Finite Group Databasebeta

← #11873469

Subgroups — #11873469

Order 1152.

1200 conjugacy classes of subgroups; only the 221 normal subgroups are shown.

normal subgroups only

This group has 1200 conjugacy classes of subgroups — too many to draw. Only its 221 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#10596159C211yesmaximal, characteristic, complemented
2#10596139C211yesmaximal, characteristic
3C32×#488C211yesmaximal, characteristic, complemented
4#10592767C211yesmaximal, characteristic, complemented
5#10592755C211yesmaximal, characteristic, complemented
6#10592503C212yesmaximal, complemented
7#10592491C212yesmaximal, complemented
8#10592471C212yesmaximal, complemented
9#10592459C212yesmaximal, complemented
10#10592396C211yesmaximal, characteristic, complemented
11C4×C8×C3⋊D3C211yesmaximal, characteristic, complemented
12#81637—34nomaximal
13C2×#3832C2211yescharacteristic
14C2×#3830C2211yescharacteristic
15C32×#125C2211yescharacteristic
16C32×#124C2211yescharacteristic
17#64153C2211yescharacteristic
18#64149C2211yescharacteristic
19C2×C8×C3⋊D3C2212yes—
20#64105—22no—
21#64101C2212yes—
22#64097C2212yes—
23#64096—22no—
24#64093—22no—
25#64090—22no—
26#64084C2211yescharacteristic
27C42×C3⋊D3C2211yescharacteristic
28#64079C2211yescharacteristic
29C32×#103C2212yes—
30C32×#102C2212yes—
31C32×C4×C8C2211yescharacteristic
32#63662C2212yes—
33#63659C2212yes—
34#63648C2212yes—
35#63643C2212yes—
36C8×C3⋊Dic3C2212yes—
37#63637C2212yes—
38#63636C2212yes—
39C4×C3⋊(C3⋊C8)C2211yescharacteristic
40#5688—34no—
41#5668—34no—
42C3×#488D314yescomplemented
43#5068—34no—
44#5056—34no—
45#4804—38no—
46#4792—38no—
47#4772—38no—
48#4760—38no—
49#4697—34no—
50C4×D3×C8—34no—
51C2×C32×Q8C2311yescharacteristic
52C2×C32×D4C2311yescharacteristic
53C2×#638—21no—
54C2×#638—22no—
55C22×C3⋊Dic3—21no—
56#3832—24no—
57#3830—24no—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)C2311yescharacteristic
60C2×C4×C3⋊D3—21no—
61C2×C4×C3⋊D3D412yes—
62C2×C4×C3⋊D3C2311yescharacteristic
63C2×#634—22no—
64C2×#634C2311yescharacteristic
65C2×C32×C8C2312yes—
66C32×C4⋊C4—22no—
67C32×C4⋊C4C2312yes—
68C32×C22⋊C4—22no—
69C32×C42C2311yescharacteristic
70#3752—22no—
71#3752—22no—
72C4⋊(C3⋊Dic3)C2312yes—
73#3750—22no—
74#3750—22no—
75#3750—22no—
76C4×C3⋊Dic3—22no—
77C4×C3⋊Dic3D412yes—
78C4×C3⋊Dic3C2311yescharacteristic
79C2×C3⋊(C3⋊C8)C2312yes—
80C8×C3⋊D3—24no—
81#3131—91noSylow
82C2×#239—34no—
83C2×#237—34no—
84C3×#125C2×D314yes—
85C3×#124C2×D314yes—
86#944—34no—
87#940—34no—
88C2×D3×C8—38no—
89#896—68no—
90#892—38no—
91#888—38no—
92#887—68no—
93#884—68no—
94#67⋊C4—68no—
95#875—34no—
96C42×D3—34no—
97#870—34no—
98C3×#103C2×D318yes—
99C3×#102C2×D318yes—
100C3×C4×C8C2×D314yes—
101#835—38no—
102#832—38no—
103#821—38no—
104#816—38no—
105C8×Dic3—38no—
106#810—38no—
107#809—38no—
108C4×C3⋊C8—34no—
109C23×C32—21no—
110C22×C3⋊D3—21no—
111C22×C3⋊D3C2×D411yescharacteristic
112C32×Q8—22no—
113C32×D4—22no—
114C2×C32×C4—22no—
115C2×C32×C4—21no—
116C2×C32×C4C2×D412yes—
117C2×C32×C4C2411yescharacteristic
118#638—42no—
119#638—44no—
120C2×C3⋊Dic3—22no—
121C2×C3⋊Dic3—21no—
122C2×C3⋊Dic3—42no—
123C2×C3⋊Dic3C2×D411yescharacteristic
124C2×C3⋊Dic3C2×D412yes—
125C4⋊(C3⋊D3)—22no—
126C4⋊(C3⋊D3)—42no—
127C4×C3⋊D3—24no—
128C4×C3⋊D3—42no—
129C4×C3⋊D3#4114yes—
130#634—22no—
131#634—44no—
132C32×C8—22no—
133C3⋊(C3⋊C8)—22no—
134#533—91no—
135#532—91no—
136#488—91no—
137#488—91no—
138#488—91no—
139#488C3⋊D311yescharacteristic, complemented
140#487—92no—
141#486—92no—
142#416—92no—
143#416—92no—
144C2×C4×C8—91no—
145C2×C3×Q8C22×D314yes—
146C2×C3×D4C22×D314yes—
147C2×#67—68no—
148C2×#67—64no—
149C22×Dic3—64no—
150#239—616no—
151#237—616no—
152C2×D12—34no—
153C2×D12—64no—
154C2×C4×D3—34no—
155C2×C4×D3—38no—
156C2×C4×D3—64no—
157C2×Dic6—34no—
158C2×Dic6—68no—
159C2×C3×C8C22×D318yes—
160C3×C4⋊C4—28no—
161C3×C4⋊C4C22×D318yes—
162C3×C22⋊C4—28no—
163C3×C42C22×D314yes—
164(C2×D3)⋊C4—68no—
165(C2×D3)⋊C4—68no—
166C4⋊Dic3—38no—
167Dic3⋊C4—68no—
168Dic3⋊C4—68no—
169Dic3⋊C4—68no—
170C4×Dic3—38no—
171C4×Dic3—34no—
172C4×Dic3—68no—
173C2×C3⋊C8—38no—
174D3×C8—616no—
175C22×C32—41no—
176C22×C32—42no—
177C22×C32C22×D411yescharacteristic
178C2×C3⋊D3—22no—
179C2×C3⋊D3—41no—
180C2×C3⋊D3—42no—
181C2×C3⋊D3#12412yes—
182C32×C4—22no—
183C32×C4—41no—
184C32×C4—42no—
185C32×C4C2×#4112yes—
186C3⋊Dic3—41no—
187C3⋊Dic3—42no—
188C3⋊Dic3#12412yes—
189C3⋊Dic3#13514yes—
190C2×#41—91no—
191C2×#41—91no—
192C22×C8—92no—
193C4⋊Q8—92no—
194C4⋊Q8—91no—
195#127—91no—
196#125—91no—
197#125C2×C3⋊D311yescharacteristic
198#124—91no—
199#124C2×C3⋊D311yescharacteristic
200C22⋊Q8—182no—
201#121—182no—
202C4×Q8—182no—
203C4×D4—182no—
204#117—92no—
205C2×C42—91no—
206#103—92no—
207#103—92no—
208#103—92no—
209#103C2×C3⋊D312yes—
210#102—92no—
211#102—92no—
212#102—92no—
213#102C2×C3⋊D312yes—
214C4×C8—92no—
215C4×C8—91no—
216C4×C8C2×C3⋊D311yescharacteristic
217C23×C3—24no—
218C22×D3—34no—
219C22×D3—64no—
220C3×Q8—28no—
221C3×D4—28no—
222C2×C3×C4—28no—
223C2×C3×C4—24no—
224C2×C3×C4D3×D418yes—
225C2×C3×C4C23×D314yes—
226#67—1216no—
227#67—128no—
228C2×Dic3—34no—
229C2×Dic3—38no—
230C2×Dic3—68no—
231C2×Dic3—64no—
232C2×Dic3—128no—
233D12—68no—
234D12—128no—
235C4×D3—316no—
236C4×D3—616no—
237C4×D3—128no—
238Dic6—68no—
239Dic6—1216no—
240C3×C8—28no—
241C3⋊C8—68no—
242C2×C32—81no—
243C2×C32C2×#12411yescharacteristic
244C2×C32C2×#13512yes—
245C3⋊D3—22no—
246C3⋊D3—81no—
247#41—184no—
248#41—184no—
249C2×Q8—91no—
250C2×Q8—182no—
251C2×Q8C22×C3⋊D311yescharacteristic
252C2×D4—91no—
253C2×D4—181no—
254C2×D4—182no—
255C2×D4—181no—
256C2×D4C22×C3⋊D311yescharacteristic
257C22×C4—91no—
258C22×C4—92no—
259C22×C4—181no—
260C22×C4—181no—
261C2×C8—92no—
262C2×C8—184no—
263C2×C8C22×C3⋊D312yes—
264C4⋊C4—22no—
265C4⋊C4—92no—
266C4⋊C4—182no—
267C4⋊C4—182no—
268C4⋊C4—182no—
269C4⋊C4C22×C3⋊D312yes—
270C22⋊C4—22no—
271C22⋊C4—182no—
272C22⋊C4—182no—
273C42—91no—
274C42—92no—
275C42—182no—
276C42C22×C3⋊D311yescharacteristic
277C22×C3—44no—
278C22×C3—48no—
279C22×C3C2×D3×D414yes—
280C2×D3—38no—
281C2×D3—68no—
282C2×D3—124no—
283C2×D3—128no—
284C3×C4—28no—
285C3×C4—44no—
286C3×C4—48no—
287C3×C4D3×#4118yes—
288Dic3—38no—
289Dic3—316no—
290Dic3—124no—
291Dic3—128no—
292C32#313111yescharacteristic, complemented, Sylow
293C23—21no—
294C23—91no—
295C23—181no—
296Q8—22no—
297Q8—182no—
298Q8—364no—
299D4—22no—
300D4—182no—
301D4—362no—
302D4—364no—
303D4—362no—
304C2×C4—22no—
305C2×C4—21no—
306C2×C4—91no—
307C2×C4—92no—
308C2×C4—94no—
309C2×C4—184no—
310C2×C4—182no—
311C2×C4—181no—
312C2×C4—362no—
313C2×C4—362no—
314C2×C4D4×C3⋊D312yes—
315C2×C4C23×C3⋊D311yescharacteristic
316C8—22no—
317C8—182no—
318C2×C3—84no—
319C2×C3D3×#12414yes—
320C2×C3D3×#13518yes—
321D3—68no—
322D3—244no—
323C22—41no—
324C22—42no—
325C22—92no—
326C22—182no—
327C22—361no—
328C22—362no—
329C22C2×D4×C3⋊D311yescharacteristic
330C4—22no—
331C4—41no—
332C4—42no—
333C4—92no—
334C4—94no—
335C4—361no—
336C4—362no—
337C4#41×C3⋊D312yes—
338C3#8163714yescomplemented
339C2—81no—
340C2—182no—
341C2—721no—
342C2C3⋊D3×#12411yescharacteristic
343C2C3⋊D3×#13512yes—
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#488C2
socleC22×C32C22×D4
prime radical#10596139C2
hypercenter#488C3⋊D3
hypocenterC32#3131
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #10596159C2semidirect
3. C32×#488C2semidirect
4. #10592767C2semidirect
5. #10592755C2semidirect
6. #10592503C2semidirect
7. #10592491C2semidirect
8. #10592471C2semidirect
9. #10592459C2semidirect
10. #10592396C2semidirect
11. C4×C8×C3⋊D3C2semidirect
42. C3×#488D3semidirect
139. #488C3⋊D3semidirect
292. C32#3131semidirect
338. C3#81637semidirect

Maximal subgroups

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

subgroupindex
#105961592
#105961392
C32×#4882
#105927672
#105927552
#105925032
#105924912
#105924712
#105924592
#105923962
C4×C8×C3⋊D32
#816373