Finite Group Databasebeta

← #26033060

Subgroups — #26033060

Order 11392.

326 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 115 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#19152323C211yesmaximal, characteristic
2#19152323C211yesmaximal, characteristic
3#19151965C212yesmaximal
4#19151907C212yesmaximal
5#19151880C211yesmaximal, characteristic
6#19151807C212yesmaximal
7#19151805C211yesmaximal, characteristic
8#19151728C211yesmaximal, characteristic
9#19151702C212yesmaximal
10C4×Dic356C211yesmaximal, characteristic
11#487×C89C211yesmaximal, characteristic
12C2×Dic356C2211yescharacteristic
13C2×#13083564C2212yes—
14#15668010—21no—
15#15668010C2212yes—
16#15668003—21no—
17#15668003C2212yes—
18#15668002—22no—
19#15668002—22no—
20Q8×Dic89—21no—
21Q8×Dic89C2212yes—
22C4×Dic178C2211yescharacteristic
23C4×Dic178C2211yescharacteristic
24C4×Dic178C2211yescharacteristic
25#15667977—21no—
26#15667977C2212yes—
27#15667946C2211yescharacteristic
28#15667943C2212yes—
29C4⋊#10623494C2211yescharacteristic
30#15667941C2212yes—
31#15667937C2211yescharacteristic
32#15667937C2211yescharacteristic
33#15667936C2212yes—
34#15667935C2212yes—
35#15667922C2212yes—
36C4⋊Q8×C89C2211yescharacteristic
37C4⋊Q8×C89C2211yescharacteristic
38#103×C89C2212yes—
39#103×C89C2212yes—
40C4×C8×C89C2211yescharacteristic
41C2×Dic178D411yescharacteristic
42C2×Dic178C2311yescharacteristic
43C2×Dic178C2311yescharacteristic
44Dic356—22no—
45#13083564—24no—
46C2×#10623494C2312yes—
47C4⋊Dic89—22no—
48C4⋊Dic89—22no—
49C4⋊Dic89D411yescharacteristic
50C4⋊Dic89C2311yescharacteristic
51C4⋊Dic89C2311yescharacteristic
52#13083553—21no—
53#13083553—21no—
54#13083553—22no—
55#13083553—22no—
56#13083553—22no—
57#13083553—22no—
58#13083553D412yes—
59C4×Dic89—21no—
60C4×Dic89—21no—
61C4×Dic89—22no—
62C4×Dic89—22no—
63C4×Dic89C2312yes—
64C2×Q8×C89—21no—
65C2×Q8×C89C2312yes—
66C2×C8×C89C2311yescharacteristic
67C2×C8×C89C2311yescharacteristic
68C4⋊C4×C89—21no—
69C4⋊C4×C89—21no—
70C4⋊C4×C89—21no—
71C4⋊C4×C89C2312yes—
72C42×C89C2311yescharacteristic
73Q8×C89—22no—
74Q8×C89—22no—
75Q8×C89—42no—
76C2×C4×C89—22no—
77C2×C4×C89—22no—
78C2×C4×C89C2×D411yescharacteristic
79C2×C4×C89C2×D411yescharacteristic
80C2×C4×C89C2411yescharacteristic
81C2×Dic89—21no—
82C2×Dic89—21no—
83C2×Dic89—21no—
84C2×Dic89—21no—
85C2×Dic89C2×D412yes—
86C2×Dic89C2×D412yes—
87Dic178—22no—
88Dic178—21no—
89Dic178—21no—
90Dic178—21no—
91Dic178#4112yes—
92C8×C89—21no—
93C8×C89—21no—
94#10623494—22no—
95C22×C89C22×D411yescharacteristic
96C4×C89—21no—
97C4×C89—42no—
98C4×C89—42no—
99C4×C89#13712yes—
100C4×C89C2×#4111yescharacteristic
101C4×C892−1+411yescharacteristic
102Dic89—22no—
103Dic89—22no—
104Dic89—22no—
105Dic89—41no—
106Dic89—41no—
107Dic89—41no—
108C2×C89#54811yescharacteristic
109C2×C89C2×#13711yescharacteristic
110C2×C89#57811yescharacteristic
111#3374—891nomaximal, Sylow
112C89#337411yescharacteristic, complemented, Sylow
113#557—891no—
114#557—891no—
115#491—892no—
116#487D8911yescharacteristic
117#479—892no—
118#475—891no—
119#462—891no—
120#462—892no—
121#446—891no—
122#441—892no—
123C4×Q16—891no—
124C2×Q16—892no—
125C2×Q16—891no—
126C4⋊Q8—892no—
127C4⋊Q8—1781no—
128C4⋊Q8C2×D8911yescharacteristic
129C4⋊Q8C2×D8911yescharacteristic
130#125—892no—
131#125—1782no—
132#125—1782no—
133#125—1781no—
134C4×Q8—891no—
135C4×Q8—892no—
136C4×Q8—892no—
137C4×Q8—891no—
138C4×Q8—891no—
139C4×Q8—1781no—
140C4×Q8—1781no—
141#107—891no—
142#106—892no—
143C4⋊C8—892no—
144C4⋊C8—891no—
145#103—892no—
146#103—891no—
147#103—891no—
148#103—892no—
149#103C2×D8912yes—
150#103C2×D8912yes—
151#97—892no—
152C4×C8C2×D8911yescharacteristic
153C2×Q8—21no—
154C2×Q8—891no—
155C2×Q8—891no—
156C2×Q8—891no—
157C2×Q8C22×D8912yes—
158Q16—1782no—
159Q16—1784no—
160C2×C8—892no—
161C2×C8C22×D8911yescharacteristic
162C2×C8C22×D8911yescharacteristic
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—891no—
167C4⋊C4—892no—
168C4⋊C4—891no—
169C4⋊C4—891no—
170C4⋊C4—1782no—
171C4⋊C4—1782no—
172C4⋊C4—1782no—
173C4⋊C4—1782no—
174C4⋊C4—1782no—
175C4⋊C4—1782no—
176C4⋊C4—1781no—
177C4⋊C4—1781no—
178C4⋊C4C22×D8912yes—
179C42—892no—
180C42—1782no—
181C42—1782no—
182C42—1781no—
183C42—1781no—
184C42C22×D8911yescharacteristic
185Q8—22no—
186Q8—22no—
187Q8—42no—
188Q8—892no—
189Q8—1781no—
190Q8—1781no—
191Q8—1782no—
192Q8—1781no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—892no—
196C2×C4—892no—
197C2×C4—1781no—
198C2×C4—1781no—
199C2×C4—1781no—
200C2×C4—1781no—
201C2×C4D4×D8911yescharacteristic
202C2×C4D4×D8911yescharacteristic
203C2×C4C23×D8911yescharacteristic
204C8—21no—
205C8—21no—
206C8—1782no—
207C22C2×D4×D8911yescharacteristic
208C4—21no—
209C4—42no—
210C4—42no—
211C4—3561no—
212C4—3561no—
213C4—3561no—
214C4—1782no—
215C4—1782no—
216C4—1782no—
217C4#1566804112yes—
218C4#41×D8911yescharacteristic
219C4#1566805911yescharacteristic
220C2#1915225611yescharacteristic
221C2C2×#1566804111yescharacteristic
222C2#1915241111yescharacteristic
subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#487×C89C2
socle, prime radicalC22×C89C22×D4
hypercenter#487D89
hypocenterC89#3374
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
112. C89#3374semidirect

Maximal subgroups

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

subgroupindex
#191523232
#191519652
#191519072
#191518802
#191518072
#191518052
#191517282
#191517022
C4×Dic3562
#487×C892
#337489