Finite Group Databasebeta

← #81522

Subgroups — #81522

Order 384.

420 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×C22⋊Q8C211yesmaximal, characteristic, complemented
2#5524C211yesmaximal, characteristic
3C3×#485C211yesmaximal, characteristic, complemented
4#5047C211yesmaximal, characteristic, complemented
5#4996C211yesmaximal, characteristic, complemented
6#4887C211yesmaximal, characteristic, complemented
7#4882C211yesmaximal, characteristic, complemented
8#4864C211yesmaximal, characteristic, complemented
9#4862C211yesmaximal, characteristic, complemented
10#4813C211yesmaximal, characteristic, complemented
11#4809C211yesmaximal, characteristic, complemented
12#4807C211yesmaximal, characteristic, complemented
13#4806C211yesmaximal, characteristic, complemented
14#4733C211yesmaximal, characteristic, complemented
15D3×C22⋊C8C211yesmaximal, characteristic, complemented
16#3190—31nomaximal, Sylow
17C2×D3×Q8C2211yescharacteristic
18C2×#235C2211yescharacteristic
19C22×C4×D3C2211yescharacteristic
20C3×C22⋊Q8C2211yescharacteristic
21C3×#117C2211yescharacteristic
22#946C2211yescharacteristic
23C2×#216C2211yescharacteristic, complemented
24C2×#215C2211yescharacteristic, complemented
25#924C2211yescharacteristic
26C2×Dic12C2211yescharacteristic, complemented
27C2×#204C2211yescharacteristic, complemented
28C2×D3×C8C2211yescharacteristic
29C2×D3×C8C2211yescharacteristic
30#897C2211yescharacteristic
31#897C2211yescharacteristic
32#897C2211yescharacteristic
33#896—21no—
34#895C2211yescharacteristic
35#895C2211yescharacteristic
36D3×C4⋊C4—21no—
37D3×C4⋊C4C2211yescharacteristic
38#886—21no—
39#882—21no—
40D3×C22⋊C4—21no—
41#878—21no—
42C4×D12—21no—
43C4×D12—21no—
44C3×#107C2211yescharacteristic, complemented
45C3×#106C2211yescharacteristic, complemented
46C3×#103C2211yescharacteristic, complemented
47C3×#103C2211yescharacteristic, complemented
48C3×C22⋊C8C2211yescharacteristic
49#830C2211yescharacteristic
50#821C2211yescharacteristic, complemented
51(C2×D3)⋊C8C2211yescharacteristic
52(C2×D3)⋊C8C2211yescharacteristic
53#816C2211yescharacteristic, complemented
54#810C2211yescharacteristic, complemented
55#810C2211yescharacteristic, complemented
56#810C2211yescharacteristic, complemented
57#809C2211yescharacteristic, complemented
58#808C2211yescharacteristic, complemented
59#807C2211yescharacteristic, complemented
60#525—31no—
61C2×C22⋊Q8—31no—
62#485—31no—
63#485D311yescharacteristic, complemented
64#483—31no—
65#480—31no—
66#467—31no—
67#467—31no—
68#465—31no—
69#465—31no—
70#452—31no—
71#452—31no—
72#451—31no—
73#448—31no—
74C2×C22⋊C8—31no—
75C23×D3D411yescharacteristic
76C2×C3×Q8C2311yescharacteristic
77C22×C3×C4C2311yescharacteristic
78C2×#67—21no—
79C22×Dic3D411yescharacteristic
80D3×Q8—41no—
81D3×Q8—41no—
82#235—41no—
83#235—41no—
84C2×D12—21no—
85C2×D12—21no—
86C2×D12C2311yescharacteristic
87C2×C4×D3—21no—
88C2×C4×D3—21no—
89C2×C4×D3—21no—
90C2×C4×D3—41no—
91C2×C4×D3—41no—
92C2×C4×D3D411yescharacteristic
93C2×C4×D3D411yescharacteristic
94C2×C4×D3C2311yescharacteristic
95C2×C4×D3C2311yescharacteristic
96C2×Dic6—21no—
97C2×Dic6C2311yescharacteristic
98C2×Dic6C2311yescharacteristic
99C2×C3×C8C2311yescharacteristic
100C2×C3×C8C2311yescharacteristic
101C3×C4⋊C4—21no—
102C3×C4⋊C4C2311yescharacteristic
103C3×C4⋊C4C2311yescharacteristic
104C3×C4⋊C4C2311yescharacteristic
105C3×C22⋊C4—21no—
106C3×C22⋊C4—21no—
107C3×C42—21no—
108#217—21no—
109#216—41no—
110#215—41no—
111(C2×D3)⋊C4—21no—
112(C2×D3)⋊C4—21no—
113(C2×D3)⋊C4—21no—
114(C2×D3)⋊C4—21no—
115(C2×D3)⋊C4—21no—
116(C2×D3)⋊C4—21no—
117C4⋊Dic3—21no—
118C4⋊Dic3—21no—
119C4⋊Dic3—21no—
120C4⋊Dic3C2311yescharacteristic
121Dic3⋊C4—21no—
122Dic3⋊C4—21no—
123Dic3⋊C4—21no—
124C2×C3⋊C8C2311yescharacteristic
125C2×C3⋊C8C2311yescharacteristic
126Dic12—41no—
127#204—41no—
128D3×C8—41no—
129D3×C8—41no—
130C2×#41—31no—
131C22×Q8—31no—
132C23×C4—31no—
133C2×Q16—31no—
134C2×Q16—31no—
135C2×SD16—31no—
136C2×SD16—31no—
137C22×C8—31no—
138C22×C8—31no—
139#123—61no—
140C22⋊Q8—31no—
141C22⋊Q8—31no—
142C22⋊Q8—31no—
143C22⋊Q8—31no—
144C22⋊Q8—31no—
145C22⋊Q8—61no—
146C22⋊Q8—61no—
147C22⋊Q8C2×D311yescharacteristic
148#121—31no—
149#121—31no—
150#120—61no—
151C4×D4—61no—
152C4×D4—61no—
153#117C2×D311yescharacteristic
154C2×C4⋊C4—31no—
155C2×C4⋊C4—61no—
156C2×C22⋊C4—61no—
157#107—31no—
158#107C2×D311yescharacteristic, complemented
159#106—31no—
160#106C2×D311yescharacteristic, complemented
161#103—31no—
162#103—31no—
163#103—31no—
164#103—31no—
165#103C2×D311yescharacteristic, complemented
166#103C2×D311yescharacteristic, complemented
167#102—31no—
168#102—31no—
169C22⋊C8—31no—
170C22⋊C8—31no—
171C22⋊C8—31no—
172C22⋊C8C2×D311yescharacteristic
173C23×C3C2×D411yescharacteristic
174C22×D3—22no—
175C22×D3—22no—
176C22×D3—21no—
177C22×D3—41no—
178C22×D3C2×D411yescharacteristic
179C22×D3C2×D411yescharacteristic
180C3×Q8—21no—
181C3×Q8—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×C4C2×D411yescharacteristic
189C2×C3×C4C2411yescharacteristic
190#67—42no—
191C2×Dic3—21no—
192C2×Dic3—21no—
193C2×Dic3—21no—
194C2×Dic3—41no—
195C2×Dic3C2×D411yescharacteristic
196C2×Dic3C2×D411yescharacteristic
197D12—21no—
198D12—21no—
199D12—42no—
200D12—42no—
201C4×D3—21no—
202C4×D3—21no—
203C4×D3—21no—
204C4×D3—21no—
205C4×D3—41no—
206C4×D3—41no—
207C4×D3—42no—
208C4×D3—42no—
209C4×D3—42no—
210Dic6—21no—
211Dic6—21no—
212Dic6—21no—
213Dic6—21no—
214Dic6—42no—
215C3×C8—21no—
216C3×C8—21no—
217C3⋊C8—21no—
218C3⋊C8—21no—
219C24—31no—
220#41—121no—
221#41—121no—
222C2×Q8—31no—
223C2×Q8—31no—
224C2×Q8—61no—
225C2×Q8—121no—
226C2×Q8—121no—
227C2×Q8C22×D311yescharacteristic
228C2×D4—31no—
229C2×D4—61no—
230C2×D4—61no—
231C2×D4—61no—
232C22×C4—31no—
233C22×C4—31no—
234C22×C4—31no—
235C22×C4—31no—
236C22×C4—31no—
237C22×C4—61no—
238C22×C4—61no—
239C22×C4—61no—
240C22×C4—121no—
241C22×C4—121no—
242C22×C4C22×D311yescharacteristic
243Q16—121no—
244Q16—121no—
245SD16—121no—
246SD16—121no—
247C2×C8—31no—
248C2×C8—31no—
249C2×C8—121no—
250C2×C8—121no—
251C2×C8C22×D311yescharacteristic
252C2×C8C22×D311yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—31no—
255C4⋊C4—61no—
256C4⋊C4—61no—
257C4⋊C4—61no—
258C4⋊C4—61no—
259C4⋊C4—61no—
260C4⋊C4—61no—
261C4⋊C4C22×D311yescharacteristic
262C4⋊C4C22×D311yescharacteristic
263C4⋊C4C22×D311yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—61no—
267C22⋊C4—61no—
268C22⋊C4—61no—
269C22⋊C4—61no—
270C22⋊C4—61no—
271C22⋊C4—61no—
272C22⋊C4—61no—
273C42—21no—
274C22×C3—21no—
275C22×C3—21no—
276C22×C3—21no—
277C22×C3C22×D411yescharacteristic
278C2×D3—21no—
279C2×D3—21no—
280C2×D3—21no—
281C2×D3—21no—
282C2×D3—44no—
283C2×D3—41no—
284C2×D3—41no—
285C2×D3—41no—
286C2×D3#13512yes—
287C2×D3#13712yes—
288C3×C4—21no—
289C3×C4—41no—
290C3×C4—41no—
291C3×C4—41no—
292C3×C4—41no—
293C3×C4H(5,𝔽2)11yescharacteristic
294C3×C4H(5,𝔽2)11yescharacteristic
295Dic3—21no—
296Dic3—21no—
297Dic3—41no—
298Dic3—41no—
299Dic3—41no—
300C23—31no—
301C23—31no—
302C23—62no—
303C23—62no—
304C23—61no—
305C23—121no—
306C23D3×D411yescharacteristic
307Q8—21no—
308Q8—21no—
309Q8—61no—
310Q8—61no—
311Q8—61no—
312Q8—61no—
313Q8—122no—
314D4—61no—
315D4—61no—
316D4—122no—
317D4—122no—
318D4—122no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—31no—
326C2×C4—31no—
327C2×C4—61no—
328C2×C4—61no—
329C2×C4—61no—
330C2×C4—61no—
331C2×C4—61no—
332C2×C4—61no—
333C2×C4—61no—
334C2×C4—121no—
335C2×C4—121no—
336C2×C4—122no—
337C2×C4—122no—
338C2×C4—122no—
339C2×C4—121no—
340C2×C4D3×D411yescharacteristic
341C2×C4C23×D311yescharacteristic
342C8—21no—
343C8—21no—
344C8—61no—
345C8—61no—
346C2×C3—41no—
347C2×C3#53411yescharacteristic
348C2×C3C2×#13511yescharacteristic
349C2×C3C2×#13711yescharacteristic
350D3—22no—
351D3—22no—
352D3—81no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—32no—
357C22—32no—
358C22—61no—
359C22—61no—
360C22—61no—
361C22—61no—
362C22—124no—
363C22—121no—
364C22—121no—
365C22—121no—
366C22C2×D3×D411yescharacteristic
367C4—21no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—61no—
373C4—61no—
374C4—121no—
375C4—121no—
376C4—121no—
377C4#100911yescharacteristic
378C4#100911yescharacteristic
379C3#319011yescharacteristic, complemented, Sylow
380C2—41no—
381C2—62no—
382C2—62no—
383C2—241no—
384C2#565311yescharacteristic
385C2D3×#13511yescharacteristic
386C2D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#485C2
socleC22×C3C22×D4
prime radical#5524C2
hypercenter#485D3
hypocenterC3#3190
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. D3×C22⋊Q8C2semidirect
3. C3×#485C2semidirect
4. #5047C2semidirect
5. #4996C2semidirect
6. #4887C2semidirect
7. #4882C2semidirect
8. #4864C2semidirect
9. #4862C2semidirect
10. #4813C2semidirect
11. #4809C2semidirect
12. #4807C2semidirect
13. #4806C2semidirect
14. #4733C2semidirect
15. D3×C22⋊C8C2semidirect
23. C2×#216C22semidirect
24. C2×#215C22semidirect
26. C2×Dic12C22semidirect
27. C2×#204C22semidirect
44. C3×#107C22semidirect
45. C3×#106C22semidirect
46. C3×#103C22semidirect
47. C3×#103C22semidirect
50. #821C22semidirect
53. #816C22semidirect
54. #810C22semidirect
55. #810C22semidirect
56. #810C22semidirect
57. #809C22semidirect
58. #808C22semidirect
59. #807C22semidirect
63. #485D3semidirect
158. #107C2×D3semidirect
160. #106C2×D3semidirect
165. #103C2×D3semidirect
166. #103C2×D3semidirect
379. C3#3190semidirect

Maximal subgroups

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

subgroupindex
D3×C22⋊Q82
#55242
C3×#4852
#50472
#49962
#48872
#48822
#48642
#48622
#48132
#48092
#48072
#48062
#47332
D3×C22⋊C82
#31903