Finite Group Databasebeta

← #11895514

Subgroups — #11895514

Order 1152.

1008 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596041C211yesmaximal, characteristic, complemented
2#10596013C211yesmaximal, characteristic
3C32×C4×SD16C211yesmaximal, characteristic
4#10592865C212yesmaximal
5#10592730C211yesmaximal, characteristic, complemented
6#10592706C211yesmaximal, characteristic
7#10592556C212yesmaximal, complemented
8#10592489C212yesmaximal, complemented
9#10592467C212yesmaximal
10#10592380C211yesmaximal, characteristic, complemented
11C8×#634C211yesmaximal, characteristic, complemented
12#79623—34nomaximal
13C2×C32×SD16C2211yescharacteristic
14C32×C4×Q8C2211yescharacteristic
15C32×C4×D4C2211yescharacteristic
16Q8×C3⋊Dic3C2212yes—
17C2×#3756C2212yes—
18#64145C2212yes—
19#64135—21no—
20#64133—21no—
21#64099—22no—
22#64099C2212yes—
23#64096C2212yes—
24#64088—22no—
25#64078—21no—
26#64078C2211yescharacteristic
27#64078C2211yescharacteristic
28C4×#634—21no—
29C4×#634C2211yescharacteristic
30C32×#106C2211yescharacteristic
31C32×#103C2211yescharacteristic
32C32×#102C2211yescharacteristic
33C32×C4×C8C2211yescharacteristic
34#63659C2212yes—
35#63643C2212yes—
36#63643C2212yes—
37#63641C2212yes—
38C8×C3⋊Dic3C2212yes—
39#63637C2212yes—
40#63634C2212yes—
41C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
42#5570—34no—
43#5542—34no—
44C3×C4×SD16D314yes—
45#5166—38no—
46#5031—34no—
47#5007—34no—
48#4857—38no—
49#4790—38no—
50#4768—38no—
51#4681—34no—
52C8×Dic6—34no—
53C2×C32×Q8C2311yescharacteristic
54C2×C32×D4C2311yescharacteristic
55C22×C32×C4—21no—
56C2×#634—21no—
57C2×#634D411yescharacteristic
58C2×#634C2312yes—
59C32×SD16—22no—
60C2×C32×C8C2311yescharacteristic
61C2×C32×C8C2311yescharacteristic
62C32×C4⋊C4—21no—
63C32×C4⋊C4C2311yescharacteristic
64C32×C4⋊C4C2311yescharacteristic
65C32×C22⋊C4—21no—
66C32×C42—21no—
67C32×C42C2311yescharacteristic
68#3757—22no—
69#3757—22no—
70#3756—24no—
71C4⋊(C3⋊Dic3)—21no—
72C4⋊(C3⋊Dic3)—21no—
73C4⋊(C3⋊Dic3)—21no—
74C4⋊(C3⋊Dic3)—22no—
75C4⋊(C3⋊Dic3)—22no—
76C4⋊(C3⋊Dic3)D411yescharacteristic
77C4⋊(C3⋊Dic3)C2312yes—
78#3750—22no—
79#3750—22no—
80#3750D412yes—
81C4×C3⋊Dic3—22no—
82C4×C3⋊Dic3—22no—
83C4×C3⋊Dic3C2312yes—
84C2×C3⋊(C3⋊C8)C2312yes—
85#3364—91noSylow
86C2×C3×SD16C2×D314yes—
87C3×C4×Q8C2×D314yes—
88C3×C4×D4C2×D314yes—
89Q8×Dic3—38no—
90C2×#216—38no—
91#936—38no—
92#926—64no—
93#924—64no—
94#890—38no—
95#890—68no—
96#887—38no—
97#879—68no—
98#869—34no—
99#869—34no—
100#869—64no—
101C4×Dic6—34no—
102C4×Dic6—64no—
103C3×#106C2×D314yes—
104C3×#103C2×D314yes—
105C3×#102C2×D314yes—
106C3×C4×C8C2×D314yes—
107#832—38no—
108#816—38no—
109#816—38no—
110Dic3⋊C8—38no—
111C8×Dic3—38no—
112#810—38no—
113#807—38no—
114C4⋊(C3⋊C8)—34no—
115C23×C32—21no—
116C32×Q8—21no—
117C32×Q8#4112yes—
118C32×D4—21no—
119C32×D4—21no—
120C2×C32×C4—21no—
121C2×C32×C4—21no—
122C2×C32×C4—21no—
123C2×C32×C4—42no—
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2411yescharacteristic
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3C2×D412yes—
130C2×C3⋊Dic3C2×D412yes—
131#634—22no—
132#634—22no—
133#634—22no—
134#634—42no—
135C32×C8—21no—
136C32×C8—21no—
137C3⋊(C3⋊C8)—22no—
138#557—91no—
139#556—91no—
140#488—92no—
141#487—91no—
142#479—92no—
143#474—91no—
144#464—92no—
145#462—91no—
146C8×Q8—91no—
147C4×Q16—92no—
148C4×SD16C3⋊D311yescharacteristic
149C2×C3×Q8C22×D314yes—
150C2×C3×D4C22×D314yes—
151C22×C3×C4—24no—
152C2×Dic6—34no—
153C2×Dic6—38no—
154C2×Dic6—64no—
155C3×SD16—28no—
156C2×C3×C8C22×D314yes—
157C2×C3×C8C22×D314yes—
158C3×C4⋊C4—24no—
159C3×C4⋊C4C22×D314yes—
160C3×C4⋊C4C22×D314yes—
161C3×C22⋊C4—24no—
162C3×C42—24no—
163C3×C42C22×D314yes—
164#217—68no—
165#217—68no—
166#216—616no—
167C4⋊Dic3—34no—
168C4⋊Dic3—38no—
169C4⋊Dic3—68no—
170C4⋊Dic3—68no—
171C4⋊Dic3—64no—
172C4⋊Dic3—64no—
173C4⋊Dic3—64no—
174Dic3⋊C4—38no—
175Dic3⋊C4—68no—
176Dic3⋊C4—68no—
177C4×Dic3—38no—
178C4×Dic3—68no—
179C4×Dic3—68no—
180C2×C3⋊C8—38no—
181C22×C32—41no—
182C22×C32—41no—
183C22×C32—41no—
184C22×C32C22×D411yescharacteristic
185C32×C4—22no—
186C32×C4—21no—
187C32×C4—41no—
188C32×C4—41no—
189C32×C4#13512yes—
190C32×C4C2×#4111yescharacteristic
191C32×C42−1+411yescharacteristic
192C3⋊Dic3—22no—
193C3⋊Dic3—22no—
194C3⋊Dic3—42no—
195C3⋊Dic3—42no—
196C2×Q16—92no—
197C2×SD16C2×C3⋊D311yescharacteristic
198C4⋊Q8—91no—
199C4⋊Q8—91no—
200C4⋊Q8—181no—
201#126—182no—
202#125—92no—
203#125—182no—
204#124—92no—
205C22⋊Q8—181no—
206C4×Q8—91no—
207C4×Q8—92no—
208C4×Q8—92no—
209C4×Q8—181no—
210C4×Q8C2×C3⋊D311yescharacteristic
211C4×D4C2×C3⋊D311yescharacteristic
212#117—181no—
213#107—92no—
214#106C2×C3⋊D311yescharacteristic
215C4⋊C8—92no—
216C4⋊C8—91no—
217#103—92no—
218#103—92no—
219#103—92no—
220#103C2×C3⋊D311yescharacteristic
221#102—92no—
222#102C2×C3⋊D311yescharacteristic
223C4×C8—92no—
224C4×C8C2×C3⋊D311yescharacteristic
225C23×C3—24no—
226C3×Q8—24no—
227C3×Q8#23518yes—
228C3×D4—24no—
229C3×D4—24no—
230C2×C3×C4—24no—
231C2×C3×C4—24no—
232C2×C3×C4—24no—
233C2×C3×C4—48no—
234C2×C3×C4D3×D414yes—
235C2×C3×C4D3×D414yes—
236C2×C3×C4C23×D314yes—
237C2×Dic3—38no—
238C2×Dic3—38no—
239C2×Dic3—68no—
240C2×Dic3—68no—
241Dic6—68no—
242Dic6—68no—
243Dic6—68no—
244Dic6—128no—
245C3×C8—24no—
246C3×C8—24no—
247C3⋊C8—68no—
248C2×C32—81no—
249C2×C32#54811yescharacteristic
250C2×C32C2×#13511yescharacteristic
251C2×C32#57811yescharacteristic
252C2×Q8—91no—
253C2×Q8—92no—
254C2×Q8—181no—
255C2×Q8C22×C3⋊D311yescharacteristic
256C2×D4C22×C3⋊D311yescharacteristic
257C22×C4—21no—
258Q16—184no—
259SD16—22no—
260C2×C8—92no—
261C2×C8C22×C3⋊D311yescharacteristic
262C2×C8C22×C3⋊D311yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—91no—
265C4⋊C4—92no—
266C4⋊C4—92no—
267C4⋊C4—182no—
268C4⋊C4—182no—
269C4⋊C4—182no—
270C4⋊C4—182no—
271C4⋊C4—181no—
272C4⋊C4—181no—
273C4⋊C4—181no—
274C4⋊C4C22×C3⋊D311yescharacteristic
275C4⋊C4C22×C3⋊D311yescharacteristic
276C22⋊C4—21no—
277C22⋊C4—182no—
278C22⋊C4—182no—
279C42—21no—
280C42—92no—
281C42—182no—
282C42—182no—
283C42C22×C3⋊D311yescharacteristic
284C22×C3—44no—
285C22×C3—44no—
286C22×C3—44no—
287C22×C3C2×D3×D414yes—
288C3×C4—24no—
289C3×C4—28no—
290C3×C4—44no—
291C3×C4—44no—
292C3×C4#91618yes—
293C3×C4C2×#23514yes—
294C3×C4#101014yes—
295Dic3—68no—
296Dic3—68no—
297Dic3—128no—
298Dic3—128no—
299C32#336411yescharacteristic, complemented, Sylow
300C23—21no—
301Q8—21no—
302Q8—182no—
303Q8—182no—
304Q8—182no—
305Q8—362no—
306Q8#382812yes—
307D4—21no—
308D4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—92no—
314C2×C4—92no—
315C2×C4—182no—
316C2×C4—182no—
317C2×C4D4×C3⋊D311yescharacteristic
318C2×C4D4×C3⋊D311yescharacteristic
319C2×C4C23×C3⋊D311yescharacteristic
320C8—21no—
321C8—21no—
322C8—182no—
323C2×C3—84no—
324C2×C3#555214yes—
325C2×C3C2×#91614yes—
326C2×C3#577114yes—
327C22—41no—
328C22—41no—
329C22—41no—
330C22C2×D4×C3⋊D311yescharacteristic
331C4—21no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—182no—
336C4—182no—
337C4—362no—
338C4—362no—
339C4#6412512yes—
340C4C2×#382811yescharacteristic
341C4#6436711yescharacteristic
342C3#7962314yescomplemented
343C2—81no—
344C2#1059602311yescharacteristic
345C2C2×#6412511yescharacteristic
346C2#1059624211yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×C4×SD16C2
socleC22×C32C22×D4
prime radicalC2×C32×D4C23
hypercenterC4×SD16C3⋊D3
hypocenterC32#3364
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #10596041C2semidirect
5. #10592730C2semidirect
7. #10592556C2semidirect
8. #10592489C2semidirect
10. #10592380C2semidirect
11. C8×#634C2semidirect
299. C32#3364semidirect
342. C3#79623semidirect

Maximal subgroups

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

subgroupindex
#105960412
#105960132
C32×C4×SD162
#105928652
#105927302
#105927062
#105925562
#105924892
#105924672
#105923802
C8×#6342
#796233