Finite Group Databasebeta

← #80019

Subgroups — #80019

Order 384.

414 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5806C211yesmaximal, characteristic, complemented
2#5616C211yesmaximal, characteristic, complemented
3C3×#447C211yesmaximal, characteristic, complemented
4#5215C211yesmaximal, characteristic, complemented
5#5158C211yesmaximal, characteristic, complemented
6#5157C211yesmaximal, characteristic, complemented
7#5153C211yesmaximal, characteristic, complemented
8#5152C211yesmaximal, characteristic, complemented
9#5042C211yesmaximal, characteristic, complemented
10#4779C211yesmaximal, characteristic, complemented
11#4772C211yesmaximal, characteristic, complemented
12#4765C211yesmaximal, characteristic, complemented
13#4759C211yesmaximal, characteristic, complemented
14#4728C211yesmaximal, characteristic, complemented
15#4723C211yesmaximal, characteristic, complemented
16#3319—31nomaximal, Sylow
17C22×C3×D4C2211yescharacteristic
18C2×#237C2211yescharacteristic
19C2×C3×D8C2211yescharacteristic
20C2×C3×D8C2211yescharacteristic
21C3×#121C2211yescharacteristic
22#953—21no—
23C2×#217—21no—
24#939—21no—
25#939—21no—
26#938C2211yescharacteristic
27#938C2211yescharacteristic, complemented
28#936—21no—
29#936C2211yescharacteristic
30#935—21no—
31D4×Dic3C2211yescharacteristic
32D4×Dic3C2211yescharacteristic, complemented
33C2×#214C2211yescharacteristic, complemented
34C4×#67C2211yescharacteristic
35#926C2211yescharacteristic
36#924C2211yescharacteristic
37C2×#208C2211yescharacteristic
38C2×D3×C8C2211yescharacteristic, complemented
39#892C2211yescharacteristic, complemented
40#888C2211yescharacteristic, complemented
41#885—21no—
42#877—21no—
43C3×#102C2211yescharacteristic
44C3×#102C2211yescharacteristic
45C3×C22⋊C8C2211yescharacteristic
46#832C2211yescharacteristic
47#832C2211yescharacteristic
48#832C2211yescharacteristic
49#832C2211yescharacteristic
50#832C2211yescharacteristic, complemented
51(C2×D3)⋊C8C2211yescharacteristic, complemented
52#818C2211yescharacteristic, complemented
53#817C2211yescharacteristic, complemented
54#816C2211yescharacteristic, complemented
55#816C2211yescharacteristic, complemented
56#815C2211yescharacteristic, complemented
57Dic3⋊C8C2211yescharacteristic, complemented
58#810C2211yescharacteristic, complemented
59#807C2211yescharacteristic, complemented
60#555—31no—
61#546—31no—
62#489—31no—
63#485—31no—
64#482—31no—
65#474—31no—
66#468—31no—
67#466—31no—
68#463—31no—
69#449—31no—
70#447D311yescharacteristic, complemented
71#442—31no—
72#435—31no—
73#418—31no—
74#416—31no—
75C24×C3—21no—
76C2×C3×D4—22no—
77C2×C3×D4—21no—
78C2×C3×D4—21no—
79C2×C3×D4—41no—
80C2×C3×D4C2311yescharacteristic
81C2×C3×D4C2311yescharacteristic
82C2×C3×D4C2311yescharacteristic
83C22×C3×C4C2311yescharacteristic
84C2×#67—21no—
85C2×#67—21no—
86C2×#67—21no—
87C2×#67D411yescharacteristic
88C22×Dic3—21no—
89C22×Dic3—21no—
90C22×Dic3—21no—
91#237—22no—
92#237—41no—
93C2×C4×D3C2311yescharacteristic
94C2×Dic6—21no—
95C2×Dic6C2311yescharacteristic
96C3×D8—22no—
97C3×D8—41no—
98C2×C3×C8C2311yescharacteristic
99C2×C3×C8C2311yescharacteristic
100C3×C4⋊C4C2311yescharacteristic
101C3×C22⋊C4—21no—
102#217—21no—
103#217—21no—
104#217—21no—
105#217—21no—
106#217—21no—
107#217—21no—
108#217—21no—
109#217—21no—
110#217D411yescharacteristic
111#214—41no—
112(C2×D3)⋊C4—21no—
113(C2×D3)⋊C4D411yescharacteristic
114C4⋊Dic3C2311yescharacteristic
115C4⋊Dic3C2311yescharacteristic
116C4⋊Dic3C2311yescharacteristic
117Dic3⋊C4—21no—
118Dic3⋊C4—21no—
119Dic3⋊C4D411yescharacteristic
120C4×Dic3—21no—
121C4×Dic3—21no—
122C4×Dic3C2311yescharacteristic
123#208—41no—
124C2×C3⋊C8C2311yescharacteristic
125C2×C3⋊C8C2311yescharacteristic
126D3×C8—41no—
127C2×#41—31no—
128C22×D4C2×D311yescharacteristic
129C2×SD16—31no—
130C2×D8C2×D311yescharacteristic
131C2×D8C2×D311yescharacteristic
132C2×M16—31no—
133C22×C8—31no—
134C4⋊Q8—31no—
135#124—31no—
136#124—61no—
137#124—61no—
138#123—61no—
139C22⋊Q8—31no—
140#121—31no—
141#121—31no—
142#121—61no—
143#121—61no—
144#121C2×D311yescharacteristic
145#120—61no—
146C4×D4—31no—
147C4×D4—31no—
148C4×D4—31no—
149#117—31no—
150#117—31no—
151#117—61no—
152C2×C22⋊C4—61no—
153#107—31no—
154#107—31no—
155#106—31no—
156C4⋊C8—31no—
157#103—31no—
158#103—31no—
159#103—31no—
160#102—31no—
161#102—31no—
162#102—31no—
163#102—31no—
164#102—31no—
165#102C2×D311yescharacteristic
166#102C2×D311yescharacteristic
167C22⋊C8—31no—
168C22⋊C8C2×D311yescharacteristic
169#97—31no—
170C23×C3—21no—
171C23×C3—21no—
172C23×C3—21no—
173C23×C3—42no—
174C23×C3—42no—
175C23×C3—81no—
176C23×C3C2×D411yescharacteristic
177C22×D3C2×D411yescharacteristic
178C3×D4—21no—
179C3×D4—21no—
180C3×D4—21no—
181C3×D4—21no—
182C3×D4—21no—
183C3×D4—42no—
184C3×D4—81no—
185C3×D4#4112yes—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4C2×D411yescharacteristic
190C2×C3×C4C2411yescharacteristic
191#67—41no—
192#67—42no—
193#67—81no—
194#67—81no—
195C2×Dic3—21no—
196C2×Dic3—21no—
197C2×Dic3—21no—
198C2×Dic3—21no—
199C2×Dic3—42no—
200C2×Dic3—42no—
201C2×Dic3—81no—
202C2×Dic3C2×D411yescharacteristic
203C2×Dic3C2×D411yescharacteristic
204C2×Dic3C2×D411yescharacteristic
205C4×D3—21no—
206C4×D3—21no—
207Dic6—21no—
208Dic6—21no—
209Dic6—81no—
210C3×C8—21no—
211C3×C8—21no—
212C3⋊C8—21no—
213C3⋊C8—21no—
214C24—21no—
215#41—62no—
216#41—121no—
217C2×Q8—31no—
218C2×Q8—61no—
219C2×D4—22no—
220C2×D4—21no—
221C2×D4—21no—
222C2×D4—31no—
223C2×D4—41no—
224C2×D4—61no—
225C2×D4—61no—
226C2×D4—61no—
227C2×D4C22×D311yescharacteristic
228C2×D4C22×D311yescharacteristic
229C2×D4C22×D311yescharacteristic
230C22×C4—31no—
231C22×C4—61no—
232C22×C4—61no—
233C22×C4—61no—
234C22×C4C22×D311yescharacteristic
235SD16—121no—
236D8—22no—
237D8—41no—
238M16—121no—
239C2×C8—31no—
240C2×C8—31no—
241C2×C8—121no—
242C2×C8C22×D311yescharacteristic
243C2×C8C22×D311yescharacteristic
244C4⋊C4—31no—
245C4⋊C4—31no—
246C4⋊C4—31no—
247C4⋊C4—31no—
248C4⋊C4—61no—
249C4⋊C4—61no—
250C4⋊C4C22×D311yescharacteristic
251C22⋊C4—21no—
252C22⋊C4—31no—
253C22⋊C4—31no—
254C22⋊C4—61no—
255C22⋊C4—61no—
256C22⋊C4—61no—
257C22⋊C4—61no—
258C22⋊C4—61no—
259C22⋊C4—61no—
260C22⋊C4—61no—
261C22⋊C4—61no—
262C22⋊C4—61no—
263C42—31no—
264C42—61no—
265C42—61no—
266C22×C3—22no—
267C22×C3—21no—
268C22×C3—21no—
269C22×C3—21no—
270C22×C3—41no—
271C22×C3—41no—
272C22×C3—41no—
273C22×C3—41no—
274C22×C3—41no—
275C22×C3—41no—
276C22×C3—41no—
277C22×C3—41no—
278C22×C3—84no—
279C22×C3C22×D411yescharacteristic
280C2×D3—21no—
281C2×D3—21no—
282C2×D3—21no—
283C3×C4—21no—
284C3×C4—41no—
285C3×C4C2×#4111yescharacteristic
286C3×C4H(5,𝔽2)11yescharacteristic
287Dic3—21no—
288Dic3—21no—
289Dic3—21no—
290Dic3—41no—
291Dic3—41no—
292Dic3—41no—
293Dic3—41no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—31no—
298C23—42no—
299C23—42no—
300C23—81no—
301C23D3×D411yescharacteristic
302Q8—61no—
303Q8—61no—
304Q8—241no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—21no—
310D4—42no—
311D4—81no—
312D4—121no—
313D4—122no—
314D4—241no—
315D4—241no—
316D4#23712yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—31no—
321C2×C4—31no—
322C2×C4—31no—
323C2×C4—61no—
324C2×C4—61no—
325C2×C4—61no—
326C2×C4—61no—
327C2×C4—61no—
328C2×C4—61no—
329C2×C4—122no—
330C2×C4—122no—
331C2×C4—241no—
332C2×C4D3×D411yescharacteristic
333C2×C4C23×D311yescharacteristic
334C8—21no—
335C8—21no—
336C8—61no—
337C8—61no—
338C2×C3—41no—
339C2×C3—42no—
340C2×C3—81no—
341C2×C3—81no—
342C2×C3#54611yescharacteristic
343C2×C3#57511yescharacteristic
344C2×C3#57611yescharacteristic
345D3—41no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—22no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—61no—
359C22—61no—
360C22—61no—
361C22—84no—
362C22C2×D3×D411yescharacteristic
363C4—21no—
364C4—41no—
365C4—61no—
366C4—61no—
367C4—61no—
368C4—121no—
369C4—121no—
370C4—121no—
371C4—121no—
372C4C2×#23711yescharacteristic
373C4#100411yescharacteristic
374C3#331911yescharacteristic, complemented, Sylow
375C2—41no—
376C2—42no—
377C2—81no—
378C2—81no—
379C2—121no—
380C2#559111yescharacteristic
381C2#575711yescharacteristic
382C2#577311yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#447C2
socleC22×C3C22×D4
hypercenter#447D3
hypocenterC3#3319
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. #5806C2semidirect
2. #5616C2semidirect
3. C3×#447C2semidirect
4. #5215C2semidirect
5. #5158C2semidirect
6. #5157C2semidirect
7. #5153C2semidirect
8. #5152C2semidirect
9. #5042C2semidirect
10. #4779C2semidirect
11. #4772C2semidirect
12. #4765C2semidirect
13. #4759C2semidirect
14. #4728C2semidirect
15. #4723C2semidirect
27. #938C22semidirect
32. D4×Dic3C22semidirect
33. C2×#214C22semidirect
38. C2×D3×C8C22semidirect
39. #892C22semidirect
40. #888C22semidirect
50. #832C22semidirect
51. (C2×D3)⋊C8C22semidirect
52. #818C22semidirect
53. #817C22semidirect
54. #816C22semidirect
55. #816C22semidirect
56. #815C22semidirect
57. Dic3⋊C8C22semidirect
58. #810C22semidirect
59. #807C22semidirect
70. #447D3semidirect
374. C3#3319semidirect

Maximal subgroups

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

subgroupindex
#58062
#56162
C3×#4472
#52152
#51582
#51572
#51532
#51522
#50422
#47792
#47722
#47652
#47592
#47282
#47232
#33193