Finite Group Databasebeta

← #86287

Subgroups — #86287

Order 384.

1022 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#533C211yesmaximal, characteristic, complemented
2#5734C211yesmaximal, characteristic, complemented
3#5730C211yesmaximal, characteristic, complemented
4#5727C211yesmaximal, characteristic, complemented
5#5726C211yesmaximal, characteristic, complemented
6#5697C212yesmaximal, complemented
7#5689C212yesmaximal, complemented
8#5647C214yesmaximal, complemented
9#5629C212yesmaximal, complemented
10#5628C212yesmaximal, complemented
11#5582C214yesmaximal, complemented
12#5581C212yesmaximal, complemented
13#5576C212yesmaximal, complemented
14#5532C212yesmaximal, complemented
15#5530C212yesmaximal, complemented
16#5479C211yesmaximal, characteristic, complemented
17#5477C211yesmaximal, characteristic, complemented
18#3547—31nomaximal, Sylow
19C2×#239C2212yes—
20C2×D3×Q8C2212yes—
21C2×#235C2212yes—
22C3×C4⋊Q8C2211yescharacteristic
23C3×C4⋊Q8C2211yescharacteristic
24C3×#125C2212yes—
25C3×C22⋊Q8C2212yes—
26C3×C22⋊Q8C2212yes—
27C3×C4×Q8C2212yes—
28C3×C4×Q8C2212yes—
29C3×#117C2212yes—
30C2×C3×C42C2211yescharacteristic
31#947C2214yes—
32#946C2214yes—
33#946C2212yes—
34#946C2212yes—
35#930C2212yes—
36#930C2211yescharacteristic
37#930C2211yescharacteristic
38#930C2211yescharacteristic
39#929C2212yes—
40C4×#67C2212yes—
41#924C2211yescharacteristic
42#897C2214yes—
43#897C2212yes—
44#896C2214yes—
45#896C2214yes—
46#895C2214yes—
47#895C2212yes—
48#895C2212yes—
49#895C2214yes—
50#895C2212yes—
51#894C2214yes—
52#894C2214yes—
53#894C2214yes—
54#893C2212yes—
55#893C2212yes—
56#892C2212yes—
57#892C2212yes—
58D3×C4⋊C4C2212yes—
59D3×C4⋊C4C2212yes—
60#890C2212yes—
61#889C2214yes—
62#888C2212yes—
63#888C2214yes—
64#885C2214yes—
65#884C2214yes—
66#884C2214yes—
67#883C2214yes—
68#876C2212yes—
69#876C2214yes—
70#875C2212yes—
71#875C2211yescharacteristic
72#875C2214yes—
73#874C2211yescharacteristic
74C4×D12C2211yescharacteristic
75C4×D12C2211yescharacteristic
76C4×D12C2211yescharacteristic
77C4×D12C2212yes—
78C4×D12C2214yes—
79#872C2212yes—
80#872C2214yes—
81#870C2211yescharacteristic
82#869C2211yescharacteristic
83C4×Dic6C2211yescharacteristic
84#562—34no—
85#555—31no—
86#555—32no—
87#554—31no—
88#553—32no—
89#552—32no—
90D4×Q8—31no—
91#548—32no—
92#547—31no—
93#544—32no—
94#542—34no—
95#540—32no—
96#537—32no—
97#536—32no—
98#533D311yescharacteristic, complemented
99#532—31no—
100#529—31no—
101C2×C3×Q8C2312yes—
102C2×C3×Q8C2312yes—
103C22×C3×C4C2311yescharacteristic
104C22×C3×C4C2311yescharacteristic
105C22×C3×C4C2311yescharacteristic
106C2×#67C2312yes—
107C2×#67C2312yes—
108C2×#67C2312yes—
109#239—44no—
110D3×Q8—44no—
111#235—44no—
112C2×D12C2311yescharacteristic
113C2×D12C2311yescharacteristic
114C2×D12C2311yescharacteristic
115C2×D12C2312yes—
116C2×D12C2314yes—
117C2×D12C2312yes—
118C2×D12C2314yes—
119C2×C4×D3C2312yes—
120C2×C4×D3C2312yes—
121C2×C4×D3C2312yes—
122C2×C4×D3C2314yes—
123C2×C4×D3C2314yes—
124C2×C4×D3C2314yes—
125C2×Dic6C2311yescharacteristic
126C2×Dic6C2312yes—
127C2×Dic6C2314yes—
128C3×C4⋊C4C2312yes—
129C3×C4⋊C4C2314yes—
130C3×C4⋊C4C2314yes—
131C3×C4⋊C4C2312yes—
132C3×C4⋊C4C2312yes—
133C3×C4⋊C4C2312yes—
134C3×C22⋊C4C2314yes—
135C3×C42C2311yescharacteristic
136C3×C42C2311yescharacteristic
137C3×C42C2311yescharacteristic
138C3×C42C2314yes—
139C3×C42C2311yescharacteristic
140#217C2312yes—
141(C2×D3)⋊C4C2312yes—
142(C2×D3)⋊C4C2312yes—
143(C2×D3)⋊C4C2312yes—
144(C2×D3)⋊C4C2314yes—
145(C2×D3)⋊C4C2312yes—
146(C2×D3)⋊C4C2312yes—
147(C2×D3)⋊C4C2312yes—
148(C2×D3)⋊C4C2312yes—
149(C2×D3)⋊C4C2312yes—
150(C2×D3)⋊C4C2314yes—
151(C2×D3)⋊C4C2314yes—
152(C2×D3)⋊C4C2314yes—
153(C2×D3)⋊C4C2314yes—
154C4⋊Dic3C2311yescharacteristic
155C4⋊Dic3C2311yescharacteristic
156C4⋊Dic3C2312yes—
157C4⋊Dic3C2311yescharacteristic
158C4⋊Dic3C2311yescharacteristic
159C4⋊Dic3C2314yes—
160Dic3⋊C4C2312yes—
161Dic3⋊C4C2312yes—
162Dic3⋊C4C2312yes—
163Dic3⋊C4C2312yes—
164Dic3⋊C4C2314yes—
165Dic3⋊C4C2314yes—
166Dic3⋊C4C2314yes—
167C4×Dic3C2312yes—
168C4×Dic3C2314yes—
169C2×#41—32no—
170C2×#41—32no—
171C22×Q8—32no—
172C4⋊Q8—34no—
173C4⋊Q8—32no—
174C4⋊Q8—31no—
175C4⋊Q8C2×D311yescharacteristic
176C4⋊Q8C2×D311yescharacteristic
177#127—31no—
178#126—32no—
179#126—34no—
180#125—34no—
181#125—32no—
182#125—31no—
183#125C2×D312yes—
184#124—34no—
185#124—34no—
186#124—31no—
187#124—32no—
188#124—34no—
189#123—32no—
190#123—34no—
191#123—34no—
192#123—34no—
193#123—34no—
194C22⋊Q8—32no—
195C22⋊Q8—32no—
196C22⋊Q8—34no—
197C22⋊Q8—31no—
198C22⋊Q8—32no—
199C22⋊Q8—34no—
200C22⋊Q8—34no—
201C22⋊Q8—34no—
202C22⋊Q8C2×D312yes—
203C22⋊Q8C2×D312yes—
204#121—31no—
205#121—31no—
206#121—31no—
207#121—32no—
208#121—34no—
209#121—32no—
210#121—32no—
211#121—34no—
212#121—32no—
213#121—34no—
214#121—34no—
215C4×Q8—31no—
216C4×Q8C2×D312yes—
217C4×Q8C2×D312yes—
218C4×D4—32no—
219C4×D4—32no—
220C4×D4—32no—
221C4×D4—31no—
222C4×D4—31no—
223C4×D4—32no—
224C4×D4—31no—
225C4×D4—34no—
226#117—32no—
227#117—32no—
228#117—32no—
229#117—34no—
230#117C2×D312yes—
231C2×C4⋊C4—32no—
232C2×C4⋊C4—32no—
233C2×C42C2×D311yescharacteristic
234C23×C3C2411yescharacteristic
235C22×D3C2412yes—
236C22×D3C2412yes—
237C22×D3C2412yes—
238C3×Q8—24no—
239C3×Q8—42no—
240C2×C3×C4—22no—
241C2×C3×C4—22no—
242C2×C3×C4—41no—
243C2×C3×C4C2414yes—
244C2×C3×C4C2411yescharacteristic
245C2×C3×C4C2411yescharacteristic
246C2×C3×C4C2411yescharacteristic
247C2×C3×C4C2411yescharacteristic
248C2×C3×C4C2414yes—
249C2×C3×C4C2411yescharacteristic
250C2×C3×C4C2411yescharacteristic
251#67—42no—
252#67—42no—
253#67—42no—
254C2×Dic3C2412yes—
255C2×Dic3C2412yes—
256C2×Dic3C2412yes—
257C2×Dic3C2412yes—
258C2×Dic3C2412yes—
259D12—22no—
260D12—22no—
261D12—22no—
262D12—44no—
263D12—42no—
264D12—42no—
265D12—44no—
266C4×D3—24no—
267C4×D3—24no—
268C4×D3—24no—
269C4×D3—44no—
270C4×D3—44no—
271C4×D3—44no—
272Dic6—22no—
273Dic6—42no—
274Dic6—44no—
275#41—124no—
276#41—124no—
277C2×Q8—31no—
278C2×Q8—34no—
279C2×Q8—32no—
280C2×Q8—124no—
281C2×Q8C22×D312yes—
282C2×Q8C22×D312yes—
283C2×D4—32no—
284C2×D4—32no—
285C2×D4—32no—
286C2×D4—31no—
287C2×D4—31no—
288C2×D4—31no—
289C2×D4—34no—
290C2×D4—32no—
291C2×D4—34no—
292C2×D4—32no—
293C22×C4—32no—
294C22×C4—32no—
295C22×C4—32no—
296C22×C4—34no—
297C22×C4—34no—
298C22×C4—34no—
299C22×C4C22×D311yescharacteristic
300C22×C4C22×D311yescharacteristic
301C22×C4C22×D311yescharacteristic
302C4⋊C4—31no—
303C4⋊C4—31no—
304C4⋊C4—34no—
305C4⋊C4—34no—
306C4⋊C4—31no—
307C4⋊C4—31no—
308C4⋊C4—32no—
309C4⋊C4—34no—
310C4⋊C4—32no—
311C4⋊C4—32no—
312C4⋊C4—32no—
313C4⋊C4—34no—
314C4⋊C4—32no—
315C4⋊C4C22×D312yes—
316C4⋊C4C22×D312yes—
317C4⋊C4C22×D312yes—
318C4⋊C4C22×D314yes—
319C4⋊C4C22×D314yes—
320C4⋊C4C22×D312yes—
321C22⋊C4—32no—
322C22⋊C4—32no—
323C22⋊C4—32no—
324C22⋊C4—32no—
325C22⋊C4—34no—
326C22⋊C4—34no—
327C22⋊C4—34no—
328C22⋊C4—32no—
329C22⋊C4—32no—
330C22⋊C4—34no—
331C22⋊C4—32no—
332C22⋊C4—34no—
333C22⋊C4—32no—
334C22⋊C4—32no—
335C22⋊C4C22×D314yes—
336C42—34no—
337C42—32no—
338C42C22×D311yescharacteristic
339C42C22×D311yescharacteristic
340C42C22×D311yescharacteristic
341C42C22×D311yescharacteristic
342C42C22×D314yes—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3C2511yescharacteristic
347C2×D3—22no—
348C2×D3—22no—
349C2×D3—22no—
350C2×D3—22no—
351C2×D3—22no—
352C2×D3—22no—
353C2×D3—22no—
354C2×D3—22no—
355C2×D3—22no—
356C3×C4—21no—
357C3×C4—24no—
358C3×C4—21no—
359C3×C4—24no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4H(5,𝔽2)12yes—
363C3×C42−1+412yes—
364Dic3—22no—
365Dic3—22no—
366Dic3—22no—
367Dic3—22no—
368Dic3—22no—
369C23—32no—
370C23—32no—
371C23—32no—
372C23C23×D311yescharacteristic
373Q8—24no—
374Q8—42no—
375Q8—62no—
376Q8—124no—
377Q8—122no—
378D4—62no—
379D4—62no—
380D4—62no—
381D4—122no—
382D4—124no—
383D4—122no—
384D4—124no—
385D4—122no—
386D4—122no—
387D4—122no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—32no—
391C2×C4—32no—
392C2×C4—32no—
393C2×C4—32no—
394C2×C4—32no—
395C2×C4—41no—
396C2×C4—64no—
397C2×C4—64no—
398C2×C4—64no—
399C2×C4—124no—
400C2×C4—124no—
401C2×C4—124no—
402C2×C4C23×D314yes—
403C2×C4C23×D311yescharacteristic
404C2×C4C23×D311yescharacteristic
405C2×C4C23×D311yescharacteristic
406C2×C4C23×D311yescharacteristic
407C2×C4C23×D314yes—
408C2×C4C23×D311yescharacteristic
409C2×C4C23×D311yescharacteristic
410C2×C3—41no—
411C2×C3C2×H(5,𝔽2)11yescharacteristic
412C2×C3C2×2−1+411yescharacteristic
413C2×C3#58511yescharacteristic
414D3—42no—
415D3—42no—
416D3—42no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—62no—
421C22—62no—
422C22—62no—
423C22—62no—
424C22—62no—
425C22—62no—
426C22—62no—
427C22—62no—
428C22—62no—
429C22C24×D311yescharacteristic
430C4—21no—
431C4—21no—
432C4—24no—
433C4—21no—
434C4—21no—
435C4—24no—
436C4—62no—
437C4—62no—
438C4—62no—
439C4—62no—
440C4—62no—
441C4#100712yes—
442C4#100912yes—
443C3#354711yescharacteristic, complemented, Sylow
444C2—41no—
445C2—122no—
446C2—122no—
447C2—122no—
448C2C2×#100711yescharacteristic
449C2C2×#100911yescharacteristic
450C2#596411yescharacteristic
subgroupG/H
center, FrattiniC22C24×D3
commutator, socle, cosocleC22×C3C25
FittingC3×#533C2
hypercenter#533D3
hypocenterC3#3547
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ #533

Complements

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

NH ≅ G/Ntype
1. C3×#533C2semidirect
2. #5734C2semidirect
3. #5730C2semidirect
4. #5727C2semidirect
5. #5726C2semidirect
6. #5697C2semidirect
7. #5689C2semidirect
8. #5647C2semidirect
9. #5629C2semidirect
10. #5628C2semidirect
11. #5582C2semidirect
12. #5581C2semidirect
13. #5576C2semidirect
14. #5532C2semidirect
15. #5530C2semidirect
16. #5479C2semidirect
17. #5477C2semidirect
98. #533D3semidirect
443. C3#3547semidirect

Maximal subgroups

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

subgroupindex
C3×#5332
#57342
#57302
#57272
#57262
#56972
#56892
#56472
#56292
#56282
#55822
#55812
#55762
#55322
#55302
#54792
#54772
#35473