Finite Group Databasebeta

← C2×#10594708 #11918502

Subgroups — C2×#10594708 #11918502

Order 1152.

3069 conjugacy classes of subgroups.

The subgroup lattice has 545 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64306C211yesmaximal, characteristic
2C2×M16×C3⋊D3C211yesmaximal, characteristic, complemented
3C2×C3×#907C212yesmaximal, complemented
4C22×#3712C211yesmaximal, characteristic, complemented
5C2×#63814C212yesmaximal, complemented
6#10594708C2116yesmaximal, direct product factor
7C2×#63805C212yesmaximal, complemented
8C2×#63803C212yesmaximal, complemented
9C2×D3×ΓL(1,𝔽25)C214yesmaximal, complemented
10C2×#5750—32nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C2×C3×#235C2212yes—
13C2×#3811C412yes—
14C2×#3805C412yes—
15#64306C418yes—
16#64306C2218yes—
17C2×#3802C411yescharacteristic
18C2×C4×D32C2212yes—
19C2×#3798C2212yes—
20C2×#3797C411yescharacteristic
21C2×#3796C412yes—
22C2×C32×M16C2211yescharacteristic, complemented
23C2×#3748C2211yescharacteristic, complemented
24M16×C3⋊D3C2218yescomplemented
25C2×#3743C2212yes—
26C2×C8×C3⋊D3C2212yescomplemented
27C22×C3×C3⋊C8C2212yescomplemented
28C3×#907C22116yescomplemented
29C2×C3×ΓL(1,𝔽25)C2214yescomplemented
30C2×C3×D3×C8C2214yescomplemented
31C2×#3712C2212yes—
32C2×#3712C2218yescomplemented
33C2×#3712C2211yescharacteristic, complemented
34C2×#3712C2211yescharacteristic, complemented
35C2×#3711C2214yescomplemented
36#63814C22116yescomplemented
37C2×D3×C3⋊C8C2214yescomplemented
38#63805C22116yescomplemented
39#63803C22116yescomplemented
40D3×ΓL(1,𝔽25)C22132yescomplemented
41C2×D3×#41—32no—
42C2×C3×#131—32no—
43C2×#948—32no—
44#5750—332no—
45C2×#907—34no—
46C2×#907D312yescomplemented
47C2×D3×M16—32no—
48C2×D3×M16—34no—
49C2×D3×M16—61no—
50C2×#901—32no—
51C2×#901—34no—
52C22×ΓL(1,𝔽25)—32no—
53C22×ΓL(1,𝔽25)—34no—
54C23×C3⋊D3C2×C411yescharacteristic
55C22×D32C2×C412yes—
56C22×C32×C4C2311yescharacteristic
57C22×C3⋊Dic3C2×C411yescharacteristic
58C2×C4×C3⋊D3C2×C411yescharacteristic
59C2×C4×C3⋊D3C2×C411yescharacteristic
60C2×C4×C3⋊D3C2×C414yes—
61C2×C4×C3⋊D3C2311yescharacteristic
62C2×C4×C3⋊D3C2311yescharacteristic
63C2×C4×C3⋊D3C2314yes—
64C2×C3×#67C2×C414yes—
65C3×#235C2×C418yes—
66C3×#235C2318yes—
67C2×C3×D12C2×C412yes—
68C2×C3×C4×D3C2314yes—
69C2×C3×Dic6C2×C412yes—
70#3811C2×C4116yes—
71C2×#627C2×C412yes—
72C2×#626C2×C414yes—
73C2×#625C2×C412yes—
74C2×#624C2×C412yes—
75#3805C2×C4116yes—
76C2×D3×Dic3C2×C414yes—
77#3802C2×C418yes—
78C4×D32C2×C418yes—
79C4×D32C2318yes—
80#3798C2×C418yes—
81#3798C2318yes—
82#3797C2×C418yes—
83#3796C2×C4116yes—
84C32×M16C2314yescomplemented
85C2×C32×C8C2312yes—
86#3748C2314yescomplemented
87C2×C3⋊(C3⋊C8)C2312yes—
88#3743C2318yes—
89C8×C3⋊D3C2318yescomplemented
90C2×C3×C3⋊C8C2312yes—
91C2×C3×C3⋊C8C2312yes—
92C2×C3×C3⋊C8C2318yescomplemented
93C3×ΓL(1,𝔽25)C23116yescomplemented
94C3×D3×C8C23116yescomplemented
95#3712C2318yes—
96#3712C2314yescomplemented
97#3712C2314yescomplemented
98#3711C23116yescomplemented
99D3×C3⋊C8C23116yescomplemented
100C2×#568—91noSylow
101C2×C3×#41—32no—
102D3×#41—316no—
103D3×#41—316no—
104C2×#239—32no—
105C2×D3×Q8—32no—
106C2×#237—34no—
107C2×#237—32no—
108C2×D3×D4—34no—
109C2×D3×D4—32no—
110C2×#235—34no—
111C2×#235C2×D312yes—
112C22×C4×D3—32no—
113C22×C4×D3—34no—
114C22×C4×D3—61no—
115C3×#131—316no—
116C2×C3×M16—21no—
117C2×C3×M16—34no—
118C2×C3×M16C2×D312yescomplemented
119C22×C3×C8—32no—
120C22×C3×C8—34no—
121#948—316no—
122C2×#208—32no—
123C2×#208—34no—
124C2×#208—61no—
125C22×C3⋊C8—34no—
126C22×C3⋊C8C2×D312yescomplemented
127#907—332no—
128#907C2×D3116yescomplemented
129D3×M16—316no—
130D3×M16—332no—
131D3×M16—68no—
132#901—316no—
133#901—332no—
134C2×ΓL(1,𝔽25)—34no—
135C2×ΓL(1,𝔽25)—34no—
136C2×ΓL(1,𝔽25)—32no—
137C2×ΓL(1,𝔽25)—32no—
138C2×ΓL(1,𝔽25)—32no—
139C2×ΓL(1,𝔽25)—32no—
140C2×ΓL(1,𝔽25)—316no—
141C2×ΓL(1,𝔽25)—332no—
142C2×ΓL(1,𝔽25)—62no—
143C2×ΓL(1,𝔽25)C2×D314yescomplemented
144C2×D3×C8—34no—
145C2×D3×C8—34no—
146C2×D3×C8—62no—
147C2×D3×C8C2×D314yescomplemented
148C23×C32C22×C411yescharacteristic
149C22×C3⋊D3—42no—
150C22×C3⋊D3C22×C411yescharacteristic
151C22×C3⋊D3C22×C411yescharacteristic
152C22×C3⋊D3C22×C414yes—
153C22×C3×D3C22×C414yes—
154C2×D32—44no—
155C2×D32C22×C418yes—
156C2×C32×C4C22×C411yescharacteristic
157C2×C32×C4C22×C412yes—
158C2×C32×C4C2411yescharacteristic
159C2×C32×C4C2412yes—
160C2×C3⋊Dic3C22×C411yescharacteristic
161C2×C3⋊Dic3C22×C414yes—
162C2×C3⋊Dic3C22×C411yescharacteristic
163C4×C3⋊D3C22×C414yes—
164C4×C3⋊D3C22×C414yes—
165C4×C3⋊D3C22×C412yes—
166C4×C3⋊D3C22×C412yes—
167C4×C3⋊D3C2412yes—
168C4×C3⋊D3C2412yes—
169C3×#67C22×C4116yes—
170C2×C3×Dic3C22×C414yes—
171C3×D12C22×C418yes—
172C3×C4×D3C22×C418yes—
173C3×C4×D3C2418yes—
174C3×Dic6C22×C418yes—
175#627C22×C418yes—
176#626C22×C4116yes—
177#625C22×C418yes—
178#624C22×C418yes—
179D3×Dic3C22×C4116yes—
180C32×C8C2414yes—
181C3⋊(C3⋊C8)C2414yes—
182C3×C3⋊C8C2414yes—
183C3×C3⋊C8C2414yes—
184C22×#41—91no—
185#568—916no—
186C2×#131—32no—
187C2×#131—92no—
188C2×#131—92no—
189C2×#131—92no—
190C22×M16—91no—
191C22×M16—94no—
192C22×M16—91no—
193C23×D3—32no—
194C23×D3—34no—
195C23×D3—61no—
196C3×#41—38no—
197C3×#41—38no—
198C2×C3×Q8—32no—
199C2×C3×D4—34no—
200C2×C3×D4—32no—
201C22×C3×C4—21no—
202C22×C3×C4—34no—
203C22×C3×C4C22×D312yes—
204C2×#67—34no—
205C2×#67—34no—
206C2×#67C4×D314yes—
207C22×Dic3—32no—
208C22×Dic3—34no—
209C22×Dic3—61no—
210#239—316no—
211D3×Q8—316no—
212#237—332no—
213#237—316no—
214D3×D4—332no—
215D3×D4—316no—
216#235—316no—
217#235—316no—
218#235C4×D318yes—
219#235C22×D318yes—
220C2×D12—34no—
221C2×D12C4×D312yes—
222C2×C4×D3—34no—
223C2×C4×D3—32no—
224C2×C4×D3—32no—
225C2×C4×D3—38no—
226C2×C4×D3—32no—
227C2×C4×D3—32no—
228C2×C4×D3—38no—
229C2×C4×D3—34no—
230C2×C4×D3—316no—
231C2×C4×D3—316no—
232C2×C4×D3—61no—
233C2×C4×D3—61no—
234C2×C4×D3—64no—
235C2×C4×D3—61no—
236C2×C4×D3—61no—
237C2×C4×D3—64no—
238C2×C4×D3C22×D314yes—
239C2×Dic6—34no—
240C2×Dic6C4×D312yes—
241C3×M16—24no—
242C3×M16—316no—
243C3×M16C22×D318yescomplemented
244C2×C3×C8—22no—
245C2×C3×C8—32no—
246C2×C3×C8—32no—
247C2×C3×C8—38no—
248C2×C3×C8—316no—
249C2×C3×C8C22×D314yes—
250#208—38no—
251#208—316no—
252#208—64no—
253C2×C3⋊C8—34no—
254C2×C3⋊C8—316no—
255C2×C3⋊C8—62no—
256C2×C3⋊C8C22×D312yes—
257C2×C3⋊C8C22×D312yes—
258C2×C3⋊C8C22×D318yescomplemented
259ΓL(1,𝔽25)—316no—
260ΓL(1,𝔽25)—316no—
261ΓL(1,𝔽25)—38no—
262ΓL(1,𝔽25)—38no—
263ΓL(1,𝔽25)—38no—
264ΓL(1,𝔽25)—38no—
265ΓL(1,𝔽25)—68no—
266ΓL(1,𝔽25)C22×D3116yescomplemented
267D3×C8—316no—
268D3×C8—316no—
269D3×C8—68no—
270D3×C8C22×D3116yescomplemented
271C22×C32—22no—
272C22×C32C23×C412yes—
273C22×C32C23×C411yescharacteristic
274C2×C3⋊D3—22no—
275C2×C3⋊D3—22no—
276C2×C3⋊D3—44no—
277C2×C3⋊D3C23×C412yes—
278C2×C3⋊D3C23×C412yes—
279C2×C3×D3—28no—
280C2×C3×D3C23×C418yes—
281D32—48no—
282C32×C4C23×C412yes—
283C32×C4C23×C411yescharacteristic
284C32×C4C2511yescharacteristic
285C3⋊Dic3C23×C412yes—
286C3⋊Dic3C23×C412yes—
287C3×Dic3C23×C418yes—
288C2×#41—32no—
289C2×#41—92no—
290C2×#41—92no—
291C2×#41—92no—
292C2×#41—98no—
293C2×#41—98no—
294C22×Q8—91no—
295C22×D4—92no—
296C22×D4—91no—
297C23×C4—92no—
298C23×C4—91no—
299#131—316no—
300#131—916no—
301#131—916no—
302#131—916no—
303C2×M16—34no—
304C2×M16—92no—
305C2×M16—91no—
306C2×M16—91no—
307C2×M16—98no—
308C2×M16—932no—
309C2×M16—94no—
310C2×M16—91no—
311C2×M16—98no—
312C2×M16—92no—
313C2×M16D3211yescharacteristic, complemented
314C22×C8—32no—
315C22×C8—34no—
316C22×C8—94no—
317C22×C8—92no—
318C23×C3—21no—
319C23×C3—34no—
320C23×C3C2×C4×D312yes—
321C22×D3—32no—
322C22×D3—32no—
323C22×D3—38no—
324C22×D3—316no—
325C22×D3—61no—
326C22×D3—61no—
327C22×D3—64no—
328C22×D3—128no—
329C22×D3—124no—
330C22×D3—124no—
331C22×D3C2×C4×D314yes—
332C3×Q8—38no—
333C3×D4—316no—
334C3×D4—38no—
335C2×C3×C4—22no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—22no—
339C2×C3×C4—34no—
340C2×C3×C4—38no—
341C2×C3×C4—38no—
342C2×C3×C4C2×C4×D312yes—
343C2×C3×C4C2×C4×D314yes—
344C2×C3×C4C23×D314yes—
345C2×C3×C4C23×D312yes—
346#67—316no—
347#67—316no—
348#67C2×C4×D3116yes—
349C2×Dic3—32no—
350C2×Dic3—32no—
351C2×Dic3—38no—
352C2×Dic3—316no—
353C2×Dic3—61no—
354C2×Dic3—61no—
355C2×Dic3—64no—
356C2×Dic3C2×C4×D314yes—
357D12—316no—
358D12C2×C4×D318yes—
359C4×D3—316no—
360C4×D3—34no—
361C4×D3—34no—
362C4×D3—38no—
363C4×D3—38no—
364C4×D3—34no—
365C4×D3—34no—
366C4×D3—316no—
367C4×D3—62no—
368C4×D3—64no—
369C4×D3—64no—
370C4×D3—62no—
371C4×D3—62no—
372C4×D3—62no—
373C4×D3C2×C4×D318yes—
374C4×D3C23×D318yes—
375Dic6—316no—
376Dic6C2×C4×D318yes—
377C3×C8—24no—
378C3×C8—34no—
379C3×C8—34no—
380C3×C8C23×D318yes—
381C3⋊C8—38no—
382C3⋊C8—64no—
383C3⋊C8C23×D314yes—
384C3⋊C8C23×D314yes—
385C2×C32—22no—
386C2×C32#56812yescomplemented
387C2×C32C24×C411yescharacteristic
388C3⋊D3—22no—
389C3⋊D3—22no—
390C3×D3—28no—
391C24—92no—
392C24—91no—
393#41—38no—
394#41—38no—
395#41—98no—
396#41—98no—
397#41—916no—
398#41—916no—
399C2×Q8—32no—
400C2×Q8—92no—
401C2×Q8—98no—
402C2×D4—34no—
403C2×D4—32no—
404C2×D4—94no—
405C2×D4—916no—
406C2×D4—98no—
407C2×D4—92no—
408C22×C4—34no—
409C22×C4—98no—
410C22×C4—92no—
411C22×C4—98no—
412C22×C4—94no—
413C22×C4—91no—
414C22×C4—94no—
415C22×C4—91no—
416C22×C4—91no—
417C22×C4—91no—
418C22×C4—91no—
419C22×C4—94no—
420C22×C4C2×D3211yescharacteristic
421M16—316no—
422M16—98no—
423M16—94no—
424M16—94no—
425M16—916no—
426M16—94no—
427M16—98no—
428M16C2×D3214yescomplemented
429C2×C8—38no—
430C2×C8—32no—
431C2×C8—32no—
432C2×C8—316no—
433C2×C8—916no—
434C2×C8—92no—
435C2×C8—98no—
436C2×C8C2×D3212yes—
437C22×C3—24no—
438C22×C3—21no—
439C22×C3—22no—
440C22×C3—38no—
441C22×C3—42no—
442C22×C3—68no—
443C22×C3C22×C4×D314yes—
444C22×C3C22×C4×D312yes—
445C2×D3—28no—
446C2×D3—34no—
447C2×D3—34no—
448C2×D3—62no—
449C2×D3—62no—
450C2×D3—64no—
451C2×D3—64no—
452C2×D3—64no—
453C2×D3—122no—
454C2×D3—1216no—
455C2×D3—128no—
456C2×D3—128no—
457C2×D3C22×C4×D318yes—
458C3×C4—21no—
459C3×C4—22no—
460C3×C4—21no—
461C3×C4—38no—
462C3×C4C22×C4×D314yes—
463C3×C4C22×C4×D312yes—
464C3×C4C24×D312yes—
465Dic3—34no—
466Dic3—34no—
467Dic3—62no—
468Dic3—62no—
469Dic3C22×C4×D318yes—
470C32C2×#56811yescharacteristic, complemented, Sylow
471C23—34no—
472C23—98no—
473C23—91no—
474C23—91no—
475C23—94no—
476C23—362no—
477C23—364no—
478C23C4×D3211yescharacteristic
479Q8—38no—
480Q8—98no—
481D4—316no—
482D4—38no—
483D4—916no—
484D4—98no—
485C2×C4—34no—
486C2×C4—38no—
487C2×C4—38no—
488C2×C4—98no—
489C2×C4—916no—
490C2×C4—91no—
491C2×C4—91no—
492C2×C4—94no—
493C2×C4—92no—
494C2×C4—94no—
495C2×C4—94no—
496C2×C4—92no—
497C2×C4—92no—
498C2×C4—92no—
499C2×C4C4×D3211yescharacteristic
500C2×C4C4×D3212yes—
501C2×C4C22×D3212yes—
502C2×C4C22×D3211yescharacteristic
503C8—34no—
504C8—34no—
505C8—94no—
506C8C22×D3214yes—
507C2×C3—24no—
508C2×C3—21no—
509C2×C3—22no—
510C2×C3—42no—
511C2×C3—68no—
512C2×C3#575014yescomplemented
513C2×C3C23×C4×D312yes—
514D3—28no—
515D3—64no—
516D3—64no—
517D3—64no—
518D3—122no—
519C22—22no—
520C22—38no—
521C22—68no—
522C22—92no—
523C22—92no—
524C22—182no—
525C22—182no—
526C22—364no—
527C22—368no—
528C22C2×C4×D3212yes—
529C22C2×C4×D3211yescharacteristic
530C4—38no—
531C4—92no—
532C4—92no—
533C4C2×C4×D3211yescharacteristic
534C4C2×C4×D3212yes—
535C4C23×D3211yescharacteristic
536C3—21no—
537C3C2×#575012yescomplemented
538C2—22no—
539C2—68no—
540C2—182no—
541C2—182no—
542C2#1059470812yesdirect product factor
543C2C22×C4×D3211yescharacteristic
subgroupG/H
centerC2×C4C22×D32
commutatorC2×C32C24×C4
FrattiniC4C23×D32
FittingC2×C32×M16C22
socleC22×C32C23×C4
prime radicalC2×#64306C2
cosocleC32×C4C25
hypercenterC2×M16D32
hypocenterC32C2×#568
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×M16×C3⋊D3C2semidirect
3. C2×C3×#907C2semidirect
4. C22×#3712C2semidirect
5. C2×#63814C2semidirect
6. #10594708C2direct (N × H)
7. C2×#63805C2semidirect
8. C2×#63803C2semidirect
9. C2×D3×ΓL(1,𝔽25)C2semidirect
22. C2×C32×M16C22semidirect
23. C2×#3748C22semidirect
24. M16×C3⋊D3C22semidirect
26. C2×C8×C3⋊D3C22semidirect
27. C22×C3×C3⋊C8C22semidirect
28. C3×#907C22semidirect
29. C2×C3×ΓL(1,𝔽25)C22semidirect
30. C2×C3×D3×C8C22semidirect
32. C2×#3712C22semidirect
33. C2×#3712C22semidirect
34. C2×#3712C22semidirect
35. C2×#3711C22semidirect
36. #63814C22semidirect
37. C2×D3×C3⋊C8C22semidirect
38. #63805C22semidirect
39. #63803C22semidirect
40. D3×ΓL(1,𝔽25)C22semidirect
46. C2×#907D3semidirect
84. C32×M16C23semidirect
86. #3748C23semidirect
89. C8×C3⋊D3C23semidirect
92. C2×C3×C3⋊C8C23semidirect
93. C3×ΓL(1,𝔽25)C23semidirect
94. C3×D3×C8C23semidirect
96. #3712C23semidirect
97. #3712C23semidirect
98. #3711C23semidirect
99. D3×C3⋊C8C23semidirect
118. C2×C3×M16C2×D3semidirect
126. C22×C3⋊C8C2×D3semidirect
128. #907C2×D3semidirect
143. C2×ΓL(1,𝔽25)C2×D3semidirect
147. C2×D3×C8C2×D3semidirect
243. C3×M16C22×D3semidirect
258. C2×C3⋊C8C22×D3semidirect
266. ΓL(1,𝔽25)C22×D3semidirect
270. D3×C8C22×D3semidirect
313. C2×M16D32semidirect
386. C2×C32#568semidirect
428. M16C2×D32semidirect
470. C32C2×#568semidirect
512. C2×C3#5750semidirect
537. C3C2×#5750semidirect
542. C2#10594708direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643062
C2×M16×C3⋊D32
C2×C3×#9072
C22×#37122
C2×#638142
#105947082
C2×#638052
C2×#638032
C2×D3×ΓL(1,𝔽25)2
C2×#57503