Finite Group Databasebeta

← #11858314

Subgroups — #11858314

Order 1152.

1031 conjugacy classes of subgroups.

The subgroup lattice has 483 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×ΓL(1,𝔽25)C212yesmaximal
2#10593992C211yesmaximal, characteristic
3#10592536C211yesmaximal, characteristic, complemented
4C3×#4839C212yesmaximal, complemented
5#10590695C212yesmaximal, complemented
6#10590694C212yesmaximal, complemented
7#10590666C212yesmaximal, complemented
8#10590340C211yesmaximal, characteristic, complemented
9#10590324C212yesmaximal, complemented
10#79080—32nomaximal
11C2×C4×D32C2211yescharacteristic
12C2×#3743C2212yes—
13C42×C3⋊D3C2211yescharacteristic
14C2×C3×ΓL(1,𝔽25)C2212yes—
15C2×C3×D3×C8C2212yes—
16C3×#872C2212yes—
17#63921C411yescharacteristic
18#63921C411yescharacteristic
19#63883C411yescharacteristic
20#63883C411yescharacteristic
21C4×#624C2211yescharacteristic
22#63878C412yes—
23#63878C412yes—
24#63855C2212yes—
25C2×#3712C2212yes—
26C2×#3711C2212yes—
27C2×D3×C3⋊C8C2212yes—
28D3×ΓL(1,𝔽25)—28no—
29C32×C4⋊C8C2211yescharacteristic, complemented
30#63641C2212yescomplemented
31C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
32C3×Dic3⋊C8C2212yescomplemented
33C3×Dic3⋊C8C2212yescomplemented
34C3×C4⋊(C3⋊C8)C2212yescomplemented
35#63572C2211yescharacteristic, complemented
36#63572C2211yescharacteristic, complemented
37Dic3⋊(C3⋊C8)C2212yescomplemented
38Dic3⋊(C3⋊C8)C2212yescomplemented
39C2×D3×M16—32no—
40C22×ΓL(1,𝔽25)—32no—
41D3×#117—32no—
42C3×#424—32no—
43#5119—32no—
44#5102—32no—
45#4999—32no—
46#4839—32no—
47#4839—32no—
48#4839—32no—
49#4839D312yescomplemented
50#4837—32no—
51#4837—32no—
52#4837—32no—
53#4837—32no—
54#4837—61no—
55C22×D32C2×C411yescharacteristic
56C2×C4×C3⋊D3C2×C411yescharacteristic
57C2×C4×C3⋊D3C2×C411yescharacteristic
58C2×C4×C3⋊D3C2311yescharacteristic
59C2×C3×C4×D3C2312yes—
60C2×#624C2×C411yescharacteristic
61C2×#624C2×C411yescharacteristic
62C2×#624C2×C411yescharacteristic
63C2×D3×Dic3C2×C412yes—
64C4×D32D414yes—
65C4×D32Q814yes—
66C2×C32×C8C2312yes—
67C32×C42C2311yescharacteristic
68C4×C3⋊Dic3C2×C411yescharacteristic
69C4×C3⋊Dic3C2×C411yescharacteristic
70C4×C3⋊Dic3C2311yescharacteristic
71C2×C3⋊(C3⋊C8)C2312yes—
72#3743—24no—
73C3×(C2×D3)⋊C4C2×C412yes—
74C3×(C2×D3)⋊C4C2×C412yes—
75C3×Dic3⋊C4C2×C412yes—
76C3×Dic3⋊C4C2×C412yes—
77C3×C4×Dic3C2312yes—
78C2×C3×C3⋊C8C2312yes—
79C2×C3×C3⋊C8C2312yes—
80C3×ΓL(1,𝔽25)—24no—
81C3×D3×C8—24no—
82Dic3⋊Dic3C2×C412yes—
83Dic3⋊Dic3C2×C412yes—
84(C2×D3)⋊Dic3C2×C412yes—
85(C2×D3)⋊Dic3C2×C412yes—
86Dic32C2×C412yes—
87#3712—24no—
88#3711—24no—
89D3×C3⋊C8—24no—
90#2905—91noSylow
91C22×C4×D3—32no—
92C2×C3×M16—32no—
93C22×C3×C8—32no—
94C3×#117—32no—
95#926—32no—
96C2×#208—32no—
97C22×C3⋊C8—32no—
98D3×M16—68no—
99C2×ΓL(1,𝔽25)—32no—
100C2×ΓL(1,𝔽25)—32no—
101C2×ΓL(1,𝔽25)—32no—
102C2×ΓL(1,𝔽25)—32no—
103C2×ΓL(1,𝔽25)—32no—
104C2×ΓL(1,𝔽25)—62no—
105C2×ΓL(1,𝔽25)—68no—
106C2×ΓL(1,𝔽25)C2×D312yes—
107C2×D3×C8—32no—
108C2×D3×C8C2×D312yes—
109#892—32no—
110#892—32no—
111D3×C4⋊C4—32no—
112D3×C4⋊C4—32no—
113D3×C22⋊C4—32no—
114D3×C22⋊C4—32no—
115#877—32no—
116#877—32no—
117#872—32no—
118#872C2×D312yes—
119C42×D3—32no—
120C42×D3—32no—
121C42×D3—61no—
122C3×C4⋊C8—21no—
123C3×C4⋊C8—32no—
124C3×C4⋊C8—32no—
125C3×C4⋊C8—32no—
126C3×C4⋊C8C2×D312yescomplemented
127Dic3⋊C8—32no—
128Dic3⋊C8—32no—
129Dic3⋊C8—32no—
130Dic3⋊C8—32no—
131Dic3⋊C8—32no—
132Dic3⋊C8—32no—
133Dic3⋊C8—62no—
134Dic3⋊C8C2×D312yescomplemented
135Dic3⋊C8C2×D312yescomplemented
136C4⋊(C3⋊C8)—32no—
137C4⋊(C3⋊C8)—32no—
138C4⋊(C3⋊C8)—32no—
139C4⋊(C3⋊C8)—61no—
140C4⋊(C3⋊C8)C2×D312yescomplemented
141C22×C3⋊D3C22×C411yescharacteristic
142C22×C3×D3C22×C412yes—
143C2×D32—41no—
144C2×D32—41no—
145C2×D32C4⋊C414yes—
146C2×C32×C4C22×C411yescharacteristic
147C2×C32×C4C22×C411yescharacteristic
148C2×C32×C4C2411yescharacteristic
149C2×C3⋊Dic3C22×C411yescharacteristic
150C2×C3⋊Dic3C22×C411yescharacteristic
151C2×C3⋊Dic3C22×C411yescharacteristic
152C4×C3⋊D3—41no—
153C4×C3⋊D3—41no—
154C4×C3⋊D3C2×D412yes—
155C4×C3⋊D3C2×Q812yes—
156C2×C3×Dic3C22×C412yes—
157C2×C3×Dic3C22×C412yes—
158C2×C3×Dic3C22×C412yes—
159C3×C4×D3C2×D414yes—
160C3×C4×D3C2×Q814yes—
161#624—41no—
162#624—41no—
163#624C4⋊C414yes—
164D3×Dic3C4⋊C418yes—
165C32×C8—22no—
166C3⋊(C3⋊C8)—22no—
167C3×C3⋊C8—22no—
168C3×C3⋊C8—22no—
169C22×M16—92no—
170C2×#117—91no—
171#424—32no—
172#424—92no—
173#424—92no—
174#424—92no—
175#423—92no—
176#423—91no—
177#423—91no—
178C23×D3—32no—
179C22×C3×C4—32no—
180C22×Dic3—32no—
181C2×C4×D3—32no—
182C2×C4×D3—32no—
183C2×C4×D3—32no—
184C2×C4×D3—38no—
185C2×C4×D3—38no—
186C2×C4×D3—32no—
187C2×C4×D3—32no—
188C2×C4×D3—32no—
189C2×C4×D3—32no—
190C2×C4×D3—61no—
191C2×C4×D3—61no—
192C2×C4×D3—61no—
193C2×C4×D3C22×D312yes—
194C3×M16—64no—
195C2×C3×C8—22no—
196C2×C3×C8—32no—
197C2×C3×C8—32no—
198C2×C3×C8—64no—
199C2×C3×C8C22×D312yes—
200C2×C3×C8C22×D312yes—
201C3×C4⋊C4—32no—
202C3×C4⋊C4—32no—
203C3×C22⋊C4—32no—
204C3×C22⋊C4—32no—
205C3×C42—21no—
206C3×C42—32no—
207C3×C42C22×D312yes—
208#217—32no—
209#217—32no—
210(C2×D3)⋊C4—32no—
211(C2×D3)⋊C4—32no—
212(C2×D3)⋊C4C4×D312yes—
213(C2×D3)⋊C4C4×D312yes—
214C4⋊Dic3—32no—
215C4⋊Dic3—32no—
216Dic3⋊C4—32no—
217Dic3⋊C4—32no—
218Dic3⋊C4C4×D312yes—
219Dic3⋊C4C4×D312yes—
220C4×Dic3—32no—
221C4×Dic3—32no—
222C4×Dic3—32no—
223C4×Dic3—32no—
224C4×Dic3—32no—
225C4×Dic3—61no—
226C4×Dic3—61no—
227C4×Dic3—61no—
228C4×Dic3C22×D312yes—
229#208—64no—
230C2×C3⋊C8—32no—
231C2×C3⋊C8—32no—
232C2×C3⋊C8—62no—
233C2×C3⋊C8—64no—
234C2×C3⋊C8C22×D312yes—
235C2×C3⋊C8C22×D312yes—
236ΓL(1,𝔽25)—24no—
237ΓL(1,𝔽25)—64no—
238ΓL(1,𝔽25)—64no—
239ΓL(1,𝔽25)—64no—
240ΓL(1,𝔽25)—64no—
241ΓL(1,𝔽25)—64no—
242ΓL(1,𝔽25)—124no—
243D3×C8—24no—
244D3×C8—64no—
245C22×C32C23×C411yescharacteristic
246C2×C3⋊D3—21no—
247C2×C3⋊D3—21no—
248C2×C3⋊D3C2×C4⋊C412yes—
249C2×C3×D3—22no—
250C2×C3×D3—22no—
251C2×C3×D3C2×C4⋊C414yes—
252D32—44no—
253C32×C4—21no—
254C32×C4—21no—
255C32×C4C22×D411yescharacteristic
256C32×C4C22×Q811yescharacteristic
257C3⋊Dic3—21no—
258C3⋊Dic3—21no—
259C3⋊Dic3C2×C4⋊C412yes—
260C3×Dic3—22no—
261C3×Dic3—22no—
262C3×Dic3C2×C4⋊C414yes—
263C23×C4—91no—
264C2×M16—32no—
265C2×M16—92no—
266C2×M16—92no—
267C2×M16—92no—
268C2×M16—188no—
269C22×C8—32no—
270C22×C8—92no—
271#117—32no—
272#117—92no—
273#117—92no—
274#117—92no—
275C2×C4⋊C4—91no—
276C2×C4⋊C4—91no—
277C2×C22⋊C4—91no—
278C2×C22⋊C4—91no—
279C2×C42—91no—
280C2×C42—91no—
281C4⋊C8—32no—
282C4⋊C8—32no—
283C4⋊C8—32no—
284C4⋊C8—92no—
285C4⋊C8—92no—
286C4⋊C8—91no—
287C4⋊C8—91no—
288C4⋊C8—92no—
289C4⋊C8—91no—
290C4⋊C8D3211yescharacteristic, complemented
291C23×C3—32no—
292C22×D3—32no—
293C22×D3—38no—
294C22×D3—61no—
295C22×D3—122no—
296C22×D3—122no—
297C22×D3C2×C4×D312yes—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—32no—
302C2×C3×C4—34no—
303C2×C3×C4—34no—
304C2×C3×C4—32no—
305C2×C3×C4—32no—
306C2×C3×C4C2×C4×D312yes—
307C2×C3×C4C2×C4×D312yes—
308C2×C3×C4C23×D312yes—
309C2×Dic3—32no—
310C2×Dic3—38no—
311C2×Dic3—32no—
312C2×Dic3—32no—
313C2×Dic3—61no—
314C2×Dic3—61no—
315C2×Dic3—61no—
316C2×Dic3C2×C4×D312yes—
317C2×Dic3C2×C4×D312yes—
318C2×Dic3C2×C4×D312yes—
319C4×D3—38no—
320C4×D3—34no—
321C4×D3—34no—
322C4×D3—38no—
323C4×D3—62no—
324C4×D3—62no—
325C4×D3—122no—
326C4×D3—122no—
327C4×D3—122no—
328C4×D3—122no—
329C4×D3—122no—
330C4×D3—122no—
331C4×D3D3×D414yes—
332C4×D3D3×Q814yes—
333C3×C8—22no—
334C3×C8—22no—
335C3×C8—42no—
336C3×C8—62no—
337C3×C8—62no—
338C3⋊C8—22no—
339C3⋊C8—22no—
340C3⋊C8—62no—
341C3⋊C8—62no—
342C3⋊C8—122no—
343C2×C32C22×C4⋊C411yescharacteristic
344C2×C32#56811yescharacteristic
345C2×C32#56811yescharacteristic
346C3⋊D3—22no—
347C3×D3—24no—
348C24—91no—
349C22×C4—32no—
350C22×C4—91no—
351C22×C4—94no—
352C22×C4—94no—
353C22×C4—91no—
354C22×C4—91no—
355C22×C4—92no—
356C22×C4—91no—
357C22×C4—91no—
358C22×C4—91no—
359M16—64no—
360M16—184no—
361M16—184no—
362M16—184no—
363C2×C8—32no—
364C2×C8—32no—
365C2×C8—64no—
366C2×C8—92no—
367C2×C8—184no—
368C2×C8C2×D3212yes—
369C4⋊C4—32no—
370C4⋊C4—32no—
371C4⋊C4—92no—
372C4⋊C4—92no—
373C22⋊C4—32no—
374C22⋊C4—32no—
375C22⋊C4—92no—
376C22⋊C4—92no—
377C42—32no—
378C42—92no—
379C42—91no—
380C42—91no—
381C42—91no—
382C42C2×D3211yescharacteristic
383C22×C3—21no—
384C22×C3—34no—
385C22×C3—62no—
386C22×C3—62no—
387C22×C3C22×C4×D312yes—
388C2×D3—22no—
389C2×D3—22no—
390C2×D3—34no—
391C2×D3—62no—
392C2×D3—62no—
393C2×D3—62no—
394C2×D3—121no—
395C2×D3—121no—
396C2×D3—128no—
397C2×D3D3×C4⋊C414yes—
398C3×C4—22no—
399C3×C4—22no—
400C3×C4—22no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—34no—
404C3×C4—41no—
405C3×C4—62no—
406C3×C4—62no—
407C3×C4C2×D3×D412yes—
408C3×C4C2×D3×Q812yes—
409Dic3—22no—
410Dic3—22no—
411Dic3—34no—
412Dic3—62no—
413Dic3—62no—
414Dic3—62no—
415Dic3—62no—
416Dic3—121no—
417Dic3D3×C4⋊C414yes—
418C32#290511yescharacteristic, complemented, Sylow
419C23—32no—
420C23—94no—
421C23—91no—
422C23—361no—
423C23—361no—
424C2×C4—32no—
425C2×C4—34no—
426C2×C4—34no—
427C2×C4—32no—
428C2×C4—32no—
429C2×C4—94no—
430C2×C4—98no—
431C2×C4—91no—
432C2×C4—92no—
433C2×C4—92no—
434C2×C4—91no—
435C2×C4—91no—
436C2×C4—361no—
437C2×C4—361no—
438C2×C4—361no—
439C2×C4—361no—
440C2×C4C4×D3211yescharacteristic
441C2×C4C4×D3211yescharacteristic
442C2×C4C22×D3211yescharacteristic
443C8—22no—
444C8—62no—
445C8—62no—
446C8—182no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—64no—
451C2×C3C2×D3×C4⋊C412yes—
452C2×C3#575012yes—
453C2×C3#575012yes—
454D3—24no—
455D3—64no—
456D3—122no—
457C22—34no—
458C22—62no—
459C22—62no—
460C22—92no—
461C22—181no—
462C22—181no—
463C22—364no—
464C22C2×C4×D3211yescharacteristic
465C4—21no—
466C4—21no—
467C4—34no—
468C4—62no—
469C4—62no—
470C4—92no—
471C4—181no—
472C4—181no—
473C4D32×D411yescharacteristic
474C4D32×Q811yescharacteristic
475C3—21no—
476C3#7908012yescomplemented
477C2—64no—
478C2—182no—
479C2D32×C4⋊C411yescharacteristic
480C2#1059467011yescharacteristic
481C2#1059470811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×C4⋊C8C22
prime radicalC22×D32C2×C4
cosocleC2×C32×C4C24
hypercenterC4⋊C8D32
hypocenterC32#2905
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
3. #10592536C2semidirect
4. C3×#4839C2semidirect
5. #10590695C2semidirect
6. #10590694C2semidirect
7. #10590666C2semidirect
8. #10590340C2semidirect
9. #10590324C2semidirect
29. C32×C4⋊C8C22semidirect
30. #63641C22semidirect
31. C4⋊(C3⋊(C3⋊C8))C22semidirect
32. C3×Dic3⋊C8C22semidirect
33. C3×Dic3⋊C8C22semidirect
34. C3×C4⋊(C3⋊C8)C22semidirect
35. #63572C22semidirect
36. #63572C22semidirect
37. Dic3⋊(C3⋊C8)C22semidirect
38. Dic3⋊(C3⋊C8)C22semidirect
49. #4839D3semidirect
126. C3×C4⋊C8C2×D3semidirect
134. Dic3⋊C8C2×D3semidirect
135. Dic3⋊C8C2×D3semidirect
140. C4⋊(C3⋊C8)C2×D3semidirect
290. C4⋊C8D32semidirect
418. C32#2905semidirect
476. C3#79080semidirect

Maximal subgroups

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

subgroupindex
C2×D3×ΓL(1,𝔽25)2
#105939922
#105925362
C3×#48392
#105906952
#105906942
#105906662
#105903402
#105903242
#790803