Finite Group Databasebeta

← #11873463

Subgroups — #11873463

Order 1152.

1200 conjugacy classes of subgroups; only the 241 normal subgroups are shown.

normal subgroups only

This group has 1200 conjugacy classes of subgroups — too many to draw. Only its 241 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596199C211yesmaximal, characteristic, complemented
2#10596187C211yesmaximal, characteristic
3C32×#486C211yesmaximal, characteristic, complemented
4#10592792C211yesmaximal, characteristic, complemented
5#10592769C211yesmaximal, characteristic, complemented
6#10592471C214yesmaximal, complemented
7#10592467C214yesmaximal, complemented
8C4×C8×C3⋊D3C211yesmaximal, characteristic, complemented
9#10592380C211yesmaximal, characteristic, complemented
10#81562—34nomaximal
11C2×#3830C2212yes—
12C32×C4⋊Q8C2211yescharacteristic
13C32×#127C2211yescharacteristic
14#64155—21no—
15Q8×C3⋊Dic3—21no—
16#64147—21no—
17#64147—21no—
18#64145C2212yes—
19D4×C3⋊Dic3—21no—
20D4×C3⋊Dic3—21no—
21C2×C8×C3⋊D3C2212yes—
22#64106—21no—
23#64101C2212yes—
24#64099C2212yes—
25#64096—21no—
26C42×C3⋊D3C2211yescharacteristic
27#64078C2211yescharacteristic
28#64078C2211yescharacteristic
29C32×#102C2214yes—
30C32×C4×C8C2211yescharacteristic
31#63659C2214yes—
32#63643C2214yes—
33C8×C3⋊Dic3C2212yes—
34#63637C2214yes—
35C4×C3⋊(C3⋊C8)C2211yescharacteristic
36#5728—34no—
37#5716—34no—
38C3×#486D314yescomplemented
39#5093—34no—
40#5070—34no—
41#4772—316no—
42#4768—316no—
43C4×D3×C8—34no—
44#4681—34no—
45C2×C32×Q8—21no—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4C2312yes—
49C2×#638—22no—
50C22×C3⋊Dic3—22no—
51#3830—28no—
52C2×C4×C3⋊D3D411yescharacteristic
53C2×C4×C3⋊D3D411yescharacteristic
54C2×C4×C3⋊D3C2311yescharacteristic
55C2×#634—21no—
56C2×#634C2312yes—
57C2×C32×C8C2312yes—
58C32×C4⋊C4—21no—
59C32×C4⋊C4C2312yes—
60C32×C42C2311yescharacteristic
61#3757—22no—
62#3757—22no—
63#3752—22no—
64C4⋊(C3⋊Dic3)—21no—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)—21no—
67C4⋊(C3⋊Dic3)—22no—
68C4⋊(C3⋊Dic3)C2312yes—
69#3750—22no—
70C4×C3⋊Dic3—22no—
71C4×C3⋊Dic3D411yescharacteristic
72C4×C3⋊Dic3D411yescharacteristic
73C4×C3⋊Dic3C2311yescharacteristic
74C2×C3⋊(C3⋊C8)C2312yes—
75C8×C3⋊D3—24no—
76#3131—91noSylow
77C2×#237—38no—
78C3×C4⋊Q8C2×D314yes—
79C3×#127C2×D314yes—
80#946—64no—
81Q8×Dic3—64no—
82#938—64no—
83#938—64no—
84#936—38no—
85D4×Dic3—64no—
86D4×Dic3—64no—
87C2×D3×C8—38no—
88#897—64no—
89#892—38no—
90#890—38no—
91#887—64no—
92C42×D3—34no—
93#869—34no—
94#869—34no—
95C3×#102C2×D3116yes—
96C3×C4×C8C2×D314yes—
97#832—316no—
98#816—316no—
99C8×Dic3—38no—
100#810—316no—
101C4×C3⋊C8—34no—
102C23×C32—22no—
103C22×C3⋊D3C2×D411yescharacteristic
104C32×Q8—42no—
105C32×D4—24no—
106C32×D4—42no—
107C32×D4—42no—
108C2×C32×C4—22no—
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2411yescharacteristic
112#638—44no—
113C2×C3⋊Dic3—22no—
114C2×C3⋊Dic3—22no—
115C2×C3⋊Dic3—44no—
116C2×C3⋊Dic3C2×D411yescharacteristic
117C2×C3⋊Dic3C2×D411yescharacteristic
118C2×C3⋊Dic3C2×D411yescharacteristic
119C4×C3⋊D3—22no—
120C4×C3⋊D3—22no—
121C4×C3⋊D3#4114yes—
122#634—24no—
123#634—42no—
124C32×C8—22no—
125C3⋊(C3⋊C8)—22no—
126#533—91no—
127#532—91no—
128#488—94no—
129#487—91no—
130#487—91no—
131#486—91no—
132#486C3⋊D311yescharacteristic, complemented
133#416—94no—
134C2×C4×C8—91no—
135C2×C3×Q8—24no—
136C2×C3×D4—24no—
137C2×C3×D4—24no—
138C2×C3×D4C22×D318yes—
139C2×#67—68no—
140C22×Dic3—68no—
141#237—632no—
142C2×C4×D3—34no—
143C2×C4×D3—34no—
144C2×C4×D3—34no—
145C2×Dic6—38no—
146C2×Dic6—64no—
147C2×C3×C8C22×D318yes—
148C3×C4⋊C4—24no—
149C3×C4⋊C4C22×D318yes—
150C3×C42C22×D314yes—
151#217—68no—
152#217—68no—
153(C2×D3)⋊C4—68no—
154C4⋊Dic3—38no—
155C4⋊Dic3—68no—
156C4⋊Dic3—64no—
157C4⋊Dic3—64no—
158C4⋊Dic3—64no—
159Dic3⋊C4—68no—
160C4×Dic3—34no—
161C4×Dic3—34no—
162C4×Dic3—34no—
163C4×Dic3—68no—
164C2×C3⋊C8—38no—
165D3×C8—616no—
166C22×C32—42no—
167C22×C32—42no—
168C22×C32—42no—
169C22×C32C22×D411yescharacteristic
170C2×C3⋊D3—21no—
171C2×C3⋊D3—21no—
172C2×C3⋊D3#12412yes—
173C32×C4—42no—
174C32×C4#13512yes—
175C32×C4#13512yes—
176C32×C4C2×#4112yes—
177C3⋊Dic3—21no—
178C3⋊Dic3—21no—
179C3⋊Dic3—42no—
180C3⋊Dic3—42no—
181C3⋊Dic3#12412yes—
182C2×#41—92no—
183C22×C8—92no—
184C4⋊Q8—91no—
185C4⋊Q8—91no—
186C4⋊Q8C2×C3⋊D311yescharacteristic
187#127C2×C3⋊D311yescharacteristic
188#125—92no—
189#124—92no—
190C22⋊Q8—181no—
191C22⋊Q8—181no—
192#121—181no—
193#121—181no—
194C4×Q8—181no—
195C4×Q8—181no—
196C4×D4—181no—
197C4×D4—181no—
198#117—92no—
199C2×C42—91no—
200#103—94no—
201#103—94no—
202#102—94no—
203#102C2×C3⋊D314yes—
204C4×C8—92no—
205C4×C8—91no—
206C4×C8C2×C3⋊D311yescharacteristic
207C23×C3—28no—
208C22×D3—34no—
209C3×Q8—48no—
210C3×D4—216no—
211C3×D4—48no—
212C3×D4—48no—
213C2×C3×C4—28no—
214C2×C3×C4D3×D414yes—
215C2×C3×C4D3×D414yes—
216C2×C3×C4C23×D314yes—
217#67—1216no—
218C2×Dic3—34no—
219C2×Dic3—34no—
220C2×Dic3—34no—
221C2×Dic3—68no—
222C2×Dic3—68no—
223C2×Dic3—1216no—
224C4×D3—316no—
225C4×D3—68no—
226C4×D3—68no—
227Dic6—616no—
228Dic6—128no—
229C3×C8—28no—
230C3⋊C8—68no—
231C2×C32—82no—
232C2×C32C2×#12411yescharacteristic
233C2×C32C2×#13511yescharacteristic
234C2×C32C2×#13511yescharacteristic
235C3⋊D3—22no—
236#41—188no—
237C2×Q8—21no—
238C2×Q8—92no—
239C2×Q8—181no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—182no—
243C2×D4C22×C3⋊D312yes—
244C22×C4—91no—
245C22×C4—91no—
246C22×C4—91no—
247C22×C4—182no—
248C2×C8—92no—
249C2×C8—184no—
250C2×C8C22×C3⋊D312yes—
251C4⋊C4—21no—
252C4⋊C4—92no—
253C4⋊C4—182no—
254C4⋊C4—182no—
255C4⋊C4—181no—
256C4⋊C4—181no—
257C4⋊C4—181no—
258C4⋊C4C22×C3⋊D312yes—
259C22⋊C4—182no—
260C22⋊C4—182no—
261C22⋊C4—182no—
262C42—91no—
263C42—91no—
264C42—91no—
265C42—182no—
266C42C22×C3⋊D311yescharacteristic
267C22×C3—48no—
268C22×C3—48no—
269C22×C3—48no—
270C22×C3C2×D3×D414yes—
271C2×D3—38no—
272C2×D3—64no—
273C2×D3—64no—
274C3×C4—48no—
275C3×C4#91218yes—
276C3×C4#91618yes—
277C3×C4D3×#4118yes—
278Dic3—38no—
279Dic3—64no—
280Dic3—64no—
281Dic3—128no—
282Dic3—128no—
283C32#313111yescharacteristic, complemented, Sylow
284C23—22no—
285C23—91no—
286Q8—42no—
287Q8—184no—
288Q8—362no—
289D4—24no—
290D4—42no—
291D4—42no—
292D4—364no—
293C2×C4—22no—
294C2×C4—91no—
295C2×C4—94no—
296C2×C4—91no—
297C2×C4—91no—
298C2×C4—182no—
299C2×C4—182no—
300C2×C4—182no—
301C2×C4—182no—
302C2×C4—364no—
303C2×C4D4×C3⋊D311yescharacteristic
304C2×C4D4×C3⋊D311yescharacteristic
305C2×C4C23×C3⋊D311yescharacteristic
306C8—22no—
307C8—182no—
308C2×C3—88no—
309C2×C3D3×#12414yes—
310C2×C3C2×#91214yes—
311C2×C3C2×#91614yes—
312D3—68no—
313C22—42no—
314C22—42no—
315C22—42no—
316C22—92no—
317C22—181no—
318C22—181no—
319C22C2×D4×C3⋊D311yescharacteristic
320C4—42no—
321C4—92no—
322C4—181no—
323C4—181no—
324C4—362no—
325C4—362no—
326C4#6412112yes—
327C4#6412512yes—
328C4#41×C3⋊D312yes—
329C3#8156214yescomplemented
330C2—82no—
331C2—182no—
332C2C3⋊D3×#12411yescharacteristic
333C2C2×#6412111yescharacteristic
334C2C2×#6412511yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#486C2
socleC22×C32C22×D4
prime radical#10596187C2
hypercenter#486C3⋊D3
hypocenterC32#3131
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #10596199C2semidirect
3. C32×#486C2semidirect
4. #10592792C2semidirect
5. #10592769C2semidirect
6. #10592471C2semidirect
7. #10592467C2semidirect
8. C4×C8×C3⋊D3C2semidirect
9. #10592380C2semidirect
38. C3×#486D3semidirect
132. #486C3⋊D3semidirect
283. C32#3131semidirect
329. C3#81562semidirect

Maximal subgroups

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

subgroupindex
#105961992
#105961872
C32×#4862
#105927922
#105927692
#105924712
#105924672
C4×C8×C3⋊D32
#105923802
#815623