Finite Group Databasebeta

← #1661×C149 #34040574

Subgroups — #1661×C149 #34040574

Order 19072.

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

normal subgroups only

This group has 208 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#562×C149C211yesmaximal, characteristic
2#501×C149C211yesmaximal, characteristic, complemented
3#497×C149C211yesmaximal, characteristic, complemented
4#489×C149C211yesmaximal, characteristic, complemented
5#330×C149C211yesmaximal, characteristic, complemented
6#329×C149C211yesmaximal, characteristic, complemented
7#329×C149C211yesmaximal, characteristic, complemented
8C2×Q16×C149—21no—
9C2×SD16×C149—21no—
10C4⋊Q8×C149C2211yescharacteristic
11#125×C149C2211yescharacteristic
12#124×C149C2211yescharacteristic
13#124×C149C2211yescharacteristic
14#123×C149—21no—
15#123×C149—21no—
16C22⋊Q8×C149—21no—
17C22⋊Q8×C149—21no—
18#121×C149—21no—
19#121×C149—21no—
20#107×C149—21no—
21#106×C149—21no—
22#103×C149—21no—
23#102×C149—21no—
24#97×C149C2211yescharacteristic
25#97×C149C2211yescharacteristic
26#97×C149C2211yescharacteristic
27C2×Q8×C149—21no—
28C2×Q8×C149D411yescharacteristic
29C2×Q8×C149D411yescharacteristic
30C2×D4×C149—21no—
31C2×D4×C149—21no—
32C2×D4×C149D411yescharacteristic
33C2×D4×C149D411yescharacteristic
34C22×C4×C149—21no—
35C22×C4×C149—21no—
36Q16×C149—42no—
37SD16×C149—42no—
38C2×C8×C149—21no—
39C2×C8×C149—21no—
40C2×C8×C149—21no—
41C4⋊C4×C149—21no—
42C4⋊C4×C149—21no—
43C4⋊C4×C149—21no—
44C4⋊C4×C149—21no—
45C4⋊C4×C149—21no—
46C4⋊C4×C149—21no—
47C4⋊C4×C149D411yescharacteristic
48C4⋊C4×C149D411yescharacteristic
49C22⋊C4×C149—21no—
50C22⋊C4×C149—21no—
51C22⋊C4×C149—21no—
52C22⋊C4×C149—21no—
53C22⋊C4×C149—21no—
54C22⋊C4×C149—21no—
55C42×C149C2311yescharacteristic
56C23×C149—21no—
57C23×C149—21no—
58Q8×C149—41no—
59Q8×C149—41no—
60Q8×C149—41no—
61Q8×C149—41no—
62D4×C149—41no—
63D4×C149—41no—
64D4×C149—81no—
65D4×C149—81no—
66C2×C4×C149—21no—
67C2×C4×C149—21no—
68C2×C4×C149—21no—
69C2×C4×C149—21no—
70C2×C4×C149—41no—
71C2×C4×C149—81no—
72C2×C4×C149—81no—
73C2×C4×C149C2×D411yescharacteristic
74C2×C4×C149C2×D411yescharacteristic
75C2×C4×C149C2×D411yescharacteristic
76C8×C149—22no—
77C8×C149—22no—
78C8×C149—41no—
79C22×C149—41no—
80C22×C149—41no—
81C22×C149—41no—
82C22×C149—41no—
83C22×C149—41no—
84C22×C149—41no—
85C22×C149#12011yescharacteristic
86C4×C149—21no—
87C4×C149—21no—
88C4×C149—21no—
89C4×C149—41no—
90C4×C149—41no—
91C4×C149—41no—
92C4×C149—41no—
93C4×C149—81no—
94C2×C149—81no—
95C2×C149—81no—
96C2×C149#45311yescharacteristic
97C2×C149#45511yescharacteristic
98C2×C149#45611yescharacteristic
99C149#166111yescharacteristic, direct product factor, Sylow
100#1661C14911yesmaximal, characteristic, direct product factor, Sylow
101#562C2×C14911yescharacteristic
102#501C2×C14911yescharacteristic, complemented
103#497C2×C14911yescharacteristic, complemented
104#489C2×C14911yescharacteristic, complemented
105#330C2×C14911yescharacteristic, complemented
106#329C2×C14911yescharacteristic, complemented
107#329C2×C14911yescharacteristic, complemented
108C2×Q16—21no—
109C2×SD16—21no—
110C4⋊Q8C22×C14911yescharacteristic
111#125C22×C14911yescharacteristic
112#124C22×C14911yescharacteristic
113#124C22×C14911yescharacteristic
114#123—21no—
115#123—21no—
116C22⋊Q8—21no—
117C22⋊Q8—21no—
118#121—21no—
119#121—21no—
120#107—21no—
121#106—21no—
122#103—21no—
123#102—21no—
124#97C22×C14911yescharacteristic
125#97C22×C14911yescharacteristic
126#97C22×C14911yescharacteristic
127C2×Q8—21no—
128C2×Q8D4×C14911yescharacteristic
129C2×Q8D4×C14911yescharacteristic
130C2×D4—21no—
131C2×D4—21no—
132C2×D4D4×C14911yescharacteristic
133C2×D4D4×C14911yescharacteristic
134C22×C4—21no—
135C22×C4—21no—
136Q16—42no—
137SD16—42no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—21no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—21no—
147C4⋊C4D4×C14911yescharacteristic
148C4⋊C4D4×C14911yescharacteristic
149C22⋊C4—21no—
150C22⋊C4—21no—
151C22⋊C4—21no—
152C22⋊C4—21no—
153C22⋊C4—21no—
154C22⋊C4—21no—
155C42C23×C14911yescharacteristic
156C23—21no—
157C23—21no—
158Q8—41no—
159Q8—41no—
160Q8—41no—
161Q8—41no—
162D4—41no—
163D4—41no—
164D4—81no—
165D4—81no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—81no—
172C2×C4—81no—
173C2×C4C2×D4×C14911yescharacteristic
174C2×C4C2×D4×C14911yescharacteristic
175C2×C4C2×D4×C14911yescharacteristic
176C8—22no—
177C8—22no—
178C8—41no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—41no—
183C22—41no—
184C22—41no—
185C22#120×C14911yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—41no—
190C4—41no—
191C4—41no—
192C4—41no—
193C4—81no—
194C2—81no—
195C2—81no—
196C2#453×C14911yescharacteristic
197C2#455×C14911yescharacteristic
198C2#456×C14911yescharacteristic
subgroupG/H
center, socleC22×C149#120
commutator, Frattini, cosocleC42C23×C149
prime radical#562×C149C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C149 ◁ C42×C149 ◁ G

Complements

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

NH ≅ G/Ntype
2. #501×C149C2semidirect
3. #497×C149C2semidirect
4. #489×C149C2semidirect
5. #330×C149C2semidirect
6. #329×C149C2semidirect
7. #329×C149C2semidirect
99. C149#1661direct (N × H)
100. #1661C149direct (N × H)
102. #501C2×C149semidirect
103. #497C2×C149semidirect
104. #489C2×C149semidirect
105. #330C2×C149semidirect
106. #329C2×C149semidirect
107. #329C2×C149semidirect

Maximal subgroups

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

subgroupindex
#562×C1492
#501×C1492
#497×C1492
#489×C1492
#330×C1492
#329×C1492
#1661149