Finite Group Databasebeta

← #76670

Subgroups — #76670

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×#939C211yesmaximal, characteristic, complemented
3C2×D4×Dic3C211yesmaximal, characteristic, complemented
4C2×#877C211yesmaximal, characteristic, complemented
5C3×#392C211yesmaximal, characteristic, complemented
6#5223C211yesmaximal, characteristic, complemented
7#5222C211yesmaximal, characteristic, complemented
8#5221C211yesmaximal, characteristic, complemented
9#4961C211yesmaximal, characteristic, complemented
10#4957C211yesmaximal, characteristic, complemented
11#4957C211yesmaximal, characteristic, complemented
12#4951C211yesmaximal, characteristic, complemented
13#4942C211yesmaximal, characteristic, complemented
14#4670C211yesmaximal, characteristic, complemented
15#4647C211yesmaximal, characteristic, complemented
16#2414—31nomaximal, Sylow
17C22×C3×D4C2211yescharacteristic
18C22×C3×D4C2211yescharacteristic
19C22×C3×D4C2211yescharacteristic
20C22×#67C2211yescharacteristic
21C22×#67C2211yescharacteristic
22C22×#67C2211yescharacteristic
23C23×Dic3C2211yescharacteristic
24C23×Dic3C2211yescharacteristic
25C2×C3×C22⋊C4C2211yescharacteristic
26C2×C3×C22⋊C4C2211yescharacteristic
27C2×C3×C22⋊C4C2211yescharacteristic
28C2×#217C2211yescharacteristic
29C2×#217C2211yescharacteristic
30C2×#217C2211yescharacteristic
31C2×#217C2211yescharacteristic
32C2×#217C2211yescharacteristic
33C2×#217C2211yescharacteristic
34C2×#217C2211yescharacteristic
35#939—24no—
36#939—24no—
37D4×Dic3—24no—
38C2×(C2×D3)⋊C4C2211yescharacteristic
39C2×(C2×D3)⋊C4C2211yescharacteristic
40C2×(C2×D3)⋊C4C2211yescharacteristic
41C2×(C2×D3)⋊C4C2211yescharacteristic
42C2×C4⋊Dic3C2211yescharacteristic
43C2×C4⋊Dic3C2211yescharacteristic
44C2×Dic3⋊C4C2211yescharacteristic
45C2×Dic3⋊C4C2211yescharacteristic
46C2×Dic3⋊C4C2211yescharacteristic
47C2×Dic3⋊C4C2211yescharacteristic
48C2×C4×Dic3C2211yescharacteristic
49C2×C4×Dic3C2211yescharacteristic
50C2×C4×Dic3C2211yescharacteristic
51#877—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#392D311yescharacteristic, complemented
64#390—31no—
65#390—31no—
66#390—31no—
67#389—31no—
68#388—31no—
69#388—31no—
70#380—31no—
71C24×C3C2311yescharacteristic
72C24×C3C2311yescharacteristic
73C24×C3C2311yescharacteristic
74C23×D3C2311yescharacteristic
75C2×C3×D4—22no—
76C2×C3×D4—22no—
77C2×C3×D4—22no—
78C2×C3×D4—22no—
79C2×C3×D4—22no—
80C2×C3×D4—22no—
81C2×C3×D4—41no—
82C2×C3×D4—41no—
83C2×C3×D4—41no—
84C22×C3×C4C2311yescharacteristic
85C22×C3×C4C2311yescharacteristic
86C22×C3×C4C2311yescharacteristic
87C22×C3×C4C2311yescharacteristic
88C2×#67—22no—
89C2×#67—22no—
90C2×#67—22no—
91C2×#67—22no—
92C2×#67—22no—
93C2×#67—22no—
94C2×#67—41no—
95C2×#67—41no—
96C2×#67—41no—
97C22×Dic3—22no—
98C22×Dic3—22no—
99C22×Dic3—22no—
100C22×Dic3—22no—
101C22×Dic3—22no—
102C22×Dic3D414yescomplemented
103C22×Dic3C2311yescharacteristic
104C22×Dic3C2311yescharacteristic
105C22×Dic3C2311yescharacteristic
106C22×Dic3C2311yescharacteristic
107C22×Dic3C2311yescharacteristic
108C22×Dic3C2311yescharacteristic
109C22×Dic3C2311yescharacteristic
110C3×C22⋊C4—22no—
111C3×C22⋊C4—22no—
112C3×C22⋊C4—41no—
113#217—22no—
114#217—22no—
115#217—22no—
116#217—22no—
117#217—22no—
118#217—41no—
119#217—41no—
120(C2×D3)⋊C4—22no—
121(C2×D3)⋊C4—22no—
122(C2×D3)⋊C4—22no—
123(C2×D3)⋊C4—41no—
124C4⋊Dic3—22no—
125C4⋊Dic3—41no—
126Dic3⋊C4—22no—
127Dic3⋊C4—22no—
128Dic3⋊C4—41no—
129Dic3⋊C4D414yescomplemented
130C4×Dic3—22no—
131C4×Dic3—22no—
132C4×Dic3—22no—
133C22×D4—31no—
134C22×D4—31no—
135C22×D4—31no—
136C22×D4C2×D311yescharacteristic
137C22×D4C2×D311yescharacteristic
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⋊C4—31no—
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×C42—31no—
168#95—31no—
169#95—31no—
170#95—31no—
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×C3—21no—
180C23×C3—21no—
181C23×C3—21no—
182C23×C3—21no—
183C23×C3—21no—
184C23×C3—21no—
185C23×C3—21no—
186C23×C3—21no—
187C23×C3—21no—
188C23×C3—21no—
189C23×C3—21no—
190C23×C3—21no—
191C23×C3C2×D412yes—
192C23×C3#4112yes—
193C23×C3C2411yescharacteristic
194C22×D3—21no—
195C22×D3—21no—
196C22×D3—21no—
197C22×D3—21no—
198C22×D3—21no—
199C22×D3—21no—
200C22×D3—21no—
201C3×D4—28no—
202C3×D4—44no—
203C3×D4—44no—
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×C4C2×D412yes—
215C2×C3×C4#4112yes—
216#67—44no—
217#67—44no—
218#67—44no—
219C2×Dic3—21no—
220C2×Dic3—21no—
221C2×Dic3—21no—
222C2×Dic3—21no—
223C2×Dic3—28no—
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—21no—
236C2×Dic3—44no—
237C2×Dic3C2×D412yes—
238C2×Dic3C2×D412yes—
239C2×Dic3C2×D412yes—
240C2×Dic3C2×D412yes—
241C2×Dic3#4112yes—
242C24—31no—
243C24C22×D311yescharacteristic
244C24C22×D311yescharacteristic
245C24C22×D311yescharacteristic
246C2×D4—22no—
247C2×D4—22no—
248C2×D4—22no—
249C2×D4—22no—
250C2×D4—22no—
251C2×D4—22no—
252C2×D4—41no—
253C2×D4—41no—
254C2×D4—41no—
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—
264C22×C4—31no—
265C22×C4—34no—
266C22×C4—31no—
267C22×C4—31no—
268C22×C4—31no—
269C22×C4—31no—
270C22×C4—31no—
271C22×C4—31no—
272C22×C4—62no—
273C22×C4—62no—
274C22×C4—62no—
275C22×C4—62no—
276C22×C4—62no—
277C22×C4C22×D311yescharacteristic
278C22×C4C22×D311yescharacteristic
279C22×C4C22×D311yescharacteristic
280C22×C4C22×D311yescharacteristic
281C4⋊C4—34no—
282C4⋊C4—62no—
283C4⋊C4—62no—
284C4⋊C4—62no—
285C4⋊C4—121no—
286C4⋊C4—121no—
287C22⋊C4—22no—
288C22⋊C4—22no—
289C22⋊C4—41no—
290C22⋊C4—62no—
291C22⋊C4—62no—
292C22⋊C4—62no—
293C22⋊C4—62no—
294C22⋊C4—62no—
295C22⋊C4—62no—
296C22⋊C4—62no—
297C22⋊C4—62no—
298C22⋊C4—121no—
299C22⋊C4—121no—
300C22⋊C4—121no—
301C42—62no—
302C42—62no—
303C42—62no—
304C22×C3—22no—
305C22×C3—22no—
306C22×C3—22no—
307C22×C3—22no—
308C22×C3—22no—
309C22×C3—22no—
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×C3—41no—
320C22×C3—41no—
321C22×C3—41no—
322C22×C3—41no—
323C22×C3—41no—
324C22×C3—41no—
325C22×C3C22×D411yescharacteristic
326C22×C3C22×D411yescharacteristic
327C22×C3C2×#4111yescharacteristic
328C22×C3C2×#4111yescharacteristic
329C22×C3C2×#4111yescharacteristic
330C22×C3H(5,𝔽2)11yescharacteristic
331C22×C3H(5,𝔽2)11yescharacteristic
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—
343Dic3—22no—
344Dic3—22no—
345Dic3—41no—
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—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—61no—
370C23—61no—
371C23—61no—
372C23—61no—
373C23—61no—
374C23—61no—
375C23—61no—
376C23D3×D412yes—
377C23#23712yes—
378C23C23×D311yescharacteristic
379D4—28no—
380D4—44no—
381D4—44no—
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—32no—
396C2×C4—32no—
397C2×C4—32no—
398C2×C4—32no—
399C2×C4—32no—
400C2×C4—68no—
401C2×C4—61no—
402C2×C4—61no—
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×C4D3×D412yes—
419C2×C4#23712yes—
420C2×C3—42no—
421C2×C3—42no—
422C2×C3—81no—
423C2×C3C2×#12111yescharacteristic
424C2×C3#52511yescharacteristic
425C2×C3#53511yescharacteristic
426C2×C3#54611yescharacteristic
427C2×C3#55011yescharacteristic
428C2×C3#55311yescharacteristic
429C2×C3#55511yescharacteristic
430D3—81no—
431C22—22no—
432C22—22no—
433C22—22no—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—121no—
453C22—121no—
454C22—121no—
455C22—121no—
456C22—121no—
457C22—121no—
458C22—121no—
459C22C2×D3×D411yescharacteristic
460C22C2×D3×D411yescharacteristic
461C22C2×#23711yescharacteristic
462C22C2×#23711yescharacteristic
463C22#100411yescharacteristic
464C22#100411yescharacteristic
465C22D3×#4111yescharacteristic
466C4—22no—
467C4—22no—
468C4—34no—
469C4—41no—
470C4—41no—
471C4—62no—
472C4—62no—
473C4—121no—
474C4—121no—
475C4—121no—
476C4—121no—
477C3#241411yescharacteristic, complemented, Sylow
478C2—42no—
479C2—42no—
480C2—81no—
481C2—241no—
482C2#558611yescharacteristic
483C2#559111yescharacteristic
484C2#559211yescharacteristic
485C2#560111yescharacteristic
486C2D3×#12111yescharacteristic
487C2#561611yescharacteristic
488C2#571811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#392C2
hypercenter#392D3
hypocenterC3#2414
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#939C2semidirect
2. C2×#939C2semidirect
3. C2×D4×Dic3C2semidirect
4. C2×#877C2semidirect
5. C3×#392C2semidirect
6. #5223C2semidirect
7. #5222C2semidirect
8. #5221C2semidirect
9. #4961C2semidirect
10. #4957C2semidirect
11. #4957C2semidirect
12. #4951C2semidirect
13. #4942C2semidirect
14. #4670C2semidirect
15. #4647C2semidirect
63. #392D3semidirect
102. C22×Dic3D4semidirect
129. 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×D4×Dic32
C2×#8772
C3×#3922
#52232
#52222
#52212
#49612
#49572
#49512
#49422
#46702
#46472
#24143