Finite Group Databasebeta

← #86278

Subgroups — #86278

Order 384.

1094 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#533C211yesmaximal, characteristic, complemented
2#5732C211yesmaximal, characteristic, complemented
3#5727C211yesmaximal, characteristic, complemented
4#5726C211yesmaximal, characteristic, complemented
5#5721C211yesmaximal, characteristic, complemented
6#5693C214yesmaximal, complemented
7#5641C212yesmaximal, complemented
8#5639C212yesmaximal, complemented
9#5633C212yesmaximal, complemented
10#5631C212yesmaximal, complemented
11#5580C212yesmaximal, complemented
12#5578C212yesmaximal, complemented
13C4×#239C212yesmaximal, complemented
14C4×D3×Q8C212yesmaximal, complemented
15#5528C214yesmaximal, complemented
16C4×#235C211yesmaximal, characteristic, complemented
17C4×#235C211yesmaximal, characteristic, complemented
18#3482—31nomaximal, Sylow
19C2×#239C2212yes—
20C2×D3×Q8C2212yes—
21C2×#235C2211yescharacteristic
22C2×#235C2211yescharacteristic
23C3×C4⋊Q8C2211yescharacteristic
24C3×C4⋊Q8C2211yescharacteristic
25C3×#125C2212yes—
26C3×C22⋊Q8C2212yes—
27C3×C22⋊Q8C2212yes—
28C3×C4×Q8C2212yes—
29C3×C4×Q8C2212yes—
30C3×#117C2212yes—
31C2×C3×C42C2211yescharacteristic
32#947C2212yes—
33#946C2212yes—
34#946C2212yes—
35Q8×Dic3C2212yes—
36Q8×Dic3C2212yes—
37#944C2212yes—
38C4×#67C2212yes—
39C4×#67C2212yes—
40C4×#67C2212yes—
41C4×#67C2212yes—
42#926C2211yescharacteristic
43#926C2211yescharacteristic
44#898C2214yes—
45#898C2214yes—
46#897C2212yes—
47#896C2214yes—
48#896C2214yes—
49#895C2212yes—
50#894C2214yes—
51#894C2214yes—
52#893C2214yes—
53#893C2212yes—
54#892C2214yes—
55#892C2212yes—
56D3×C4⋊C4C2212yes—
57D3×C4⋊C4C2214yes—
58#890C2212yes—
59#889C2214yes—
60#889C2214yes—
61#888C2212yes—
62#887C2212yes—
63#887C2214yes—
64#885C2214yes—
65#884C2214yes—
66#883C2214yes—
67#879C2214yes—
68C4×D12C2211yescharacteristic
69C4×D12C2211yescharacteristic
70C4×D12C2211yescharacteristic
71C4×D12C2211yescharacteristic
72C4×D12C2214yes—
73#872C2212yes—
74#872C2212yes—
75#872C2214yes—
76C42×D3C2212yes—
77C42×D3C2212yes—
78C42×D3C2214yes—
79C4×Dic6C2211yescharacteristic
80C4×Dic6C2211yescharacteristic
81C4×Dic6C2211yescharacteristic
82C4×Dic6C2211yescharacteristic
83C4×Dic6C2214yes—
84#557—31no—
85#556—31no—
86#556—32no—
87#552—34no—
88#552—32no—
89D4×Q8—31no—
90#548—32no—
91#547—31no—
92#547—32no—
93#533—32no—
94#533D311yescharacteristic, complemented
95#529—32no—
96#529—34no—
97C4×#41—32no—
98C4×#41—31no—
99C4×#41—31no—
100C2×C4×Q8—32no—
101C2×C3×Q8C2312yes—
102C2×C3×Q8C2312yes—
103C22×C3×C4C2311yescharacteristic
104C22×C3×C4C2311yescharacteristic
105C22×C3×C4C2311yescharacteristic
106C2×#67C2312yes—
107C2×#67C2312yes—
108#239—28no—
109D3×Q8—28no—
110#235—24no—
111#235—24no—
112C2×D12C2311yescharacteristic
113C2×D12C2314yes—
114C2×D12C2311yescharacteristic
115C2×C4×D3C2312yes—
116C2×C4×D3C2312yes—
117C2×C4×D3C2312yes—
118C2×C4×D3C2312yes—
119C2×C4×D3C2312yes—
120C2×C4×D3C2312yes—
121C2×C4×D3C2314yes—
122C2×C4×D3C2314yes—
123C2×Dic6C2311yescharacteristic
124C2×Dic6C2314yes—
125C2×Dic6C2311yescharacteristic
126C3×C4⋊C4C2312yes—
127C3×C4⋊C4C2314yes—
128C3×C4⋊C4C2312yes—
129C3×C4⋊C4C2312yes—
130C3×C4⋊C4C2314yes—
131C3×C4⋊C4C2312yes—
132C3×C22⋊C4C2314yes—
133C3×C42C2311yescharacteristic
134C3×C42C2311yescharacteristic
135C3×C42C2311yescharacteristic
136C3×C42C2314yes—
137C3×C42C2311yescharacteristic
138#217C2312yes—
139#217C2312yes—
140(C2×D3)⋊C4C2312yes—
141(C2×D3)⋊C4C2312yes—
142(C2×D3)⋊C4C2312yes—
143(C2×D3)⋊C4C2312yes—
144(C2×D3)⋊C4C2314yes—
145(C2×D3)⋊C4C2314yes—
146(C2×D3)⋊C4C2314yes—
147(C2×D3)⋊C4C2314yes—
148C4⋊Dic3C2311yescharacteristic
149C4⋊Dic3C2311yescharacteristic
150C4⋊Dic3C2311yescharacteristic
151C4⋊Dic3C2311yescharacteristic
152C4⋊Dic3C2314yes—
153C4⋊Dic3C2314yes—
154Dic3⋊C4C2312yes—
155Dic3⋊C4C2312yes—
156Dic3⋊C4C2312yes—
157Dic3⋊C4C2312yes—
158Dic3⋊C4C2314yes—
159Dic3⋊C4C2314yes—
160Dic3⋊C4C2314yes—
161Dic3⋊C4C2314yes—
162C4×Dic3C2312yes—
163C4×Dic3C2312yes—
164C4×Dic3C2312yes—
165C4×Dic3C2312yes—
166C4×Dic3C2312yes—
167C4×Dic3C2312yes—
168C4×Dic3C2314yes—
169C4×Dic3C2314yes—
170C2×#41—32no—
171C2×#41—31no—
172C2×#41—31no—
173C22×Q8—32no—
174C4⋊Q8—32no—
175C4⋊Q8—32no—
176C4⋊Q8C2×D311yescharacteristic
177C4⋊Q8C2×D311yescharacteristic
178#126—34no—
179#126—34no—
180#126—34no—
181#125—34no—
182#125—32no—
183#125—34no—
184#125C2×D312yes—
185#124—32no—
186#124—34no—
187#123—34no—
188#123—34no—
189#123—34no—
190C22⋊Q8—32no—
191C22⋊Q8—32no—
192C22⋊Q8—34no—
193C22⋊Q8—32no—
194C22⋊Q8—34no—
195C22⋊Q8C2×D312yes—
196C22⋊Q8C2×D312yes—
197#121—32no—
198#121—34no—
199C4×Q8—32no—
200C4×Q8—32no—
201C4×Q8—32no—
202C4×Q8—34no—
203C4×Q8—31no—
204C4×Q8—34no—
205C4×Q8—31no—
206C4×Q8—31no—
207C4×Q8—31no—
208C4×Q8C2×D312yes—
209C4×Q8C2×D312yes—
210C4×D4—32no—
211C4×D4—32no—
212C4×D4—32no—
213C4×D4—32no—
214C4×D4—32no—
215C4×D4—34no—
216C4×D4—31no—
217C4×D4—31no—
218C4×D4—34no—
219C4×D4—31no—
220C4×D4—31no—
221#117—31no—
222#117—31no—
223#117—34no—
224#117—32no—
225#117—32no—
226#117—32no—
227#117—34no—
228#117C2×D312yes—
229C2×C4⋊C4—34no—
230C2×C4⋊C4—32no—
231C2×C42—34no—
232C2×C42—32no—
233C2×C42—32no—
234C2×C42C2×D311yescharacteristic
235C23×C3C2411yescharacteristic
236C22×D3C2412yes—
237C22×D3C2412yes—
238C3×Q8—24no—
239C3×Q8—24no—
240C2×C3×C4—22no—
241C2×C3×C4—22no—
242C2×C3×C4—22no—
243C2×C3×C4C2411yescharacteristic
244C2×C3×C4C2411yescharacteristic
245C2×C3×C4C2414yes—
246C2×C3×C4C2414yes—
247C2×C3×C4C2411yescharacteristic
248C2×C3×C4C2411yescharacteristic
249C2×C3×C4C2411yescharacteristic
250C2×C3×C4C2411yescharacteristic
251#67—24no—
252#67—24no—
253C2×Dic3C2412yes—
254C2×Dic3C2412yes—
255C2×Dic3C2412yes—
256C2×Dic3C2412yes—
257C2×Dic3C2412yes—
258C2×Dic3C2412yes—
259D12—28no—
260D12—22no—
261D12#4114yescomplemented
262C4×D3—24no—
263C4×D3—28no—
264C4×D3—24no—
265C4×D3—24no—
266C4×D3—24no—
267C4×D3—24no—
268C4×D3—24no—
269C4×D3—28no—
270Dic6—22no—
271Dic6—28no—
272Dic6#4114yescomplemented
273#41—64no—
274#41—64no—
275#41—68no—
276C2×Q8—31no—
277C2×Q8—34no—
278C2×Q8—31no—
279C2×Q8—68no—
280C2×Q8C22×D312yes—
281C2×Q8C22×D312yes—
282C2×D4—32no—
283C2×D4—32no—
284C2×D4—31no—
285C2×D4—34no—
286C2×D4—31no—
287C22×C4—34no—
288C22×C4—32no—
289C22×C4—34no—
290C22×C4—32no—
291C22×C4—32no—
292C22×C4—32no—
293C22×C4—32no—
294C22×C4—32no—
295C22×C4C22×D311yescharacteristic
296C22×C4C22×D311yescharacteristic
297C22×C4C22×D311yescharacteristic
298C4⋊C4—32no—
299C4⋊C4—31no—
300C4⋊C4—34no—
301C4⋊C4—34no—
302C4⋊C4—34no—
303C4⋊C4—31no—
304C4⋊C4—32no—
305C4⋊C4—32no—
306C4⋊C4—31no—
307C4⋊C4—31no—
308C4⋊C4—32no—
309C4⋊C4—34no—
310C4⋊C4—34no—
311C4⋊C4—34no—
312C4⋊C4C22×D312yes—
313C4⋊C4C22×D314yes—
314C4⋊C4C22×D314yes—
315C4⋊C4C22×D312yes—
316C4⋊C4C22×D312yes—
317C4⋊C4C22×D312yes—
318C22⋊C4—32no—
319C22⋊C4—32no—
320C22⋊C4—32no—
321C22⋊C4—34no—
322C22⋊C4—32no—
323C22⋊C4—32no—
324C22⋊C4—32no—
325C22⋊C4—34no—
326C22⋊C4—34no—
327C22⋊C4—34no—
328C22⋊C4C22×D314yes—
329C42—32no—
330C42—34no—
331C42—32no—
332C42—32no—
333C42—34no—
334C42—32no—
335C42—32no—
336C42—32no—
337C42C22×D311yescharacteristic
338C42C22×D311yescharacteristic
339C42C22×D311yescharacteristic
340C42C22×D311yescharacteristic
341C42C22×D314yes—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3C2511yescharacteristic
346C2×D3—22no—
347C2×D3—22no—
348C2×D3—22no—
349C2×D3—22no—
350C2×D3—22no—
351C2×D3C2×#4114yes—
352C3×C4—24no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—24no—
356C3×C4—21no—
357C3×C4C2×#4112yes—
358C3×C4C2×#4112yes—
359C3×C42−1+412yes—
360Dic3—22no—
361Dic3—22no—
362Dic3—22no—
363Dic3—22no—
364Dic3—22no—
365Dic3C2×#4114yes—
366C23—32no—
367C23—32no—
368C23C23×D311yescharacteristic
369Q8—24no—
370Q8—24no—
371Q8—34no—
372Q8—68no—
373Q8—62no—
374D4—34no—
375D4—68no—
376D4—64no—
377D4—64no—
378D4—62no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—32no—
383C2×C4—32no—
384C2×C4—32no—
385C2×C4—32no—
386C2×C4—32no—
387C2×C4—32no—
388C2×C4—68no—
389C2×C4—64no—
390C2×C4—64no—
391C2×C4—68no—
392C2×C4—64no—
393C2×C4—64no—
394C2×C4—64no—
395C2×C4—64no—
396C2×C4C23×D311yescharacteristic
397C2×C4C23×D311yescharacteristic
398C2×C4C23×D314yes—
399C2×C4C23×D314yes—
400C2×C4C23×D311yescharacteristic
401C2×C4C23×D311yescharacteristic
402C2×C4C23×D311yescharacteristic
403C2×C4C23×D311yescharacteristic
404C2×C3—41no—
405C2×C3C22×#4111yescharacteristic
406C2×C3C22×#4111yescharacteristic
407C2×C3C2×2−1+411yescharacteristic
408D3—24no—
409D3—42no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—34no—
414C22—62no—
415C22—62no—
416C22—62no—
417C22—62no—
418C22—62no—
419C22C24×D311yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—24no—
424C4—24no—
425C4—34no—
426C4—62no—
427C4—62no—
428C4—62no—
429C4—62no—
430C4—62no—
431C4#100712yes—
432C4D3×#4112yes—
433C4D3×#4112yes—
434C3#348211yescharacteristic, complemented, Sylow
435C2—41no—
436C2—64no—
437C2—122no—
438C2C2×#100711yescharacteristic
439C2C2×D3×#4111yescharacteristic
440C2C2×D3×#4111yescharacteristic
subgroupG/H
centerC2×C4C23×D3
commutator, socle, cosocleC22×C3C25
FrattiniC22C24×D3
FittingC3×#533C2
hypercenter#533D3
hypocenterC3#3482
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ #533

Complements

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

NH ≅ G/Ntype
1. C3×#533C2semidirect
2. #5732C2semidirect
3. #5727C2semidirect
4. #5726C2semidirect
5. #5721C2semidirect
6. #5693C2semidirect
7. #5641C2semidirect
8. #5639C2semidirect
9. #5633C2semidirect
10. #5631C2semidirect
11. #5580C2semidirect
12. #5578C2semidirect
13. C4×#239C2semidirect
14. C4×D3×Q8C2semidirect
15. #5528C2semidirect
16. C4×#235C2semidirect
17. C4×#235C2semidirect
94. #533D3semidirect
261. D12#41semidirect
272. Dic6#41semidirect
434. C3#3482semidirect

Maximal subgroups

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

subgroupindex
C3×#5332
#57322
#57272
#57262
#57212
#56932
#56412
#56392
#56332
#56312
#55802
#55782
C4×#2392
C4×D3×Q82
#55282
C4×#2352
#34823