Finite Group Databasebeta

← #11858516

Subgroups — #11858516

Order 1152.

1149 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×#117C211yesmaximal, characteristic
2C2×#63849C211yesmaximal, characteristic
3C2×#63818C211yesmaximal, characteristic
4C3×#4995C212yesmaximal, complemented
5#10591130C212yesmaximal, complemented
6#10590583C214yesmaximal, complemented
7#10590574C214yesmaximal, complemented
8#79208—32nomaximal
9C22×C4×C3⋊D3C2211yescharacteristic
10C32×#117C2211yescharacteristic
11#64135C2211yescharacteristic
12#64101C2212yes—
13C4⋊C4×C3⋊D3C2212yes—
14C22⋊C4×C3⋊D3—21no—
15#64086—21no—
16#64081—21no—
17C42×C3⋊D3—21no—
18C2×C3×C4⋊Dic3C2212yes—
19C2×C3×#208C2212yes—
20C2×#3722—21no—
21C2×Dic32—21no—
22#63849—21no—
23#63849—21no—
24#63849C2212yes—
25#63849C2212yes—
26C2×#3712C2212yes—
27#63818C418yescomplemented
28C2×#3710C2212yes—
29C3×#808C2214yescomplemented
30C3×#807C2214yescomplemented
31#63575C2214yescomplemented
32#63573C2214yescomplemented
33C2×D3×M16—32no—
34D3×#117—32no—
35D3×#117—61no—
36C2×#892—32no—
37C3×#428—32no—
38#5121—32no—
39#4995D312yescomplemented
40#4964—32no—
41#4881—34no—
42#4880—34no—
43#4861—34no—
44#4860—34no—
45C23×C3⋊D3D411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3D411yescharacteristic
48C2×C4×C3⋊D3—22no—
49C2×C4×C3⋊D3C2×C414yes—
50C2×C4×C3⋊D3D411yescharacteristic
51C2×C4×C3⋊D3D411yescharacteristic
52C2×C4×C3⋊D3Q814yes—
53C2×C4×C3⋊D3C2311yescharacteristic
54C2×C4×C3⋊D3C2311yescharacteristic
55C22×C3×Dic3—22no—
56C32×C4⋊C4C2312yes—
57C32×C22⋊C4—21no—
58C32×C42—21no—
59#3757—21no—
60#3752—22no—
61C4⋊(C3⋊Dic3)C2312yes—
62#3750—22no—
63C4×C3⋊Dic3—21no—
64C4×C3⋊Dic3—22no—
65C3×C4⋊Dic3—22no—
66C3×C4⋊Dic3C2314yes—
67C3×#208C2×C418yescomplemented
68C2×C3×C3⋊C8C2314yes—
69#3722—22no—
70#3722—22no—
71Dic32—22no—
72Dic32—22no—
73#3712C2×C418yescomplemented
74#3710C2×C418yescomplemented
75#2911—91noSylow
76C22×C4×D3—32no—
77C22×C4×D3—61no—
78C2×C3×M16—32no—
79C3×#117—21no—
80C3×#117C2×D312yes—
81C2×C3×C4⋊C4—32no—
82C2×(C2×D3)⋊C4—62no—
83#926—32no—
84#926—61no—
85C2×C4⋊Dic3C2×D312yes—
86C2×C4×Dic3—62no—
87C2×#208C2×D312yes—
88D3×M16—316no—
89C2×ΓL(1,𝔽25)—34no—
90C2×D3×C8—34no—
91#892—32no—
92#892—32no—
93#892—34no—
94#892—34no—
95#892—62no—
96#892—62no—
97#892—62no—
98D3×C4⋊C4—32no—
99D3×C4⋊C4—32no—
100D3×C4⋊C4—62no—
101D3×C22⋊C4—62no—
102D3×C22⋊C4—62no—
103#877—62no—
104#877—62no—
105#872—62no—
106#872—62no—
107C42×D3—62no—
108C42×D3—62no—
109C3×#107—34no—
110C3×#106—34no—
111#818—34no—
112#817—34no—
113#808—34no—
114#808C2×D314yescomplemented
115#807—34no—
116#807C2×D314yescomplemented
117C23×C32C2×D411yescharacteristic
118C22×C3⋊D3—42no—
119C22×C3⋊D3C4⋊C414yes—
120C22×C3⋊D3C2×D411yescharacteristic
121C22×C3⋊D3C2×D411yescharacteristic
122C2×C32×C4—22no—
123C2×C32×C4C22×C412yes—
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×Q812yes—
126C2×C32×C4C2411yescharacteristic
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3C4⋊C414yes—
129C2×C3⋊Dic3C2×D411yescharacteristic
130C2×C3⋊Dic3C2×D411yescharacteristic
131C4×C3⋊D3—44no—
132C4×C3⋊D3C4⋊C414yes—
133C4×C3⋊D3C4⋊C414yes—
134C4×C3⋊D3C22×C412yes—
135C4×C3⋊D3C22×C412yes—
136C4×C3⋊D3C2×Q812yes—
137C4×C3⋊D3C2×Q812yes—
138C2×C3×Dic3—24no—
139C2×C3×Dic3—44no—
140C3×C3⋊C8C22×C418yes—
141C22×M16—91no—
142C2×#117—91no—
143C2×#117—91no—
144#428—32no—
145#428—94no—
146#428—92no—
147#427—94no—
148C23×D3—32no—
149C23×D3—61no—
150C22×C3×C4—21no—
151C22×C3×C4—62no—
152C22×C3×C4C22×D312yes—
153C22×Dic3—22no—
154C22×Dic3—32no—
155C22×Dic3—61no—
156C2×C4×D3—38no—
157C2×C4×D3—32no—
158C2×C4×D3—32no—
159C2×C4×D3—38no—
160C2×C4×D3—32no—
161C2×C4×D3—32no—
162C2×C4×D3—61no—
163C2×C4×D3—61no—
164C2×C4×D3—61no—
165C2×C4×D3—61no—
166C2×C4×D3—64no—
167C2×C4×D3—64no—
168C2×C4×D3—62no—
169C2×C4×D3—62no—
170C2×C4×D3—64no—
171C3×M16—38no—
172C2×C3×C8—34no—
173C3×C4⋊C4—22no—
174C3×C4⋊C4—34no—
175C3×C4⋊C4—62no—
176C3×C4⋊C4C22×D312yes—
177C3×C4⋊C4C22×D312yes—
178C3×C22⋊C4—22no—
179C3×C22⋊C4—22no—
180C3×C42—22no—
181C3×C42—22no—
182#217—62no—
183#217—62no—
184(C2×D3)⋊C4—64no—
185(C2×D3)⋊C4—64no—
186(C2×D3)⋊C4—62no—
187(C2×D3)⋊C4—62no—
188(C2×D3)⋊C4—64no—
189C4⋊Dic3—22no—
190C4⋊Dic3—32no—
191C4⋊Dic3—32no—
192C4⋊Dic3—62no—
193C4⋊Dic3C22×D314yes—
194Dic3⋊C4—62no—
195Dic3⋊C4—62no—
196Dic3⋊C4—64no—
197C4×Dic3—64no—
198C4×Dic3—64no—
199C4×Dic3—62no—
200C4×Dic3—62no—
201C4×Dic3—62no—
202C4×Dic3—64no—
203C4×Dic3—62no—
204#208C4×D318yescomplemented
205C2×C3⋊C8C22×D314yes—
206ΓL(1,𝔽25)—316no—
207D3×C8—316no—
208C22×C32—22no—
209C22×C32C2×C4⋊C412yes—
210C22×C32C22×D411yescharacteristic
211C2×C3⋊D3—22no—
212C2×C3⋊D3—22no—
213C2×C3⋊D3—44no—
214C2×C3⋊D3C2×C4⋊C412yes—
215C2×C3⋊D3C2×C4⋊C412yes—
216C32×C4—42no—
217C32×C4C2×C4⋊C412yes—
218C32×C4C23×C411yescharacteristic
219C32×C4C22×Q811yescharacteristic
220C3⋊Dic3—42no—
221C3⋊Dic3C2×C4⋊C412yes—
222C3⋊Dic3C2×C4⋊C412yes—
223C3×Dic3—44no—
224C23×C4—91no—
225C2×M16—32no—
226C2×M16—92no—
227C2×M16—98no—
228C22×C8—92no—
229#117—92no—
230#117—92no—
231#117—91no—
232#117—92no—
233#117—181no—
234#117—181no—
235#117—181no—
236#117—181no—
237#117D3211yescharacteristic
238C2×C4⋊C4—32no—
239C2×C4⋊C4—92no—
240C2×C22⋊C4—181no—
241C2×C22⋊C4—181no—
242C2×C42—181no—
243C2×C42—181no—
244#107—34no—
245#107—94no—
246#106—34no—
247#106—94no—
248C23×C3—21no—
249C23×C3D3×D412yes—
250C22×D3—32no—
251C22×D3—32no—
252C22×D3—38no—
253C22×D3—61no—
254C22×D3—64no—
255C22×D3—61no—
256C22×D3—122no—
257C22×D3—122no—
258C22×D3—124no—
259C2×C3×C4—24no—
260C2×C3×C4—22no—
261C2×C3×C4—22no—
262C2×C3×C4—21no—
263C2×C3×C4—22no—
264C2×C3×C4—22no—
265C2×C3×C4—21no—
266C2×C3×C4—64no—
267C2×C3×C4—124no—
268C2×C3×C4C2×C4×D314yes—
269C2×C3×C4D3×D412yes—
270C2×C3×C4D3×Q814yes—
271C2×C3×C4C23×D312yes—
272C2×Dic3—24no—
273C2×Dic3—38no—
274C2×Dic3—32no—
275C2×Dic3—32no—
276C2×Dic3—44no—
277C2×Dic3—64no—
278C2×Dic3—61no—
279C2×Dic3—61no—
280C2×Dic3—64no—
281C2×Dic3—62no—
282C2×Dic3—62no—
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—124no—
297C4×D3—124no—
298C3×C8—38no—
299C3⋊C8C2×C4×D318yes—
300C2×C32—22no—
301C2×C32C22×C4⋊C411yescharacteristic
302C2×C32#57512yes—
303C3⋊D3—22no—
304C3⋊D3—22no—
305C24—91no—
306C22×C4—62no—
307C22×C4—91no—
308C22×C4—91no—
309C22×C4—91no—
310C22×C4—94no—
311C22×C4—94no—
312C22×C4—91no—
313C22×C4—91no—
314C22×C4—182no—
315C22×C4C2×D3211yescharacteristic
316M16—38no—
317M16—98no—
318C2×C8—34no—
319C2×C8—98no—
320C4⋊C4—34no—
321C4⋊C4—62no—
322C4⋊C4—92no—
323C4⋊C4—182no—
324C4⋊C4C2×D3212yes—
325C22⋊C4—21no—
326C22⋊C4—182no—
327C22⋊C4—182no—
328C22⋊C4—182no—
329C22⋊C4—181no—
330C42—21no—
331C42—182no—
332C42—182no—
333C42—182no—
334C42—181no—
335C22×C3—22no—
336C22×C3—22no—
337C22×C3—21no—
338C22×C3—22no—
339C22×C3—42no—
340C22×C3D3×C4⋊C414yes—
341C22×C3C2×D3×D412yes—
342C2×D3—34no—
343C2×D3—34no—
344C2×D3—62no—
345C2×D3—62no—
346C2×D3—64no—
347C2×D3—62no—
348C2×D3—62no—
349C2×D3—62no—
350C2×D3—62no—
351C2×D3—122no—
352C2×D3—128no—
353C2×D3—128no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—22no—
357C3×C4—44no—
358C3×C4—42no—
359C3×C4—42no—
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—122no—
371Dic3—122no—
372C32#291111yescharacteristic, complemented, Sylow
373C23—91no—
374C23—91no—
375C23—94no—
376C23—362no—
377C23#381111yescharacteristic
378C2×C4—22no—
379C2×C4—64no—
380C2×C4—91no—
381C2×C4—91no—
382C2×C4—94no—
383C2×C4—92no—
384C2×C4—92no—
385C2×C4—92no—
386C2×C4—92no—
387C2×C4—94no—
388C2×C4—94no—
389C2×C4—124no—
390C2×C4—182no—
391C2×C4—364no—
392C2×C4#379712yes—
393C2×C4C4×D3212yes—
394C2×C4#381111yescharacteristic
395C2×C4C22×D3211yescharacteristic
396C8—38no—
397C2×C3—24no—
398C2×C3—21no—
399C2×C3—22no—
400C2×C3—42no—
401C2×C3C2×D3×C4⋊C412yes—
402C2×C3#577312yes—
403C2×C3#577712yes—
404D3—64no—
405D3—64no—
406D3—64no—
407D3—122no—
408C22—22no—
409C22—92no—
410C22—92no—
411C22—182no—
412C22—182no—
413C22—364no—
414C22#6388312yes—
415C22C2×#381111yescharacteristic
416C4—42no—
417C4—92no—
418C4—92no—
419C4—124no—
420C4—362no—
421C4#6388312yes—
422C4C2×#379711yescharacteristic
423C4C2×C4×D3211yescharacteristic
424C3—21no—
425C3#7920812yescomplemented
426C2—22no—
427C2—182no—
428C2—182no—
429C2C2×#6388311yescharacteristic
430C2#1059547112yes—
subgroupG/H
centerC22C2×#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 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
4. C3×#4995C2semidirect
5. #10591130C2semidirect
6. #10590583C2semidirect
7. #10590574C2semidirect
27. #63818C4semidirect
29. C3×#808C22semidirect
30. C3×#807C22semidirect
31. #63575C22semidirect
32. #63573C22semidirect
39. #4995D3semidirect
67. C3×#208C2×C4semidirect
73. #3712C2×C4semidirect
74. #3710C2×C4semidirect
114. #808C2×D3semidirect
116. #807C2×D3semidirect
204. #208C4×D3semidirect
372. C32#2911semidirect
425. C3#79208semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1172
C2×#638492
C2×#638182
C3×#49952
#105911302
#105905832
#105905742
#792083