Finite Group Databasebeta

← #1976×C151 #34065308

Subgroups — #1976×C151 #34065308

Order 19328.

284 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 108 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×#135×C151C211yesmaximal, characteristic
2#427×C151C211yesmaximal, characteristic, complemented
3#421×C151C212yesmaximal, complemented
4#410×C151C212yesmaximal, complemented
5#405×C151C211yesmaximal, characteristic, complemented
6C2×#41×C151C2212yes—
7#135×C151—21no—
8#135×C151—21no—
9#135×C151—21no—
10#135×C151—21no—
11C2×Q16×C151C411yescharacteristic, complemented
12C2×SD16×C151C412yescomplemented
13C2×D8×C151C411yescharacteristic, complemented
14C2×M16×C151C2211yescharacteristic
15C22×C8×C151C2211yescharacteristic
16#117×C151C2212yes—
17#117×C151C2211yescharacteristic
18#107×C151—21no—
19#106×C151—21no—
20#104×C151—24no—
21#99×C151—24no—
22#97×C151—21no—
23C4×C8×C151—21no—
24#41×C151—22no—
25#41×C151—22no—
26#41×C151—22no—
27#41×C151—22no—
28C2×Q8×C151C2×C412yes—
29C2×D4×C151—22no—
30C2×D4×C151C2×C412yes—
31C22×C4×C151—22no—
32C22×C4×C151C2311yescharacteristic
33Q16×C151—21no—
34Q16×C151—21no—
35SD16×C151—22no—
36SD16×C151—22no—
37D8×C151—21no—
38D8×C151—21no—
39M16×C151—21no—
40M16×C151D412yes—
41C2×C8×C151—21no—
42C2×C8×C151C2×C411yescharacteristic
43C2×C8×C151C2×C411yescharacteristic
44C2×C8×C151D411yescharacteristic
45C2×C8×C151D411yescharacteristic
46C2×C8×C151D411yescharacteristic
47C2×C8×C151D411yescharacteristic
48C4⋊C4×C151—21no—
49C4⋊C4×C151—22no—
50C22⋊C4×C151—22no—
51C22⋊C4×C151D412yes—
52C42×C151—21no—
53C42×C151—22no—
54C23×C151—22no—
55C23×C151C2×D411yescharacteristic
56Q8×C151—22no—
57Q8×C151—22no—
58D4×C151—22no—
59D4×C151—22no—
60D4×C151—42no—
61D4×C151—42no—
62C2×C4×C151—22no—
63C2×C4×C151—22no—
64C2×C4×C151—42no—
65C2×C4×C151—42no—
66C2×C4×C151—42no—
67C2×C4×C151C22×C411yescharacteristic
68C2×C4×C151C2×D411yescharacteristic
69C2×C4×C151C2×D411yescharacteristic
70C2×C4×C151C2×D411yescharacteristic
71C2×C4×C151#4111yescharacteristic
72C2×C4×C151#4111yescharacteristic
73C8×C151—22no—
74C8×C151C22⋊C411yescharacteristic
75C8×C151C22⋊C411yescharacteristic
76C8×C151C22⋊C411yescharacteristic
77C8×C151C22⋊C411yescharacteristic
78C22×C151—41no—
79C22×C151—42no—
80C22×C151—82no—
81C22×C151C4×D411yescharacteristic
82C22×C151#12111yescharacteristic
83C22×C151#12711yescharacteristic
84C4×C151—42no—
85C4×C151—42no—
86C4×C151—82no—
87C4×C151C2×C22⋊C411yescharacteristic
88C4×C151C4×D411yescharacteristic
89C4×C151#12111yescharacteristic
90C4×C151#12411yescharacteristic
91C2×C151—21no—
92C2×C151—21no—
93C2×C151—21no—
94C2×C151—82no—
95C2×C151#39011yescharacteristic
96C151#197611yescharacteristic, direct product factor, Sylow
97#1976C15111yesmaximal, characteristic, direct product factor, Sylow
98C2×#135C2×C15111yescharacteristic
99#427C2×C15111yescharacteristic, complemented
100#421C2×C15112yescomplemented
101#410C2×C15112yescomplemented
102#405C2×C15111yescharacteristic, complemented
103C2×#41C22×C15112yes—
104#135—21no—
105#135—21no—
106#135—21no—
107#135—21no—
108C2×Q16C4×C15111yescharacteristic, complemented
109C2×SD16C4×C15112yescomplemented
110C2×D8C4×C15111yescharacteristic, complemented
111C2×M16C22×C15111yescharacteristic
112C22×C8C22×C15111yescharacteristic
113#117C22×C15112yes—
114#117C22×C15111yescharacteristic
115#107—21no—
116#106—21no—
117#104—24no—
118#99—24no—
119#97—21no—
120C4×C8—21no—
121#41—22no—
122#41—22no—
123#41—22no—
124#41—22no—
125C2×Q8C2×C4×C15112yes—
126C2×D4—22no—
127C2×D4C2×C4×C15112yes—
128C22×C4—22no—
129C22×C4C23×C15111yescharacteristic
130Q16—21no—
131Q16—21no—
132SD16—22no—
133SD16—22no—
134D8—21no—
135D8—21no—
136M16—21no—
137M16D4×C15112yes—
138C2×C8—21no—
139C2×C8C2×C4×C15111yescharacteristic
140C2×C8C2×C4×C15111yescharacteristic
141C2×C8D4×C15111yescharacteristic
142C2×C8D4×C15111yescharacteristic
143C2×C8D4×C15111yescharacteristic
144C2×C8D4×C15111yescharacteristic
145C4⋊C4—21no—
146C4⋊C4—22no—
147C22⋊C4—22no—
148C22⋊C4D4×C15112yes—
149C42—21no—
150C42—22no—
151C23—22no—
152C23C2×D4×C15111yescharacteristic
153Q8—22no—
154Q8—22no—
155D4—22no—
156D4—22no—
157D4—42no—
158D4—42no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4C22×C4×C15111yescharacteristic
165C2×C4C2×D4×C15111yescharacteristic
166C2×C4C2×D4×C15111yescharacteristic
167C2×C4C2×D4×C15111yescharacteristic
168C2×C4#41×C15111yescharacteristic
169C2×C4#41×C15111yescharacteristic
170C8—22no—
171C8C22⋊C4×C15111yescharacteristic
172C8C22⋊C4×C15111yescharacteristic
173C8C22⋊C4×C15111yescharacteristic
174C8C22⋊C4×C15111yescharacteristic
175C22—41no—
176C22—42no—
177C22—82no—
178C22C4×D4×C15111yescharacteristic
179C22#121×C15111yescharacteristic
180C22#127×C15111yescharacteristic
181C4—42no—
182C4—42no—
183C4—82no—
184C4C2×C22⋊C4×C15111yescharacteristic
185C4C4×D4×C15111yescharacteristic
186C4#121×C15111yescharacteristic
187C4#124×C15111yescharacteristic
188C2—21no—
189C2—21no—
190C2—21no—
191C2—82no—
192C2#390×C15111yescharacteristic
subgroupG/H
centerC4×C151#121
commutatorC2×C4C22×C4×C151
Frattini, cosocleC22×C4C23×C151
socleC2×C151#390
prime radicalC2×#135×C151C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C151 ◁ C22×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #427×C151C2semidirect
3. #421×C151C2semidirect
4. #410×C151C2semidirect
5. #405×C151C2semidirect
11. C2×Q16×C151C4semidirect
12. C2×SD16×C151C4semidirect
13. C2×D8×C151C4semidirect
96. C151#1976direct (N × H)
97. #1976C151direct (N × H)
99. #427C2×C151semidirect
100. #421C2×C151semidirect
101. #410C2×C151semidirect
102. #405C2×C151semidirect
108. C2×Q16C4×C151semidirect
109. C2×SD16C4×C151semidirect
110. C2×D8C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#135×C1512
#427×C1512
#421×C1512
#410×C1512
#405×C1512
#1976151