Finite Group Databasebeta

← #77424

Subgroups — #77424

Order 384.

668 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#896C211yesmaximal, characteristic, complemented
2C2×D3×C22⋊C4C211yesmaximal, characteristic
3C3×#396C211yesmaximal, characteristic, complemented
4#4994C211yesmaximal, characteristic, complemented
5#4994C211yesmaximal, characteristic, complemented
6#4993C211yesmaximal, characteristic, complemented
7#4989C211yesmaximal, characteristic, complemented
8#4987C211yesmaximal, characteristic, complemented
9#4955C211yesmaximal, characteristic
10#4955C211yesmaximal, characteristic
11#4949C211yesmaximal, characteristic, complemented
12#4948C211yesmaximal, characteristic, complemented
13#4947C211yesmaximal, characteristic, complemented
14#4673C211yesmaximal, characteristic, complemented
15#4668C211yesmaximal, characteristic, complemented
16#2626—31nomaximal, Sylow
17C24×D3C2211yescharacteristic
18C22×C4×D3C2211yescharacteristic
19C22×C4×D3C2211yescharacteristic
20C22×Dic6C2211yescharacteristic, complemented
21C2×C3×C4⋊C4C2211yescharacteristic, complemented
22C2×C3×C4⋊C4C2211yescharacteristic, complemented
23C2×C3×C4⋊C4C2211yescharacteristic, complemented
24C2×C3×C22⋊C4C2211yescharacteristic
25C2×C3×C22⋊C4C2211yescharacteristic
26C2×C3×C22⋊C4C2211yescharacteristic
27C2×#217C2211yescharacteristic
28C2×#217C2211yescharacteristic
29C2×#217C2211yescharacteristic
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×(C2×D3)⋊C4C2211yescharacteristic
40C2×C4⋊Dic3C2211yescharacteristic, complemented
41C2×C4⋊Dic3C2211yescharacteristic, complemented
42C2×Dic3⋊C4C2211yescharacteristic, complemented
43C2×Dic3⋊C4C2211yescharacteristic, complemented
44C2×Dic3⋊C4C2211yescharacteristic, complemented
45C2×Dic3⋊C4C2211yescharacteristic, complemented
46#896—24no—
47D3×C22⋊C4—24no—
48C3×#95C2211yescharacteristic, complemented
49C3⋊#95C2211yescharacteristic, complemented
50C3⋊#95C2211yescharacteristic, complemented
51C3⋊#95C2211yescharacteristic, complemented
52C3⋊#95C2211yescharacteristic, complemented
53C3⋊#95C2211yescharacteristic, complemented
54C2×C22⋊Q8—31no—
55C22×C22⋊C4—31no—
56#399—31no—
57#399—31no—
58#396—31no—
59#396—31no—
60#396—31no—
61#396D311yescharacteristic, complemented
62#393—31no—
63#393—31no—
64#385—31no—
65#385—31no—
66#380—31no—
67#379—31no—
68#379—31no—
69C24×C3C2311yescharacteristic
70C23×D3—22no—
71C23×D3—22no—
72C23×D3—41no—
73C23×D3—41no—
74C23×D3—41no—
75C23×D3—41no—
76C23×D3Q814yescomplemented
77C23×D3C2311yescharacteristic
78C23×D3C2311yescharacteristic
79C22×C3×C4C2311yescharacteristic
80C22×C3×C4C2311yescharacteristic
81C22×C3×C4C2311yescharacteristic
82C22×C3×C4C2311yescharacteristic
83C22×C3×C4C2311yescharacteristic
84C22×C3×C4C2311yescharacteristic
85C22×Dic3C2311yescharacteristic
86C22×Dic3C2311yescharacteristic
87C22×Dic3C2311yescharacteristic
88C22×Dic3C2311yescharacteristic
89C22×Dic3C2311yescharacteristic
90C22×Dic3C2311yescharacteristic
91C2×C4×D3—22no—
92C2×C4×D3—41no—
93C2×C4×D3—41no—
94C2×C4×D3—41no—
95C2×C4×D3—41no—
96C2×C4×D3D414yes—
97C2×Dic6—22no—
98C2×Dic6—41no—
99C2×Dic6—41no—
100C3×C4⋊C4—22no—
101C3×C4⋊C4—41no—
102C3×C4⋊C4—41no—
103C3×C22⋊C4—22no—
104C3×C22⋊C4—41no—
105C3×C22⋊C4—41no—
106#217—22no—
107#217—41no—
108#217—41no—
109(C2×D3)⋊C4—22no—
110(C2×D3)⋊C4—22no—
111(C2×D3)⋊C4—22no—
112(C2×D3)⋊C4—22no—
113(C2×D3)⋊C4—22no—
114(C2×D3)⋊C4—22no—
115(C2×D3)⋊C4—41no—
116(C2×D3)⋊C4—41no—
117(C2×D3)⋊C4—41no—
118(C2×D3)⋊C4—41no—
119C4⋊Dic3—41no—
120C4⋊Dic3—41no—
121Dic3⋊C4—22no—
122Dic3⋊C4—22no—
123Dic3⋊C4—41no—
124Dic3⋊C4—41no—
125C25—31no—
126C22×Q8—31no—
127C23×C4—31no—
128C23×C4—31no—
129C22⋊Q8—64no—
130C2×C4⋊C4—31no—
131C2×C4⋊C4—31no—
132C2×C4⋊C4—31no—
133C2×C4⋊C4—31no—
134C2×C4⋊C4—31no—
135C2×C4⋊C4—31no—
136C2×C4⋊C4C2×D311yescharacteristic, complemented
137C2×C4⋊C4C2×D311yescharacteristic, complemented
138C2×C4⋊C4C2×D311yescharacteristic, complemented
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—64no—
153C2×C22⋊C4C2×D311yescharacteristic
154C2×C22⋊C4C2×D311yescharacteristic
155C2×C22⋊C4C2×D311yescharacteristic
156#95—31no—
157#95—31no—
158#95—31no—
159#95—31no—
160#95—31no—
161#95C2×D311yescharacteristic, complemented
162C23×C3—21no—
163C23×C3—21no—
164C23×C3—21no—
165C23×C3—21no—
166C23×C3—21no—
167C23×C3—21no—
168C23×C3C2×Q812yes—
169C23×C3C2411yescharacteristic
170C22×D3—21no—
171C22×D3—21no—
172C22×D3—21no—
173C22×D3—21no—
174C22×D3—21no—
175C22×D3—21no—
176C22×D3—21no—
177C22×D3—21no—
178C22×D3—21no—
179C22×D3—21no—
180C22×D3—28no—
181C22×D3—44no—
182C22×D3—44no—
183C22×D3—44no—
184C22×D3—44no—
185C22×D3—44no—
186C22×D3—44no—
187C22×D3C2×D412yes—
188C22×D3C2×Q812yes—
189C22×D3C2×Q812yes—
190C22×D3#4112yes—
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×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
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×C4C2×D412yes—
209C2×Dic3—21no—
210C2×Dic3—21no—
211C2×Dic3—21no—
212C2×Dic3—21no—
213C2×Dic3—21no—
214C2×Dic3—21no—
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×Dic3C2×D412yes—
227C4×D3—44no—
228C4×D3—44no—
229Dic6—44no—
230C24—31no—
231C24—31no—
232C24—34no—
233C24—62no—
234C24—62no—
235C24—121no—
236C24—121no—
237C24—121no—
238C24—121no—
239C24C22×D311yescharacteristic
240C2×Q8—62no—
241C2×Q8—121no—
242C2×Q8—121no—
243C22×C4—31no—
244C22×C4—34no—
245C22×C4—31no—
246C22×C4—31no—
247C22×C4—31no—
248C22×C4—31no—
249C22×C4—31no—
250C22×C4—62no—
251C22×C4—121no—
252C22×C4—121no—
253C22×C4—121no—
254C22×C4—121no—
255C22×C4C22×D311yescharacteristic
256C22×C4C22×D311yescharacteristic
257C22×C4C22×D311yescharacteristic
258C22×C4C22×D311yescharacteristic
259C22×C4C22×D311yescharacteristic
260C22×C4C22×D311yescharacteristic
261C4⋊C4—22no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—62no—
265C4⋊C4—62no—
266C4⋊C4—121no—
267C4⋊C4—121no—
268C4⋊C4—121no—
269C4⋊C4—121no—
270C22⋊C4—22no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—62no—
274C22⋊C4—62no—
275C22⋊C4—62no—
276C22⋊C4—62no—
277C22⋊C4—62no—
278C22⋊C4—62no—
279C22⋊C4—62no—
280C22⋊C4—121no—
281C22⋊C4—121no—
282C22⋊C4—121no—
283C22⋊C4—121no—
284C22⋊C4—121no—
285C22⋊C4—121no—
286C22×C3—22no—
287C22×C3—22no—
288C22×C3—22no—
289C22×C3—41no—
290C22×C3—41no—
291C22×C3—41no—
292C22×C3—41no—
293C22×C3C22×D411yescharacteristic
294C22×C3C22×Q811yescharacteristic
295C22×C3C2×#4111yescharacteristic
296C22×C3H(5,𝔽2)11yescharacteristic
297C22×C3H(5,𝔽2)11yescharacteristic
298C22×C3H(5,𝔽2)11yescharacteristic
299C22×C3H(5,𝔽2)11yescharacteristic
300C2×D3—22no—
301C2×D3—22no—
302C2×D3—22no—
303C2×D3—22no—
304C2×D3—22no—
305C2×D3—22no—
306C2×D3—22no—
307C2×D3—22no—
308C2×D3—22no—
309C2×D3—416no—
310C2×D3—41no—
311C2×D3—41no—
312C2×D3—41no—
313C2×D3—41no—
314C2×D3C22⋊Q814yes—
315C3×C4—22no—
316C3×C4—41no—
317C3×C4—41no—
318C3×C4—41no—
319C3×C4—41no—
320C3×C4—41no—
321Dic3—22no—
322Dic3—41no—
323Dic3—41no—
324Dic3—41no—
325Dic3—41no—
326Dic3—41no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—32no—
334C23—32no—
335C23—32no—
336C23—32no—
337C23—68no—
338C23—61no—
339C23—61no—
340C23—61no—
341C23—61no—
342C23—61no—
343C23—61no—
344C23—61no—
345C23—61no—
346C23—61no—
347C23—61no—
348C23—124no—
349C23—124no—
350C23—124no—
351C23—124no—
352C23—124no—
353C23—124no—
354C23D3×Q812yes—
355C23C23×D311yescharacteristic
356Q8—124no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—32no—
375C2×C4—61no—
376C2×C4—61no—
377C2×C4—61no—
378C2×C4—61no—
379C2×C4—61no—
380C2×C4—61no—
381C2×C4—61no—
382C2×C4—61no—
383C2×C4—61no—
384C2×C4—61no—
385C2×C4—61no—
386C2×C4—61no—
387C2×C4—61no—
388C2×C4—61no—
389C2×C4—61no—
390C2×C4—61no—
391C2×C4—61no—
392C2×C4—124no—
393C2×C4—124no—
394C2×C4D3×D412yes—
395C2×C3—42no—
396C2×C3C2×C22⋊Q811yescharacteristic
397C2×C3#53411yescharacteristic
398C2×C3#53511yescharacteristic
399C2×C3#53811yescharacteristic
400C2×C3#53811yescharacteristic
401C2×C3#54311yescharacteristic
402C2×C3#54311yescharacteristic
403D3—24no—
404D3—42no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22—34no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—62no—
414C22—62no—
415C22—62no—
416C22—62no—
417C22—62no—
418C22—62no—
419C22—62no—
420C22—62no—
421C22—62no—
422C22—1216no—
423C22—121no—
424C22—121no—
425C22—121no—
426C22—121no—
427C22C2×D3×D411yescharacteristic
428C22#100411yescharacteristic
429C22#100411yescharacteristic
430C22C2×D3×Q811yescharacteristic
431C22D3×#4111yescharacteristic
432C22#100911yescharacteristic
433C22#100911yescharacteristic
434C4—22no—
435C4—41no—
436C4—41no—
437C4—41no—
438C4—41no—
439C4—41no—
440C4—62no—
441C4—121no—
442C4—121no—
443C4—121no—
444C4—121no—
445C4—121no—
446C3#262611yescharacteristic, complemented, Sylow
447C2—42no—
448C2—64no—
449C2—122no—
450C2#560511yescharacteristic
451C2#560711yescharacteristic
452C2#561311yescharacteristic
453C2D3×C22⋊Q811yescharacteristic
454C2#563411yescharacteristic
455C2#563411yescharacteristic
456C2#570411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#396C2
prime radicalC24×D3C22
hypercenter#396D3
hypocenterC3#2626
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×#896C2semidirect
3. C3×#396C2semidirect
4. #4994C2semidirect
5. #4994C2semidirect
6. #4993C2semidirect
7. #4989C2semidirect
8. #4987C2semidirect
11. #4949C2semidirect
12. #4948C2semidirect
13. #4947C2semidirect
14. #4673C2semidirect
15. #4668C2semidirect
20. C22×Dic6C22semidirect
21. C2×C3×C4⋊C4C22semidirect
22. C2×C3×C4⋊C4C22semidirect
23. C2×C3×C4⋊C4C22semidirect
40. C2×C4⋊Dic3C22semidirect
41. C2×C4⋊Dic3C22semidirect
42. C2×Dic3⋊C4C22semidirect
43. C2×Dic3⋊C4C22semidirect
44. C2×Dic3⋊C4C22semidirect
45. C2×Dic3⋊C4C22semidirect
48. C3×#95C22semidirect
49. C3⋊#95C22semidirect
50. C3⋊#95C22semidirect
51. C3⋊#95C22semidirect
52. C3⋊#95C22semidirect
53. C3⋊#95C22semidirect
61. #396D3semidirect
76. C23×D3Q8semidirect
136. C2×C4⋊C4C2×D3semidirect
137. C2×C4⋊C4C2×D3semidirect
138. C2×C4⋊C4C2×D3semidirect
161. #95C2×D3semidirect
446. C3#2626semidirect

Maximal subgroups

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

subgroupindex
C2×#8962
C2×D3×C22⋊C42
C3×#3962
#49942
#49932
#49892
#49872
#49552
#49492
#49482
#49472
#46732
#46682
#26263