Finite Group Databasebeta

← #34060828

Subgroups — #34060828

Order 19072.

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

normal subgroups only

This group has 320 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
1#23750629C211yesmaximal, characteristic, complemented
2C2×#18011976C212yesmaximal, complemented
3C2×#18011975C212yesmaximal, complemented
4#23750561C211yesmaximal, characteristic, complemented
5#23750174C211yesmaximal, characteristic
6C2×#14558746C2212yes—
7C2×C4×#10597010C2212yes—
8C4⋊#11924753—22no—
9#18011976—24no—
10#18011975—24no—
11(C2×#10597010)⋊C4—22no—
12C2×#14558737C2211yescharacteristic
13C2×#14558735C2211yescharacteristic
14#18011909C411yescharacteristic, complemented
15#18011907C411yescharacteristic, complemented
16#18011899C411yescharacteristic, complemented
17#18011884—22no—
18#18011871—22no—
19C42×D149C2211yescharacteristic
20#124×C149C411yescharacteristic, complemented
21C22×#10597010—22no—
22#14558746—22no—
23#14558746—22no—
24C2×#11924753—22no—
25C4×#10597010—22no—
26C4×#10597010D414yescomplemented
27#14558737—22no—
28#14558737—22no—
29#14558735—22no—
30#14558735—22no—
31C2×Dic298C2×C411yescharacteristic
32C2×D596—21no—
33C2×D596C2×C411yescharacteristic
34C2×C22⋊D149—21no—
35C2×C22⋊D149—22no—
36C22×Dic149—21no—
37C2×C4×D149—21no—
38C2×C4×D149D412yes—
39C2×C4×D149C2311yescharacteristic
40#14558715—22no—
41#14558713—22no—
42C4×Dic149C2×C411yescharacteristic
43C4×Dic149D412yes—
44C2×Q8×C149C2×C411yescharacteristic
45C2×D4×C149C2×C411yescharacteristic
46C22⋊C4×C149—22no—
47C42×C149C2×C411yescharacteristic
48C2×#10597010—24no—
49C2×#10597010—44no—
50#11924753—42no—
51C22×D149—21no—
52C22×D149C2×D411yescharacteristic
53Dic298—22no—
54D596—22no—
55D596—42no—
56C22⋊D149—44no—
57C22⋊D149—42no—
58C2×Dic149—21no—
59C2×Dic149—41no—
60C2×Dic149—41no—
61C2×Dic149C22⋊C412yes—
62C2×Dic149C2×D411yescharacteristic
63C4×D149—42no—
64C4×D149—41no—
65C4×D149—41no—
66C4×D149C2×D412yes—
67C4×D149#4112yes—
68C23×C149—21no—
69Q8×C149—22no—
70D4×C149—22no—
71C2×C4×C149—21no—
72C2×C4×C149C22⋊C412yes—
73C2×C4×C149C22×C411yescharacteristic
74C22×C149—41no—
75C22×C149—42no—
76C22×C149C2×C22⋊C411yescharacteristic
77C2×D149—22no—
78C2×D149—41no—
79C2×D149—42no—
80C2×D149#12112yes—
81#10597010—44no—
82C4×C149—22no—
83C4×C149—41no—
84C4×C149C4×D412yes—
85Dic149—22no—
86Dic149—41no—
87Dic149#12411yescharacteristic
88Dic149#12711yescharacteristic
89C2×C149—81no—
90C2×C149#39011yescharacteristic
91C2×C149#42112yes—
92D149—22no—
93D149—81no—
94C149#196311yescharacteristic, complemented, Sylow
95#1963—1491nomaximal, Sylow
96#532—1491no—
97#423—1491no—
98C2×#104—1492no—
99C2×#104—1492no—
100#376—1491no—
101C2×#41—1491no—
102C2×#41—1491no—
103C2×M16—1492no—
104C4⋊Q8—1491no—
105#127—1491no—
106#124—1491no—
107#124#1059701011yescharacteristic, complemented
108#121—2982no—
109C4×D4—2982no—
110C2×C42—1492no—
111C2×C42—1491no—
112C4⋊C8—2982no—
113#104—2984no—
114#104—2984no—
115#95—2982no—
116#41—2982no—
117#41—2982no—
118#41—2982no—
119#41—2982no—
120C2×Q8—1491no—
121C2×Q8C2×#1059701011yescharacteristic
122C2×D4—2981no—
123C2×D4—2981no—
124C2×D4—2982no—
125C2×D4—1491no—
126C2×D4C2×#1059701011yescharacteristic
127C22×C4—2981no—
128C22×C4—2982no—
129C22×C4—2981no—
130C22×C4—1492no—
131C22×C4—1491no—
132M16—2982no—
133M16—2982no—
134C2×C8—2982no—
135C4⋊C4—2982no—
136C22⋊C4—22no—
137C22⋊C4—2982no—
138C42—2982no—
139C42—1494no—
140C42—1492no—
141C42—1491no—
142C42C2×#1059701011yescharacteristic
143C23—21no—
144C23—2981no—
145C23—1491no—
146Q8—22no—
147Q8—2982no—
148D4—22no—
149D4—2982no—
150D4—5962no—
151D4—5964no—
152D4—5962no—
153C2×C4—21no—
154C2×C4—2984no—
155C2×C4—2981no—
156C2×C4—5962no—
157C2×C4—5961no—
158C2×C4—5961no—
159C2×C4—5964no—
160C2×C4—5961no—
161C2×C4—5961no—
162C2×C4—1492no—
163C2×C4—1491no—
164C2×C4—1492no—
165C2×C4—1492no—
166C2×C4C22⋊#1059701012yes—
167C2×C4C22×#1059701011yescharacteristic
168C8—5962no—
169C22—41no—
170C22—42no—
171C22—2982no—
172C22—5961no—
173C22—5962no—
174C22—1492no—
175C22C2×C22⋊#1059701011yescharacteristic
176C4—22no—
177C4—41no—
178C4—2982no—
179C4—5964no—
180C4—5961no—
181C4—1491no—
182C4—1491no—
183C4D4×#1059701012yes—
184C2—81no—
185C2—2982no—
186C2—11921no—
187C2#2375057711yescharacteristic
188C2#2375062212yes—
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#124×C149C4
socleC22×C149C2×C22⋊C4
prime radical#23750174C2
cosocleC2×C4×D149C23
hypercenter#124#10597010
hypocenterC149#1963
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #23750629C2semidirect
2. C2×#18011976C2semidirect
3. C2×#18011975C2semidirect
4. #23750561C2semidirect
14. #18011909C4semidirect
15. #18011907C4semidirect
16. #18011899C4semidirect
20. #124×C149C4semidirect
26. C4×#10597010D4semidirect
94. C149#1963semidirect
107. #124#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506292
C2×#180119762
C2×#180119752
#237505612
#237501742
#1963149