Finite Group Databasebeta

← #34044007

Subgroups — #34044007

Order 19072.

208 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 45 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#23750369C211yesmaximal, characteristic
2#23750031C211yesmaximal, characteristic, complemented
3#23750017C211yesmaximal, characteristic, complemented
4#23749366C211yesmaximal, characteristic, complemented
5#23749365C211yesmaximal, characteristic, complemented
6#23749364C211yesmaximal, characteristic, complemented
7#489×C149C211yesmaximal, characteristic, complemented
8C2×#14558726—21no—
9C2×#14558723—21no—
10#18011903C2211yescharacteristic
11#18011899C2211yescharacteristic
12#18011895—21no—
13#18011893—21no—
14#18011888—21no—
15#18011887—21no—
16#18011884—21no—
17#18011883—21no—
18#18011844—21no—
19#18011842—21no—
20#18011822C2211yescharacteristic
21#18011822C2211yescharacteristic
22C4⋊Q8×C149C2211yescharacteristic
23#124×C149C2211yescharacteristic
24#103×C149—21no—
25#102×C149—21no—
26#97×C149C2211yescharacteristic
27C2×Dic298D411yescharacteristic
28C2×D596D411yescharacteristic
29C2×C22⋊D149—21no—
30C2×C22⋊D149—21no—
31C22×Dic149—21no—
32C2×C4×D149—21no—
33#14558726—42no—
34#14558723—42no—
35C2×#11924746—21no—
36C2×#11924746—21no—
37C4⋊Dic149—21no—
38C4⋊Dic149D411yescharacteristic
39C4⋊Dic149D411yescharacteristic
40#14558715—21no—
41#14558715—21no—
42#14558715—21no—
43C22⋊Dic149—21no—
44#14558713—21no—
45#14558713—21no—
46#14558713—21no—
47C2×Q8×C149—21no—
48C2×Q8×C149D411yescharacteristic
49C2×D4×C149D411yescharacteristic
50C2×C8×C149—21no—
51C4⋊C4×C149—21no—
52C4⋊C4×C149—21no—
53C22⋊C4×C149—21no—
54C22⋊C4×C149—21no—
55C42×C149C2311yescharacteristic
56C22×D149—21no—
57Dic298—41no—
58D596—41no—
59C22⋊D149—81no—
60C22⋊D149—81no—
61C2×Dic149—21no—
62C2×Dic149—21no—
63C2×Dic149—21no—
64C2×Dic149—81no—
65C4×D149—81no—
66#11924746—22no—
67#11924746—22no—
68C23×C149—21no—
69Q8×C149—41no—
70Q8×C149—41no—
71Q8×C149—41no—
72D4×C149—41no—
73C2×C4×C149—21no—
74C2×C4×C149—41no—
75C2×C4×C149C2×D411yescharacteristic
76C2×C4×C149C2×D411yescharacteristic
77C2×C4×C149C2×D411yescharacteristic
78C8×C149—41no—
79C22×C149—41no—
80C22×C149—41no—
81C22×C149—41no—
82C22×C149#12011yescharacteristic
83C2×D149—41no—
84C2×D149—41no—
85C2×D149—41no—
86C4×C149—21no—
87C4×C149—21no—
88C4×C149—21no—
89C4×C149—41no—
90C4×C149—81no—
91Dic149—41no—
92Dic149—41no—
93Dic149—41no—
94C2×C149—81no—
95C2×C149#45311yescharacteristic
96C2×C149#45511yescharacteristic
97C2×C149#45611yescharacteristic
98D149—81no—
99C149#166111yescharacteristic, complemented, Sylow
100#1661—1491nomaximal, Sylow
101#562—1491no—
102#501—1491no—
103#497—1491no—
104#489D14911yescharacteristic, complemented
105#330—1491no—
106#329—1491no—
107#329—1491no—
108C2×Q16—2981no—
109C2×SD16—2981no—
110C4⋊Q8C2×D14911yescharacteristic
111#125—1491no—
112#124—1491no—
113#124C2×D14911yescharacteristic
114#123—2981no—
115#123—2981no—
116C22⋊Q8—2981no—
117C22⋊Q8—2981no—
118#121—2981no—
119#121—2981no—
120#107—2981no—
121#106—2981no—
122#103—21no—
123#102—21no—
124#97—1491no—
125#97—1491no—
126#97C2×D14911yescharacteristic
127C2×Q8—21no—
128C2×Q8—1491no—
129C2×Q8C22⋊D14911yescharacteristic
130C2×D4—2981no—
131C2×D4—2981no—
132C2×D4—1491no—
133C2×D4C22⋊D14911yescharacteristic
134C22×C4—2981no—
135C22×C4—2981no—
136Q16—5962no—
137SD16—5962no—
138C2×C8—21no—
139C2×C8—2981no—
140C2×C8—2981no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—2981no—
144C4⋊C4—2981no—
145C4⋊C4—2981no—
146C4⋊C4—2981no—
147C4⋊C4—1491no—
148C4⋊C4—1491no—
149C22⋊C4—21no—
150C22⋊C4—21no—
151C22⋊C4—2981no—
152C22⋊C4—2981no—
153C22⋊C4—2981no—
154C22⋊C4—2981no—
155C42C22×D14911yescharacteristic
156C23—21no—
157C23—2981no—
158Q8—41no—
159Q8—41no—
160Q8—41no—
161Q8—5961no—
162D4—41no—
163D4—5961no—
164D4—11921no—
165D4—11921no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—2981no—
169C2×C4—2981no—
170C2×C4—2981no—
171C2×C4—11921no—
172C2×C4—11921no—
173C2×C4D4×D14911yescharacteristic
174C2×C4D4×D14911yescharacteristic
175C2×C4C2×C22⋊D14911yescharacteristic
176C8—41no—
177C8—2982no—
178C8—2982no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—5961no—
183C22—5961no—
184C22—5961no—
185C22#1801187911yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—41no—
190C4—81no—
191C4—5961no—
192C4—5961no—
193C4—5961no—
194C2—81no—
195C2—11921no—
196C2#2374979111yescharacteristic
197C2#2374980211yescharacteristic
198C2#2374980611yescharacteristic
subgroupG/H
centerC22#18011879
commutator, cosocleC42×C149C23
FrattiniC42C22×D149
Fitting#489×C149C2
socleC22×C149#120
prime radical#23750369C2
hypercenter#489D149
hypocenterC149#1661
LCSG ▷ C42×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
2. #23750031C2semidirect
3. #23750017C2semidirect
4. #23749366C2semidirect
5. #23749365C2semidirect
6. #23749364C2semidirect
7. #489×C149C2semidirect
99. C149#1661semidirect
104. #489D149semidirect

Maximal subgroups

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

subgroupindex
#237503692
#237500312
#237500172
#237493662
#237493652
#237493642
#489×C1492
#1661149