Finite Group Databasebeta

← #80014

Subgroups — #80014

Order 384.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#67C211yesmaximal, characteristic, complemented
2#5611C211yesmaximal, characteristic, complemented
3C3×#447C211yesmaximal, characteristic, complemented
4C2×#832C211yesmaximal, characteristic, complemented
5#5157C211yesmaximal, characteristic, complemented
6#5156C211yesmaximal, characteristic, complemented
7#5150C211yesmaximal, characteristic, complemented
8Dic3×D8C211yesmaximal, characteristic, complemented
9#5038C211yesmaximal, characteristic, complemented
10#4774C211yesmaximal, characteristic, complemented
11D3×#102C211yesmaximal, characteristic, complemented
12#4760C211yesmaximal, characteristic, complemented
13#4759C211yesmaximal, characteristic, complemented
14#4736C211yesmaximal, characteristic, complemented
15#67⋊C8C211yesmaximal, characteristic, complemented
16#3294—31nomaximal, Sylow
17C22×C3×D4C2211yescharacteristic
18C22×#67—21no—
19C2×#237—21no—
20C2×D3×D4C2211yescharacteristic
21C2×C3×D8C2211yescharacteristic
22C2×C3×D8C2211yescharacteristic, complemented
23C3×#121C2211yescharacteristic, complemented
24#953—21no—
25#940C2211yescharacteristic
26#939—21no—
27#938C2211yescharacteristic
28#938C2211yescharacteristic, complemented
29#937—21no—
30#935—21no—
31D4×Dic3C2211yescharacteristic
32D4×Dic3C2211yescharacteristic, complemented
33C2×#213C2211yescharacteristic, complemented
34#930C2211yescharacteristic
35C4×#67C2211yescharacteristic
36C2×C4⋊Dic3C2211yescharacteristic, complemented
37C22×C3⋊C8C2211yescharacteristic, complemented
38C2×D3×C8C2211yescharacteristic, complemented
39D3×C4⋊C4C2211yescharacteristic, complemented
40#888C2211yescharacteristic, complemented
41#883—21no—
42#878—21no—
43C3×#102C2211yescharacteristic
44C3×#102C2211yescharacteristic, complemented
45C3×C22⋊C8C2211yescharacteristic, complemented
46#832C2211yescharacteristic
47#832C2211yescharacteristic
48#832C2211yescharacteristic, complemented
49#832C2211yescharacteristic, complemented
50#832C2211yescharacteristic, complemented
51#821C2211yescharacteristic, complemented
52#821C2211yescharacteristic, complemented
53(C2×D3)⋊C8C2211yescharacteristic, complemented
54#818C2211yescharacteristic, complemented
55#818C2211yescharacteristic, complemented
56Dic3⋊C8C2211yescharacteristic, complemented
57C8×Dic3C2211yescharacteristic, complemented
58#809C2211yescharacteristic, complemented
59#807C2211yescharacteristic, complemented
60#547—31no—
61D42—31no—
62#486—31no—
63#480—31no—
64#480—31no—
65#474—31no—
66#466—31no—
67#466—31no—
68#459—31no—
69#447—31no—
70#447D311yescharacteristic, complemented
71C4×D8—31no—
72C8×D4—31no—
73C2×#102—31no—
74C2×#102—31no—
75C24×C3—21no—
76C23×D3—21no—
77C2×C3×D4—22no—
78C2×C3×D4—21no—
79C2×C3×D4—21no—
80C2×C3×D4—41no—
81C2×C3×D4C2311yescharacteristic
82C2×C3×D4C2311yescharacteristic
83C2×C3×D4C2311yescharacteristic
84C22×C3×C4C2311yescharacteristic
85C2×#67—21no—
86C2×#67—21no—
87C2×#67—21no—
88C2×#67—21no—
89C2×#67—21no—
90C2×#67—21no—
91C2×#67—44no—
92C2×#67D411yescharacteristic
93C22×Dic3—21no—
94C22×Dic3—21no—
95C22×Dic3—21no—
96#237—44no—
97D3×D4—22no—
98D3×D4—41no—
99C2×D12C2311yescharacteristic
100C2×C4×D3—21no—
101C2×C4×D3C2311yescharacteristic
102C2×Dic6—21no—
103C3×D8—22no—
104C3×D8—41no—
105C2×C3×C8C2311yescharacteristic
106C2×C3×C8C2311yescharacteristic
107C3×C4⋊C4C2311yescharacteristic
108C3×C22⋊C4—21no—
109#217—21no—
110#217—21no—
111#217—21no—
112#217—21no—
113#217D411yescharacteristic
114#213—41no—
115(C2×D3)⋊C4—21no—
116(C2×D3)⋊C4D411yescharacteristic
117C4⋊Dic3—21no—
118C4⋊Dic3C2311yescharacteristic
119C4⋊Dic3C2311yescharacteristic
120C4⋊Dic3C2311yescharacteristic
121Dic3⋊C4—21no—
122Dic3⋊C4—21no—
123Dic3⋊C4D411yescharacteristic
124C4×Dic3C2311yescharacteristic
125C2×C3⋊C8—41no—
126C2×C3⋊C8C2311yescharacteristic
127C2×C3⋊C8C2311yescharacteristic
128D3×C8—41no—
129C2×#41—61no—
130C22×D4—31no—
131C22×D4—61no—
132C22×D4C2×D311yescharacteristic
133C2×D8—31no—
134C2×D8C2×D311yescharacteristic
135C2×D8C2×D311yescharacteristic, complemented
136C22×C8—31no—
137C22×C8—31no—
138C4⋊Q8—31no—
139#127—31no—
140#123—61no—
141#123—61no—
142C22⋊Q8—61no—
143#121—31no—
144#121—31no—
145#121—31no—
146#121—61no—
147#121C2×D311yescharacteristic, complemented
148#120—61no—
149#120—61no—
150C4×D4—31no—
151C4×D4—31no—
152C4×D4—31no—
153C2×C4⋊C4—31no—
154C2×C4⋊C4—31no—
155#107—31no—
156#107—31no—
157#107—31no—
158C4⋊C8—31no—
159#102—31no—
160#102—31no—
161#102—31no—
162#102—31no—
163#102—31no—
164#102—31no—
165#102—31no—
166#102—31no—
167#102C2×D311yescharacteristic
168#102C2×D311yescharacteristic, complemented
169C22⋊C8—31no—
170C22⋊C8C2×D311yescharacteristic, complemented
171C4×C8—31no—
172C23×C3—21no—
173C23×C3—21no—
174C23×C3—21no—
175C23×C3—42no—
176C23×C3—42no—
177C23×C3—81no—
178C23×C3C2×D411yescharacteristic
179C22×D3—21no—
180C22×D3—42no—
181C22×D3—42no—
182C22×D3—81no—
183C22×D3C2×D411yescharacteristic
184C3×D4—21no—
185C3×D4—21no—
186C3×D4—21no—
187C3×D4—21no—
188C3×D4—21no—
189C3×D4—42no—
190C3×D4—42no—
191C3×D4#4112yescomplemented
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4C2×D411yescharacteristic
196C2×C3×C4C2411yescharacteristic
197#67—42no—
198#67—42no—
199#67—42no—
200#67—42no—
201#67—42no—
202#67—81no—
203#67D814yescomplemented
204C2×Dic3—21no—
205C2×Dic3—21no—
206C2×Dic3—21no—
207C2×Dic3—42no—
208C2×Dic3—42no—
209C2×Dic3—42no—
210C2×Dic3C2×D411yescharacteristic
211C2×Dic3C2×D411yescharacteristic
212C2×Dic3C2×D411yescharacteristic
213D12—21no—
214D12—21no—
215C4×D3—21no—
216C4×D3—21no—
217C4×D3—42no—
218Dic6—42no—
219C3×C8—21no—
220C3×C8—21no—
221C3⋊C8—21no—
222C3⋊C8—21no—
223C24—21no—
224C24—61no—
225#41—124no—
226C2×Q8—61no—
227C2×D4—22no—
228C2×D4—21no—
229C2×D4—21no—
230C2×D4—31no—
231C2×D4—31no—
232C2×D4—41no—
233C2×D4—61no—
234C2×D4—61no—
235C2×D4—61no—
236C2×D4—62no—
237C2×D4—61no—
238C2×D4—61no—
239C2×D4—61no—
240C2×D4—121no—
241C2×D4—124no—
242C2×D4C22×D311yescharacteristic
243C2×D4C22×D311yescharacteristic
244C2×D4C22×D311yescharacteristic
245C22×C4—31no—
246C22×C4—61no—
247C22×C4—61no—
248C22×C4—61no—
249C22×C4—61no—
250C22×C4C22×D311yescharacteristic
251D8—22no—
252D8—41no—
253D8—121no—
254C2×C8—31no—
255C2×C8—31no—
256C2×C8—121no—
257C2×C8—121no—
258C2×C8C22×D311yescharacteristic
259C2×C8C22×D311yescharacteristic
260C4⋊C4—31no—
261C4⋊C4—31no—
262C4⋊C4—31no—
263C4⋊C4—31no—
264C4⋊C4—61no—
265C4⋊C4—61no—
266C4⋊C4—61no—
267C4⋊C4C22×D311yescharacteristic
268C22⋊C4—21no—
269C22⋊C4—31no—
270C22⋊C4—31no—
271C22⋊C4—61no—
272C22⋊C4—61no—
273C22⋊C4—61no—
274C22⋊C4—61no—
275C22⋊C4—61no—
276C42—31no—
277C22×C3—21no—
278C22×C3—21no—
279C22×C3—22no—
280C22×C3—41no—
281C22×C3—41no—
282C22×C3—41no—
283C22×C3—41no—
284C22×C3—41no—
285C22×C3—41no—
286C22×C3—41no—
287C22×C3—41no—
288C22×C3—84no—
289C22×C3C2×D812yes—
290C22×C3C22×D411yescharacteristic
291C2×D3—21no—
292C2×D3—21no—
293C2×D3—41no—
294C2×D3—41no—
295C2×D3—41no—
296C2×D3—84no—
297C2×D3C2×D812yes—
298C3×C4—21no—
299C3×C4—41no—
300C3×C4C2×#4111yescharacteristic
301C3×C4H(5,𝔽2)11yescharacteristic
302Dic3—21no—
303Dic3—21no—
304Dic3—41no—
305Dic3—41no—
306Dic3—41no—
307Dic3C2×D812yes—
308C23—21no—
309C23—21no—
310C23—21no—
311C23—31no—
312C23—42no—
313C23—42no—
314C23—61no—
315C23—81no—
316C23—122no—
317C23—122no—
318C23—241no—
319C23D3×D411yescharacteristic
320Q8—122no—
321D4—21no—
322D4—21no—
323D4—21no—
324D4—21no—
325D4—21no—
326D4—34no—
327D4—42no—
328D4—42no—
329D4—61no—
330D4—61no—
331D4—122no—
332D4—122no—
333D4—122no—
334D4—122no—
335D4—122no—
336D4—241no—
337D4#23712yescomplemented
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—31no—
342C2×C4—31no—
343C2×C4—31no—
344C2×C4—61no—
345C2×C4—61no—
346C2×C4—61no—
347C2×C4—61no—
348C2×C4—61no—
349C2×C4—122no—
350C2×C4—122no—
351C2×C4—122no—
352C2×C4—122no—
353C2×C4D3×D411yescharacteristic
354C2×C4C23×D311yescharacteristic
355C8—21no—
356C8—21no—
357C8—61no—
358C8—61no—
359C2×C3—22no—
360C2×C3—42no—
361C2×C3—81no—
362C2×C3—81no—
363C2×C3#54611yescharacteristic
364C2×C3C22×D811yescharacteristic
365C2×C3#57711yescharacteristic
366D3—22no—
367D3—81no—
368C22—21no—
369C22—21no—
370C22—22no—
371C22—32no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—61no—
381C22—61no—
382C22—84no—
383C22—121no—
384C22—121no—
385C22—121no—
386C22—244no—
387C22D3×D812yes—
388C22C2×D3×D411yescharacteristic
389C4—21no—
390C4—32no—
391C4—41no—
392C4—61no—
393C4—61no—
394C4—121no—
395C4—121no—
396C4—121no—
397C4C2×#23711yescharacteristic
398C4#100411yescharacteristic
399C3#329411yescharacteristic, complemented, Sylow
400C2—22no—
401C2—42no—
402C2—62no—
403C2—81no—
404C2—81no—
405C2—241no—
406C2#559111yescharacteristic
407C2C2×D3×D811yescharacteristic
408C2#577511yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#447C2
socleC22×C3C22×D4
hypercenter#447D3
hypocenterC3#3294
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. D4×#67C2semidirect
2. #5611C2semidirect
3. C3×#447C2semidirect
4. C2×#832C2semidirect
5. #5157C2semidirect
6. #5156C2semidirect
7. #5150C2semidirect
8. Dic3×D8C2semidirect
9. #5038C2semidirect
10. #4774C2semidirect
11. D3×#102C2semidirect
12. #4760C2semidirect
13. #4759C2semidirect
14. #4736C2semidirect
15. #67⋊C8C2semidirect
22. C2×C3×D8C22semidirect
23. C3×#121C22semidirect
28. #938C22semidirect
32. D4×Dic3C22semidirect
33. C2×#213C22semidirect
36. C2×C4⋊Dic3C22semidirect
37. C22×C3⋊C8C22semidirect
38. C2×D3×C8C22semidirect
39. D3×C4⋊C4C22semidirect
40. #888C22semidirect
44. C3×#102C22semidirect
45. C3×C22⋊C8C22semidirect
48. #832C22semidirect
49. #832C22semidirect
50. #832C22semidirect
51. #821C22semidirect
52. #821C22semidirect
53. (C2×D3)⋊C8C22semidirect
54. #818C22semidirect
55. #818C22semidirect
56. Dic3⋊C8C22semidirect
57. C8×Dic3C22semidirect
58. #809C22semidirect
59. #807C22semidirect
70. #447D3semidirect
135. C2×D8C2×D3semidirect
147. #121C2×D3semidirect
168. #102C2×D3semidirect
170. C22⋊C8C2×D3semidirect
191. C3×D4#41semidirect
203. #67D8semidirect
337. D4#237semidirect
399. C3#3294semidirect

Maximal subgroups

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

subgroupindex
D4×#672
#56112
C3×#4472
C2×#8322
#51572
#51562
#51502
Dic3×D82
#50382
#47742
D3×#1022
#47602
#47592
#47362
#67⋊C82
#32943