Finite Group Databasebeta

← #79775

Subgroups — #79775

Order 384.

506 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#914C211yesmaximal, characteristic
2#5574C211yesmaximal, characteristic, complemented
3#5545C211yesmaximal, characteristic, complemented
4C3×#440C211yesmaximal, characteristic, complemented
5Dic3×SD16C211yesmaximal, characteristic, complemented
6C4×#215C211yesmaximal, characteristic, complemented
7C4×#213C211yesmaximal, characteristic, complemented
8#4881C211yesmaximal, characteristic, complemented
9#4872C211yesmaximal, characteristic, complemented
10#4817C211yesmaximal, characteristic, complemented
11#4804C211yesmaximal, characteristic, complemented
12#4785C211yesmaximal, characteristic, complemented
13D3×#102C211yesmaximal, characteristic, complemented
14#4711C211yesmaximal, characteristic, complemented
15#4708C211yesmaximal, characteristic, complemented
16#2946—31nomaximal, Sylow
17C2×#239C2211yescharacteristic
18C2×D3×D4C2211yescharacteristic
19C2×C3×SD16C2211yescharacteristic
20C3×C4×Q8C2211yescharacteristic, complemented
21C3×C4×D4C2211yescharacteristic
22Q8×Dic3C2211yescharacteristic, complemented
23C2×#215C2211yescharacteristic
24D4×Dic3C2211yescharacteristic
25C2×#213C2211yescharacteristic
26C4×#67—21no—
27C2×(C2×D3)⋊C4—21no—
28#914C418yescomplemented
29C2×D24C2211yescharacteristic
30C2×ΓL(1,𝔽25)C2211yescharacteristic
31C2×D3×C8C2211yescharacteristic
32#893—21no—
33#893C2211yescharacteristic
34#893C2211yescharacteristic, complemented
35#892C2211yescharacteristic
36D3×C4⋊C4—21no—
37D3×C4⋊C4C2211yescharacteristic
38#67⋊C4—21no—
39D3×C22⋊C4—21no—
40C4×D12—21no—
41C4×D12C2211yescharacteristic
42C4×D12C2211yescharacteristic, complemented
43#872—21no—
44#872C2211yescharacteristic
45C3×#107C2211yescharacteristic, complemented
46C3×#103C2211yescharacteristic, complemented
47C3×#102C2211yescharacteristic
48C3×#97C2211yescharacteristic, complemented
49#835C2211yescharacteristic, complemented
50#832C2211yescharacteristic
51#821C2211yescharacteristic
52#821C2211yescharacteristic, complemented
53#817C2211yescharacteristic, complemented
54#815C2211yescharacteristic, complemented
55C8×Dic3C2211yescharacteristic, complemented
56#809C2211yescharacteristic
57#809C2211yescharacteristic, complemented
58#808C2211yescharacteristic, complemented
59#807C2211yescharacteristic, complemented
60C4×C3⋊C8C2211yescharacteristic, complemented
61C2×AGL(1,ℤ/8)—31no—
62#520—31no—
63#518—31no—
64#442—31no—
65#442—31no—
66#440—31no—
67#440D311yescharacteristic, complemented
68C4×SD16—31no—
69C4×SD16—31no—
70C4×D8—31no—
71C4×D8—31no—
72#428—31no—
73#416—31no—
74C2×#102—31no—
75#405—31no—
76C23×D3—21no—
77C2×C3×Q8C2311yescharacteristic
78C2×C3×D4C2311yescharacteristic
79C22×C3×C4—21no—
80C2×#67—21no—
81C22×Dic3—21no—
82#239—22no—
83#239C2×C414yescomplemented
84D3×D4—22no—
85D3×D4C2×C414yescomplemented
86C2×D12—21no—
87C2×D12C2311yescharacteristic
88C2×D12C2311yescharacteristic
89C2×C4×D3—21no—
90C2×C4×D3—21no—
91C2×C4×D3—21no—
92C2×C4×D3—21no—
93C2×C4×D3—21no—
94C2×C4×D3—21no—
95C2×C4×D3C2311yescharacteristic
96C3×SD16C2×C414yescomplemented
97C2×C3×C8C2311yescharacteristic
98C2×C3×C8C2311yescharacteristic
99C3×C4⋊C4—21no—
100C3×C4⋊C4C2311yescharacteristic
101C3×C4⋊C4C2311yescharacteristic
102C3×C22⋊C4—21no—
103C3×C42—21no—
104C3×C42C2311yescharacteristic
105#217—21no—
106#215C2×C414yescomplemented
107#213C2×C414yescomplemented
108(C2×D3)⋊C4—21no—
109(C2×D3)⋊C4—21no—
110(C2×D3)⋊C4—21no—
111(C2×D3)⋊C4—21no—
112(C2×D3)⋊C4—21no—
113(C2×D3)⋊C4D411yescharacteristic
114(C2×D3)⋊C4D411yescharacteristic
115C4⋊Dic3—21no—
116C4⋊Dic3C2311yescharacteristic
117C4⋊Dic3C2311yescharacteristic
118Dic3⋊C4—21no—
119Dic3⋊C4D411yescharacteristic
120Dic3⋊C4D411yescharacteristic
121C4×Dic3—21no—
122C4×Dic3—21no—
123C4×Dic3C2311yescharacteristic
124C2×C3⋊C8C2311yescharacteristic
125C2×C3⋊C8C2311yescharacteristic
126D24C2×C414yescomplemented
127ΓL(1,𝔽25)C2×C414yescomplemented
128D3×C8—22no—
129C2×#41—31no—
130C22×D4—31no—
131AGL(1,ℤ/8)—38no—
132C2×SD16—31no—
133C2×SD16C2×D311yescharacteristic
134C2×D8—31no—
135C2×D8—31no—
136C2×M16—31no—
137C22×C8—31no—
138C4×Q8—31no—
139C4×Q8C2×D311yescharacteristic, complemented
140C4×D4—31no—
141C4×D4—31no—
142C4×D4—31no—
143C4×D4—31no—
144C4×D4—31no—
145C4×D4—61no—
146C4×D4—61no—
147C4×D4—61no—
148C4×D4—61no—
149C4×D4C2×D311yescharacteristic
150#117—31no—
151#117—31no—
152#117—61no—
153C2×C4⋊C4—31no—
154C2×C4⋊C4—61no—
155C2×C22⋊C4—61no—
156C2×C22⋊C4—61no—
157#107—31no—
158#107C2×D311yescharacteristic, complemented
159#106—31no—
160#106—31no—
161#103—31no—
162#103C2×D311yescharacteristic, complemented
163#102—31no—
164#102—31no—
165#102—31no—
166#102—31no—
167#102—31no—
168#102C2×D311yescharacteristic
169#97—31no—
170#97C2×D311yescharacteristic, complemented
171C4×C8—31no—
172C4×C8—31no—
173C23×C3—21no—
174C22×D3—21no—
175C22×D3—21no—
176C22×D3—24no—
177C22×D3—81no—
178C22×D3—81no—
179C22×D3C2×D411yescharacteristic
180C3×Q8—21no—
181C3×Q8C22×C412yes—
182C3×D4—21no—
183C3×D4C22×C412yes—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—81no—
188C2×C3×C4C2×D411yescharacteristic
189C2×C3×C4C2×D411yescharacteristic
190C2×C3×C4C2411yescharacteristic
191#67—24no—
192C2×Dic3—21no—
193C2×Dic3—21no—
194C2×Dic3—81no—
195C2×Dic3C2×D411yescharacteristic
196C2×Dic3C2×D411yescharacteristic
197C2×Dic3C2×D411yescharacteristic
198D12—24no—
199D12—21no—
200D12—21no—
201D12C22×C412yes—
202D12C22×C412yes—
203C4×D3—24no—
204C4×D3—81no—
205C4×D3—81no—
206C4×D3—81no—
207C4×D3—81no—
208C4×D3—81no—
209C4×D3C22×C412yes—
210C4×D3#4112yes—
211C3×C8—21no—
212C3×C8C22×C412yes—
213C3⋊C8—21no—
214C3⋊C8C22×C412yes—
215C24—61no—
216#41—34no—
217#41—62no—
218C2×Q8C22×D311yescharacteristic
219C2×D4—34no—
220C2×D4—31no—
221C2×D4—31no—
222C2×D4—61no—
223C2×D4—62no—
224C2×D4—61no—
225C2×D4C22×D311yescharacteristic
226C22×C4—21no—
227C22×C4—31no—
228C22×C4—61no—
229C22×C4—61no—
230C22×C4—61no—
231C22×C4—61no—
232C22×C4—61no—
233C22×C4—61no—
234C22×C4—61no—
235SD16—34no—
236SD16C4×D314yescomplemented
237D8—34no—
238D8—34no—
239M16—34no—
240C2×C8—31no—
241C2×C8—31no—
242C2×C8—62no—
243C2×C8C22×D311yescharacteristic
244C2×C8C22×D311yescharacteristic
245C4⋊C4—21no—
246C4⋊C4—31no—
247C4⋊C4—31no—
248C4⋊C4—31no—
249C4⋊C4—31no—
250C4⋊C4—61no—
251C4⋊C4—61no—
252C4⋊C4C22×D311yescharacteristic
253C4⋊C4C22×D311yescharacteristic
254C22⋊C4—21no—
255C22⋊C4—31no—
256C22⋊C4—31no—
257C22⋊C4—61no—
258C22⋊C4—61no—
259C22⋊C4—61no—
260C22⋊C4—61no—
261C22⋊C4—61no—
262C22⋊C4—61no—
263C42—21no—
264C42—31no—
265C42—61no—
266C42—61no—
267C42C22×D311yescharacteristic
268C22×C3—22no—
269C22×C3—41no—
270C22×C3—41no—
271C22×C3C22×D411yescharacteristic
272C2×D3—21no—
273C2×D3—21no—
274C2×D3—22no—
275C2×D3—22no—
276C2×D3—41no—
277C2×D3—41no—
278C2×D3—41no—
279C2×D3—41no—
280C2×D3—84no—
281C2×D3C4×D412yes—
282C3×C4—22no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—41no—
286C3×C4—41no—
287C3×C4C23×C411yescharacteristic
288C3×C4C2×#4111yescharacteristic
289Dic3—21no—
290Dic3—21no—
291Dic3—41no—
292Dic3—41no—
293Dic3C4×D412yes—
294C23—21no—
295C23—31no—
296C23—64no—
297C23—61no—
298C23—61no—
299C23—241no—
300C23—241no—
301Q8—21no—
302Q8C2×C4×D312yes—
303D4—21no—
304D4—32no—
305D4—32no—
306D4—64no—
307D4—64no—
308D4—61no—
309D4—61no—
310D4C2×C4×D312yes—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—31no—
315C2×C4—32no—
316C2×C4—32no—
317C2×C4—31no—
318C2×C4—31no—
319C2×C4—64no—
320C2×C4—61no—
321C2×C4—61no—
322C2×C4—81no—
323C2×C4—241no—
324C2×C4—241no—
325C2×C4—241no—
326C2×C4—241no—
327C2×C4—241no—
328C2×C4—241no—
329C2×C4D3×D411yescharacteristic
330C2×C4D3×D411yescharacteristic
331C2×C4C23×D311yescharacteristic
332C8—21no—
333C8—32no—
334C8—61no—
335C8C2×C4×D312yes—
336C2×C3—42no—
337C2×C3C2×C4×D411yescharacteristic
338C2×C3#57611yescharacteristic
339C2×C3#57711yescharacteristic
340D3—22no—
341D3—42no—
342D3—42no—
343C22—22no—
344C22—32no—
345C22—41no—
346C22—41no—
347C22—61no—
348C22—61no—
349C22—62no—
350C22—62no—
351C22—121no—
352C22—121no—
353C22—121no—
354C22—121no—
355C22—244no—
356C22C2×D3×D411yescharacteristic
357C4—21no—
358C4—21no—
359C4—22no—
360C4—32no—
361C4—41no—
362C4—41no—
363C4—61no—
364C4—61no—
365C4—121no—
366C4—121no—
367C4C22×C4×D311yescharacteristic
368C4D3×#4111yescharacteristic
369C3#294611yescharacteristic, complemented, Sylow
370C2—42no—
371C2—62no—
372C2—122no—
373C2—122no—
374C2C4×D3×D411yescharacteristic
375C2#577411yescharacteristic
376C2#577811yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutatorC3×C4C23×C4
FrattiniC2×C4C23×D3
FittingC3×#440C2
socleC22×C3C22×D4
prime radicalC2×#914C2
cosocleC2×C3×C4C24
hypercenter#440D3
hypocenterC3#2946
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. #5574C2semidirect
3. #5545C2semidirect
4. C3×#440C2semidirect
5. Dic3×SD16C2semidirect
6. C4×#215C2semidirect
7. C4×#213C2semidirect
8. #4881C2semidirect
9. #4872C2semidirect
10. #4817C2semidirect
11. #4804C2semidirect
12. #4785C2semidirect
13. D3×#102C2semidirect
14. #4711C2semidirect
15. #4708C2semidirect
20. C3×C4×Q8C22semidirect
22. Q8×Dic3C22semidirect
28. #914C4semidirect
34. #893C22semidirect
42. C4×D12C22semidirect
45. C3×#107C22semidirect
46. C3×#103C22semidirect
48. C3×#97C22semidirect
49. #835C22semidirect
52. #821C22semidirect
53. #817C22semidirect
54. #815C22semidirect
55. C8×Dic3C22semidirect
57. #809C22semidirect
58. #808C22semidirect
59. #807C22semidirect
60. C4×C3⋊C8C22semidirect
67. #440D3semidirect
83. #239C2×C4semidirect
85. D3×D4C2×C4semidirect
96. C3×SD16C2×C4semidirect
106. #215C2×C4semidirect
107. #213C2×C4semidirect
126. D24C2×C4semidirect
127. ΓL(1,𝔽25)C2×C4semidirect
139. C4×Q8C2×D3semidirect
158. #107C2×D3semidirect
162. #103C2×D3semidirect
170. #97C2×D3semidirect
236. SD16C4×D3semidirect
369. C3#2946semidirect

Maximal subgroups

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

subgroupindex
C2×#9142
#55742
#55452
C3×#4402
Dic3×SD162
C4×#2152
C4×#2132
#48812
#48722
#48172
#48042
#47852
D3×#1022
#47112
#47082
#29463