Finite Group Databasebeta

← #76447

Subgroups — #76447

Order 384.

710 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#939C211yesmaximal, characteristic, complemented
2C2×#894C211yesmaximal, characteristic, complemented
3C2×#884C211yesmaximal, characteristic, complemented
4C2×#67⋊C4C211yesmaximal, characteristic, complemented
5C3×#390C211yesmaximal, characteristic, complemented
6#5223C211yesmaximal, characteristic, complemented
7#4983C211yesmaximal, characteristic, complemented
8#4960C211yesmaximal, characteristic, complemented
9#4959C211yesmaximal, characteristic, complemented
10#4956C211yesmaximal, characteristic, complemented
11#4956C211yesmaximal, characteristic, complemented
12#4946C211yesmaximal, characteristic, complemented
13#4944C211yesmaximal, characteristic, complemented
14#4940C211yesmaximal, characteristic, complemented
15C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
16#2464—31nomaximal, Sylow
17C22×C3×D4C2211yescharacteristic
18C22×#67C2211yescharacteristic
19C22×#67C2211yescharacteristic
20C22×#67C2211yescharacteristic
21C22×#67C2211yescharacteristic
22C23×Dic3C2211yescharacteristic
23C22×D12C2211yescharacteristic
24C22×C4×D3C2211yescharacteristic
25C22×C4×D3C2211yescharacteristic
26C2×C3×C4⋊C4C2211yescharacteristic
27C2×C3×C22⋊C4C2211yescharacteristic
28C2×C3×C22⋊C4C2211yescharacteristic
29C2×C3×C22⋊C4C2211yescharacteristic
30C2×C3×C22⋊C4C2211yescharacteristic
31C2×C3×C42C2211yescharacteristic
32C2×#217C2211yescharacteristic
33C2×#217C2211yescharacteristic
34C2×#217C2211yescharacteristic
35#939—24no—
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×C4×Dic3C2211yescharacteristic
47#894—24no—
48#884—24no—
49#67⋊C4—24no—
50C3⋊#95C2211yescharacteristic
51C3⋊#95C2211yescharacteristic
52C3⋊#95C2211yescharacteristic
53C3⋊#95C2211yescharacteristic
54C3⋊#95C2211yescharacteristic
55C3⋊#95C2211yescharacteristic
56C2×#123—31no—
57C2×#121—31no—
58C2×#121—31no—
59C2×C4×D4—31no—
60#398—31no—
61#394—31no—
62#392—31no—
63#392—31no—
64#390D311yescharacteristic, complemented
65#388—31no—
66#388—31no—
67#386—31no—
68#386—31no—
69#385—31no—
70C4×C22⋊C4—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—41no—
98C22×Dic3C2311yescharacteristic
99C22×Dic3C2311yescharacteristic
100C22×Dic3C2311yescharacteristic
101C22×Dic3C2311yescharacteristic
102C22×Dic3C2311yescharacteristic
103C22×Dic3C2311yescharacteristic
104C2×D12—22no—
105C2×D12—22no—
106C2×D12—41no—
107C2×C4×D3—22no—
108C2×C4×D3—22no—
109C2×C4×D3—22no—
110C2×C4×D3—22no—
111C2×C4×D3—41no—
112C2×C4×D3—41no—
113C3×C4⋊C4—22no—
114C3×C22⋊C4—22no—
115C3×C22⋊C4—22no—
116C3×C22⋊C4—41no—
117C3×C22⋊C4—41no—
118C3×C42—41no—
119#217—22no—
120#217—22no—
121#217—22no—
122(C2×D3)⋊C4—22no—
123(C2×D3)⋊C4—22no—
124(C2×D3)⋊C4—22no—
125(C2×D3)⋊C4—41no—
126(C2×D3)⋊C4D414yescomplemented
127(C2×D3)⋊C4D414yescomplemented
128Dic3⋊C4—22no—
129Dic3⋊C4—22no—
130Dic3⋊C4—22no—
131Dic3⋊C4—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—
141C23×C4—31no—
142#123—64no—
143#121—64no—
144#121—64no—
145C4×D4—64no—
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⋊C4C2×D311yescharacteristic
161C2×C22⋊C4C2×D311yescharacteristic
162C2×C22⋊C4C2×D311yescharacteristic
163C2×C22⋊C4C2×D311yescharacteristic
164C2×C42—31no—
165C2×C42C2×D311yescharacteristic
166#95—31no—
167#95—31no—
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×D3C2×D412yes—
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—21no—
235C2×Dic3—44no—
236C2×Dic3C2×D412yes—
237C2×Dic3C2×D412yes—
238C2×Dic3#4112yes—
239C2×Dic3#4112yes—
240D12—44no—
241C4×D3—44no—
242C4×D3—44no—
243C24—31no—
244C24—31no—
245C24C22×D311yescharacteristic
246C24C22×D311yescharacteristic
247C2×D4—22no—
248C2×D4—22no—
249C2×D4—41no—
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—62no—
260C2×D4—62no—
261C2×D4—121no—
262C2×D4—121no—
263C2×D4—121no—
264C2×D4—121no—
265C22×C4—31no—
266C22×C4—31no—
267C22×C4—31no—
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×C4—62no—
277C22×C4—121no—
278C22×C4—121no—
279C22×C4—121no—
280C22×C4C22×D311yescharacteristic
281C22×C4C22×D311yescharacteristic
282C22×C4C22×D311yescharacteristic
283C22×C4C22×D311yescharacteristic
284C22×C4C22×D311yescharacteristic
285C4⋊C4—22no—
286C4⋊C4—62no—
287C4⋊C4—62no—
288C4⋊C4—62no—
289C4⋊C4—62no—
290C22⋊C4—22no—
291C22⋊C4—22no—
292C22⋊C4—34no—
293C22⋊C4—34no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—62no—
297C22⋊C4—62no—
298C22⋊C4—62no—
299C22⋊C4—62no—
300C22⋊C4—62no—
301C22⋊C4—62no—
302C22⋊C4—121no—
303C42—41no—
304C42—62no—
305C22×C3—22no—
306C22×C3—22no—
307C22×C3—22no—
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×C3—41no—
319C22×C3C22×D411yescharacteristic
320C22×C3C22×D411yescharacteristic
321C22×C3C2×#4111yescharacteristic
322C22×C3C2×#4111yescharacteristic
323C22×C3C2×#4111yescharacteristic
324C22×C3H(5,𝔽2)11yescharacteristic
325C22×C3H(5,𝔽2)11yescharacteristic
326C2×D3—22no—
327C2×D3—22no—
328C2×D3—22no—
329C2×D3—22no—
330C2×D3—22no—
331C2×D3—22no—
332C2×D3—41no—
333C2×D3—41no—
334C2×D3—41no—
335C2×D3—41no—
336C2×D3—41no—
337C2×D3—41no—
338C2×D3—41no—
339C2×D3—41no—
340C3×C4—22no—
341C3×C4—22no—
342C3×C4—41no—
343C3×C4—41no—
344C3×C4—41no—
345Dic3—22no—
346Dic3—22no—
347Dic3—22no—
348Dic3—22no—
349Dic3—41no—
350Dic3—41no—
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—21no—
364C23—32no—
365C23—32no—
366C23—61no—
367C23—61no—
368C23—61no—
369C23—61no—
370C23—61no—
371C23—61no—
372C23—61no—
373C23—61no—
374C23—61no—
375C23—61no—
376C23—61no—
377C23—61no—
378C23#23512yes—
379C23C23×D311yescharacteristic
380D4—44no—
381D4—68no—
382D4—124no—
383D4—124no—
384D4—124no—
385D4—124no—
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—32no—
400C2×C4—32no—
401C2×C4—32no—
402C2×C4—32no—
403C2×C4—61no—
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×C4—124no—
419C2×C4—124no—
420C2×C4D3×D412yes—
421C2×C4D3×D412yes—
422C2×C3—42no—
423C2×C3—81no—
424C2×C3#52511yescharacteristic
425C2×C3#53211yescharacteristic
426C2×C3#54011yescharacteristic
427C2×C3D4211yescharacteristic
428C2×C3#54611yescharacteristic
429C2×C3#54611yescharacteristic
430C2×C3#55311yescharacteristic
431D3—42no—
432D3—42no—
433C22—22no—
434C22—22no—
435C22—22no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—62no—
448C22—62no—
449C22—62no—
450C22—62no—
451C22—62no—
452C22—62no—
453C22—121no—
454C22—121no—
455C22—121no—
456C22—121no—
457C22—121no—
458C22—121no—
459C22—121no—
460C22—121no—
461C22C2×#23511yescharacteristic
462C22C2×D3×D411yescharacteristic
463C22C2×D3×D411yescharacteristic
464C22#100411yescharacteristic
465C22#100411yescharacteristic
466C22D3×#4111yescharacteristic
467C22D3×#4111yescharacteristic
468C4—22no—
469C4—22no—
470C4—41no—
471C4—41no—
472C4—41no—
473C4—62no—
474C4—62no—
475C4—62no—
476C4—62no—
477C4—121no—
478C4—121no—
479C3#246411yescharacteristic, complemented, Sylow
480C2—42no—
481C2—81no—
482C2—122no—
483C2—122no—
484C2#549011yescharacteristic
485C2#554011yescharacteristic
486C2#554711yescharacteristic
487C2#561011yescharacteristic
488C2#561511yescharacteristic
489C2#566811yescharacteristic
490C2#571711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#390C2
hypercenter#390D3
hypocenterC3#2464
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×#894C2semidirect
3. C2×#884C2semidirect
4. C2×#67⋊C4C2semidirect
5. C3×#390C2semidirect
6. #5223C2semidirect
7. #4983C2semidirect
8. #4960C2semidirect
9. #4959C2semidirect
10. #4956C2semidirect
11. #4956C2semidirect
12. #4946C2semidirect
13. #4944C2semidirect
14. #4940C2semidirect
15. C4×(C2×D3)⋊C4C2semidirect
64. #390D3semidirect
126. (C2×D3)⋊C4D4semidirect
127. (C2×D3)⋊C4D4semidirect
479. C3#2464semidirect

Maximal subgroups

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

subgroupindex
C2×#9392
C2×#8942
C2×#8842
C2×#67⋊C42
C3×#3902
#52232
#49832
#49602
#49592
#49562
#49462
#49442
#49402
C4×(C2×D3)⋊C42
#24643