Finite Group Databasebeta

← #86680

Subgroups — #86680

Order 384.

1104 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#547C211yesmaximal, characteristic, complemented
2#5832C212yesmaximal, complemented
3#5831C212yesmaximal, complemented
4#5732C211yesmaximal, characteristic, complemented
5D3×C4⋊Q8C211yesmaximal, characteristic, complemented
6#5662C214yesmaximal, complemented
7#5661C214yesmaximal, complemented
8#5633C212yesmaximal, complemented
9#5622C212yesmaximal, complemented
10#5616C212yesmaximal, complemented
11#5608C212yesmaximal, complemented
12#5551C211yesmaximal, characteristic, complemented
13#5548C211yesmaximal, characteristic, complemented
14#5542C211yesmaximal, characteristic, complemented
15C4×#237C211yesmaximal, characteristic, complemented
16#5511C212yesmaximal, complemented
17#5504C212yesmaximal, complemented
18#3511—31nomaximal, Sylow
19C2×C3×#41C2212yes—
20C2×D3×Q8C2212yes—
21C2×#237C2211yescharacteristic
22C2×#235C2212yes—
23C2×#235C2212yes—
24C3×C4⋊Q8C2211yescharacteristic
25C3×#123C2214yes—
26C3×C22⋊Q8C2212yes—
27C3×#121C2212yes—
28C3×C4×D4C2211yescharacteristic
29C3×C4×D4C2211yescharacteristic
30C2×C3×C4⋊C4C2212yes—
31#947C2212yes—
32Q8×Dic3C2212yes—
33#944C2212yes—
34#940C2211yescharacteristic
35#939C2214yes—
36#939C2214yes—
37#938C2214yes—
38#938C2211yescharacteristic
39#938C2212yes—
40#936C2214yes—
41#936C2212yes—
42D4×Dic3C2211yescharacteristic
43C4×#67C2212yes—
44C4×#67C2214yes—
45C4×#67C2214yes—
46C4×#67C2214yes—
47C4×#67C2212yes—
48#926C2212yes—
49#924C2214yes—
50#924C2212yes—
51#924C2212yes—
52C2×C4×Dic3C2212yes—
53#898C2214yes—
54#897C2212yes—
55#896C2214yes—
56#895C2211yescharacteristic
57#893C2214yes—
58#892C2212yes—
59#892C2211yescharacteristic
60D3×C4⋊C4C2212yes—
61D3×C4⋊C4C2212yes—
62D3×C4⋊C4C2212yes—
63#889C2214yes—
64#888C2212yes—
65#888C2212yes—
66#888C2211yescharacteristic
67#887C2212yes—
68#887C2214yes—
69#887C2211yescharacteristic
70#885C2214yes—
71#885C2212yes—
72#884C2214yes—
73#884C2212yes—
74#883C2214yes—
75#67⋊C4C2212yes—
76#879C2214yes—
77#878C2214yes—
78#877C2214yes—
79#877C2212yes—
80C4×D12C2211yescharacteristic
81C42×D3C2211yescharacteristic
82#869C2211yescharacteristic
83C4×Dic6C2211yescharacteristic
84#556—31no—
85#556—31no—
86#555—32no—
87#554—32no—
88#553—34no—
89#548—32no—
90#548—32no—
91#547—31no—
92#547D311yescharacteristic, complemented
93#542—34no—
94#537—32no—
95#533—32no—
96#532—32no—
97#532—31no—
98C2×C4⋊Q8—31no—
99#520—32no—
100C4×#41—31no—
101C3×#41—44no—
102C2×C3×Q8C2312yes—
103C2×C3×D4C2311yescharacteristic
104C2×C3×D4C2311yescharacteristic
105C2×C3×D4C2314yes—
106C22×C3×C4C2312yes—
107C22×C3×C4C2312yes—
108C22×C3×C4C2314yes—
109C2×#67C2312yes—
110C2×#67C2312yes—
111C2×#67C2312yes—
112C2×#67C2312yes—
113C2×#67C2314yes—
114C22×Dic3C2312yes—
115C22×Dic3C2312yes—
116D3×Q8—44no—
117#237—24no—
118#235—28no—
119#235—44no—
120C2×D12C2311yescharacteristic
121C2×D12C2312yes—
122C2×C4×D3C2311yescharacteristic
123C2×C4×D3C2311yescharacteristic
124C2×C4×D3C2312yes—
125C2×C4×D3C2314yes—
126C2×C4×D3C2314yes—
127C2×C4×D3C2311yescharacteristic
128C2×Dic6C2311yescharacteristic
129C2×Dic6C2312yes—
130C2×Dic6C2312yes—
131C2×Dic6C2314yes—
132C3×C4⋊C4C2311yescharacteristic
133C3×C4⋊C4C2314yes—
134C3×C4⋊C4C2311yescharacteristic
135C3×C4⋊C4C2312yes—
136C3×C4⋊C4C2312yes—
137C3×C22⋊C4C2314yes—
138C3×C22⋊C4C2312yes—
139C3×C22⋊C4C2312yes—
140C3×C42C2311yescharacteristic
141#217C2314yes—
142#217C2312yes—
143#217C2314yes—
144#217C2314yes—
145#217C2312yes—
146(C2×D3)⋊C4C2312yes—
147(C2×D3)⋊C4C2312yes—
148(C2×D3)⋊C4C2314yes—
149(C2×D3)⋊C4C2312yes—
150(C2×D3)⋊C4C2314yes—
151C4⋊Dic3C2311yescharacteristic
152C4⋊Dic3C2312yes—
153C4⋊Dic3C2312yes—
154C4⋊Dic3C2311yescharacteristic
155C4⋊Dic3C2314yes—
156Dic3⋊C4C2312yes—
157Dic3⋊C4C2312yes—
158Dic3⋊C4C2312yes—
159Dic3⋊C4C2314yes—
160Dic3⋊C4C2314yes—
161Dic3⋊C4C2314yes—
162Dic3⋊C4C2314yes—
163C4×Dic3C2312yes—
164C4×Dic3C2311yescharacteristic
165C4×Dic3C2311yescharacteristic
166C4×Dic3C2311yescharacteristic
167C4×Dic3C2314yes—
168C4×Dic3C2312yes—
169C4×Dic3C2314yes—
170C4×Dic3C2312yes—
171C2×#41—31no—
172C2×#41—32no—
173C2×#41—32no—
174C2×#41C2×D312yes—
175C22×Q8—32no—
176C4⋊Q8—32no—
177C4⋊Q8—32no—
178C4⋊Q8—32no—
179C4⋊Q8—31no—
180C4⋊Q8—31no—
181C4⋊Q8C2×D311yescharacteristic
182#127—31no—
183#126—34no—
184#126—34no—
185#125—34no—
186#124—32no—
187#124—32no—
188#124—34no—
189#124—32no—
190#124—34no—
191#123—34no—
192#123C2×D314yes—
193C22⋊Q8—32no—
194C22⋊Q8—32no—
195C22⋊Q8—34no—
196C22⋊Q8—32no—
197C22⋊Q8—34no—
198C22⋊Q8—34no—
199C22⋊Q8C2×D312yes—
200#121—34no—
201#121—31no—
202#121—34no—
203#121—32no—
204#121—34no—
205#121—31no—
206#121—32no—
207#121—34no—
208#121C2×D312yes—
209C4×Q8—32no—
210C4×Q8—31no—
211C4×Q8—34no—
212C4×Q8—32no—
213C4×Q8—31no—
214C4×D4—31no—
215C4×D4—32no—
216C4×D4—34no—
217C4×D4—34no—
218C4×D4—34no—
219C4×D4—32no—
220C4×D4—34no—
221C4×D4—32no—
222C4×D4—31no—
223C4×D4C2×D311yescharacteristic
224C4×D4C2×D311yescharacteristic
225#117—32no—
226#117—31no—
227#117—32no—
228#117—32no—
229#117—34no—
230C2×C4⋊C4—32no—
231C2×C4⋊C4—32no—
232C2×C4⋊C4—32no—
233C2×C4⋊C4C2×D312yes—
234C2×C42—32no—
235C2×C42—31no—
236C23×C3C2412yes—
237C23×C3C2412yes—
238C22×D3C2412yes—
239C22×D3C2411yescharacteristic
240C3×Q8—24no—
241C3×D4—22no—
242C3×D4—22no—
243C3×D4—44no—
244C2×C3×C4—24no—
245C2×C3×C4—24no—
246C2×C3×C4—44no—
247C2×C3×C4C2412yes—
248C2×C3×C4C2412yes—
249C2×C3×C4C2411yescharacteristic
250C2×C3×C4C2414yes—
251C2×C3×C4C2411yescharacteristic
252C2×C3×C4C2411yescharacteristic
253#67—24no—
254#67—24no—
255#67—24no—
256#67—24no—
257#67—44no—
258C2×Dic3—24no—
259C2×Dic3—24no—
260C2×Dic3C2412yes—
261C2×Dic3C2412yes—
262C2×Dic3C2412yes—
263C2×Dic3C2411yescharacteristic
264C2×Dic3C2414yes—
265C2×Dic3C2411yescharacteristic
266C2×Dic3C2411yescharacteristic
267D12—24no—
268D12—22no—
269C4×D3—24no—
270C4×D3—22no—
271C4×D3—22no—
272C4×D3—44no—
273C4×D3—44no—
274C4×D3#4114yescomplemented
275Dic6—22no—
276Dic6—24no—
277Dic6—24no—
278Dic6—44no—
279#41—44no—
280#41—68no—
281#41—64no—
282#41—124no—
283C2×Q8—31no—
284C2×Q8—32no—
285C2×Q8—32no—
286C2×Q8—34no—
287C2×Q8—124no—
288C2×Q8C22×D312yes—
289C2×D4—32no—
290C2×D4—32no—
291C2×D4—32no—
292C2×D4—32no—
293C2×D4—34no—
294C2×D4—32no—
295C2×D4—31no—
296C2×D4C22×D311yescharacteristic
297C2×D4C22×D311yescharacteristic
298C2×D4C22×D314yes—
299C22×C4—31no—
300C22×C4—32no—
301C22×C4—32no—
302C22×C4—31no—
303C22×C4—31no—
304C22×C4—32no—
305C22×C4—34no—
306C22×C4—34no—
307C22×C4C22×D312yes—
308C22×C4C22×D312yes—
309C22×C4C22×D314yes—
310C4⋊C4—32no—
311C4⋊C4—34no—
312C4⋊C4—34no—
313C4⋊C4—34no—
314C4⋊C4—32no—
315C4⋊C4—31no—
316C4⋊C4—32no—
317C4⋊C4—32no—
318C4⋊C4—32no—
319C4⋊C4—31no—
320C4⋊C4—34no—
321C4⋊C4—34no—
322C4⋊C4C22×D311yescharacteristic
323C4⋊C4C22×D312yes—
324C4⋊C4C22×D312yes—
325C4⋊C4C22×D314yes—
326C4⋊C4C22×D311yescharacteristic
327C22⋊C4—34no—
328C22⋊C4—32no—
329C22⋊C4—34no—
330C22⋊C4—34no—
331C22⋊C4—32no—
332C22⋊C4—32no—
333C22⋊C4—34no—
334C22⋊C4—34no—
335C22⋊C4—32no—
336C22⋊C4—32no—
337C22⋊C4C22×D312yes—
338C22⋊C4C22×D314yes—
339C22⋊C4C22×D312yes—
340C42—31no—
341C42—32no—
342C42—31no—
343C42—32no—
344C42—31no—
345C42—32no—
346C42—34no—
347C42—34no—
348C42C22×D311yescharacteristic
349C22×C3—22no—
350C22×C3—22no—
351C22×C3—22no—
352C22×C3—22no—
353C22×C3—22no—
354C22×C3—22no—
355C22×C3C2511yescharacteristic
356C2×D3—21no—
357C2×D3—21no—
358C2×D3—22no—
359C2×D3—22no—
360C2×D3—22no—
361C2×D3C2×#4112yes—
362C3×C4—22no—
363C3×C4—24no—
364C3×C4—22no—
365C3×C4—21no—
366C3×C4C2×#4112yes—
367C3×C4H(5,𝔽2)12yes—
368Dic3—22no—
369Dic3—22no—
370Dic3—24no—
371Dic3—21no—
372Dic3—22no—
373Dic3C2×#4112yes—
374Dic32−1+412yes—
375C23—31no—
376C23—32no—
377C23C23×D312yes—
378C23C23×D312yes—
379Q8—24no—
380Q8—64no—
381Q8—64no—
382Q8—62no—
383Q8—124no—
384D4—22no—
385D4—22no—
386D4—44no—
387D4—64no—
388D4—64no—
389D4—64no—
390D4—64no—
391D4—64no—
392D4—62no—
393D4—124no—
394C2×C4—24no—
395C2×C4—24no—
396C2×C4—31no—
397C2×C4—31no—
398C2×C4—34no—
399C2×C4—32no—
400C2×C4—31no—
401C2×C4—32no—
402C2×C4—32no—
403C2×C4—34no—
404C2×C4—44no—
405C2×C4—62no—
406C2×C4—64no—
407C2×C4—64no—
408C2×C4—62no—
409C2×C4—64no—
410C2×C4—124no—
411C2×C4—124no—
412C2×C4C23×D312yes—
413C2×C4C23×D312yes—
414C2×C4C23×D311yescharacteristic
415C2×C4C23×D314yes—
416C2×C4C23×D311yescharacteristic
417C2×C4C23×D311yescharacteristic
418C2×C3—42no—
419C2×C3—42no—
420C2×C3C22×#4111yescharacteristic
421C2×C3C2×H(5,𝔽2)11yescharacteristic
422C2×C3C2×2−1+411yescharacteristic
423D3—22no—
424D3—42no—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—22no—
429C22—22no—
430C22—22no—
431C22—32no—
432C22—61no—
433C22—61no—
434C22—62no—
435C22—62no—
436C22—62no—
437C22C24×D311yescharacteristic
438C4—22no—
439C4—24no—
440C4—22no—
441C4—21no—
442C4—32no—
443C4—32no—
444C4—61no—
445C4—64no—
446C4—62no—
447C4—62no—
448C4—62no—
449C4#100412yes—
450C4D3×#4112yes—
451C3#351111yescharacteristic, complemented, Sylow
452C2—42no—
453C2—42no—
454C2—62no—
455C2—122no—
456C2C2×#100411yescharacteristic
457C2C2×D3×#4111yescharacteristic
458C2D3×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C24×D3
commutator, socle, cosocleC22×C3C25
FittingC3×#547C2
hypercenter#547D3
hypocenterC3#3511
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ #547

Complements

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

NH ≅ G/Ntype
1. C3×#547C2semidirect
2. #5832C2semidirect
3. #5831C2semidirect
4. #5732C2semidirect
5. D3×C4⋊Q8C2semidirect
6. #5662C2semidirect
7. #5661C2semidirect
8. #5633C2semidirect
9. #5622C2semidirect
10. #5616C2semidirect
11. #5608C2semidirect
12. #5551C2semidirect
13. #5548C2semidirect
14. #5542C2semidirect
15. C4×#237C2semidirect
16. #5511C2semidirect
17. #5504C2semidirect
92. #547D3semidirect
274. C4×D3#41semidirect
451. C3#3511semidirect

Maximal subgroups

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

subgroupindex
C3×#5472
#58322
#58312
#57322
D3×C4⋊Q82
#56622
#56612
#56332
#56222
#56162
#56082
#55512
#55482
#55422
C4×#2372
#55112
#55042
#35113