Finite Group Databasebeta

← #26019317

Subgroups — #26019317

Order 11392.

278 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 61 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#19151974C211yesmaximal, characteristic, complemented
2#19151798C211yesmaximal, characteristic, complemented
3#19151793C211yesmaximal, characteristic, complemented
4#19151342C211yesmaximal, characteristic, complemented
5Q8⋊#10623494C211yesmaximal, characteristic, complemented
6D4⋊#10623494C211yesmaximal, characteristic, complemented
7#550×C89C211yesmaximal, characteristic, complemented
8C2×#13083561—21no—
9C2×#13083559—22no—
10C2×#13083559—21no—
11#15668009C2211yescharacteristic
12C4⋊#10623494C2211yescharacteristic
13C4⋊#10623494C2211yescharacteristic
14#15667932—21no—
15#15667932—21no—
16C4×#10623494C2211yescharacteristic
17C2×#41×C89—21no—
18#127×C89—21no—
19#127×C89C2211yescharacteristic
20#121×C89—22no—
21#121×C89—21no—
22C4×Q8×C89C2211yescharacteristic
23C4×D4×C89—21no—
24C4×D4×C89C2211yescharacteristic
25C2×D356—21no—
26C2×D356—21no—
27C2×D356—21no—
28#13083561—42no—
29#13083559—44no—
30#13083559—42no—
31C2×#10623494—21no—
32C2×#10623494—21no—
33C2×#10623494—21no—
34#41×C89—42no—
35#41×C89—42no—
36C2×Q8×C89D411yescharacteristic
37C2×D4×C89—22no—
38C2×D4×C89—22no—
39C2×D4×C89—21no—
40C2×D4×C89—21no—
41C2×D4×C89D411yescharacteristic
42C2×D4×C89D412yes—
43C22×C4×C89—22no—
44C22×C4×C89—21no—
45C4⋊C4×C89—21no—
46C4⋊C4×C89D411yescharacteristic
47C4⋊C4×C89D411yescharacteristic
48C22⋊C4×C89—22no—
49C22⋊C4×C89—21no—
50C42×C89—21no—
51C42×C89C2311yescharacteristic
52C23×C89—21no—
53C23×C89—22no—
54C22×D89—41no—
55Q8×C89—21no—
56Q8×C89D812yescomplemented
57D4×C89—21no—
58D4×C89—21no—
59D4×C89—42no—
60D4×C89—44no—
61D4×C89—41no—
62D4×C89—41no—
63D4×C89—41no—
64D4×C89—41no—
65D4×C89—82no—
66C2×C4×C89—21no—
67C2×C4×C89—21no—
68C2×C4×C89—21no—
69C2×C4×C89—44no—
70C2×C4×C89—41no—
71C2×C4×C89—41no—
72C2×C4×C89C2×D411yescharacteristic
73C2×C4×C89C2×D411yescharacteristic
74C2×C4×C89C2×D411yescharacteristic
75D356—42no—
76D356—41no—
77D356—41no—
78D356—41no—
79D356—41no—
80#10623494—22no—
81#10623494—41no—
82#10623494—41no—
83C22×C89—42no—
84C22×C89—41no—
85C22×C89—41no—
86C22×C89—42no—
87C22×C89—42no—
88C22×C89—41no—
89C22×C89#12011yescharacteristic
90C2×D89—81no—
91C2×D89—81no—
92C2×D89—81no—
93C4×C89—22no—
94C4×C89—21no—
95C4×C89—41no—
96C4×C89—41no—
97C4×C89C2×D811yescharacteristic
98C4×C89#13511yescharacteristic
99C4×C89AGL(1,ℤ/8)11yescharacteristic
100C4×C89AGL(1,ℤ/8)11yescharacteristic
101C2×C89—81no—
102C2×C89—82no—
103C2×C89#44711yescharacteristic
104C2×C89#44911yescharacteristic
105C2×C89#45311yescharacteristic
106D89—161no—
107#1621—891nomaximal, Sylow
108C89#162111yescharacteristic, complemented, Sylow
109#550D8911yescharacteristic, complemented
110#493—891no—
111#460—891no—
112#459—891no—
113#331—891no—
114Q8⋊C8—891no—
115D4⋊C8—891no—
116C2×#41—21no—
117C2×SD16—1781no—
118C2×D8—1781no—
119C2×D8—1782no—
120#127—21no—
121#127—891no—
122#127C2×D8911yescharacteristic
123#121—22no—
124#121—21no—
125C4×Q8C2×D8911yescharacteristic
126C4×D4—21no—
127C4×D4C2×D8911yescharacteristic
128C4⋊C8—891no—
129C4⋊C8—891no—
130#102—1781no—
131#102—1781no—
132C4×C8—891no—
133#41—42no—
134#41—42no—
135C2×Q8C22⋊D8911yescharacteristic
136C2×D4—22no—
137C2×D4—22no—
138C2×D4—21no—
139C2×D4—21no—
140C2×D4—1781no—
141C2×D4—1781no—
142C2×D4—1781no—
143C2×D4C22⋊D8911yescharacteristic
144C2×D4C22⋊D8912yes—
145C22×C4—22no—
146C22×C4—21no—
147SD16—3562no—
148D8—3562no—
149D8—3564no—
150C2×C8—1781no—
151C2×C8—1781no—
152C2×C8—1781no—
153C4⋊C4—21no—
154C4⋊C4C22⋊D8911yescharacteristic
155C4⋊C4C22⋊D8911yescharacteristic
156C22⋊C4—22no—
157C22⋊C4—21no—
158C42—21no—
159C42C22×D8911yescharacteristic
160C23—21no—
161C23—22no—
162C23—3561no—
163Q8—21no—
164Q8#1308355912yescomplemented
165D4—21no—
166D4—21no—
167D4—42no—
168D4—44no—
169D4—41no—
170D4—41no—
171D4—41no—
172D4—41no—
173D4—82no—
174D4—3562no—
175D4—3561no—
176D4—3561no—
177D4—3561no—
178D4—3561no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—44no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4C2×C22⋊D8911yescharacteristic
186C2×C4C2×C22⋊D8911yescharacteristic
187C2×C4C2×C22⋊D8911yescharacteristic
188C8—3561no—
189C8—3561no—
190C8—1782no—
191C22—42no—
192C22—41no—
193C22—41no—
194C22—42no—
195C22—42no—
196C22—41no—
197C22—7121no—
198C22—7121no—
199C22—7121no—
200C22#1566798111yescharacteristic
201C4—22no—
202C4—21no—
203C4—41no—
204C4—41no—
205C4C2×#1308355911yescharacteristic
206C4#1566803211yescharacteristic
207C4#1566803711yescharacteristic
208C4#1566803811yescharacteristic
209C2—81no—
210C2—82no—
211C2—14241no—
212C2#1915173211yescharacteristic
213C2#1915174311yescharacteristic
214C2#1915176611yescharacteristic
subgroupG/H
centerC22#15667981
commutator, cosocleC42×C89C23
FrattiniC42C22×D89
Fitting#550×C89C2
socleC22×C89#120
hypercenter#550D89
hypocenterC89#1621
LCSG ▷ C42×C89 ▷ C22×C89 ▷ C89
UCSC1 ◁ C22 ◁ C42 ◁ #550

Complements

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

NH ≅ G/Ntype
1. #19151974C2semidirect
2. #19151798C2semidirect
3. #19151793C2semidirect
4. #19151342C2semidirect
5. Q8⋊#10623494C2semidirect
6. D4⋊#10623494C2semidirect
7. #550×C89C2semidirect
56. Q8×C89D8semidirect
108. C89#1621semidirect
109. #550D89semidirect
164. Q8#13083559semidirect

Maximal subgroups

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

subgroupindex
#191519742
#191517982
#191517932
#191513422
Q8⋊#106234942
D4⋊#106234942
#550×C892
#162189