Finite Group Databasebeta

← #11861114

Subgroups — #11861114

Order 1152.

1045 conjugacy classes of subgroups.

The subgroup lattice has 643 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64110C211yesmaximal, characteristic, complemented
2C2×C3×#901C211yesmaximal, characteristic, complemented
3#10594795C211yesmaximal, characteristic
4C3×#5101C211yesmaximal, characteristic, complemented
5#10591141C211yesmaximal, characteristic, complemented
6#10591113C211yesmaximal, characteristic, complemented
7#10591111C211yesmaximal, characteristic, complemented
8#10590924C214yesmaximal, complemented
9#10590923C214yesmaximal, complemented
10#83792—31nomaximal
11#78579—31nomaximal
12C2×#3828C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C22×C32×C8C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16#64110—21no—
17#64110—21no—
18#64110C2212yescomplemented
19#64110C2212yescomplemented
20C2×#3743—21no—
21C2×C8×C3⋊D3—21no—
22C3×#926C2211yescharacteristic
23C2×C3×#208C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25C3×#901—21no—
26C3×#901—21no—
27C3×#901C2212yescomplemented
28C3×#901C2212yescomplemented
29C2×C3×ΓL(1,𝔽25)—21no—
30C2×C3×D3×C8—21no—
31#63833C412yescomplemented
32#63831C412yescomplemented
33#63830C412yescomplemented
34#63829C2214yes—
35#63825C412yescomplemented
36C3×#815C2212yescomplemented
37C3×C8×Dic3C2212yescomplemented
38#63577C2214yescomplemented
39#63570C2214yescomplemented
40#63569C2214yescomplemented
41C2×C3×#131—31no—
42#5822—31no—
43#5748—31no—
44C2×#901—31no—
45C2×#901—31no—
46C2×#901—61no—
47C2×#901D311yescharacteristic, complemented
48C3×#405—31no—
49#5236—31no—
50#5145—34no—
51#5144—34no—
52#5139—31no—
53#5125—31no—
54#5124—31no—
55#5101D311yescharacteristic, complemented
56#5005—31no—
57#5005—31no—
58#4717—34no—
59#4700—34no—
60C22×C32×C4C2311yescharacteristic
61C2×#638—21no—
62#3828—21no—
63#3828—21no—
64#3828C2×C412yes—
65#3828C2312yes—
66C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
67C2×C4×C3⋊D3—21no—
68C2×#634C2×C411yescharacteristic
69C2×C3×#67—21no—
70C3×#235—21no—
71C3×#235—21no—
72C3×#235C2×C412yes—
73C3×#235C2312yes—
74C2×C3×D12C2×C411yescharacteristic
75C2×C3×C4×D3—21no—
76C2×C3×Dic6C2×C411yescharacteristic
77C2×C32×C8D411yescharacteristic
78C2×C32×C8D411yescharacteristic
79C2×C32×C8D411yescharacteristic
80C2×C32×C8D411yescharacteristic
81C2×C32×C8C2311yescharacteristic
82C2×C32×C8C2311yescharacteristic
83#3748—21no—
84#3748C2312yes—
85C2×C3⋊(C3⋊C8)—21no—
86#3743—22no—
87#3743—22no—
88C8×C3⋊D3—22no—
89C8×C3⋊D3—22no—
90C3×#217—21no—
91C3×C4⋊Dic3—21no—
92C3×C4×Dic3C2312yes—
93C3×#208—21no—
94C3×#208C2×C412yes—
95C3×#208C2×C412yes—
96C3×#208C2312yes—
97C2×C3×C3⋊C8—21no—
98C2×C3×C3⋊C8C2312yes—
99C3×ΓL(1,𝔽25)—22no—
100C3×ΓL(1,𝔽25)—22no—
101C3×D3×C8—22no—
102C3×D3×C8—22no—
103#3719C2×C414yes—
104#3717C2×C414yes—
105#3716C2×C414yes—
106#3714C2×C414yes—
107#2955—91noSylow
108C2×C3×#41—31no—
109C2×#235—31no—
110C2×#235—31no—
111C2×#235—61no—
112C2×#235C2×D311yescharacteristic
113C3×#131—32no—
114C3×#131—32no—
115C3×#131—61no—
116C3×#131—61no—
117C2×C3×M16—31no—
118C2×C3×M16—31no—
119C2×C3×M16—61no—
120C22×C3×C8—21no—
121C22×C3×C8—61no—
122C22×C3×C8C2×D311yescharacteristic
123C22×C3×C8C2×D311yescharacteristic
124C3×#117—31no—
125#951—32no—
126#950—34no—
127#949—32no—
128#942—32no—
129#932—32no—
130#926C2×D311yescharacteristic
131C2×#208—31no—
132C2×#208—31no—
133C2×#208—61no—
134C2×#208C2×D311yescharacteristic
135C2×#208C2×D311yescharacteristic
136#909—32no—
137#909—32no—
138#908—32no—
139#908—32no—
140#904—34no—
141#901—21no—
142#901—21no—
143#901—32no—
144#901—32no—
145#901—32no—
146#901—32no—
147#901—62no—
148#901—62no—
149#901—62no—
150#901—62no—
151#901—61no—
152#901—61no—
153#901—61no—
154#901—61no—
155#901C2×D312yescomplemented
156#901C2×D312yescomplemented
157C2×ΓL(1,𝔽25)—21no—
158C2×ΓL(1,𝔽25)—62no—
159C2×ΓL(1,𝔽25)—61no—
160C2×ΓL(1,𝔽25)—61no—
161C2×D3×C8—21no—
162C2×D3×C8—62no—
163C2×D3×C8—61no—
164C2×D3×C8—61no—
165C3×#97—32no—
166C3×C4×C8—32no—
167#837—34no—
168#825—34no—
169#822—34no—
170#819—34no—
171#815C2×D312yescomplemented
172C8×Dic3C2×D312yescomplemented
173#805—34no—
174#805—34no—
175C23×C32#4111yescharacteristic
176C22×C3⋊D3—21no—
177C22×C3×D3—21no—
178C2×C32×C4C22×C411yescharacteristic
179C2×C32×C4C22×C411yescharacteristic
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4#4111yescharacteristic
183C2×C32×C4C2411yescharacteristic
184#638—22no—
185#638—22no—
186C2×C3⋊Dic3—21no—
187C4⋊(C3⋊D3)—21no—
188C4⋊(C3⋊D3)C22×C412yes—
189C4×C3⋊D3—22no—
190C4×C3⋊D3—22no—
191#634—21no—
192#634C22×C412yes—
193C3×#67—22no—
194C3×#67—22no—
195C2×C3×Dic3—21no—
196C2×C3×Dic3—22no—
197C3×D12—21no—
198C3×D12C22×C412yes—
199C3×C4×D3—22no—
200C3×C4×D3—22no—
201C3×Dic6—21no—
202C3×Dic6C22×C412yes—
203C32×C8C2×D411yescharacteristic
204C32×C8C2×D411yescharacteristic
205C32×C8C2×D411yescharacteristic
206C32×C8C2×D411yescharacteristic
207C3⋊(C3⋊C8)—22no—
208C3×C3⋊C8—22no—
209C3×C3⋊C8C22×C414yes—
210#575—91no—
211C2×#131—31no—
212C2×#131—91no—
213#444—94no—
214#443—94no—
215#430—91no—
216#421—91no—
217#421—91no—
218#405—31no—
219C3×#41—32no—
220C3×#41—32no—
221C3×#41—61no—
222C3×#41—61no—
223C2×C3×Q8—31no—
224C2×C3×D4—31no—
225C2×C3×D4—61no—
226C22×C3×C4—21no—
227C22×C3×C4—61no—
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D311yescharacteristic
230C2×#67—21no—
231C2×#67—62no—
232C2×#67—61no—
233C2×#67—61no—
234#235—21no—
235#235—21no—
236#235—32no—
237#235—32no—
238#235—32no—
239#235—32no—
240#235—62no—
241#235—62no—
242#235—62no—
243#235—62no—
244#235—61no—
245#235—61no—
246#235—61no—
247#235—61no—
248#235C4×D312yes—
249#235C22×D312yes—
250C2×D12—31no—
251C2×D12—31no—
252C2×D12—61no—
253C2×D12C4×D311yescharacteristic
254C2×C4×D3—21no—
255C2×C4×D3—62no—
256C2×C4×D3—61no—
257C2×C4×D3—61no—
258C2×Dic6—31no—
259C2×Dic6—31no—
260C2×Dic6—61no—
261C2×Dic6C4×D311yescharacteristic
262C3×M16—32no—
263C3×M16—32no—
264C3×M16—32no—
265C3×M16—61no—
266C3×M16—62no—
267C3×M16—62no—
268C2×C3×C8—21no—
269C2×C3×C8—21no—
270C2×C3×C8—21no—
271C2×C3×C8—21no—
272C2×C3×C8—21no—
273C2×C3×C8—21no—
274C2×C3×C8—32no—
275C2×C3×C8—61no—
276C2×C3×C8—62no—
277C2×C3×C8—62no—
278C2×C3×C8D1211yescharacteristic
279C2×C3×C8D1211yescharacteristic
280C2×C3×C8D1211yescharacteristic
281C2×C3×C8D1211yescharacteristic
282C2×C3×C8#6711yescharacteristic
283C2×C3×C8#6711yescharacteristic
284C2×C3×C8#6711yescharacteristic
285C2×C3×C8#6711yescharacteristic
286C2×C3×C8C22×D311yescharacteristic
287C2×C3×C8C22×D311yescharacteristic
288C2×C3×C8C22×D311yescharacteristic
289C2×C3×C8C22×D311yescharacteristic
290C3×C4⋊C4—61no—
291C3×C22⋊C4—61no—
292C3×C42—32no—
293#217—21no—
294#216—34no—
295#215—34no—
296#214—34no—
297#213—34no—
298C4⋊Dic3—21no—
299C4×Dic3C22×D312yes—
300#208—21no—
301#208—32no—
302#208—32no—
303#208—62no—
304#208—62no—
305#208—61no—
306#208—61no—
307#208C4×D312yes—
308#208C4×D312yes—
309#208C22×D312yes—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—62no—
312C2×C3⋊C8—61no—
313C2×C3⋊C8—61no—
314C2×C3⋊C8C22×D312yes—
315Dic12—34no—
316D24—34no—
317#204—34no—
318#204—34no—
319ΓL(1,𝔽25)—22no—
320ΓL(1,𝔽25)—22no—
321ΓL(1,𝔽25)—64no—
322ΓL(1,𝔽25)—64no—
323ΓL(1,𝔽25)—62no—
324ΓL(1,𝔽25)—62no—
325ΓL(1,𝔽25)—62no—
326ΓL(1,𝔽25)—62no—
327D3×C8—22no—
328D3×C8—22no—
329D3×C8—64no—
330D3×C8—64no—
331D3×C8—62no—
332D3×C8—62no—
333D3×C8—62no—
334D3×C8—62no—
335C22×C32—41no—
336C22×C32C4×D411yescharacteristic
337C22×C32C4×D411yescharacteristic
338C22×C32C2×#4111yescharacteristic
339C2×C3⋊D3—22no—
340C2×C3⋊D3—42no—
341C2×C3×D3—22no—
342C2×C3×D3—42no—
343C32×C4C4×D411yescharacteristic
344C32×C4C4×D411yescharacteristic
345C32×C4C23×C411yescharacteristic
346C32×C4C22×D411yescharacteristic
347C3⋊Dic3—22no—
348C3×Dic3—22no—
349C3×Dic3—42no—
350C2×#41—31no—
351C2×#41—91no—
352#137—92no—
353#137—92no—
354AGL(1,ℤ/8)—92no—
355AGL(1,ℤ/8)—92no—
356#135—94no—
357#131—32no—
358#131—32no—
359#131—61no—
360#131—61no—
361#131—92no—
362#131—92no—
363#131—181no—
364#131—181no—
365C2×M16—31no—
366C2×M16—31no—
367C2×M16—61no—
368C2×M16—91no—
369C2×M16—181no—
370C22×C8—61no—
371C22×C8—181no—
372C22×C8D3211yescharacteristic
373#117—31no—
374#108—94no—
375#104—94no—
376#104—94no—
377#97—32no—
378C4×C8—32no—
379C23×C3—21no—
380C23×C3—61no—
381C23×C3#23511yescharacteristic
382C23×C3#23511yescharacteristic
383C22×D3—21no—
384C22×D3—62no—
385C22×D3—61no—
386C22×D3—61no—
387C3×Q8—32no—
388C3×Q8—61no—
389C3×D4—32no—
390C3×D4—62no—
391C3×D4—62no—
392C3×D4—61no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—61no—
400C2×C3×C4—62no—
401C2×C3×C4—62no—
402C2×C3×C4—62no—
403C2×C3×C4C2×C4×D311yescharacteristic
404C2×C3×C4C2×C4×D311yescharacteristic
405C2×C3×C4C2×C4×D311yescharacteristic
406C2×C3×C4C2×C4×D311yescharacteristic
407C2×C3×C4C2×D1211yescharacteristic
408C2×C3×C4C2×D1211yescharacteristic
409C2×C3×C4#23511yescharacteristic
410C2×C3×C4#23511yescharacteristic
411C2×C3×C4C2×#6711yescharacteristic
412C2×C3×C4C2×#6711yescharacteristic
413C2×C3×C4C23×D311yescharacteristic
414C2×C3×C4C23×D311yescharacteristic
415#67—22no—
416#67—22no—
417#67—64no—
418#67—64no—
419#67—62no—
420#67—62no—
421#67—62no—
422#67—62no—
423C2×Dic3—21no—
424C2×Dic3—22no—
425C2×Dic3—62no—
426C2×Dic3—61no—
427C2×Dic3—61no—
428D12—21no—
429D12—32no—
430D12—32no—
431D12—62no—
432D12—62no—
433D12—61no—
434D12—61no—
435D12C2×C4×D312yes—
436C4×D3—22no—
437C4×D3—22no—
438C4×D3—64no—
439C4×D3—64no—
440C4×D3—62no—
441C4×D3—62no—
442C4×D3—62no—
443C4×D3—62no—
444Dic6—21no—
445Dic6—32no—
446Dic6—32no—
447Dic6—62no—
448Dic6—62no—
449Dic6—61no—
450Dic6—61no—
451Dic6C2×C4×D312yes—
452C3×C8—21no—
453C3×C8—21no—
454C3×C8—21no—
455C3×C8—21no—
456C3×C8—34no—
457C3×C8—62no—
458C3×C8C2×D1211yescharacteristic
459C3×C8C2×D1211yescharacteristic
460C3×C8C2×D1211yescharacteristic
461C3×C8C2×D1211yescharacteristic
462C3×C8C2×#6711yescharacteristic
463C3×C8C2×#6711yescharacteristic
464C3×C8C2×#6711yescharacteristic
465C3×C8C2×#6711yescharacteristic
466C3⋊C8—22no—
467C3⋊C8—64no—
468C3⋊C8—62no—
469C3⋊C8—62no—
470C3⋊C8C2×C4×D314yes—
471C2×C32—21no—
472C2×C32—21no—
473C2×C32—21no—
474C2×C32C2×C4×D411yescharacteristic
475C3⋊D3—42no—
476C3×D3—42no—
477#41—32no—
478#41—32no—
479#41—61no—
480#41—61no—
481#41—92no—
482#41—92no—
483#41—181no—
484#41—181no—
485C2×Q8—31no—
486C2×Q8—91no—
487C2×D4—31no—
488C2×D4—61no—
489C2×D4—91no—
490C2×D4—181no—
491C22×C4—61no—
492C22×C4—181no—
493C22×C4C2×D3211yescharacteristic
494Q16—94no—
495SD16—94no—
496SD16—94no—
497D8—94no—
498M16—32no—
499M16—32no—
500M16—32no—
501M16—61no—
502M16—62no—
503M16—62no—
504M16—92no—
505M16—181no—
506M16—182no—
507M16—182no—
508C2×C8—32no—
509C2×C8—61no—
510C2×C8—62no—
511C2×C8—62no—
512C2×C8—181no—
513C2×C8—182no—
514C2×C8—182no—
515C2×C8#62611yescharacteristic
516C2×C8#62611yescharacteristic
517C2×C8#62611yescharacteristic
518C2×C8#62611yescharacteristic
519C2×C8C2×D3211yescharacteristic
520C2×C8C2×D3211yescharacteristic
521C4⋊C4—61no—
522C22⋊C4—61no—
523C42—32no—
524C22×C3—21no—
525C22×C3—21no—
526C22×C3—21no—
527C22×C3—41no—
528C22×C3—41no—
529C22×C3—42no—
530C22×C3—62no—
531C22×C3—122no—
532C22×C3C4×D1211yescharacteristic
533C22×C3C4×D1211yescharacteristic
534C22×C3C4×#6711yescharacteristic
535C22×C3C4×#6711yescharacteristic
536C22×C3C2×#23511yescharacteristic
537C22×C3C2×#23511yescharacteristic
538C2×D3—22no—
539C2×D3—42no—
540C2×D3—64no—
541C2×D3—62no—
542C2×D3—62no—
543C2×D3—124no—
544C2×D3—122no—
545C2×D3—122no—
546C3×C4—21no—
547C3×C4—21no—
548C3×C4—21no—
549C3×C4—21no—
550C3×C4—62no—
551C3×C4—122no—
552C3×C4C4×D1211yescharacteristic
553C3×C4C4×D1211yescharacteristic
554C3×C4C4×#6711yescharacteristic
555C3×C4C4×#6711yescharacteristic
556C3×C4C22×C4×D311yescharacteristic
557C3×C4C22×C4×D311yescharacteristic
558C3×C4C22×D1211yescharacteristic
559C3×C4C22×#6711yescharacteristic
560Dic3—22no—
561Dic3—42no—
562Dic3—64no—
563Dic3—62no—
564Dic3—62no—
565C32#295511yescharacteristic, complemented, Sylow
566C23—61no—
567C23—181no—
568C23#379811yescharacteristic
569Q8—32no—
570Q8—61no—
571Q8—92no—
572Q8—181no—
573D4—32no—
574D4—62no—
575D4—62no—
576D4—61no—
577D4—92no—
578D4—182no—
579D4—182no—
580D4—181no—
581C2×C4—61no—
582C2×C4—62no—
583C2×C4—62no—
584C2×C4—62no—
585C2×C4—181no—
586C2×C4—182no—
587C2×C4—182no—
588C2×C4#379811yescharacteristic
589C2×C4C4×D3211yescharacteristic
590C2×C4C4×D3211yescharacteristic
591C2×C4C2×#62611yescharacteristic
592C2×C4C2×#62611yescharacteristic
593C2×C4C22×D3211yescharacteristic
594C8—34no—
595C8—62no—
596C8—182no—
597C8C2×#62611yescharacteristic
598C8C2×#62611yescharacteristic
599C8C2×#62611yescharacteristic
600C8C2×#62611yescharacteristic
601C2×C3—22no—
602C2×C3—21no—
603C2×C3—21no—
604C2×C3—21no—
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—21no—
608C2×C3—21no—
609C2×C3—41no—
610C2×C3—41no—
611C2×C3—122no—
612C2×C3C2×C4×D1211yescharacteristic
613C2×C3C2×C4×#6711yescharacteristic
614D3—42no—
615D3—124no—
616D3—122no—
617D3—122no—
618C22—41no—
619C22—62no—
620C22—122no—
621C22—182no—
622C22—362no—
623C22C4×#62611yescharacteristic
624C22C4×#62611yescharacteristic
625C22C2×#379811yescharacteristic
626C4—62no—
627C4—122no—
628C4—182no—
629C4C4×#62611yescharacteristic
630C4C4×#62611yescharacteristic
631C4C2×C4×D3211yescharacteristic
632C4C22×#62611yescharacteristic
633C3—21no—
634C3#7857911yescharacteristic, complemented
635C3#8379211yescharacteristic, complemented
636C2—21no—
637C2—21no—
638C2—21no—
639C2—122no—
640C2—362no—
641C2C2×C4×#62611yescharacteristic
subgroupG/H
centerC8C2×#626
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC2×C32C2×C4×D4
prime radical#10594795C2
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32#2955
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C8 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×#64110C2semidirect
2. C2×C3×#901C2semidirect
4. C3×#5101C2semidirect
5. #10591141C2semidirect
6. #10591113C2semidirect
7. #10591111C2semidirect
8. #10590924C2semidirect
9. #10590923C2semidirect
18. #64110C22semidirect
19. #64110C22semidirect
27. C3×#901C22semidirect
28. C3×#901C22semidirect
31. #63833C4semidirect
32. #63831C4semidirect
33. #63830C4semidirect
35. #63825C4semidirect
36. C3×#815C22semidirect
37. C3×C8×Dic3C22semidirect
38. #63577C22semidirect
39. #63570C22semidirect
40. #63569C22semidirect
47. C2×#901D3semidirect
55. #5101D3semidirect
155. #901C2×D3semidirect
156. #901C2×D3semidirect
171. #815C2×D3semidirect
172. C8×Dic3C2×D3semidirect
565. C32#2955semidirect
634. C3#78579semidirect
635. C3#83792semidirect

Maximal subgroups

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

subgroupindex
C2×#641102
C2×C3×#9012
#105947952
C3×#51012
#105911412
#105911132
#105911112
#105909242
#105909232
#837923
#785793