Finite Group Databasebeta

← #79497

Subgroups — #79497

Order 384.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#908C211yesmaximal, characteristic, complemented
2C2×#904C211yesmaximal, characteristic, complemented
3#5553C211yesmaximal, characteristic, complemented
4#5550C211yesmaximal, characteristic, complemented
5C3×#435C211yesmaximal, characteristic, complemented
6#5134C211yesmaximal, characteristic, complemented
7#5115C211yesmaximal, characteristic, complemented
8#4845C211yesmaximal, characteristic, complemented
9#4843C211yesmaximal, characteristic, complemented
10#4734C211yesmaximal, characteristic, complemented
11#4734C211yesmaximal, characteristic, complemented
12#4733C211yesmaximal, characteristic, complemented
13#4732C211yesmaximal, characteristic, complemented
14#4712C211yesmaximal, characteristic, complemented
15#4710C211yesmaximal, characteristic, complemented
16#3268—31nomaximal, Sylow
17C2×#235C2211yescharacteristic
18C2×#235C2211yescharacteristic
19C2×#235C2211yescharacteristic, complemented
20C22×D12C2211yescharacteristic
21C2×C3×M16C2211yescharacteristic
22C22×C3×C8C2211yescharacteristic, complemented
23C3×C4×D4C2211yescharacteristic
24#940—21no—
25#937—21no—
26#930C2211yescharacteristic
27#930C2211yescharacteristic
28#930C2211yescharacteristic, complemented
29#924C2211yescharacteristic
30#908—24no—
31C2×Dic12C2211yescharacteristic, complemented
32#904—24no—
33C2×D24C2211yescharacteristic
34C2×D24C2211yescharacteristic
35C2×D24C2211yescharacteristic
36C2×D24C2211yescharacteristic
37C2×#204C2211yescharacteristic
38C2×#204C2211yescharacteristic
39C2×#204C2211yescharacteristic, complemented
40C2×#204C2211yescharacteristic, complemented
41#894—21no—
42#893—21no—
43#884—21no—
44#884—21no—
45#884—21no—
46D3×C22⋊C4—21no—
47#875C2211yescharacteristic
48#874C2211yescharacteristic, complemented
49C4×D12C2211yescharacteristic
50C4×Dic6C2211yescharacteristic, complemented
51C3×C4⋊C8C2211yescharacteristic, complemented
52C3×C22⋊C8C2211yescharacteristic
53C3×C22⋊C8C2211yescharacteristic, complemented
54C3×#97C2211yescharacteristic, complemented
55#821C2211yescharacteristic
56#821C2211yescharacteristic
57#821C2211yescharacteristic, complemented
58#821C2211yescharacteristic, complemented
59#818C2211yescharacteristic, complemented
60#816C2211yescharacteristic, complemented
61#816C2211yescharacteristic, complemented
62C2×AGL(1,ℤ/8)—31no—
63C2×#135—31no—
64#550—31no—
65#546—31no—
66#496—31no—
67#468—31no—
68#466—31no—
69#464—31no—
70#459—31no—
71#452—31no—
72#449—31no—
73#449—31no—
74#447—31no—
75#440—31no—
76#435D311yescharacteristic, complemented
77C23×D3—21no—
78C2×C3×D4D411yescharacteristic
79C22×C3×C4C2311yescharacteristic
80C22×C3×C4C2311yescharacteristic
81C2×#67—21no—
82C2×#67—21no—
83C2×#67—21no—
84C2×#67—21no—
85C2×#67—21no—
86C2×#67—21no—
87#235—22no—
88#235—22no—
89#235—22no—
90#235—41no—
91#235—41no—
92#235—41no—
93C2×D12—22no—
94C2×D12—21no—
95C2×D12—21no—
96C2×D12—21no—
97C2×D12—41no—
98C2×D12C2311yescharacteristic
99C2×D12C2311yescharacteristic
100C2×D12C2311yescharacteristic
101C2×D12C2311yescharacteristic
102C2×C4×D3—21no—
103C2×C4×D3—21no—
104C2×C4×D3—21no—
105C2×C4×D3—21no—
106C2×Dic6C2311yescharacteristic
107C2×Dic6C2311yescharacteristic
108C3×M16—22no—
109C2×C3×C8—22no—
110C2×C3×C8C2311yescharacteristic
111C2×C3×C8C2311yescharacteristic
112C2×C3×C8C2311yescharacteristic
113C2×C3×C8C2311yescharacteristic
114C3×C4⋊C4D411yescharacteristic
115C3×C22⋊C4D411yescharacteristic
116C3×C22⋊C4D411yescharacteristic
117C3×C42C2311yescharacteristic
118#217—21no—
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—
125C4⋊Dic3C2311yescharacteristic
126C4⋊Dic3C2311yescharacteristic
127Dic3⋊C4—21no—
128Dic3⋊C4—21no—
129C4×Dic3—21no—
130Dic12—22no—
131D24—22no—
132D24—22no—
133D24—22no—
134D24—41no—
135#204—22no—
136#204—22no—
137#204—41no—
138#204D414yescomplemented
139C2×#41—31no—
140C2×#41—31no—
141C2×#41—31no—
142C22×D4—31no—
143AGL(1,ℤ/8)—64no—
144#135—64no—
145C2×Q16—31no—
146C2×SD16—31no—
147C2×SD16—31no—
148C2×SD16—31no—
149C2×SD16—31no—
150C2×D8—31no—
151C2×D8—31no—
152C2×D8—31no—
153C2×D8—31no—
154C2×M16C2×D311yescharacteristic
155C22×C8C2×D311yescharacteristic, complemented
156#127—31no—
157#127—61no—
158#124—31no—
159#123—61no—
160C22⋊Q8—31no—
161#121—31no—
162#121—31no—
163#121—31no—
164#121—61no—
165#121—61no—
166#121—61no—
167#120—61no—
168C4×Q8—31no—
169C4×D4—31no—
170C4×D4—61no—
171C4×D4C2×D311yescharacteristic
172C2×C22⋊C4—61no—
173#107—31no—
174C4⋊C8C2×D311yescharacteristic, complemented
175#103—31no—
176#103—31no—
177#102—31no—
178#102—31no—
179#102—31no—
180#102—31no—
181C22⋊C8C2×D311yescharacteristic
182C22⋊C8C2×D311yescharacteristic, complemented
183#97C2×D311yescharacteristic, complemented
184C23×C3C2×D411yescharacteristic
185C23×C3C2×D411yescharacteristic
186C22×D3—21no—
187C22×D3—21no—
188C22×D3—21no—
189C22×D3—21no—
190C22×D3—42no—
191C22×D3—42no—
192C22×D3—81no—
193C3×D4—41no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4C2×D411yescharacteristic
199C2×C3×C4C2×D411yescharacteristic
200C2×C3×C4C2×D411yescharacteristic
201C2×C3×C4C2×D411yescharacteristic
202C2×C3×C4C2411yescharacteristic
203#67—42no—
204#67—42no—
205#67—42no—
206#67—81no—
207#67—81no—
208#67—81no—
209C2×Dic3—21no—
210C2×Dic3—21no—
211C2×Dic3—21no—
212C2×Dic3—21no—
213D12—21no—
214D12—21no—
215D12—21no—
216D12—21no—
217D12—21no—
218D12—21no—
219D12—21no—
220D12—42no—
221D12—42no—
222D12—81no—
223D12C2×D412yes—
224C4×D3—42no—
225C4×D3—42no—
226C4×D3—42no—
227C4×D3—81no—
228Dic6—21no—
229Dic6—21no—
230Dic6—21no—
231Dic6C2×D412yes—
232C3×C8—21no—
233C3×C8—21no—
234C3×C8—21no—
235C3×C8C2×D412yes—
236C24—61no—
237#41—62no—
238#41—62no—
239#41—62no—
240#41—121no—
241#41—121no—
242#41—121no—
243C2×Q8—31no—
244C2×Q8—31no—
245C2×D4—31no—
246C2×D4—31no—
247C2×D4—31no—
248C2×D4—31no—
249C2×D4—62no—
250C2×D4—61no—
251C2×D4—61no—
252C2×D4—61no—
253C2×D4—61no—
254C2×D4—61no—
255C2×D4—61no—
256C2×D4—61no—
257C2×D4—61no—
258C2×D4—61no—
259C2×D4—121no—
260C2×D4D1211yescharacteristic
261C22×C4—61no—
262C22×C4—61no—
263C22×C4—61no—
264C22×C4—61no—
265C22×C4C22×D311yescharacteristic
266C22×C4C22×D311yescharacteristic
267Q16—62no—
268SD16—34no—
269SD16—62no—
270SD16—62no—
271SD16—121no—
272D8—62no—
273D8—62no—
274D8—62no—
275D8—121no—
276M16—22no—
277C2×C8—22no—
278C2×C8C22×D311yescharacteristic
279C2×C8C22×D311yescharacteristic
280C2×C8C22×D311yescharacteristic
281C2×C8C22×D311yescharacteristic
282C4⋊C4—31no—
283C4⋊C4—31no—
284C4⋊C4—61no—
285C4⋊C4—61no—
286C4⋊C4D1211yescharacteristic
287C22⋊C4—61no—
288C22⋊C4—61no—
289C22⋊C4—61no—
290C22⋊C4—61no—
291C22⋊C4—61no—
292C22⋊C4—61no—
293C22⋊C4—61no—
294C22⋊C4D1211yescharacteristic
295C22⋊C4D1211yescharacteristic
296C42—61no—
297C42C22×D311yescharacteristic
298C22×C3—21no—
299C22×C3—21no—
300C22×C3—21no—
301C22×C3—21no—
302C22×C3—21no—
303C22×C3—21no—
304C22×C3C22×D411yescharacteristic
305C2×D3—22no—
306C2×D3—41no—
307C2×D3—41no—
308C2×D3—41no—
309C2×D3—41no—
310C2×D3—41no—
311C2×D3—41no—
312C2×D3—41no—
313C2×D3—41no—
314C2×D3—41no—
315C2×D3—41no—
316C2×D3—41no—
317C2×D3—84no—
318C3×C4—21no—
319C3×C4—21no—
320C3×C4—21no—
321C3×C4—21no—
322C3×C4C22×D411yescharacteristic
323C3×C4H(5,𝔽2)11yescharacteristic
324Dic3—22no—
325Dic3—41no—
326Dic3—41no—
327Dic3—41no—
328C23—61no—
329C23—61no—
330C23—61no—
331C23—61no—
332C23—122no—
333C23—122no—
334C23—241no—
335C23C2×D1211yescharacteristic
336C23C2×D1211yescharacteristic
337Q8—32no—
338Q8—61no—
339Q8—61no—
340Q8—61no—
341D4—32no—
342D4—41no—
343D4—61no—
344D4—61no—
345D4—61no—
346D4—61no—
347D4—61no—
348D4—61no—
349D4—61no—
350D4—122no—
351D4—122no—
352D4—122no—
353D4—122no—
354D4—122no—
355D4—241no—
356D4—241no—
357D4—241no—
358D4—241no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—61no—
364C2×C4—61no—
365C2×C4—61no—
366C2×C4—61no—
367C2×C4—122no—
368C2×C4—122no—
369C2×C4—122no—
370C2×C4—241no—
371C2×C4C2×D1211yescharacteristic
372C2×C4C2×D1211yescharacteristic
373C2×C4C2×D1211yescharacteristic
374C2×C4C2×D1211yescharacteristic
375C2×C4C23×D311yescharacteristic
376C8—21no—
377C8—21no—
378C8—21no—
379C8D3×D412yes—
380C2×C3—41no—
381C2×C3—41no—
382C2×C3D4211yescharacteristic
383C2×C3#57511yescharacteristic
384C2×C3#57611yescharacteristic
385D3—42no—
386D3—81no—
387D3—81no—
388D3—81no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—62no—
396C22—121no—
397C22—121no—
398C22—121no—
399C22—121no—
400C22—121no—
401C22—121no—
402C22—121no—
403C22—121no—
404C22—121no—
405C22—121no—
406C22—121no—
407C22—244no—
408C22C22×D1211yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—21no—
413C4—62no—
414C4—121no—
415C4—121no—
416C4—121no—
417C4C2×D3×D411yescharacteristic
418C4#100911yescharacteristic
419C3#326811yescharacteristic, complemented, Sylow
420C2—41no—
421C2—41no—
422C2—122no—
423C2—241no—
424C2—241no—
425C2—241no—
426C2D4×D1211yescharacteristic
427C2#574811yescharacteristic
428C2#575211yescharacteristic
subgroupG/H
centerC22C22×D12
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#435C2
socleC22×C3C22×D4
hypercenter#435D3
hypocenterC3#3268
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×#908C2semidirect
2. C2×#904C2semidirect
3. #5553C2semidirect
4. #5550C2semidirect
5. C3×#435C2semidirect
6. #5134C2semidirect
7. #5115C2semidirect
8. #4845C2semidirect
9. #4843C2semidirect
10. #4734C2semidirect
11. #4734C2semidirect
12. #4733C2semidirect
13. #4732C2semidirect
14. #4712C2semidirect
15. #4710C2semidirect
19. C2×#235C22semidirect
22. C22×C3×C8C22semidirect
28. #930C22semidirect
31. C2×Dic12C22semidirect
39. C2×#204C22semidirect
40. C2×#204C22semidirect
48. #874C22semidirect
50. C4×Dic6C22semidirect
51. C3×C4⋊C8C22semidirect
53. C3×C22⋊C8C22semidirect
54. C3×#97C22semidirect
57. #821C22semidirect
58. #821C22semidirect
59. #818C22semidirect
60. #816C22semidirect
61. #816C22semidirect
76. #435D3semidirect
138. #204D4semidirect
155. C22×C8C2×D3semidirect
174. C4⋊C8C2×D3semidirect
182. C22⋊C8C2×D3semidirect
183. #97C2×D3semidirect
419. C3#3268semidirect

Maximal subgroups

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

subgroupindex
C2×#9082
C2×#9042
#55532
#55502
C3×#4352
#51342
#51152
#48452
#48432
#47342
#47332
#47322
#47122
#47102
#32683