Finite Group Databasebeta

← #26025242

Subgroups — #26025242

Order 11392.

540 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 177 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
1C2×#15668012C211yesmaximal, characteristic
2C2×#15668010C211yesmaximal, characteristic
3C2×#15668010C211yesmaximal, characteristic
4C2×#15667977C211yesmaximal, characteristic
5#19151532C214yesmaximal
6#19151503C211yesmaximal, characteristic
7#19151495C214yesmaximal
8C4×#13083553C211yesmaximal, characteristic
9#391×C89C211yesmaximal, characteristic
10C22×Dic178C2211yescharacteristic
11C22×Dic178C2211yescharacteristic
12#15668012—24no—
13#15668010—24no—
14#15668010—24no—
15#15667977—24no—
16C2×C4⋊Dic89C2214yes—
17C2×#13083553C2212yes—
18C2×#13083553C2214yes—
19C2×#13083553C2212yes—
20C2×#13083553C2212yes—
21C2×#13083553C2212yes—
22C2×C4×Dic89C2211yescharacteristic
23C2×C4×Dic89C2212yes—
24C2×C4×Dic89C2211yescharacteristic
25#15667919C2212yes—
26#15667919C2214yes—
27C22×Q8×C89C2211yescharacteristic
28C2×C4⋊C4×C89C2211yescharacteristic
29C2×C42×C89C2211yescharacteristic
30#95×C89C2214yes—
31C2×Dic178—22no—
32C2×Dic178—22no—
33C2×Dic178—22no—
34C2×Dic178—22no—
35C2×Dic178—22no—
36C2×Dic178D414yes—
37C22×Dic89C2312yes—
38C22×Dic89C2312yes—
39C22×Dic89C2311yescharacteristic
40C22×Dic89C2312yes—
41C22×Dic89C2311yescharacteristic
42C4⋊Dic89—28no—
43#13083553—24no—
44#13083553—28no—
45#13083553—24no—
46#13083553—24no—
47#13083553Q818yescomplemented
48C4×Dic89—22no—
49C4×Dic89—24no—
50C4×Dic89D414yes—
51C2×Q8×C89—22no—
52C2×Q8×C89—22no—
53C2×Q8×C89—22no—
54C22×C4×C89C2312yes—
55C22×C4×C89C2312yes—
56C22×C4×C89C2312yes—
57C22×C4×C89C2311yescharacteristic
58C4⋊C4×C89—22no—
59C42×C89—22no—
60C23×C89C2411yescharacteristic
61Q8×C89—44no—
62C2×C4×C89—22no—
63C2×C4×C89—22no—
64C2×C4×C89—22no—
65C2×C4×C89—22no—
66C2×C4×C89—22no—
67C2×C4×C89—22no—
68C2×C4×C89—24no—
69C2×C4×C89C2×D412yes—
70C2×C4×C89C2×D412yes—
71C2×C4×C89C2×Q814yes—
72C2×C4×C89#4112yes—
73C2×Dic89—22no—
74C2×Dic89—22no—
75C2×Dic89—22no—
76C2×Dic89—22no—
77C2×Dic89—22no—
78C2×Dic89—22no—
79C2×Dic89—22no—
80C2×Dic89—22no—
81C2×Dic89C2×D412yes—
82C2×Dic89C2×D414yes—
83C2×Dic89C2×D412yes—
84C2×Dic89C2×Q814yes—
85C2×Dic89C2×Q814yes—
86Dic178—28no—
87Dic178—44no—
88C22×C89C22×D411yescharacteristic
89C22×C89C22×D411yescharacteristic
90C22×C89C22×Q812yes—
91C22×C89C2×#4111yescharacteristic
92C22×C892−1+412yes—
93C4×C89—24no—
94C4×C89—42no—
95C4×C89—42no—
96C4×C89#12114yes—
97Dic89—24no—
98Dic89—22no—
99Dic89—24no—
100Dic89—42no—
101Dic89C4⋊Q814yescomplemented
102C2×C89C2×#12111yescharacteristic
103C2×C89C2×C4⋊Q811yescharacteristic
104C2×C89#53611yescharacteristic
105C2×C89D4×Q812yes—
106C2×C89#55712yes—
107#2546—891nomaximal, Sylow
108C89#254611yescharacteristic, complemented, Sylow
109C2×C4⋊Q8—891no—
110C2×C4⋊Q8—891no—
111C2×C4⋊Q8—891no—
112C2×C4×Q8—891no—
113#398—894no—
114#391—891no—
115#391D8911yescharacteristic
116#389—894no—
117C4×C4⋊C4—891no—
118C22×Q8—891no—
119C22×Q8—891no—
120C22×Q8C2×D8911yescharacteristic
121C4⋊Q8—1784no—
122C4⋊Q8—1784no—
123C4⋊Q8—1784no—
124C4×Q8—1784no—
125C2×C4⋊C4—892no—
126C2×C4⋊C4—892no—
127C2×C4⋊C4—892no—
128C2×C4⋊C4—894no—
129C2×C4⋊C4—894no—
130C2×C4⋊C4—892no—
131C2×C4⋊C4C2×D8911yescharacteristic
132C2×C42—891no—
133C2×C42—892no—
134C2×C42—891no—
135C2×C42C2×D8911yescharacteristic
136#95—892no—
137#95—894no—
138#95C2×D8914yes—
139C2×Q8—22no—
140C2×Q8—22no—
141C2×Q8—22no—
142C2×Q8—894no—
143C2×Q8—1782no—
144C2×Q8—1782no—
145C2×Q8—1782no—
146C2×Q8—1782no—
147C2×Q8—1782no—
148C22×C4—891no—
149C22×C4—892no—
150C22×C4—891no—
151C22×C4—892no—
152C22×C4—892no—
153C22×C4C22×D8912yes—
154C22×C4C22×D8912yes—
155C22×C4C22×D8912yes—
156C22×C4C22×D8911yescharacteristic
157C4⋊C4—22no—
158C4⋊C4—898no—
159C4⋊C4—1784no—
160C4⋊C4—1784no—
161C4⋊C4—1784no—
162C4⋊C4—1788no—
163C4⋊C4—1788no—
164C42—22no—
165C42—894no—
166C42—1784no—
167C42—1782no—
168C23C23×D8911yescharacteristic
169Q8—44no—
170Q8—3564no—
171Q8—1788no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—24no—
179C2×C4—892no—
180C2×C4—894no—
181C2×C4—892no—
182C2×C4—894no—
183C2×C4—894no—
184C2×C4—1782no—
185C2×C4—1782no—
186C2×C4—1782no—
187C2×C4—1782no—
188C2×C4—1782no—
189C2×C4—1782no—
190C2×C4—1782no—
191C2×C4—1782no—
192C2×C4D4×D8912yes—
193C2×C4D4×D8912yes—
194C2×C4Q8×D8914yes—
195C2×C4#1308357412yes—
196C22C2×D4×D8911yescharacteristic
197C22C2×D4×D8911yescharacteristic
198C22C2×Q8×D8912yes—
199C22C2×#1308357411yescharacteristic
200C22#1566805912yes—
201C4—24no—
202C4—42no—
203C4—42no—
204C4—894no—
205C4—3562no—
206C4—1782no—
207C4—1784no—
208C4—1784no—
209C4#1566798514yes—
210C2C2×#1566798511yescharacteristic
211C2C4⋊Q8×D8911yescharacteristic
212C2#1915216811yescharacteristic
213C2#1915226112yes—
214C2#1915232612yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, prime radical, cosocleC23×C89C24
Fitting#391×C89C2
hypercenter#391D89
hypocenterC89#2546
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
47. #13083553Q8semidirect
101. Dic89C4⋊Q8semidirect
108. C89#2546semidirect

Maximal subgroups

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

subgroupindex
C2×#156680122
C2×#156680102
C2×#156679772
#191515322
#191515032
#191514952
C4×#130835532
#391×C892
#254689