Finite Group Databasebeta

← #79696

Subgroups — #79696

Order 384.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5582C211yesmaximal, characteristic, complemented
2#5545C211yesmaximal, characteristic, complemented
3C3×C4×SD16C211yesmaximal, characteristic, complemented
4#5169C211yesmaximal, characteristic, complemented
5#5165C211yesmaximal, characteristic, complemented
6#5026C211yesmaximal, characteristic, complemented
7#5014C211yesmaximal, characteristic, complemented
8#4870C211yesmaximal, characteristic, complemented
9#4866C211yesmaximal, characteristic, complemented
10#4819C211yesmaximal, characteristic, complemented
11#4814C211yesmaximal, characteristic, complemented
12#4773C211yesmaximal, characteristic
13#4759C211yesmaximal, characteristic, complemented
14C4×D24C211yesmaximal, characteristic, complemented
15#4690C211yesmaximal, characteristic, complemented
16#3118—31nomaximal, Sylow
17C2×D3×D4C2211yescharacteristic
18C2×C3×SD16C2211yescharacteristic
19C3×C4×Q8C2211yescharacteristic, complemented
20C3×C4×D4C2211yescharacteristic
21#947C2211yescharacteristic, complemented
22#946C2211yescharacteristic
23C2×#215C2211yescharacteristic
24D4×Dic3C2211yescharacteristic
25C2×#213C2211yescharacteristic
26C4×#67—21no—
27C2×(C2×D3)⋊C4—21no—
28C2×D24C2211yescharacteristic
29#896—21no—
30#895C2211yescharacteristic
31#894—21no—
32#893C2211yescharacteristic
33#892C2211yescharacteristic
34#888C2211yescharacteristic, complemented
35#67⋊C4—21no—
36D3×C22⋊C4—21no—
37#876—21no—
38#875—21no—
39C4×D12C2211yescharacteristic
40C4×D12C2211yescharacteristic, complemented
41#872C2211yescharacteristic
42C3×#106C2211yescharacteristic, complemented
43C3×#103C2211yescharacteristic, complemented
44C3×#102C2211yescharacteristic
45C3×C4×C8C2211yescharacteristic, complemented
46#835C2211yescharacteristic, complemented
47#832C2211yescharacteristic
48#821C2211yescharacteristic
49#821C2211yescharacteristic, complemented
50(C2×D3)⋊C8C2211yescharacteristic
51(C2×D3)⋊C8C2211yescharacteristic
52#818C2211yescharacteristic, complemented
53Dic3⋊C8C2211yescharacteristic, complemented
54Dic3⋊C8C2211yescharacteristic, complemented
55#809C2211yescharacteristic
56#809C2211yescharacteristic, complemented
57#808C2211yescharacteristic, complemented
58#807C2211yescharacteristic, complemented
59#803C2211yescharacteristic, complemented
60#542—31no—
61#518—31no—
62#485—31no—
63#482—31no—
64#476—31no—
65#474—31no—
66#463—31no—
67#463—31no—
68#450—31no—
69#447—31no—
70#442—31no—
71#440—31no—
72C4×SD16D311yescharacteristic, complemented
73C4×D8—31no—
74#433—31no—
75C23×D3—21no—
76C2×C3×Q8C2311yescharacteristic
77C2×C3×D4C2311yescharacteristic
78C22×C3×C4—21no—
79C2×#67—21no—
80C22×Dic3—21no—
81D3×D4—22no—
82D3×D4—22no—
83C2×D12—21no—
84C2×D12C2311yescharacteristic
85C2×D12C2311yescharacteristic
86C2×C4×D3—21no—
87C2×C4×D3—21no—
88C2×C4×D3—21no—
89C2×C4×D3C2311yescharacteristic
90C2×Dic6—21no—
91C3×SD16—22no—
92C2×C3×C8C2311yescharacteristic
93C2×C3×C8C2311yescharacteristic
94C3×C4⋊C4—21no—
95C3×C4⋊C4C2311yescharacteristic
96C3×C4⋊C4C2311yescharacteristic
97C3×C22⋊C4—21no—
98C3×C42—21no—
99C3×C42C2311yescharacteristic
100#217—21no—
101#215—22no—
102#213—22no—
103(C2×D3)⋊C4—21no—
104(C2×D3)⋊C4—21no—
105(C2×D3)⋊C4—21no—
106(C2×D3)⋊C4—21no—
107(C2×D3)⋊C4—21no—
108(C2×D3)⋊C4—21no—
109(C2×D3)⋊C4—21no—
110(C2×D3)⋊C4—21no—
111(C2×D3)⋊C4D411yescharacteristic
112(C2×D3)⋊C4D411yescharacteristic
113C4⋊Dic3C2311yescharacteristic
114C4⋊Dic3C2311yescharacteristic
115Dic3⋊C4—21no—
116Dic3⋊C4—21no—
117Dic3⋊C4D411yescharacteristic
118Dic3⋊C4D411yescharacteristic
119C4×Dic3—21no—
120C4×Dic3C2311yescharacteristic
121C2×C3⋊C8C2311yescharacteristic
122C2×C3⋊C8C2311yescharacteristic
123D24—22no—
124C22×D4—31no—
125C2×SD16—31no—
126C2×SD16C2×D311yescharacteristic
127C2×D8—31no—
128C2×D8—31no—
129C4⋊Q8—31no—
130#126—61no—
131#124—31no—
132#124—61no—
133#123—61no—
134C22⋊Q8—31no—
135C22⋊Q8—61no—
136#121—31no—
137C4×Q8C2×D311yescharacteristic, complemented
138C4×D4—31no—
139C4×D4—31no—
140C4×D4—31no—
141C4×D4—31no—
142C4×D4—61no—
143C4×D4—61no—
144C4×D4C2×D311yescharacteristic
145#117—31no—
146#117—31no—
147C2×C22⋊C4—61no—
148C2×C22⋊C4—61no—
149#107—31no—
150#107—31no—
151#106—31no—
152#106C2×D311yescharacteristic, complemented
153C4⋊C8—31no—
154C4⋊C8—31no—
155#103—31no—
156#103C2×D311yescharacteristic, complemented
157#102—31no—
158#102—31no—
159#102—31no—
160#102—31no—
161#102—31no—
162#102C2×D311yescharacteristic
163C22⋊C8—31no—
164C22⋊C8—31no—
165#97—31no—
166C4×C8C2×D311yescharacteristic, complemented
167C23×C3—21no—
168C22×D3—21no—
169C22×D3—24no—
170C22×D3—21no—
171C22×D3—81no—
172C22×D3—81no—
173C22×D3C2×D411yescharacteristic
174C3×Q8—21no—
175C3×Q8—21no—
176C3×D4—21no—
177C3×D4#4112yes—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—81no—
182C2×C3×C4C2×D411yescharacteristic
183C2×C3×C4C2×D411yescharacteristic
184C2×C3×C4C2411yescharacteristic
185#67—24no—
186C2×Dic3—21no—
187C2×Dic3—21no—
188C2×Dic3—81no—
189C2×Dic3C2×D411yescharacteristic
190C2×Dic3C2×D411yescharacteristic
191C2×Dic3C2×D411yescharacteristic
192D12—21no—
193D12—21no—
194D12—21no—
195D12—81no—
196D12#4112yes—
197C4×D3—21no—
198C4×D3—21no—
199C4×D3—81no—
200C4×D3—81no—
201C4×D3—81no—
202Dic6—81no—
203C3×C8—21no—
204C3×C8—21no—
205C3⋊C8—21no—
206C3⋊C8—21no—
207C24—61no—
208C2×Q8—61no—
209C2×Q8C22×D311yescharacteristic
210C2×D4—31no—
211C2×D4—31no—
212C2×D4—61no—
213C2×D4—61no—
214C2×D4—62no—
215C2×D4—62no—
216C2×D4C22×D311yescharacteristic
217C22×C4—21no—
218C22×C4—31no—
219C22×C4—61no—
220C22×C4—61no—
221C22×C4—61no—
222C22×C4—61no—
223SD16—22no—
224SD16—62no—
225D8—62no—
226D8—62no—
227C2×C8—31no—
228C2×C8—31no—
229C2×C8C22×D311yescharacteristic
230C2×C8C22×D311yescharacteristic
231C4⋊C4—21no—
232C4⋊C4—31no—
233C4⋊C4—31no—
234C4⋊C4—31no—
235C4⋊C4—31no—
236C4⋊C4—61no—
237C4⋊C4—61no—
238C4⋊C4C22×D311yescharacteristic
239C4⋊C4C22×D311yescharacteristic
240C22⋊C4—21no—
241C22⋊C4—31no—
242C22⋊C4—31no—
243C22⋊C4—61no—
244C22⋊C4—61no—
245C22⋊C4—61no—
246C22⋊C4—61no—
247C22⋊C4—61no—
248C22⋊C4—61no—
249C22⋊C4—61no—
250C22⋊C4—61no—
251C22⋊C4—61no—
252C42—21no—
253C42—31no—
254C42—61no—
255C42C22×D311yescharacteristic
256C22×C3—22no—
257C22×C3—41no—
258C22×C3—41no—
259C22×C3C22×D411yescharacteristic
260C2×D3—21no—
261C2×D3—22no—
262C2×D3—21no—
263C2×D3—21no—
264C2×D3—41no—
265C2×D3—41no—
266C2×D3—41no—
267C2×D3—41no—
268C2×D3—41no—
269C2×D3—84no—
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—41no—
273C3×C4—41no—
274C3×C4—41no—
275C3×C4C2×#4111yescharacteristic
276C3×C4C2×#4111yescharacteristic
277Dic3—21no—
278Dic3—21no—
279Dic3—21no—
280Dic3—41no—
281Dic3—41no—
282C23—21no—
283C23—31no—
284C23—64no—
285C23—61no—
286C23—61no—
287C23—241no—
288C23—241no—
289Q8—21no—
290Q8—21no—
291Q8—241no—
292D4—21no—
293D4—32no—
294D4—64no—
295D4—61no—
296D4—61no—
297D4—61no—
298D4—241no—
299D4#23512yes—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—31no—
304C2×C4—31no—
305C2×C4—31no—
306C2×C4—61no—
307C2×C4—61no—
308C2×C4—61no—
309C2×C4—61no—
310C2×C4—81no—
311C2×C4—241no—
312C2×C4—241no—
313C2×C4—241no—
314C2×C4—241no—
315C2×C4D3×D411yescharacteristic
316C2×C4D3×D411yescharacteristic
317C2×C4C23×D311yescharacteristic
318C8—21no—
319C8—21no—
320C8—61no—
321C8—61no—
322C2×C3—42no—
323C2×C3#52511yescharacteristic
324C2×C3#57611yescharacteristic
325C2×C3#57711yescharacteristic
326D3—41no—
327D3—42no—
328D3—81no—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—61no—
333C22—61no—
334C22—61no—
335C22—62no—
336C22—121no—
337C22—121no—
338C22—121no—
339C22—121no—
340C22—121no—
341C22—244no—
342C22C2×D3×D411yescharacteristic
343C4—21no—
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—61no—
349C4—61no—
350C4—61no—
351C4—121no—
352C4—121no—
353C4C2×#23511yescharacteristic
354C4D3×#4111yescharacteristic
355C3#311811yescharacteristic, complemented, Sylow
356C2—42no—
357C2—121no—
358C2—122no—
359C2—241no—
360C2#554711yescharacteristic
361C2#576211yescharacteristic
362C2#576911yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×C4×SD16C2
socleC22×C3C22×D4
prime radical#4773C2
hypercenterC4×SD16D3
hypocenterC3#3118
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #5582C2semidirect
2. #5545C2semidirect
3. C3×C4×SD16C2semidirect
4. #5169C2semidirect
5. #5165C2semidirect
6. #5026C2semidirect
7. #5014C2semidirect
8. #4870C2semidirect
9. #4866C2semidirect
10. #4819C2semidirect
11. #4814C2semidirect
13. #4759C2semidirect
14. C4×D24C2semidirect
15. #4690C2semidirect
19. C3×C4×Q8C22semidirect
21. #947C22semidirect
34. #888C22semidirect
40. C4×D12C22semidirect
42. C3×#106C22semidirect
43. C3×#103C22semidirect
45. C3×C4×C8C22semidirect
46. #835C22semidirect
49. #821C22semidirect
52. #818C22semidirect
53. Dic3⋊C8C22semidirect
54. Dic3⋊C8C22semidirect
56. #809C22semidirect
57. #808C22semidirect
58. #807C22semidirect
59. #803C22semidirect
72. C4×SD16D3semidirect
137. C4×Q8C2×D3semidirect
152. #106C2×D3semidirect
156. #103C2×D3semidirect
166. C4×C8C2×D3semidirect
355. C3#3118semidirect

Maximal subgroups

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

subgroupindex
#55822
#55452
C3×C4×SD162
#51692
#51652
#50262
#50142
#48702
#48662
#48192
#48142
#47732
#47592
C4×D242
#46902
#31183