Finite Group Databasebeta

← #26027958

Subgroups — #26027958

Order 11392.

428 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 121 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#19151518C211yesmaximal, characteristic, complemented
2#19151516C212yesmaximal
3#19151515C211yesmaximal, characteristic
4#19151511C212yesmaximal, complemented
5#19151489C212yesmaximal, complemented
6#19151488C212yesmaximal, complemented
7#19151487C212yesmaximal, complemented
8#19151462C212yesmaximal, complemented
9#382×C89C211yesmaximal, characteristic, complemented
10C22×Dic178C2211yescharacteristic
11C22×D356C2211yescharacteristic
12C2×#13083553C2212yes—
13C2×#13083553C2212yes—
14C2×#13083551C2212yes—
15C2×#13083551C2212yes—
16C2×#13083551C2212yes—
17C2×#13083551C2212yes—
18C2×#13083551C2212yes—
19C2×#13083551C2212yes—
20C2×C4×Dic89C2212yes—
21#15667919C2211yescharacteristic
22#15667919C2212yes—
23#15667919C2212yes—
24#15667919C2211yescharacteristic
25#15667919C2212yes—
26C2×C4⋊C4×C89C2211yescharacteristic
27C2×C4⋊C4×C89C2211yescharacteristic
28C2×C42×C89C2211yescharacteristic
29#95×C89C2212yes—
30#95×C89C2212yes—
31C23×D89C2312yes—
32C2×Dic178—41no—
33C2×Dic178—42no—
34C2×D356—41no—
35C2×D356—42no—
36C22×Dic89C2312yes—
37C22×Dic89C2312yes—
38C22×Dic89C2312yes—
39#13083553—42no—
40#13083553—42no—
41#13083551—24no—
42#13083551—24no—
43#13083551—24no—
44#13083551—42no—
45#13083551—42no—
46#13083551—42no—
47C4×Dic89—24no—
48C22×C4×C89C2311yescharacteristic
49C22×C4×C89C2311yescharacteristic
50C22×C4×C89C2312yes—
51C22×C4×C89C2312yes—
52C22×C4×C89C2311yescharacteristic
53C4⋊C4×C89—41no—
54C4⋊C4×C89—41no—
55C42×C89—22no—
56C23×C89C2411yescharacteristic
57C22×D89—22no—
58C22×D89—22no—
59C22×D89—22no—
60C22×D89—22no—
61C22×D89—22no—
62C22×D89—22no—
63C22×D89—22no—
64C2×C4×C89—21no—
65C2×C4×C89—21no—
66C2×C4×C89—22no—
67C2×C4×C89—22no—
68C2×C4×C89—22no—
69C2×C4×C89—22no—
70C2×C4×C89—22no—
71C2×C4×C89—21no—
72C2×C4×C89—21no—
73C2×C4×C89—22no—
74C2×C4×C89—22no—
75C2×C4×C89—22no—
76C2×C4×C89#4112yes—
77C2×Dic89—22no—
78C2×Dic89—22no—
79C2×Dic89—22no—
80C2×Dic89—22no—
81C2×Dic89—22no—
82C2×Dic89—22no—
83C2×Dic89—22no—
84C2×Dic89—22no—
85C2×Dic89#4114yes—
86D356—44no—
87Dic178—44no—
88C22×C89C2×#4112yes—
89C22×C89C2×#4111yescharacteristic
90C22×C89H(5,𝔽2)11yescharacteristic
91C22×C89H(5,𝔽2)12yes—
92C22×C892−1+411yescharacteristic
93C2×D89—42no—
94C2×D89—42no—
95C2×D89—42no—
96C2×D89—42no—
97C2×D89—42no—
98C2×D89—42no—
99C2×D89—42no—
100C4×C89—22no—
101C4×C89—42no—
102C4×C89—42no—
103C4×C89—41no—
104C4×C89—41no—
105Dic89—24no—
106Dic89—42no—
107Dic89—42no—
108C2×C89#53911yescharacteristic
109C2×C89#53912yes—
110C2×C89#55511yescharacteristic
111C2×C89#55512yes—
112C2×C89H(3,𝔽4)11yescharacteristic
113D89—82no—
114#2785—891nomaximal, Sylow
115C89#278511yescharacteristic, complemented, Sylow
116#395—891no—
117#394—891no—
118#394—892no—
119#393—892no—
120#388—892no—
121#388—892no—
122#388—892no—
123#382—892no—
124#382D8911yescharacteristic, complemented
125C22×Q8—891no—
126C22×D4—891no—
127C2×C4⋊C4—892no—
128C2×C4⋊C4—892no—
129C2×C4⋊C4C2×D8911yescharacteristic
130C2×C4⋊C4C2×D8911yescharacteristic
131C2×C22⋊C4—892no—
132C2×C22⋊C4—892no—
133C2×C22⋊C4—892no—
134C2×C22⋊C4—892no—
135C2×C22⋊C4—892no—
136C2×C22⋊C4—892no—
137C2×C42—892no—
138C2×C42C2×D8911yescharacteristic
139#95—891no—
140#95—892no—
141#95—892no—
142#95—891no—
143#95—892no—
144#95C2×D8912yes—
145#95C2×D8912yes—
146C24—892no—
147C2×Q8—3561no—
148C2×Q8—3562no—
149C2×D4—3561no—
150C2×D4—3562no—
151C22×C4—892no—
152C22×C4—892no—
153C22×C4—892no—
154C22×C4C22×D8912yes—
155C22×C4C22×D8912yes—
156C22×C4C22×D8911yescharacteristic
157C22×C4C22×D8911yescharacteristic
158C22×C4C22×D8911yescharacteristic
159C4⋊C4—41no—
160C4⋊C4—41no—
161C4⋊C4—3562no—
162C4⋊C4—3562no—
163C22⋊C4—3562no—
164C22⋊C4—3562no—
165C22⋊C4—3562no—
166C22⋊C4—1784no—
167C22⋊C4—1784no—
168C22⋊C4—1784no—
169C42—22no—
170C42—1784no—
171C23—1782no—
172C23—1782no—
173C23—1782no—
174C23—1782no—
175C23—1782no—
176C23—1782no—
177C23—1782no—
178C23C23×D8911yescharacteristic
179Q8—3564no—
180D4—3564no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—894no—
194C2×C4—1782no—
195C2×C4—1782no—
196C2×C4—1782no—
197C2×C4—1782no—
198C2×C4—1782no—
199C2×C4—1782no—
200C2×C4—1782no—
201C2×C4—1782no—
202C2×C4#1308357412yes—
203C22—3562no—
204C22—3562no—
205C22—3562no—
206C22—3562no—
207C22—3562no—
208C22—3562no—
209C22—3562no—
210C22#41×D8912yes—
211C22C2×#1308357411yescharacteristic
212C22#1566805711yescharacteristic
213C22#1566805812yes—
214C22#1566806011yescharacteristic
215C4—22no—
216C4—42no—
217C4—42no—
218C4—41no—
219C4—41no—
220C4—3562no—
221C4—3562no—
222C4—1784no—
223C2—7122no—
224C2#1915219511yescharacteristic
225C2#1915219612yes—
226C2#1915231011yescharacteristic
227C2#1915231112yes—
228C2#1915234011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#382×C89C2
prime radicalC22×D356C22
hypercenter#382D89
hypocenterC89#2785
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
1. #19151518C2semidirect
4. #19151511C2semidirect
5. #19151489C2semidirect
6. #19151488C2semidirect
7. #19151487C2semidirect
8. #19151462C2semidirect
9. #382×C89C2semidirect
115. C89#2785semidirect
124. #382D89semidirect

Maximal subgroups

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

subgroupindex
#191515182
#191515162
#191515152
#191515112
#191514892
#191514882
#191514872
#191514622
#382×C892
#278589