Finite Group Databasebeta

← #26020883

Subgroups — #26020883

Order 11392.

254 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 95 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×#15667943C211yesmaximal, characteristic
2C2×#15667936C211yesmaximal, characteristic
3C2×#15667936C211yesmaximal, characteristic
4C4×C4⋊Dic89C211yesmaximal, characteristic
5#19151360C211yesmaximal, characteristic
6#19151353C211yesmaximal, characteristic
7#391×C89C211yesmaximal, characteristic
8C22×#10623494C2211yescharacteristic
9C22×#10623494C2211yescharacteristic
10C2×C4⋊Dic89C2211yescharacteristic
11C2×C4⋊Dic89C2211yescharacteristic
12C2×C4×Dic89—21no—
13#15667943—22no—
14#15667936—22no—
15#15667936C414yescomplemented
16#15667919—21no—
17C22×Q8×C89C2211yescharacteristic
18C2×C4⋊C4×C89C2211yescharacteristic
19C2×C42×C89C2211yescharacteristic
20#95×C89—21no—
21#95×C89—21no—
22C22×Dic89—21no—
23C22×Dic89—21no—
24C2×#10623494—21no—
25C2×#10623494—21no—
26C2×#10623494—21no—
27C2×#10623494—21no—
28C2×#10623494—21no—
29C2×#10623494C2×C412yes—
30C4⋊Dic89—21no—
31C4⋊Dic89—21no—
32C4⋊Dic89C2×C412yes—
33C4⋊Dic89D412yes—
34C4×Dic89—42no—
35C2×Q8×C89—21no—
36C2×Q8×C89—21no—
37C2×Q8×C89—21no—
38C2×Q8×C89—21no—
39C2×Q8×C89—21no—
40C2×Q8×C89C2×C412yes—
41C22×C4×C89—21no—
42C22×C4×C89—21no—
43C22×C4×C89D411yescharacteristic
44C22×C4×C89D411yescharacteristic
45C22×C4×C89C2311yescharacteristic
46C4⋊C4×C89—21no—
47C4⋊C4×C89—21no—
48C42×C89—21no—
49C42×C89—21no—
50C23×C89C2×D411yescharacteristic
51Q8×C89—22no—
52Q8×C89—22no—
53Q8×C89—41no—
54Q8×C89—41no—
55C2×C4×C89—21no—
56C2×C4×C89—21no—
57C2×C4×C89—22no—
58C2×C4×C89—21no—
59C2×C4×C89—21no—
60C2×C4×C89—21no—
61C2×C4×C89—41no—
62C2×C4×C89—41no—
63C2×C4×C89—41no—
64C2×C4×C89—41no—
65C2×C4×C89—41no—
66C2×C4×C89SD1612yes—
67C2×C4×C89C22×C411yescharacteristic
68C2×C4×C89C2×D411yescharacteristic
69C2×C4×C89#4111yescharacteristic
70C2×C4×C89#4111yescharacteristic
71C2×C4×C89#4111yescharacteristic
72C2×C4×C89#4111yescharacteristic
73C2×Dic89—22no—
74C2×Dic89—22no—
75C2×Dic89—41no—
76C2×Dic89—41no—
77C2×Dic89—41no—
78C2×Dic89—41no—
79#10623494—22no—
80#10623494—41no—
81C22×C89C4×D411yescharacteristic
82C22×C89#12111yescharacteristic
83C22×C89#12311yescharacteristic
84C22×C89C2×SD1611yescharacteristic
85C22×C89#13511yescharacteristic
86C22×C89#13711yescharacteristic
87C22×C89#13711yescharacteristic
88C4×C89—22no—
89C4×C89—42no—
90C4×C89—41no—
91C4×C89—81no—
92C4×C89#11711yescharacteristic
93C4×C89C4×D411yescharacteristic
94C4×C89#12411yescharacteristic
95C4×C89#12611yescharacteristic
96Dic89—42no—
97Dic89—42no—
98C2×C89#38811yescharacteristic
99C2×C89C4×SD1611yescharacteristic
100C2×C89#44111yescharacteristic
101C2×C89#46111yescharacteristic
102C2×C89#46411yescharacteristic
103C2×C89#48311yescharacteristic
104C2×C89#48511yescharacteristic
105#1927—891nomaximal, Sylow
106C89#192711yescharacteristic, complemented, Sylow
107C2×#106—891no—
108C2×#103—891no—
109C2×#103—891no—
110#391D8911yescharacteristic
111C4×C4⋊C4—891no—
112#340—891no—
113#336—891no—
114C22×Q8C2×D8911yescharacteristic
115C22×C8—891no—
116C22×C8—891no—
117C2×C4⋊C4—891no—
118C2×C4⋊C4—891no—
119C2×C4⋊C4C2×D8911yescharacteristic
120C2×C42—1781no—
121C2×C42C2×D8911yescharacteristic
122#106—1782no—
123#103—894no—
124#103—1782no—
125#95—21no—
126#95—21no—
127#95—1781no—
128C2×Q8—21no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8C4×D8912yes—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—1781no—
137C22×C4—1781no—
138C22×C4C22⋊D8911yescharacteristic
139C22×C4C22⋊D8911yescharacteristic
140C22×C4C22×D8911yescharacteristic
141C2×C8—892no—
142C2×C8—1781no—
143C2×C8—1781no—
144C2×C8—1781no—
145C2×C8—1781no—
146C2×C8—1781no—
147C4⋊C4—21no—
148C4⋊C4—21no—
149C4⋊C4—892no—
150C4⋊C4—892no—
151C4⋊C4—1781no—
152C4⋊C4—1781no—
153C42—21no—
154C42—21no—
155C42—3562no—
156C23C2×C22⋊D8911yescharacteristic
157Q8—22no—
158Q8—22no—
159Q8—41no—
160Q8—41no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—3561no—
173C2×C4—3561no—
174C2×C4—3561no—
175C2×C4—3561no—
176C2×C4—1782no—
177C2×C4—1782no—
178C2×C4#1308356112yes—
179C2×C4C2×C4×D8911yescharacteristic
180C2×C4D4×D8911yescharacteristic
181C2×C4#1308357311yescharacteristic
182C2×C4#1308357311yescharacteristic
183C2×C4#1308357311yescharacteristic
184C2×C4#1308357411yescharacteristic
185C8—3561no—
186C8—1782no—
187C22C4×C22⋊D8911yescharacteristic
188C22#1566798311yescharacteristic
189C22#1566799311yescharacteristic
190C22C2×#1308356111yescharacteristic
191C22#1566803211yescharacteristic
192C22#1566804211yescharacteristic
193C22#1566804311yescharacteristic
194C4—22no—
195C4—41no—
196C4—42no—
197C4—81no—
198C4—3562no—
199C4—3562no—
200C4#1566796811yescharacteristic
201C4#1566797211yescharacteristic
202C4#1566799811yescharacteristic
203C4#1566800511yescharacteristic
204C2#1915148611yescharacteristic
205C2C4×#1308356111yescharacteristic
206C2#1915170311yescharacteristic
207C2#1915180011yescharacteristic
208C2#1915181711yescharacteristic
209C2#1915192611yescharacteristic
210C2#1915193611yescharacteristic
subgroupG/H
centerC23C2×C22⋊D89
commutatorC2×C4×C89C22×C4
FrattiniC22×C4C22×D89
Fitting#391×C89C2
socle, prime radicalC23×C89C2×D4
cosocleC22×C4×C89C23
hypercenter#391D89
hypocenterC89#1927
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
15. #15667936C4semidirect
106. C89#1927semidirect

Maximal subgroups

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

subgroupindex
C2×#156679432
C2×#156679362
C4×C4⋊Dic892
#191513602
#191513532
#391×C892
#192789