Finite Group Databasebeta

← #11859374

Subgroups — #11859374

Order 1152.

1105 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63805C211yesmaximal, characteristic, complemented
2C2×D32×C8C211yesmaximal, characteristic, complemented
3#10594006C211yesmaximal, characteristic
4#10592407C211yesmaximal, characteristic, complemented
5C3×#4706C212yesmaximal, complemented
6#10590959C211yesmaximal, characteristic, complemented
7#10590937C211yesmaximal, characteristic, complemented
8#10590722C212yesmaximal, complemented
9#10590718C212yesmaximal, complemented
10#10590332C211yesmaximal, characteristic, complemented
11#10590329C212yesmaximal, complemented
12#79478—32nomaximal
13C2×C4×D32C2211yescharacteristic
14C2×#3798C2211yescharacteristic
15C2×#3743C2211yescharacteristic
16C2×C8×C3⋊D3C2211yescharacteristic
17#64081C2211yescharacteristic
18C2×C3×ΓL(1,𝔽25)C2212yescomplemented
19C2×C3×D3×C8C2212yes—
20C3×C4×D12C2212yes—
21#63922C412yes—
22C4×#625C2212yes—
23#63899C412yes—
24#63885C412yes—
25#63854C412yes—
26C2×#3712C2211yescharacteristic
27C2×#3710C2211yescharacteristic
28C2×D3×C3⋊C8C2212yes—
29C2×D3×C3⋊C8C2212yescomplemented
30#63805—24no—
31D32×C8—24no—
32C32×#97C2211yescharacteristic, complemented
33#63642C2211yescharacteristic, complemented
34C8×C3⋊Dic3C2211yescharacteristic, complemented
35C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
36C3×(C2×D3)⋊C8C2212yes—
37C3×(C2×D3)⋊C8C2212yescomplemented
38C3×C4⋊(C3⋊C8)C2212yescomplemented
39#63572C2212yescomplemented
40(C2×D3)⋊(C3⋊C8)C2212yes—
41(C2×D3)⋊(C3⋊C8)C2212yescomplemented
42C2×#907—32no—
43C22×D3×C8—32no—
44#5547—32no—
45C3×#435—32no—
46#5127—32no—
47#5111—32no—
48D4×C3⋊C8—32no—
49#4839—32no—
50#4834—32no—
51#4727—32no—
52#4726—32no—
53#67⋊C8—32no—
54#67⋊C8—32no—
55#4708—32no—
56#4708—61no—
57#4706D312yescomplemented
58C22×D32C2×C411yescharacteristic
59C2×C4×C3⋊D3C2311yescharacteristic
60C2×C3×D12C2×C412yes—
61C2×C3×C4×D3C2312yes—
62C2×C3×C4×D3C2312yes—
63C2×#627C2×C411yescharacteristic
64C2×#626C2×C412yes—
65C2×#625C2×C411yescharacteristic
66C2×#625C2×C412yes—
67C2×#624C2×C411yescharacteristic
68C2×D3×Dic3C2×C412yes—
69C4×D32—22no—
70C4×D32—22no—
71#3798—22no—
72#3798—22no—
73C2×C32×C8C2311yescharacteristic
74C2×C32×C8C2311yescharacteristic
75C32×C42C2311yescharacteristic
76#3752C2×C412yes—
77#3750C2×C412yes—
78C4×C3⋊Dic3C2311yescharacteristic
79C2×C3⋊(C3⋊C8)C2311yescharacteristic
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81#3743—22no—
82C8×C3⋊D3D414yescomplemented
83C3×(C2×D3)⋊C4C2×C412yes—
84C3×(C2×D3)⋊C4C2×C412yes—
85C3×C4⋊Dic3C2×C412yes—
86C2×C3×C3⋊C8C2312yes—
87C2×C3×C3⋊C8C2312yes—
88C3×ΓL(1,𝔽25)—24no—
89C3×D3×C8—24no—
90#3724C2×C412yes—
91(C2×D3)⋊Dic3C2×C412yes—
92(C2×D3)⋊Dic3C2×C412yes—
93#3712—22no—
94#3710—22no—
95D3×C3⋊C8—24no—
96D3×C3⋊C8—24no—
97#2929—91noSylow
98C2×#235—32no—
99C22×C4×D3—32no—
100C2×C3×M16—32no—
101C22×C3×C8—32no—
102C3×C4×D4—32no—
103#939—32no—
104#937—32no—
105C4×#67—32no—
106C4×#67—32no—
107C22×C3⋊C8—32no—
108C22×C3⋊C8—32no—
109#907—68no—
110C2×ΓL(1,𝔽25)—32no—
111C2×ΓL(1,𝔽25)—32no—
112C2×ΓL(1,𝔽25)—61no—
113C2×ΓL(1,𝔽25)C2×D312yescomplemented
114C2×D3×C8—32no—
115C2×D3×C8—32no—
116C2×D3×C8—32no—
117C2×D3×C8—32no—
118C2×D3×C8—61no—
119C2×D3×C8—68no—
120C2×D3×C8C2×D312yes—
121#896—32no—
122#894—32no—
123#884—32no—
124#883—32no—
125#882—32no—
126#878—32no—
127C4×D12C2×D312yes—
128#872—32no—
129#872—61no—
130C3×C4⋊C8—32no—
131C3×C22⋊C8—32no—
132C3×C22⋊C8—32no—
133C3×#97—21no—
134C3×#97C2×D312yescomplemented
135#830—32no—
136#830—32no—
137(C2×D3)⋊C8—32no—
138(C2×D3)⋊C8—32no—
139(C2×D3)⋊C8C2×D312yes—
140(C2×D3)⋊C8C2×D312yescomplemented
141#815—32no—
142#815—61no—
143Dic3⋊C8—32no—
144Dic3⋊C8—32no—
145C8×Dic3—32no—
146C8×Dic3—61no—
147C4⋊(C3⋊C8)C2×D312yescomplemented
148C4×C3⋊C8—32no—
149C4×C3⋊C8—61no—
150C22×C3⋊D3C22×C411yescharacteristic
151C22×C3×D3C22×C412yes—
152C22×C3×D3C22×C412yes—
153C2×D32—22no—
154C2×D32—24no—
155C2×C32×C4C22×C412yes—
156C2×C32×C4C2411yescharacteristic
157C2×C3⋊Dic3C22×C412yes—
158C2×C3⋊Dic3C22×C411yescharacteristic
159C4×C3⋊D3C2×D412yes—
160C4×C3⋊D3#4112yes—
161C2×C3×Dic3C22×C412yes—
162C2×C3×Dic3C22×C412yes—
163C3×D12—24no—
164C3×C4×D3—22no—
165C3×C4×D3—22no—
166C3×C4×D3—22no—
167C3×C4×D3—22no—
168#627—22no—
169#626—24no—
170#625—24no—
171#625—22no—
172#624—22no—
173D3×Dic3—24no—
174C32×C8—21no—
175C32×C8C2×D412yes—
176C3⋊(C3⋊C8)—21no—
177C3⋊(C3⋊C8)C2×D412yes—
178C3×C3⋊C8—22no—
179C3×C3⋊C8—22no—
180C2×#131—91no—
181C23×C8—91no—
182#525—91no—
183#435—32no—
184#435—92no—
185C8×D4—92no—
186C8×D4—92no—
187#424—91no—
188#408—91no—
189#407—91no—
190#405—91no—
191C23×D3—32no—
192C2×C3×D4—32no—
193C22×C3×C4—32no—
194C22×C3×C4—32no—
195C2×#67—32no—
196C2×#67—32no—
197C2×#67—32no—
198C2×#67—32no—
199C22×Dic3—32no—
200#235—64no—
201#235—64no—
202C2×D12—32no—
203C2×D12C4×D312yes—
204C2×C4×D3—32no—
205C2×C4×D3—32no—
206C2×C4×D3—32no—
207C2×C4×D3—61no—
208C2×C4×D3—64no—
209C2×C4×D3—64no—
210C2×C4×D3C22×D312yes—
211C2×C4×D3C22×D312yes—
212C2×Dic6—32no—
213C3×M16—64no—
214C2×C3×C8—21no—
215C2×C3×C8—21no—
216C2×C3×C8—32no—
217C2×C3×C8—32no—
218C2×C3×C8—64no—
219C2×C3×C8C22×D312yes—
220C2×C3×C8C22×D312yes—
221C3×C4⋊C4—32no—
222C3×C22⋊C4—32no—
223C3×C22⋊C4—32no—
224C3×C42—21no—
225C3×C42C22×D312yes—
226#217—32no—
227#217—32no—
228(C2×D3)⋊C4—32no—
229(C2×D3)⋊C4—32no—
230(C2×D3)⋊C4—32no—
231(C2×D3)⋊C4—32no—
232(C2×D3)⋊C4—62no—
233(C2×D3)⋊C4C4×D312yes—
234(C2×D3)⋊C4C4×D312yes—
235C4⋊Dic3C4×D312yes—
236Dic3⋊C4—32no—
237Dic3⋊C4—32no—
238Dic3⋊C4—32no—
239Dic3⋊C4—32no—
240Dic3⋊C4—62no—
241C4×Dic3—32no—
242C4×Dic3—61no—
243C2×C3⋊C8—32no—
244C2×C3⋊C8—32no—
245C2×C3⋊C8—61no—
246C2×C3⋊C8—61no—
247C2×C3⋊C8—64no—
248C2×C3⋊C8—64no—
249C2×C3⋊C8C22×D312yes—
250C2×C3⋊C8C22×D312yes—
251ΓL(1,𝔽25)—24no—
252ΓL(1,𝔽25)—64no—
253ΓL(1,𝔽25)—64no—
254ΓL(1,𝔽25)—64no—
255D3×C8—24no—
256D3×C8—38no—
257D3×C8—64no—
258D3×C8—64no—
259D3×C8—64no—
260D3×C8—64no—
261C22×C32C23×C411yescharacteristic
262C2×C3⋊D3—22no—
263C2×C3⋊D3C4×D412yes—
264C2×C3×D3—22no—
265C2×C3×D3—22no—
266C2×C3×D3—22no—
267C2×C3×D3—22no—
268C2×C3×D3—22no—
269C2×C3×D3#13114yescomplemented
270D32—28no—
271C32×C4—22no—
272C32×C4C22×D411yescharacteristic
273C32×C4C2×#4111yescharacteristic
274C3⋊Dic3—22no—
275C3⋊Dic3C4×D412yes—
276C3×Dic3—22no—
277C3×Dic3—22no—
278C2×#41—91no—
279C23×C4—91no—
280#131—184no—
281C2×M16—32no—
282C2×M16—91no—
283C2×M16—91no—
284C22×C8—32no—
285C22×C8—91no—
286C22×C8—92no—
287C22×C8—92no—
288C22×C8—91no—
289C22×C8—184no—
290#123—92no—
291C22⋊Q8—92no—
292#121—92no—
293#120—92no—
294C4×D4—32no—
295C4×D4—92no—
296#117—91no—
297C4⋊C8—32no—
298C4⋊C8—92no—
299C22⋊C8—32no—
300C22⋊C8—32no—
301C22⋊C8—92no—
302C22⋊C8—92no—
303#97—91no—
304#97D3211yescharacteristic, complemented
305C4×C8—91no—
306C4×C8—91no—
307C23×C3—32no—
308C23×C3—32no—
309C22×D3—32no—
310C22×D3—61no—
311C22×D3—64no—
312C22×D3—64no—
313C22×D3—64no—
314C22×D3C2×C4×D312yes—
315C22×D3C2×C4×D312yes—
316C3×D4—64no—
317C2×C3×C4—21no—
318C2×C3×C4—22no—
319C2×C3×C4—32no—
320C2×C3×C4—32no—
321C2×C3×C4—62no—
322C2×C3×C4—62no—
323C2×C3×C4—62no—
324C2×C3×C4—62no—
325C2×C3×C4C2×C4×D312yes—
326C2×C3×C4C2×C4×D312yes—
327C2×C3×C4C23×D312yes—
328#67—64no—
329#67—64no—
330#67—64no—
331#67—64no—
332C2×Dic3—32no—
333C2×Dic3—32no—
334C2×Dic3—32no—
335C2×Dic3—61no—
336C2×Dic3—62no—
337C2×Dic3—64no—
338C2×Dic3C2×C4×D312yes—
339C2×Dic3C2×C4×D312yes—
340D12—24no—
341D12—64no—
342C4×D3—22no—
343C4×D3—22no—
344C4×D3—22no—
345C4×D3—22no—
346C4×D3—34no—
347C4×D3—34no—
348C4×D3—62no—
349C4×D3—62no—
350C4×D3—64no—
351C4×D3—64no—
352Dic6—64no—
353C3×C8—22no—
354C3×C8—22no—
355C3×C8—22no—
356C3×C8—62no—
357C3×C8—62no—
358C3×C8D3×D414yes—
359C3⋊C8—22no—
360C3⋊C8—22no—
361C3⋊C8—34no—
362C3⋊C8—62no—
363C3⋊C8—62no—
364C3⋊C8—62no—
365C2×C32C2×C4×D411yescharacteristic
366C2×C32C2×#13112yes—
367C3⋊D3—22no—
368C3×D3—24no—
369C3×D3—42no—
370C24—91no—
371#41—182no—
372#41—182no—
373C2×Q8—91no—
374C2×D4—32no—
375C2×D4—92no—
376C2×D4—92no—
377C2×D4—91no—
378C22×C4—32no—
379C22×C4—32no—
380C22×C4—91no—
381C22×C4—92no—
382C22×C4—91no—
383C22×C4—182no—
384C22×C4—182no—
385M16—64no—
386M16—182no—
387M16—182no—
388C2×C8—32no—
389C2×C8—32no—
390C2×C8—64no—
391C2×C8—91no—
392C2×C8—94no—
393C2×C8—91no—
394C2×C8—182no—
395C2×C8—184no—
396C2×C8—184no—
397C2×C8C2×D3211yescharacteristic
398C2×C8C2×D3211yescharacteristic
399C4⋊C4—32no—
400C4⋊C4—92no—
401C4⋊C4—92no—
402C22⋊C4—32no—
403C22⋊C4—32no—
404C22⋊C4—92no—
405C22⋊C4—92no—
406C22⋊C4—92no—
407C42—91no—
408C42C2×D3211yescharacteristic
409C22×C3—21no—
410C22×C3—34no—
411C22×C3—62no—
412C22×C3—62no—
413C22×C3—62no—
414C22×C3—62no—
415C22×C3—62no—
416C22×C3C22×C4×D312yes—
417C2×D3—22no—
418C2×D3—22no—
419C2×D3—22no—
420C2×D3—22no—
421C2×D3—22no—
422C2×D3—34no—
423C2×D3—62no—
424C2×D3—616no—
425C2×D3—62no—
426C2×D3—62no—
427C2×D3—122no—
428C2×D3#90714yescomplemented
429C3×C4—22no—
430C3×C4—22no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—42no—
434C3×C4—62no—
435C3×C4—62no—
436C3×C4C2×D3×D412yes—
437C3×C4D3×#4112yes—
438Dic3—22no—
439Dic3—22no—
440Dic3—34no—
441Dic3—62no—
442Dic3—62no—
443Dic3—62no—
444Dic3—122no—
445C32#292911yescharacteristic, complemented, Sylow
446C23—32no—
447C23—32no—
448C23—91no—
449C23—184no—
450C23—182no—
451Q8—182no—
452D4—64no—
453D4—184no—
454D4—182no—
455D4—184no—
456C2×C4—32no—
457C2×C4—32no—
458C2×C4—62no—
459C2×C4—62no—
460C2×C4—62no—
461C2×C4—62no—
462C2×C4—91no—
463C2×C4—92no—
464C2×C4—92no—
465C2×C4—92no—
466C2×C4—182no—
467C2×C4—184no—
468C2×C4C4×D3212yes—
469C2×C4C22×D3211yescharacteristic
470C8—21no—
471C8—62no—
472C8—62no—
473C8—92no—
474C8—181no—
475C8#380212yes—
476C2×C3—22no—
477C2×C3—21no—
478C2×C3—64no—
479C2×C3—122no—
480C2×C3C4×D3×D412yes—
481C2×C3C2×#90712yes—
482C2×C3D3×#13112yes—
483D3—24no—
484D3—42no—
485D3—64no—
486D3—122no—
487C22—34no—
488C22—62no—
489C22—62no—
490C22—62no—
491C22—62no—
492C22—62no—
493C22—92no—
494C22—188no—
495C22—182no—
496C22C2×C4×D3211yescharacteristic
497C4—22no—
498C4—62no—
499C4—62no—
500C4—92no—
501C4—182no—
502C4C2×#380211yescharacteristic
503C4#6430611yescharacteristic
504C3—21no—
505C3#7947812yescomplemented
506C2—64no—
507C2—122no—
508C2—182no—
509C2C4×#380211yescharacteristic
510C2D3×#90712yes—
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×#97C22
prime radical#10594006C2
cosocleC2×C32×C4C24
hypercenter#97D32
hypocenterC32#2929
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #97

Complements

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

NH ≅ G/Ntype
1. C2×#63805C2semidirect
2. C2×D32×C8C2semidirect
4. #10592407C2semidirect
5. C3×#4706C2semidirect
6. #10590959C2semidirect
7. #10590937C2semidirect
8. #10590722C2semidirect
9. #10590718C2semidirect
10. #10590332C2semidirect
11. #10590329C2semidirect
18. C2×C3×ΓL(1,𝔽25)C22semidirect
29. C2×D3×C3⋊C8C22semidirect
32. C32×#97C22semidirect
33. #63642C22semidirect
34. C8×C3⋊Dic3C22semidirect
35. C4×C3⋊(C3⋊C8)C22semidirect
37. C3×(C2×D3)⋊C8C22semidirect
38. C3×C4⋊(C3⋊C8)C22semidirect
39. #63572C22semidirect
41. (C2×D3)⋊(C3⋊C8)C22semidirect
57. #4706D3semidirect
82. C8×C3⋊D3D4semidirect
113. C2×ΓL(1,𝔽25)C2×D3semidirect
134. C3×#97C2×D3semidirect
140. (C2×D3)⋊C8C2×D3semidirect
147. C4⋊(C3⋊C8)C2×D3semidirect
269. C2×C3×D3#131semidirect
304. #97D32semidirect
428. C2×D3#907semidirect
445. C32#2929semidirect
505. C3#79478semidirect

Maximal subgroups

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

subgroupindex
C2×#638052
C2×D32×C82
#105940062
#105924072
C3×#47062
#105909592
#105909372
#105907222
#105907182
#105903322
#105903292
#794783