Finite Group Databasebeta

← #11857195

Subgroups — #11857195

Order 1152.

1257 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
2C2×D32×C8C211yesmaximal, characteristic
3#10593992C211yesmaximal, characteristic
4C3⋊D3×#97C211yesmaximal, characteristic, complemented
5C3×#4708C212yesmaximal, complemented
6#10590908C212yesmaximal, complemented
7#10590693C212yesmaximal, complemented
8#10590668C211yesmaximal, characteristic, complemented
9C8×#624C211yesmaximal, characteristic, complemented
10C4×#3710C211yesmaximal, characteristic, complemented
11#10590318C212yesmaximal, complemented
12D3×#405—32nomaximal
13C2×C4×D32C2211yescharacteristic
14C2×C8×C3⋊D3C2211yescharacteristic
15C2×C8×C3⋊D3C2211yescharacteristic
16C42×C3⋊D3C2211yescharacteristic
17C2×C3×ΓL(1,𝔽25)C2212yes—
18C2×C3×D3×C8C2212yes—
19C3×#872C2212yes—
20#63921C412yes—
21#63883C412yes—
22C4×#624C2211yescharacteristic
23#63878C414yes—
24#63855C2212yes—
25C2×#3711C2212yes—
26C2×#3710C2211yescharacteristic
27C2×#3710C2211yescharacteristic
28C2×D3×C3⋊C8C2212yes—
29#63791C418yescomplemented
30D32×C8C418yescomplemented
31C32×#97C2211yescharacteristic, complemented
32#63642C2211yescharacteristic, complemented
33#63642C2211yescharacteristic, complemented
34#63630C2211yescharacteristic, complemented
35C3×#815C2212yescomplemented
36C3×C8×Dic3C2212yescomplemented
37C3×C4×C3⋊C8C2212yescomplemented
38#63554C2212yescomplemented
39#63553C2212yescomplemented
40Dic3×C3⋊C8C2212yescomplemented
41C2×D3×M16—32no—
42C22×D3×C8—32no—
43D3×#117—32no—
44C3×#405—32no—
45#5122—32no—
46#5101—32no—
47#4997—32no—
48#4708—32no—
49#4708D312yescomplemented
50D3×#97—32no—
51D3×#97—32no—
52D3×#97—61no—
53#4689—32no—
54#4689—32no—
55C4×D3×C8—32no—
56C4×D3×C8—32no—
57C22×D32C2×C411yescharacteristic
58C2×C4×C3⋊D3C2×C412yes—
59C2×C4×C3⋊D3C2311yescharacteristic
60C2×C3×C4×D3C2312yes—
61C2×#624C2×C412yes—
62C2×#624C2×C411yescharacteristic
63C2×D3×Dic3C2×C412yes—
64C4×D32C2×C414yes—
65C4×D32C2×C414yes—
66C2×C32×C8C2311yescharacteristic
67C2×C32×C8C2311yescharacteristic
68C32×C42C2311yescharacteristic
69C4×C3⋊Dic3C2×C412yes—
70C4×C3⋊Dic3C2311yescharacteristic
71C2×C3⋊(C3⋊C8)C2311yescharacteristic
72C2×C3⋊(C3⋊C8)C2311yescharacteristic
73C8×C3⋊D3C2×C414yes—
74C8×C3⋊D3C2×C414yes—
75C3×(C2×D3)⋊C4C2×C414yes—
76C3×Dic3⋊C4C2×C414yes—
77C3×C4×Dic3C2312yes—
78C2×C3×C3⋊C8C2312yes—
79C2×C3×C3⋊C8C2312yes—
80C3×ΓL(1,𝔽25)C2×C418yescomplemented
81C3×D3×C8C2×C418yescomplemented
82Dic3⋊Dic3C2×C414yes—
83(C2×D3)⋊Dic3C2×C414yes—
84Dic32C2×C412yes—
85#3711C2×C418yescomplemented
86#3710C2×C414yes—
87#3710C2×C414yes—
88D3×C3⋊C8C2×C418yescomplemented
89C2×#405—91noSylow
90C22×C4×D3—32no—
91C2×C3×M16—32no—
92C22×C3×C8—32no—
93C3×#117—32no—
94#926—32no—
95C2×#208—32no—
96C22×C3⋊C8—32no—
97D3×M16—316no—
98C2×ΓL(1,𝔽25)—32no—
99C2×ΓL(1,𝔽25)C2×D312yes—
100C2×D3×C8—32no—
101C2×D3×C8—32no—
102C2×D3×C8—32no—
103C2×D3×C8—32no—
104C2×D3×C8—32no—
105C2×D3×C8—316no—
106C2×D3×C8—61no—
107C2×D3×C8—61no—
108C2×D3×C8C2×D312yes—
109#892—34no—
110D3×C4⋊C4—34no—
111D3×C22⋊C4—34no—
112#877—34no—
113#872—32no—
114#872C2×D312yes—
115C42×D3—32no—
116C42×D3—32no—
117C42×D3—61no—
118C3×#97—21no—
119C3×#97—32no—
120C3×#97C2×D312yescomplemented
121C3×C4×C8—32no—
122C3×C4×C8—32no—
123#815—32no—
124#815—32no—
125#815—32no—
126#815—61no—
127#815—61no—
128#815C2×D312yescomplemented
129C8×Dic3—32no—
130C8×Dic3—32no—
131C8×Dic3—32no—
132C8×Dic3C2×D312yescomplemented
133#803—32no—
134#803—32no—
135#803—61no—
136C4×C3⋊C8—32no—
137C4×C3⋊C8C2×D312yescomplemented
138C22×C3⋊D3C22×C411yescharacteristic
139C22×C3×D3C22×C412yes—
140C2×D32—24no—
141C2×D32C4214yes—
142C2×C32×C4C22×C412yes—
143C2×C32×C4C2411yescharacteristic
144C2×C3⋊Dic3C22×C412yes—
145C2×C3⋊Dic3C22×C411yescharacteristic
146C4×C3⋊D3—24no—
147C4×C3⋊D3C22×C412yes—
148C4×C3⋊D3C22×C412yes—
149C2×C3×Dic3C22×C414yes—
150C2×C3×Dic3C22×C412yes—
151C3×C4×D3C22×C414yes—
152C3×C4×D3C22×C414yes—
153#624—24no—
154#624C4214yes—
155D3×Dic3C4218yes—
156C32×C8C22×C412yes—
157C32×C8C22×C412yes—
158C3⋊(C3⋊C8)C22×C412yes—
159C3⋊(C3⋊C8)C22×C412yes—
160C3×C3⋊C8C22×C414yes—
161C3×C3⋊C8C22×C414yes—
162C22×M16—91no—
163C23×C8—91no—
164C2×#117—91no—
165#405—32no—
166#405—92no—
167#405—92no—
168#405—92no—
169C2×#97—91no—
170C2×#97—91no—
171C2×C4×C8—91no—
172C2×C4×C8—91no—
173C23×D3—32no—
174C22×C3×C4—32no—
175C22×Dic3—32no—
176C2×C4×D3—32no—
177C2×C4×D3—32no—
178C2×C4×D3—32no—
179C2×C4×D3—38no—
180C2×C4×D3—38no—
181C2×C4×D3—34no—
182C2×C4×D3—34no—
183C2×C4×D3—61no—
184C2×C4×D3—62no—
185C2×C4×D3C22×D312yes—
186C3×M16—38no—
187C2×C3×C8—21no—
188C2×C3×C8—21no—
189C2×C3×C8—32no—
190C2×C3×C8—32no—
191C2×C3×C8—38no—
192C2×C3×C8C22×D312yes—
193C2×C3×C8C22×D312yes—
194C3×C4⋊C4—34no—
195C3×C22⋊C4—34no—
196C3×C42—21no—
197C3×C42—32no—
198C3×C42C22×D312yes—
199#217—34no—
200(C2×D3)⋊C4—34no—
201(C2×D3)⋊C4C4×D314yes—
202C4⋊Dic3—34no—
203Dic3⋊C4—34no—
204Dic3⋊C4C4×D314yes—
205C4×Dic3—34no—
206C4×Dic3—32no—
207C4×Dic3—34no—
208C4×Dic3—61no—
209C4×Dic3—62no—
210C4×Dic3C22×D312yes—
211#208—38no—
212C2×C3⋊C8—32no—
213C2×C3⋊C8—32no—
214C2×C3⋊C8—38no—
215C2×C3⋊C8—61no—
216C2×C3⋊C8—61no—
217C2×C3⋊C8C22×D312yes—
218C2×C3⋊C8C22×D312yes—
219ΓL(1,𝔽25)—38no—
220ΓL(1,𝔽25)C4×D318yescomplemented
221D3×C8—38no—
222D3×C8—38no—
223D3×C8—38no—
224D3×C8—38no—
225D3×C8—38no—
226D3×C8—64no—
227D3×C8—64no—
228D3×C8C4×D318yescomplemented
229C22×C32C23×C411yescharacteristic
230C2×C3⋊D3C2×C4212yes—
231C2×C3⋊D3#13114yes—
232C2×C3×D3—24no—
233C2×C3×D3C2×C4214yes—
234D32—28no—
235C32×C4—22no—
236C32×C4C23×C411yescharacteristic
237C32×C4C23×C411yescharacteristic
238C3⋊Dic3—22no—
239C3⋊Dic3C2×C4212yes—
240C3×Dic3—24no—
241C3×Dic3C2×C4214yes—
242C23×C4—91no—
243C2×M16—32no—
244C2×M16—92no—
245C2×M16—98no—
246C22×C8—32no—
247C22×C8—98no—
248C22×C8—91no—
249C22×C8—91no—
250C22×C8—92no—
251C22×C8—91no—
252C22×C8—91no—
253#117—32no—
254#117—92no—
255#117—94no—
256C2×C4⋊C4—92no—
257C2×C22⋊C4—92no—
258C2×C42—91no—
259C2×C42—91no—
260#97—32no—
261#97—92no—
262#97—91no—
263#97—91no—
264#97—91no—
265#97D3211yescharacteristic, complemented
266C4×C8—32no—
267C4×C8—32no—
268C4×C8—92no—
269C4×C8—92no—
270C23×C3—32no—
271C22×D3—32no—
272C22×D3—38no—
273C22×D3—61no—
274C22×D3—68no—
275C22×D3C2×C4×D312yes—
276C2×C3×C4—21no—
277C2×C3×C4—22no—
278C2×C3×C4—32no—
279C2×C3×C4—34no—
280C2×C3×C4—34no—
281C2×C3×C4—34no—
282C2×C3×C4C2×C4×D314yes—
283C2×C3×C4C23×D312yes—
284C2×Dic3—32no—
285C2×Dic3—38no—
286C2×Dic3—34no—
287C2×Dic3—61no—
288C2×Dic3—62no—
289C2×Dic3C2×C4×D314yes—
290C2×Dic3C2×C4×D312yes—
291C4×D3—38no—
292C4×D3—34no—
293C4×D3—34no—
294C4×D3—38no—
295C4×D3—62no—
296C4×D3—62no—
297C4×D3—68no—
298C4×D3—68no—
299C4×D3—124no—
300C4×D3C2×C4×D314yes—
301C4×D3C2×C4×D314yes—
302C3×C8—22no—
303C3×C8—22no—
304C3×C8—34no—
305C3×C8—34no—
306C3×C8C2×C4×D314yes—
307C3×C8C2×C4×D314yes—
308C3⋊C8—34no—
309C3⋊C8—34no—
310C3⋊C8—62no—
311C3⋊C8—62no—
312C3⋊C8C2×C4×D314yes—
313C3⋊C8C2×C4×D314yes—
314C2×C32C22×C4211yescharacteristic
315C2×C32C2×#13112yes—
316C3⋊D3#40514yescomplemented
317C3×D3—24no—
318C24—91no—
319C22×C4—32no—
320C22×C4—91no—
321C22×C4—94no—
322C22×C4—94no—
323C22×C4—92no—
324C22×C4—92no—
325C22×C4—91no—
326C22×C4—92no—
327M16—38no—
328M16—98no—
329C2×C8—32no—
330C2×C8—32no—
331C2×C8—38no—
332C2×C8—94no—
333C2×C8—94no—
334C2×C8—98no—
335C2×C8—91no—
336C2×C8—91no—
337C2×C8—94no—
338C2×C8—94no—
339C2×C8C2×D3211yescharacteristic
340C2×C8C2×D3211yescharacteristic
341C4⋊C4—34no—
342C4⋊C4—94no—
343C22⋊C4—34no—
344C22⋊C4—94no—
345C42—32no—
346C42—92no—
347C42—91no—
348C42—92no—
349C42C2×D3211yescharacteristic
350C22×C3—21no—
351C22×C3—34no—
352C22×C3—64no—
353C22×C3C22×C4×D312yes—
354C2×D3—24no—
355C2×D3—34no—
356C2×D3—38no—
357C2×D3—62no—
358C2×D3—64no—
359C2×D3—616no—
360C2×D3C42×D314yes—
361C3×C4—24no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—34no—
365C3×C4—42no—
366C3×C4—64no—
367C3×C4C22×C4×D312yes—
368C3×C4C22×C4×D312yes—
369Dic3—24no—
370Dic3—34no—
371Dic3—62no—
372Dic3—64no—
373Dic3—122no—
374Dic3C42×D314yes—
375C32C2×#40511yescharacteristic, complemented, Sylow
376C23—32no—
377C23—94no—
378C23—91no—
379C23—184no—
380C2×C4—32no—
381C2×C4—34no—
382C2×C4—34no—
383C2×C4—34no—
384C2×C4—94no—
385C2×C4—98no—
386C2×C4—91no—
387C2×C4—92no—
388C2×C4—92no—
389C2×C4—92no—
390C2×C4—184no—
391C2×C4—184no—
392C2×C4C4×D3212yes—
393C2×C4C22×D3211yescharacteristic
394C8—34no—
395C8—34no—
396C8—92no—
397C8—92no—
398C8C4×D3212yes—
399C8C4×D3212yes—
400C2×C3—22no—
401C2×C3—21no—
402C2×C3—64no—
403C2×C3C2×C42×D312yes—
404C2×C3D3×#13114yes—
405D3—24no—
406D3—38no—
407D3—64no—
408C22—34no—
409C22—64no—
410C22—94no—
411C22—92no—
412C22—188no—
413C22C2×C4×D3211yescharacteristic
414C4—22no—
415C4—34no—
416C4—64no—
417C4—92no—
418C4—182no—
419C4C2×C4×D3211yescharacteristic
420C4C2×C4×D3211yescharacteristic
421C3—21no—
422C3D3×#40512yescomplemented
423C2—64no—
424C2—94no—
425C2C42×D3211yescharacteristic
426C2#1059470712yes—
subgroupG/H
center, FrattiniC2×C4C22×D32
commutatorC2×C32C22×C42
FittingC32×#97C22
socleC22×C32C23×C4
prime radicalC22×D32C2×C4
cosocleC2×C32×C4C24
hypercenter#97D32
hypocenterC32C2×#405
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #97

Complements

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

NH ≅ G/Ntype
4. C3⋊D3×#97C2semidirect
5. C3×#4708C2semidirect
6. #10590908C2semidirect
7. #10590693C2semidirect
8. #10590668C2semidirect
9. C8×#624C2semidirect
10. C4×#3710C2semidirect
11. #10590318C2semidirect
29. #63791C4semidirect
30. D32×C8C4semidirect
31. C32×#97C22semidirect
32. #63642C22semidirect
33. #63642C22semidirect
34. #63630C22semidirect
35. C3×#815C22semidirect
36. C3×C8×Dic3C22semidirect
37. C3×C4×C3⋊C8C22semidirect
38. #63554C22semidirect
39. #63553C22semidirect
40. Dic3×C3⋊C8C22semidirect
49. #4708D3semidirect
80. C3×ΓL(1,𝔽25)C2×C4semidirect
81. C3×D3×C8C2×C4semidirect
85. #3711C2×C4semidirect
88. D3×C3⋊C8C2×C4semidirect
120. C3×#97C2×D3semidirect
128. #815C2×D3semidirect
132. C8×Dic3C2×D3semidirect
137. C4×C3⋊C8C2×D3semidirect
220. ΓL(1,𝔽25)C4×D3semidirect
228. D3×C8C4×D3semidirect
265. #97D32semidirect
316. C3⋊D3#405semidirect
375. C32C2×#405semidirect
422. C3D3×#405semidirect

Maximal subgroups

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

subgroupindex
C2×#637912
C2×D32×C82
#105939922
C3⋊D3×#972
C3×#47082
#105909082
#105906932
#105906682
C8×#6242
C4×#37102
#105903182
D3×#4053