Finite Group Databasebeta

← #11858508

Subgroups — #11858508

Order 1152.

1041 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63791C211yesmaximal, characteristic
2D3×#892C212yesmaximal
3#10592559C211yesmaximal, characteristic, complemented
4C3×#4861C212yesmaximal, complemented
5#10590714C211yesmaximal, characteristic, complemented
6#10590683C212yesmaximal, complemented
7#10590581C212yesmaximal, complemented
8#10590574C212yesmaximal, complemented
9#10590436C212yesmaximal, complemented
10#79208—32nomaximal
11C2×C4×D32C2211yescharacteristic
12C2×C8×C3⋊D3C2211yescharacteristic
13#64101C2212yes—
14C2×C3×ΓL(1,𝔽25)C2212yes—
15C3×#892C2212yes—
16C3×D3×C4⋊C4C2212yes—
17D3×(C2×D3)⋊C4—22no—
18D3×C4⋊Dic3C2212yes—
19#63878—22no—
20C4×D3×Dic3—22no—
21#63849C2212yes—
22#63841C2212yes—
23#63836—22no—
24C2×#3711C2212yes—
25C2×#3710C2211yescharacteristic
26#63791C418yescomplemented
27C32×#106C2211yescharacteristic, complemented
28#63644C2211yescharacteristic, complemented
29#63634C2212yescomplemented
30C3×#818C2212yescomplemented
31C3×#808C2212yescomplemented
32C3×#807C2212yescomplemented
33#63575C2212yescomplemented
34#63574C2211yescharacteristic, complemented
35#63574C2211yescharacteristic, complemented
36#63573C2212yescomplemented
37C2×D3×M16—32no—
38D3×#117—32no—
39C2×#892—32no—
40C3×#428—32no—
41#5121—32no—
42#4995—32no—
43#4964—32no—
44#4881—32no—
45#4881—32no—
46#4880—32no—
47#4880—32no—
48#4861—32no—
49#4861D312yescomplemented
50#4860—32no—
51#4860—32no—
52#4860—61no—
53C22×D32D411yescharacteristic
54C2×C4×C3⋊D3C2311yescharacteristic
55C2×C3×C4×D3—22no—
56C2×C3×C4×D3C2312yes—
57C2×#624D411yescharacteristic
58C2×D3×Dic3—22no—
59C2×D3×Dic3D412yes—
60C4×D32C2×C414yes—
61C4×D32Q814yes—
62C2×C32×C8C2311yescharacteristic
63C32×C4⋊C4C2312yes—
64#3752—22no—
65C4⋊(C3⋊Dic3)C2312yes—
66C4×C3⋊Dic3—22no—
67C2×C3⋊(C3⋊C8)C2311yescharacteristic
68C8×C3⋊D3C2×C414yescomplemented
69C3×(C2×D3)⋊C4—22no—
70C3×C4⋊Dic3C2312yes—
71C3×C4⋊Dic3C2312yes—
72C3×Dic3⋊C4—22no—
73C3×C4×Dic3—22no—
74C2×C3×C3⋊C8C2312yes—
75C3×ΓL(1,𝔽25)C2×C418yescomplemented
76Dic3⋊Dic3—22no—
77#3722—22no—
78(C2×D3)⋊Dic3—22no—
79Dic32—22no—
80Dic32—22no—
81#3711C2×C418yescomplemented
82#3710C2×C414yescomplemented
83#2911—91noSylow
84C22×C4×D3—32no—
85C2×C3×M16—32no—
86C3×#117—32no—
87C2×C3×C4⋊C4—32no—
88C2×(C2×D3)⋊C4—62no—
89#926—32no—
90C2×C4⋊Dic3—32no—
91C2×C4×Dic3—62no—
92C2×#208—32no—
93D3×M16—316no—
94C2×ΓL(1,𝔽25)—32no—
95C2×ΓL(1,𝔽25)C2×D312yes—
96C2×D3×C8—32no—
97C2×D3×C8—32no—
98C2×D3×C8—61no—
99#892—32no—
100#892—32no—
101#892—32no—
102#892—32no—
103#892—32no—
104#892—62no—
105#892—62no—
106#892—62no—
107#892C2×D312yes—
108D3×C4⋊C4—32no—
109D3×C4⋊C4C2×D312yes—
110D3×C22⋊C4—62no—
111#877—62no—
112#872—62no—
113C42×D3—62no—
114C3×#107—32no—
115C3×#107—32no—
116C3×#106—21no—
117C3×#106—32no—
118C3×#106C2×D312yescomplemented
119#818—32no—
120#818C2×D312yescomplemented
121#817—32no—
122#817—32no—
123#817—61no—
124#808—32no—
125#808—32no—
126#808—32no—
127#808C2×D312yescomplemented
128#807—32no—
129#807—32no—
130#807—32no—
131#807—62no—
132#807C2×D312yescomplemented
133C22×C3⋊D3C2×D411yescharacteristic
134C22×C3×D3C2×D412yes—
135C2×D32—42no—
136C2×D32C4⋊C414yes—
137C2×C32×C4—22no—
138C2×C32×C4C2411yescharacteristic
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3C2×D411yescharacteristic
141C4×C3⋊D3C22×C412yes—
142C4×C3⋊D3C2×Q812yes—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3C2×D412yes—
146C3×C4×D3—44no—
147C3×C4×D3C22×C414yes—
148C3×C4×D3C2×Q814yes—
149#624C4⋊C414yes—
150D3×Dic3—44no—
151D3×Dic3C4⋊C418yes—
152C32×C8C22×C412yes—
153C3⋊(C3⋊C8)C22×C412yes—
154C3×C3⋊C8C22×C414yes—
155C22×M16—91no—
156C2×#117—92no—
157#428—32no—
158#428—92no—
159#428—92no—
160#428—92no—
161#427—92no—
162#427—91no—
163#427—91no—
164C23×D3—32no—
165C22×C3×C4—32no—
166C22×C3×C4—62no—
167C22×Dic3—32no—
168C22×Dic3—62no—
169C2×C4×D3—22no—
170C2×C4×D3—32no—
171C2×C4×D3—32no—
172C2×C4×D3—32no—
173C2×C4×D3—38no—
174C2×C4×D3—38no—
175C2×C4×D3—61no—
176C2×C4×D3—62no—
177C2×C4×D3C22×D312yes—
178C3×M16—38no—
179C2×C3×C8—21no—
180C2×C3×C8—32no—
181C2×C3×C8C22×D312yes—
182C3×C4⋊C4—22no—
183C3×C4⋊C4—32no—
184C3×C4⋊C4—32no—
185C3×C4⋊C4—62no—
186C3×C4⋊C4C22×D312yes—
187C3×C4⋊C4C22×D312yes—
188C3×C22⋊C4—62no—
189C3×C42—62no—
190#217—62no—
191(C2×D3)⋊C4—22no—
192(C2×D3)⋊C4—62no—
193(C2×D3)⋊C4—62no—
194(C2×D3)⋊C4—62no—
195(C2×D3)⋊C4—62no—
196(C2×D3)⋊C4—62no—
197(C2×D3)⋊C4—122no—
198C4⋊Dic3—32no—
199C4⋊Dic3—32no—
200C4⋊Dic3—62no—
201C4⋊Dic3—62no—
202C4⋊Dic3C22×D312yes—
203C4⋊Dic3C22×D312yes—
204Dic3⋊C4—22no—
205Dic3⋊C4—62no—
206C4×Dic3—22no—
207C4×Dic3—62no—
208C4×Dic3—62no—
209C4×Dic3—62no—
210C4×Dic3—62no—
211C4×Dic3—62no—
212C4×Dic3—62no—
213C4×Dic3—122no—
214#208—38no—
215C2×C3⋊C8—32no—
216C2×C3⋊C8—61no—
217C2×C3⋊C8C22×D312yes—
218ΓL(1,𝔽25)—38no—
219ΓL(1,𝔽25)C4×D318yescomplemented
220D3×C8—38no—
221D3×C8—38no—
222D3×C8—64no—
223C22×C32C22×D411yescharacteristic
224C2×C3⋊D3—22no—
225C2×C3⋊D3C2×C4⋊C412yes—
226C2×C3×D3—22no—
227C2×C3×D3—22no—
228C2×C3×D3C2×C4⋊C414yes—
229D32—44no—
230C32×C4—42no—
231C32×C4C23×C411yescharacteristic
232C32×C4C22×Q811yescharacteristic
233C3⋊Dic3—42no—
234C3⋊Dic3C2×C4⋊C412yes—
235C3×Dic3—42no—
236C3×Dic3—42no—
237C3×Dic3C2×C4⋊C414yes—
238C23×C4—91no—
239C2×M16—32no—
240C2×M16—92no—
241C2×M16—98no—
242C22×C8—91no—
243C22×C8—91no—
244#117—32no—
245#117—92no—
246#117—92no—
247#117—92no—
248#117—182no—
249#117—182no—
250C2×C4⋊C4—32no—
251C2×C4⋊C4—92no—
252C2×C22⋊C4—182no—
253C2×C42—182no—
254#107—32no—
255#107—32no—
256#107—92no—
257#107—92no—
258#106—32no—
259#106—91no—
260#106—91no—
261#106—92no—
262#106—91no—
263#106D3211yescharacteristic, complemented
264C23×C3—32no—
265C22×D3—32no—
266C22×D3—38no—
267C22×D3—61no—
268C22×D3—122no—
269C22×D3—122no—
270C22×D3D3×D412yes—
271C2×C3×C4—22no—
272C2×C3×C4—22no—
273C2×C3×C4—21no—
274C2×C3×C4—32no—
275C2×C3×C4—34no—
276C2×C3×C4—34no—
277C2×C3×C4—42no—
278C2×C3×C4—62no—
279C2×C3×C4—62no—
280C2×C3×C4—124no—
281C2×C3×C4C23×D312yes—
282C2×Dic3—22no—
283C2×Dic3—22no—
284C2×Dic3—32no—
285C2×Dic3—38no—
286C2×Dic3—61no—
287C2×Dic3—62no—
288C2×Dic3—62no—
289C2×Dic3—122no—
290C2×Dic3—124no—
291C2×Dic3D3×D412yes—
292C4×D3—38no—
293C4×D3—34no—
294C4×D3—34no—
295C4×D3—38no—
296C4×D3—44no—
297C4×D3—62no—
298C4×D3—62no—
299C4×D3—124no—
300C4×D3C2×C4×D314yes—
301C4×D3D3×Q814yes—
302C3×C8—22no—
303C3×C8—34no—
304C3×C8C2×C4×D314yes—
305C3⋊C8—34no—
306C3⋊C8—62no—
307C3⋊C8C2×C4×D314yes—
308C2×C32C22×C4⋊C411yescharacteristic
309C2×C32#57512yes—
310C3⋊D3—22no—
311C3×D3—24no—
312C24—91no—
313C22×C4—32no—
314C22×C4—62no—
315C22×C4—91no—
316C22×C4—94no—
317C22×C4—94no—
318C22×C4—92no—
319C22×C4—91no—
320C22×C4—182no—
321M16—38no—
322M16—98no—
323C2×C8—32no—
324C2×C8—94no—
325C2×C8—91no—
326C2×C8—94no—
327C2×C8C2×D3211yescharacteristic
328C4⋊C4—32no—
329C4⋊C4—32no—
330C4⋊C4—62no—
331C4⋊C4—92no—
332C4⋊C4—182no—
333C4⋊C4C2×D3212yes—
334C22⋊C4—62no—
335C22⋊C4—182no—
336C22⋊C4—182no—
337C22⋊C4—182no—
338C42—62no—
339C42—182no—
340C42—182no—
341C42—182no—
342C22×C3—21no—
343C22×C3—34no—
344C22×C3—62no—
345C22×C3—62no—
346C22×C3C2×D3×D412yes—
347C2×D3—22no—
348C2×D3—22no—
349C2×D3—34no—
350C2×D3—62no—
351C2×D3—62no—
352C2×D3—62no—
353C2×D3—122no—
354C2×D3—128no—
355C2×D3D3×C4⋊C414yes—
356C3×C4—21no—
357C3×C4—21no—
358C3×C4—34no—
359C3×C4—42no—
360C3×C4—42no—
361C3×C4—82no—
362C3×C4—122no—
363C3×C4—122no—
364C3×C4C22×C4×D312yes—
365C3×C4C2×D3×Q812yes—
366Dic3—34no—
367Dic3—42no—
368Dic3—42no—
369Dic3—62no—
370Dic3—122no—
371Dic3—122no—
372Dic3—242no—
373Dic3D3×C4⋊C414yes—
374C32#291111yescharacteristic, complemented, Sylow
375C23—32no—
376C23—94no—
377C23—91no—
378C23—362no—
379C2×C4—22no—
380C2×C4—32no—
381C2×C4—34no—
382C2×C4—34no—
383C2×C4—62no—
384C2×C4—62no—
385C2×C4—94no—
386C2×C4—98no—
387C2×C4—91no—
388C2×C4—92no—
389C2×C4—92no—
390C2×C4—124no—
391C2×C4—182no—
392C2×C4—364no—
393C2×C4C22×D3211yescharacteristic
394C8—34no—
395C8—92no—
396C8C4×D3212yes—
397C2×C3—21no—
398C2×C3—22no—
399C2×C3—64no—
400C2×C3C2×D3×C4⋊C412yes—
401C2×C3#577312yes—
402C2×C3#577712yes—
403D3—24no—
404D3—64no—
405D3—122no—
406C22—34no—
407C22—62no—
408C22—62no—
409C22—92no—
410C22—182no—
411C22—364no—
412C22D32×D411yescharacteristic
413C4—34no—
414C4—42no—
415C4—92no—
416C4—122no—
417C4—122no—
418C4—362no—
419C4C2×C4×D3211yescharacteristic
420C4D32×Q811yescharacteristic
421C3—21no—
422C3#7920812yescomplemented
423C2—64no—
424C2—182no—
425C2D32×C4⋊C411yescharacteristic
426C2#1059474412yes—
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC22×D32D4
cosocleC2×C32×C4C24
hypercenter#106D32
hypocenterC32#2911
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
3. #10592559C2semidirect
4. C3×#4861C2semidirect
5. #10590714C2semidirect
6. #10590683C2semidirect
7. #10590581C2semidirect
8. #10590574C2semidirect
9. #10590436C2semidirect
26. #63791C4semidirect
27. C32×#106C22semidirect
28. #63644C22semidirect
29. #63634C22semidirect
30. C3×#818C22semidirect
31. C3×#808C22semidirect
32. C3×#807C22semidirect
33. #63575C22semidirect
34. #63574C22semidirect
35. #63574C22semidirect
36. #63573C22semidirect
49. #4861D3semidirect
68. C8×C3⋊D3C2×C4semidirect
75. C3×ΓL(1,𝔽25)C2×C4semidirect
81. #3711C2×C4semidirect
82. #3710C2×C4semidirect
118. C3×#106C2×D3semidirect
120. #818C2×D3semidirect
127. #808C2×D3semidirect
132. #807C2×D3semidirect
219. ΓL(1,𝔽25)C4×D3semidirect
263. #106D32semidirect
374. C32#2911semidirect
422. C3#79208semidirect

Maximal subgroups

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

subgroupindex
C2×#637912
D3×#8922
#105925592
C3×#48612
#105907142
#105906832
#105905812
#105905742
#105904362
#792083