Finite Group Databasebeta

← #86936

Subgroups — #86936

Order 384.

1104 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#554C211yesmaximal, characteristic, complemented
2#5725C211yesmaximal, characteristic, complemented
3#5722C211yesmaximal, characteristic, complemented
4#5691C212yesmaximal, complemented
5#5690C212yesmaximal, complemented
6#5643C212yesmaximal, complemented
7#5640C214yesmaximal, complemented
8#5633C212yesmaximal, complemented
9#5631C214yesmaximal, complemented
10#5585C211yesmaximal, characteristic, complemented
11C4×D3×Q8C211yesmaximal, characteristic, complemented
12#5559C212yesmaximal, complemented
13#5557C211yesmaximal, characteristic, complemented
14#5553C211yesmaximal, characteristic, complemented
15#5548C212yesmaximal, complemented
16#5507C212yesmaximal, complemented
17#5504C212yesmaximal, complemented
18#3522—31nomaximal, Sylow
19C2×#239C2212yes—
20C2×D3×Q8C2211yescharacteristic
21C2×#235C2212yes—
22C2×#235C2214yes—
23C3×C4⋊Q8C2211yescharacteristic
24C3×#125C2212yes—
25C3×C22⋊Q8C2212yes—
26C3×C22⋊Q8C2214yes—
27C3×C4×Q8C2211yescharacteristic
28C3×C4×D4C2212yes—
29C3×C4×D4C2211yescharacteristic
30C2×C3×C4⋊C4C2212yes—
31#947C2212yes—
32#947C2212yes—
33Q8×Dic3C2211yescharacteristic
34#944C2214yes—
35#940C2212yes—
36#938C2211yescharacteristic
37#936C2211yescharacteristic
38#930C2212yes—
39#929C2214yes—
40C4×#67C2212yes—
41C4×#67C2214yes—
42C4×#67C2214yes—
43#926C2212yes—
44#898C2214yes—
45#897C2214yes—
46#897C2211yescharacteristic
47#896C2214yes—
48#896C2214yes—
49#895C2212yes—
50#895C2212yes—
51#894C2214yes—
52#894C2214yes—
53#893C2214yes—
54#893C2212yes—
55#893C2212yes—
56#893C2212yes—
57#893C2212yes—
58#892C2214yes—
59D3×C4⋊C4C2214yes—
60D3×C4⋊C4C2211yescharacteristic
61D3×C4⋊C4C2212yes—
62#890C2211yescharacteristic
63#888C2212yes—
64#888C2212yes—
65#887C2212yes—
66#887C2212yes—
67#887C2212yes—
68#887C2211yescharacteristic
69#885C2214yes—
70#885C2214yes—
71#884C2214yes—
72#884C2214yes—
73#883C2214yes—
74#883C2212yes—
75#879C2212yes—
76#875C2212yes—
77#874C2211yescharacteristic
78C4×D12C2212yes—
79C42×D3C2212yes—
80C42×D3C2211yescharacteristic
81C4×Dic6C2212yes—
82C4×Dic6C2211yescharacteristic
83C4×Dic6C2211yescharacteristic
84#559—31no—
85#559—32no—
86Q82—31no—
87#554—32no—
88#554D311yescharacteristic, complemented
89#550—31no—
90#548—32no—
91#547—34no—
92#547—32no—
93#542—34no—
94#542—32no—
95#532—31no—
96#532—32no—
97#529—32no—
98#529—31no—
99#520—32no—
100C2×C4×Q8—31no—
101C2×C3×Q8C2311yescharacteristic
102C2×C3×Q8C2312yes—
103C2×C3×D4C2311yescharacteristic
104C22×C3×C4C2312yes—
105C22×C3×C4C2314yes—
106C2×#67C2312yes—
107C2×#67C2314yes—
108C2×#67C2314yes—
109#239—44no—
110D3×Q8—24no—
111#235—28no—
112#235—48no—
113C2×D12C2312yes—
114C2×D12C2312yes—
115C2×D12C2314yes—
116C2×D12C2312yes—
117C2×C4×D3C2311yescharacteristic
118C2×C4×D3C2311yescharacteristic
119C2×C4×D3C2312yes—
120C2×C4×D3C2312yes—
121C2×C4×D3C2311yescharacteristic
122C2×C4×D3C2314yes—
123C2×C4×D3C2314yes—
124C2×C4×D3C2314yes—
125C2×Dic6C2311yescharacteristic
126C2×Dic6C2312yes—
127C2×Dic6C2314yes—
128C2×Dic6C2311yescharacteristic
129C3×C4⋊C4C2312yes—
130C3×C4⋊C4C2312yes—
131C3×C4⋊C4C2311yescharacteristic
132C3×C4⋊C4C2312yes—
133C3×C4⋊C4C2311yescharacteristic
134C3×C4⋊C4C2314yes—
135C3×C4⋊C4C2314yes—
136C3×C22⋊C4C2312yes—
137C3×C22⋊C4C2314yes—
138C3×C42C2311yescharacteristic
139C3×C42C2312yes—
140#217C2312yes—
141#217C2312yes—
142#217C2312yes—
143(C2×D3)⋊C4C2314yes—
144(C2×D3)⋊C4C2314yes—
145(C2×D3)⋊C4C2314yes—
146(C2×D3)⋊C4C2312yes—
147(C2×D3)⋊C4C2314yes—
148(C2×D3)⋊C4C2314yes—
149(C2×D3)⋊C4C2314yes—
150C4⋊Dic3C2311yescharacteristic
151C4⋊Dic3C2312yes—
152C4⋊Dic3C2311yescharacteristic
153C4⋊Dic3C2312yes—
154C4⋊Dic3C2312yes—
155Dic3⋊C4C2312yes—
156Dic3⋊C4C2312yes—
157Dic3⋊C4C2312yes—
158Dic3⋊C4C2312yes—
159Dic3⋊C4C2312yes—
160Dic3⋊C4C2314yes—
161Dic3⋊C4C2314yes—
162C4×Dic3C2312yes—
163C4×Dic3C2311yescharacteristic
164C4×Dic3C2312yes—
165C4×Dic3C2311yescharacteristic
166C4×Dic3C2312yes—
167C4×Dic3C2312yes—
168C4×Dic3C2311yescharacteristic
169C4×Dic3C2314yes—
170C2×#41—32no—
171C2×#41—32no—
172C2×#41—34no—
173C22×Q8—31no—
174C4⋊Q8—34no—
175C4⋊Q8—32no—
176C4⋊Q8—32no—
177C4⋊Q8C2×D311yescharacteristic
178#127—32no—
179#127—31no—
180#126—34no—
181#126—32no—
182#125—31no—
183#125C2×D312yes—
184#124—32no—
185#124—32no—
186#124—31no—
187#124—34no—
188#124—34no—
189#124—32no—
190#123—34no—
191#123—34no—
192#123—34no—
193#123—32no—
194#123—34no—
195C22⋊Q8—31no—
196C22⋊Q8—34no—
197C22⋊Q8—34no—
198C22⋊Q8—34no—
199C22⋊Q8C2×D314yes—
200C22⋊Q8C2×D312yes—
201#121—31no—
202#121—32no—
203#121—32no—
204#121—32no—
205#121—34no—
206#121—34no—
207C4×Q8—31no—
208C4×Q8—31no—
209C4×Q8—32no—
210C4×Q8—32no—
211C4×Q8—32no—
212C4×Q8—31no—
213C4×Q8—32no—
214C4×Q8—31no—
215C4×Q8C2×D311yescharacteristic
216C4×D4—34no—
217C4×D4—34no—
218C4×D4—32no—
219C4×D4—32no—
220C4×D4—32no—
221C4×D4—34no—
222C4×D4—32no—
223C4×D4—32no—
224C4×D4—32no—
225C4×D4C2×D311yescharacteristic
226C4×D4C2×D312yes—
227#117—32no—
228#117—34no—
229C2×C4⋊C4—32no—
230C2×C4⋊C4—31no—
231C2×C4⋊C4—34no—
232C2×C4⋊C4C2×D312yes—
233C2×C42—31no—
234C2×C42—32no—
235C23×C3C2412yes—
236C22×D3C2414yes—
237C22×D3C2411yescharacteristic
238C3×Q8—22no—
239C3×Q8—42no—
240C3×D4—22no—
241C2×C3×C4—24no—
242C2×C3×C4—44no—
243C2×C3×C4C2411yescharacteristic
244C2×C3×C4C2412yes—
245C2×C3×C4C2414yes—
246C2×C3×C4C2412yes—
247C2×C3×C4C2412yes—
248C2×C3×C4C2411yescharacteristic
249C2×C3×C4C2411yescharacteristic
250#67—24no—
251#67—28no—
252#67—44no—
253C2×Dic3C2411yescharacteristic
254C2×Dic3C2412yes—
255C2×Dic3C2412yes—
256C2×Dic3C2411yescharacteristic
257C2×Dic3C2411yescharacteristic
258C2×Dic3C2412yes—
259C2×Dic3C2412yes—
260D12—28no—
261D12—24no—
262D12—24no—
263D12—42no—
264C4×D3—24no—
265C4×D3—22no—
266C4×D3—22no—
267C4×D3—22no—
268C4×D3—28no—
269C4×D3—24no—
270C4×D3—44no—
271C4×D3—44no—
272Dic6—22no—
273Dic6—24no—
274Dic6—44no—
275Dic6#4114yescomplemented
276#41—68no—
277#41—128no—
278#41—124no—
279C2×Q8—31no—
280C2×Q8—31no—
281C2×Q8—32no—
282C2×Q8—34no—
283C2×Q8—64no—
284C2×Q8C22×D311yescharacteristic
285C2×Q8C22×D312yes—
286C2×D4—34no—
287C2×D4—32no—
288C2×D4—34no—
289C2×D4—32no—
290C2×D4—32no—
291C2×D4—34no—
292C2×D4—32no—
293C2×D4C22×D311yescharacteristic
294C22×C4—31no—
295C22×C4—31no—
296C22×C4—32no—
297C22×C4—32no—
298C22×C4—31no—
299C22×C4—34no—
300C22×C4—34no—
301C22×C4—34no—
302C22×C4C22×D312yes—
303C22×C4C22×D314yes—
304C4⋊C4—32no—
305C4⋊C4—32no—
306C4⋊C4—34no—
307C4⋊C4—32no—
308C4⋊C4—31no—
309C4⋊C4—32no—
310C4⋊C4—32no—
311C4⋊C4—32no—
312C4⋊C4—31no—
313C4⋊C4—32no—
314C4⋊C4—34no—
315C4⋊C4—32no—
316C4⋊C4C22×D311yescharacteristic
317C4⋊C4C22×D314yes—
318C4⋊C4C22×D312yes—
319C4⋊C4C22×D312yes—
320C4⋊C4C22×D311yescharacteristic
321C4⋊C4C22×D312yes—
322C4⋊C4C22×D314yes—
323C22⋊C4—32no—
324C22⋊C4—32no—
325C22⋊C4—32no—
326C22⋊C4—34no—
327C22⋊C4—34no—
328C22⋊C4—32no—
329C22⋊C4—34no—
330C22⋊C4—34no—
331C22⋊C4—34no—
332C22⋊C4—34no—
333C22⋊C4C22×D312yes—
334C22⋊C4C22×D314yes—
335C42—32no—
336C42—31no—
337C42—31no—
338C42—32no—
339C42—31no—
340C42—32no—
341C42—34no—
342C42—32no—
343C42C22×D312yes—
344C42C22×D311yescharacteristic
345C22×C3—22no—
346C22×C3—22no—
347C22×C3—22no—
348C22×C3C2511yescharacteristic
349C2×D3—21no—
350C2×D3—21no—
351C2×D3—24no—
352C2×D3—24no—
353C2×D3—24no—
354C2×D3H(5,𝔽2)12yes—
355C3×C4—22no—
356C3×C4—22no—
357C3×C4—24no—
358C3×C4—22no—
359C3×C4—21no—
360C3×C4C2×#4112yes—
361C3×C42−1+412yes—
362Dic3—21no—
363Dic3—22no—
364Dic3—22no—
365Dic3—21no—
366Dic3—22no—
367Dic3—21no—
368Dic3C2×#4114yes—
369C23—31no—
370C23—34no—
371C23C23×D312yes—
372Q8—22no—
373Q8—34no—
374Q8—42no—
375Q8—64no—
376Q8—62no—
377Q8—124no—
378D4—22no—
379D4—68no—
380D4—68no—
381D4—64no—
382D4—64no—
383D4—64no—
384D4—122no—
385D4—124no—
386C2×C4—24no—
387C2×C4—32no—
388C2×C4—31no—
389C2×C4—32no—
390C2×C4—31no—
391C2×C4—31no—
392C2×C4—32no—
393C2×C4—32no—
394C2×C4—44no—
395C2×C4—64no—
396C2×C4—68no—
397C2×C4—64no—
398C2×C4—62no—
399C2×C4—62no—
400C2×C4—62no—
401C2×C4—124no—
402C2×C4—124no—
403C2×C4C23×D312yes—
404C2×C4C23×D312yes—
405C2×C4C23×D311yescharacteristic
406C2×C4C23×D314yes—
407C2×C4C23×D312yes—
408C2×C4C23×D311yescharacteristic
409C2×C4C23×D311yescharacteristic
410C2×C3—42no—
411C2×C3C22×#4111yescharacteristic
412C2×C3C2×H(5,𝔽2)11yescharacteristic
413C2×C3C2×2−1+411yescharacteristic
414D3—22no—
415D3—44no—
416C22—22no—
417C22—22no—
418C22—22no—
419C22—32no—
420C22—61no—
421C22—61no—
422C22—64no—
423C22—64no—
424C22—64no—
425C22C24×D311yescharacteristic
426C4—22no—
427C4—22no—
428C4—22no—
429C4—24no—
430C4—21no—
431C4—34no—
432C4—61no—
433C4—62no—
434C4—61no—
435C4—61no—
436C4—62no—
437C4—62no—
438C4#100712yes—
439C4D3×#4112yes—
440C3#352211yescharacteristic, complemented, Sylow
441C2—42no—
442C2—62no—
443C2—124no—
444C2C2×#100711yescharacteristic
445C2C2×D3×#4111yescharacteristic
446C2D3×H(5,𝔽2)11yescharacteristic
subgroupG/H
center, FrattiniC22C24×D3
commutator, socle, cosocleC22×C3C25
FittingC3×#554C2
hypercenter#554D3
hypocenterC3#3522
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. #5725C2semidirect
3. #5722C2semidirect
4. #5691C2semidirect
5. #5690C2semidirect
6. #5643C2semidirect
7. #5640C2semidirect
8. #5633C2semidirect
9. #5631C2semidirect
10. #5585C2semidirect
11. C4×D3×Q8C2semidirect
12. #5559C2semidirect
13. #5557C2semidirect
14. #5553C2semidirect
15. #5548C2semidirect
16. #5507C2semidirect
17. #5504C2semidirect
88. #554D3semidirect
275. Dic6#41semidirect
440. C3#3522semidirect

Maximal subgroups

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

subgroupindex
C3×#5542
#57252
#57222
#56912
#56902
#56432
#56402
#56332
#56312
#55852
C4×D3×Q82
#55592
#55572
#55532
#55482
#55072
#55042
#35223