Finite Group Databasebeta

← #79507

Subgroups — #79507

Order 384.

472 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#909C211yesmaximal, characteristic, complemented
2C22×Dic12C211yesmaximal, characteristic, complemented
3#5552C211yesmaximal, characteristic
4D4×Dic6C211yesmaximal, characteristic, complemented
5C3×#435C211yesmaximal, characteristic, complemented
6#5137C211yesmaximal, characteristic, complemented
7#5114C211yesmaximal, characteristic, complemented
8#4849C211yesmaximal, characteristic, complemented
9#4845C211yesmaximal, characteristic, complemented
10#4739C211yesmaximal, characteristic, complemented
11#4739C211yesmaximal, characteristic, complemented
12#4738C211yesmaximal, characteristic, complemented
13#4733C211yesmaximal, characteristic, complemented
14#4716C211yesmaximal, characteristic, complemented
15#4715C211yesmaximal, characteristic, complemented
16#3270—31nomaximal, Sylow
17C2×#235C2211yescharacteristic
18C22×Dic6C2211yescharacteristic
19C22×Dic6C2211yescharacteristic
20C22×Dic6C2211yescharacteristic
21C2×C3×M16C2211yescharacteristic
22C22×C3×C8C2211yescharacteristic
23C3×C4×D4C2211yescharacteristic
24#939—21no—
25D4×Dic3—21no—
26#930C2211yescharacteristic
27#924C2211yescharacteristic
28#924C2211yescharacteristic
29#924C2211yescharacteristic
30#909—24no—
31C2×Dic12—24no—
32C2×Dic12C2211yescharacteristic
33C2×Dic12C2211yescharacteristic
34C2×Dic12C2211yescharacteristic
35C2×Dic12C2211yescharacteristic
36C2×Dic12C2211yescharacteristic
37C2×Dic12C2211yescharacteristic
38C2×#204C2211yescharacteristic
39C2×#204C2211yescharacteristic
40C2×#204C2211yescharacteristic
41#896—21no—
42#888—21no—
43#885—21no—
44#67⋊C4—21no—
45#878—21no—
46#878—21no—
47#875C2211yescharacteristic
48#869C2211yescharacteristic
49C4×Dic6C2211yescharacteristic
50C4×Dic6C2211yescharacteristic
51C3×C4⋊C8C2211yescharacteristic
52C3×C22⋊C8C2211yescharacteristic
53C3×C22⋊C8C2211yescharacteristic
54C3×#97C2211yescharacteristic
55#821C2211yescharacteristic
56#817C2211yescharacteristic
57#816C2211yescharacteristic
58#816C2211yescharacteristic
59#816C2211yescharacteristic
60#816C2211yescharacteristic
61#816C2211yescharacteristic
62C2×#137—31no—
63C22×Q16—31no—
64D4×Q8—31no—
65#548—31no—
66#497—31no—
67#470—31no—
68#465—31no—
69#464—31no—
70#462—31no—
71#452—31no—
72#451—31no—
73#451—31no—
74#448—31no—
75#441—31no—
76#435D311yescharacteristic, complemented
77C2×C3×D4D411yescharacteristic
78C22×C3×C4C2311yescharacteristic
79C22×C3×C4C2311yescharacteristic
80C2×#67—21no—
81C2×#67—21no—
82C22×Dic3—21no—
83C22×Dic3—21no—
84C22×Dic3—21no—
85#235—22no—
86#235—41no—
87C2×D12C2311yescharacteristic
88C2×C4×D3—21no—
89C2×Dic6—22no—
90C2×Dic6—22no—
91C2×Dic6—22no—
92C2×Dic6—21no—
93C2×Dic6—21no—
94C2×Dic6—21no—
95C2×Dic6—41no—
96C2×Dic6—41no—
97C2×Dic6—41no—
98C2×Dic6C2311yescharacteristic
99C2×Dic6C2311yescharacteristic
100C2×Dic6C2311yescharacteristic
101C2×Dic6C2311yescharacteristic
102C2×Dic6C2311yescharacteristic
103C3×M16—22no—
104C2×C3×C8—22no—
105C2×C3×C8C2311yescharacteristic
106C2×C3×C8C2311yescharacteristic
107C2×C3×C8C2311yescharacteristic
108C2×C3×C8C2311yescharacteristic
109C3×C4⋊C4D411yescharacteristic
110C3×C22⋊C4D411yescharacteristic
111C3×C22⋊C4D411yescharacteristic
112C3×C42C2311yescharacteristic
113#217—21no—
114#217—21no—
115#217—21no—
116(C2×D3)⋊C4—21no—
117(C2×D3)⋊C4—21no—
118(C2×D3)⋊C4—21no—
119C4⋊Dic3—21no—
120C4⋊Dic3—21no—
121C4⋊Dic3C2311yescharacteristic
122C4⋊Dic3C2311yescharacteristic
123Dic3⋊C4—21no—
124Dic3⋊C4—21no—
125Dic3⋊C4—21no—
126Dic3⋊C4—21no—
127Dic3⋊C4—21no—
128C4×Dic3—21no—
129C4×Dic3—21no—
130Dic12—22no—
131Dic12—22no—
132Dic12—22no—
133Dic12—22no—
134Dic12—41no—
135Dic12D414yescomplemented
136#204—22no—
137#204—22no—
138#204—41no—
139C2×#41—31no—
140C22×Q8—31no—
141C22×Q8—31no—
142C22×Q8—31no—
143#137—64no—
144C2×Q16—31no—
145C2×Q16—31no—
146C2×Q16—31no—
147C2×Q16—31no—
148C2×Q16—31no—
149C2×Q16—31no—
150C2×Q16—64no—
151C2×SD16—31no—
152C2×SD16—31no—
153C2×SD16—31no—
154C2×M16C2×D311yescharacteristic
155C22×C8C2×D311yescharacteristic
156C4⋊Q8—31no—
157C4⋊Q8—61no—
158#124—31no—
159#124—61no—
160C22⋊Q8—31no—
161C22⋊Q8—31no—
162C22⋊Q8—31no—
163C22⋊Q8—61no—
164C22⋊Q8—61no—
165C22⋊Q8—61no—
166#121—31no—
167#121—61no—
168C4×Q8—31no—
169C4×Q8—31no—
170C4×D4—61no—
171C4×D4—61no—
172C4×D4C2×D311yescharacteristic
173#106—31no—
174C4⋊C8C2×D311yescharacteristic
175#103—31no—
176#103—31no—
177#103—31no—
178#103—31no—
179#103—31no—
180#102—31no—
181C22⋊C8C2×D311yescharacteristic
182C22⋊C8C2×D311yescharacteristic
183#97C2×D311yescharacteristic
184C23×C3C2×D411yescharacteristic
185C23×C3C2×D411yescharacteristic
186C22×D3—21no—
187C3×D4—22no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4C2×D411yescharacteristic
193C2×C3×C4C2×D411yescharacteristic
194C2×C3×C4C2×D411yescharacteristic
195C2×C3×C4C2×D411yescharacteristic
196C2×C3×C4C2411yescharacteristic
197#67—42no—
198#67—42no—
199C2×Dic3—21no—
200C2×Dic3—21no—
201C2×Dic3—21no—
202C2×Dic3—21no—
203C2×Dic3—21no—
204C2×Dic3—21no—
205C2×Dic3—21no—
206C2×Dic3—42no—
207C2×Dic3—42no—
208C2×Dic3—42no—
209D12—21no—
210D12—21no—
211C4×D3—42no—
212Dic6—21no—
213Dic6—21no—
214Dic6—21no—
215Dic6—21no—
216Dic6—21no—
217Dic6—21no—
218Dic6—21no—
219Dic6—21no—
220Dic6—42no—
221Dic6—42no—
222Dic6—42no—
223Dic6C2×D412yes—
224Dic6C2×D412yes—
225C3×C8—21no—
226C3×C8—21no—
227C3×C8—21no—
228C3×C8C2×D412yes—
229#41—62no—
230#41—121no—
231C2×Q8—31no—
232C2×Q8—31no—
233C2×Q8—31no—
234C2×Q8—31no—
235C2×Q8—31no—
236C2×Q8—62no—
237C2×Q8—62no—
238C2×Q8—62no—
239C2×Q8—61no—
240C2×Q8—61no—
241C2×Q8—61no—
242C2×Q8—121no—
243C2×Q8—121no—
244C2×Q8—121no—
245C2×D4—31no—
246C2×D4—61no—
247C2×D4—61no—
248C2×D4D1211yescharacteristic
249C22×C4—61no—
250C22×C4—61no—
251C22×C4—61no—
252C22×C4—61no—
253C22×C4C22×D311yescharacteristic
254C22×C4C22×D311yescharacteristic
255Q16—34no—
256Q16—62no—
257Q16—62no—
258Q16—62no—
259Q16—62no—
260Q16—121no—
261SD16—62no—
262SD16—62no—
263SD16—121no—
264M16—22no—
265C2×C8—22no—
266C2×C8C22×D311yescharacteristic
267C2×C8C22×D311yescharacteristic
268C2×C8C22×D311yescharacteristic
269C2×C8C22×D311yescharacteristic
270C4⋊C4—31no—
271C4⋊C4—31no—
272C4⋊C4—61no—
273C4⋊C4—61no—
274C4⋊C4—61no—
275C4⋊C4—61no—
276C4⋊C4—61no—
277C4⋊C4—61no—
278C4⋊C4—61no—
279C4⋊C4D1211yescharacteristic
280C22⋊C4—61no—
281C22⋊C4—61no—
282C22⋊C4—61no—
283C22⋊C4—61no—
284C22⋊C4—61no—
285C22⋊C4—61no—
286C22⋊C4D1211yescharacteristic
287C22⋊C4D1211yescharacteristic
288C42—61no—
289C42—61no—
290C42C22×D311yescharacteristic
291C22×C3—21no—
292C22×C3—21no—
293C22×C3—21no—
294C22×C3—21no—
295C22×C3—21no—
296C22×C3#13712yescomplemented
297C22×C3C22×D411yescharacteristic
298C2×D3—41no—
299C2×D3—41no—
300C2×D3—41no—
301C3×C4—21no—
302C3×C4—21no—
303C3×C4—21no—
304C3×C4—21no—
305C3×C4C22×D411yescharacteristic
306C3×C4H(5,𝔽2)11yescharacteristic
307Dic3—22no—
308Dic3—22no—
309Dic3—41no—
310Dic3—41no—
311Dic3—41no—
312Dic3—41no—
313Dic3—41no—
314C23—61no—
315C23C2×D1211yescharacteristic
316C23C2×D1211yescharacteristic
317Q8—32no—
318Q8—32no—
319Q8—61no—
320Q8—61no—
321Q8—61no—
322Q8—61no—
323Q8—61no—
324Q8—61no—
325Q8—61no—
326Q8—61no—
327Q8—122no—
328Q8—122no—
329Q8—122no—
330D4—22no—
331D4—61no—
332D4—61no—
333D4—122no—
334D4—122no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—61no—
340C2×C4—61no—
341C2×C4—61no—
342C2×C4—61no—
343C2×C4—61no—
344C2×C4—61no—
345C2×C4—61no—
346C2×C4—122no—
347C2×C4—122no—
348C2×C4—122no—
349C2×C4—122no—
350C2×C4C2×D1211yescharacteristic
351C2×C4C2×D1211yescharacteristic
352C2×C4C2×D1211yescharacteristic
353C2×C4C2×D1211yescharacteristic
354C2×C4C23×D311yescharacteristic
355C8—21no—
356C8—21no—
357C8—21no—
358C8D3×D412yes—
359C2×C3—22no—
360C2×C3—41no—
361C2×C3D4211yescharacteristic
362C2×C3C2×#13711yescharacteristic
363C2×C3#57811yescharacteristic
364D3—81no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—121no—
371C22—121no—
372C22—121no—
373C22#90912yescomplemented
374C22C22×D1211yescharacteristic
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—62no—
380C4—62no—
381C4—121no—
382C4—121no—
383C4—121no—
384C4—121no—
385C4—121no—
386C4C2×D3×D411yescharacteristic
387C4#100911yescharacteristic
388C3#327011yescharacteristic, complemented, Sylow
389C2—22no—
390C2—41no—
391C2—241no—
392C2D4×D1211yescharacteristic
393C2C2×#90911yescharacteristic
394C2#575311yescharacteristic
subgroupG/H
centerC22C22×D12
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#435C2
socleC22×C3C22×D4
prime radical#5552C2
hypercenter#435D3
hypocenterC3#3270
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#909C2semidirect
2. C22×Dic12C2semidirect
4. D4×Dic6C2semidirect
5. C3×#435C2semidirect
6. #5137C2semidirect
7. #5114C2semidirect
8. #4849C2semidirect
9. #4845C2semidirect
10. #4739C2semidirect
11. #4739C2semidirect
12. #4738C2semidirect
13. #4733C2semidirect
14. #4716C2semidirect
15. #4715C2semidirect
76. #435D3semidirect
135. Dic12D4semidirect
296. C22×C3#137semidirect
373. C22#909semidirect
388. C3#3270semidirect

Maximal subgroups

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

subgroupindex
C2×#9092
C22×Dic122
#55522
D4×Dic62
C3×#4352
#51372
#51142
#48492
#48452
#47392
#47382
#47332
#47162
#47152
#32703