Finite Group Databasebeta

← #80601

Subgroups — #80601

Order 384.

458 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×Q16C211yesmaximal, characteristic, complemented
2C2×#915C211yesmaximal, characteristic
3#5675C211yesmaximal, characteristic
4#5572C211yesmaximal, characteristic, complemented
5C3×#464C211yesmaximal, characteristic, complemented
6#5182C211yesmaximal, characteristic, complemented
7#5166C211yesmaximal, characteristic, complemented
8#5054C211yesmaximal, characteristic, complemented
9#5031C211yesmaximal, characteristic, complemented
10#4849C211yesmaximal, characteristic, complemented
11#4839C211yesmaximal, characteristic, complemented
12#4802C211yesmaximal, characteristic, complemented
13#4795C211yesmaximal, characteristic, complemented
14#4772C211yesmaximal, characteristic
15#4767C211yesmaximal, characteristic, complemented
16#3044—31nomaximal, Sylow
17C2×D3×Q8C2211yescharacteristic
18C2×D3×Q8C2211yescharacteristic
19C2×#237C2211yescharacteristic
20C2×C3×Q16C2211yescharacteristic
21C2×C3×SD16C2211yescharacteristic
22C3×#124C2211yescharacteristic
23C3×C4×Q8C2211yescharacteristic
24Q8×Dic3C2211yescharacteristic
25#944C2211yescharacteristic
26C2×#216C2211yescharacteristic
27C2×#216C2211yescharacteristic
28C2×#216C2211yescharacteristic
29#936C2211yescharacteristic
30C2×#214C2211yescharacteristic
31D3×Q16—24no—
32#915—24no—
33C2×Dic12C2211yescharacteristic
34C2×Dic12C2211yescharacteristic
35C2×ΓL(1,𝔽25)C2211yescharacteristic
36C2×D3×C8C2211yescharacteristic
37#892—21no—
38#892C2211yescharacteristic
39#887—21no—
40#887C2211yescharacteristic
41#883—21no—
42#883—21no—
43#878—21no—
44#878—21no—
45#872—21no—
46#872C2211yescharacteristic
47#869C2211yescharacteristic
48C4×Dic6—21no—
49C4×Dic6C2211yescharacteristic
50C3×C4⋊C8C2211yescharacteristic
51C3×#103C2211yescharacteristic
52C3×#102C2211yescharacteristic
53#835C2211yescharacteristic
54#832C2211yescharacteristic
55#816C2211yescharacteristic
56#816C2211yescharacteristic
57Dic3⋊C8C2211yescharacteristic
58Dic3⋊C8C2211yescharacteristic
59#810C2211yescharacteristic
60#810C2211yescharacteristic
61C4⋊(C3⋊C8)C2211yescharacteristic
62C2×#137—31no—
63C22×Q16—31no—
64#536—31no—
65#519—31no—
66#464—31no—
67#464—31no—
68#464—31no—
69#464D311yescharacteristic, complemented
70#462—31no—
71#462—31no—
72#462—31no—
73#462—31no—
74#424—31no—
75#419—31no—
76#416—31no—
77C2×C3×Q8C2311yescharacteristic
78C2×C3×Q8C2311yescharacteristic
79C2×C3×D4C2311yescharacteristic
80C2×#67—21no—
81C22×Dic3—21no—
82D3×Q8—22no—
83D3×Q8—22no—
84D3×Q8—22no—
85D3×Q8D414yes—
86#237—22no—
87#237—22no—
88C2×C4×D3—21no—
89C2×C4×D3—21no—
90C2×C4×D3C2311yescharacteristic
91C2×Dic6—21no—
92C2×Dic6—21no—
93C2×Dic6C2311yescharacteristic
94C2×Dic6C2311yescharacteristic
95C2×Dic6C2311yescharacteristic
96C3×Q16—22no—
97C3×SD16—22no—
98C2×C3×C8C2311yescharacteristic
99C2×C3×C8C2311yescharacteristic
100C3×C4⋊C4—21no—
101C3×C4⋊C4C2311yescharacteristic
102C3×C22⋊C4—21no—
103C3×C22⋊C4—21no—
104C3×C42—21no—
105C3×C42C2311yescharacteristic
106#217—21no—
107#217—21no—
108#216—22no—
109#216—22no—
110#216—22no—
111#214—22no—
112(C2×D3)⋊C4—21no—
113(C2×D3)⋊C4D411yescharacteristic
114(C2×D3)⋊C4D411yescharacteristic
115C4⋊Dic3—21no—
116C4⋊Dic3—21no—
117C4⋊Dic3—21no—
118C4⋊Dic3C2311yescharacteristic
119Dic3⋊C4—21no—
120Dic3⋊C4—21no—
121Dic3⋊C4—21no—
122Dic3⋊C4—21no—
123Dic3⋊C4D411yescharacteristic
124Dic3⋊C4D411yescharacteristic
125C4×Dic3—21no—
126C4×Dic3—21no—
127C4×Dic3—21no—
128C4×Dic3—21no—
129C4×Dic3C2311yescharacteristic
130C2×C3⋊C8C2311yescharacteristic
131C2×C3⋊C8C2311yescharacteristic
132Dic12—22no—
133Dic12—22no—
134ΓL(1,𝔽25)—22no—
135D3×C8—22no—
136C2×#41—31no—
137C22×Q8—31no—
138C22×Q8—31no—
139#137—64no—
140C2×Q16—31no—
141C2×Q16—31no—
142C2×Q16—31no—
143C2×Q16—31no—
144C2×Q16—31no—
145C2×Q16—64no—
146C2×Q16C2×D311yescharacteristic
147C2×SD16—31no—
148C2×SD16C2×D311yescharacteristic
149C2×M16—31no—
150C22×C8—31no—
151C4⋊Q8—31no—
152C4⋊Q8—31no—
153#124—31no—
154#124C2×D311yescharacteristic
155#123—61no—
156#123—61no—
157C22⋊Q8—61no—
158C22⋊Q8—61no—
159C4×Q8—31no—
160C4×Q8—31no—
161C4×Q8—31no—
162C4×Q8—61no—
163C4×Q8—61no—
164C4×Q8C2×D311yescharacteristic
165#117—31no—
166#117—31no—
167#117—61no—
168#117—61no—
169C4⋊C8—31no—
170C4⋊C8—31no—
171C4⋊C8—31no—
172C4⋊C8C2×D311yescharacteristic
173#103—31no—
174#103—31no—
175#103—31no—
176#103—31no—
177#103—31no—
178#103C2×D311yescharacteristic
179#102—31no—
180#102C2×D311yescharacteristic
181C23×C3—21no—
182C22×D3C2×D411yescharacteristic
183C3×Q8—21no—
184C3×Q8—21no—
185C3×Q8—21no—
186C3×Q8C2×D412yes—
187C3×D4—21no—
188C3×D4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4C2×D411yescharacteristic
193C2×C3×C4C2×D411yescharacteristic
194C2×C3×C4C2411yescharacteristic
195#67—42no—
196C2×Dic3—21no—
197C2×Dic3—21no—
198C2×Dic3—21no—
199C2×Dic3—21no—
200C2×Dic3—42no—
201C2×Dic3C2×D411yescharacteristic
202C2×Dic3C2×D411yescharacteristic
203C2×Dic3C2×D411yescharacteristic
204C4×D3—24no—
205C4×D3—42no—
206C4×D3C2×D412yes—
207C4×D3#4112yes—
208Dic6—21no—
209Dic6—24no—
210Dic6—21no—
211Dic6—21no—
212Dic6—21no—
213Dic6—21no—
214Dic6—42no—
215Dic6C2×D412yes—
216C3×C8—21no—
217C3×C8—21no—
218C3⋊C8—21no—
219C3⋊C8—21no—
220#41—62no—
221#41—62no—
222C2×Q8—34no—
223C2×Q8—31no—
224C2×Q8—31no—
225C2×Q8—31no—
226C2×Q8—61no—
227C2×Q8—61no—
228C2×Q8—62no—
229C2×Q8—62no—
230C2×Q8—62no—
231C2×Q8C22×D311yescharacteristic
232C2×Q8C22×D311yescharacteristic
233C2×D4—61no—
234C2×D4C22×D311yescharacteristic
235C22×C4—31no—
236C22×C4—61no—
237C22×C4—61no—
238C22×C4—61no—
239Q16—22no—
240Q16—62no—
241Q16—62no—
242Q16—62no—
243Q16—62no—
244Q16—62no—
245SD16—22no—
246SD16—62no—
247M16—62no—
248C2×C8—31no—
249C2×C8—31no—
250C2×C8—62no—
251C2×C8C22×D311yescharacteristic
252C2×C8C22×D311yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—31no—
255C4⋊C4—31no—
256C4⋊C4—31no—
257C4⋊C4—61no—
258C4⋊C4—61no—
259C4⋊C4—61no—
260C4⋊C4—61no—
261C4⋊C4—61no—
262C4⋊C4—61no—
263C4⋊C4—61no—
264C4⋊C4C22×D311yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—31no—
268C22⋊C4—31no—
269C22⋊C4—61no—
270C22⋊C4—61no—
271C22⋊C4—61no—
272C42—21no—
273C42—31no—
274C42—61no—
275C42—61no—
276C42—61no—
277C42—61no—
278C42C22×D311yescharacteristic
279C22×C3—41no—
280C22×C3—41no—
281C22×C3—41no—
282C22×C3C22×D411yescharacteristic
283C2×D3—21no—
284C2×D3—21no—
285C2×D3#12112yes—
286C3×C4—22no—
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—41no—
290C3×C4—41no—
291C3×C4C22×D411yescharacteristic
292C3×C4C2×#4111yescharacteristic
293Dic3—22no—
294Dic3—21no—
295Dic3—21no—
296Dic3—41no—
297Dic3—41no—
298Dic3—41no—
299Dic3#12112yes—
300C23—21no—
301C23—31no—
302Q8—21no—
303Q8—21no—
304Q8—21no—
305Q8—32no—
306Q8—64no—
307Q8—61no—
308Q8—61no—
309Q8—61no—
310Q8—61no—
311Q8—61no—
312Q8—122no—
313Q8D3×D412yes—
314D4—21no—
315D4—21no—
316D4—122no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—31no—
321C2×C4—32no—
322C2×C4—32no—
323C2×C4—31no—
324C2×C4—31no—
325C2×C4—64no—
326C2×C4—61no—
327C2×C4—61no—
328C2×C4—61no—
329C2×C4—61no—
330C2×C4—122no—
331C2×C4—122no—
332C2×C4D3×D411yescharacteristic
333C2×C4D3×D411yescharacteristic
334C2×C4C23×D311yescharacteristic
335C8—21no—
336C8—21no—
337C8—61no—
338C8—61no—
339C2×C3—81no—
340C2×C3C2×#12111yescharacteristic
341C2×C3#57811yescharacteristic
342C2×C3#57811yescharacteristic
343D3—22no—
344C22—32no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—61no—
349C22—61no—
350C22C2×D3×D411yescharacteristic
351C4—21no—
352C4—21no—
353C4—22no—
354C4—32no—
355C4—41no—
356C4—41no—
357C4—61no—
358C4—61no—
359C4—62no—
360C4—121no—
361C4—121no—
362C4—121no—
363C4C2×D3×D411yescharacteristic
364C4D3×#4111yescharacteristic
365C3#304411yescharacteristic, complemented, Sylow
366C2—62no—
367C2—81no—
368C2D3×#12111yescharacteristic
369C2#577111yescharacteristic
370C2#577911yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#464C2
socleC22×C3C22×D4
prime radicalC2×#237C22
hypercenter#464D3
hypocenterC3#3044
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×D3×Q16C2semidirect
4. #5572C2semidirect
5. C3×#464C2semidirect
6. #5182C2semidirect
7. #5166C2semidirect
8. #5054C2semidirect
9. #5031C2semidirect
10. #4849C2semidirect
11. #4839C2semidirect
12. #4802C2semidirect
13. #4795C2semidirect
15. #4767C2semidirect
69. #464D3semidirect
365. C3#3044semidirect

Maximal subgroups

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

subgroupindex
C2×D3×Q162
C2×#9152
#56752
#55722
C3×#4642
#51822
#51662
#50542
#50312
#48492
#48392
#48022
#47952
#47722
#47672
#30443