Finite Group Databasebeta

← #11861110

Subgroups — #11861110

Order 1152.

963 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#907C211yesmaximal, characteristic, complemented
2#10594786C211yesmaximal, characteristic
3C2×#63814C211yesmaximal, characteristic, complemented
4#10592823C211yesmaximal, characteristic, complemented
5C3×#5139C211yesmaximal, characteristic, complemented
6#10591111C211yesmaximal, characteristic, complemented
7#10591055C211yesmaximal, characteristic, complemented
8#10590976C214yesmaximal, complemented
9#10590975C214yesmaximal, complemented
10#83792—31nomaximal
11#78989—31nomaximal
12C2×C3×#235C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17C3×#926C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C3×#907—21no—
20C3×#907—21no—
21C3×#907C2212yescomplemented
22C3×#907C2212yescomplemented
23C2×C3×ΓL(1,𝔽25)—21no—
24C2×C3×D3×C8—21no—
25#63827C412yescomplemented
26#63827C412yescomplemented
27#63823C412yescomplemented
28#63823C412yescomplemented
29#63822C2214yes—
30C2×#3711—21no—
31#63814—21no—
32#63814—21no—
33#63814C2212yescomplemented
34#63814C2212yescomplemented
35C2×D3×C3⋊C8—21no—
36#63649C2214yescomplemented
37C3×#825C2214yescomplemented
38#63569C2214yescomplemented
39#63554C2212yescomplemented
40Dic3×C3⋊C8C2212yescomplemented
41C2×C3×#131—31no—
42#5822—31no—
43#5822—31no—
44C2×#948—31no—
45C2×#907D311yescharacteristic, complemented
46C2×#901—31no—
47C3×#421—31no—
48#5236—31no—
49#5145—34no—
50#5144—34no—
51#5139D311yescharacteristic, complemented
52#5124—31no—
53#5124—31no—
54#5124—61no—
55#5101—31no—
56#5005—31no—
57#4997—31no—
58#4824—34no—
59#4823—34no—
60C22×C32×C4C2311yescharacteristic
61C2×C3×#67—21no—
62C2×C3×#67—21no—
63C3×#235—21no—
64C3×#235—21no—
65C3×#235—21no—
66C3×#235—21no—
67C3×#235C2×C412yes—
68C3×#235C2×C412yes—
69C3×#235C2312yes—
70C3×#235C2312yes—
71C2×C3×D12C2×C411yescharacteristic
72C2×C3×D12C2×C411yescharacteristic
73C2×C3×C4×D3—21no—
74C2×C3×C4×D3—21no—
75C2×C3×Dic6C2×C411yescharacteristic
76C2×C3×Dic6C2×C411yescharacteristic
77C32×M16—21no—
78C32×M16C2312yes—
79C2×C32×C8—21no—
80#3748—21no—
81#3748C2×C412yes—
82#3748C2×C412yes—
83#3748C2312yes—
84C2×C3⋊(C3⋊C8)—21no—
85C2×C3⋊(C3⋊C8)C2312yes—
86C3×#217—21no—
87C3×C4⋊Dic3—21no—
88C3×C4×Dic3C2312yes—
89C2×C3×C3⋊C8D411yescharacteristic
90C2×C3×C3⋊C8D411yescharacteristic
91C2×C3×C3⋊C8D411yescharacteristic
92C2×C3×C3⋊C8D411yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95C3×ΓL(1,𝔽25)—22no—
96C3×ΓL(1,𝔽25)—22no—
97C3×D3×C8—22no—
98C3×D3×C8—22no—
99#3718C2×C414yes—
100#3715C2×C414yes—
101#3715C2×C414yes—
102#3713C2×C414yes—
103#3711—22no—
104#3711—22no—
105D3×C3⋊C8—22no—
106D3×C3⋊C8—22no—
107#2955—91noSylow
108C2×C3×#41—31no—
109C2×C3×#41—31no—
110C2×#235C2×D311yescharacteristic
111C2×#235C2×D311yescharacteristic
112C3×#131—32no—
113C3×#131—32no—
114C3×#131—61no—
115C3×#131—61no—
116C2×C3×M16—21no—
117C2×C3×M16—61no—
118C2×C3×M16C2×D311yescharacteristic
119C2×C3×M16C2×D311yescharacteristic
120C22×C3×C8—31no—
121C22×C3×C8—61no—
122C3×#117—31no—
123#951—32no—
124#951—32no—
125#950—34no—
126#950—34no—
127#949—32no—
128#949—32no—
129#948—32no—
130#948—32no—
131#948—61no—
132#948—61no—
133#942—32no—
134#942—32no—
135#932—32no—
136#932—32no—
137#926C2×D311yescharacteristic
138C2×#208—31no—
139C2×#208—31no—
140C2×#208—31no—
141C2×#208—31no—
142C2×#208—61no—
143C2×#208—61no—
144C2×#208—61no—
145C22×C3⋊C8—61no—
146C22×C3⋊C8C2×D311yescharacteristic
147#907—21no—
148#907—21no—
149#907C2×D312yescomplemented
150#907C2×D312yescomplemented
151#901—32no—
152#901—32no—
153#901—61no—
154#901—61no—
155C2×ΓL(1,𝔽25)—21no—
156C2×ΓL(1,𝔽25)—61no—
157C2×D3×C8—21no—
158C2×D3×C8—61no—
159C3×#104—34no—
160#837—34no—
161#825C2×D314yescomplemented
162#822—34no—
163#822—34no—
164#822—64no—
165#815—32no—
166C8×Dic3—32no—
167#805—34no—
168#803—32no—
169C4×C3⋊C8—32no—
170C23×C32#4111yescharacteristic
171C22×C3×D3—21no—
172C22×C3×D3—21no—
173C2×C32×C4C22×C411yescharacteristic
174C2×C32×C4C22×C411yescharacteristic
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4#4111yescharacteristic
178C2×C32×C4C2411yescharacteristic
179C3×#67—22no—
180C3×#67—22no—
181C3×#67—22no—
182C3×#67—22no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—22no—
186C3×D12—21no—
187C3×D12—21no—
188C3×D12C22×C412yes—
189C3×D12C22×C412yes—
190C3×C4×D3—22no—
191C3×C4×D3—22no—
192C3×C4×D3—22no—
193C3×C4×D3—22no—
194C3×Dic6—21no—
195C3×Dic6—21no—
196C3×Dic6C22×C412yes—
197C3×Dic6C22×C412yes—
198C32×C8—22no—
199C3⋊(C3⋊C8)—22no—
200C3⋊(C3⋊C8)C22×C414yes—
201C3×C3⋊C8C2×D411yescharacteristic
202C3×C3⋊C8C2×D411yescharacteristic
203C3×C3⋊C8C2×D411yescharacteristic
204C3×C3⋊C8C2×D411yescharacteristic
205#575—91no—
206C2×#131—31no—
207C2×#131—91no—
208#444—94no—
209#443—94no—
210#430—91no—
211#421—31no—
212#421—91no—
213#405—91no—
214C3×#41—32no—
215C3×#41—32no—
216C3×#41—32no—
217C3×#41—32no—
218C3×#41—61no—
219C3×#41—61no—
220C3×#41—61no—
221C3×#41—61no—
222C2×C3×Q8—31no—
223C2×C3×Q8—31no—
224C2×C3×D4—31no—
225C2×C3×D4—31no—
226C2×C3×D4—61no—
227C2×C3×D4—61no—
228C22×C3×C4—21no—
229C22×C3×C4—61no—
230C22×C3×C4—61no—
231C22×C3×C4C22×D311yescharacteristic
232C22×C3×C4C22×D311yescharacteristic
233C2×#67—21no—
234C2×#67—21no—
235#235—21no—
236#235—21no—
237#235—21no—
238#235—21no—
239#235C4×D312yes—
240#235C4×D312yes—
241#235C22×D312yes—
242#235C22×D312yes—
243C2×D12C4×D311yescharacteristic
244C2×D12C4×D311yescharacteristic
245C2×C4×D3—21no—
246C2×C4×D3—21no—
247C2×Dic6C4×D311yescharacteristic
248C2×Dic6C4×D311yescharacteristic
249C3×M16—21no—
250C3×M16—21no—
251C3×M16—22no—
252C3×M16—41no—
253C3×M16—62no—
254C3×M16—62no—
255C3×M16C22×D312yes—
256C3×M16C22×D312yes—
257C2×C3×C8—21no—
258C2×C3×C8—21no—
259C2×C3×C8—31no—
260C2×C3×C8—31no—
261C2×C3×C8—31no—
262C2×C3×C8—31no—
263C2×C3×C8—31no—
264C2×C3×C8—31no—
265C2×C3×C8—41no—
266C2×C3×C8—62no—
267C2×C3×C8—62no—
268C3×C4⋊C4—61no—
269C3×C22⋊C4—61no—
270C3×C42—32no—
271#217—21no—
272#216—34no—
273#216—34no—
274#215—34no—
275#215—34no—
276#214—34no—
277#214—34no—
278#213—34no—
279#213—34no—
280C4⋊Dic3—21no—
281C4×Dic3C22×D312yes—
282#208—32no—
283#208—32no—
284#208—32no—
285#208—32no—
286#208—32no—
287#208—32no—
288#208—62no—
289#208—62no—
290#208—62no—
291#208—61no—
292#208—61no—
293#208—62no—
294#208—62no—
295#208—121no—
296C2×C3⋊C8—32no—
297C2×C3⋊C8—32no—
298C2×C3⋊C8—62no—
299C2×C3⋊C8—61no—
300C2×C3⋊C8—61no—
301C2×C3⋊C8—62no—
302C2×C3⋊C8—62no—
303C2×C3⋊C8—121no—
304C2×C3⋊C8#6711yescharacteristic
305C2×C3⋊C8#6711yescharacteristic
306C2×C3⋊C8#6711yescharacteristic
307C2×C3⋊C8#6711yescharacteristic
308C2×C3⋊C8C22×D311yescharacteristic
309C2×C3⋊C8C22×D311yescharacteristic
310ΓL(1,𝔽25)—22no—
311ΓL(1,𝔽25)—22no—
312ΓL(1,𝔽25)—62no—
313ΓL(1,𝔽25)—62no—
314D3×C8—22no—
315D3×C8—22no—
316D3×C8—62no—
317D3×C8—62no—
318C22×C32—41no—
319C22×C32C4×D411yescharacteristic
320C22×C32C4×D411yescharacteristic
321C22×C32C2×#4111yescharacteristic
322C2×C3×D3—22no—
323C2×C3×D3—22no—
324C2×C3×D3—42no—
325C2×C3×D3—42no—
326C32×C4C4×D411yescharacteristic
327C32×C4C4×D411yescharacteristic
328C32×C4C23×C411yescharacteristic
329C32×C4C22×D411yescharacteristic
330C3×Dic3—22no—
331C3×Dic3—22no—
332C3×Dic3—42no—
333C2×#41—31no—
334C2×#41—31no—
335#137—92no—
336#137—92no—
337AGL(1,ℤ/8)—92no—
338AGL(1,ℤ/8)—92no—
339#135—94no—
340#131—32no—
341#131—32no—
342#131—61no—
343#131—61no—
344#131—92no—
345#131—92no—
346#131—181no—
347#131—181no—
348C2×M16—61no—
349C2×M16—91no—
350C2×M16—91no—
351C2×M16—181no—
352C2×M16D3211yescharacteristic
353C22×C8—31no—
354C22×C8—61no—
355C22×C8—181no—
356#117—31no—
357#108—94no—
358#104—34no—
359#104—94no—
360#97—92no—
361C4×C8—92no—
362C23×C3—21no—
363C23×C3—61no—
364C23×C3—61no—
365C23×C3#23511yescharacteristic
366C23×C3#23711yescharacteristic
367C22×D3—21no—
368C22×D3—21no—
369C3×Q8—32no—
370C3×Q8—32no—
371C3×Q8—61no—
372C3×Q8—61no—
373C3×D4—32no—
374C3×D4—32no—
375C3×D4—62no—
376C3×D4—62no—
377C3×D4—62no—
378C3×D4—62no—
379C3×D4—61no—
380C3×D4—61no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—61no—
388C2×C3×C4—61no—
389C2×C3×C4—62no—
390C2×C3×C4—62no—
391C2×C3×C4—62no—
392C2×C3×C4—62no—
393C2×C3×C4—62no—
394C2×C3×C4C2×C4×D311yescharacteristic
395C2×C3×C4C2×C4×D311yescharacteristic
396C2×C3×C4C2×C4×D311yescharacteristic
397C2×C3×C4C2×C4×D311yescharacteristic
398C2×C3×C4#23511yescharacteristic
399C2×C3×C4D3×D411yescharacteristic
400C2×C3×C4D3×D411yescharacteristic
401C2×C3×C4#23711yescharacteristic
402C2×C3×C4C2×#6711yescharacteristic
403C2×C3×C4C2×#6711yescharacteristic
404C2×C3×C4C23×D311yescharacteristic
405C2×C3×C4C23×D311yescharacteristic
406#67—22no—
407#67—22no—
408#67—22no—
409#67—22no—
410C2×Dic3—21no—
411C2×Dic3—21no—
412C2×Dic3—22no—
413D12—21no—
414D12—21no—
415D12C2×C4×D312yes—
416D12C2×C4×D312yes—
417C4×D3—22no—
418C4×D3—22no—
419C4×D3—22no—
420C4×D3—22no—
421Dic6—21no—
422Dic6—21no—
423Dic6C2×C4×D312yes—
424Dic6C2×C4×D312yes—
425C3×C8—22no—
426C3×C8—22no—
427C3×C8—31no—
428C3×C8—31no—
429C3×C8—31no—
430C3×C8—31no—
431C3×C8—42no—
432C3⋊C8—34no—
433C3⋊C8—34no—
434C3⋊C8—64no—
435C3⋊C8—62no—
436C3⋊C8—62no—
437C3⋊C8—122no—
438C3⋊C8C2×#6711yescharacteristic
439C3⋊C8C2×#6711yescharacteristic
440C3⋊C8C2×#6711yescharacteristic
441C3⋊C8C2×#6711yescharacteristic
442C2×C32—21no—
443C2×C32—21no—
444C2×C32—21no—
445C2×C32C2×C4×D411yescharacteristic
446C3×D3—42no—
447C3×D3—42no—
448#41—32no—
449#41—32no—
450#41—32no—
451#41—32no—
452#41—61no—
453#41—61no—
454#41—61no—
455#41—61no—
456C2×Q8—31no—
457C2×Q8—31no—
458C2×D4—31no—
459C2×D4—31no—
460C2×D4—61no—
461C2×D4—61no—
462C22×C4—61no—
463C22×C4—61no—
464C22×C4C2×D3211yescharacteristic
465Q16—94no—
466SD16—94no—
467SD16—94no—
468D8—94no—
469M16—21no—
470M16—62no—
471M16—62no—
472M16—92no—
473M16—92no—
474M16—92no—
475M16—182no—
476M16—182no—
477M16—181no—
478M16C2×D3212yes—
479C2×C8—21no—
480C2×C8—31no—
481C2×C8—31no—
482C2×C8—31no—
483C2×C8—31no—
484C2×C8—31no—
485C2×C8—31no—
486C2×C8—62no—
487C2×C8—62no—
488C2×C8—92no—
489C2×C8—182no—
490C2×C8—182no—
491C2×C8—181no—
492C4⋊C4—61no—
493C22⋊C4—61no—
494C42—32no—
495C22×C3—21no—
496C22×C3—21no—
497C22×C3—21no—
498C22×C3—41no—
499C22×C3—41no—
500C22×C3—62no—
501C22×C3—62no—
502C22×C3—81no—
503C22×C3—122no—
504C22×C3—122no—
505C22×C3#67⋊C411yescharacteristic
506C22×C3#67⋊C411yescharacteristic
507C22×C3C4×#6711yescharacteristic
508C22×C3C4×#6711yescharacteristic
509C22×C3C2×#23511yescharacteristic
510C22×C3C2×#23711yescharacteristic
511C2×D3—22no—
512C2×D3—22no—
513C2×D3—42no—
514C2×D3—42no—
515C3×C4—21no—
516C3×C4—21no—
517C3×C4—21no—
518C3×C4—21no—
519C3×C4—62no—
520C3×C4—62no—
521C3×C4—122no—
522C3×C4#67⋊C411yescharacteristic
523C3×C4#67⋊C411yescharacteristic
524C3×C4C4×#6711yescharacteristic
525C3×C4C4×#6711yescharacteristic
526C3×C4C22×C4×D311yescharacteristic
527C3×C4C22×C4×D311yescharacteristic
528C3×C4C2×D3×D411yescharacteristic
529C3×C4C22×#6711yescharacteristic
530Dic3—22no—
531Dic3—22no—
532Dic3—42no—
533C32#295511yescharacteristic, complemented, Sylow
534C23—61no—
535C23—61no—
536C23#379511yescharacteristic
537Q8—32no—
538Q8—32no—
539Q8—61no—
540Q8—61no—
541D4—32no—
542D4—32no—
543D4—62no—
544D4—62no—
545D4—62no—
546D4—62no—
547D4—61no—
548D4—61no—
549C2×C4—61no—
550C2×C4—61no—
551C2×C4—62no—
552C2×C4—62no—
553C2×C4—62no—
554C2×C4—62no—
555C2×C4—62no—
556C2×C4#379511yescharacteristic
557C2×C4C4×D3211yescharacteristic
558C2×C4C4×D3211yescharacteristic
559C2×C4D3×#6711yescharacteristic
560C2×C4D3×#6711yescharacteristic
561C2×C4C22×D3211yescharacteristic
562C8—22no—
563C8—31no—
564C8—31no—
565C8—31no—
566C8—31no—
567C8—94no—
568C8—182no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—41no—
577C2×C3—41no—
578C2×C3—41no—
579C2×C3—122no—
580C2×C3—122no—
581C2×C3C2×#67⋊C411yescharacteristic
582C2×C3C2×C4×#6711yescharacteristic
583D3—42no—
584D3—42no—
585C22—41no—
586C22—62no—
587C22—62no—
588C22—122no—
589C22—122no—
590C22#6387911yescharacteristic
591C22#6387911yescharacteristic
592C22C2×#379511yescharacteristic
593C4—62no—
594C4—62no—
595C4—122no—
596C4#6387911yescharacteristic
597C4#6387911yescharacteristic
598C4C2×C4×D3211yescharacteristic
599C4C2×D3×#6711yescharacteristic
600C3—21no—
601C3#7898911yescharacteristic, complemented
602C3#8379211yescharacteristic, complemented
603C2—21no—
604C2—21no—
605C2—21no—
606C2—122no—
607C2—122no—
608C2C2×#6387911yescharacteristic
subgroupG/H
centerC4C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC2×C32C2×C4×D4
prime radical#10594786C2
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2955
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#907C2semidirect
3. C2×#63814C2semidirect
4. #10592823C2semidirect
5. C3×#5139C2semidirect
6. #10591111C2semidirect
7. #10591055C2semidirect
8. #10590976C2semidirect
9. #10590975C2semidirect
21. C3×#907C22semidirect
22. C3×#907C22semidirect
25. #63827C4semidirect
26. #63827C4semidirect
27. #63823C4semidirect
28. #63823C4semidirect
33. #63814C22semidirect
34. #63814C22semidirect
36. #63649C22semidirect
37. C3×#825C22semidirect
38. #63569C22semidirect
39. #63554C22semidirect
40. Dic3×C3⋊C8C22semidirect
45. C2×#907D3semidirect
51. #5139D3semidirect
149. #907C2×D3semidirect
150. #907C2×D3semidirect
161. #825C2×D3semidirect
533. C32#2955semidirect
601. C3#78989semidirect
602. C3#83792semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9072
#105947862
C2×#638142
#105928232
C3×#51392
#105911112
#105910552
#105909762
#105909752
#837923
#789893