Finite Group Databasebeta

← #34060842

Subgroups — #34060842

Order 19072.

300 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 70 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×#18011982C211yesmaximal, characteristic, complemented
2C2×#18011976C212yesmaximal, complemented
3#23750600C212yesmaximal, complemented
4C2×C8×#10597010C211yesmaximal, characteristic, complemented
5C2×#18011934C211yesmaximal, characteristic
6C2×#14558746C2212yes—
7C2×D149⋊C8C2211yescharacteristic
8C2×C4×#10597010C2211yescharacteristic
9#18011982—22no—
10#18011976—24no—
11#18011968—24no—
12C8×#10597010—22no—
13C2×#14558737C2212yes—
14#18011934—22no—
15#18011934—22no—
16C2×#14558723C412yescomplemented
17C2×D1192C411yescharacteristic, complemented
18C2×C8×D149C2211yescharacteristic
19C2×Q16×C149C411yescharacteristic, complemented
20C22×#10597010—21no—
21#14558746—22no—
22#14558746—22no—
23D149⋊C8—21no—
24D149⋊C8—21no—
25C2×#11924753—22no—
26C2×#11924753D412yes—
27C4×#10597010—21no—
28C4×#10597010D412yes—
29#14558737—22no—
30#14558737—22no—
31#14558737—22no—
32#14558737—22no—
33C2×D596—22no—
34C2×D596C2×C412yes—
35C2×C4×D149—22no—
36C2×C4×D149C2311yescharacteristic
37#14558723—24no—
38D1192—22no—
39C2×#11924746C2×C411yescharacteristic
40C8×D149D412yes—
41C8×D149D412yes—
42C2×Q8×C149C2×C412yes—
43Q16×C149—22no—
44C2×C8×C149C2×C411yescharacteristic
45C2×#10597010—24no—
46C2×#10597010—22no—
47#11924753—22no—
48#11924753—42no—
49C22×D149—22no—
50C22×D149#4111yescharacteristic
51D596—22no—
52D596—22no—
53D596—42no—
54D596—42no—
55C2×Dic149C2×D411yescharacteristic
56C4×D149—42no—
57C4×D149—42no—
58C4×D149C2×D411yescharacteristic
59C4×D149C2×D411yescharacteristic
60C4×D149C2×D411yescharacteristic
61C4×D149#4111yescharacteristic
62#11924746C22⋊C412yes—
63Q8×C149—22no—
64Q8×C149—22no—
65C2×C4×C149—22no—
66C2×C4×C149C22×C411yescharacteristic
67C8×C149C22⋊C412yes—
68C22×C149C4×D411yescharacteristic
69C2×D149—22no—
70C2×D149—42no—
71C2×D149—44no—
72C2×D149#12111yescharacteristic
73C2×D149#12411yescharacteristic
74#10597010—24no—
75C4×C149—42no—
76C4×C149C2×C22⋊C411yescharacteristic
77C4×C149C4×D411yescharacteristic
78Dic149#12111yescharacteristic
79Dic149#12711yescharacteristic
80C2×C149#39011yescharacteristic
81C2×C149#44312yes—
82D149—21no—
83D149—21no—
84D149—82no—
85C149#197411yescharacteristic, complemented, Sylow
86#1974—1491nomaximal, Sylow
87C2×#135—1491no—
88C2×#108—1491no—
89C2×#104—1492no—
90#408—1492no—
91C2×C4×C8—1491no—
92C2×#41—1492no—
93#135—2982no—
94#135—2982no—
95C2×Q16#1059701011yescharacteristic, complemented
96C2×SD16—1492no—
97C2×D8—1491no—
98C2×M16—1492no—
99C22×C8—1491no—
100C22×C8—1491no—
101C2×C42—1491no—
102#108—2982no—
103#104—2984no—
104C22⋊C8—2984no—
105C4×C8—2982no—
106#41—2982no—
107#41—2982no—
108#41—2982no—
109#41—2982no—
110C2×Q8C2×#1059701012yes—
111C2×D4—2982no—
112C2×D4—1492no—
113C22×C4—2982no—
114C22×C4—2981no—
115C22×C4—1491no—
116Q16—22no—
117SD16—2984no—
118D8—2982no—
119M16—2982no—
120M16—2982no—
121C2×C8—2981no—
122C2×C8—2981no—
123C2×C8—2982no—
124C2×C8—1492no—
125C2×C8—1491no—
126C2×C8—1492no—
127C2×C8—1492no—
128C2×C8C2×#1059701011yescharacteristic
129C42—2981no—
130C42—1492no—
131C23—2982no—
132C23—1491no—
133Q8—22no—
134Q8—22no—
135D4—2982no—
136D4—2982no—
137D4—5962no—
138D4—5962no—
139C2×C4—22no—
140C2×C4—2984no—
141C2×C4—2982no—
142C2×C4—5962no—
143C2×C4—5962no—
144C2×C4—1491no—
145C2×C4—1491no—
146C2×C4—1491no—
147C2×C4—1491no—
148C2×C4—1491no—
149C2×C4C22×#1059701011yescharacteristic
150C8—2982no—
151C8—5962no—
152C8—1492no—
153C8C22⋊#1059701012yes—
154C22—2982no—
155C22—5964no—
156C22—5962no—
157C22—1491no—
158C22—1491no—
159C22D4×#1059701011yescharacteristic
160C4—42no—
161C4—2984no—
162C4—1491no—
163C4—1491no—
164C4C2×C22⋊#1059701011yescharacteristic
165C4D4×#1059701011yescharacteristic
166C2—2981no—
167C2—2981no—
168C2—11922no—
169C2#2375057711yescharacteristic
170C2#2375066912yes—
subgroupG/H
centerC22D4×#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC2×Q16×C149C4
socleC22×C149C4×D4
prime radicalC2×#18011934C2
cosocleC2×C4×D149C23
hypercenterC2×Q16#10597010
hypocenterC149#1974
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C2×#18011982C2semidirect
2. C2×#18011976C2semidirect
3. #23750600C2semidirect
4. C2×C8×#10597010C2semidirect
16. C2×#14558723C4semidirect
17. C2×D1192C4semidirect
19. C2×Q16×C149C4semidirect
85. C149#1974semidirect
95. C2×Q16#10597010semidirect

Maximal subgroups

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

subgroupindex
C2×#180119822
C2×#180119762
#237506002
C2×C8×#105970102
C2×#180119342
#1974149