Finite Group Databasebeta

← #75495

Subgroups — #75495

Order 384.

704 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#893C211yesmaximal, characteristic, complemented
2C2×#884C211yesmaximal, characteristic, complemented
3C2×#884C211yesmaximal, characteristic, complemented
4C2×#872C211yesmaximal, characteristic, complemented
5C3×#388C211yesmaximal, characteristic, complemented
6#4990C211yesmaximal, characteristic, complemented
7#4961C211yesmaximal, characteristic, complemented
8#4960C211yesmaximal, characteristic, complemented
9#4957C211yesmaximal, characteristic, complemented
10#4957C211yesmaximal, characteristic, complemented
11#4939C211yesmaximal, characteristic, complemented
12#4672C211yesmaximal, characteristic, complemented
13#4671C211yesmaximal, characteristic, complemented
14#4667C211yesmaximal, characteristic, complemented
15#4647C211yesmaximal, characteristic, complemented
16#2414—31nomaximal, Sylow
17C22×#67C2211yescharacteristic
18C22×#67C2211yescharacteristic
19C22×#67C2211yescharacteristic
20C22×D12C2211yescharacteristic
21C22×D12C2211yescharacteristic
22C22×D12C2211yescharacteristic
23C22×C4×D3C2211yescharacteristic
24C22×C4×D3C2211yescharacteristic
25C2×C3×C4⋊C4C2211yescharacteristic
26C2×C3×C22⋊C4C2211yescharacteristic
27C2×C3×C22⋊C4C2211yescharacteristic
28C2×C3×C22⋊C4C2211yescharacteristic
29C2×C3×C42C2211yescharacteristic
30C2×#217C2211yescharacteristic
31C2×(C2×D3)⋊C4C2211yescharacteristic
32C2×(C2×D3)⋊C4C2211yescharacteristic
33C2×(C2×D3)⋊C4C2211yescharacteristic
34C2×(C2×D3)⋊C4C2211yescharacteristic
35C2×(C2×D3)⋊C4C2211yescharacteristic
36C2×(C2×D3)⋊C4C2211yescharacteristic
37C2×(C2×D3)⋊C4C2211yescharacteristic
38C2×(C2×D3)⋊C4C2211yescharacteristic
39C2×(C2×D3)⋊C4C2211yescharacteristic
40C2×(C2×D3)⋊C4C2211yescharacteristic
41C2×C4⋊Dic3C2211yescharacteristic
42C2×Dic3⋊C4C2211yescharacteristic
43C2×Dic3⋊C4C2211yescharacteristic
44C2×Dic3⋊C4C2211yescharacteristic
45C2×Dic3⋊C4C2211yescharacteristic
46C2×C4×Dic3C2211yescharacteristic
47C2×C4×Dic3C2211yescharacteristic
48#893—24no—
49#884—24no—
50#884—24no—
51#872—24no—
52C3×#95C2211yescharacteristic
53C3×#95C2211yescharacteristic
54C3⋊#95C2211yescharacteristic
55C3⋊#95C2211yescharacteristic
56C2×#121—31no—
57C2×#121—31no—
58C2×C4×D4—31no—
59C2×#117—31no—
60#394—31no—
61#394—31no—
62#392—31no—
63#392—31no—
64#390—31no—
65#390—31no—
66#390—31no—
67#389—31no—
68#388—31no—
69#388D311yescharacteristic, complemented
70#380—31no—
71C24×C3C2311yescharacteristic
72C23×D3C2311yescharacteristic
73C23×D3C2311yescharacteristic
74C23×D3C2311yescharacteristic
75C22×C3×C4C2311yescharacteristic
76C22×C3×C4C2311yescharacteristic
77C22×C3×C4C2311yescharacteristic
78C22×C3×C4C2311yescharacteristic
79C22×C3×C4C2311yescharacteristic
80C22×C3×C4C2311yescharacteristic
81C2×#67—22no—
82C2×#67—22no—
83C2×#67—22no—
84C2×#67—22no—
85C2×#67—22no—
86C2×#67—22no—
87C2×#67—41no—
88C2×#67—41no—
89C2×#67—41no—
90C22×Dic3C2311yescharacteristic
91C22×Dic3C2311yescharacteristic
92C22×Dic3C2311yescharacteristic
93C22×Dic3C2311yescharacteristic
94C22×Dic3C2311yescharacteristic
95C2×D12—22no—
96C2×D12—22no—
97C2×D12—22no—
98C2×D12—22no—
99C2×D12—22no—
100C2×D12—22no—
101C2×D12—41no—
102C2×D12—41no—
103C2×D12—41no—
104C2×C4×D3—22no—
105C2×C4×D3—22no—
106C2×C4×D3—22no—
107C2×C4×D3—22no—
108C2×C4×D3—22no—
109C2×C4×D3D414yescomplemented
110C3×C4⋊C4—22no—
111C3×C22⋊C4—22no—
112C3×C22⋊C4—22no—
113C3×C22⋊C4—22no—
114C3×C42—22no—
115#217—41no—
116(C2×D3)⋊C4—22no—
117(C2×D3)⋊C4—22no—
118(C2×D3)⋊C4—22no—
119(C2×D3)⋊C4—22no—
120(C2×D3)⋊C4—22no—
121(C2×D3)⋊C4—22no—
122(C2×D3)⋊C4—22no—
123(C2×D3)⋊C4—41no—
124(C2×D3)⋊C4—41no—
125(C2×D3)⋊C4—41no—
126C4⋊Dic3—41no—
127Dic3⋊C4—22no—
128Dic3⋊C4—22no—
129Dic3⋊C4—41no—
130Dic3⋊C4D414yescomplemented
131C4×Dic3—22no—
132C4×Dic3—22no—
133C22×D4—31no—
134C22×D4—31no—
135C22×D4—31no—
136C22×D4—31no—
137C22×D4—31no—
138C22×D4—31no—
139C23×C4—31no—
140C23×C4—31no—
141#121—64no—
142#121—64no—
143C4×D4—64no—
144#117—64no—
145C2×C4⋊C4—31no—
146C2×C4⋊C4—31no—
147C2×C4⋊C4—31no—
148C2×C4⋊C4—31no—
149C2×C4⋊C4—31no—
150C2×C4⋊C4C2×D311yescharacteristic
151C2×C22⋊C4—31no—
152C2×C22⋊C4—31no—
153C2×C22⋊C4—31no—
154C2×C22⋊C4—31no—
155C2×C22⋊C4—31no—
156C2×C22⋊C4—31no—
157C2×C22⋊C4—31no—
158C2×C22⋊C4—31no—
159C2×C22⋊C4—31no—
160C2×C22⋊C4—31no—
161C2×C22⋊C4—31no—
162C2×C22⋊C4C2×D311yescharacteristic
163C2×C22⋊C4C2×D311yescharacteristic
164C2×C22⋊C4C2×D311yescharacteristic
165C2×C42—31no—
166C2×C42—31no—
167C2×C42C2×D311yescharacteristic
168#95—31no—
169#95—31no—
170#95C2×D311yescharacteristic
171#95C2×D311yescharacteristic
172C23×C3—21no—
173C23×C3—21no—
174C23×C3—21no—
175C23×C3—21no—
176C23×C3—21no—
177C23×C3—21no—
178C23×C3—21no—
179C23×C3C2411yescharacteristic
180C22×D3—21no—
181C22×D3—21no—
182C22×D3—21no—
183C22×D3—21no—
184C22×D3—21no—
185C22×D3—21no—
186C22×D3—21no—
187C22×D3—21no—
188C22×D3—21no—
189C22×D3—21no—
190C22×D3—21no—
191C22×D3—21no—
192C22×D3—21no—
193C22×D3—21no—
194C22×D3—21no—
195C22×D3—21no—
196C22×D3—21no—
197C22×D3—21no—
198C22×D3—21no—
199C22×D3C2×D412yes—
200C22×D3#4112yes—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4C2×D412yes—
217C2×C3×C4C2×D412yes—
218C2×C3×C4#4112yes—
219#67—44no—
220#67—44no—
221#67—44no—
222C2×Dic3—21no—
223C2×Dic3—21no—
224C2×Dic3—21no—
225C2×Dic3—21no—
226C2×Dic3—21no—
227C2×Dic3—21no—
228C2×Dic3—21no—
229C2×Dic3—21no—
230C2×Dic3—21no—
231C2×Dic3—21no—
232C2×Dic3—21no—
233C2×Dic3C2×D412yes—
234C2×Dic3C2×D412yes—
235C2×Dic3C2×D412yes—
236C2×Dic3#4112yes—
237D12—28no—
238D12—44no—
239D12—44no—
240C4×D3—28no—
241C4×D3—44no—
242C24—31no—
243C24—31no—
244C24—31no—
245C24C22×D311yescharacteristic
246C2×D4—62no—
247C2×D4—62no—
248C2×D4—62no—
249C2×D4—62no—
250C2×D4—62no—
251C2×D4—62no—
252C2×D4—62no—
253C2×D4—62no—
254C2×D4—62no—
255C2×D4—62no—
256C2×D4—62no—
257C2×D4—62no—
258C2×D4—121no—
259C2×D4—121no—
260C2×D4—121no—
261C2×D4—121no—
262C2×D4—121no—
263C2×D4—121no—
264C22×C4—31no—
265C22×C4—31no—
266C22×C4—34no—
267C22×C4—31no—
268C22×C4—31no—
269C22×C4—31no—
270C22×C4—62no—
271C22×C4—62no—
272C22×C4—62no—
273C22×C4—62no—
274C22×C4—62no—
275C22×C4C22×D311yescharacteristic
276C22×C4C22×D311yescharacteristic
277C22×C4C22×D311yescharacteristic
278C22×C4C22×D311yescharacteristic
279C22×C4C22×D311yescharacteristic
280C22×C4C22×D311yescharacteristic
281C4⋊C4—22no—
282C4⋊C4—34no—
283C4⋊C4—62no—
284C4⋊C4—62no—
285C4⋊C4—121no—
286C4⋊C4—121no—
287C22⋊C4—22no—
288C22⋊C4—22no—
289C22⋊C4—22no—
290C22⋊C4—62no—
291C22⋊C4—62no—
292C22⋊C4—62no—
293C22⋊C4—62no—
294C22⋊C4—62no—
295C22⋊C4—62no—
296C22⋊C4—62no—
297C22⋊C4—121no—
298C22⋊C4—121no—
299C22⋊C4—121no—
300C22⋊C4—121no—
301C42—22no—
302C42—62no—
303C42—62no—
304C22×C3—41no—
305C22×C3—41no—
306C22×C3—41no—
307C22×C3—41no—
308C22×C3—41no—
309C22×C3—41no—
310C22×C3—41no—
311C22×C3C22×D411yescharacteristic
312C22×C3C22×D411yescharacteristic
313C22×C3C2×#4111yescharacteristic
314C22×C3C2×#4111yescharacteristic
315C22×C3C2×#4111yescharacteristic
316C22×C3H(5,𝔽2)11yescharacteristic
317C22×C3H(5,𝔽2)11yescharacteristic
318C2×D3—22no—
319C2×D3—22no—
320C2×D3—22no—
321C2×D3—22no—
322C2×D3—22no—
323C2×D3—22no—
324C2×D3—41no—
325C2×D3—41no—
326C2×D3—41no—
327C2×D3—41no—
328C2×D3—41no—
329C2×D3—41no—
330C2×D3—41no—
331C2×D3—41no—
332C2×D3—41no—
333C2×D3—41no—
334C2×D3—41no—
335C2×D3—41no—
336C2×D3—41no—
337C2×D3—41no—
338C2×D3—41no—
339C3×C4—22no—
340C3×C4—22no—
341C3×C4—22no—
342C3×C4—41no—
343C3×C4—41no—
344C3×C4—41no—
345Dic3—22no—
346Dic3—41no—
347Dic3—41no—
348Dic3—41no—
349Dic3#12114yes—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—32no—
358C23—32no—
359C23—61no—
360C23—61no—
361C23—61no—
362C23—61no—
363C23—61no—
364C23—61no—
365C23—61no—
366C23—61no—
367C23—61no—
368C23—61no—
369C23—61no—
370C23—61no—
371C23—61no—
372C23—61no—
373C23—61no—
374C23—61no—
375C23—61no—
376C23—61no—
377C23—61no—
378C23C23×D311yescharacteristic
379D4—68no—
380D4—124no—
381D4—124no—
382D4—124no—
383D4—124no—
384D4—124no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—32no—
401C2×C4—32no—
402C2×C4—32no—
403C2×C4—32no—
404C2×C4—68no—
405C2×C4—61no—
406C2×C4—61no—
407C2×C4—61no—
408C2×C4—61no—
409C2×C4—61no—
410C2×C4—61no—
411C2×C4—61no—
412C2×C4—61no—
413C2×C4—61no—
414C2×C4—61no—
415C2×C4—61no—
416C2×C4—124no—
417C2×C4#23512yes—
418C2×C4D3×D412yes—
419C2×C4D3×D412yes—
420C2×C3—81no—
421C2×C3C2×#12111yescharacteristic
422C2×C3#52511yescharacteristic
423C2×C3#53511yescharacteristic
424C2×C3#54611yescharacteristic
425C2×C3#55011yescharacteristic
426C2×C3#55311yescharacteristic
427C2×C3#55511yescharacteristic
428D3—42no—
429D3—42no—
430D3—81no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—62no—
439C22—62no—
440C22—62no—
441C22—62no—
442C22—62no—
443C22—62no—
444C22—121no—
445C22—121no—
446C22—121no—
447C22—121no—
448C22—121no—
449C22—121no—
450C22—121no—
451C22—121no—
452C22—121no—
453C22—121no—
454C22—121no—
455C22—121no—
456C22—121no—
457C22—121no—
458C22—121no—
459C22C2×#23511yescharacteristic
460C22C2×D3×D411yescharacteristic
461C22C2×D3×D411yescharacteristic
462C22D3×#4111yescharacteristic
463C22D3×#4111yescharacteristic
464C22#100911yescharacteristic
465C22#100911yescharacteristic
466C4—22no—
467C4—22no—
468C4—22no—
469C4—34no—
470C4—41no—
471C4—41no—
472C4—41no—
473C4—62no—
474C4—121no—
475C4—121no—
476C4—121no—
477C3#241411yescharacteristic, complemented, Sylow
478C2—81no—
479C2—122no—
480C2—122no—
481C2—241no—
482C2#553211yescharacteristic
483C2#554711yescharacteristic
484C2#555311yescharacteristic
485C2D3×#12111yescharacteristic
486C2#565411yescharacteristic
487C2#567411yescharacteristic
488C2#570911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#388C2
hypercenter#388D3
hypocenterC3#2414
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#893C2semidirect
2. C2×#884C2semidirect
3. C2×#884C2semidirect
4. C2×#872C2semidirect
5. C3×#388C2semidirect
6. #4990C2semidirect
7. #4961C2semidirect
8. #4960C2semidirect
9. #4957C2semidirect
10. #4957C2semidirect
11. #4939C2semidirect
12. #4672C2semidirect
13. #4671C2semidirect
14. #4667C2semidirect
15. #4647C2semidirect
69. #388D3semidirect
109. C2×C4×D3D4semidirect
130. Dic3⋊C4D4semidirect
477. C3#2414semidirect

Maximal subgroups

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

subgroupindex
C2×#8932
C2×#8842
C2×#8722
C3×#3882
#49902
#49612
#49602
#49572
#49392
#46722
#46712
#46672
#46472
#24143