Finite Group Databasebeta

← #34045921

Subgroups — #34045921

Order 19072.

290 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 67 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#23750206C211yesmaximal, characteristic
2C2×#18011837C212yesmaximal, complemented
3#23749627C212yesmaximal, complemented
4#23749490C211yesmaximal, characteristic, complemented
5#343×C149C211yesmaximal, characteristic, complemented
6C2×#14558736C2212yes—
7#18011891—22no—
8#18011886—22no—
9#18011885—22no—
10C2×C4⋊Dic149C2211yescharacteristic
11C2×C4×Dic149C2211yescharacteristic
12#18011837—24no—
13#18011836—22no—
14#18011833—22no—
15#18011818—22no—
16C2×M16×C149C2212yes—
17C2×C4⋊C4×C149C2211yescharacteristic
18#14558736—22no—
19#14558736—22no—
20#14558736—22no—
21#14558736—22no—
22C2×Dic298D412yes—
23C2×D596—22no—
24C2×D596D412yes—
25C2×C22⋊D149—22no—
26C22×Dic149—21no—
27C22×Dic149—21no—
28C2×C4×D149—22no—
29C4⋊Dic149—22no—
30C4⋊Dic149—22no—
31#14558713—24no—
32C4×Dic149—21no—
33C4×Dic149D412yescomplemented
34C22×C4×C149D412yes—
35C22×C4×C149C2311yescharacteristic
36M16×C149—22no—
37M16×C149—22no—
38C2×C8×C149—22no—
39C4⋊C4×C149—22no—
40C22×D149—22no—
41Dic298—22no—
42Dic298—22no—
43D596—22no—
44D596—22no—
45D596—82no—
46C22⋊D149—42no—
47C22⋊D149—42no—
48C2×Dic149—22no—
49C2×Dic149—22no—
50C2×Dic149—41no—
51C2×Dic149—41no—
52C2×Dic149—42no—
53C2×Dic149—41no—
54C4×D149—42no—
55C4×D149—42no—
56C23×C149C2×D411yescharacteristic
57C2×C4×C149—22no—
58C2×C4×C149—42no—
59C2×C4×C149C2×D411yescharacteristic
60C2×C4×C149C2×D412yes—
61C2×C4×C149#4112yes—
62C2×C4×C149#4111yescharacteristic
63C8×C149—42no—
64C22×C149—21no—
65C22×C149—21no—
66C22×C149#12011yescharacteristic
67C22×C149#12111yescharacteristic
68C22×C149#12411yescharacteristic
69C2×D149—42no—
70C2×D149—42no—
71C2×D149—42no—
72C4×C149—42no—
73C4×C149#12112yes—
74C4×C149#12312yes—
75Dic149—42no—
76Dic149—42no—
77Dic149—81no—
78C2×C149—21no—
79C2×C149—21no—
80C2×C149#39411yescharacteristic
81C2×C149#45411yescharacteristic
82C2×C149#45511yescharacteristic
83D149—82no—
84C149#204011yescharacteristic, complemented, Sylow
85#2040—1491nomaximal, Sylow
86#537—1491no—
87C2×#104—1492no—
88#417—1492no—
89#382—1491no—
90#343D14911yescharacteristic, complemented
91C2×#41—1492no—
92C2×M16C2×D14912yes—
93C22⋊Q8—2982no—
94#121—2982no—
95#121—2982no—
96C2×C4⋊C4—1491no—
97C2×C4⋊C4C2×D14911yescharacteristic
98C2×C42—1491no—
99#104—2984no—
100#103—2982no—
101#102—2982no—
102#95—2982no—
103#41—2982no—
104#41—2982no—
105#41—2982no—
106#41—2982no—
107C2×Q8—1492no—
108C2×D4—2982no—
109C2×D4—2982no—
110C2×D4—1492no—
111C22×C4—2981no—
112C22×C4—2982no—
113C22×C4—2981no—
114C22×C4D59612yes—
115C22×C4C22×D14911yescharacteristic
116M16—22no—
117M16—22no—
118C2×C8—22no—
119C4⋊C4—22no—
120C4⋊C4—2982no—
121C4⋊C4—2982no—
122C22⋊C4—2984no—
123C42—2981no—
124C42—1492no—
125C23—2982no—
126C23C2×D59611yescharacteristic
127Q8—2982no—
128Q8—2982no—
129D4—2982no—
130D4—2982no—
131D4—5962no—
132D4—5962no—
133D4—11922no—
134C2×C4—22no—
135C2×C4—42no—
136C2×C4—2982no—
137C2×C4—2982no—
138C2×C4—5961no—
139C2×C4—5961no—
140C2×C4—5962no—
141C2×C4—5962no—
142C2×C4—5962no—
143C2×C4—5961no—
144C2×C4D4×D14911yescharacteristic
145C2×C4D4×D14912yes—
146C2×C4#1455873612yes—
147C2×C4#1455873711yescharacteristic
148C8—42no—
149C22—21no—
150C22—21no—
151C22—5962no—
152C22—5962no—
153C22—5962no—
154C22#1801188111yescharacteristic
155C22#1801188611yescharacteristic
156C22#1801189911yescharacteristic
157C4—42no—
158C4—5962no—
159C4—5962no—
160C4—11921no—
161C4#1801188412yes—
162C4#1801189612yes—
163C2—21no—
164C2—21no—
165C2—11922no—
166C2#2374954311yescharacteristic
167C2#2374980011yescharacteristic
168C2#2374980511yescharacteristic
subgroupG/H
centerC22#18011881
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting#343×C149C2
socleC22×C149#120
prime radical#23750206C2
hypercenter#343D149
hypocenterC149#2040
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
2. C2×#18011837C2semidirect
3. #23749627C2semidirect
4. #23749490C2semidirect
5. #343×C149C2semidirect
33. C4×Dic149D4semidirect
84. C149#2040semidirect
90. #343D149semidirect

Maximal subgroups

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

subgroupindex
#237502062
C2×#180118372
#237496272
#237494902
#343×C1492
#2040149