Finite Group Databasebeta

← #80445

Subgroups — #80445

Order 384.

500 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#916C211yesmaximal, characteristic, complemented
2C2×#914C211yesmaximal, characteristic, complemented
3#5726C211yesmaximal, characteristic, complemented
4#5554C211yesmaximal, characteristic, complemented
5C3×#461C211yesmaximal, characteristic, complemented
6#5173C211yesmaximal, characteristic, complemented
7#5169C211yesmaximal, characteristic, complemented
8#5086C211yesmaximal, characteristic, complemented
9#5014C211yesmaximal, characteristic, complemented
10#4844C211yesmaximal, characteristic, complemented
11#4836C211yesmaximal, characteristic, complemented
12#4816C211yesmaximal, characteristic, complemented
13#4810C211yesmaximal, characteristic, complemented
14#4808C211yesmaximal, characteristic, complemented
15#4807C211yesmaximal, characteristic, complemented
16#3267—31nomaximal, Sylow
17C2×#239C2211yescharacteristic
18C2×#239C2211yescharacteristic, complemented
19C2×#237C2211yescharacteristic
20C2×D3×D4C2211yescharacteristic
21C2×C3×SD16C2211yescharacteristic
22C2×C3×SD16C2211yescharacteristic
23C3×C4⋊Q8C2211yescharacteristic, complemented
24C3×C4×D4C2211yescharacteristic
25#946C2211yescharacteristic
26#946C2211yescharacteristic, complemented
27C2×#216C2211yescharacteristic, complemented
28C2×#216C2211yescharacteristic, complemented
29C2×#215C2211yescharacteristic
30C2×#215C2211yescharacteristic
31C2×#213C2211yescharacteristic
32#930—21no—
33C2×(C2×D3)⋊C4—21no—
34#916—24no—
35#914—24no—
36C2×D24C2211yescharacteristic
37C2×#204C2211yescharacteristic, complemented
38C2×ΓL(1,𝔽25)C2211yescharacteristic
39C2×D3×C8C2211yescharacteristic, complemented
40#897C2211yescharacteristic
41#895—21no—
42#895C2211yescharacteristic
43#894—21no—
44#894—21no—
45D3×C4⋊C4—21no—
46#886—21no—
47#882—21no—
48#875C2211yescharacteristic
49C4×D12C2211yescharacteristic
50C4×D12C2211yescharacteristic, complemented
51C3×C4⋊C8C2211yescharacteristic, complemented
52C3×#103C2211yescharacteristic, complemented
53C3×#103C2211yescharacteristic, complemented
54#832C2211yescharacteristic
55#821C2211yescharacteristic
56(C2×D3)⋊C8C2211yescharacteristic
57(C2×D3)⋊C8C2211yescharacteristic, complemented
58#816C2211yescharacteristic, complemented
59#809C2211yescharacteristic, complemented
60#808C2211yescharacteristic, complemented
61#803C2211yescharacteristic, complemented
62C2×AGL(1,ℤ/8)—31no—
63C2×#135—31no—
64#547—31no—
65#546—31no—
66#497—31no—
67#470—31no—
68#465—31no—
69#463—31no—
70#461D311yescharacteristic, complemented
71#452—31no—
72#452—31no—
73#450—31no—
74#449—31no—
75#442—31no—
76#435—31no—
77C23×D3—21no—
78C2×C3×Q8C2311yescharacteristic
79C2×C3×Q8C2311yescharacteristic
80C2×C3×D4C2311yescharacteristic
81C22×C3×C4—21no—
82C2×#67—21no—
83C2×#67—21no—
84C22×Dic3—21no—
85#239—22no—
86#239—22no—
87#239—41no—
88#239—41no—
89#237—22no—
90#237—41no—
91D3×D4—22no—
92D3×D4—41no—
93C2×D12—21no—
94C2×D12—21no—
95C2×D12—21no—
96C2×D12D411yescharacteristic
97C2×D12C2311yescharacteristic
98C2×D12C2311yescharacteristic
99C2×C4×D3—21no—
100C2×C4×D3—21no—
101C2×C4×D3—21no—
102C2×C4×D3C2311yescharacteristic
103C2×C4×D3C2311yescharacteristic
104C2×Dic6C2311yescharacteristic
105C3×SD16—22no—
106C3×SD16—22no—
107C2×C3×C8C2311yescharacteristic
108C2×C3×C8C2311yescharacteristic
109C3×C4⋊C4—21no—
110C3×C4⋊C4—21no—
111C3×C4⋊C4C2311yescharacteristic
112C3×C22⋊C4—21no—
113C3×C42C2311yescharacteristic
114#216—22no—
115#216—41no—
116#215—22no—
117#215—41no—
118#213D414yescomplemented
119(C2×D3)⋊C4—21no—
120(C2×D3)⋊C4—21no—
121(C2×D3)⋊C4—21no—
122(C2×D3)⋊C4—21no—
123(C2×D3)⋊C4—21no—
124(C2×D3)⋊C4—21no—
125(C2×D3)⋊C4—21no—
126(C2×D3)⋊C4D411yescharacteristic
127(C2×D3)⋊C4D411yescharacteristic
128C4⋊Dic3—21no—
129C4⋊Dic3D411yescharacteristic
130C4⋊Dic3C2311yescharacteristic
131Dic3⋊C4—21no—
132Dic3⋊C4—21no—
133C2×C3⋊C8C2311yescharacteristic
134C2×C3⋊C8C2311yescharacteristic
135D24—22no—
136#204—22no—
137ΓL(1,𝔽25)—22no—
138D3×C8—22no—
139C2×#41—31no—
140C2×#41—31no—
141C2×#41—31no—
142C22×D4—31no—
143AGL(1,ℤ/8)—64no—
144#135—64no—
145C2×Q16—31no—
146C2×Q16—31no—
147C2×SD16—31no—
148C2×SD16—31no—
149C2×SD16—31no—
150C2×SD16C2×D311yescharacteristic
151C2×SD16C2×D311yescharacteristic
152C2×D8—31no—
153C2×D8—31no—
154C2×M16—31no—
155C22×C8—31no—
156C4⋊Q8C2×D311yescharacteristic, complemented
157#124—31no—
158#123—61no—
159#123—61no—
160#123—61no—
161C22⋊Q8—31no—
162C22⋊Q8—31no—
163C22⋊Q8—31no—
164#121—31no—
165#121—61no—
166#121—61no—
167#120—61no—
168C4×D4—31no—
169C4×D4—31no—
170C4×D4C2×D311yescharacteristic
171C2×C4⋊C4—61no—
172C2×C22⋊C4—61no—
173#106—31no—
174C4⋊C8C2×D311yescharacteristic, complemented
175#103—31no—
176#103C2×D311yescharacteristic, complemented
177#103C2×D311yescharacteristic, complemented
178#102—31no—
179#102—31no—
180#102—31no—
181C22⋊C8—31no—
182C22⋊C8—31no—
183#97—31no—
184C23×C3—21no—
185C22×D3—21no—
186C22×D3—21no—
187C22×D3—42no—
188C22×D3—42no—
189C22×D3—81no—
190C22×D3C2×D411yescharacteristic
191C22×D3C2×D411yescharacteristic
192C3×Q8—21no—
193C3×Q8—21no—
194C3×Q8—21no—
195C3×Q8—21no—
196C3×D4—21no—
197C3×D4C2×D412yes—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—81no—
202C2×C3×C4C2×D411yescharacteristic
203C2×C3×C4C2×D411yescharacteristic
204C2×C3×C4C2411yescharacteristic
205#67—42no—
206#67—42no—
207C2×Dic3—21no—
208C2×Dic3—21no—
209C2×Dic3—42no—
210C2×Dic3C2×D411yescharacteristic
211C2×Dic3C2×D411yescharacteristic
212D12—21no—
213D12—21no—
214D12—21no—
215D12—41no—
216D12—42no—
217D12—42no—
218D12—81no—
219D12C2×D412yes—
220C4×D3—21no—
221C4×D3—21no—
222C4×D3—21no—
223C4×D3—21no—
224C4×D3—42no—
225C4×D3—42no—
226C4×D3—42no—
227Dic6—21no—
228Dic6—21no—
229C3×C8—21no—
230C3×C8—21no—
231C3⋊C8—21no—
232C3⋊C8C2×D412yes—
233C24—61no—
234#41—62no—
235#41—62no—
236#41—62no—
237#41—121no—
238#41—121no—
239#41—121no—
240C2×Q8—31no—
241C2×Q8C22×D311yescharacteristic
242C2×Q8C22×D311yescharacteristic
243C2×D4—31no—
244C2×D4—31no—
245C2×D4—31no—
246C2×D4—61no—
247C2×D4—61no—
248C2×D4—61no—
249C2×D4—61no—
250C2×D4—62no—
251C2×D4—61no—
252C2×D4—121no—
253C2×D4C22×D311yescharacteristic
254C22×C4—21no—
255C22×C4—31no—
256C22×C4—31no—
257C22×C4—61no—
258C22×C4—61no—
259C22×C4—61no—
260C22×C4—61no—
261Q16—62no—
262Q16—121no—
263SD16—22no—
264SD16—22no—
265SD16—62no—
266SD16—62no—
267SD16—121no—
268D8—34no—
269D8—62no—
270M16—62no—
271C2×C8—31no—
272C2×C8—31no—
273C2×C8—62no—
274C2×C8C22×D311yescharacteristic
275C2×C8C22×D311yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—31no—
279C4⋊C4—31no—
280C4⋊C4—61no—
281C4⋊C4—61no—
282C4⋊C4—61no—
283C4⋊C4C22×D311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—31no—
286C22⋊C4—31no—
287C22⋊C4—61no—
288C22⋊C4—61no—
289C22⋊C4—61no—
290C22⋊C4—61no—
291C22⋊C4—61no—
292C22⋊C4—61no—
293C22⋊C4—61no—
294C42C22×D311yescharacteristic
295C22×C3—22no—
296C22×C3—41no—
297C22×C3—41no—
298C22×C3C22×D411yescharacteristic
299C2×D3—21no—
300C2×D3—21no—
301C2×D3—22no—
302C2×D3—21no—
303C2×D3—21no—
304C2×D3—21no—
305C2×D3—21no—
306C2×D3—41no—
307C2×D3—41no—
308C2×D3—41no—
309C2×D3—41no—
310C2×D3—41no—
311C2×D3—84no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—41no—
315C3×C4—41no—
316C3×C4—41no—
317C3×C4C22×D411yescharacteristic
318C3×C4H(5,𝔽2)11yescharacteristic
319Dic3—21no—
320Dic3—21no—
321Dic3—41no—
322Dic3—41no—
323C23—21no—
324C23—31no—
325C23—31no—
326C23—61no—
327C23—61no—
328C23—122no—
329C23—122no—
330C23—241no—
331Q8—21no—
332Q8—21no—
333Q8—21no—
334Q8—21no—
335Q8—61no—
336Q8—61no—
337D4—21no—
338D4—32no—
339D4—61no—
340D4—61no—
341D4—61no—
342D4—121no—
343D4—122no—
344D4—122no—
345D4—122no—
346D4—122no—
347D4—241no—
348D4D3×D412yes—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—31no—
353C2×C4—31no—
354C2×C4—61no—
355C2×C4—61no—
356C2×C4—61no—
357C2×C4—61no—
358C2×C4—61no—
359C2×C4—61no—
360C2×C4—81no—
361C2×C4—122no—
362C2×C4—122no—
363C2×C4—122no—
364C2×C4—122no—
365C2×C4D3×D411yescharacteristic
366C2×C4D3×D411yescharacteristic
367C2×C4C23×D311yescharacteristic
368C8—21no—
369C8—21no—
370C8—32no—
371C8—61no—
372C2×C3—42no—
373C2×C3D4211yescharacteristic
374C2×C3#57511yescharacteristic
375C2×C3#57711yescharacteristic
376D3—41no—
377D3—41no—
378D3—42no—
379D3—81no—
380C22—22no—
381C22—41no—
382C22—41no—
383C22—61no—
384C22—61no—
385C22—61no—
386C22—61no—
387C22—61no—
388C22—61no—
389C22—62no—
390C22—121no—
391C22—121no—
392C22—121no—
393C22—121no—
394C22—121no—
395C22—244no—
396C22C2×D3×D411yescharacteristic
397C4—21no—
398C4—21no—
399C4—41no—
400C4—41no—
401C4—41no—
402C4—61no—
403C4—61no—
404C4—121no—
405C4—121no—
406C4C2×D3×D411yescharacteristic
407C4#100911yescharacteristic
408C3#326711yescharacteristic, complemented, Sylow
409C2—42no—
410C2—121no—
411C2—121no—
412C2—122no—
413C2—241no—
414C2#560911yescharacteristic
415C2#576211yescharacteristic
416C2#577711yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#461C2
socleC22×C3C22×D4
hypercenter#461D3
hypocenterC3#3267
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. C2×#916C2semidirect
2. C2×#914C2semidirect
3. #5726C2semidirect
4. #5554C2semidirect
5. C3×#461C2semidirect
6. #5173C2semidirect
7. #5169C2semidirect
8. #5086C2semidirect
9. #5014C2semidirect
10. #4844C2semidirect
11. #4836C2semidirect
12. #4816C2semidirect
13. #4810C2semidirect
14. #4808C2semidirect
15. #4807C2semidirect
18. C2×#239C22semidirect
23. C3×C4⋊Q8C22semidirect
26. #946C22semidirect
27. C2×#216C22semidirect
28. C2×#216C22semidirect
37. C2×#204C22semidirect
39. C2×D3×C8C22semidirect
50. C4×D12C22semidirect
51. C3×C4⋊C8C22semidirect
52. C3×#103C22semidirect
53. C3×#103C22semidirect
57. (C2×D3)⋊C8C22semidirect
58. #816C22semidirect
59. #809C22semidirect
60. #808C22semidirect
61. #803C22semidirect
70. #461D3semidirect
118. #213D4semidirect
156. C4⋊Q8C2×D3semidirect
174. C4⋊C8C2×D3semidirect
176. #103C2×D3semidirect
177. #103C2×D3semidirect
408. C3#3267semidirect

Maximal subgroups

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

subgroupindex
C2×#9162
C2×#9142
#57262
#55542
C3×#4612
#51732
#51692
#50862
#50142
#48442
#48362
#48162
#48102
#48082
#48072
#32673