Finite Group Databasebeta

← #34060756

Subgroups — #34060756

Order 19072.

186 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 60 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#23750632C211yesmaximal, characteristic
2#23750590C211yesmaximal, characteristic
3#23750501C211yesmaximal, characteristic
4#23750495C211yesmaximal, characteristic
5#23750495C211yesmaximal, characteristic
6(C2×#10597010)⋊C8C211yesmaximal, characteristic
7#23749662C211yesmaximal, characteristic
8C2×#14558746C2211yescharacteristic
9C2×#14558746C2211yescharacteristic
10C2×D149⋊C8C2211yescharacteristic
11C2×C4×#10597010C2211yescharacteristic
12#18011978—21no—
13C4⋊#11924753—21no—
14#18011966—21no—
15C4×#11924753—21no—
16C2×C8×D149C2211yescharacteristic
17#18011869C2211yescharacteristic
18#18011869C2211yescharacteristic
19#18011845C411yescharacteristic, complemented
20#18011842C411yescharacteristic, complemented
21#18011842C411yescharacteristic, complemented
22#107×C149C411yescharacteristic, complemented
23C22×#10597010—21no—
24#14558746—21no—
25#14558746—21no—
26#14558746—21no—
27#14558746Q812yes—
28D149⋊C8—21no—
29D149⋊C8—21no—
30C2×#11924753—21no—
31C2×#11924753—21no—
32C2×#11924753D411yescharacteristic
33C2×#11924753D411yescharacteristic
34C4×#10597010—21no—
35C4×#10597010—21no—
36C2×C4×D149C2311yescharacteristic
37C2×#11924746C2×C411yescharacteristic
38C8×D149—21no—
39C8×D149—21no—
40C4⋊Dic149C2×C411yescharacteristic
41C4⋊Dic149C2×C411yescharacteristic
42#14558713—21no—
43#14558713—21no—
44C4×Dic149—21no—
45C4×Dic149—21no—
46C2×C8×C149C2×C411yescharacteristic
47C4⋊C4×C149C2×C411yescharacteristic
48C4⋊C4×C149C2×C411yescharacteristic
49C2×#10597010—22no—
50C2×#10597010—41no—
51C2×#10597010—41no—
52#11924753—22no—
53#11924753—21no—
54#11924753—21no—
55#11924753—41no—
56C22×D149#4111yescharacteristic
57C2×Dic149—21no—
58C2×Dic149—21no—
59C2×Dic149C2×D411yescharacteristic
60C4×D149C2×Q811yescharacteristic
61C4×D149#4111yescharacteristic
62C4×D149#4111yescharacteristic
63C4×D149#4111yescharacteristic
64#11924746—21no—
65C2×C4×C149—21no—
66C2×C4×C149—21no—
67C2×C4×C149C22×C411yescharacteristic
68C8×C149—21no—
69C22×C149C4×D411yescharacteristic
70C2×D149—21no—
71C2×D149—21no—
72C2×D149#12511yescharacteristic
73C2×D149#12611yescharacteristic
74#10597010—42no—
75C4×C149—41no—
76C4×C149—41no—
77C4×C149#11711yescharacteristic
78C4×C149C4×Q811yescharacteristic
79Dic149—41no—
80Dic149—41no—
81Dic149C22⋊Q811yescharacteristic
82Dic149#12311yescharacteristic
83C2×C149#38711yescharacteristic
84C2×C149#44311yescharacteristic
85C2×C149#44411yescharacteristic
86D149—21no—
87D149—21no—
88C149#192211yescharacteristic, complemented, Sylow
89#1922—1491nomaximal, Sylow
90#427—1491no—
91#424—1491no—
92#405—1491no—
93#341—1491no—
94#339—1491no—
95#339—1491no—
96#336—1491no—
97C2×M16—1491no—
98C2×M16—1491no—
99C22×C8—1491no—
100C22×C8—1491no—
101#117—1491no—
102#117—1491no—
103C2×C42—1491no—
104#107—1491no—
105#107#1059701011yescharacteristic, complemented
106#106—1491no—
107#106—1491no—
108C4⋊C8—2981no—
109C4⋊C8—2981no—
110#97—2981no—
111C4×C8—2981no—
112C22×C4—2981no—
113C22×C4—1491no—
114M16—2981no—
115M16—2981no—
116M16—2981no—
117M16—1492no—
118C2×C8—2981no—
119C2×C8—2981no—
120C2×C8—2981no—
121C2×C8—2981no—
122C2×C8—2981no—
123C2×C8—2981no—
124C2×C8—1491no—
125C2×C8—1491no—
126C2×C8—1491no—
127C2×C8C2×#1059701011yescharacteristic
128C4⋊C4—1491no—
129C4⋊C4—1491no—
130C4⋊C4C2×#1059701011yescharacteristic
131C4⋊C4C2×#1059701011yescharacteristic
132C22⋊C4—2981no—
133C22⋊C4—2981no—
134C42—2981no—
135C42—2981no—
136C42—2981no—
137C42—2981no—
138C23—1491no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—2982no—
142C2×C4—2981no—
143C2×C4—2981no—
144C2×C4—5961no—
145C2×C4—5961no—
146C2×C4—1491no—
147C2×C4—1491no—
148C2×C4—1491no—
149C2×C4—1491no—
150C2×C4—1491no—
151C2×C4C22×#1059701011yescharacteristic
152C8—21no—
153C8—2981no—
154C8—2981no—
155C8—2982no—
156C8—2981no—
157C8—5961no—
158C22—2981no—
159C22—2981no—
160C22—1491no—
161C22—1491no—
162C22D4×#1059701011yescharacteristic
163C4—41no—
164C4—41no—
165C4—5962no—
166C4—5961no—
167C4—5961no—
168C4—1491no—
169C4—1491no—
170C4#1801199011yescharacteristic
171C4Q8×#1059701011yescharacteristic
172C2—2981no—
173C2—2981no—
174C2#2375057411yescharacteristic
175C2#2375066711yescharacteristic
176C2#2375067111yescharacteristic
subgroupG/H
centerC22D4×#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#107×C149C4
socleC22×C149C4×D4
prime radicalC22×D149#41
cosocleC2×C4×D149C23
hypercenter#107#10597010
hypocenterC149#1922
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
19. #18011845C4semidirect
20. #18011842C4semidirect
21. #18011842C4semidirect
22. #107×C149C4semidirect
88. C149#1922semidirect
105. #107#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506322
#237505902
#237505012
#237504952
(C2×#10597010)⋊C82
#237496622
#1922149