Finite Group Databasebeta

← #11857912

Subgroups — #11857912

Order 1152.

1781 conjugacy classes of subgroups.

The subgroup lattice has 563 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×#63900C211yesmaximal, characteristic, complemented
4C3×#5133C212yesmaximal, complemented
5#10591087C212yesmaximal, complemented
6#10590957C214yesmaximal, complemented
7#10590940C212yesmaximal, complemented
8#10590672C212yesmaximal, complemented
9D3×#417—32nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C2×C3×#235C2212yes—
12C2×#3811—21no—
13C22×#624—21no—
14C2×#3805—21no—
15#64306—24no—
16#64306C418yescomplemented
17C2×#3802C2211yescharacteristic
18C2×C4×D32—21no—
19C2×#3798—21no—
20C2×#3797C2211yescharacteristic
21C2×#3796C2212yes—
22C2×C32×M16C2211yescharacteristic, complemented
23C2×#3748C2211yescharacteristic, complemented
24M16×C3⋊D3—24no—
25C2×#3743C2212yescomplemented
26C2×C8×C3⋊D3C2212yes—
27C2×C3×C4⋊Dic3C2212yescomplemented
28C2×#3724—21no—
29#63900—21no—
30#63900—21no—
31#63900C2212yes—
32#63900C2212yescomplemented
33C3×#821C2214yescomplemented
34C3×#816C2214yescomplemented
35#63565C2214yescomplemented
36#63562C2214yescomplemented
37C2×D3×#41—32no—
38C2×D3×M16—32no—
39C2×D3×M16—61no—
40C2×D3×C4⋊C4—32no—
41C3×#417—32no—
42#5232—32no—
43#5133D312yescomplemented
44#4966—32no—
45#4803—34no—
46D3×#103—34no—
47#4771—34no—
48D3×#102—34no—
49C23×C3⋊D3D411yescharacteristic
50C22×D32—21no—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3D411yescharacteristic
53C2×C4×C3⋊D3C2×C414yes—
54C2×C4×C3⋊D3D411yescharacteristic
55C2×C4×C3⋊D3D411yescharacteristic
56C2×C4×C3⋊D3D414yes—
57C2×C4×C3⋊D3C2311yescharacteristic
58C2×C4×C3⋊D3C2311yescharacteristic
59C2×C3×#67—22no—
60C22×C3×Dic3—22no—
61C3×#235—24no—
62C3×#235C2×C418yescomplemented
63C2×C3×D12C2312yes—
64C2×C3×C4×D3—22no—
65C2×C3×Dic6C2312yes—
66#3811—28no—
67C2×#627—21no—
68C2×#626—22no—
69C2×#625—21no—
70C2×#624—21no—
71C2×#624—22no—
72C2×#624—22no—
73C2×#624—44no—
74#3805—28no—
75C2×D3×Dic3—22no—
76#3802—22no—
77#3802C2×C414yescomplemented
78C4×D32—28no—
79#3798—28no—
80#3797—22no—
81#3797C2×C414yescomplemented
82#3796—24no—
83#3796C2×C418yescomplemented
84C32×M16—22no—
85C2×C32×C8C2312yes—
86#3748—22no—
87C2×C3⋊(C3⋊C8)C2312yes—
88#3743—24no—
89C8×C3⋊D3—24no—
90C3×C4⋊Dic3—22no—
91C3×C4⋊Dic3C2314yes—
92#3724—22no—
93#3724—22no—
94C2×#417—91noSylow
95C2×C3×#41—32no—
96D3×#41—316no—
97D3×#41—68no—
98C2×#239—32no—
99C2×D3×Q8—32no—
100C2×#237—32no—
101C2×#237—62no—
102C2×D3×D4—32no—
103C2×D3×D4—62no—
104C2×#235—62no—
105C2×#235C2×D312yes—
106C22×C4×D3—32no—
107C22×C4×D3—61no—
108C22×C4×D3—62no—
109C22×C4×D3—62no—
110C2×C3×M16—21no—
111C2×C3×M16C2×D312yescomplemented
112C2×C3×C4⋊C4—32no—
113C2×C4⋊Dic3C2×D312yescomplemented
114C2×Dic3⋊C4—62no—
115C2×#208—32no—
116C2×#208—61no—
117D3×M16—68no—
118D3×M16—68no—
119C2×ΓL(1,𝔽25)—34no—
120C2×ΓL(1,𝔽25)—62no—
121C2×D3×C8—34no—
122C2×D3×C8—62no—
123D3×C4⋊C4—34no—
124D3×C4⋊C4—34no—
125D3×C4⋊C4—62no—
126D3×C4⋊C4—62no—
127C3×#103—34no—
128C3×#102—34no—
129#835—34no—
130#832—34no—
131#821C2×D314yescomplemented
132#816C2×D314yescomplemented
133#810—34no—
134#809—34no—
135C23×C32C2×D411yescharacteristic
136C22×C3⋊D3—22no—
137C22×C3⋊D3—22no—
138C22×C3⋊D3C22⋊C414yes—
139C22×C3⋊D3C2×D411yescharacteristic
140C22×C3⋊D3C2×D411yescharacteristic
141C22×C3×D3—22no—
142C2×D32—24no—
143C2×D32—42no—
144C2×D32—42no—
145C2×C32×C4C22×C412yes—
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D412yes—
148C2×C32×C4C2411yescharacteristic
149C2×C3⋊Dic3C22⋊C414yes—
150C2×C3⋊Dic3C2×D411yescharacteristic
151C2×C3⋊Dic3C2×D411yescharacteristic
152C4×C3⋊D3C22⋊C414yes—
153C4×C3⋊D3C22⋊C414yes—
154C4×C3⋊D3C22×C412yes—
155C4×C3⋊D3C22×C412yes—
156C4×C3⋊D3C2×D412yes—
157C4×C3⋊D3C2×D412yes—
158C3×#67—28no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—24no—
161C2×C3×Dic3—44no—
162C3×D12—22no—
163C3×D12C22×C414yescomplemented
164C3×C4×D3—28no—
165C3×Dic6—22no—
166C3×Dic6C22×C414yescomplemented
167#627—24no—
168#626—28no—
169#625—24no—
170#624—24no—
171#624—44no—
172#624—44no—
173D3×Dic3—28no—
174C32×C8—22no—
175C3⋊(C3⋊C8)—22no—
176C22×#41—91no—
177C22×M16—91no—
178C22×C4⋊C4—91no—
179#417—32no—
180#417—94no—
181#417—92no—
182C2×#103—92no—
183C2×#102—92no—
184C23×D3—32no—
185C23×D3—61no—
186C23×D3—62no—
187C3×#41—38no—
188C3×#41—64no—
189C2×C3×Q8—32no—
190C2×C3×D4—32no—
191C2×C3×D4—62no—
192C22×C3×C4—21no—
193C22×C3×C4—62no—
194C22×C3×C4—62no—
195C22×C3×C4C22×D312yes—
196C2×#67—22no—
197C2×#67—62no—
198C2×#67—62no—
199C22×Dic3—22no—
200C22×Dic3—32no—
201C22×Dic3—61no—
202C22×Dic3—62no—
203#239—38no—
204#239—64no—
205D3×Q8—38no—
206D3×Q8—64no—
207#237—38no—
208#237—64no—
209#237—616no—
210D3×D4—38no—
211D3×D4—64no—
212D3×D4—616no—
213#235—24no—
214#235—616no—
215#235C4×D318yescomplemented
216C2×D12—62no—
217C2×D12C22×D312yes—
218C2×C4×D3—22no—
219C2×C4×D3—38no—
220C2×C4×D3—32no—
221C2×C4×D3—32no—
222C2×C4×D3—38no—
223C2×C4×D3—32no—
224C2×C4×D3—32no—
225C2×C4×D3—61no—
226C2×C4×D3—61no—
227C2×C4×D3—64no—
228C2×C4×D3—64no—
229C2×C4×D3—61no—
230C2×C4×D3—61no—
231C2×C4×D3—616no—
232C2×C4×D3—62no—
233C2×C4×D3—62no—
234C2×C4×D3—64no—
235C2×C4×D3—64no—
236C2×C4×D3—128no—
237C2×Dic6—62no—
238C2×Dic6C22×D312yes—
239C3×M16—24no—
240C3×M16—24no—
241C2×C3×C8—22no—
242C2×C3×C8C22×D314yes—
243C3×C4⋊C4—34no—
244C3×C4⋊C4—62no—
245C4⋊Dic3—22no—
246C4⋊Dic3C22×D314yes—
247Dic3⋊C4—64no—
248Dic3⋊C4—64no—
249#208—64no—
250#208—64no—
251C2×C3⋊C8—34no—
252C2×C3⋊C8—62no—
253ΓL(1,𝔽25)—68no—
254ΓL(1,𝔽25)—68no—
255D3×C8—68no—
256D3×C8—68no—
257C22×C32—21no—
258C22×C32—21no—
259C22×C32C2×C22⋊C412yes—
260C22×C32C22×D411yescharacteristic
261C2×C3⋊D3—21no—
262C2×C3⋊D3—21no—
263C2×C3⋊D3—28no—
264C2×C3⋊D3C2×C22⋊C412yes—
265C2×C3⋊D3C2×C22⋊C412yes—
266C2×C3⋊D3AGL(1,ℤ/8)12yes—
267C2×C3⋊D3#13712yes—
268C2×C3×D3—24no—
269C2×C3×D3—42no—
270C2×C3×D3—42no—
271D32—48no—
272C32×C4C2×C22⋊C412yes—
273C32×C4C23×C411yescharacteristic
274C32×C4C22×D411yescharacteristic
275C3⋊Dic3C2×C22⋊C412yes—
276C3⋊Dic3C2×C22⋊C412yes—
277C3×Dic3—24no—
278C3×Dic3—44no—
279C2×#41—32no—
280C2×#41—92no—
281C2×#41—98no—
282C2×#41—181no—
283C2×#41—181no—
284C2×#41—184no—
285C22×Q8—91no—
286C22×D4—91no—
287C22×D4—181no—
288C23×C4—91no—
289C23×C4—181no—
290C23×C4—181no—
291C2×M16—91no—
292C2×M16—92no—
293C2×M16—184no—
294C2×M16D3211yescharacteristic, complemented
295C22×C8—92no—
296C2×C4⋊C4—32no—
297C2×C4⋊C4—92no—
298C2×C4⋊C4—92no—
299C2×C4⋊C4—181no—
300C2×C4⋊C4—181no—
301C2×C4⋊C4—181no—
302#103—34no—
303#103—94no—
304#102—34no—
305#102—94no—
306C23×C3—21no—
307C23×C3—62no—
308C23×C3D3×D412yes—
309C22×D3—22no—
310C22×D3—32no—
311C22×D3—38no—
312C22×D3—32no—
313C22×D3—61no—
314C22×D3—64no—
315C22×D3—61no—
316C22×D3—68no—
317C22×D3—64no—
318C22×D3—64no—
319C22×D3—122no—
320C22×D3—122no—
321C22×D3—124no—
322C22×D3—124no—
323C3×Q8—34no—
324C3×Q8—62no—
325C3×D4—34no—
326C3×D4—68no—
327C3×D4—62no—
328C2×C3×C4—21no—
329C2×C3×C4—22no—
330C2×C3×C4—21no—
331C2×C3×C4—22no—
332C2×C3×C4—62no—
333C2×C3×C4—68no—
334C2×C3×C4—64no—
335C2×C3×C4—124no—
336C2×C3×C4C2×C4×D314yes—
337C2×C3×C4D3×D412yes—
338C2×C3×C4D3×D414yes—
339C2×C3×C4C23×D312yes—
340#67—28no—
341#67—68no—
342#67—68no—
343C2×Dic3—22no—
344C2×Dic3—24no—
345C2×Dic3—38no—
346C2×Dic3—32no—
347C2×Dic3—32no—
348C2×Dic3—44no—
349C2×Dic3—64no—
350C2×Dic3—61no—
351C2×Dic3—61no—
352C2×Dic3—68no—
353D12—22no—
354D12—68no—
355D12C2×C4×D314yescomplemented
356C4×D3—28no—
357C4×D3—38no—
358C4×D3—38no—
359C4×D3—34no—
360C4×D3—34no—
361C4×D3—34no—
362C4×D3—34no—
363C4×D3—64no—
364C4×D3—64no—
365C4×D3—62no—
366C4×D3—62no—
367C4×D3—62no—
368C4×D3—62no—
369C4×D3—68no—
370C4×D3—68no—
371C4×D3—128no—
372C4×D3—128no—
373Dic6—22no—
374Dic6—68no—
375Dic6C2×C4×D314yescomplemented
376C3×C8—24no—
377C3×C8—24no—
378C3⋊C8—64no—
379C3⋊C8—64no—
380C2×C32—22no—
381C2×C32C22×C22⋊C411yescharacteristic
382C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
383C2×C32C2×#13711yescharacteristic
384C3⋊D3—22no—
385C3⋊D3#41714yescomplemented
386C3×D3—44no—
387C24—91no—
388C24—181no—
389#41—38no—
390#41—64no—
391#41—98no—
392#41—188no—
393#41—188no—
394#41—184no—
395C2×Q8—32no—
396C2×Q8—94no—
397C2×Q8—181no—
398C2×Q8—182no—
399C2×D4—32no—
400C2×D4—62no—
401C2×D4—94no—
402C2×D4—182no—
403C2×D4—182no—
404C2×D4—181no—
405C2×D4—188no—
406C22×C4—62no—
407C22×C4—62no—
408C22×C4—91no—
409C22×C4—91no—
410C22×C4—91no—
411C22×C4—94no—
412C22×C4—91no—
413C22×C4—91no—
414C22×C4—94no—
415C22×C4—188no—
416C22×C4—181no—
417C22×C4—182no—
418C22×C4—182no—
419C22×C4—182no—
420C22×C4—364no—
421C22×C4C2×D3211yescharacteristic
422M16—22no—
423M16—184no—
424M16—182no—
425C2×C8—92no—
426C2×C8—184no—
427C2×C8C2×D3212yes—
428C4⋊C4—34no—
429C4⋊C4—62no—
430C4⋊C4—182no—
431C4⋊C4—182no—
432C22×C3—22no—
433C22×C3—22no—
434C22×C3—21no—
435C22×C3—22no—
436C22×C3—41no—
437C22×C3—41no—
438C22×C3—64no—
439C22×C3—122no—
440C22×C3—122no—
441C22×C3D3×C22⋊C414yes—
442C22×C3C2×D3×D412yes—
443C2×D3—24no—
444C2×D3—34no—
445C2×D3—34no—
446C2×D3—34no—
447C2×D3—34no—
448C2×D3—42no—
449C2×D3—42no—
450C2×D3—62no—
451C2×D3—62no—
452C2×D3—62no—
453C2×D3—62no—
454C2×D3—616no—
455C2×D3—62no—
456C2×D3—62no—
457C2×D3—128no—
458C2×D3—121no—
459C2×D3—121no—
460C2×D3—1216no—
461C3×C4—21no—
462C3×C4—21no—
463C3×C4—22no—
464C3×C4—64no—
465C3×C4—124no—
466C3×C4D3×C22⋊C414yes—
467C3×C4C22×C4×D312yes—
468C3×C4C2×D3×D412yes—
469Dic3—24no—
470Dic3—34no—
471Dic3—34no—
472Dic3—44no—
473Dic3—62no—
474Dic3—62no—
475C32C2×#41711yescharacteristic, complemented, Sylow
476C23—62no—
477C23—91no—
478C23—91no—
479C23—94no—
480C23—182no—
481C23—182no—
482C23—184no—
483C23—362no—
484C23—362no—
485C23#380211yescharacteristic
486Q8—34no—
487Q8—62no—
488Q8—184no—
489D4—34no—
490D4—68no—
491D4—62no—
492D4—188no—
493D4—184no—
494C2×C4—62no—
495C2×C4—68no—
496C2×C4—64no—
497C2×C4—91no—
498C2×C4—91no—
499C2×C4—94no—
500C2×C4—92no—
501C2×C4—92no—
502C2×C4—92no—
503C2×C4—92no—
504C2×C4—94no—
505C2×C4—94no—
506C2×C4—124no—
507C2×C4—184no—
508C2×C4—188no—
509C2×C4—364no—
510C2×C4—364no—
511C2×C4C4×D3212yes—
512C2×C4#380211yescharacteristic
513C2×C4#381112yes—
514C2×C4C22×D3211yescharacteristic
515C8—22no—
516C8—182no—
517C2×C3—24no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—42no—
522C2×C3—124no—
523C2×C3C2×D3×C22⋊C412yes—
524C2×C3D3×AGL(1,ℤ/8)12yes—
525C2×C3D3×#13712yes—
526D3—38no—
527D3—44no—
528D3—64no—
529D3—64no—
530D3—122no—
531C22—21no—
532C22—21no—
533C22—64no—
534C22—92no—
535C22—92no—
536C22—92no—
537C22—92no—
538C22—122no—
539C22—122no—
540C22—188no—
541C22—181no—
542C22—181no—
543C22—368no—
544C22#6392112yes—
545C22C2×#380211yescharacteristic
546C4—64no—
547C4—92no—
548C4—92no—
549C4—124no—
550C4#6392112yes—
551C4C2×C4×D3211yescharacteristic
552C4C2×#381111yescharacteristic
553C3—21no—
554C3D3×#41712yescomplemented
555C2—22no—
556C2—94no—
557C2—124no—
558C2—182no—
559C2#1059471611yescharacteristic
560C2#1059471711yescharacteristic
561C2C2×#6392111yescharacteristic
subgroupG/H
centerC22C2×#3802
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC2×#64306C2
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32C2×#417
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×M16×C3⋊D3C2semidirect
3. C2×#63900C2semidirect
4. C3×#5133C2semidirect
5. #10591087C2semidirect
6. #10590957C2semidirect
7. #10590940C2semidirect
8. #10590672C2semidirect
16. #64306C4semidirect
22. C2×C32×M16C22semidirect
23. C2×#3748C22semidirect
25. C2×#3743C22semidirect
27. C2×C3×C4⋊Dic3C22semidirect
32. #63900C22semidirect
33. C3×#821C22semidirect
34. C3×#816C22semidirect
35. #63565C22semidirect
36. #63562C22semidirect
43. #5133D3semidirect
62. C3×#235C2×C4semidirect
77. #3802C2×C4semidirect
81. #3797C2×C4semidirect
83. #3796C2×C4semidirect
111. C2×C3×M16C2×D3semidirect
113. C2×C4⋊Dic3C2×D3semidirect
131. #821C2×D3semidirect
132. #816C2×D3semidirect
163. C3×D12C22×C4semidirect
166. C3×Dic6C22×C4semidirect
215. #235C4×D3semidirect
294. C2×M16D32semidirect
355. D12C2×C4×D3semidirect
375. Dic6C2×C4×D3semidirect
385. C3⋊D3#417semidirect
475. C32C2×#417semidirect
554. C3D3×#417semidirect

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×#639002
C3×#51332
#105910872
#105909572
#105909402
#105906722
D3×#4173