Finite Group Databasebeta

← #11858518

Subgroups — #11858518

Order 1152.

1149 conjugacy classes of subgroups.

The subgroup lattice has 431 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×#117C211yesmaximal, characteristic
2#10594969C211yesmaximal, characteristic
3C22×#3712C211yesmaximal, characteristic
4C3×#4998C212yesmaximal, complemented
5#10591122C212yesmaximal, complemented
6#10590584C212yesmaximal, complemented
7#10590583C214yesmaximal, complemented
8#10590582C212yesmaximal, complemented
9#79177—32nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C32×#117C2211yescharacteristic
12#64135C2211yescharacteristic
13#64101C2212yes—
14C4⋊C4×C3⋊D3C2212yes—
15C22⋊C4×C3⋊D3—21no—
16#64086—21no—
17#64081—21no—
18C42×C3⋊D3—21no—
19C3×#926C2212yes—
20C22×C3×C3⋊C8C2212yes—
21#63974—21no—
22#63957—21no—
23#63900C2212yes—
24C4×#624—21no—
25#63874—21no—
26#63849C2212yes—
27C2×#3712C418yescomplemented
28C2×#3712C2211yescharacteristic
29C2×#3712C2212yes—
30C2×#3712C2211yescharacteristic
31C3×#808C2214yescomplemented
32C3×#807C2214yescomplemented
33#63575C2214yescomplemented
34#63573C2214yescomplemented
35C22×ΓL(1,𝔽25)—32no—
36D3×#117—32no—
37D3×#117—32no—
38D3×#117—61no—
39C3×#427—32no—
40#5106—32no—
41#4998—32no—
42#4998D312yescomplemented
43#4881—34no—
44#4881—34no—
45#4861—34no—
46#4861—34no—
47C23×C3⋊D3D411yescharacteristic
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3D411yescharacteristic
50C2×C4×C3⋊D3—22no—
51C2×C4×C3⋊D3C2×C414yes—
52C2×C4×C3⋊D3D411yescharacteristic
53C2×C4×C3⋊D3D411yescharacteristic
54C2×C4×C3⋊D3Q814yes—
55C2×C4×C3⋊D3C2311yescharacteristic
56C2×C4×C3⋊D3C2311yescharacteristic
57C2×#624—22no—
58C32×C4⋊C4C2312yes—
59C32×C22⋊C4—21no—
60C32×C42—21no—
61#3757—21no—
62#3752—22no—
63C4⋊(C3⋊Dic3)C2312yes—
64#3750—22no—
65C4×C3⋊Dic3—21no—
66C4×C3⋊Dic3—22no—
67C3×#217—22no—
68C3×C4⋊Dic3C2314yes—
69C3×C4×Dic3—22no—
70C2×C3×C3⋊C8C2×C418yescomplemented
71C2×C3×C3⋊C8C2312yes—
72C2×C3×C3⋊C8C2312yes—
73#3724—22no—
74#3722—22no—
75Dic32—22no—
76#3712C2×C414yescomplemented
77#3712C2×C418yescomplemented
78#3712C2×C414yescomplemented
79#2911—91noSylow
80C22×C4×D3—32no—
81C22×C4×D3—61no—
82C22×C3×C8—32no—
83C3×#117—21no—
84C3×#117—32no—
85C3×#117C2×D312yes—
86#926—32no—
87#926—61no—
88#926C2×D312yes—
89C22×C3⋊C8C2×D312yes—
90C2×ΓL(1,𝔽25)—316no—
91C2×ΓL(1,𝔽25)—32no—
92C2×ΓL(1,𝔽25)—32no—
93C2×ΓL(1,𝔽25)—32no—
94C2×ΓL(1,𝔽25)—32no—
95#892—34no—
96#892—34no—
97#892—62no—
98D3×C4⋊C4—34no—
99D3×C4⋊C4—34no—
100D3×C4⋊C4—62no—
101D3×C22⋊C4—62no—
102D3×C22⋊C4—62no—
103D3×C22⋊C4—62no—
104#877—62no—
105#877—62no—
106#877—62no—
107#872—62no—
108#872—62no—
109#872—62no—
110C42×D3—62no—
111C42×D3—62no—
112C42×D3—62no—
113C3×#107—34no—
114C3×#106—34no—
115#818—34no—
116#817—34no—
117#808—34no—
118#808C2×D314yescomplemented
119#807—34no—
120#807C2×D314yescomplemented
121C23×C32C2×D411yescharacteristic
122C22×C3⋊D3—42no—
123C22×C3⋊D3C4⋊C414yes—
124C22×C3⋊D3C2×D411yescharacteristic
125C22×C3⋊D3C2×D411yescharacteristic
126C2×C32×C4—22no—
127C2×C32×C4C22×C412yes—
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×Q812yes—
130C2×C32×C4C2411yescharacteristic
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3C4⋊C414yes—
133C2×C3⋊Dic3C2×D411yescharacteristic
134C2×C3⋊Dic3C2×D411yescharacteristic
135C4×C3⋊D3—44no—
136C4×C3⋊D3C4⋊C414yes—
137C4×C3⋊D3C4⋊C414yes—
138C4×C3⋊D3C22×C412yes—
139C4×C3⋊D3C22×C412yes—
140C4×C3⋊D3C2×Q812yes—
141C4×C3⋊D3C2×Q812yes—
142C2×C3×Dic3—24no—
143#624—44no—
144C3×C3⋊C8C22×C414yes—
145C3×C3⋊C8C22×C414yes—
146C22×M16—91no—
147C2×#117—91no—
148C2×#117—91no—
149#428—92no—
150#428—94no—
151#428—92no—
152#427—32no—
153#427—92no—
154C23×D3—32no—
155C23×D3—61no—
156C22×C3×C4—21no—
157C22×C3×C4C22×D312yes—
158C22×Dic3—32no—
159C22×Dic3—61no—
160C2×C4×D3—38no—
161C2×C4×D3—32no—
162C2×C4×D3—32no—
163C2×C4×D3—38no—
164C2×C4×D3—32no—
165C2×C4×D3—32no—
166C2×C4×D3—61no—
167C2×C4×D3—61no—
168C2×C4×D3—61no—
169C2×C4×D3—61no—
170C2×C4×D3—64no—
171C2×C4×D3—64no—
172C2×C4×D3—64no—
173C2×C4×D3—64no—
174C2×C4×D3—64no—
175C2×C3×C8—38no—
176C2×C3×C8—32no—
177C2×C3×C8—32no—
178C3×C4⋊C4—22no—
179C3×C4⋊C4—34no—
180C3×C4⋊C4C22×D314yes—
181C3×C22⋊C4—22no—
182C3×C22⋊C4—22no—
183C3×C22⋊C4—62no—
184C3×C42—22no—
185C3×C42—22no—
186C3×C42—62no—
187#217—22no—
188#217—62no—
189#217—62no—
190(C2×D3)⋊C4—64no—
191(C2×D3)⋊C4—64no—
192(C2×D3)⋊C4—64no—
193C4⋊Dic3—34no—
194C4⋊Dic3—62no—
195C4⋊Dic3C22×D314yes—
196Dic3⋊C4—64no—
197Dic3⋊C4—64no—
198Dic3⋊C4—64no—
199C4×Dic3—22no—
200C4×Dic3—64no—
201C4×Dic3—64no—
202C4×Dic3—62no—
203C4×Dic3—64no—
204C4×Dic3—62no—
205C2×C3⋊C8C4×D318yescomplemented
206C2×C3⋊C8C22×D312yes—
207C2×C3⋊C8C22×D312yes—
208ΓL(1,𝔽25)—38no—
209ΓL(1,𝔽25)—38no—
210ΓL(1,𝔽25)—38no—
211ΓL(1,𝔽25)—38no—
212C22×C32—22no—
213C22×C32C2×C4⋊C412yes—
214C22×C32C22×D411yescharacteristic
215C2×C3⋊D3—22no—
216C2×C3⋊D3—22no—
217C2×C3⋊D3—44no—
218C2×C3⋊D3C2×C4⋊C412yes—
219C2×C3⋊D3C2×C4⋊C412yes—
220C32×C4—42no—
221C32×C4C2×C4⋊C412yes—
222C32×C4C23×C411yescharacteristic
223C32×C4C22×Q811yescharacteristic
224C3⋊Dic3—42no—
225C3⋊Dic3C2×C4⋊C412yes—
226C3⋊Dic3C2×C4⋊C412yes—
227C3×Dic3—44no—
228C23×C4—91no—
229C2×M16—98no—
230C2×M16—91no—
231C2×M16—92no—
232C2×M16—91no—
233C22×C8—32no—
234#117—32no—
235#117—92no—
236#117—91no—
237#117—92no—
238#117—181no—
239#117—181no—
240#117—181no—
241#117—181no—
242#117D3211yescharacteristic
243C2×C4⋊C4—92no—
244C2×C4⋊C4—92no—
245C2×C22⋊C4—181no—
246C2×C22⋊C4—181no—
247C2×C42—181no—
248C2×C42—181no—
249#107—34no—
250#107—94no—
251#106—34no—
252#106—94no—
253C23×C3—21no—
254C23×C3D3×D412yes—
255C22×D3—32no—
256C22×D3—32no—
257C22×D3—38no—
258C22×D3—61no—
259C22×D3—64no—
260C22×D3—61no—
261C22×D3—124no—
262C22×D3—124no—
263C2×C3×C4—24no—
264C2×C3×C4—24no—
265C2×C3×C4—21no—
266C2×C3×C4—22no—
267C2×C3×C4—22no—
268C2×C3×C4—21no—
269C2×C3×C4—64no—
270C2×C3×C4C2×C4×D314yes—
271C2×C3×C4D3×D412yes—
272C2×C3×C4D3×Q814yes—
273C2×C3×C4C23×D312yes—
274C2×Dic3—24no—
275C2×Dic3—38no—
276C2×Dic3—32no—
277C2×Dic3—32no—
278C2×Dic3—64no—
279C2×Dic3—61no—
280C2×Dic3—61no—
281C2×Dic3—64no—
282C2×Dic3—64no—
283C4×D3—38no—
284C4×D3—38no—
285C4×D3—34no—
286C4×D3—34no—
287C4×D3—34no—
288C4×D3—34no—
289C4×D3—64no—
290C4×D3—64no—
291C4×D3—62no—
292C4×D3—62no—
293C4×D3—62no—
294C4×D3—62no—
295C4×D3—128no—
296C4×D3—128no—
297C4×D3—128no—
298C3×C8—34no—
299C3×C8—34no—
300C3⋊C8C2×C4×D314yes—
301C3⋊C8C2×C4×D314yes—
302C2×C32—22no—
303C2×C32C22×C4⋊C411yescharacteristic
304C2×C32#57512yes—
305C3⋊D3—22no—
306C3⋊D3—22no—
307C24—91no—
308C22×C4—91no—
309C22×C4—91no—
310C22×C4—91no—
311C22×C4—94no—
312C22×C4—94no—
313C22×C4—91no—
314C22×C4—91no—
315C22×C4—182no—
316C22×C4—182no—
317C22×C4C2×D3211yescharacteristic
318M16—94no—
319M16—98no—
320M16—94no—
321C2×C8—32no—
322C2×C8—32no—
323C2×C8—38no—
324C4⋊C4—34no—
325C4⋊C4—92no—
326C4⋊C4—182no—
327C4⋊C4—182no—
328C4⋊C4C2×D3212yes—
329C22⋊C4—21no—
330C22⋊C4—62no—
331C22⋊C4—182no—
332C22⋊C4—182no—
333C22⋊C4—181no—
334C42—21no—
335C42—62no—
336C42—182no—
337C42—182no—
338C42—181no—
339C22×C3—24no—
340C22×C3—21no—
341C22×C3—22no—
342C22×C3—42no—
343C22×C3D3×C4⋊C414yes—
344C22×C3C2×D3×D412yes—
345C2×D3—34no—
346C2×D3—34no—
347C2×D3—62no—
348C2×D3—62no—
349C2×D3—64no—
350C2×D3—64no—
351C2×D3—64no—
352C2×D3—122no—
353C2×D3—128no—
354C2×D3—128no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—22no—
358C3×C4—44no—
359C3×C4—44no—
360C3×C4—124no—
361C3×C4D3×C4⋊C414yes—
362C3×C4C22×C4×D312yes—
363C3×C4C2×D3×Q812yes—
364Dic3—34no—
365Dic3—34no—
366Dic3—44no—
367Dic3—62no—
368Dic3—62no—
369Dic3—124no—
370Dic3—124no—
371C32#291111yescharacteristic, complemented, Sylow
372C23—91no—
373C23—91no—
374C23—94no—
375C23—362no—
376C23#381111yescharacteristic
377C2×C4—22no—
378C2×C4—64no—
379C2×C4—91no—
380C2×C4—91no—
381C2×C4—94no—
382C2×C4—92no—
383C2×C4—92no—
384C2×C4—92no—
385C2×C4—92no—
386C2×C4—94no—
387C2×C4—94no—
388C2×C4—182no—
389C2×C4—364no—
390C2×C4—364no—
391C2×C4#379712yes—
392C2×C4C4×D3212yes—
393C2×C4#381111yescharacteristic
394C2×C4C22×D3211yescharacteristic
395C8—34no—
396C8—34no—
397C2×C3—24no—
398C2×C3—21no—
399C2×C3—22no—
400C2×C3—42no—
401C2×C3C2×D3×C4⋊C412yes—
402C2×C3#576814yes—
403D3—64no—
404D3—64no—
405D3—64no—
406D3—122no—
407C22—22no—
408C22—92no—
409C22—92no—
410C22—182no—
411C22—182no—
412C22—364no—
413C22#6388312yes—
414C22C2×#381111yescharacteristic
415C4—42no—
416C4—92no—
417C4—92no—
418C4—124no—
419C4—362no—
420C4#6388312yes—
421C4C2×#379711yescharacteristic
422C4C2×C4×D3211yescharacteristic
423C3—21no—
424C3#7917712yescomplemented
425C2—22no—
426C2—182no—
427C2—182no—
428C2C2×#6388311yescharacteristic
429C2#1059546012yes—
subgroupG/H
centerC2×C4#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC23×C3⋊D3D4
cosocleC2×C32×C4C24
hypercenter#117D32
hypocenterC32#2911
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
4. C3×#4998C2semidirect
5. #10591122C2semidirect
6. #10590584C2semidirect
7. #10590583C2semidirect
8. #10590582C2semidirect
27. C2×#3712C4semidirect
31. C3×#808C22semidirect
32. C3×#807C22semidirect
33. #63575C22semidirect
34. #63573C22semidirect
42. #4998D3semidirect
70. C2×C3×C3⋊C8C2×C4semidirect
76. #3712C2×C4semidirect
77. #3712C2×C4semidirect
78. #3712C2×C4semidirect
118. #808C2×D3semidirect
120. #807C2×D3semidirect
205. C2×C3⋊C8C4×D3semidirect
371. C32#2911semidirect
424. C3#79177semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1172
#105949692
C22×#37122
C3×#49982
#105911222
#105905842
#105905832
#105905822
#791773