Finite Group Databasebeta

← #74924

Subgroups — #74924

Order 384.

680 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#937C211yesmaximal, characteristic
2C2×#929C211yesmaximal, characteristic, complemented
3C3×#386C211yesmaximal, characteristic, complemented
4#5222C211yesmaximal, characteristic, complemented
5#5213C211yesmaximal, characteristic, complemented
6#4961C211yesmaximal, characteristic, complemented
7#4957C211yesmaximal, characteristic, complemented
8#4955C211yesmaximal, characteristic, complemented
9#4955C211yesmaximal, characteristic, complemented
10#4948C211yesmaximal, characteristic, complemented
11#4944C211yesmaximal, characteristic, complemented
12#4676C211yesmaximal, characteristic, complemented
13#4675C211yesmaximal, characteristic, complemented
14#4674C211yesmaximal, characteristic, complemented
15#4669C211yesmaximal, characteristic, complemented
16#2697—31nomaximal, Sylow
17C24×D3C2211yescharacteristic
18C22×C3×D4C2211yescharacteristic
19C23×C3×C4C2211yescharacteristic, complemented
20C22×#67C2211yescharacteristic
21C22×#67C2211yescharacteristic
22C2×C3×C22⋊C4C2211yescharacteristic
23C2×C3×C22⋊C4C2211yescharacteristic
24C2×C3×C22⋊C4C2211yescharacteristic, complemented
25C2×#217C2211yescharacteristic
26C2×#217C2211yescharacteristic
27C2×#217C2211yescharacteristic
28C2×#217C2211yescharacteristic, complemented
29C2×#217C2211yescharacteristic, complemented
30#937—24no—
31#929—24no—
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×(C2×D3)⋊C4C2211yescharacteristic
42C2×C4⋊Dic3C2211yescharacteristic, complemented
43C2×Dic3⋊C4C2211yescharacteristic, complemented
44C2×Dic3⋊C4C2211yescharacteristic, complemented
45C2×Dic3⋊C4C2211yescharacteristic, complemented
46C2×Dic3⋊C4C2211yescharacteristic, complemented
47C2×C4×Dic3C2211yescharacteristic, complemented
48C3×#95C2211yescharacteristic, complemented
49C3×#95C2211yescharacteristic, complemented
50C3⋊#95C2211yescharacteristic, complemented
51C3⋊#95C2211yescharacteristic, complemented
52C3⋊#95C2211yescharacteristic, complemented
53C3⋊#95C2211yescharacteristic, complemented
54C2×#123—31no—
55C2×#120—31no—
56#397—31no—
57#397—31no—
58#396—31no—
59#396—31no—
60#394—31no—
61#394—31no—
62#390—31no—
63#388—31no—
64#388—31no—
65#386—31no—
66#386D311yescharacteristic, complemented
67#379—31no—
68#379—31no—
69C24×C3C2311yescharacteristic
70C24×C3C2311yescharacteristic
71C23×D3—22no—
72C23×D3—22no—
73C23×D3—22no—
74C23×D3—41no—
75C23×D3—41no—
76C23×D3—41no—
77C23×D3—41no—
78C23×D3C2311yescharacteristic
79C23×D3C2311yescharacteristic
80C2×C3×D4—22no—
81C2×C3×D4—22no—
82C2×C3×D4—41no—
83C22×C3×C4—22no—
84C22×C3×C4—41no—
85C22×C3×C4—41no—
86C22×C3×C4C2311yescharacteristic
87C22×C3×C4C2311yescharacteristic
88C22×C3×C4C2311yescharacteristic
89C22×C3×C4C2311yescharacteristic
90C22×C3×C4C2311yescharacteristic
91C2×#67—22no—
92C2×#67—22no—
93C2×#67—41no—
94C2×#67—41no—
95C2×#67—41no—
96C2×#67D414yes—
97C22×Dic3C2311yescharacteristic
98C22×Dic3C2311yescharacteristic
99C22×Dic3C2311yescharacteristic
100C22×Dic3C2311yescharacteristic
101C22×Dic3C2311yescharacteristic
102C22×Dic3C2311yescharacteristic
103C3×C22⋊C4—41no—
104C3×C22⋊C4—41no—
105C3×C22⋊C4—41no—
106#217—22no—
107#217—22no—
108#217—22no—
109#217—41no—
110#217—41no—
111(C2×D3)⋊C4—22no—
112(C2×D3)⋊C4—22no—
113(C2×D3)⋊C4—22no—
114(C2×D3)⋊C4—22no—
115(C2×D3)⋊C4—22no—
116(C2×D3)⋊C4—41no—
117(C2×D3)⋊C4—41no—
118(C2×D3)⋊C4—41no—
119(C2×D3)⋊C4—41no—
120(C2×D3)⋊C4—41no—
121C4⋊Dic3—41no—
122Dic3⋊C4—22no—
123Dic3⋊C4—22no—
124Dic3⋊C4—41no—
125Dic3⋊C4—41no—
126C4×Dic3—41no—
127C25—31no—
128C22×D4—31no—
129C22×D4—31no—
130C22×D4C2×D311yescharacteristic
131C23×C4C2×D311yescharacteristic, complemented
132#123—64no—
133#120—64no—
134C2×C4⋊C4—31no—
135C2×C4⋊C4—31no—
136C2×C4⋊C4—31no—
137C2×C4⋊C4—31no—
138C2×C4⋊C4—31no—
139C2×C22⋊C4—31no—
140C2×C22⋊C4—31no—
141C2×C22⋊C4—31no—
142C2×C22⋊C4—31no—
143C2×C22⋊C4—31no—
144C2×C22⋊C4—31no—
145C2×C22⋊C4—31no—
146C2×C22⋊C4—31no—
147C2×C22⋊C4—31no—
148C2×C22⋊C4—31no—
149C2×C22⋊C4—31no—
150C2×C22⋊C4—31no—
151C2×C22⋊C4—31no—
152C2×C22⋊C4—31no—
153C2×C22⋊C4—31no—
154C2×C22⋊C4C2×D311yescharacteristic
155C2×C22⋊C4C2×D311yescharacteristic
156C2×C22⋊C4C2×D311yescharacteristic, complemented
157C2×C42—31no—
158#95—31no—
159#95—31no—
160#95—31no—
161#95—31no—
162#95C2×D311yescharacteristic, complemented
163#95C2×D311yescharacteristic, complemented
164C23×C3—21no—
165C23×C3—21no—
166C23×C3—21no—
167C23×C3—21no—
168C23×C3—21no—
169C23×C3—21no—
170C23×C3—21no—
171C23×C3—21no—
172C23×C3—21no—
173C23×C3—21no—
174C23×C3—21no—
175C23×C3—21no—
176C23×C3C2×D412yes—
177C23×C3#4112yes—
178C23×C3C2411yescharacteristic
179C22×D3—21no—
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—44no—
192C22×D3—44no—
193C22×D3—44no—
194C22×D3—44no—
195C22×D3—44no—
196C22×D3—44no—
197C22×D3—44no—
198C22×D3C2×D412yes—
199C22×D3#4112yes—
200C3×D4—44no—
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×C4—44no—
217#67—44no—
218#67—44no—
219C2×Dic3—21no—
220C2×Dic3—21no—
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—21no—
236C2×Dic3C2×D412yes—
237C24—31no—
238C24—31no—
239C24—62no—
240C24—62no—
241C24—62no—
242C24—121no—
243C24—121no—
244C24—121no—
245C24—121no—
246C24C22×D311yescharacteristic
247C24C22×D311yescharacteristic
248C2×D4—22no—
249C2×D4—22no—
250C2×D4—34no—
251C2×D4—41no—
252C2×D4—62no—
253C2×D4—62no—
254C2×D4—121no—
255C2×D4—121no—
256C2×D4—121no—
257C22×C4—22no—
258C22×C4—31no—
259C22×C4—31no—
260C22×C4—31no—
261C22×C4—31no—
262C22×C4—31no—
263C22×C4—31no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4C22×D311yescharacteristic
267C22×C4C22×D311yescharacteristic
268C22×C4C22×D311yescharacteristic
269C22×C4C22×D311yescharacteristic
270C22×C4C22×D311yescharacteristic
271C4⋊C4—62no—
272C4⋊C4—62no—
273C4⋊C4—121no—
274C4⋊C4—121no—
275C4⋊C4—121no—
276C22⋊C4—41no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—62no—
280C22⋊C4—62no—
281C22⋊C4—62no—
282C22⋊C4—62no—
283C22⋊C4—62no—
284C22⋊C4—62no—
285C22⋊C4—62no—
286C22⋊C4—62no—
287C22⋊C4—121no—
288C22⋊C4—121no—
289C22⋊C4—121no—
290C22⋊C4—121no—
291C22⋊C4—121no—
292C22⋊C4—121no—
293C22⋊C4—121no—
294C42—121no—
295C22×C3—22no—
296C22×C3—22no—
297C22×C3—22no—
298C22×C3—22no—
299C22×C3—22no—
300C22×C3—22no—
301C22×C3—41no—
302C22×C3—41no—
303C22×C3—41no—
304C22×C3—41no—
305C22×C3—41no—
306C22×C3—41no—
307C22×C3—41no—
308C22×C3—41no—
309C22×C3C22×D411yescharacteristic
310C22×C3C2×#4111yescharacteristic
311C22×C3C2×#4111yescharacteristic
312C22×C3H(5,𝔽2)11yescharacteristic
313C22×C3H(5,𝔽2)11yescharacteristic
314C22×C3H(5,𝔽2)11yescharacteristic
315C22×C3H(5,𝔽2)11yescharacteristic
316C2×D3—22no—
317C2×D3—22no—
318C2×D3—22no—
319C2×D3—22no—
320C2×D3—22no—
321C2×D3—22no—
322C2×D3—416no—
323C2×D3—41no—
324C2×D3—41no—
325C2×D3—41no—
326C2×D3—41no—
327C2×D3—41no—
328C2×D3—41no—
329C2×D3—41no—
330C2×D3—41no—
331C3×C4—41no—
332C3×C4—41no—
333C3×C4—41no—
334C3×C4—41no—
335C3×C4—41no—
336Dic3—22no—
337Dic3—41no—
338Dic3—41no—
339Dic3—41no—
340Dic3—41no—
341Dic3—41no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—32no—
355C23—32no—
356C23—61no—
357C23—61no—
358C23—61no—
359C23—61no—
360C23—61no—
361C23—61no—
362C23—61no—
363C23—61no—
364C23—61no—
365C23—61no—
366C23—61no—
367C23—61no—
368C23—124no—
369C23—124no—
370C23—124no—
371C23—124no—
372C23—124no—
373C23—124no—
374C23—124no—
375C23#23512yes—
376C23D3×D412yes—
377C23C23×D311yescharacteristic
378D4—44no—
379D4—124no—
380D4—124no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
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—32no—
397C2×C4—44no—
398C2×C4—61no—
399C2×C4—61no—
400C2×C4—61no—
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×C3—42no—
416C2×C3—42no—
417C2×C3#53411yescharacteristic
418C2×C3#53811yescharacteristic
419C2×C3#53811yescharacteristic
420C2×C3#54611yescharacteristic
421C2×C3#54611yescharacteristic
422C2×C3#55111yescharacteristic
423C2×C3#56011yescharacteristic
424D3—42no—
425D3—42no—
426C22—22no—
427C22—22no—
428C22—22no—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—62no—
441C22—62no—
442C22—62no—
443C22—62no—
444C22—62no—
445C22—62no—
446C22—1216no—
447C22—121no—
448C22—121no—
449C22—121no—
450C22—121no—
451C22—121no—
452C22—121no—
453C22—121no—
454C22—121no—
455C22C2×#23511yescharacteristic
456C22C2×D3×D411yescharacteristic
457C22#100411yescharacteristic
458C22#100411yescharacteristic
459C22#100411yescharacteristic
460C22D3×#4111yescharacteristic
461C22#100911yescharacteristic
462C4—41no—
463C4—41no—
464C4—41no—
465C4—41no—
466C4—41no—
467C4—62no—
468C4—121no—
469C4—121no—
470C4—121no—
471C4—121no—
472C4—121no—
473C3#269711yescharacteristic, complemented, Sylow
474C2—42no—
475C2—42no—
476C2—122no—
477C2—122no—
478C2#549011yescharacteristic
479C2#555611yescharacteristic
480C2#556011yescharacteristic
481C2#558911yescharacteristic
482C2#561311yescharacteristic
483C2#562011yescharacteristic
484C2#565411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#386C2
prime radicalC2×#937C2
hypercenter#386D3
hypocenterC3#2697
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×#929C2semidirect
3. C3×#386C2semidirect
4. #5222C2semidirect
5. #5213C2semidirect
6. #4961C2semidirect
7. #4957C2semidirect
8. #4955C2semidirect
9. #4955C2semidirect
10. #4948C2semidirect
11. #4944C2semidirect
12. #4676C2semidirect
13. #4675C2semidirect
14. #4674C2semidirect
15. #4669C2semidirect
19. C23×C3×C4C22semidirect
24. C2×C3×C22⋊C4C22semidirect
28. C2×#217C22semidirect
29. C2×#217C22semidirect
42. C2×C4⋊Dic3C22semidirect
43. C2×Dic3⋊C4C22semidirect
44. C2×Dic3⋊C4C22semidirect
45. C2×Dic3⋊C4C22semidirect
46. C2×Dic3⋊C4C22semidirect
47. C2×C4×Dic3C22semidirect
48. C3×#95C22semidirect
49. C3×#95C22semidirect
50. C3⋊#95C22semidirect
51. C3⋊#95C22semidirect
52. C3⋊#95C22semidirect
53. C3⋊#95C22semidirect
66. #386D3semidirect
131. C23×C4C2×D3semidirect
156. C2×C22⋊C4C2×D3semidirect
162. #95C2×D3semidirect
163. #95C2×D3semidirect
473. C3#2697semidirect

Maximal subgroups

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

subgroupindex
C2×#9372
C2×#9292
C3×#3862
#52222
#52132
#49612
#49572
#49552
#49482
#49442
#46762
#46752
#46742
#46692
#26973