Finite Group Databasebeta

← #73840

Subgroups — #73840

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×#953C211yesmaximal, characteristic
2C2×#883C211yesmaximal, characteristic, complemented
3C3×#379C211yesmaximal, characteristic, complemented
4#5247C211yesmaximal, characteristic, complemented
5#4961C211yesmaximal, characteristic, complemented
6#4959C211yesmaximal, characteristic, complemented
7#4957C211yesmaximal, characteristic, complemented
8#4956C211yesmaximal, characteristic, complemented
9#4956C211yesmaximal, characteristic, complemented
10#4953C211yesmaximal, characteristic, complemented
11#4952C211yesmaximal, characteristic, complemented
12#4951C211yesmaximal, characteristic, complemented
13#4948C211yesmaximal, characteristic, complemented
14#4948C211yesmaximal, characteristic, complemented
15#4944C211yesmaximal, characteristic, complemented
16#2697—31nomaximal, Sylow
17C25×C3C2211yescharacteristic
18C22×#67C2211yescharacteristic
19C22×#67C2211yescharacteristic
20C22×#67C2211yescharacteristic
21C22×C4×D3C2211yescharacteristic, complemented
22C2×C3×C22⋊C4C2211yescharacteristic
23C2×C3×C22⋊C4C2211yescharacteristic
24C2×C3×C22⋊C4C2211yescharacteristic
25C2×C3×C22⋊C4C2211yescharacteristic
26C2×C3×C22⋊C4C2211yescharacteristic
27C2×C3×C22⋊C4C2211yescharacteristic
28#953—24no—
29C2×#217C2211yescharacteristic
30C2×#217C2211yescharacteristic
31C2×#217C2211yescharacteristic
32C2×#217C2211yescharacteristic
33C2×#217C2211yescharacteristic
34C2×#217C2211yescharacteristic
35C2×#217C2211yescharacteristic
36C2×#217C2211yescharacteristic
37C2×#217C2211yescharacteristic
38C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
39C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
40C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C2×C4⋊Dic3C2211yescharacteristic, complemented
42C2×C4⋊Dic3C2211yescharacteristic, complemented
43C2×Dic3⋊C4C2211yescharacteristic, complemented
44C2×Dic3⋊C4C2211yescharacteristic, complemented
45C2×Dic3⋊C4C2211yescharacteristic, complemented
46C2×C4×Dic3C2211yescharacteristic, complemented
47#883—24no—
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#386—31no—
67#379—31no—
68#379D311yescharacteristic, complemented
69C24×C3—22no—
70C24×C3—22no—
71C24×C3—22no—
72C24×C3—41no—
73C24×C3—41no—
74C24×C3—41no—
75C24×C3—41no—
76C24×C3C2311yescharacteristic
77C24×C3C2311yescharacteristic
78C24×C3C2311yescharacteristic
79C23×D3C2311yescharacteristic
80C22×C3×C4C2311yescharacteristic
81C22×C3×C4C2311yescharacteristic
82C22×C3×C4C2311yescharacteristic
83C22×C3×C4C2311yescharacteristic
84C2×#67—22no—
85C2×#67—22no—
86C2×#67—22no—
87C2×#67—22no—
88C2×#67—41no—
89C2×#67—41no—
90C2×#67—41no—
91C2×#67—41no—
92C2×#67D414yes—
93C22×Dic3C2311yescharacteristic
94C22×Dic3C2311yescharacteristic
95C22×Dic3C2311yescharacteristic
96C22×Dic3C2311yescharacteristic
97C22×Dic3C2311yescharacteristic
98C22×Dic3C2311yescharacteristic
99C22×Dic3C2311yescharacteristic
100C2×C4×D3—22no—
101C2×C4×D3—41no—
102C2×C4×D3—41no—
103C3×C22⋊C4—22no—
104C3×C22⋊C4—22no—
105C3×C22⋊C4—41no—
106C3×C22⋊C4—41no—
107C3×C22⋊C4—41no—
108C3×C22⋊C4—41no—
109#217—22no—
110#217—22no—
111#217—22no—
112#217—22no—
113#217—22no—
114#217—41no—
115#217—41no—
116#217—41no—
117#217—41no—
118(C2×D3)⋊C4—22no—
119(C2×D3)⋊C4—41no—
120(C2×D3)⋊C4—41no—
121C4⋊Dic3—22no—
122C4⋊Dic3—41no—
123Dic3⋊C4—22no—
124Dic3⋊C4—41no—
125Dic3⋊C4—41no—
126C4×Dic3—41no—
127C25C2×D311yescharacteristic
128C22×D4—31no—
129C22×D4—31no—
130C22×D4—31no—
131C23×C4—31no—
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⋊C4C2×D311yescharacteristic
152C2×C22⋊C4C2×D311yescharacteristic
153C2×C22⋊C4C2×D311yescharacteristic
154C2×C22⋊C4C2×D311yescharacteristic
155C2×C22⋊C4C2×D311yescharacteristic
156C2×C22⋊C4C2×D311yescharacteristic
157C2×C42—31no—
158#95—31no—
159#95—31no—
160#95—31no—
161#95—31no—
162#95—31no—
163#95—31no—
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×C3—21no—
177C23×C3—21no—
178C23×C3—21no—
179C23×C3—21no—
180C23×C3—21no—
181C23×C3—21no—
182C23×C3—44no—
183C23×C3—44no—
184C23×C3—44no—
185C23×C3—44no—
186C23×C3—44no—
187C23×C3—44no—
188C23×C3—44no—
189C23×C3C2×D412yes—
190C23×C3#4112yes—
191C23×C3#4112yes—
192C23×C3C2411yescharacteristic
193C22×D3—21no—
194C22×D3—21no—
195C22×D3—21no—
196C22×D3—21no—
197C22×D3—21no—
198C22×D3—21no—
199C22×D3C2×D412yes—
200C2×C3×C4—21no—
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—
212#67—44no—
213#67—44no—
214#67—44no—
215C2×Dic3—21no—
216C2×Dic3—21no—
217C2×Dic3—21no—
218C2×Dic3—21no—
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×Dic3C2×D412yes—
236C4×D3—44no—
237C24—22no—
238C24—22no—
239C24—22no—
240C24—31no—
241C24—41no—
242C24—41no—
243C24—41no—
244C24—41no—
245C24C22×D311yescharacteristic
246C24C22×D311yescharacteristic
247C24C22×D311yescharacteristic
248C2×D4—34no—
249C2×D4—62no—
250C2×D4—62no—
251C2×D4—62no—
252C2×D4—62no—
253C2×D4—121no—
254C2×D4—121no—
255C2×D4—121no—
256C2×D4—121no—
257C22×C4—31no—
258C22×C4—31no—
259C22×C4—31no—
260C22×C4—31no—
261C22×C4—31no—
262C22×C4—31no—
263C22×C4—31no—
264C22×C4—62no—
265C22×C4—121no—
266C22×C4—121no—
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—22no—
277C22⋊C4—22no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C22⋊C4—62no—
283C22⋊C4—62no—
284C22⋊C4—62no—
285C22⋊C4—62no—
286C22⋊C4—62no—
287C22⋊C4—62no—
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—22no—
302C22×C3—22no—
303C22×C3—22no—
304C22×C3—416no—
305C22×C3—41no—
306C22×C3—41no—
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×C3C22×D411yescharacteristic
318C22×C3C2×#4111yescharacteristic
319C22×C3C2×#4111yescharacteristic
320C22×C3H(5,𝔽2)11yescharacteristic
321C22×C3H(5,𝔽2)11yescharacteristic
322C22×C3H(5,𝔽2)11yescharacteristic
323C22×C3H(5,𝔽2)11yescharacteristic
324C2×D3—22no—
325C2×D3—22no—
326C2×D3—22no—
327C2×D3—41no—
328C2×D3—41no—
329C2×D3—41no—
330C2×D3—41no—
331C3×C4—41no—
332C3×C4—41no—
333C3×C4—41no—
334C3×C4—41no—
335Dic3—22no—
336Dic3—41no—
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—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—32no—
361C23—44no—
362C23—44no—
363C23—44no—
364C23—44no—
365C23—44no—
366C23—44no—
367C23—44no—
368C23—61no—
369C23—61no—
370C23—61no—
371C23—61no—
372C23—61no—
373C23—61no—
374C23#23512yes—
375C23D3×D412yes—
376C23#23712yes—
377C23C23×D311yescharacteristic
378D4—124no—
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—32no—
394C2×C4—61no—
395C2×C4—61no—
396C2×C4—61no—
397C2×C4—61no—
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—124no—
415C2×C3—42no—
416C2×C3—42no—
417C2×C3—42no—
418C2×C3#53411yescharacteristic
419C2×C3#53811yescharacteristic
420C2×C3#53811yescharacteristic
421C2×C3#54611yescharacteristic
422C2×C3#54611yescharacteristic
423C2×C3#55111yescharacteristic
424C2×C3#56011yescharacteristic
425D3—42no—
426C22—22no—
427C22—22no—
428C22—22no—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—22no—
433C22—22no—
434C22—22no—
435C22—416no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—62no—
449C22—62no—
450C22—62no—
451C22—121no—
452C22—121no—
453C22—121no—
454C22—121no—
455C22C2×#23511yescharacteristic
456C22C2×D3×D411yescharacteristic
457C22C2×#23711yescharacteristic
458C22#100411yescharacteristic
459C22#100411yescharacteristic
460C22#100411yescharacteristic
461C22#100411yescharacteristic
462C4—41no—
463C4—41no—
464C4—41no—
465C4—41no—
466C4—62no—
467C4—121no—
468C4—121no—
469C4—121no—
470C4—121no—
471C4—121no—
472C4—121no—
473C3#269711yescharacteristic, complemented, Sylow
474C2—42no—
475C2—42no—
476C2—42no—
477C2—122no—
478C2#549011yescharacteristic
479C2#549411yescharacteristic
480C2#549511yescharacteristic
481C2#558911yescharacteristic
482C2#559111yescharacteristic
483C2#559311yescharacteristic
484C2#559511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#379C2
prime radicalC2×#953C2
hypercenter#379D3
hypocenterC3#2697
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
2. C2×#883C2semidirect
3. C3×#379C2semidirect
4. #5247C2semidirect
5. #4961C2semidirect
6. #4959C2semidirect
7. #4957C2semidirect
8. #4956C2semidirect
9. #4956C2semidirect
10. #4953C2semidirect
11. #4952C2semidirect
12. #4951C2semidirect
13. #4948C2semidirect
14. #4948C2semidirect
15. #4944C2semidirect
21. C22×C4×D3C22semidirect
38. C2×(C2×D3)⋊C4C22semidirect
39. C2×(C2×D3)⋊C4C22semidirect
40. C2×(C2×D3)⋊C4C22semidirect
41. C2×C4⋊Dic3C22semidirect
42. C2×C4⋊Dic3C22semidirect
43. C2×Dic3⋊C4C22semidirect
44. C2×Dic3⋊C4C22semidirect
45. C2×Dic3⋊C4C22semidirect
46. C2×C4×Dic3C22semidirect
48. C3⋊#95C22semidirect
49. C3⋊#95C22semidirect
50. C3⋊#95C22semidirect
51. C3⋊#95C22semidirect
52. C3⋊#95C22semidirect
53. C3⋊#95C22semidirect
68. #379D3semidirect
473. C3#2697semidirect

Maximal subgroups

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

subgroupindex
C2×#9532
C2×#8832
C3×#3792
#52472
#49612
#49592
#49572
#49562
#49532
#49522
#49512
#49482
#49442
#26973