Finite Group Databasebeta

← C149×#7417 #49186366

Subgroups — C149×#7417 #49186366

Order 38144.

228 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 46 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#2039×C149C211yesmaximal, characteristic
2#1325×C149C211yesmaximal, characteristic, complemented
3#1296×C149C211yesmaximal, characteristic, complemented
4#537×C149C411yescharacteristic
5C2×C4⋊C8×C149—21no—
6C2×#104×C149—21no—
7#417×C149—21no—
8#384×C149C2211yescharacteristic
9#343×C149C411yescharacteristic
10#324×C149—21no—
11C2×#41×C149—21no—
12C2×M16×C149—21no—
13C22×C8×C149—41no—
14C22⋊Q8×C149—41no—
15#121×C149—41no—
16#121×C149—41no—
17C2×C4⋊C4×C149—41no—
18C2×C4⋊C4×C149C2×C411yescharacteristic
19C2×C4⋊C4×C149D411yescharacteristic
20C2×C42×C149D411yescharacteristic
21C4⋊C8×C149—22no—
22C4⋊C8×C149—41no—
23#104×C149—41no—
24#104×C149—41no—
25#103×C149—41no—
26#102×C149—41no—
27C22⋊C8×C149—41no—
28#41×C149—41no—
29#41×C149—41no—
30#41×C149—41no—
31#41×C149—41no—
32C2×Q8×C149—21no—
33C2×D4×C149—21no—
34C2×D4×C149—41no—
35C2×D4×C149—41no—
36C22×C4×C149—21no—
37C22×C4×C149—21no—
38C22×C4×C149—21no—
39C22×C4×C149—41no—
40C22×C4×C149C22⋊C411yescharacteristic
41M16×C149—41no—
42M16×C149—41no—
43C2×C8×C149—41no—
44C2×C8×C149—42no—
45C2×C8×C149—81no—
46C2×C8×C149—81no—
47C2×C8×C149—81no—
48C4⋊C4×C149—41no—
49C4⋊C4×C149—41no—
50C4⋊C4×C149—41no—
51C4⋊C4×C149—81no—
52C4⋊C4×C149—81no—
53C22⋊C4×C149—42no—
54C42×C149—21no—
55C42×C149D811yescharacteristic
56C42×C149SD1611yescharacteristic
57C23×C149—41no—
58C23×C149#9911yescharacteristic
59Q8×C149—41no—
60Q8×C149—41no—
61D4×C149—41no—
62D4×C149—41no—
63D4×C149—81no—
64D4×C149—81no—
65D4×C149—161no—
66C2×C4×C149—21no—
67C2×C4×C149—21no—
68C2×C4×C149—21no—
69C2×C4×C149—21no—
70C2×C4×C149—21no—
71C2×C4×C149—21no—
72C2×C4×C149—21no—
73C2×C4×C149—21no—
74C2×C4×C149—41no—
75C2×C4×C149—41no—
76C2×C4×C149—41no—
77C2×C4×C149—81no—
78C2×C4×C149—81no—
79C2×C4×C149—81no—
80C2×C4×C149—81no—
81C2×C4×C149#10211yescharacteristic
82C2×C4×C149#10411yescharacteristic
83C8×C149—82no—
84C8×C149—81no—
85C8×C149—161no—
86C22×C149—21no—
87C22×C149—21no—
88C22×C149—81no—
89C22×C149—81no—
90C22×C149—81no—
91C22×C149#32711yescharacteristic
92C22×C149AΣL(1,𝔽16)11yescharacteristic
93C22×C149#35511yescharacteristic
94C4×C149—21no—
95C4×C149—21no—
96C4×C149—21no—
97C4×C149—21no—
98C4×C149—21no—
99C4×C149—21no—
100C4×C149—81no—
101C4×C149—81no—
102C4×C149—81no—
103C2×C149—21no—
104C2×C149—21no—
105C2×C149—161no—
106C2×C149#134511yescharacteristic
107C2×C149#140211yescharacteristic
108C2×C149#140511yescharacteristic
109#7417C14911yesmaximal, characteristic, direct product factor, Sylow
110C149#741711yescharacteristic, direct product factor, Sylow
111#2039C2×C14911yescharacteristic
112#1325C2×C14911yescharacteristic, complemented
113#1296C2×C14911yescharacteristic, complemented
114#537C4×C14911yescharacteristic
115C2×C4⋊C8—21no—
116C2×#104—21no—
117#417—21no—
118#384C22×C14911yescharacteristic
119#343C4×C14911yescharacteristic
120#324—21no—
121C2×#41—21no—
122C2×M16—21no—
123C22×C8—41no—
124C22⋊Q8—41no—
125#121—41no—
126#121—41no—
127C2×C4⋊C4—41no—
128C2×C4⋊C4C2×C4×C14911yescharacteristic
129C2×C4⋊C4D4×C14911yescharacteristic
130C2×C42D4×C14911yescharacteristic
131C4⋊C8—22no—
132C4⋊C8—41no—
133#104—41no—
134#104—41no—
135#103—41no—
136#102—41no—
137C22⋊C8—41no—
138#41—41no—
139#41—41no—
140#41—41no—
141#41—41no—
142C2×Q8—21no—
143C2×D4—21no—
144C2×D4—41no—
145C2×D4—41no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—41no—
150C22×C4C22⋊C4×C14911yescharacteristic
151M16—41no—
152M16—41no—
153C2×C8—41no—
154C2×C8—42no—
155C2×C8—81no—
156C2×C8—81no—
157C2×C8—81no—
158C4⋊C4—41no—
159C4⋊C4—41no—
160C4⋊C4—41no—
161C4⋊C4—81no—
162C4⋊C4—81no—
163C22⋊C4—42no—
164C42—21no—
165C42D8×C14911yescharacteristic
166C42SD16×C14911yescharacteristic
167C23—41no—
168C23#99×C14911yescharacteristic
169Q8—41no—
170Q8—41no—
171D4—41no—
172D4—41no—
173D4—81no—
174D4—81no—
175D4—161no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—81no—
188C2×C4—81no—
189C2×C4—81no—
190C2×C4—81no—
191C2×C4#102×C14911yescharacteristic
192C2×C4#104×C14911yescharacteristic
193C8—82no—
194C8—81no—
195C8—161no—
196C22—21no—
197C22—21no—
198C22—81no—
199C22—81no—
200C22—81no—
201C22#327×C14911yescharacteristic
202C22AΣL(1,𝔽16)×C14911yescharacteristic
203C22#355×C14911yescharacteristic
204C4—21no—
205C4—21no—
206C4—21no—
207C4—21no—
208C4—21no—
209C4—21no—
210C4—81no—
211C4—81no—
212C4—81no—
213C2—21no—
214C2—21no—
215C2—161no—
216C2#1345×C14911yescharacteristic
217C2#1402×C14911yescharacteristic
218C2#1405×C14911yescharacteristic
subgroupG/H
center, socleC22×C149AΣL(1,𝔽16)
commutatorC2×C4⋊C4C2×C4×C149
Frattini, cosocle#384C22×C149
prime radical#537×C149C4
LCSG ▷ C2×C4⋊C4 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C149 ◁ C23×C149 ◁ C22×C4×C149 ◁ #384×C149 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1325×C149C2semidirect
3. #1296×C149C2semidirect
109. #7417C149direct (N × H)
110. C149#7417direct (N × H)
112. #1325C2×C149semidirect
113. #1296C2×C149semidirect

Maximal subgroups

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

subgroupindex
#2039×C1492
#1325×C1492
#1296×C1492
#7417149