Finite Group Databasebeta

← #37573040

Subgroups — #37573040

Order 24448.

312 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 85 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#27133430C211yesmaximal, characteristic
2#27133234C211yesmaximal, characteristic
3#27132671C212yesmaximal, complemented
4#27132419C212yesmaximal, complemented
5#410×C191C211yesmaximal, characteristic
6C22×Dic382C2211yescharacteristic
7#20259329—24no—
8C2×#15690271—22no—
9C2×#15690271C2212yes—
10#20259320C412yescomplemented
11#20259309C412yescomplemented
12#20259303—22no—
13#20259301—22no—
14#20259281C2211yescharacteristic
15#20259245—24no—
16C2×#41×C191C2211yescharacteristic
17#117×C191C2212yes—
18#99×C191—22no—
19C2×Dic382—21no—
20C2×Dic382—22no—
21C2×Dic382—22no—
22C2×Dic382C2×C412yes—
23C22×Dic191—21no—
24#15690271—24no—
25#15690271—22no—
26#15690271—22no—
27C2×C191⋊C8—24no—
28C2×C191⋊C8D414yes—
29C4⋊Dic191—21no—
30Dic191⋊C4—24no—
31C22⋊Dic191—24no—
32C22⋊Dic191—21no—
33C4×Dic191C2×C412yes—
34#41×C191—22no—
35#41×C191—22no—
36C2×Q8×C191C2×C411yescharacteristic
37C2×D4×C191C2×C411yescharacteristic
38C2×D4×C191D412yes—
39C22×C4×C191D412yes—
40C22×C4×C191C2311yescharacteristic
41C4⋊C4×C191—22no—
42C22⋊C4×C191—22no—
43C42×C191—22no—
44Dic382—24no—
45Dic382—41no—
46Dic382—41no—
47C2×Dic191—22no—
48C2×Dic191—22no—
49C2×Dic191—42no—
50C191⋊C8—24no—
51C23×C191C22⋊C412yes—
52C23×C191C2×D411yescharacteristic
53Q8×C191—22no—
54D4×C191—24no—
55D4×C191—22no—
56C2×C4×C191—22no—
57C2×C4×C191—22no—
58C2×C4×C191—42no—
59C2×C4×C191C22⋊C412yes—
60C2×C4×C191C22×C411yescharacteristic
61C2×C4×C191C2×D412yes—
62C2×C4×C191C2×D411yescharacteristic
63C2×C4×C191#4112yes—
64C22×C191—22no—
65C22×C191—41no—
66C22×C191—42no—
67C22×C191C2×C22⋊C411yescharacteristic
68C22×C191#12112yes—
69C4×C191—22no—
70C4×C191—82no—
71C4×C191C4×D412yes—
72C4×C191#12011yescharacteristic
73C4×C191#12311yescharacteristic
74Dic191—42no—
75Dic191—42no—
76C2×C191—21no—
77C2×C191—22no—
78C2×C191—42no—
79C2×C191#38611yescharacteristic
80C191#190911yescharacteristic, complemented, Sylow
81#1909—1911nomaximal, Sylow
82#568—1911no—
83#536—1911no—
84#419—1912no—
85#410D19111yescharacteristic
86H(3,ℤ/4)—1912no—
87C2×#41C2×D19111yescharacteristic
88C22×Q8—1911no—
89#131—3824no—
90C2×M16—3822no—
91C2×M16—1912no—
92C4⋊Q8—1912no—
93#124—1912no—
94#123—3822no—
95C22⋊Q8—3822no—
96#117—1911no—
97#117C2×D19112yes—
98#103—3824no—
99#99—22no—
100#41—22no—
101#41—22no—
102C2×Q8—3821no—
103C2×Q8—3822no—
104C2×Q8—3822no—
105C2×Q8—1912no—
106C2×Q8C4×D19111yescharacteristic
107C2×D4C4×D19111yescharacteristic
108C2×D4C22⋊D19112yes—
109C22×C4—3821no—
110C22×C4D76412yes—
111C22×C4C22×D19111yescharacteristic
112M16—3824no—
113M16—3822no—
114M16—3822no—
115C2×C8—3824no—
116C2×C8—1914no—
117C4⋊C4—22no—
118C4⋊C4—3824no—
119C4⋊C4—3821no—
120C22⋊C4—22no—
121C22⋊C4—3824no—
122C22⋊C4—3821no—
123C42—22no—
124C42—1912no—
125C23(C2×D191)⋊C412yes—
126C23C2×C22⋊D19111yescharacteristic
127Q8—22no—
128Q8—3824no—
129Q8—7641no—
130Q8—7641no—
131D4—24no—
132D4—22no—
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—42no—
136C2×C4—3822no—
137C2×C4—3822no—
138C2×C4—7642no—
139C2×C4(C2×D191)⋊C412yes—
140C2×C4C2×C4×D19111yescharacteristic
141C2×C4D4×D19112yes—
142C2×C4C2×D76411yescharacteristic
143C2×C4#1569028612yes—
144C8—3824no—
145C22—22no—
146C22—41no—
147C22—42no—
148C22C2×(C2×D191)⋊C411yescharacteristic
149C22#2025929412yes—
150C4—22no—
151C4—82no—
152C4—7642no—
153C4—7642no—
154C4(C22⋊D191)⋊C412yes—
155C4#2025929211yescharacteristic
156C4#2025930611yescharacteristic
157C2—22no—
158C2—21no—
159C2—42no—
160C2#2713254011yescharacteristic
subgroupG/H
centerC2#27132540
commutatorC2×C4×C191C22×C4
FrattiniC22×C4C22×D191
Fitting#410×C191C2
socleC2×C191#386
prime radicalC2×#41×C191C22
cosocleC22×C4×C191C23
hypercenter#410D191
hypocenterC191#1909
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
3. #27132671C2semidirect
4. #27132419C2semidirect
10. #20259320C4semidirect
11. #20259309C4semidirect
80. C191#1909semidirect

Maximal subgroups

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

subgroupindex
#271334302
#271332342
#271326712
#271324192
#410×C1912
#1909191