Finite Group Databasebeta

← #73841

Subgroups — #73841

Order 384.

552 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#379C211yesmaximal, characteristic
2#5247C211yesmaximal, characteristic
3#5247C211yesmaximal, characteristic
4#4953C211yesmaximal, characteristic, complemented
5#4952C211yesmaximal, characteristic, complemented
6#4952C211yesmaximal, characteristic, complemented
7#4951C211yesmaximal, characteristic, complemented
8#4951C211yesmaximal, characteristic, complemented
9#4949C211yesmaximal, characteristic, complemented
10#4948C211yesmaximal, characteristic, complemented
11#4948C211yesmaximal, characteristic, complemented
12#4945C211yesmaximal, characteristic, complemented
13#4945C211yesmaximal, characteristic, complemented
14#4944C211yesmaximal, characteristic, complemented
15#4944C211yesmaximal, characteristic, complemented
16#2735—31nomaximal, Sylow
17C25×C3C2211yescharacteristic
18C2×C3×C22⋊C4C2211yescharacteristic
19C2×C3×C22⋊C4C2211yescharacteristic
20C2×C3×C22⋊C4C2211yescharacteristic
21C2×C3×C22⋊C4C2211yescharacteristic
22C2×C3×C22⋊C4C2211yescharacteristic
23C2×C3×C22⋊C4C2211yescharacteristic
24C2×#217C2211yescharacteristic
25C2×#217C2211yescharacteristic
26C2×#217C2211yescharacteristic
27C2×#217C2211yescharacteristic
28C2×#217C2211yescharacteristic
29C2×#217C2211yescharacteristic
30C2×#217C2211yescharacteristic
31C2×#217C2211yescharacteristic
32C2×#217C2211yescharacteristic
33C2×#217C2211yescharacteristic
34C2×#217C2211yescharacteristic
35C2×#217C2211yescharacteristic
36C2×C4⋊Dic3C2211yescharacteristic, complemented
37C2×C4⋊Dic3C2211yescharacteristic, complemented
38C2×Dic3⋊C4C2211yescharacteristic, complemented
39C2×Dic3⋊C4C2211yescharacteristic, complemented
40C2×Dic3⋊C4C2211yescharacteristic, complemented
41C2×Dic3⋊C4C2211yescharacteristic, complemented
42C2×C4×Dic3C2211yescharacteristic, complemented
43C2×C4×Dic3C2211yescharacteristic, 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#399—31no—
53#397—31no—
54#397—31no—
55#397—31no—
56#396—31no—
57#396—31no—
58#388—31no—
59#388—31no—
60#388—31no—
61#388—31no—
62#388—31no—
63#388—31no—
64#379—31no—
65#379—31no—
66#379D311yescharacteristic
67C24×C3—22no—
68C24×C3—22no—
69C24×C3—22no—
70C24×C3—41no—
71C24×C3—41no—
72C24×C3—41no—
73C24×C3—41no—
74C24×C3C2311yescharacteristic
75C24×C3C2311yescharacteristic
76C24×C3C2311yescharacteristic
77C22×C3×C4C2311yescharacteristic
78C22×C3×C4C2311yescharacteristic
79C22×C3×C4C2311yescharacteristic
80C22×C3×C4C2311yescharacteristic
81C22×Dic3C2311yescharacteristic
82C22×Dic3C2311yescharacteristic
83C22×Dic3C2311yescharacteristic
84C22×Dic3C2311yescharacteristic
85C22×Dic3C2311yescharacteristic
86C22×Dic3C2311yescharacteristic
87C22×Dic3C2311yescharacteristic
88C22×Dic3C2311yescharacteristic
89C3×C22⋊C4—22no—
90C3×C22⋊C4—22no—
91C3×C22⋊C4—41no—
92C3×C22⋊C4—41no—
93C3×C22⋊C4—41no—
94C3×C22⋊C4—41no—
95#217—22no—
96#217—22no—
97#217—22no—
98#217—22no—
99#217—41no—
100#217—41no—
101#217—41no—
102#217—41no—
103#217—41no—
104#217—41no—
105#217—41no—
106#217—41no—
107C4⋊Dic3—41no—
108C4⋊Dic3—41no—
109Dic3⋊C4—41no—
110Dic3⋊C4—41no—
111Dic3⋊C4—41no—
112Dic3⋊C4—41no—
113C4×Dic3—41no—
114C4×Dic3—41no—
115C25C2×D311yescharacteristic
116C2×C4⋊C4—31no—
117C2×C4⋊C4—31no—
118C2×C4⋊C4—31no—
119C2×C4⋊C4—31no—
120C2×C4⋊C4—31no—
121C2×C4⋊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⋊C4C2×D311yescharacteristic
135C2×C22⋊C4C2×D311yescharacteristic
136C2×C22⋊C4C2×D311yescharacteristic
137C2×C22⋊C4C2×D311yescharacteristic
138C2×C22⋊C4C2×D311yescharacteristic
139C2×C22⋊C4C2×D311yescharacteristic
140C2×C42—31no—
141C2×C42—31no—
142#95—31no—
143#95—31no—
144#95—31no—
145#95—31no—
146#95—31no—
147#95—31no—
148#95—31no—
149#95—31no—
150C23×C3—21no—
151C23×C3—21no—
152C23×C3—21no—
153C23×C3—21no—
154C23×C3—21no—
155C23×C3—21no—
156C23×C3—21no—
157C23×C3—21no—
158C23×C3—21no—
159C23×C3—21no—
160C23×C3—21no—
161C23×C3—21no—
162C23×C3—21no—
163C23×C3—21no—
164C23×C3—21no—
165C23×C3—21no—
166C23×C3—21no—
167C23×C3—21no—
168C23×C3—44no—
169C23×C3—44no—
170C23×C3—44no—
171C23×C3—44no—
172C23×C3—44no—
173C23×C3—44no—
174C23×C3—44no—
175C23×C3#4112yes—
176C23×C3#4112yes—
177C23×C3#4112yes—
178C23×C3C2411yescharacteristic
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×Dic3—21no—
192C2×Dic3—21no—
193C2×Dic3—21no—
194C2×Dic3—21no—
195C2×Dic3—21no—
196C2×Dic3—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—
215C24—22no—
216C24—22no—
217C24—22no—
218C24—41no—
219C24—41no—
220C24—41no—
221C24—41no—
222C24C22×D311yescharacteristic
223C24C22×D311yescharacteristic
224C24C22×D311yescharacteristic
225C22×C4—31no—
226C22×C4—31no—
227C22×C4—31no—
228C22×C4—31no—
229C22×C4—31no—
230C22×C4—31no—
231C22×C4—31no—
232C22×C4—31no—
233C22×C4C22×D311yescharacteristic
234C22×C4C22×D311yescharacteristic
235C22×C4C22×D311yescharacteristic
236C22×C4C22×D311yescharacteristic
237C4⋊C4—121no—
238C4⋊C4—121no—
239C4⋊C4—121no—
240C4⋊C4—121no—
241C4⋊C4—121no—
242C4⋊C4—121no—
243C22⋊C4—22no—
244C22⋊C4—22no—
245C22⋊C4—41no—
246C22⋊C4—41no—
247C22⋊C4—41no—
248C22⋊C4—41no—
249C22⋊C4—62no—
250C22⋊C4—62no—
251C22⋊C4—62no—
252C22⋊C4—62no—
253C22⋊C4—121no—
254C22⋊C4—121no—
255C22⋊C4—121no—
256C22⋊C4—121no—
257C22⋊C4—121no—
258C22⋊C4—121no—
259C22⋊C4—121no—
260C22⋊C4—121no—
261C42—121no—
262C42—121no—
263C22×C3—22no—
264C22×C3—22no—
265C22×C3—22no—
266C22×C3—22no—
267C22×C3—22no—
268C22×C3—22no—
269C22×C3—22no—
270C22×C3—22no—
271C22×C3—22no—
272C22×C3—416no—
273C22×C3—41no—
274C22×C3—41no—
275C22×C3—41no—
276C22×C3—41no—
277C22×C3—41no—
278C22×C3—41no—
279C22×C3—41no—
280C22×C3—41no—
281C22×C3—41no—
282C22×C3—41no—
283C22×C3—41no—
284C22×C3—41no—
285C22×C3C2×#4111yescharacteristic
286C22×C3C2×#4111yescharacteristic
287C22×C3C2×#4111yescharacteristic
288C22×C3H(5,𝔽2)11yescharacteristic
289C22×C3H(5,𝔽2)11yescharacteristic
290C22×C3H(5,𝔽2)11yescharacteristic
291C22×C3H(5,𝔽2)11yescharacteristic
292C3×C4—41no—
293C3×C4—41no—
294C3×C4—41no—
295C3×C4—41no—
296Dic3—41no—
297Dic3—41no—
298Dic3—41no—
299Dic3—41no—
300Dic3—41no—
301Dic3—41no—
302Dic3—41no—
303Dic3—41no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—44no—
323C23—44no—
324C23—44no—
325C23—44no—
326C23—44no—
327C23—44no—
328C23—44no—
329C23#23512yes—
330C23#23712yes—
331C23#23712yes—
332C23C23×D311yescharacteristic
333C2×C4—21no—
334C2×C4—21no—
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—61no—
346C2×C4—61no—
347C2×C4—61no—
348C2×C4—61no—
349C2×C4—61no—
350C2×C4—61no—
351C2×C4—61no—
352C2×C4—61no—
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×C3—42no—
370C2×C3—42no—
371C2×C3—42no—
372C2×C3#53811yescharacteristic
373C2×C3#53811yescharacteristic
374C2×C3#53811yescharacteristic
375C2×C3#55111yescharacteristic
376C2×C3#55111yescharacteristic
377C2×C3#55111yescharacteristic
378C2×C3#56011yescharacteristic
379C22—22no—
380C22—22no—
381C22—22no—
382C22—22no—
383C22—22no—
384C22—22no—
385C22—22no—
386C22—22no—
387C22—22no—
388C22—416no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22C2×#23511yescharacteristic
402C22C2×#23711yescharacteristic
403C22C2×#23711yescharacteristic
404C22#100411yescharacteristic
405C22#100411yescharacteristic
406C22#100411yescharacteristic
407C22#100411yescharacteristic
408C4—41no—
409C4—41no—
410C4—41no—
411C4—41no—
412C4—121no—
413C4—121no—
414C4—121no—
415C4—121no—
416C4—121no—
417C4—121no—
418C4—121no—
419C4—121no—
420C3#273511yescharacteristic, complemented, Sylow
421C2—42no—
422C2—42no—
423C2—42no—
424C2#549411yescharacteristic
425C2#549511yescharacteristic
426C2#549511yescharacteristic
427C2#558711yescharacteristic
428C2#559311yescharacteristic
429C2#559311yescharacteristic
430C2#559511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#379C2
prime radicalC25×C3C22
hypercenter#379D3
hypocenterC3#2735
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
4. #4953C2semidirect
5. #4952C2semidirect
6. #4952C2semidirect
7. #4951C2semidirect
8. #4951C2semidirect
9. #4949C2semidirect
10. #4948C2semidirect
11. #4948C2semidirect
12. #4945C2semidirect
13. #4945C2semidirect
14. #4944C2semidirect
15. #4944C2semidirect
36. C2×C4⋊Dic3C22semidirect
37. C2×C4⋊Dic3C22semidirect
38. C2×Dic3⋊C4C22semidirect
39. C2×Dic3⋊C4C22semidirect
40. C2×Dic3⋊C4C22semidirect
41. C2×Dic3⋊C4C22semidirect
42. C2×C4×Dic3C22semidirect
43. C2×C4×Dic3C22semidirect
44. C3⋊#95C22semidirect
45. C3⋊#95C22semidirect
46. C3⋊#95C22semidirect
47. C3⋊#95C22semidirect
48. C3⋊#95C22semidirect
49. C3⋊#95C22semidirect
50. C3⋊#95C22semidirect
51. C3⋊#95C22semidirect
420. C3#2735semidirect

Maximal subgroups

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

subgroupindex
C3×#3792
#52472
#49532
#49522
#49512
#49492
#49482
#49452
#49442
#27353