Finite Group Databasebeta

← #26028626

Subgroups — #26028626

Order 11392.

524 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 153 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×#15668003C211yesmaximal, characteristic, complemented
2C2×#15668001C211yesmaximal, characteristic
3#19151505C211yesmaximal, characteristic, complemented
4#19151500C211yesmaximal, characteristic
5#19151499C211yesmaximal, characteristic
6#19151490C214yesmaximal, complemented
7#19151487C214yesmaximal, complemented
8C42×Dic89C211yesmaximal, characteristic, complemented
9#391×C89C211yesmaximal, characteristic, complemented
10C22×D356C2211yescharacteristic
11#15668003—24no—
12#15668001—24no—
13C2×C4⋊Dic89C2212yes—
14C2×C4⋊Dic89C2211yescharacteristic
15C2×#13083553C2212yes—
16C2×#13083551C2212yes—
17C2×#13083551C2214yes—
18C2×#13083551C2214yes—
19C2×#13083551C2212yes—
20C2×C4×Dic89C2212yes—
21C2×C4×Dic89C2212yes—
22C2×C4×Dic89C2211yescharacteristic
23C2×C4×Dic89C2211yescharacteristic
24#15667919C2214yes—
25C22×Q8×C89C2211yescharacteristic
26C2×C4⋊C4×C89C2211yescharacteristic
27C2×C42×C89C2211yescharacteristic
28#95×C89C2214yes—
29C23×D89C2312yes—
30C2×D356—22no—
31C2×D356—22no—
32C2×D356—22no—
33C22×Dic89C2312yes—
34C22×Dic89C2311yescharacteristic
35C22×Dic89C2311yescharacteristic
36C22×Dic89C2312yes—
37C4⋊Dic89—22no—
38C4⋊Dic89—24no—
39#13083553—24no—
40#13083551—28no—
41#13083551—24no—
42#13083551—24no—
43#13083551—28no—
44C4×Dic89—22no—
45C4×Dic89—24no—
46C4×Dic89—24no—
47C4×Dic89D414yes—
48C2×Q8×C89—22no—
49C2×Q8×C89—22no—
50C2×Q8×C89—22no—
51C22×C4×C89C2312yes—
52C22×C4×C89C2312yes—
53C22×C4×C89C2312yes—
54C22×C4×C89C2311yescharacteristic
55C4⋊C4×C89—22no—
56C42×C89—22no—
57C23×C89C2411yescharacteristic
58C22×D89—22no—
59C22×D89—24no—
60C22×D89—24no—
61C22×D89—22no—
62C22×D89—22no—
63Q8×C89—44no—
64C2×C4×C89—22no—
65C2×C4×C89—22no—
66C2×C4×C89—22no—
67C2×C4×C89—22no—
68C2×C4×C89—22no—
69C2×C4×C89—22no—
70C2×C4×C89—24no—
71C2×C4×C89C2×D412yes—
72C2×C4×C89#4112yes—
73C2×C4×C89#4112yes—
74C2×C4×C89#4114yes—
75C2×Dic89—22no—
76C2×Dic89—22no—
77C2×Dic89—22no—
78C2×Dic89—22no—
79C2×Dic89—22no—
80C2×Dic89—24no—
81C2×Dic89C2×D412yes—
82C2×Dic89C2×D412yes—
83C2×Dic89#4114yes—
84D356—44no—
85C22×C89C22×D411yescharacteristic
86C22×C89C2×#4111yescharacteristic
87C22×C89C2×#4111yescharacteristic
88C22×C89C2×#4112yes—
89C22×C89C2×#4112yes—
90C2×D89—42no—
91C2×D89—44no—
92C2×D89—44no—
93C2×D89—42no—
94C2×D89—42no—
95C4×C89—24no—
96C4×C89—42no—
97C4×C89—42no—
98C4×C89#12414yes—
99Dic89—24no—
100Dic89—22no—
101Dic89—22no—
102Dic89—42no—
103C2×C89C2×#12411yescharacteristic
104C2×C89#52912yes—
105C2×C89#52912yes—
106C2×C89#53211yescharacteristic
107C2×C89#53211yescharacteristic
108D89—82no—
109#2861—891nomaximal, Sylow
110C89#286111yescharacteristic, complemented, Sylow
111C2×#125—891no—
112C2×#124—891no—
113#391—891no—
114#391D8911yescharacteristic, complemented
115#390—891no—
116#390—891no—
117#388—894no—
118#388—894no—
119C43—891no—
120C22×Q8C2×D8911yescharacteristic
121C22×D4—891no—
122#125—1784no—
123#124—1784no—
124C2×C4⋊C4—892no—
125C2×C4⋊C4—892no—
126C2×C4⋊C4—891no—
127C2×C4⋊C4C2×D8911yescharacteristic
128C2×C22⋊C4—892no—
129C2×C22⋊C4—892no—
130C2×C22⋊C4—894no—
131C2×C22⋊C4—894no—
132C2×C42—891no—
133C2×C42—892no—
134C2×C42—892no—
135C2×C42—891no—
136C2×C42C2×D8911yescharacteristic
137#95—894no—
138#95C2×D8914yes—
139C24—892no—
140C2×Q8—22no—
141C2×Q8—22no—
142C2×Q8—22no—
143C2×D4—1782no—
144C2×D4—1782no—
145C2×D4—1782no—
146C22×C4—892no—
147C22×C4—891no—
148C22×C4—891no—
149C22×C4—892no—
150C22×C4C22×D8912yes—
151C22×C4C22×D8912yes—
152C22×C4C22×D8912yes—
153C22×C4C22×D8911yescharacteristic
154C4⋊C4—22no—
155C4⋊C4—1784no—
156C4⋊C4—1784no—
157C4⋊C4—1782no—
158C22⋊C4—1784no—
159C22⋊C4—1784no—
160C22⋊C4—1788no—
161C22⋊C4—1788no—
162C42—22no—
163C42—894no—
164C42—1784no—
165C42—1782no—
166C42—1784no—
167C23—1782no—
168C23—1784no—
169C23—1782no—
170C23—1782no—
171C23—1784no—
172C23C23×D8911yescharacteristic
173Q8—44no—
174D4—3564no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—24no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—892no—
183C2×C4—892no—
184C2×C4—894no—
185C2×C4—1782no—
186C2×C4—1784no—
187C2×C4—1782no—
188C2×C4—1782no—
189C2×C4—1782no—
190C2×C4—1782no—
191C2×C4D4×D8912yes—
192C2×C4#1308357312yes—
193C2×C4#1308357412yes—
194C2×C4#1308357514yes—
195C22—3564no—
196C22—3564no—
197C22—3562no—
198C22—3562no—
199C22—3562no—
200C22C2×D4×D8911yescharacteristic
201C22#41×D8912yes—
202C22C2×#1308357311yescharacteristic
203C22C2×#1308357411yescharacteristic
204C22C2×#1308357512yes—
205C4—24no—
206C4—42no—
207C4—42no—
208C4—3562no—
209C4—1784no—
210C4—1782no—
211C4—1782no—
212C4#1566799814yes—
213C2—7122no—
214C2C2×#1566799811yescharacteristic
215C2#1915213412yes—
216C2#1915213512yes—
217C2#1915214711yescharacteristic
218C2#1915214911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#391×C89C2
prime radicalC22×D356C22
hypercenter#391D89
hypocenterC89#2861
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#15668003C2semidirect
3. #19151505C2semidirect
6. #19151490C2semidirect
7. #19151487C2semidirect
8. C42×Dic89C2semidirect
9. #391×C89C2semidirect
110. C89#2861semidirect
114. #391D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156680032
C2×#156680012
#191515052
#191515002
#191514992
#191514902
#191514872
C42×Dic892
#391×C892
#286189