Finite Group Databasebeta

← #81410

Subgroups — #81410

Order 384.

392 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5598C211yesmaximal, characteristic, complemented
2#5530C211yesmaximal, characteristic, complemented
3C3×#482C211yesmaximal, characteristic, complemented
4#5039C211yesmaximal, characteristic, complemented
5#5004C211yesmaximal, characteristic, complemented
6#4886C211yesmaximal, characteristic, complemented
7#4877C211yesmaximal, characteristic, complemented
8#4862C211yesmaximal, characteristic, complemented
9#4852C211yesmaximal, characteristic, complemented
10#4787C211yesmaximal, characteristic, complemented
11#4781C211yesmaximal, characteristic, complemented
12#4771C211yesmaximal, characteristic, complemented
13#4768C211yesmaximal, characteristic, complemented
14#4738C211yesmaximal, characteristic, complemented
15#4729C211yesmaximal, characteristic, complemented
16#3326—31nomaximal, Sylow
17C2×#237C2211yescharacteristic
18C22×Dic6C2211yescharacteristic
19C3×#121C2211yescharacteristic
20C3×#117C2211yescharacteristic
21#939—21no—
22#936C2211yescharacteristic
23D4×Dic3—21no—
24C2×#213C2211yescharacteristic
25#930C2211yescharacteristic
26C4×#67C2211yescharacteristic
27C2×#208C2211yescharacteristic
28C2×#204C2211yescharacteristic
29C2×#204C2211yescharacteristic
30C2×ΓL(1,𝔽25)C2211yescharacteristic
31#897C2211yescharacteristic
32#895C2211yescharacteristic
33#893C2211yescharacteristic
34D3×C4⋊C4C2211yescharacteristic
35#890C2211yescharacteristic
36#887C2211yescharacteristic
37#885—21no—
38#884—21no—
39#883—21no—
40#878—21no—
41#876—21no—
42C4×D12—21no—
43C3×#107C2211yescharacteristic
44C3×#106C2211yescharacteristic
45C3×#102C2211yescharacteristic
46C3×#102C2211yescharacteristic
47C3×C22⋊C8C2211yescharacteristic
48#832C2211yescharacteristic
49(C2×D3)⋊C8C2211yescharacteristic
50#816C2211yescharacteristic
51#816C2211yescharacteristic
52Dic3⋊C8C2211yescharacteristic
53C8×Dic3C2211yescharacteristic
54#810C2211yescharacteristic
55#810C2211yescharacteristic
56#810C2211yescharacteristic
57#810C2211yescharacteristic
58#809C2211yescharacteristic
59#808C2211yescharacteristic
60#553—31no—
61#548—31no—
62#488—31no—
63#483—31no—
64#482D311yescharacteristic, complemented
65#479—31no—
66#469—31no—
67#468—31no—
68#463—31no—
69#449—31no—
70#448—31no—
71C4×SD16—31no—
72#436—31no—
73#419—31no—
74#417—31no—
75C2×C3×D4—21no—
76C2×C3×D4C2311yescharacteristic
77C22×C3×C4C2311yescharacteristic
78C2×#67—21no—
79C2×#67—21no—
80C2×#67D411yescharacteristic
81C22×Dic3—21no—
82C22×Dic3—21no—
83#237—22no—
84#237—41no—
85C2×D12—21no—
86C2×D12C2311yescharacteristic
87C2×C4×D3—21no—
88C2×C4×D3—21no—
89C2×C4×D3C2311yescharacteristic
90C2×Dic6—22no—
91C2×Dic6—21no—
92C2×Dic6—41no—
93C2×Dic6C2311yescharacteristic
94C2×Dic6C2311yescharacteristic
95C2×C3×C8C2311yescharacteristic
96C2×C3×C8C2311yescharacteristic
97C3×C4⋊C4C2311yescharacteristic
98C3×C4⋊C4C2311yescharacteristic
99C3×C4⋊C4C2311yescharacteristic
100C3×C22⋊C4—21no—
101C3×C22⋊C4—21no—
102C3×C42—21no—
103#217—21no—
104#217—21no—
105#217D411yescharacteristic
106#213—41no—
107(C2×D3)⋊C4—21no—
108(C2×D3)⋊C4—21no—
109(C2×D3)⋊C4—21no—
110(C2×D3)⋊C4—21no—
111(C2×D3)⋊C4D411yescharacteristic
112C4⋊Dic3—21no—
113C4⋊Dic3—21no—
114C4⋊Dic3C2311yescharacteristic
115Dic3⋊C4—21no—
116Dic3⋊C4—21no—
117Dic3⋊C4—21no—
118Dic3⋊C4D411yescharacteristic
119C4×Dic3—21no—
120C4×Dic3C2311yescharacteristic
121#208—41no—
122C2×C3⋊C8C2311yescharacteristic
123C2×C3⋊C8C2311yescharacteristic
124#204—22no—
125#204—41no—
126ΓL(1,𝔽25)—41no—
127C2×#41—31no—
128C22×Q8—31no—
129C2×SD16—31no—
130C2×SD16—31no—
131C2×D8—31no—
132C2×M16—31no—
133C2×M16—31no—
134#126—61no—
135#125—31no—
136#124—31no—
137#124—61no—
138#123—61no—
139C22⋊Q8—31no—
140C22⋊Q8—61no—
141#121—31no—
142#121—31no—
143#121—61no—
144#121—61no—
145#121C2×D311yescharacteristic
146C4×Q8—31no—
147C4×D4—31no—
148C4×D4—31no—
149C4×D4—61no—
150C4×D4—61no—
151#117C2×D311yescharacteristic
152C2×C4⋊C4—31no—
153#107C2×D311yescharacteristic
154#106—31no—
155#106C2×D311yescharacteristic
156C4⋊C8—31no—
157#103—31no—
158#103—31no—
159#103—31no—
160#103—31no—
161#103—31no—
162#103—31no—
163#102—31no—
164#102—31no—
165#102C2×D311yescharacteristic
166#102C2×D311yescharacteristic
167C22⋊C8—31no—
168C22⋊C8C2×D311yescharacteristic
169C4×C8—31no—
170C23×C3—21no—
171C23×C3C2×D411yescharacteristic
172C22×D3—21no—
173C22×D3C2×D411yescharacteristic
174C3×D4—21no—
175C3×D4—21no—
176C3×D4—42no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4C2×D411yescharacteristic
183C2×C3×C4C2411yescharacteristic
184#67—41no—
185#67—42no—
186#67—81no—
187C2×Dic3—21no—
188C2×Dic3—21no—
189C2×Dic3—21no—
190C2×Dic3—42no—
191C2×Dic3—42no—
192C2×Dic3C2×D411yescharacteristic
193C2×Dic3C2×D411yescharacteristic
194C2×Dic3C2×D411yescharacteristic
195D12—21no—
196D12—21no—
197D12—42no—
198C4×D3—21no—
199C4×D3—21no—
200C4×D3—81no—
201C4×D3—81no—
202Dic6—21no—
203Dic6—21no—
204Dic6—21no—
205Dic6—42no—
206Dic6#4112yes—
207C3×C8—21no—
208C3×C8—21no—
209C3⋊C8—21no—
210C3⋊C8—21no—
211#41—62no—
212#41—121no—
213C2×Q8—31no—
214C2×Q8—31no—
215C2×Q8—62no—
216C2×Q8—61no—
217C2×Q8—121no—
218C2×D4—21no—
219C2×D4—31no—
220C2×D4—31no—
221C2×D4—61no—
222C2×D4—61no—
223C2×D4—61no—
224C2×D4C22×D311yescharacteristic
225C22×C4—31no—
226C22×C4—61no—
227C22×C4—61no—
228C22×C4—61no—
229C22×C4—61no—
230C22×C4C22×D311yescharacteristic
231SD16—62no—
232SD16—121no—
233D8—121no—
234M16—121no—
235M16—121no—
236C2×C8—31no—
237C2×C8—31no—
238C2×C8C22×D311yescharacteristic
239C2×C8C22×D311yescharacteristic
240C4⋊C4—31no—
241C4⋊C4—31no—
242C4⋊C4—61no—
243C4⋊C4—61no—
244C4⋊C4—61no—
245C4⋊C4—61no—
246C4⋊C4—61no—
247C4⋊C4C22×D311yescharacteristic
248C4⋊C4C22×D311yescharacteristic
249C4⋊C4C22×D311yescharacteristic
250C22⋊C4—21no—
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—
260C42—21no—
261C42—31no—
262C42—61no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—21no—
266C22×C3—41no—
267C22×C3—41no—
268C22×C3—41no—
269C22×C3C22×D411yescharacteristic
270C2×D3—21no—
271C2×D3—21no—
272C2×D3—21no—
273C2×D3—41no—
274C2×D3—41no—
275C2×D3—41no—
276C3×C4—21no—
277C3×C4—41no—
278C3×C4—41no—
279C3×C4—41no—
280C3×C4C2×#4111yescharacteristic
281C3×C4H(5,𝔽2)11yescharacteristic
282Dic3—22no—
283Dic3—21no—
284Dic3—21no—
285Dic3—21no—
286Dic3—41no—
287Dic3—41no—
288C23—21no—
289C23—31no—
290C23—61no—
291C23D3×D411yescharacteristic
292Q8—32no—
293Q8—61no—
294Q8—61no—
295Q8—61no—
296Q8—122no—
297D4—21no—
298D4—21no—
299D4—42no—
300D4—61no—
301D4—61no—
302D4—122no—
303D4—121no—
304D4—122no—
305D4—241no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—31no—
312C2×C4—31no—
313C2×C4—31no—
314C2×C4—61no—
315C2×C4—61no—
316C2×C4—61no—
317C2×C4—61no—
318C2×C4—61no—
319C2×C4—122no—
320C2×C4—122no—
321C2×C4—241no—
322C2×C4—241no—
323C2×C4D3×D411yescharacteristic
324C2×C4C23×D311yescharacteristic
325C8—21no—
326C8—21no—
327C8—61no—
328C8—61no—
329C2×C3—41no—
330C2×C3—81no—
331C2×C3#54611yescharacteristic
332C2×C3#57511yescharacteristic
333C2×C3#57711yescharacteristic
334D3—41no—
335D3—81no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—61no—
343C22—61no—
344C22—61no—
345C22—121no—
346C22—121no—
347C22—121no—
348C22C2×D3×D411yescharacteristic
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—61no—
354C4—62no—
355C4—61no—
356C4—61no—
357C4—121no—
358C4—121no—
359C4D3×#4111yescharacteristic
360C4#100911yescharacteristic
361C3#332611yescharacteristic, complemented, Sylow
362C2—41no—
363C2—81no—
364C2—121no—
365C2—241no—
366C2#565411yescharacteristic
367C2#577011yescharacteristic
368C2#577311yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#482C2
socleC22×C3C22×D4
hypercenter#482D3
hypocenterC3#3326
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. #5598C2semidirect
2. #5530C2semidirect
3. C3×#482C2semidirect
4. #5039C2semidirect
5. #5004C2semidirect
6. #4886C2semidirect
7. #4877C2semidirect
8. #4862C2semidirect
9. #4852C2semidirect
10. #4787C2semidirect
11. #4781C2semidirect
12. #4771C2semidirect
13. #4768C2semidirect
14. #4738C2semidirect
15. #4729C2semidirect
64. #482D3semidirect
361. C3#3326semidirect

Maximal subgroups

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

subgroupindex
#55982
#55302
C3×#4822
#50392
#50042
#48862
#48772
#48622
#48522
#47872
#47812
#47712
#47682
#47382
#47292
#33263