Finite Group Databasebeta

← #11898343

Subgroups — #11898343

Order 1152.

1080 conjugacy classes of subgroups; only the 233 normal subgroups are shown.

normal subgroups only

This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 233 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#10596013C212yesmaximal, complemented
2C32×C4×D8C211yesmaximal, characteristic
3#10592854C212yesmaximal
4#10592718C212yesmaximal, complemented
5#10592572C212yesmaximal, complemented
6#10592466C214yesmaximal, complemented
7#10592398C211yesmaximal, characteristic, complemented
8C8×#634C211yesmaximal, characteristic, complemented
9#79579—34nomaximal
10C2×C32×D8C2211yescharacteristic
11C32×C4×D4C2212yes—
12#64145C2214yes—
13C2×#3754C2214yes—
14#64135—22no—
15#64133—22no—
16C2×#3746C2212yes—
17C2×#3746C2212yes—
18#64096C2214yes—
19#64088—24no—
20#64078C2212yes—
21C4×#634C2211yescharacteristic
22C32×#107C2211yescharacteristic
23C32×#102C2212yes—
24C32×C4×C8C2211yescharacteristic
25#63641C2212yes—
26C8×C3⋊Dic3C2212yes—
27#63637C2214yes—
28C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
29#5542—38no—
30C3×C4×D8D314yes—
31#5155—38no—
32#5019—38no—
33#4873—38no—
34#4767—316no—
35#4699—34no—
36C8×Dic6—34no—
37C2×C32×D4C2312yes—
38C22×C32×C4—22no—
39C2×#634D411yescharacteristic
40C2×#634C2314yes—
41C32×D8—22no—
42C2×C32×C8C2311yescharacteristic
43C2×C32×C8C2311yescharacteristic
44C32×C4⋊C4C2312yes—
45C32×C22⋊C4—22no—
46C32×C42C2311yescharacteristic
47#3757—24no—
48#3757—24no—
49#3754—44no—
50C4⋊(C3⋊Dic3)—22no—
51C4⋊(C3⋊Dic3)—22no—
52C4⋊(C3⋊Dic3)D411yescharacteristic
53#3750—24no—
54#3750D412yes—
55C4×C3⋊Dic3—24no—
56C4×C3⋊Dic3C2312yes—
57C2×C3⋊(C3⋊C8)C2312yes—
58#3746—24no—
59#3746—42no—
60#3393—91noSylow
61C2×C3×D8C2×D314yes—
62C3×C4×D4C2×D318yes—
63#936—316no—
64C2×#214—316no—
65#926—68no—
66#924—68no—
67C2×Dic12—38no—
68C2×Dic12—38no—
69#887—316no—
70#879—616no—
71#869—38no—
72C4×Dic6—34no—
73C3×#107C2×D314yes—
74C3×#102C2×D318yes—
75C3×C4×C8C2×D314yes—
76Dic3⋊C8—38no—
77C8×Dic3—38no—
78#810—316no—
79C4⋊(C3⋊C8)—34no—
80C23×C32—22no—
81C32×D4—22no—
82C32×D4—22no—
83C2×C32×C4—22no—
84C2×C32×C4—44no—
85C2×C32×C4C2×D411yescharacteristic
86C2×C32×C4C2×D411yescharacteristic
87C2×C32×C4C2411yescharacteristic
88C2×C3⋊Dic3—24no—
89C2×C3⋊Dic3C2×D412yes—
90C2×C3⋊Dic3C2×D412yes—
91#634—22no—
92#634—24no—
93#634—24no—
94C32×C8—21no—
95C32×C8#4112yes—
96C3⋊(C3⋊C8)—22no—
97#556—92no—
98#495—92no—
99#494—91no—
100#464—94no—
101#461—92no—
102C8×Q8—91no—
103C4×Q16—92no—
104C4×D8C3⋊D311yescharacteristic
105C2×C3×D4C22×D318yes—
106C22×C3×C4—28no—
107C2×Dic6—34no—
108C2×Dic6—316no—
109C3×D8—28no—
110C2×C3×C8C22×D314yes—
111C2×C3×C8C22×D314yes—
112C3×C4⋊C4C22×D318yes—
113C3×C22⋊C4—28no—
114C3×C42C22×D314yes—
115#217—616no—
116#217—616no—
117#214—1216no—
118C4⋊Dic3—34no—
119C4⋊Dic3—68no—
120C4⋊Dic3—68no—
121Dic3⋊C4—38no—
122Dic3⋊C4—616no—
123C4×Dic3—38no—
124C4×Dic3—616no—
125C2×C3⋊C8—38no—
126Dic12—616no—
127Dic12—128no—
128C22×C32—42no—
129C22×C32—42no—
130C22×C32—42no—
131C22×C32C22×D411yescharacteristic
132C32×C4—21no—
133C32×C4—42no—
134C32×C4#13512yes—
135C32×C4C2×#4111yescharacteristic
136C32×C4H(5,𝔽2)11yescharacteristic
137C3⋊Dic3—22no—
138C3⋊Dic3—22no—
139C3⋊Dic3—44no—
140C2×Q16—92no—
141C2×Q16—92no—
142C2×SD16—94no—
143C2×D8C2×C3⋊D311yescharacteristic
144C4⋊Q8—92no—
145#126—184no—
146#124—94no—
147C22⋊Q8—182no—
148C4×Q8—91no—
149C4×Q8—94no—
150C4×D4C2×C3⋊D312yes—
151#117—182no—
152#107C2×C3⋊D311yescharacteristic
153C4⋊C8—92no—
154C4⋊C8—91no—
155#103—94no—
156#102C2×C3⋊D312yes—
157C4×C8—92no—
158C4×C8C2×C3⋊D311yescharacteristic
159C23×C3—28no—
160C3×D4—28no—
161C3×D4—28no—
162C2×C3×C4—28no—
163C2×C3×C4—416no—
164C2×C3×C4D3×D414yes—
165C2×C3×C4D3×D414yes—
166C2×C3×C4C23×D314yes—
167C2×Dic3—38no—
168C2×Dic3—38no—
169C2×Dic3—616no—
170Dic6—68no—
171Dic6—616no—
172Dic6—616no—
173C3×C8—24no—
174C3×C8#23518yes—
175C3⋊C8—68no—
176C2×C32—82no—
177C2×C32#55011yescharacteristic
178C2×C32C2×#13511yescharacteristic
179C2×C32#57811yescharacteristic
180C2×Q8—91no—
181C2×Q8—94no—
182C2×D4C22×C3⋊D312yes—
183C22×C4—22no—
184Q16—184no—
185Q16—362no—
186SD16—364no—
187D8—22no—
188C2×C8—92no—
189C2×C8C22×C3⋊D311yescharacteristic
190C2×C8C22×C3⋊D311yescharacteristic
191C4⋊C4—91no—
192C4⋊C4—92no—
193C4⋊C4—184no—
194C4⋊C4—182no—
195C4⋊C4—182no—
196C4⋊C4C22×C3⋊D312yes—
197C22⋊C4—22no—
198C22⋊C4—184no—
199C22⋊C4—184no—
200C42—92no—
201C42—184no—
202C42C22×C3⋊D311yescharacteristic
203C22×C3—48no—
204C22×C3—48no—
205C22×C3—48no—
206C22×C3C2×D3×D414yes—
207C3×C4—24no—
208C3×C4—48no—
209C3×C4#91218yes—
210C3×C4C2×#23514yes—
211C3×C4#100914yes—
212Dic3—68no—
213Dic3—68no—
214Dic3—1216no—
215C32#339311yescharacteristic, complemented, Sylow
216C23—22no—
217Q8—182no—
218Q8—184no—
219Q8—184no—
220D4—22no—
221D4—22no—
222C2×C4—22no—
223C2×C4—44no—
224C2×C4—92no—
225C2×C4—92no—
226C2×C4—184no—
227C2×C4D4×C3⋊D311yescharacteristic
228C2×C4D4×C3⋊D311yescharacteristic
229C2×C4C23×C3⋊D311yescharacteristic
230C8—21no—
231C8—182no—
232C8#382812yes—
233C2×C3—88no—
234C2×C3#555314yes—
235C2×C3C2×#91214yes—
236C2×C3#577114yes—
237C22—42no—
238C22—42no—
239C22—42no—
240C22C2×D4×C3⋊D311yescharacteristic
241C4—21no—
242C4—42no—
243C4—182no—
244C4—182no—
245C4—364no—
246C4#6412112yes—
247C4C2×#382811yescharacteristic
248C4#6436611yescharacteristic
249C3#7957914yescomplemented
250C2—82no—
251C2#1059602411yescharacteristic
252C2C2×#6412111yescharacteristic
253C2#1059624211yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×C4×D8C2
socleC22×C32C22×D4
prime radicalC2×C32×D8C22
hypercenterC4×D8C3⋊D3
hypocenterC32#3393
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #10596013C2semidirect
4. #10592718C2semidirect
5. #10592572C2semidirect
6. #10592466C2semidirect
7. #10592398C2semidirect
8. C8×#634C2semidirect
215. C32#3393semidirect
249. C3#79579semidirect

Maximal subgroups

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

subgroupindex
#105960132
C32×C4×D82
#105928542
#105927182
#105925722
#105924662
#105923982
C8×#6342
#795793