Finite Group Databasebeta

← #81398

Subgroups — #81398

Order 384.

418 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5606C211yesmaximal, characteristic, complemented
2#5524C211yesmaximal, characteristic, complemented
3C3×#482C211yesmaximal, characteristic, complemented
4#5037C211yesmaximal, characteristic, complemented
5#4996C211yesmaximal, characteristic, complemented
6#4888C211yesmaximal, characteristic, complemented
7#4886C211yesmaximal, characteristic, complemented
8#4867C211yesmaximal, characteristic, complemented
9#4866C211yesmaximal, characteristic, complemented
10#4783C211yesmaximal, characteristic, complemented
11#4782C211yesmaximal, characteristic, complemented
12#4781C211yesmaximal, characteristic, complemented
13#4780C211yesmaximal, characteristic, complemented
14#4733C211yesmaximal, characteristic, complemented
15#4726C211yesmaximal, characteristic, complemented
16#3197—31nomaximal, Sylow
17C2×#237C2211yescharacteristic
18C2×#235C2211yescharacteristic
19C22×C4×D3C2211yescharacteristic
20C3×#121C2211yescharacteristic
21C3×#117C2211yescharacteristic
22#938C2211yescharacteristic
23#937—21no—
24D4×Dic3—21no—
25C2×#214C2211yescharacteristic, complemented
26C2×#213C2211yescharacteristic, complemented
27#924C2211yescharacteristic
28C2×Dic12C2211yescharacteristic, complemented
29C2×#204C2211yescharacteristic, complemented
30C2×ΓL(1,𝔽25)C2211yescharacteristic
31C2×ΓL(1,𝔽25)C2211yescharacteristic
32#897C2211yescharacteristic
33#897C2211yescharacteristic
34#897C2211yescharacteristic
35#895C2211yescharacteristic
36#895C2211yescharacteristic
37#892C2211yescharacteristic
38#886—21no—
39#883—21no—
40#882—21no—
41#67⋊C4—21no—
42C4×D12—21no—
43C4×D12—21no—
44C3×#107C2211yescharacteristic, complemented
45C3×#106C2211yescharacteristic, complemented
46C3×#102C2211yescharacteristic, complemented
47C3×#102C2211yescharacteristic, 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—
61#525—31no—
62#485—31no—
63#485—31no—
64#482—31no—
65#482D311yescharacteristic, complemented
66#470—31no—
67#469—31no—
68#468—31no—
69#468—31no—
70#452—31no—
71#452—31no—
72#449—31no—
73#449—31no—
74#407—31no—
75C23×D3D411yescharacteristic
76C2×C3×D4—21no—
77C2×C3×D4C2311yescharacteristic
78C22×C3×C4C2311yescharacteristic
79C2×#67—21no—
80C2×#67—21no—
81C2×#67—21no—
82C22×Dic3—21no—
83C22×Dic3D411yescharacteristic
84#237—41no—
85#237—41no—
86#235—41no—
87#235—41no—
88C2×D12—21no—
89C2×D12—21no—
90C2×D12C2311yescharacteristic
91C2×C4×D3—21no—
92C2×C4×D3—41no—
93C2×C4×D3—41no—
94C2×C4×D3D411yescharacteristic
95C2×C4×D3D411yescharacteristic
96C2×C4×D3C2311yescharacteristic
97C2×C4×D3C2311yescharacteristic
98C2×Dic6C2311yescharacteristic
99C2×Dic6C2311yescharacteristic
100C2×C3×C8C2311yescharacteristic
101C2×C3×C8C2311yescharacteristic
102C3×C4⋊C4C2311yescharacteristic
103C3×C4⋊C4C2311yescharacteristic
104C3×C4⋊C4C2311yescharacteristic
105C3×C22⋊C4—21no—
106C3×C22⋊C4—21no—
107C3×C42—21no—
108#217—21no—
109#217—21no—
110#214—41no—
111#213—41no—
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—
117(C2×D3)⋊C4—21no—
118C4⋊Dic3—21no—
119C4⋊Dic3—21no—
120C4⋊Dic3—21no—
121C4⋊Dic3C2311yescharacteristic
122Dic3⋊C4—21no—
123C4×Dic3—21no—
124C2×C3⋊C8C2311yescharacteristic
125C2×C3⋊C8C2311yescharacteristic
126Dic12—41no—
127#204—41no—
128ΓL(1,𝔽25)—41no—
129ΓL(1,𝔽25)—41no—
130C2×#41—31no—
131C2×#41—31no—
132C23×C4—31no—
133C2×Q16—31no—
134C2×SD16—31no—
135C2×SD16—31no—
136C2×D8—31no—
137C2×M16—31no—
138C2×M16—31no—
139#123—61no—
140#123—61no—
141C22⋊Q8—31no—
142C22⋊Q8—31no—
143C22⋊Q8—31no—
144C22⋊Q8—31no—
145#121—31no—
146#121—31no—
147#121—31no—
148#121C2×D311yescharacteristic
149#120—61no—
150#120—61no—
151C4×D4—61no—
152C4×D4—61no—
153C4×D4—61no—
154C4×D4—61no—
155#117—31no—
156#117C2×D311yescharacteristic
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#102—31no—
166#102—31no—
167#102C2×D311yescharacteristic, complemented
168#102C2×D311yescharacteristic, complemented
169C22⋊C8—31no—
170C22⋊C8—31no—
171C22⋊C8—31no—
172C22⋊C8C2×D311yescharacteristic
173C23×C3—21no—
174C23×C3C2×D411yescharacteristic
175C22×D3—21no—
176C22×D3—41no—
177C22×D3—41no—
178C22×D3—41no—
179C22×D3C2×D411yescharacteristic
180C22×D3C2×D411yescharacteristic
181C3×D4—21no—
182C3×D4—21no—
183C3×D4—42no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4C2×D411yescharacteristic
190C2×C3×C4C2411yescharacteristic
191#67—42no—
192#67—42no—
193#67—42no—
194C2×Dic3—21no—
195C2×Dic3—21no—
196C2×Dic3—21no—
197C2×Dic3—41no—
198C2×Dic3—42no—
199C2×Dic3C2×D411yescharacteristic
200C2×Dic3C2×D411yescharacteristic
201D12—21no—
202D12—21no—
203D12—42no—
204D12—42no—
205C4×D3—21no—
206C4×D3—21no—
207C4×D3—21no—
208C4×D3—21no—
209C4×D3—41no—
210C4×D3—41no—
211C4×D3—42no—
212Dic6—21no—
213Dic6—21no—
214Dic6—21no—
215Dic6—21no—
216C3×C8—21no—
217C3×C8—21no—
218C3⋊C8—21no—
219C3⋊C8—21no—
220C24—31no—
221#41—121no—
222#41—121no—
223#41—121no—
224#41—121no—
225C2×Q8—31no—
226C2×Q8—31no—
227C2×D4—21no—
228C2×D4—31no—
229C2×D4—61no—
230C2×D4—61no—
231C2×D4—61no—
232C2×D4—61no—
233C2×D4—61no—
234C2×D4C22×D311yescharacteristic
235C22×C4—31no—
236C22×C4—31no—
237C22×C4—31no—
238C22×C4—31no—
239C22×C4—31no—
240C22×C4—61no—
241C22×C4—61no—
242C22×C4—121no—
243C22×C4—121no—
244C22×C4C22×D311yescharacteristic
245Q16—121no—
246SD16—121no—
247SD16—121no—
248D8—121no—
249M16—121no—
250M16—121no—
251C2×C8—31no—
252C2×C8—31no—
253C2×C8C22×D311yescharacteristic
254C2×C8C22×D311yescharacteristic
255C4⋊C4—31no—
256C4⋊C4—61no—
257C4⋊C4—61no—
258C4⋊C4—61no—
259C4⋊C4—61no—
260C4⋊C4C22×D311yescharacteristic
261C4⋊C4C22×D311yescharacteristic
262C4⋊C4C22×D311yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—21no—
265C22⋊C4—61no—
266C22⋊C4—61no—
267C22⋊C4—61no—
268C22⋊C4—61no—
269C22⋊C4—61no—
270C22⋊C4—61no—
271C22⋊C4—61no—
272C22⋊C4—61no—
273C42—21no—
274C42—61no—
275C22×C3—21no—
276C22×C3—21no—
277C22×C3—21no—
278C22×C3—41no—
279C22×C3—41no—
280C22×C3—41no—
281C22×C3C22×D411yescharacteristic
282C2×D3—21no—
283C2×D3—21no—
284C2×D3—21no—
285C2×D3—21no—
286C2×D3—21no—
287C2×D3—21no—
288C2×D3—44no—
289C2×D3—41no—
290C2×D3—41no—
291C2×D3—41no—
292C3×C4—21no—
293C3×C4—41no—
294C3×C4—41no—
295C3×C4—41no—
296C3×C4H(5,𝔽2)11yescharacteristic
297C3×C4H(5,𝔽2)11yescharacteristic
298Dic3—21no—
299Dic3—21no—
300Dic3—41no—
301Dic3—41no—
302Dic3—41no—
303C23—21no—
304C23—31no—
305C23—31no—
306C23—61no—
307C23—121no—
308C23—121no—
309C23—121no—
310C23D3×D411yescharacteristic
311Q8—61no—
312Q8—61no—
313Q8—61no—
314Q8—61no—
315D4—21no—
316D4—21no—
317D4—42no—
318D4—61no—
319D4—61no—
320D4—122no—
321D4—122no—
322D4—122no—
323D4—122no—
324D4—122no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—31no—
331C2×C4—31no—
332C2×C4—61no—
333C2×C4—61no—
334C2×C4—61no—
335C2×C4—61no—
336C2×C4—61no—
337C2×C4—61no—
338C2×C4—61no—
339C2×C4—121no—
340C2×C4—121no—
341C2×C4—122no—
342C2×C4—121no—
343C2×C4—122no—
344C2×C4D3×D411yescharacteristic
345C2×C4C23×D311yescharacteristic
346C8—21no—
347C8—21no—
348C8—61no—
349C8—61no—
350C2×C3—41no—
351C2×C3—81no—
352C2×C3#53411yescharacteristic
353C2×C3#57511yescharacteristic
354C2×C3#57511yescharacteristic
355D3—41no—
356D3—41no—
357D3—81no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—61no—
365C22—61no—
366C22—61no—
367C22—61no—
368C22—61no—
369C22—61no—
370C22—124no—
371C22—121no—
372C22—121no—
373C22—121no—
374C22C2×D3×D411yescharacteristic
375C4—21no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—61no—
380C4—61no—
381C4—121no—
382C4—121no—
383C4—121no—
384C4#100911yescharacteristic
385C4#100911yescharacteristic
386C3#319711yescharacteristic, complemented, Sylow
387C2—41no—
388C2—81no—
389C2—121no—
390C2—121no—
391C2—241no—
392C2#565311yescharacteristic
393C2#576811yescharacteristic
394C2#577311yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#482C2
socleC22×C3C22×D4
hypercenter#482D3
hypocenterC3#3197
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #5606C2semidirect
2. #5524C2semidirect
3. C3×#482C2semidirect
4. #5037C2semidirect
5. #4996C2semidirect
6. #4888C2semidirect
7. #4886C2semidirect
8. #4867C2semidirect
9. #4866C2semidirect
10. #4783C2semidirect
11. #4782C2semidirect
12. #4781C2semidirect
13. #4780C2semidirect
14. #4733C2semidirect
15. #4726C2semidirect
25. C2×#214C22semidirect
26. C2×#213C22semidirect
28. C2×Dic12C22semidirect
29. C2×#204C22semidirect
44. C3×#107C22semidirect
45. C3×#106C22semidirect
46. C3×#102C22semidirect
47. C3×#102C22semidirect
50. #821C22semidirect
53. #816C22semidirect
54. #810C22semidirect
55. #810C22semidirect
56. #810C22semidirect
57. #809C22semidirect
58. #808C22semidirect
59. #807C22semidirect
65. #482D3semidirect
158. #107C2×D3semidirect
160. #106C2×D3semidirect
167. #102C2×D3semidirect
168. #102C2×D3semidirect
386. C3#3197semidirect

Maximal subgroups

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

subgroupindex
#56062
#55242
C3×#4822
#50372
#49962
#48882
#48862
#48672
#48662
#47832
#47822
#47812
#47802
#47332
#47262
#31973