Finite Group Databasebeta

← #34054982

Subgroups — #34054982

Order 19072.

382 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 125 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#23750230C211yesmaximal, characteristic
2#23749949C212yesmaximal, complemented
3#23749932C212yesmaximal, complemented
4#23749825C212yesmaximal, complemented
5#23749764C212yesmaximal, complemented
6#23749723C212yesmaximal, complemented
7C4×#14558723C212yesmaximal, complemented
8#23749686C211yesmaximal, characteristic, complemented
9#519×C149C211yesmaximal, characteristic, complemented
10C2×#14558723C2212yes—
11C2×#14558723C2212yes—
12#18011908C2211yescharacteristic
13#18011903C2211yescharacteristic
14#18011896—22no—
15#18011885C2212yes—
16#18011884—22no—
17C4×D596C2212yes—
18#18011844C2212yes—
19#18011842C2212yes—
20C4⋊#11924746C2212yes—
21#18011835C2212yes—
22#18011835C2212yes—
23#18011831C2212yes—
24#18011831C2212yes—
25C22⋊#11924746C2212yes—
26#18011822C2211yescharacteristic
27C4×#11924746C2211yescharacteristic
28C22×Q8×C149C2211yescharacteristic
29C4×Q8×C149—22no—
30C4×Q8×C149C2212yes—
31C4×Q8×C149C2212yes—
32#117×C149—22no—
33#117×C149C2211yescharacteristic
34#117×C149C2211yescharacteristic
35C2×D596—22no—
36C2×D596C2312yes—
37C2×C22⋊D149—22no—
38C2×C4×D149—22no—
39#14558723—24no—
40#14558723—24no—
41C2×#11924746C2312yes—
42C2×#11924746C2312yes—
43C4⋊Dic149C2312yes—
44#14558715—22no—
45#14558713—22no—
46#14558713—22no—
47C2×Q8×C149—24no—
48C2×Q8×C149—21no—
49C2×Q8×C149C2312yes—
50C22×C4×C149—21no—
51C22×C4×C149C2311yescharacteristic
52C4⋊C4×C149—22no—
53C4⋊C4×C149—22no—
54C4⋊C4×C149D412yes—
55C4⋊C4×C149C2312yes—
56C22⋊C4×C149—21no—
57C22⋊C4×C149D412yes—
58C42×C149—22no—
59C42×C149—22no—
60C42×C149—21no—
61C42×C149C2311yescharacteristic
62C42×C149C2311yescharacteristic
63C22×D149—22no—
64D596—22no—
65D596—22no—
66D596—82no—
67C22⋊D149—82no—
68C2×Dic149—22no—
69C4×D149—82no—
70#11924746—22no—
71#11924746—22no—
72C23×C149C2×D411yescharacteristic
73Q8×C149—24no—
74Q8×C149—22no—
75Q8×C149#4114yes—
76C2×C4×C149—24no—
77C2×C4×C149—22no—
78C2×C4×C149—22no—
79C2×C4×C149—22no—
80C2×C4×C149C2×D412yes—
81C2×C4×C149C2×D412yes—
82C2×C4×C149C2×D411yescharacteristic
83C2×C4×C149C2411yescharacteristic
84C22×C149—21no—
85C22×C149—22no—
86C22×C149C22×D411yescharacteristic
87C2×D149—42no—
88C2×D149—42no—
89C2×D149—42no—
90C4×C149—24no—
91C4×C149—21no—
92C4×C149—22no—
93C4×C149—22no—
94C4×C149—42no—
95C4×C149C2×#4112yes—
96Dic149—42no—
97C2×C149—41no—
98C2×C149#52511yescharacteristic
99C2×C149#57712yes—
100D149—82no—
101C149#312611yescharacteristic, complemented, Sylow
102#3126—1491nomaximal, Sylow
103#540—1491no—
104#519D14911yescharacteristic, complemented
105#482—1492no—
106#479—1492no—
107#460—1492no—
108#448—1492no—
109#440—1492no—
110C4×SD16—1492no—
111#433—1491no—
112C22×Q8C2×D14911yescharacteristic
113C2×SD16—1492no—
114C2×SD16—1492no—
115#127—1491no—
116#125—1491no—
117#123—2982no—
118#121—2982no—
119#121—1492no—
120C4×Q8—22no—
121C4×Q8C2×D14912yes—
122C4×Q8C2×D14912yes—
123C4×D4—1492no—
124#117—22no—
125#117C2×D14911yescharacteristic
126#117C2×D14911yescharacteristic
127#107—1492no—
128#106—1492no—
129C4⋊C8—1492no—
130#103—1492no—
131#103—1492no—
132#102—1492no—
133#102—1492no—
134C22⋊C8—1492no—
135#97—1491no—
136C4×C8—1491no—
137C2×Q8—24no—
138C2×Q8—21no—
139C2×Q8C22×D14912yes—
140C2×D4—2982no—
141C2×D4—2982no—
142C2×D4—1492no—
143C22×C4—21no—
144C22×C4—2982no—
145C22×C4C22×D14911yescharacteristic
146SD16—2984no—
147SD16—2984no—
148C2×C8—1492no—
149C2×C8—1492no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—2982no—
153C4⋊C4—1492no—
154C4⋊C4C22⋊D14912yes—
155C4⋊C4C22×D14912yes—
156C22⋊C4—21no—
157C22⋊C4—2982no—
158C22⋊C4—2982no—
159C22⋊C4C22⋊D14912yes—
160C42—22no—
161C42—22no—
162C42—21no—
163C42C22×D14911yescharacteristic
164C42C22×D14911yescharacteristic
165C23—2982no—
166C23C2×C22⋊D14911yescharacteristic
167Q8—24no—
168Q8—22no—
169Q8#1455873614yes—
170D4—2982no—
171D4—2982no—
172D4—11922no—
173D4—11922no—
174C2×C4—24no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—2982no—
179C2×C4—11922no—
180C2×C4C2×C22⋊D14912yes—
181C2×C4C2×C22⋊D14912yes—
182C2×C4C2×C22⋊D14911yescharacteristic
183C2×C4C23×D14911yescharacteristic
184C8—2982no—
185C8—2982no—
186C22—22no—
187C22—21no—
188C22—5962no—
189C22—5962no—
190C22—5962no—
191C22C22×C22⋊D14911yescharacteristic
192C4—22no—
193C4—22no—
194C4—24no—
195C4—21no—
196C4—42no—
197C4—5962no—
198C4C2×#1455873612yes—
199C2—41no—
200C2—11922no—
201C2#2375013611yescharacteristic
202C2#2375043312yes—
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#519×C149C2
socleC22×C149C22×D4
prime radical#23750230C2
hypercenter#519D149
hypocenterC149#3126
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ #117 ◁ #519

Complements

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

NH ≅ G/Ntype
2. #23749949C2semidirect
3. #23749932C2semidirect
4. #23749825C2semidirect
5. #23749764C2semidirect
6. #23749723C2semidirect
7. C4×#14558723C2semidirect
8. #23749686C2semidirect
9. #519×C149C2semidirect
101. C149#3126semidirect
104. #519D149semidirect

Maximal subgroups

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

subgroupindex
#237502302
#237499492
#237499322
#237498252
#237497642
#237497232
C4×#145587232
#237496862
#519×C1492
#3126149