Finite Group Databasebeta

← #86928

Subgroups — #86928

Order 384.

1104 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#554C211yesmaximal, characteristic, complemented
2#5734C211yesmaximal, characteristic, complemented
3D3×C4⋊Q8C211yesmaximal, characteristic, complemented
4#5695C212yesmaximal, complemented
5#5688C212yesmaximal, complemented
6#5641C212yesmaximal, complemented
7#5640C214yesmaximal, complemented
8#5633C214yesmaximal, complemented
9#5629C212yesmaximal, complemented
10#5579C211yesmaximal, characteristic, complemented
11C4×#239C211yesmaximal, characteristic, complemented
12#5563C211yesmaximal, characteristic, complemented
13#5558C212yesmaximal, complemented
14#5548C212yesmaximal, complemented
15#5548C211yesmaximal, characteristic, complemented
16#5507C212yesmaximal, complemented
17#5504C212yesmaximal, complemented
18#3511—31nomaximal, Sylow
19C2×#239C2211yescharacteristic
20C2×D3×Q8C2212yes—
21C2×#235C2212yes—
22C2×#235C2214yes—
23C3×C4⋊Q8C2211yescharacteristic
24C3×#125C2212yes—
25C3×C22⋊Q8C2214yes—
26C3×C22⋊Q8C2212yes—
27C3×C4×Q8C2211yescharacteristic
28C3×C4×D4C2212yes—
29C3×C4×D4C2211yescharacteristic
30C2×C3×C4⋊C4C2212yes—
31#947C2214yes—
32#946C2212yes—
33Q8×Dic3C2211yescharacteristic
34#944C2212yes—
35#940C2211yescharacteristic
36#938C2211yescharacteristic
37#938C2212yes—
38#930C2212yes—
39#929C2214yes—
40C4×#67C2214yes—
41C4×#67C2214yes—
42C4×#67C2212yes—
43#926C2212yes—
44#898C2214yes—
45#896C2214yes—
46#896C2214yes—
47#896C2214yes—
48#895C2214yes—
49#895C2211yescharacteristic
50#895C2212yes—
51#895C2212yes—
52#894C2214yes—
53#893C2212yes—
54#893C2214yes—
55#893C2211yescharacteristic
56#892C2212yes—
57#892C2212yes—
58#892C2212yes—
59#892C2212yes—
60#892C2211yescharacteristic
61D3×C4⋊C4C2212yes—
62D3×C4⋊C4C2212yes—
63D3×C4⋊C4C2212yes—
64#888C2212yes—
65#888C2211yescharacteristic
66#888C2212yes—
67#887C2214yes—
68#887C2214yes—
69#885C2214yes—
70#885C2214yes—
71#885C2212yes—
72#884C2212yes—
73#884C2214yes—
74#884C2214yes—
75#879C2214yes—
76C4×D12C2212yes—
77C4×D12C2212yes—
78C4×D12C2211yescharacteristic
79C4×D12C2211yescharacteristic
80C42×D3C2212yes—
81C42×D3C2211yescharacteristic
82#870C2212yes—
83#869C2211yescharacteristic
84#556—32no—
85#555—31no—
86#555—31no—
87#554—31no—
88#554D311yescharacteristic, complemented
89#553—32no—
90#553—32no—
91#548—34no—
92#547—32no—
93#542—34no—
94#537—32no—
95#533—32no—
96#532—31no—
97#532—32no—
98C2×C4⋊Q8—31no—
99#520—32no—
100C4×#41—31no—
101C2×C3×Q8C2311yescharacteristic
102C2×C3×Q8C2312yes—
103C2×C3×D4C2311yescharacteristic
104C22×C3×C4C2312yes—
105C22×C3×C4C2314yes—
106C2×#67C2312yes—
107C2×#67C2312yes—
108C2×#67C2312yes—
109C2×#67C2314yes—
110#239—24no—
111D3×Q8—44no—
112#235—28no—
113#235—48no—
114C2×D12C2311yescharacteristic
115C2×D12C2312yes—
116C2×D12C2311yescharacteristic
117C2×D12C2312yes—
118C2×D12C2314yes—
119C2×C4×D3C2311yescharacteristic
120C2×C4×D3C2312yes—
121C2×C4×D3C2312yes—
122C2×C4×D3C2311yescharacteristic
123C2×C4×D3C2312yes—
124C2×C4×D3C2312yes—
125C2×C4×D3C2314yes—
126C2×C4×D3C2314yes—
127C2×C4×D3C2311yescharacteristic
128C2×Dic6C2312yes—
129C2×Dic6C2314yes—
130C2×Dic6C2312yes—
131C3×C4⋊C4C2314yes—
132C3×C4⋊C4C2314yes—
133C3×C4⋊C4C2312yes—
134C3×C4⋊C4C2312yes—
135C3×C4⋊C4C2311yescharacteristic
136C3×C4⋊C4C2311yescharacteristic
137C3×C4⋊C4C2312yes—
138C3×C22⋊C4C2314yes—
139C3×C22⋊C4C2312yes—
140C3×C42C2311yescharacteristic
141C3×C42C2312yes—
142#217C2312yes—
143#217C2314yes—
144(C2×D3)⋊C4C2314yes—
145(C2×D3)⋊C4C2312yes—
146(C2×D3)⋊C4C2312yes—
147(C2×D3)⋊C4C2312yes—
148(C2×D3)⋊C4C2312yes—
149(C2×D3)⋊C4C2314yes—
150(C2×D3)⋊C4C2314yes—
151(C2×D3)⋊C4C2314yes—
152(C2×D3)⋊C4C2312yes—
153C4⋊Dic3C2312yes—
154C4⋊Dic3C2312yes—
155C4⋊Dic3C2311yescharacteristic
156C4⋊Dic3C2312yes—
157C4⋊Dic3C2311yescharacteristic
158Dic3⋊C4C2314yes—
159Dic3⋊C4C2314yes—
160Dic3⋊C4C2314yes—
161Dic3⋊C4C2312yes—
162Dic3⋊C4C2314yes—
163C4×Dic3C2311yescharacteristic
164C4×Dic3C2312yes—
165C4×Dic3C2311yescharacteristic
166C4×Dic3C2312yes—
167C4×Dic3C2311yescharacteristic
168C4×Dic3C2314yes—
169C4×Dic3C2314yes—
170C2×#41—31no—
171C2×#41—32no—
172C2×#41—34no—
173C22×Q8—32no—
174C4⋊Q8—32no—
175C4⋊Q8—32no—
176C4⋊Q8—32no—
177C4⋊Q8—31no—
178C4⋊Q8—31no—
179C4⋊Q8C2×D311yescharacteristic
180#127—31no—
181#126—34no—
182#126—34no—
183#125—32no—
184#125C2×D312yes—
185#124—34no—
186#124—32no—
187#124—34no—
188#124—34no—
189#123—34no—
190#123—34no—
191C22⋊Q8—32no—
192C22⋊Q8—34no—
193C22⋊Q8—34no—
194C22⋊Q8—34no—
195C22⋊Q8C2×D312yes—
196C22⋊Q8C2×D314yes—
197#121—31no—
198#121—32no—
199#121—32no—
200#121—31no—
201#121—32no—
202#121—32no—
203#121—34no—
204#121—34no—
205#121—32no—
206#121—34no—
207C4×Q8—31no—
208C4×Q8—34no—
209C4×Q8—34no—
210C4×Q8C2×D311yescharacteristic
211C4×D4—34no—
212C4×D4—34no—
213C4×D4—32no—
214C4×D4—31no—
215C4×D4—32no—
216C4×D4—34no—
217C4×D4—32no—
218C4×D4—31no—
219C4×D4—32no—
220C4×D4—31no—
221C4×D4C2×D312yes—
222C4×D4C2×D311yescharacteristic
223#117—32no—
224#117—31no—
225#117—32no—
226#117—32no—
227#117—32no—
228#117—32no—
229C2×C4⋊C4—32no—
230C2×C4⋊C4—32no—
231C2×C4⋊C4—32no—
232C2×C4⋊C4C2×D312yes—
233C2×C42—31no—
234C2×C42—32no—
235C23×C3C2412yes—
236C22×D3C2412yes—
237C22×D3C2412yes—
238C22×D3C2411yescharacteristic
239C3×Q8—22no—
240C3×Q8—42no—
241C3×D4—22no—
242C2×C3×C4—24no—
243C2×C3×C4—44no—
244C2×C3×C4C2412yes—
245C2×C3×C4C2412yes—
246C2×C3×C4C2412yes—
247C2×C3×C4C2414yes—
248C2×C3×C4C2411yescharacteristic
249C2×C3×C4C2411yescharacteristic
250C2×C3×C4C2411yescharacteristic
251#67—24no—
252#67—24no—
253#67—24no—
254#67—44no—
255C2×Dic3C2412yes—
256C2×Dic3C2412yes—
257C2×Dic3C2411yescharacteristic
258C2×Dic3C2414yes—
259C2×Dic3C2411yescharacteristic
260C2×Dic3C2411yescharacteristic
261D12—24no—
262D12—24no—
263D12—22no—
264D12—22no—
265D12—44no—
266C4×D3—24no—
267C4×D3—22no—
268C4×D3—24no—
269C4×D3—24no—
270C4×D3—24no—
271C4×D3—22no—
272C4×D3—44no—
273C4×D3—44no—
274C4×D3#4114yescomplemented
275Dic6—24no—
276Dic6—28no—
277Dic6—42no—
278#41—68no—
279#41—64no—
280#41—128no—
281C2×Q8—32no—
282C2×Q8—34no—
283C2×Q8—32no—
284C2×Q8—124no—
285C2×Q8C22×D311yescharacteristic
286C2×Q8C22×D312yes—
287C2×D4—32no—
288C2×D4—32no—
289C2×D4—32no—
290C2×D4—34no—
291C2×D4—31no—
292C2×D4—32no—
293C2×D4—32no—
294C2×D4—31no—
295C2×D4—34no—
296C2×D4C22×D311yescharacteristic
297C22×C4—31no—
298C22×C4—31no—
299C22×C4—32no—
300C22×C4—32no—
301C22×C4—31no—
302C22×C4—32no—
303C22×C4—32no—
304C22×C4—34no—
305C22×C4—34no—
306C22×C4C22×D312yes—
307C22×C4C22×D314yes—
308C4⋊C4—32no—
309C4⋊C4—32no—
310C4⋊C4—34no—
311C4⋊C4—34no—
312C4⋊C4—34no—
313C4⋊C4—31no—
314C4⋊C4—31no—
315C4⋊C4—32no—
316C4⋊C4—32no—
317C4⋊C4—34no—
318C4⋊C4C22×D311yescharacteristic
319C4⋊C4C22×D312yes—
320C4⋊C4C22×D312yes—
321C4⋊C4C22×D314yes—
322C4⋊C4C22×D311yescharacteristic
323C4⋊C4C22×D312yes—
324C4⋊C4C22×D314yes—
325C22⋊C4—34no—
326C22⋊C4—32no—
327C22⋊C4—32no—
328C22⋊C4—34no—
329C22⋊C4—32no—
330C22⋊C4—32no—
331C22⋊C4—34no—
332C22⋊C4—34no—
333C22⋊C4—34no—
334C22⋊C4—32no—
335C22⋊C4—32no—
336C22⋊C4C22×D314yes—
337C22⋊C4C22×D312yes—
338C42—31no—
339C42—32no—
340C42—31no—
341C42—31no—
342C42—32no—
343C42—34no—
344C42—34no—
345C42C22×D312yes—
346C42C22×D311yescharacteristic
347C22×C3—22no—
348C22×C3—22no—
349C22×C3—22no—
350C22×C3C2511yescharacteristic
351C2×D3—21no—
352C2×D3—21no—
353C2×D3—22no—
354C2×D3—22no—
355C2×D3—22no—
356C2×D3—22no—
357C2×D3—22no—
358C2×D3—22no—
359C2×D3C2×#4112yes—
360C3×C4—22no—
361C3×C4—22no—
362C3×C4—24no—
363C3×C4—21no—
364C3×C4—22no—
365C3×C4C2×#4112yes—
366C3×C42−1+412yes—
367Dic3—22no—
368Dic3—24no—
369Dic3—22no—
370Dic3—21no—
371Dic3C2×#4112yes—
372Dic3H(5,𝔽2)12yes—
373C23—31no—
374C23—32no—
375C23—32no—
376C23C23×D312yes—
377Q8—22no—
378Q8—42no—
379Q8—68no—
380Q8—64no—
381Q8—122no—
382D4—22no—
383D4—64no—
384D4—64no—
385D4—64no—
386D4—64no—
387D4—64no—
388D4—62no—
389D4—62no—
390D4—124no—
391D4—124no—
392C2×C4—24no—
393C2×C4—31no—
394C2×C4—31no—
395C2×C4—34no—
396C2×C4—32no—
397C2×C4—31no—
398C2×C4—32no—
399C2×C4—34no—
400C2×C4—44no—
401C2×C4—62no—
402C2×C4—64no—
403C2×C4—64no—
404C2×C4—62no—
405C2×C4—64no—
406C2×C4—64no—
407C2×C4—124no—
408C2×C4—124no—
409C2×C4C23×D312yes—
410C2×C4C23×D311yescharacteristic
411C2×C4C23×D312yes—
412C2×C4C23×D312yes—
413C2×C4C23×D314yes—
414C2×C4C23×D311yescharacteristic
415C2×C4C23×D311yescharacteristic
416C2×C3—42no—
417C2×C3C22×#4111yescharacteristic
418C2×C3C2×H(5,𝔽2)11yescharacteristic
419C2×C3C2×2−1+411yescharacteristic
420D3—22no—
421D3—42no—
422D3—42no—
423C22—22no—
424C22—22no—
425C22—22no—
426C22—32no—
427C22—61no—
428C22—61no—
429C22—62no—
430C22—62no—
431C22—62no—
432C22—62no—
433C22—62no—
434C22—62no—
435C22C24×D311yescharacteristic
436C4—22no—
437C4—22no—
438C4—22no—
439C4—24no—
440C4—21no—
441C4—32no—
442C4—32no—
443C4—62no—
444C4—61no—
445C4—62no—
446C4—64no—
447C4#100712yes—
448C4D3×#4112yes—
449C3#351111yescharacteristic, complemented, Sylow
450C2—42no—
451C2—62no—
452C2—122no—
453C2—122no—
454C2C2×#100711yescharacteristic
455C2C2×D3×#4111yescharacteristic
456C2D3×H(5,𝔽2)11yescharacteristic
subgroupG/H
center, FrattiniC22C24×D3
commutator, socle, cosocleC22×C3C25
FittingC3×#554C2
hypercenter#554D3
hypocenterC3#3511
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ #554

Complements

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

NH ≅ G/Ntype
1. C3×#554C2semidirect
2. #5734C2semidirect
3. D3×C4⋊Q8C2semidirect
4. #5695C2semidirect
5. #5688C2semidirect
6. #5641C2semidirect
7. #5640C2semidirect
8. #5633C2semidirect
9. #5629C2semidirect
10. #5579C2semidirect
11. C4×#239C2semidirect
12. #5563C2semidirect
13. #5558C2semidirect
14. #5548C2semidirect
15. #5548C2semidirect
16. #5507C2semidirect
17. #5504C2semidirect
88. #554D3semidirect
274. C4×D3#41semidirect
449. C3#3511semidirect

Maximal subgroups

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

subgroupindex
C3×#5542
#57342
D3×C4⋊Q82
#56952
#56882
#56412
#56402
#56332
#56292
#55792
C4×#2392
#55632
#55582
#55482
#55072
#55042
#35113