×#135—32no—
112C3×#135—32no—
113C3×#135—32no—
114C3×#135—32no—
115C2×C3×Q16—31no—
116C2×C3×SD16—31no—
117C2×C3×SD16—31no—
118C2×C3×D8—31no—
119C3×#131—34no—
120C3×#131—62no—
121C2×C3×M16—31no—
122C2×C3×M16—31no—
123C2×C3×M16—62no—
124C22×C3×C8—31no—
125#950Dic312yescomplemented
126#950Dic312yescomplemented
127#950C2×D312yes—
128#950C2×D312yes—
129#948—22no—
130#948—34no—
131#948—62no—
132#948C2×D314yescomplemented
133C2×#216Dic311yescharacteristic, complemented
134C2×#215Dic311yescharacteristic, complemented
135C2×#214Dic311yescharacteristic, complemented
136C2×#213Dic311yescharacteristic, complemented
137#926—31no—
138#926—31no—
139#926—61no—
140C2×#208—22no—
141C2×#208—31no—
142C2×#208—31no—
143C2×#208—61no—
144C2×#208—62no—
145C2×#208C2×D311yescharacteristic
146C2×#208C2×D311yescharacteristic
147C22×C3⋊C8C2×D311yescharacteristic
148#907—62no—
149D3×M16—62no—
150#901—34no—
151#837—34no—
152#837—34no—
153#837—34no—
154#837—64no—
155#825—34no—
156#822—32no—
157#822—32no—
158#819—32no—
159#819—32no—
160#815—32no—
161#815—32no—
162C8×Dic3—32no—
163C8×Dic3—32no—
164C23×C32—21no—
165C23×C32#4111yescharacteristic
166C22×C3×D3—21no—
167C32×Q8—21no—
168C32×Q8C22×C412yes—
169C32×D4—22no—
170C32×D4—22no—
171C32×D4—21no—
172C32×D4C22×C412yes—
173C2×C32×C4—21no—
174C2×C32×C4—22no—
175C2×C32×C4—22no—
176C2×C32×C4C22×C411yescharacteristic
177C2×C32×C4C22×C411yescharacteristic
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4#4111yescharacteristic
181C2×C32×C4C2411yescharacteristic
182C2×C3⋊Dic3—22no—
183C3×#67—22no—
184C3×#67—22no—
185C2×C3×Dic3—21no—
186C3×D12—21no—
187C3×D12C22×C412yes—
188C3×C4×D3—22no—
189C3×C4×D3—22no—
190C3×Dic6—21no—
191C3×Dic6C22×C412yes—
192C3⋊(C3⋊C8)—22no—
193C3×C3⋊C8—22no—
194C3×C3⋊C8C22×C411yescharacteristic
195C3×C3⋊C8C22×C411yescharacteristic
196C3×C3⋊C8C22×C411yescharacteristic
197C3×C3⋊C8C22×C411yescharacteristic
198C3×C3⋊C8C2×D414yes—
199C2×#135—31no—
200#568—31no—
201#568—91no—
202#444—94no—
203#443—94no—
204C2×#108—91no—
205#421—91no—
206#421—91no—
207#405—91no—
208C3×#41—21no—
209C3×#41—21no—
210C3×#41—21no—
211C3×#41—21no—
212C3×#41—22no—
213C3×#41—22no—
214C3×#41—32no—
215C3×#41—32no—
216C3×#41—41no—
217C3×#41—41no—
218C3×#41—61no—
219C3×#41—61no—
220C3×#41C4×D312yes—
221C3×#41C2×Dic312yes—
222C3×#41C22×D312yes—
223C3×#41C22×D312yes—
224C2×C3×Q8—21no—
225C2×C3×Q8—31no—
226C2×C3×Q8C4×D311yescharacteristic
227C2×C3×Q8C2×Dic311yescharacteristic
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—31no—
232C2×C3×D4—41no—
233C2×C3×D4—61no—
234C2×C3×D4C4×D311yescharacteristic
235C2×C3×D4C2×Dic311yescharacteristic
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—41no—
240C22×C3×C4—61no—
241C22×C3×C4C22×D311yescharacteristic
242C22×C3×C4C22×D311yescharacteristic
243C2×#67—21no—
244#235—21no—
245#235—21no—
246#235C2×Dic312yes—
247#235C22×D312yes—
248C2×D12C2×Dic311yescharacteristic
249C2×C4×D3—21no—
250C2×Dic6C2×Dic311yescharacteristic
251C3×Q16—32no—
252C3×Q16—32no—
253C3×SD16—32no—
254C3×SD16—32no—
255C3×SD16—32no—
256C3×SD16—32no—
257C3×D8—32no—
258C3×D8—32no—
259C3×M16—32no—
260C3×M16—32no—
261C3×M16—32no—
262C3×M16—64no—
263C3×M16—61no—
264C2×C3×C8—31no—
265C2×C3×C8—31no—
266C2×C3×C8—31no—
267C2×C3×C8—31no—
268C2×C3×C8—31no—
269C2×C3×C8—32no—
270C2×C3×C8—31no—
271C2×C3×C8—64no—
272C2×C3×C8—61no—
273#217—61no—
274#217—61no—
275#217—121no—
276#216C2×Dic312yes—
277#216C2×Dic312yes—
278#215C2×Dic312yes—
279#215C2×Dic312yes—
280#214C2×Dic312yes—
281#214C2×Dic312yes—
282#213C2×Dic312yes—
283#213C2×Dic312yes—
284C4⋊Dic3—61no—
285C4⋊Dic3—61no—
286C4⋊Dic3—121no—
287C4×Dic3—32no—
288C4×Dic3—32no—
289C4×Dic3—62no—
290#208—21no—
291#208—24no—
292#208—32no—
293#208—32no—
294#208—62no—
295#208—61no—
296#208—61no—
297#208—64no—
298#208—121no—
299#208#6712yes—
300#208#6712yes—
301#208C22×D312yes—
302C2×C3⋊C8—21no—
303C2×C3⋊C8—24no—
304C2×C3⋊C8—61no—
305C2×C3⋊C8—61no—
306C2×C3⋊C8—64no—
307C2×C3⋊C8—121no—
308C2×C3⋊C8C2×Dic311yescharacteristic
309C2×C3⋊C8C2×Dic311yescharacteristic
310C2×C3⋊C8C2×Dic311yescharacteristic
311C2×C3⋊C8C2×Dic311yescharacteristic
312C2×C3⋊C8C22×D311yescharacteristic
313C2×C3⋊C8C22×D311yescharacteristic
314C2×C3⋊C8C22×D312yes—
315ΓL(1,𝔽25)—64no—
316D3×C8—64no—
317C22×C32—22no—
318C22×C32—41no—
319C22×C32—81no—
320C22×C32C4×D411yescharacteristic
321C22×C32C4×D411yescharacteristic
322C22×C32C2×#4111yescharacteristic
323C2×C3×D3—22no—
324C2×C3×D3—81no—
325C32×C4—22no—
326C32×C4C4×D411yescharacteristic
327C32×C4C4×D411yescharacteristic
328C32×C4C23×C411yescharacteristic
329C32×C4C22×D411yescharacteristic
330C3⋊Dic3—42no—
331C3×Dic3—22no—
332C2×#41—31no—
333C2×#41D3211yescharacteristic
334#135—32no—
335#135—32no—
336#135—32no—
337#135—32no—
338C2×Q16—31no—
339C2×SD16—31no—
340C2×SD16—31no—
341C2×D8—31no—
342#131—34no—
343#131—62no—
344#131—94no—
345#131—182no—
346C2×M16—31no—
347C2×M16—31no—
348C2×M16—62no—
349C2×M16—91no—
350C2×M16—182no—
351C22×C8—31no—
352#117—91no—
353#108—92no—
354#108—92no—
355#104—94no—
356#104—94no—
357#97—92no—
358C4×C8—92no—
359C23×C3—21no—
360C23×C3—21no—
361C23×C3—21no—
362C23×C3—41no—
363C23×C3—61no—
364C23×C3#23511yescharacteristic
365C23×C3#23711yescharacteristic
366C22×D3—21no—
367C3×Q8—21no—
368C3×Q8—21no—
369C3×Q8—22no—
370C3×Q8—32no—
371C3×Q8—41no—
372C3×Q8—61no—
373C3×Q8C2×C4×D312yes—
374C3×Q8C22×Dic312yes—
375C3×D4—22no—
376C3×D4—22no—
377C3×D4—22no—
378C3×D4—22no—
379C3×D4—21no—
380C3×D4—21no—
381C3×D4—22no—
382C3×D4—32no—
383C3×D4—41no—
384C3×D4—42no—
385C3×D4—42no—
386C3×D4—62no—
387C3×D4—62no—
388C3×D4—61no—
389C3×D4C2×C4×D312yes—
390C3×D4C22×Dic312yes—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—42no—
404C2×C3×C4—42no—
405C2×C3×C4—41no—
406C2×C3×C4—61no—
407C2×C3×C4—62no—
408C2×C3×C4—62no—
409C2×C3×C4C2×C4×D311yescharacteristic
410C2×C3×C4C2×C4×D311yescharacteristic
411C2×C3×C4#23511yescharacteristic
412C2×C3×C4D3×D411yescharacteristic
413C2×C3×C4D3×D411yescharacteristic
414C2×C3×C4#23711yescharacteristic
415C2×C3×C4C22×Dic311yescharacteristic
416C2×C3×C4C22×Dic311yescharacteristic
417C2×C3×C4C2×#6711yescharacteristic
418C2×C3×C4C2×#6711yescharacteristic
419C2×C3×C4C23×D311yescharacteristic
420C2×C3×C4C23×D311yescharacteristic
421#67—22no—
422#67—22no—
423C2×Dic3—21no—
424C2×Dic3—62no—
425C2×Dic3—62no—
426C2×Dic3—122no—
427D12—21no—
428D12C22×Dic312yes—
429C4×D3—22no—
430C4×D3—22no—
431Dic6—21no—
432Dic6C22×Dic312yes—
433C3×C8—31no—
434C3×C8—31no—
435C3×C8—31no—
436C3×C8—31no—
437C3×C8—34no—
438C3×C8—62no—
439C3⋊C8—22no—
440C3⋊C8—62no—
441C3⋊C8—62no—
442C3⋊C8—122no—
443C3⋊C8C22×Dic311yescharacteristic
444C3⋊C8C22×Dic311yescharacteristic
445C3⋊C8C22×Dic311yescharacteristic
446C3⋊C8C22×Dic311yescharacteristic
447C3⋊C8C2×#6714yes—
448C2×C32—21no—
449C2×C32—21no—
450C2×C32—21no—
451C2×C32—42no—
452C2×C32C2×C4×D411yescharacteristic
453C3×D3—42no—
454#41—21no—
455#41—21no—
456#41—32no—
457#41—32no—
458#41—61no—
459#41—61no—
460#41D3×Dic312yes—
461#41C2×D3212yes—
462C2×Q8—31no—
463C2×Q8D3×Dic311yescharacteristic
464C2×D4—21no—
465C2×D4—31no—
466C2×D4—61no—
467C2×D4D3×Dic311yescharacteristic
468C22×C4—21no—
469C22×C4—61no—
470C22×C4C2×D3211yescharacteristic
471Q16—32no—
472Q16—32no—
473SD16—32no—
474SD16—32no—
475SD16—32no—
476SD16—32no—
477D8—32no—
478D8—32no—
479M16—32no—
480M16—32no—
481M16—32no—
482M16—64no—
483M16—61no—
484M16—92no—
485M16—184no—
486M16—181no—
487C2×C8—31no—
488C2×C8—32no—
489C2×C8—31no—
490C2×C8—31no—
491C2×C8—31no—
492C2×C8—31no—
493C2×C8—31no—
494C2×C8—64no—
495C2×C8—61no—
496C2×C8—184no—
497C2×C8—181no—
498C4⋊C4—181no—
499C22⋊C4—181no—
500C42—92no—
501C22×C3—22no—
502C22×C3—22no—
503C22×C3—21no—
504C22×C3—21no—
505C22×C3—21no—
506C22×C3—42no—
507C22×C3—41no—
508C22×C3—41no—
509C22×C3—62no—
510C22×C3—81no—
511C22×C3—81no—
512C22×C3—81no—
513C22×C3—82no—
514C22×C3—241no—
515C22×C3C4×#6711yescharacteristic
516C22×C3C4×#6711yescharacteristic
517C22×C3D4×Dic311yescharacteristic
518C22×C3D4×Dic311yescharacteristic
519C22×C3C2×#23511yescharacteristic
520C22×C3C2×#23711yescharacteristic
521C2×D3—22no—
522C2×D3—81no—
523C3×C4—22no—
524C3×C4—22no—
525C3×C4—21no—
526C3×C4—21no—
527C3×C4—21no—
528C3×C4—21no—
529C3×C4—42no—
530C3×C4—62no—
531C3×C4C4×#6711yescharacteristic
532C3×C4C4×#6711yescharacteristic
533C3×C4D4×Dic311yescharacteristic
534C3×C4D4×Dic311yescharacteristic
535C3×C4C22×C4×D311yescharacteristic
536C3×C4C2×D3×D411yescharacteristic
537C3×C4C23×Dic311yescharacteristic
538C3×C4C22×#6711yescharacteristic
539Dic3—22no—
540Dic3—122no—
541Dic3—122no—
542Dic3—242no—
543C32#295711yescharacteristic, complemented, Sylow
544C23—21no—
545C23—61no—
546C23#380411yescharacteristic
547Q8—21no—
548Q8—32no—
549Q8—61no—
550Q8C2×D3×Dic312yes—
551D4—22no—
552D4—22no—
553D4—21no—
554D4—32no—
555D4—62no—
556D4—62no—
557D4—61no—
558D4C2×D3×Dic312yes—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—61no—
563C2×C4—62no—
564C2×C4—62no—
565C2×C4—182no—
566C2×C4C2×D3×Dic311yescharacteristic
567C2×C4C2×D3×Dic311yescharacteristic
568C2×C4#380411yescharacteristic
569C2×C4D3×#6711yescharacteristic
570C2×C4D3×#6711yescharacteristic
571C2×C4C22×D3211yescharacteristic
572C8—31no—
573C8—31no—
574C8—31no—
575C8—31no—
576C8—34no—
577C8—62no—
578C8—182no—
579C2×C3—21no—
580C2×C3—21no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—21no—
585C2×C3—21no—
586C2×C3—41no—
587C2×C3—41no—
588C2×C3—41no—
589C2×C3—42no—
590C2×C3—42no—
591C2×C3—82no—
592C2×C3—122no—
593C2×C3C2×C4×#6711yescharacteristic
594C2×C3C2×D4×Dic311yescharacteristic
595D3—42no—
596C22—22no—
597C22—41no—
598C22—62no—
599C22—81no—
600C22—241no—
601C22Dic3×#6711yescharacteristic
602C22Dic3×#6711yescharacteristic
603C22C2×#380411yescharacteristic
604C4—22no—
605C4—62no—
606C4—362no—
607C4Dic3×#6711yescharacteristic
608C4Dic3×#6711yescharacteristic
609C4C22×D3×Dic311yescharacteristic
610C4C2×D3×#6711yescharacteristic
611C3—21no—
612C3#8381211yescharacteristic, complemented
613C3#8391011yescharacteristic, complemented
614C2—21no—
615C2—21no—
616C2—21no—
617C2—42no—
618C2—122no—
619C2C2×Dic3×#6711yescharacteristic
subgroupG/H
centerC4C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC2×C32C2×C4×D4
prime radicalC2×C3×#950C2
cosocleC2×C32×C4C24
hypercenterC2×#41D32
hypocenterC32#2957
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C3×#5819C2semidirect
3. #10594776C2semidirect
4. #10592935C2semidirect
5. #10591674C2semidirect
6. #10591673C2semidirect
7. C2×#63577C2semidirect
8. #10591110C2semidirect
9. #10591059C2semidirect
16. C3×#950C4semidirect
17. C3×#950C4semidirect
21. C3×#948C22semidirect
22. C2×C3×#216C4semidirect
23. C2×C3×#215C4semidirect
24. C2×C3×#214C4semidirect
25. C2×C3×#213C4semidirect
31. #63814C22semidirect
33. #63664C22semidirect
34. #63577C22semidirect
35. #63577C22semidirect
36. #63568C22semidirect
37. #63555C22semidirect
38. #63553C22semidirect
43. #5819D3semidirect
125. #950Dic3semidirect
126. #950Dic3semidirect
132. #948C2×D3semidirect
133. C2×#216Dic3semidirect
134. C2×#215Dic3semidirect
135. C2×#214Dic3semidirect
136. C2×#213Dic3semidirect
543. C32#2957semidirect
612. C3#83812semidirect
613. C3#83910semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9502
C3×#58192
#105947762
#105929352
#105916742
#105916732
C2×#635772
#105911102
#105910592
#839103
#838123