Finite Group Databasebeta

← C2×#1410×C149 #49192536

Subgroups — C2×#1410×C149 #49192536

Order 38144.

450 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 94 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
1C2×#492×C149C211yesmaximal, characteristic
2C2×#356×C149C212yesmaximal, complemented
3#1410×C149C214yesmaximal, direct product factor
4C22×SD16×C149—22no—
5C2×C4⋊Q8×C149C2211yescharacteristic
6C2×#127×C149C411yescharacteristic
7#492×C149—22no—
8#492×C149C412yes—
9#492×C149C2212yes—
10C2×#101×C149—22no—
11C2×C4×C8×C149C411yescharacteristic
12#356×C149—22no—
13#356×C149C2214yescomplemented
14C22×Q8×C149D412yes—
15C22×D4×C149—21no—
16C22×D4×C149—41no—
17C2×SD16×C149—24no—
18C2×SD16×C149—24no—
19C2×SD16×C149—44no—
20C2×SD16×C149—44no—
21C2×M16×C149—42no—
22C22×C8×C149—21no—
23C4⋊Q8×C149—41no—
24C4⋊Q8×C149C2×C411yescharacteristic
25C4⋊Q8×C149D412yes—
26C4⋊Q8×C149C2311yescharacteristic
27#127×C149—21no—
28#127×C149—41no—
29#127×C149C2×C412yes—
30C2×C4⋊C4×C149—41no—
31C2×C42×C149C2×C411yescharacteristic
32#101×C149—24no—
33#101×C149—42no—
34C4×C8×C149—21no—
35C4×C8×C149C2×C412yes—
36C24×C149—41no—
37C2×Q8×C149—22no—
38C2×Q8×C149—42no—
39C2×Q8×C149—42no—
40C2×Q8×C149C22⋊C412yes—
41C2×Q8×C149C2×D412yes—
42C2×D4×C149—22no—
43C2×D4×C149—42no—
44C2×D4×C149—42no—
45C2×D4×C149—42no—
46C2×D4×C149—42no—
47C2×D4×C149—41no—
48C2×D4×C149—84no—
49C22×C4×C149—21no—
50C22×C4×C149—22no—
51C22×C4×C149C22⋊C411yescharacteristic
52SD16×C149—48no—
53SD16×C149—48no—
54M16×C149—44no—
55M16×C149—82no—
56C2×C8×C149—22no—
57C2×C8×C149—22no—
58C2×C8×C149—22no—
59C2×C8×C149—82no—
60C4⋊C4×C149—41no—
61C4⋊C4×C149—42no—
62C4⋊C4×C149—41no—
63C42×C149—21no—
64C42×C149C22⋊C411yescharacteristic
65C42×C149C22×C411yescharacteristic
66C23×C149—42no—
67C23×C149—84no—
68C23×C149—81no—
69C23×C149—81no—
70C23×C149#9911yescharacteristic
71Q8×C149—42no—
72Q8×C149—42no—
73Q8×C149—82no—
74D4×C149—44no—
75D4×C149—82no—
76D4×C149—84no—
77D4×C149—84no—
78C2×C4×C149—24no—
79C2×C4×C149—21no—
80C2×C4×C149—21no—
81C2×C4×C149—21no—
82C2×C4×C149—21no—
83C2×C4×C149—22no—
84C2×C4×C149—22no—
85C2×C4×C149—42no—
86C2×C4×C149—42no—
87C2×C4×C149#9911yescharacteristic
88C2×C4×C149C2×C22⋊C411yescharacteristic
89C8×C149—24no—
90C8×C149—84no—
91C22×C149—22no—
92C22×C149—84no—
93C22×C149—82no—
94C22×C149—162no—
95C22×C149—162no—
96C22×C149#35311yescharacteristic
97C22×C149#35311yescharacteristic
98C22×C149C2×#9911yescharacteristic
99C4×C149—22no—
100C4×C149—22no—
101C4×C149—21no—
102C4×C149—21no—
103C4×C149—42no—
104C4×C149—42no—
105C2×C149—21no—
106C2×C149—21no—
107C2×C149—162no—
108C2×C149#141012yesdirect product factor
109C2×C149C2×#35311yescharacteristic
110C2×#1410C14911yesmaximal, characteristic, direct product factor, Sylow
111C149C2×#141011yescharacteristic, direct product factor, Sylow
112C2×#492C2×C14911yescharacteristic
113C2×#356C2×C14912yescomplemented
114#1410C2×C14914yesdirect product factor
115C22×SD16—22no—
116C2×C4⋊Q8C22×C14911yescharacteristic
117C2×#127C4×C14911yescharacteristic
118#492—22no—
119#492C4×C14912yes—
120#492C22×C14912yes—
121C2×#101—22no—
122C2×C4×C8C4×C14911yescharacteristic
123#356—22no—
124#356C22×C14914yescomplemented
125C22×Q8D4×C14912yes—
126C22×D4—21no—
127C22×D4—41no—
128C2×SD16—24no—
129C2×SD16—24no—
130C2×SD16—44no—
131C2×SD16—44no—
132C2×M16—42no—
133C22×C8—21no—
134C4⋊Q8—41no—
135C4⋊Q8C2×C4×C14911yescharacteristic
136C4⋊Q8D4×C14912yes—
137C4⋊Q8C23×C14911yescharacteristic
138#127—21no—
139#127—41no—
140#127C2×C4×C14912yes—
141C2×C4⋊C4—41no—
142C2×C42C2×C4×C14911yescharacteristic
143#101—24no—
144#101—42no—
145C4×C8—21no—
146C4×C8C2×C4×C14912yes—
147C24—41no—
148C2×Q8—22no—
149C2×Q8—42no—
150C2×Q8—42no—
151C2×Q8C22⋊C4×C14912yes—
152C2×Q8C2×D4×C14912yes—
153C2×D4—22no—
154C2×D4—42no—
155C2×D4—42no—
156C2×D4—42no—
157C2×D4—42no—
158C2×D4—41no—
159C2×D4—84no—
160C22×C4—21no—
161C22×C4—22no—
162C22×C4C22⋊C4×C14911yescharacteristic
163SD16—48no—
164SD16—48no—
165M16—44no—
166M16—82no—
167C2×C8—22no—
168C2×C8—22no—
169C2×C8—22no—
170C2×C8—82no—
171C4⋊C4—41no—
172C4⋊C4—42no—
173C4⋊C4—41no—
174C42—21no—
175C42C22⋊C4×C14911yescharacteristic
176C42C22×C4×C14911yescharacteristic
177C23—42no—
178C23—84no—
179C23—81no—
180C23—81no—
181C23#99×C14911yescharacteristic
182Q8—42no—
183Q8—42no—
184Q8—82no—
185D4—44no—
186D4—82no—
187D4—84no—
188D4—84no—
189C2×C4—24no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4#99×C14911yescharacteristic
199C2×C4C2×C22⋊C4×C14911yescharacteristic
200C8—24no—
201C8—84no—
202C22—22no—
203C22—84no—
204C22—82no—
205C22—162no—
206C22—162no—
207C22#353×C14911yescharacteristic
208C22#353×C14911yescharacteristic
209C22C2×#99×C14911yescharacteristic
210C4—22no—
211C4—22no—
212C4—21no—
213C4—21no—
214C4—42no—
215C4—42no—
216C2—21no—
217C2—21no—
218C2—162no—
219C2#1410×C14912yesdirect product factor
220C2C2×#353×C14911yescharacteristic
subgroupG/H
center, socleC22×C149#353
commutatorC42C22×C4×C149
Frattini, cosocleC4⋊Q8C23×C149
prime radicalC2×#127×C149C4
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C149 ◁ C23×C149 ◁ C22×C4×C149 ◁ C2×C4⋊Q8×C149 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#356×C149C2semidirect
3. #1410×C149C2direct (N × H)
13. #356×C149C22semidirect
108. C2×C149#1410direct (N × H)
110. C2×#1410C149direct (N × H)
111. C149C2×#1410direct (N × H)
113. C2×#356C2×C149semidirect
114. #1410C2×C149direct (N × H)
124. #356C22×C149semidirect
219. C2#1410×C149direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#492×C1492
C2×#356×C1492
#1410×C1492
C2×#1410149