Finite Group Databasebeta

← #80660

Subgroups — #80660

Order 384.

484 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#916C211yesmaximal, characteristic, complemented
2C2×#901C211yesmaximal, characteristic, complemented
3#5629C211yesmaximal, characteristic, complemented
4#5608C211yesmaximal, characteristic, complemented
5C3×#465C211yesmaximal, characteristic, complemented
6#5171C211yesmaximal, characteristic, complemented
7#5114C211yesmaximal, characteristic, complemented
8#5052C211yesmaximal, characteristic, complemented
9#5039C211yesmaximal, characteristic, complemented
10#4864C211yesmaximal, characteristic, complemented
11D3×#106C211yesmaximal, characteristic, complemented
12#4816C211yesmaximal, characteristic, complemented
13#4803C211yesmaximal, characteristic, complemented
14#4782C211yesmaximal, characteristic, complemented
15#4771C211yesmaximal, characteristic, complemented
16#3060—31nomaximal, Sylow
17C2×#239C2211yescharacteristic
18C2×#237C2211yescharacteristic
19C2×#235C2211yescharacteristic
20C2×C3×SD16C2211yescharacteristic
21C22×C3×C8C2211yescharacteristic
22C3×C22⋊Q8C2211yescharacteristic
23C3×#121C2211yescharacteristic
24#946C2211yescharacteristic
25C2×#216C2211yescharacteristic
26#939—21no—
27#938—21no—
28#938C2211yescharacteristic
29C2×#213C2211yescharacteristic
30#930C2211yescharacteristic
31#924C2211yescharacteristic
32C2×#208C2211yescharacteristic
33#916—24no—
34C2×#204C2211yescharacteristic
35#901—24no—
36C2×ΓL(1,𝔽25)C2211yescharacteristic
37C2×ΓL(1,𝔽25)C2211yescharacteristic
38C2×D3×C8C2211yescharacteristic
39C2×D3×C8C2211yescharacteristic
40#897C2211yescharacteristic
41#896—21no—
42#895—21no—
43#895C2211yescharacteristic
44D3×C4⋊C4C2211yescharacteristic
45D3×C4⋊C4C2211yescharacteristic
46#884—21no—
47#884—21no—
48#884—21no—
49#878—21no—
50C3×#106C2211yescharacteristic
51C3×#103C2211yescharacteristic
52C3×#102C2211yescharacteristic
53#835C2211yescharacteristic
54#832C2211yescharacteristic
55#821C2211yescharacteristic
56#817C2211yescharacteristic
57#816C2211yescharacteristic
58#810C2211yescharacteristic
59#809C2211yescharacteristic
60#808C2211yescharacteristic
61#808C2211yescharacteristic
62C2×#135—31no—
63C2×#131—31no—
64#537—31no—
65#537—31no—
66#470—31no—
67#470—31no—
68#469—31no—
69#469—31no—
70#465—31no—
71#465—31no—
72#465—31no—
73#465D311yescharacteristic, complemented
74C2×#106—31no—
75#417—31no—
76#417—31no—
77C2×C3×Q8C2311yescharacteristic
78C2×C3×D4—21no—
79C2×C3×D4C2311yescharacteristic
80C22×C3×C4C2311yescharacteristic
81C2×#67—21no—
82C2×#67—21no—
83C2×#67—21no—
84C2×#67D411yescharacteristic
85C2×#67D411yescharacteristic
86C22×Dic3—21no—
87#239—22no—
88#239—22no—
89#237—22no—
90#237—22no—
91#235—22no—
92#235—22no—
93C2×D12—21no—
94C2×D12—21no—
95C2×D12D411yescharacteristic
96C2×D12C2311yescharacteristic
97C2×C4×D3—21no—
98C2×C4×D3—21no—
99C2×C4×D3—21no—
100C2×C4×D3C2311yescharacteristic
101C2×C4×D3C2311yescharacteristic
102C2×Dic6D411yescharacteristic
103C2×Dic6C2311yescharacteristic
104C3×SD16—22no—
105C2×C3×C8—22no—
106C2×C3×C8C2311yescharacteristic
107C2×C3×C8C2311yescharacteristic
108C3×C4⋊C4—21no—
109C3×C4⋊C4C2311yescharacteristic
110C3×C4⋊C4C2311yescharacteristic
111C3×C22⋊C4—21no—
112C3×C22⋊C4—21no—
113#217—21no—
114#217—21no—
115#216—22no—
116#213—22no—
117(C2×D3)⋊C4—21no—
118(C2×D3)⋊C4—21no—
119(C2×D3)⋊C4—21no—
120(C2×D3)⋊C4—21no—
121C4⋊Dic3—21no—
122C4⋊Dic3C2311yescharacteristic
123C4⋊Dic3C2311yescharacteristic
124Dic3⋊C4—21no—
125Dic3⋊C4—21no—
126Dic3⋊C4—21no—
127Dic3⋊C4—21no—
128#208—22no—
129C2×C3⋊C8C2311yescharacteristic
130C2×C3⋊C8C2311yescharacteristic
131#204—22no—
132ΓL(1,𝔽25)—22no—
133ΓL(1,𝔽25)—22no—
134D3×C8—22no—
135D3×C8D414yescomplemented
136C2×#41—31no—
137C2×#41—31no—
138C2×#41—31no—
139#135—64no—
140C2×Q16—31no—
141C2×SD16—31no—
142C2×SD16C2×D311yescharacteristic
143C2×D8—31no—
144#131—64no—
145C2×M16—31no—
146C2×M16—31no—
147C2×M16—31no—
148C22×C8—31no—
149C22×C8—31no—
150C22×C8C2×D311yescharacteristic
151C22⋊Q8—31no—
152C22⋊Q8—31no—
153C22⋊Q8—31no—
154C22⋊Q8—61no—
155C22⋊Q8—61no—
156C22⋊Q8C2×D311yescharacteristic
157#121—31no—
158#121—31no—
159#121—31no—
160#121—61no—
161#121—61no—
162#121—61no—
163#121—61no—
164#121—61no—
165#121—61no—
166#121C2×D311yescharacteristic
167C2×C4⋊C4—31no—
168C2×C4⋊C4—31no—
169#106—31no—
170#106—31no—
171#106—31no—
172#106C2×D311yescharacteristic
173#103—31no—
174#103—31no—
175#103—31no—
176#103C2×D311yescharacteristic
177#102—31no—
178#102—31no—
179#102—31no—
180#102C2×D311yescharacteristic
181C23×C3—21no—
182C23×C3C2×D411yescharacteristic
183C22×D3—21no—
184C22×D3C2×D411yescharacteristic
185C22×D3C2×D411yescharacteristic
186C3×Q8—21no—
187C3×Q8—21no—
188C3×D4—21no—
189C3×D4—21no—
190C3×D4—81no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4C2×D411yescharacteristic
197C2×C3×C4C2411yescharacteristic
198#67—22no—
199#67—22no—
200#67—42no—
201#67—81no—
202#67—81no—
203C2×Dic3—21no—
204C2×Dic3—21no—
205C2×Dic3—21no—
206C2×Dic3—42no—
207C2×Dic3C2×D411yescharacteristic
208C2×Dic3C2×D411yescharacteristic
209D12—22no—
210D12—21no—
211D12—21no—
212D12—42no—
213D12—81no—
214C4×D3—21no—
215C4×D3—21no—
216C4×D3—42no—
217C4×D3—81no—
218C4×D3—81no—
219C4×D3C2×D412yes—
220C4×D3#4112yes—
221Dic6—22no—
222Dic6—21no—
223Dic6—21no—
224C3×C8—21no—
225C3×C8C2×D412yes—
226C3⋊C8—21no—
227C3⋊C8C2×D412yes—
228#41—62no—
229#41—62no—
230#41—62no—
231#41—62no—
232#41—62no—
233#41—62no—
234C2×Q8—31no—
235C2×Q8—31no—
236C2×Q8C22×D311yescharacteristic
237C2×D4—21no—
238C2×D4—31no—
239C2×D4—31no—
240C2×D4—31no—
241C2×D4—31no—
242C2×D4—61no—
243C2×D4—61no—
244C2×D4—61no—
245C2×D4—61no—
246C2×D4—61no—
247C2×D4C22×D311yescharacteristic
248C22×C4—31no—
249C22×C4—31no—
250C22×C4—61no—
251C22×C4—61no—
252C22×C4—61no—
253C22×C4—61no—
254C22×C4C22×D311yescharacteristic
255Q16—62no—
256SD16—22no—
257SD16—62no—
258D8—62no—
259M16—62no—
260M16—62no—
261M16—62no—
262C2×C8—22no—
263C2×C8—31no—
264C2×C8—34no—
265C2×C8—31no—
266C2×C8—62no—
267C2×C8C22×D311yescharacteristic
268C2×C8C22×D311yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—31no—
271C4⋊C4—31no—
272C4⋊C4—61no—
273C4⋊C4—61no—
274C4⋊C4—61no—
275C4⋊C4—61no—
276C4⋊C4—61no—
277C4⋊C4C22×D311yescharacteristic
278C4⋊C4C22×D311yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—61no—
282C22⋊C4—61no—
283C22⋊C4—61no—
284C22⋊C4—61no—
285C22⋊C4—61no—
286C22⋊C4—61no—
287C22×C3—21no—
288C22×C3—21no—
289C22×C3—21no—
290C22×C3—41no—
291C22×C3—41no—
292C22×C3—41no—
293C22×C3C22×D411yescharacteristic
294C2×D3—21no—
295C2×D3—21no—
296C2×D3—21no—
297C2×D3—21no—
298C2×D3—21no—
299C2×D3—41no—
300C2×D3—41no—
301C2×D3—41no—
302C2×D3#12112yes—
303C3×C4—21no—
304C3×C4—41no—
305C3×C4—41no—
306C3×C4—41no—
307C3×C4C22×D411yescharacteristic
308C3×C4C2×#4111yescharacteristic
309Dic3—21no—
310Dic3—41no—
311Dic3—41no—
312Dic3—41no—
313Dic3#12112yes—
314C23—21no—
315C23—31no—
316C23—31no—
317C23—61no—
318C23D3×D411yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—62no—
322Q8—61no—
323Q8—61no—
324D4—21no—
325D4—21no—
326D4—62no—
327D4—62no—
328D4—62no—
329D4—61no—
330D4—61no—
331D4—81no—
332D4—122no—
333D4—122no—
334D4—241no—
335D4—241no—
336D4—241no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—31no—
343C2×C4—32no—
344C2×C4—32no—
345C2×C4—31no—
346C2×C4—61no—
347C2×C4—61no—
348C2×C4—61no—
349C2×C4—61no—
350C2×C4—61no—
351C2×C4—122no—
352C2×C4—122no—
353C2×C4—241no—
354C2×C4—241no—
355C2×C4D3×D411yescharacteristic
356C2×C4C23×D311yescharacteristic
357C8—21no—
358C8—32no—
359C8—61no—
360C8D3×D412yes—
361C2×C3—41no—
362C2×C3—81no—
363C2×C3C2×#12111yescharacteristic
364C2×C3#57711yescharacteristic
365C2×C3#57711yescharacteristic
366D3—22no—
367D3—41no—
368D3—81no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—32no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—61no—
377C22—61no—
378C22—61no—
379C22—61no—
380C22—61no—
381C22—121no—
382C22—121no—
383C22—121no—
384C22C2×D3×D411yescharacteristic
385C4—21no—
386C4—32no—
387C4—41no—
388C4—41no—
389C4—41no—
390C4—61no—
391C4—121no—
392C4—121no—
393C4—121no—
394C4C2×D3×D411yescharacteristic
395C4D3×#4111yescharacteristic
396C3#306011yescharacteristic, complemented, Sylow
397C2—41no—
398C2—62no—
399C2—81no—
400C2—121no—
401C2—241no—
402C2D3×#12111yescharacteristic
403C2#576211yescharacteristic
404C2#577011yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#465C2
socleC22×C3C22×D4
hypercenter#465D3
hypocenterC3#3060
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×#916C2semidirect
2. C2×#901C2semidirect
3. #5629C2semidirect
4. #5608C2semidirect
5. C3×#465C2semidirect
6. #5171C2semidirect
7. #5114C2semidirect
8. #5052C2semidirect
9. #5039C2semidirect
10. #4864C2semidirect
11. D3×#106C2semidirect
12. #4816C2semidirect
13. #4803C2semidirect
14. #4782C2semidirect
15. #4771C2semidirect
73. #465D3semidirect
135. D3×C8D4semidirect
396. C3#3060semidirect

Maximal subgroups

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

subgroupindex
C2×#9162
C2×#9012
#56292
#56082
C3×#4652
#51712
#51142
#50522
#50392
#48642
D3×#1062
#48162
#48032
#47822
#47712
#30603