Finite Group Databasebeta

← #76311

Subgroups — #76311

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×#939C211yesmaximal, characteristic, complemented
2C2×#884C211yesmaximal, characteristic, complemented
3C2×#67⋊C4C211yesmaximal, characteristic, complemented
4C2×#872C211yesmaximal, characteristic, complemented
5C3×#390C211yesmaximal, characteristic, complemented
6#5223C211yesmaximal, characteristic, complemented
7#4991C211yesmaximal, characteristic, complemented
8#4976C211yesmaximal, characteristic, complemented
9#4960C211yesmaximal, characteristic, complemented
10#4959C211yesmaximal, characteristic, complemented
11#4957C211yesmaximal, characteristic, complemented
12#4957C211yesmaximal, characteristic, complemented
13#4945C211yesmaximal, characteristic, complemented
14#4942C211yesmaximal, characteristic, complemented
15#4940C211yesmaximal, characteristic, complemented
16#2414—31nomaximal, Sylow
17C22×C3×D4C2211yescharacteristic
18C22×#67C2211yescharacteristic
19C22×#67C2211yescharacteristic
20C22×#67C2211yescharacteristic
21C22×#67C2211yescharacteristic
22C23×Dic3C2211yescharacteristic
23C22×D12C2211yescharacteristic
24C22×C4×D3C2211yescharacteristic
25C2×C3×C4⋊C4C2211yescharacteristic
26C2×C3×C22⋊C4C2211yescharacteristic
27C2×C3×C22⋊C4C2211yescharacteristic
28C2×C3×C22⋊C4C2211yescharacteristic
29C2×C3×C22⋊C4C2211yescharacteristic
30C2×C3×C42C2211yescharacteristic
31C2×#217C2211yescharacteristic
32C2×#217C2211yescharacteristic
33C2×#217C2211yescharacteristic
34#939—24no—
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×(C2×D3)⋊C4C2211yescharacteristic
42C2×Dic3⋊C4C2211yescharacteristic
43C2×Dic3⋊C4C2211yescharacteristic
44C2×Dic3⋊C4C2211yescharacteristic
45C2×Dic3⋊C4C2211yescharacteristic
46C2×Dic3⋊C4C2211yescharacteristic
47C2×C4×Dic3C2211yescharacteristic
48C2×C4×Dic3C2211yescharacteristic
49#884—24no—
50#67⋊C4—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#390D311yescharacteristic, complemented
67#389—31no—
68#388—31no—
69#388—31no—
70#380—31no—
71C24×C3C2311yescharacteristic
72C24×C3C2311yescharacteristic
73C23×D3C2311yescharacteristic
74C23×D3C2311yescharacteristic
75C2×C3×D4—22no—
76C2×C3×D4—22no—
77C2×C3×D4—41no—
78C22×C3×C4C2311yescharacteristic
79C22×C3×C4C2311yescharacteristic
80C22×C3×C4C2311yescharacteristic
81C22×C3×C4C2311yescharacteristic
82C22×C3×C4C2311yescharacteristic
83C2×#67—22no—
84C2×#67—22no—
85C2×#67—22no—
86C2×#67—22no—
87C2×#67—22no—
88C2×#67—22no—
89C2×#67—22no—
90C2×#67—22no—
91C2×#67—22no—
92C2×#67—41no—
93C2×#67—41no—
94C2×#67—41no—
95C22×Dic3—22no—
96C22×Dic3—22no—
97C22×Dic3—22no—
98C22×Dic3C2311yescharacteristic
99C22×Dic3C2311yescharacteristic
100C22×Dic3C2311yescharacteristic
101C22×Dic3C2311yescharacteristic
102C22×Dic3C2311yescharacteristic
103C22×Dic3C2311yescharacteristic
104C2×D12—22no—
105C2×D12—41no—
106C2×D12—41no—
107C2×C4×D3—22no—
108C2×C4×D3—22no—
109C2×C4×D3D414yescomplemented
110C3×C4⋊C4—41no—
111C3×C22⋊C4—22no—
112C3×C22⋊C4—22no—
113C3×C22⋊C4—41no—
114C3×C22⋊C4—41no—
115C3×C42—22no—
116#217—22no—
117#217—22no—
118#217—41no—
119(C2×D3)⋊C4—22no—
120(C2×D3)⋊C4—22no—
121(C2×D3)⋊C4—22no—
122(C2×D3)⋊C4—22no—
123(C2×D3)⋊C4—22no—
124(C2×D3)⋊C4—22no—
125(C2×D3)⋊C4—41no—
126Dic3⋊C4—22no—
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×D4C2×D311yescharacteristic
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⋊C4C2×D311yescharacteristic
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#95—31no—
171#95—31no—
172C23×C3—21no—
173C23×C3—21no—
174C23×C3—21no—
175C23×C3—21no—
176C23×C3—21no—
177C23×C3—21no—
178C23×C3—21no—
179C23×C3—21no—
180C23×C3—21no—
181C23×C3—21no—
182C23×C3—21no—
183C23×C3—21no—
184C23×C3—21no—
185C23×C3#4112yes—
186C23×C3C2411yescharacteristic
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×D3—21no—
200C22×D3C2×D412yes—
201C3×D4—44no—
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×C4C2×D412yes—
216C2×C3×C4C2×D412yes—
217#67—28no—
218#67—44no—
219#67—44no—
220#67—44no—
221C2×Dic3—21no—
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×Dic3—21no—
234C2×Dic3—44no—
235C2×Dic3C2×D412yes—
236C2×Dic3C2×D412yes—
237C2×Dic3C2×D412yes—
238C2×Dic3#4112yes—
239C2×Dic3#4112yes—
240D12—44no—
241C4×D3—28no—
242C24—31no—
243C24—31no—
244C24C22×D311yescharacteristic
245C24C22×D311yescharacteristic
246C2×D4—22no—
247C2×D4—22no—
248C2×D4—41no—
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—62no—
259C2×D4—121no—
260C2×D4—121no—
261C2×D4—121no—
262C2×D4—121no—
263C2×D4—121no—
264C22×C4—31no—
265C22×C4—31no—
266C22×C4—31no—
267C22×C4—34no—
268C22×C4—31no—
269C22×C4—31no—
270C22×C4—31no—
271C22×C4—62no—
272C22×C4—62no—
273C22×C4—62no—
274C22×C4—62no—
275C22×C4—62no—
276C22×C4C22×D311yescharacteristic
277C22×C4C22×D311yescharacteristic
278C22×C4C22×D311yescharacteristic
279C22×C4C22×D311yescharacteristic
280C22×C4C22×D311yescharacteristic
281C4⋊C4—34no—
282C4⋊C4—41no—
283C4⋊C4—62no—
284C4⋊C4—62no—
285C4⋊C4—62no—
286C4⋊C4—121no—
287C22⋊C4—22no—
288C22⋊C4—22no—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C22⋊C4—62no—
292C22⋊C4—62no—
293C22⋊C4—62no—
294C22⋊C4—62no—
295C22⋊C4—62no—
296C22⋊C4—62no—
297C22⋊C4—62no—
298C22⋊C4—62no—
299C22⋊C4—121no—
300C22⋊C4—121no—
301C42—22no—
302C42—62no—
303C42—62no—
304C22×C3—22no—
305C22×C3—22no—
306C22×C3—22no—
307C22×C3—41no—
308C22×C3—41no—
309C22×C3—41no—
310C22×C3—41no—
311C22×C3—41no—
312C22×C3—41no—
313C22×C3—41no—
314C22×C3—41no—
315C22×C3—41no—
316C22×C3—41no—
317C22×C3—41no—
318C22×C3C22×D411yescharacteristic
319C22×C3C22×D411yescharacteristic
320C22×C3C2×#4111yescharacteristic
321C22×C3C2×#4111yescharacteristic
322C22×C3C2×#4111yescharacteristic
323C22×C3H(5,𝔽2)11yescharacteristic
324C22×C3H(5,𝔽2)11yescharacteristic
325C2×D3—22no—
326C2×D3—22no—
327C2×D3—22no—
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—41no—
342C3×C4—41no—
343C3×C4—41no—
344Dic3—22no—
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—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—32no—
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#23512yes—
378C23C23×D311yescharacteristic
379D4—44no—
380D4—68no—
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—32no—
399C2×C4—32no—
400C2×C4—32no—
401C2×C4—32no—
402C2×C4—32no—
403C2×C4—68no—
404C2×C4—61no—
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—61no—
417C2×C4—124no—
418C2×C4D3×D412yes—
419C2×C4D3×D412yes—
420C2×C3—42no—
421C2×C3—81no—
422C2×C3C2×#12111yescharacteristic
423C2×C3#52511yescharacteristic
424C2×C3#53511yescharacteristic
425C2×C3#54611yescharacteristic
426C2×C3#55011yescharacteristic
427C2×C3#55311yescharacteristic
428C2×C3#55511yescharacteristic
429D3—42no—
430D3—81no—
431C22—22no—
432C22—22no—
433C22—22no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—62no—
446C22—62no—
447C22—62no—
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
462C22#100411yescharacteristic
463C22#100411yescharacteristic
464C22D3×#4111yescharacteristic
465C22D3×#4111yescharacteristic
466C4—22no—
467C4—22no—
468C4—34no—
469C4—41no—
470C4—41no—
471C4—41no—
472C4—62no—
473C4—62no—
474C4—121no—
475C4—121no—
476C4—121no—
477C3#241411yescharacteristic, complemented, Sylow
478C2—42no—
479C2—81no—
480C2—122no—
481C2—241no—
482C2#549011yescharacteristic
483C2#554011yescharacteristic
484C2#554711yescharacteristic
485C2#559911yescharacteristic
486C2D3×#12111yescharacteristic
487C2#567011yescharacteristic
488C2#571511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#390C2
hypercenter#390D3
hypocenterC3#2414
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#939C2semidirect
2. C2×#884C2semidirect
3. C2×#67⋊C4C2semidirect
4. C2×#872C2semidirect
5. C3×#390C2semidirect
6. #5223C2semidirect
7. #4991C2semidirect
8. #4976C2semidirect
9. #4960C2semidirect
10. #4959C2semidirect
11. #4957C2semidirect
12. #4957C2semidirect
13. #4945C2semidirect
14. #4942C2semidirect
15. #4940C2semidirect
66. #390D3semidirect
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×#9392
C2×#8842
C2×#67⋊C42
C2×#8722
C3×#3902
#52232
#49912
#49762
#49602
#49592
#49572
#49452
#49422
#49402
#24143