Finite Group Databasebeta

← #75936

Subgroups — #75936

Order 384.

560 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#388C211yesmaximal, characteristic, complemented
2#4992C211yesmaximal, characteristic, complemented
3#4990C211yesmaximal, characteristic, complemented
4#4955C211yesmaximal, characteristic
5#4955C211yesmaximal, characteristic
6#4955C211yesmaximal, characteristic
7#4952C211yesmaximal, characteristic, complemented
8#4947C211yesmaximal, characteristic, complemented
9#4944C211yesmaximal, characteristic, complemented
10#4940C211yesmaximal, characteristic, complemented
11#4940C211yesmaximal, characteristic, complemented
12#4675C211yesmaximal, characteristic, complemented
13#4673C211yesmaximal, characteristic, complemented
14#4673C211yesmaximal, characteristic, complemented
15#4669C211yesmaximal, characteristic, complemented
16#2736—31nomaximal, Sylow
17C24×D3C2211yescharacteristic
18C22×Dic6C2211yescharacteristic, complemented
19C2×C3×C4⋊C4C2211yescharacteristic, complemented
20C2×C3×C22⋊C4C2211yescharacteristic
21C2×C3×C22⋊C4C2211yescharacteristic
22C2×C3×C22⋊C4C2211yescharacteristic
23C2×C3×C42C2211yescharacteristic, complemented
24C2×#217C2211yescharacteristic
25C2×#217C2211yescharacteristic
26C2×#217C2211yescharacteristic
27C2×(C2×D3)⋊C4C2211yescharacteristic
28C2×(C2×D3)⋊C4C2211yescharacteristic
29C2×(C2×D3)⋊C4C2211yescharacteristic
30C2×(C2×D3)⋊C4C2211yescharacteristic
31C2×(C2×D3)⋊C4C2211yescharacteristic
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×Dic3⋊C4C2211yescharacteristic, complemented
40C2×Dic3⋊C4C2211yescharacteristic, complemented
41C2×C4×Dic3C2211yescharacteristic, complemented
42C3×#95C2211yescharacteristic, complemented
43C3×#95C2211yescharacteristic, complemented
44C3⋊#95C2211yescharacteristic, complemented
45C3⋊#95C2211yescharacteristic, complemented
46C3⋊#95C2211yescharacteristic, complemented
47C3⋊#95C2211yescharacteristic, complemented
48C3⋊#95C2211yescharacteristic, complemented
49C3⋊#95C2211yescharacteristic, complemented
50C3⋊#95C2211yescharacteristic, complemented
51C3⋊#95C2211yescharacteristic, complemented
52#397—31no—
53#397—31no—
54#397—31no—
55#393—31no—
56#393—31no—
57#393—31no—
58#388—31no—
59#388—31no—
60#388—31no—
61#388—31no—
62#388—31no—
63#388D311yescharacteristic, complemented
64#379—31no—
65#379—31no—
66#379—31no—
67C24×C3C2311yescharacteristic
68C23×D3—22no—
69C23×D3—22no—
70C23×D3—22no—
71C23×D3—41no—
72C23×D3—41no—
73C23×D3—41no—
74C23×D3—41no—
75C23×D3C2311yescharacteristic
76C23×D3C2311yescharacteristic
77C22×C3×C4C2311yescharacteristic
78C22×C3×C4C2311yescharacteristic
79C22×C3×C4C2311yescharacteristic
80C22×C3×C4C2311yescharacteristic
81C22×C3×C4C2311yescharacteristic
82C22×C3×C4C2311yescharacteristic
83C22×Dic3C2311yescharacteristic
84C22×Dic3C2311yescharacteristic
85C22×Dic3C2311yescharacteristic
86C22×Dic3C2311yescharacteristic
87C22×Dic3C2311yescharacteristic
88C22×Dic3C2311yescharacteristic
89C2×Dic6—41no—
90C2×Dic6—41no—
91C2×Dic6—41no—
92C3×C4⋊C4—41no—
93C3×C22⋊C4—22no—
94C3×C22⋊C4—41no—
95C3×C22⋊C4—41no—
96C3×C42—41no—
97#217—22no—
98#217—41no—
99#217—41no—
100(C2×D3)⋊C4—22no—
101(C2×D3)⋊C4—22no—
102(C2×D3)⋊C4—22no—
103(C2×D3)⋊C4—22no—
104(C2×D3)⋊C4—41no—
105(C2×D3)⋊C4—41no—
106(C2×D3)⋊C4—41no—
107(C2×D3)⋊C4—41no—
108(C2×D3)⋊C4—41no—
109(C2×D3)⋊C4—41no—
110(C2×D3)⋊C4—41no—
111(C2×D3)⋊C4—41no—
112Dic3⋊C4—41no—
113Dic3⋊C4—41no—
114C4×Dic3—41no—
115C25—31no—
116C22×Q8—31no—
117C2×C4⋊C4—31no—
118C2×C4⋊C4—31no—
119C2×C4⋊C4C2×D311yescharacteristic, complemented
120C2×C22⋊C4—31no—
121C2×C22⋊C4—31no—
122C2×C22⋊C4—31no—
123C2×C22⋊C4—31no—
124C2×C22⋊C4—31no—
125C2×C22⋊C4—31no—
126C2×C22⋊C4—31no—
127C2×C22⋊C4—31no—
128C2×C22⋊C4—31no—
129C2×C22⋊C4—31no—
130C2×C22⋊C4—31no—
131C2×C22⋊C4—31no—
132C2×C22⋊C4—31no—
133C2×C22⋊C4—31no—
134C2×C22⋊C4—31no—
135C2×C22⋊C4C2×D311yescharacteristic
136C2×C22⋊C4C2×D311yescharacteristic
137C2×C22⋊C4C2×D311yescharacteristic
138C2×C42—31no—
139C2×C42C2×D311yescharacteristic, complemented
140#95—31no—
141#95—31no—
142#95—31no—
143#95—31no—
144#95—31no—
145#95—31no—
146#95—31no—
147#95—31no—
148#95C2×D311yescharacteristic, complemented
149#95C2×D311yescharacteristic, complemented
150C23×C3—21no—
151C23×C3—21no—
152C23×C3—21no—
153C23×C3—21no—
154C23×C3—21no—
155C23×C3—21no—
156C23×C3#4112yes—
157C23×C3C2411yescharacteristic
158C22×D3—21no—
159C22×D3—21no—
160C22×D3—21no—
161C22×D3—21no—
162C22×D3—21no—
163C22×D3—21no—
164C22×D3—21no—
165C22×D3—21no—
166C22×D3—21no—
167C22×D3—21no—
168C22×D3—21no—
169C22×D3—21no—
170C22×D3—44no—
171C22×D3—44no—
172C22×D3—44no—
173C22×D3—44no—
174C22×D3—44no—
175C22×D3—44no—
176C22×D3—44no—
177C22×D3#4112yes—
178C22×D3#4112yes—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×Dic3—21no—
198C2×Dic3—21no—
199C2×Dic3—21no—
200C2×Dic3—21no—
201C2×Dic3—21no—
202C2×Dic3—21no—
203C2×Dic3—21no—
204C2×Dic3—21no—
205C2×Dic3—21no—
206C2×Dic3—21no—
207C2×Dic3—21no—
208C2×Dic3—21no—
209C2×Dic3—21no—
210C2×Dic3—21no—
211C2×Dic3—21no—
212C2×Dic3—21no—
213C2×Dic3—21no—
214C2×Dic3—21no—
215Dic6—44no—
216C24—31no—
217C24—31no—
218C24—62no—
219C24—62no—
220C24—62no—
221C24—121no—
222C24—121no—
223C24—121no—
224C24—121no—
225C24C22×D311yescharacteristic
226C2×Q8—121no—
227C2×Q8—121no—
228C2×Q8—121no—
229C22×C4—31no—
230C22×C4—31no—
231C22×C4—31no—
232C22×C4—31no—
233C22×C4—31no—
234C22×C4—31no—
235C22×C4C22×D311yescharacteristic
236C22×C4C22×D311yescharacteristic
237C22×C4C22×D311yescharacteristic
238C22×C4C22×D311yescharacteristic
239C22×C4C22×D311yescharacteristic
240C22×C4C22×D311yescharacteristic
241C4⋊C4—41no—
242C4⋊C4—121no—
243C4⋊C4—121no—
244C22⋊C4—22no—
245C22⋊C4—41no—
246C22⋊C4—41no—
247C22⋊C4—62no—
248C22⋊C4—62no—
249C22⋊C4—62no—
250C22⋊C4—62no—
251C22⋊C4—62no—
252C22⋊C4—121no—
253C22⋊C4—121no—
254C22⋊C4—121no—
255C22⋊C4—121no—
256C22⋊C4—121no—
257C22⋊C4—121no—
258C22⋊C4—121no—
259C22⋊C4—121no—
260C22⋊C4—121no—
261C22⋊C4—121no—
262C42—41no—
263C42—121no—
264C22×C3—22no—
265C22×C3—22no—
266C22×C3—22no—
267C22×C3—41no—
268C22×C3—41no—
269C22×C3—41no—
270C22×C3—41no—
271C22×C3C2×#4111yescharacteristic
272C22×C3C2×#4111yescharacteristic
273C22×C3C2×#4111yescharacteristic
274C22×C3H(5,𝔽2)11yescharacteristic
275C22×C3H(5,𝔽2)11yescharacteristic
276C22×C3H(5,𝔽2)11yescharacteristic
277C22×C3H(5,𝔽2)11yescharacteristic
278C2×D3—22no—
279C2×D3—22no—
280C2×D3—22no—
281C2×D3—22no—
282C2×D3—22no—
283C2×D3—22no—
284C2×D3—416no—
285C2×D3—41no—
286C2×D3—41no—
287C2×D3—41no—
288C2×D3—41no—
289C2×D3—41no—
290C2×D3—41no—
291C2×D3—41no—
292C2×D3—41no—
293C3×C4—41no—
294C3×C4—41no—
295C3×C4—41no—
296C3×C4—41no—
297C3×C4—41no—
298C3×C4—41no—
299Dic3—41no—
300Dic3—41no—
301Dic3—41no—
302Dic3—41no—
303Dic3—41no—
304Dic3—41no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23—32no—
312C23—32no—
313C23—61no—
314C23—61no—
315C23—61no—
316C23—61no—
317C23—61no—
318C23—61no—
319C23—61no—
320C23—61no—
321C23—61no—
322C23—61no—
323C23—61no—
324C23—61no—
325C23—124no—
326C23—124no—
327C23—124no—
328C23—124no—
329C23—124no—
330C23—124no—
331C23—124no—
332C23#23512yes—
333C23C23×D311yescharacteristic
334Q8—124no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—61no—
354C2×C4—61no—
355C2×C4—61no—
356C2×C4—61no—
357C2×C4—61no—
358C2×C4—61no—
359C2×C4—61no—
360C2×C4—61no—
361C2×C4—61no—
362C2×C4—61no—
363C2×C4—61no—
364C2×C4—61no—
365C2×C4—61no—
366C2×C4—61no—
367C2×C4—61no—
368C2×C4—61no—
369C2×C4—61no—
370C2×C4—61no—
371C2×C3—42no—
372C2×C3#53811yescharacteristic
373C2×C3#53811yescharacteristic
374C2×C3#53811yescharacteristic
375C2×C3#55111yescharacteristic
376C2×C3#55111yescharacteristic
377C2×C3#55111yescharacteristic
378C2×C3H(3,𝔽4)11yescharacteristic
379D3—42no—
380D3—42no—
381C22—22no—
382C22—22no—
383C22—22no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—62no—
389C22—62no—
390C22—62no—
391C22—62no—
392C22—62no—
393C22—62no—
394C22—1216no—
395C22—121no—
396C22—121no—
397C22—121no—
398C22—121no—
399C22—121no—
400C22—121no—
401C22—121no—
402C22—121no—
403C22C2×#23511yescharacteristic
404C22#100411yescharacteristic
405C22#100411yescharacteristic
406C22D3×#4111yescharacteristic
407C22D3×#4111yescharacteristic
408C22#100911yescharacteristic
409C22#100911yescharacteristic
410C4—41no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—41no—
415C4—41no—
416C4—121no—
417C4—121no—
418C4—121no—
419C4—121no—
420C4—121no—
421C4—121no—
422C3#273611yescharacteristic, complemented, Sylow
423C2—42no—
424C2—122no—
425C2—122no—
426C2#552711yescharacteristic
427C2#555611yescharacteristic
428C2#556011yescharacteristic
429C2#561311yescharacteristic
430C2#565711yescharacteristic
431C2#568311yescharacteristic
432C2#570511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#388C2
prime radicalC24×D3C22
hypercenter#388D3
hypocenterC3#2736
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C3×#388C2semidirect
2. #4992C2semidirect
3. #4990C2semidirect
7. #4952C2semidirect
8. #4947C2semidirect
9. #4944C2semidirect
10. #4940C2semidirect
11. #4940C2semidirect
12. #4675C2semidirect
13. #4673C2semidirect
14. #4673C2semidirect
15. #4669C2semidirect
18. C22×Dic6C22semidirect
19. C2×C3×C4⋊C4C22semidirect
23. C2×C3×C42C22semidirect
39. C2×Dic3⋊C4C22semidirect
40. C2×Dic3⋊C4C22semidirect
41. C2×C4×Dic3C22semidirect
42. C3×#95C22semidirect
43. C3×#95C22semidirect
44. C3⋊#95C22semidirect
45. C3⋊#95C22semidirect
46. C3⋊#95C22semidirect
47. C3⋊#95C22semidirect
48. C3⋊#95C22semidirect
49. C3⋊#95C22semidirect
50. C3⋊#95C22semidirect
51. C3⋊#95C22semidirect
63. #388D3semidirect
119. C2×C4⋊C4C2×D3semidirect
139. C2×C42C2×D3semidirect
148. #95C2×D3semidirect
149. #95C2×D3semidirect
422. C3#2736semidirect

Maximal subgroups

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

subgroupindex
C3×#3882
#49922
#49902
#49552
#49522
#49472
#49442
#49402
#46752
#46732
#46692
#27363